/src/icu/source/i18n/decNumber.cpp
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1 | | // © 2016 and later: Unicode, Inc. and others. |
2 | | // License & terms of use: http://www.unicode.org/copyright.html |
3 | | /* ------------------------------------------------------------------ */ |
4 | | /* Decimal Number arithmetic module */ |
5 | | /* ------------------------------------------------------------------ */ |
6 | | /* Copyright (c) IBM Corporation, 2000-2014. All rights reserved. */ |
7 | | /* */ |
8 | | /* This software is made available under the terms of the */ |
9 | | /* ICU License -- ICU 1.8.1 and later. */ |
10 | | /* */ |
11 | | /* The description and User's Guide ("The decNumber C Library") for */ |
12 | | /* this software is called decNumber.pdf. This document is */ |
13 | | /* available, together with arithmetic and format specifications, */ |
14 | | /* testcases, and Web links, on the General Decimal Arithmetic page. */ |
15 | | /* */ |
16 | | /* Please send comments, suggestions, and corrections to the author: */ |
17 | | /* mfc@uk.ibm.com */ |
18 | | /* Mike Cowlishaw, IBM Fellow */ |
19 | | /* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ |
20 | | /* ------------------------------------------------------------------ */ |
21 | | |
22 | | /* Modified version, for use from within ICU. |
23 | | * Renamed public functions, to avoid an unwanted export of the |
24 | | * standard names from the ICU library. |
25 | | * |
26 | | * Use ICU's uprv_malloc() and uprv_free() |
27 | | * |
28 | | * Revert comment syntax to plain C |
29 | | * |
30 | | * Remove a few compiler warnings. |
31 | | */ |
32 | | |
33 | | /* This module comprises the routines for arbitrary-precision General */ |
34 | | /* Decimal Arithmetic as defined in the specification which may be */ |
35 | | /* found on the General Decimal Arithmetic pages. It implements both */ |
36 | | /* the full ('extended') arithmetic and the simpler ('subset') */ |
37 | | /* arithmetic. */ |
38 | | /* */ |
39 | | /* Usage notes: */ |
40 | | /* */ |
41 | | /* 1. This code is ANSI C89 except: */ |
42 | | /* */ |
43 | | /* a) C99 line comments (double forward slash) are used. (Most C */ |
44 | | /* compilers accept these. If yours does not, a simple script */ |
45 | | /* can be used to convert them to ANSI C comments.) */ |
46 | | /* */ |
47 | | /* b) Types from C99 stdint.h are used. If you do not have this */ |
48 | | /* header file, see the User's Guide section of the decNumber */ |
49 | | /* documentation; this lists the necessary definitions. */ |
50 | | /* */ |
51 | | /* c) If DECDPUN>4 or DECUSE64=1, the C99 64-bit int64_t and */ |
52 | | /* uint64_t types may be used. To avoid these, set DECUSE64=0 */ |
53 | | /* and DECDPUN<=4 (see documentation). */ |
54 | | /* */ |
55 | | /* The code also conforms to C99 restrictions; in particular, */ |
56 | | /* strict aliasing rules are observed. */ |
57 | | /* */ |
58 | | /* 2. The decNumber format which this library uses is optimized for */ |
59 | | /* efficient processing of relatively short numbers; in particular */ |
60 | | /* it allows the use of fixed sized structures and minimizes copy */ |
61 | | /* and move operations. It does, however, support arbitrary */ |
62 | | /* precision (up to 999,999,999 digits) and arbitrary exponent */ |
63 | | /* range (Emax in the range 0 through 999,999,999 and Emin in the */ |
64 | | /* range -999,999,999 through 0). Mathematical functions (for */ |
65 | | /* example decNumberExp) as identified below are restricted more */ |
66 | | /* tightly: digits, emax, and -emin in the context must be <= */ |
67 | | /* DEC_MAX_MATH (999999), and their operand(s) must be within */ |
68 | | /* these bounds. */ |
69 | | /* */ |
70 | | /* 3. Logical functions are further restricted; their operands must */ |
71 | | /* be finite, positive, have an exponent of zero, and all digits */ |
72 | | /* must be either 0 or 1. The result will only contain digits */ |
73 | | /* which are 0 or 1 (and will have exponent=0 and a sign of 0). */ |
74 | | /* */ |
75 | | /* 4. Operands to operator functions are never modified unless they */ |
76 | | /* are also specified to be the result number (which is always */ |
77 | | /* permitted). Other than that case, operands must not overlap. */ |
78 | | /* */ |
79 | | /* 5. Error handling: the type of the error is ORed into the status */ |
80 | | /* flags in the current context (decContext structure). The */ |
81 | | /* SIGFPE signal is then raised if the corresponding trap-enabler */ |
82 | | /* flag in the decContext is set (is 1). */ |
83 | | /* */ |
84 | | /* It is the responsibility of the caller to clear the status */ |
85 | | /* flags as required. */ |
86 | | /* */ |
87 | | /* The result of any routine which returns a number will always */ |
88 | | /* be a valid number (which may be a special value, such as an */ |
89 | | /* Infinity or NaN). */ |
90 | | /* */ |
91 | | /* 6. The decNumber format is not an exchangeable concrete */ |
92 | | /* representation as it comprises fields which may be machine- */ |
93 | | /* dependent (packed or unpacked, or special length, for example). */ |
94 | | /* Canonical conversions to and from strings are provided; other */ |
95 | | /* conversions are available in separate modules. */ |
96 | | /* */ |
97 | | /* 7. Normally, input operands are assumed to be valid. Set DECCHECK */ |
98 | | /* to 1 for extended operand checking (including NULL operands). */ |
99 | | /* Results are undefined if a badly-formed structure (or a NULL */ |
100 | | /* pointer to a structure) is provided, though with DECCHECK */ |
101 | | /* enabled the operator routines are protected against exceptions. */ |
102 | | /* (Except if the result pointer is NULL, which is unrecoverable.) */ |
103 | | /* */ |
104 | | /* However, the routines will never cause exceptions if they are */ |
105 | | /* given well-formed operands, even if the value of the operands */ |
106 | | /* is inappropriate for the operation and DECCHECK is not set. */ |
107 | | /* (Except for SIGFPE, as and where documented.) */ |
108 | | /* */ |
109 | | /* 8. Subset arithmetic is available only if DECSUBSET is set to 1. */ |
110 | | /* ------------------------------------------------------------------ */ |
111 | | /* Implementation notes for maintenance of this module: */ |
112 | | /* */ |
113 | | /* 1. Storage leak protection: Routines which use malloc are not */ |
114 | | /* permitted to use return for fastpath or error exits (i.e., */ |
115 | | /* they follow strict structured programming conventions). */ |
116 | | /* Instead they have a do{}while(0); construct surrounding the */ |
117 | | /* code which is protected -- break may be used to exit this. */ |
118 | | /* Other routines can safely use the return statement inline. */ |
119 | | /* */ |
120 | | /* Storage leak accounting can be enabled using DECALLOC. */ |
121 | | /* */ |
122 | | /* 2. All loops use the for(;;) construct. Any do construct does */ |
123 | | /* not loop; it is for allocation protection as just described. */ |
124 | | /* */ |
125 | | /* 3. Setting status in the context must always be the very last */ |
126 | | /* action in a routine, as non-0 status may raise a trap and hence */ |
127 | | /* the call to set status may not return (if the handler uses long */ |
128 | | /* jump). Therefore all cleanup must be done first. In general, */ |
129 | | /* to achieve this status is accumulated and is only applied just */ |
130 | | /* before return by calling decContextSetStatus (via decStatus). */ |
131 | | /* */ |
132 | | /* Routines which allocate storage cannot, in general, use the */ |
133 | | /* 'top level' routines which could cause a non-returning */ |
134 | | /* transfer of control. The decXxxxOp routines are safe (do not */ |
135 | | /* call decStatus even if traps are set in the context) and should */ |
136 | | /* be used instead (they are also a little faster). */ |
137 | | /* */ |
138 | | /* 4. Exponent checking is minimized by allowing the exponent to */ |
139 | | /* grow outside its limits during calculations, provided that */ |
140 | | /* the decFinalize function is called later. Multiplication and */ |
141 | | /* division, and intermediate calculations in exponentiation, */ |
142 | | /* require more careful checks because of the risk of 31-bit */ |
143 | | /* overflow (the most negative valid exponent is -1999999997, for */ |
144 | | /* a 999999999-digit number with adjusted exponent of -999999999). */ |
145 | | /* */ |
146 | | /* 5. Rounding is deferred until finalization of results, with any */ |
147 | | /* 'off to the right' data being represented as a single digit */ |
148 | | /* residue (in the range -1 through 9). This avoids any double- */ |
149 | | /* rounding when more than one shortening takes place (for */ |
150 | | /* example, when a result is subnormal). */ |
151 | | /* */ |
152 | | /* 6. The digits count is allowed to rise to a multiple of DECDPUN */ |
153 | | /* during many operations, so whole Units are handled and exact */ |
154 | | /* accounting of digits is not needed. The correct digits value */ |
155 | | /* is found by decGetDigits, which accounts for leading zeros. */ |
156 | | /* This must be called before any rounding if the number of digits */ |
157 | | /* is not known exactly. */ |
158 | | /* */ |
159 | | /* 7. The multiply-by-reciprocal 'trick' is used for partitioning */ |
160 | | /* numbers up to four digits, using appropriate constants. This */ |
161 | | /* is not useful for longer numbers because overflow of 32 bits */ |
162 | | /* would lead to 4 multiplies, which is almost as expensive as */ |
163 | | /* a divide (unless a floating-point or 64-bit multiply is */ |
164 | | /* assumed to be available). */ |
165 | | /* */ |
166 | | /* 8. Unusual abbreviations that may be used in the commentary: */ |
167 | | /* lhs -- left hand side (operand, of an operation) */ |
168 | | /* lsd -- least significant digit (of coefficient) */ |
169 | | /* lsu -- least significant Unit (of coefficient) */ |
170 | | /* msd -- most significant digit (of coefficient) */ |
171 | | /* msi -- most significant item (in an array) */ |
172 | | /* msu -- most significant Unit (of coefficient) */ |
173 | | /* rhs -- right hand side (operand, of an operation) */ |
174 | | /* +ve -- positive */ |
175 | | /* -ve -- negative */ |
176 | | /* ** -- raise to the power */ |
177 | | /* ------------------------------------------------------------------ */ |
178 | | |
179 | | #include <stdlib.h> /* for malloc, free, etc. */ |
180 | | /* #include <stdio.h> */ /* for printf [if needed] */ |
181 | | #include <string.h> /* for strcpy */ |
182 | | #include <ctype.h> /* for lower */ |
183 | | #include "cmemory.h" /* for uprv_malloc, etc., in ICU */ |
184 | | #include "decNumber.h" /* base number library */ |
185 | | #include "decNumberLocal.h" /* decNumber local types, etc. */ |
186 | | #include "uassert.h" |
187 | | |
188 | | /* Constants */ |
189 | | /* Public lookup table used by the D2U macro */ |
190 | | static const uByte d2utable[DECMAXD2U+1]=D2UTABLE; |
191 | | |
192 | | #define DECVERB 1 /* set to 1 for verbose DECCHECK */ |
193 | 0 | #define powers DECPOWERS /* old internal name */ |
194 | | |
195 | | /* Local constants */ |
196 | 0 | #define DIVIDE 0x80 /* Divide operators */ |
197 | 0 | #define REMAINDER 0x40 /* .. */ |
198 | 0 | #define DIVIDEINT 0x20 /* .. */ |
199 | 0 | #define REMNEAR 0x10 /* .. */ |
200 | 0 | #define COMPARE 0x01 /* Compare operators */ |
201 | 0 | #define COMPMAX 0x02 /* .. */ |
202 | 0 | #define COMPMIN 0x03 /* .. */ |
203 | 0 | #define COMPTOTAL 0x04 /* .. */ |
204 | 0 | #define COMPNAN 0x05 /* .. [NaN processing] */ |
205 | 0 | #define COMPSIG 0x06 /* .. [signaling COMPARE] */ |
206 | 0 | #define COMPMAXMAG 0x07 /* .. */ |
207 | 0 | #define COMPMINMAG 0x08 /* .. */ |
208 | | |
209 | 0 | #define DEC_sNaN 0x40000000 /* local status: sNaN signal */ |
210 | 0 | #define BADINT (Int)0x80000000 /* most-negative Int; error indicator */ |
211 | | /* Next two indicate an integer >= 10**6, and its parity (bottom bit) */ |
212 | 0 | #define BIGEVEN (Int)0x80000002 |
213 | 0 | #define BIGODD (Int)0x80000003 |
214 | | |
215 | | static const Unit uarrone[1]={1}; /* Unit array of 1, used for incrementing */ |
216 | | |
217 | | /* ------------------------------------------------------------------ */ |
218 | | /* round-for-reround digits */ |
219 | | /* ------------------------------------------------------------------ */ |
220 | | #if 0 |
221 | | static const uByte DECSTICKYTAB[10]={1,1,2,3,4,6,6,7,8,9}; /* used if sticky */ |
222 | | #endif |
223 | | |
224 | | /* ------------------------------------------------------------------ */ |
225 | | /* Powers of ten (powers[n]==10**n, 0<=n<=9) */ |
226 | | /* ------------------------------------------------------------------ */ |
227 | | static const uInt DECPOWERS[10]={1, 10, 100, 1000, 10000, 100000, 1000000, |
228 | | 10000000, 100000000, 1000000000}; |
229 | | |
230 | | |
231 | | /* Granularity-dependent code */ |
232 | | #if DECDPUN<=4 |
233 | 0 | #define eInt Int /* extended integer */ |
234 | | #define ueInt uInt /* unsigned extended integer */ |
235 | | /* Constant multipliers for divide-by-power-of five using reciprocal */ |
236 | | /* multiply, after removing powers of 2 by shifting, and final shift */ |
237 | | /* of 17 [we only need up to **4] */ |
238 | | static const uInt multies[]={131073, 26215, 5243, 1049, 210}; |
239 | | /* QUOT10 -- macro to return the quotient of unit u divided by 10**n */ |
240 | 0 | #define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17) |
241 | | #else |
242 | | /* For DECDPUN>4 non-ANSI-89 64-bit types are needed. */ |
243 | | #if !DECUSE64 |
244 | | #error decNumber.c: DECUSE64 must be 1 when DECDPUN>4 |
245 | | #endif |
246 | | #define eInt Long /* extended integer */ |
247 | | #define ueInt uLong /* unsigned extended integer */ |
248 | | #endif |
249 | | |
250 | | /* Local routines */ |
251 | | static decNumber * decAddOp(decNumber *, const decNumber *, const decNumber *, |
252 | | decContext *, uByte, uInt *); |
253 | | static Flag decBiStr(const char *, const char *, const char *); |
254 | | static uInt decCheckMath(const decNumber *, decContext *, uInt *); |
255 | | static void decApplyRound(decNumber *, decContext *, Int, uInt *); |
256 | | static Int decCompare(const decNumber *lhs, const decNumber *rhs, Flag); |
257 | | static decNumber * decCompareOp(decNumber *, const decNumber *, |
258 | | const decNumber *, decContext *, |
259 | | Flag, uInt *); |
260 | | static void decCopyFit(decNumber *, const decNumber *, decContext *, |
261 | | Int *, uInt *); |
262 | | static decNumber * decDecap(decNumber *, Int); |
263 | | static decNumber * decDivideOp(decNumber *, const decNumber *, |
264 | | const decNumber *, decContext *, Flag, uInt *); |
265 | | static decNumber * decExpOp(decNumber *, const decNumber *, |
266 | | decContext *, uInt *); |
267 | | static void decFinalize(decNumber *, decContext *, Int *, uInt *); |
268 | | static Int decGetDigits(Unit *, Int); |
269 | | static Int decGetInt(const decNumber *); |
270 | | static decNumber * decLnOp(decNumber *, const decNumber *, |
271 | | decContext *, uInt *); |
272 | | static decNumber * decMultiplyOp(decNumber *, const decNumber *, |
273 | | const decNumber *, decContext *, |
274 | | uInt *); |
275 | | static decNumber * decNaNs(decNumber *, const decNumber *, |
276 | | const decNumber *, decContext *, uInt *); |
277 | | static decNumber * decQuantizeOp(decNumber *, const decNumber *, |
278 | | const decNumber *, decContext *, Flag, |
279 | | uInt *); |
280 | | static void decReverse(Unit *, Unit *); |
281 | | static void decSetCoeff(decNumber *, decContext *, const Unit *, |
282 | | Int, Int *, uInt *); |
283 | | static void decSetMaxValue(decNumber *, decContext *); |
284 | | static void decSetOverflow(decNumber *, decContext *, uInt *); |
285 | | static void decSetSubnormal(decNumber *, decContext *, Int *, uInt *); |
286 | | static Int decShiftToLeast(Unit *, Int, Int); |
287 | | static Int decShiftToMost(Unit *, Int, Int); |
288 | | static void decStatus(decNumber *, uInt, decContext *); |
289 | | static void decToString(const decNumber *, char[], Flag); |
290 | | static decNumber * decTrim(decNumber *, decContext *, Flag, Flag, Int *); |
291 | | static Int decUnitAddSub(const Unit *, Int, const Unit *, Int, Int, |
292 | | Unit *, Int); |
293 | | static Int decUnitCompare(const Unit *, Int, const Unit *, Int, Int); |
294 | | |
295 | | #if !DECSUBSET |
296 | | /* decFinish == decFinalize when no subset arithmetic needed */ |
297 | 0 | #define decFinish(a,b,c,d) decFinalize(a,b,c,d) |
298 | | #else |
299 | | static void decFinish(decNumber *, decContext *, Int *, uInt *); |
300 | | static decNumber * decRoundOperand(const decNumber *, decContext *, uInt *); |
301 | | #endif |
302 | | |
303 | | /* Local macros */ |
304 | | /* masked special-values bits */ |
305 | 0 | #define SPECIALARG (rhs->bits & DECSPECIAL) |
306 | 0 | #define SPECIALARGS ((lhs->bits | rhs->bits) & DECSPECIAL) |
307 | | |
308 | | /* For use in ICU */ |
309 | 0 | #define malloc(a) uprv_malloc(a) |
310 | 0 | #define free(a) uprv_free(a) |
311 | | |
312 | | /* Diagnostic macros, etc. */ |
313 | | #if DECALLOC |
314 | | /* Handle malloc/free accounting. If enabled, our accountable routines */ |
315 | | /* are used; otherwise the code just goes straight to the system malloc */ |
316 | | /* and free routines. */ |
317 | | #define malloc(a) decMalloc(a) |
318 | | #define free(a) decFree(a) |
319 | | #define DECFENCE 0x5a /* corruption detector */ |
320 | | /* 'Our' malloc and free: */ |
321 | | static void *decMalloc(size_t); |
322 | | static void decFree(void *); |
323 | | uInt decAllocBytes=0; /* count of bytes allocated */ |
324 | | /* Note that DECALLOC code only checks for storage buffer overflow. */ |
325 | | /* To check for memory leaks, the decAllocBytes variable must be */ |
326 | | /* checked to be 0 at appropriate times (e.g., after the test */ |
327 | | /* harness completes a set of tests). This checking may be unreliable */ |
328 | | /* if the testing is done in a multi-thread environment. */ |
329 | | #endif |
330 | | |
331 | | #if DECCHECK |
332 | | /* Optional checking routines. Enabling these means that decNumber */ |
333 | | /* and decContext operands to operator routines are checked for */ |
334 | | /* correctness. This roughly doubles the execution time of the */ |
335 | | /* fastest routines (and adds 600+ bytes), so should not normally be */ |
336 | | /* used in 'production'. */ |
337 | | /* decCheckInexact is used to check that inexact results have a full */ |
338 | | /* complement of digits (where appropriate -- this is not the case */ |
339 | | /* for Quantize, for example) */ |
340 | | #define DECUNRESU ((decNumber *)(void *)0xffffffff) |
341 | | #define DECUNUSED ((const decNumber *)(void *)0xffffffff) |
342 | | #define DECUNCONT ((decContext *)(void *)(0xffffffff)) |
343 | | static Flag decCheckOperands(decNumber *, const decNumber *, |
344 | | const decNumber *, decContext *); |
345 | | static Flag decCheckNumber(const decNumber *); |
346 | | static void decCheckInexact(const decNumber *, decContext *); |
347 | | #endif |
348 | | |
349 | | #if DECTRACE || DECCHECK |
350 | | /* Optional trace/debugging routines (may or may not be used) */ |
351 | | void decNumberShow(const decNumber *); /* displays the components of a number */ |
352 | | static void decDumpAr(char, const Unit *, Int); |
353 | | #endif |
354 | | |
355 | | /* ================================================================== */ |
356 | | /* Conversions */ |
357 | | /* ================================================================== */ |
358 | | |
359 | | /* ------------------------------------------------------------------ */ |
360 | | /* from-int32 -- conversion from Int or uInt */ |
361 | | /* */ |
362 | | /* dn is the decNumber to receive the integer */ |
363 | | /* in or uin is the integer to be converted */ |
364 | | /* returns dn */ |
365 | | /* */ |
366 | | /* No error is possible. */ |
367 | | /* ------------------------------------------------------------------ */ |
368 | 0 | U_CAPI decNumber * U_EXPORT2 uprv_decNumberFromInt32(decNumber *dn, Int in) { |
369 | 0 | uInt unsig; |
370 | 0 | if (in>=0) unsig=in; |
371 | 0 | else { /* negative (possibly BADINT) */ |
372 | 0 | if (in==BADINT) unsig=(uInt)1073741824*2; /* special case */ |
373 | 0 | else unsig=-in; /* invert */ |
374 | 0 | } |
375 | | /* in is now positive */ |
376 | 0 | uprv_decNumberFromUInt32(dn, unsig); |
377 | 0 | if (in<0) dn->bits=DECNEG; /* sign needed */ |
378 | 0 | return dn; |
379 | 0 | } /* decNumberFromInt32 */ |
380 | | |
381 | 0 | U_CAPI decNumber * U_EXPORT2 uprv_decNumberFromUInt32(decNumber *dn, uInt uin) { |
382 | 0 | Unit *up; /* work pointer */ |
383 | 0 | uprv_decNumberZero(dn); /* clean */ |
384 | 0 | if (uin==0) return dn; /* [or decGetDigits bad call] */ |
385 | 0 | for (up=dn->lsu; uin>0; up++) { |
386 | 0 | *up=(Unit)(uin%(DECDPUNMAX+1)); |
387 | 0 | uin=uin/(DECDPUNMAX+1); |
388 | 0 | } |
389 | 0 | dn->digits=decGetDigits(dn->lsu, static_cast<int32_t>(up - dn->lsu)); |
390 | 0 | return dn; |
391 | 0 | } /* decNumberFromUInt32 */ |
392 | | |
393 | | /* ------------------------------------------------------------------ */ |
394 | | /* to-int32 -- conversion to Int or uInt */ |
395 | | /* */ |
396 | | /* dn is the decNumber to convert */ |
397 | | /* set is the context for reporting errors */ |
398 | | /* returns the converted decNumber, or 0 if Invalid is set */ |
399 | | /* */ |
400 | | /* Invalid is set if the decNumber does not have exponent==0 or if */ |
401 | | /* it is a NaN, Infinite, or out-of-range. */ |
402 | | /* ------------------------------------------------------------------ */ |
403 | 0 | U_CAPI Int U_EXPORT2 uprv_decNumberToInt32(const decNumber *dn, decContext *set) { |
404 | | #if DECCHECK |
405 | | if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; |
406 | | #endif |
407 | | |
408 | | /* special or too many digits, or bad exponent */ |
409 | 0 | if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0) ; /* bad */ |
410 | 0 | else { /* is a finite integer with 10 or fewer digits */ |
411 | 0 | Int d; /* work */ |
412 | 0 | const Unit *up; /* .. */ |
413 | 0 | uInt hi=0, lo; /* .. */ |
414 | 0 | up=dn->lsu; /* -> lsu */ |
415 | 0 | lo=*up; /* get 1 to 9 digits */ |
416 | | #if DECDPUN>1 /* split to higher */ |
417 | | hi=lo/10; |
418 | | lo=lo%10; |
419 | | #endif |
420 | 0 | up++; |
421 | | /* collect remaining Units, if any, into hi */ |
422 | 0 | for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1]; |
423 | | /* now low has the lsd, hi the remainder */ |
424 | 0 | if (hi>214748364 || (hi==214748364 && lo>7)) { /* out of range? */ |
425 | | /* most-negative is a reprieve */ |
426 | 0 | if (dn->bits&DECNEG && hi==214748364 && lo==8) return 0x80000000; |
427 | | /* bad -- drop through */ |
428 | 0 | } |
429 | 0 | else { /* in-range always */ |
430 | 0 | Int i=X10(hi)+lo; |
431 | 0 | if (dn->bits&DECNEG) return -i; |
432 | 0 | return i; |
433 | 0 | } |
434 | 0 | } /* integer */ |
435 | 0 | uprv_decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */ |
436 | 0 | return 0; |
437 | 0 | } /* decNumberToInt32 */ |
438 | | |
439 | 0 | U_CAPI uInt U_EXPORT2 uprv_decNumberToUInt32(const decNumber *dn, decContext *set) { |
440 | | #if DECCHECK |
441 | | if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; |
442 | | #endif |
443 | | /* special or too many digits, or bad exponent, or negative (<0) */ |
444 | 0 | if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0 |
445 | 0 | || (dn->bits&DECNEG && !ISZERO(dn))); /* bad */ |
446 | 0 | else { /* is a finite integer with 10 or fewer digits */ |
447 | 0 | Int d; /* work */ |
448 | 0 | const Unit *up; /* .. */ |
449 | 0 | uInt hi=0, lo; /* .. */ |
450 | 0 | up=dn->lsu; /* -> lsu */ |
451 | 0 | lo=*up; /* get 1 to 9 digits */ |
452 | | #if DECDPUN>1 /* split to higher */ |
453 | | hi=lo/10; |
454 | | lo=lo%10; |
455 | | #endif |
456 | 0 | up++; |
457 | | /* collect remaining Units, if any, into hi */ |
458 | 0 | for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1]; |
459 | | |
460 | | /* now low has the lsd, hi the remainder */ |
461 | 0 | if (hi>429496729 || (hi==429496729 && lo>5)) ; /* no reprieve possible */ |
462 | 0 | else return X10(hi)+lo; |
463 | 0 | } /* integer */ |
464 | 0 | uprv_decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */ |
465 | 0 | return 0; |
466 | 0 | } /* decNumberToUInt32 */ |
467 | | |
468 | | /* ------------------------------------------------------------------ */ |
469 | | /* to-scientific-string -- conversion to numeric string */ |
470 | | /* to-engineering-string -- conversion to numeric string */ |
471 | | /* */ |
472 | | /* decNumberToString(dn, string); */ |
473 | | /* decNumberToEngString(dn, string); */ |
474 | | /* */ |
475 | | /* dn is the decNumber to convert */ |
476 | | /* string is the string where the result will be laid out */ |
477 | | /* */ |
478 | | /* string must be at least dn->digits+14 characters long */ |
479 | | /* */ |
480 | | /* No error is possible, and no status can be set. */ |
481 | | /* ------------------------------------------------------------------ */ |
482 | 0 | U_CAPI char * U_EXPORT2 uprv_decNumberToString(const decNumber *dn, char *string){ |
483 | 0 | decToString(dn, string, 0); |
484 | 0 | return string; |
485 | 0 | } /* DecNumberToString */ |
486 | | |
487 | 0 | U_CAPI char * U_EXPORT2 uprv_decNumberToEngString(const decNumber *dn, char *string){ |
488 | 0 | decToString(dn, string, 1); |
489 | 0 | return string; |
490 | 0 | } /* DecNumberToEngString */ |
491 | | |
492 | | /* ------------------------------------------------------------------ */ |
493 | | /* to-number -- conversion from numeric string */ |
494 | | /* */ |
495 | | /* decNumberFromString -- convert string to decNumber */ |
496 | | /* dn -- the number structure to fill */ |
497 | | /* chars[] -- the string to convert ('\0' terminated) */ |
498 | | /* set -- the context used for processing any error, */ |
499 | | /* determining the maximum precision available */ |
500 | | /* (set.digits), determining the maximum and minimum */ |
501 | | /* exponent (set.emax and set.emin), determining if */ |
502 | | /* extended values are allowed, and checking the */ |
503 | | /* rounding mode if overflow occurs or rounding is */ |
504 | | /* needed. */ |
505 | | /* */ |
506 | | /* The length of the coefficient and the size of the exponent are */ |
507 | | /* checked by this routine, so the correct error (Underflow or */ |
508 | | /* Overflow) can be reported or rounding applied, as necessary. */ |
509 | | /* */ |
510 | | /* If bad syntax is detected, the result will be a quiet NaN. */ |
511 | | /* ------------------------------------------------------------------ */ |
512 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberFromString(decNumber *dn, const char chars[], |
513 | 0 | decContext *set) { |
514 | 0 | Int exponent=0; /* working exponent [assume 0] */ |
515 | 0 | uByte bits=0; /* working flags [assume +ve] */ |
516 | 0 | Unit *res; /* where result will be built */ |
517 | 0 | Unit resbuff[SD2U(DECBUFFER+9)];/* local buffer in case need temporary */ |
518 | | /* [+9 allows for ln() constants] */ |
519 | 0 | Unit *allocres=NULL; /* -> allocated result, iff allocated */ |
520 | 0 | Int d=0; /* count of digits found in decimal part */ |
521 | 0 | const char *dotchar=NULL; /* where dot was found */ |
522 | 0 | const char *cfirst=chars; /* -> first character of decimal part */ |
523 | 0 | const char *last=NULL; /* -> last digit of decimal part */ |
524 | 0 | const char *c; /* work */ |
525 | 0 | Unit *up; /* .. */ |
526 | | #if DECDPUN>1 |
527 | | Int cut, out; /* .. */ |
528 | | #endif |
529 | 0 | Int residue; /* rounding residue */ |
530 | 0 | uInt status=0; /* error code */ |
531 | |
|
532 | | #if DECCHECK |
533 | | if (decCheckOperands(DECUNRESU, DECUNUSED, DECUNUSED, set)) |
534 | | return uprv_decNumberZero(dn); |
535 | | #endif |
536 | |
|
537 | 0 | do { /* status & malloc protection */ |
538 | 0 | for (c=chars;; c++) { /* -> input character */ |
539 | 0 | if (*c>='0' && *c<='9') { /* test for Arabic digit */ |
540 | 0 | last=c; |
541 | 0 | d++; /* count of real digits */ |
542 | 0 | continue; /* still in decimal part */ |
543 | 0 | } |
544 | 0 | if (*c=='.' && dotchar==NULL) { /* first '.' */ |
545 | 0 | dotchar=c; /* record offset into decimal part */ |
546 | 0 | if (c==cfirst) cfirst++; /* first digit must follow */ |
547 | 0 | continue;} |
548 | 0 | if (c==chars) { /* first in string... */ |
549 | 0 | if (*c=='-') { /* valid - sign */ |
550 | 0 | cfirst++; |
551 | 0 | bits=DECNEG; |
552 | 0 | continue;} |
553 | 0 | if (*c=='+') { /* valid + sign */ |
554 | 0 | cfirst++; |
555 | 0 | continue;} |
556 | 0 | } |
557 | | /* *c is not a digit, or a valid +, -, or '.' */ |
558 | 0 | break; |
559 | 0 | } /* c */ |
560 | |
|
561 | 0 | if (last==NULL) { /* no digits yet */ |
562 | 0 | status=DEC_Conversion_syntax;/* assume the worst */ |
563 | 0 | if (*c=='\0') break; /* and no more to come... */ |
564 | | #if DECSUBSET |
565 | | /* if subset then infinities and NaNs are not allowed */ |
566 | | if (!set->extended) break; /* hopeless */ |
567 | | #endif |
568 | | /* Infinities and NaNs are possible, here */ |
569 | 0 | if (dotchar!=NULL) break; /* .. unless had a dot */ |
570 | 0 | uprv_decNumberZero(dn); /* be optimistic */ |
571 | 0 | if (decBiStr(c, "infinity", "INFINITY") |
572 | 0 | || decBiStr(c, "inf", "INF")) { |
573 | 0 | dn->bits=bits | DECINF; |
574 | 0 | status=0; /* is OK */ |
575 | 0 | break; /* all done */ |
576 | 0 | } |
577 | | /* a NaN expected */ |
578 | | /* 2003.09.10 NaNs are now permitted to have a sign */ |
579 | 0 | dn->bits=bits | DECNAN; /* assume simple NaN */ |
580 | 0 | if (*c=='s' || *c=='S') { /* looks like an sNaN */ |
581 | 0 | c++; |
582 | 0 | dn->bits=bits | DECSNAN; |
583 | 0 | } |
584 | 0 | if (*c!='n' && *c!='N') break; /* check caseless "NaN" */ |
585 | 0 | c++; |
586 | 0 | if (*c!='a' && *c!='A') break; /* .. */ |
587 | 0 | c++; |
588 | 0 | if (*c!='n' && *c!='N') break; /* .. */ |
589 | 0 | c++; |
590 | | /* now either nothing, or nnnn payload, expected */ |
591 | | /* -> start of integer and skip leading 0s [including plain 0] */ |
592 | 0 | for (cfirst=c; *cfirst=='0';) cfirst++; |
593 | 0 | if (*cfirst=='\0') { /* "NaN" or "sNaN", maybe with all 0s */ |
594 | 0 | status=0; /* it's good */ |
595 | 0 | break; /* .. */ |
596 | 0 | } |
597 | | /* something other than 0s; setup last and d as usual [no dots] */ |
598 | 0 | for (c=cfirst;; c++, d++) { |
599 | 0 | if (*c<'0' || *c>'9') break; /* test for Arabic digit */ |
600 | 0 | last=c; |
601 | 0 | } |
602 | 0 | if (*c!='\0') break; /* not all digits */ |
603 | 0 | if (d>set->digits-1) { |
604 | | /* [NB: payload in a decNumber can be full length unless */ |
605 | | /* clamped, in which case can only be digits-1] */ |
606 | 0 | if (set->clamp) break; |
607 | 0 | if (d>set->digits) break; |
608 | 0 | } /* too many digits? */ |
609 | | /* good; drop through to convert the integer to coefficient */ |
610 | 0 | status=0; /* syntax is OK */ |
611 | 0 | bits=dn->bits; /* for copy-back */ |
612 | 0 | } /* last==NULL */ |
613 | | |
614 | 0 | else if (*c!='\0') { /* more to process... */ |
615 | | /* had some digits; exponent is only valid sequence now */ |
616 | 0 | Flag nege; /* 1=negative exponent */ |
617 | 0 | const char *firstexp; /* -> first significant exponent digit */ |
618 | 0 | status=DEC_Conversion_syntax;/* assume the worst */ |
619 | 0 | if (*c!='e' && *c!='E') break; |
620 | | /* Found 'e' or 'E' -- now process explicit exponent */ |
621 | | /* 1998.07.11: sign no longer required */ |
622 | 0 | nege=0; |
623 | 0 | c++; /* to (possible) sign */ |
624 | 0 | if (*c=='-') {nege=1; c++;} |
625 | 0 | else if (*c=='+') c++; |
626 | 0 | if (*c=='\0') break; |
627 | | |
628 | 0 | for (; *c=='0' && *(c+1)!='\0';) c++; /* strip insignificant zeros */ |
629 | 0 | firstexp=c; /* save exponent digit place */ |
630 | 0 | uInt uexponent = 0; /* Avoid undefined behavior on signed int overflow */ |
631 | 0 | for (; ;c++) { |
632 | 0 | if (*c<'0' || *c>'9') break; /* not a digit */ |
633 | 0 | uexponent=X10(uexponent)+(uInt)*c-(uInt)'0'; |
634 | 0 | } /* c */ |
635 | 0 | exponent = (Int)uexponent; |
636 | | /* if not now on a '\0', *c must not be a digit */ |
637 | 0 | if (*c!='\0') break; |
638 | | |
639 | | /* (this next test must be after the syntax checks) */ |
640 | | /* if it was too long the exponent may have wrapped, so check */ |
641 | | /* carefully and set it to a certain overflow if wrap possible */ |
642 | 0 | if (c>=firstexp+9+1) { |
643 | 0 | if (c>firstexp+9+1 || *firstexp>'1') exponent=DECNUMMAXE*2; |
644 | | /* [up to 1999999999 is OK, for example 1E-1000000998] */ |
645 | 0 | } |
646 | 0 | if (nege) exponent=-exponent; /* was negative */ |
647 | 0 | status=0; /* is OK */ |
648 | 0 | } /* stuff after digits */ |
649 | | |
650 | | /* Here when whole string has been inspected; syntax is good */ |
651 | | /* cfirst->first digit (never dot), last->last digit (ditto) */ |
652 | | |
653 | | /* strip leading zeros/dot [leave final 0 if all 0's] */ |
654 | 0 | if (*cfirst=='0') { /* [cfirst has stepped over .] */ |
655 | 0 | for (c=cfirst; c<last; c++, cfirst++) { |
656 | 0 | if (*c=='.') continue; /* ignore dots */ |
657 | 0 | if (*c!='0') break; /* non-zero found */ |
658 | 0 | d--; /* 0 stripped */ |
659 | 0 | } /* c */ |
660 | | #if DECSUBSET |
661 | | /* make a rapid exit for easy zeros if !extended */ |
662 | | if (*cfirst=='0' && !set->extended) { |
663 | | uprv_decNumberZero(dn); /* clean result */ |
664 | | break; /* [could be return] */ |
665 | | } |
666 | | #endif |
667 | 0 | } /* at least one leading 0 */ |
668 | | |
669 | | /* Handle decimal point... */ |
670 | 0 | if (dotchar!=NULL && dotchar<last) /* non-trailing '.' found? */ |
671 | 0 | exponent -= static_cast<int32_t>(last-dotchar); /* adjust exponent */ |
672 | | /* [we can now ignore the .] */ |
673 | | |
674 | | /* OK, the digits string is good. Assemble in the decNumber, or in */ |
675 | | /* a temporary units array if rounding is needed */ |
676 | 0 | if (d<=set->digits) res=dn->lsu; /* fits into supplied decNumber */ |
677 | 0 | else { /* rounding needed */ |
678 | 0 | Int needbytes=D2U(d)*sizeof(Unit);/* bytes needed */ |
679 | 0 | res=resbuff; /* assume use local buffer */ |
680 | 0 | if (needbytes>(Int)sizeof(resbuff)) { /* too big for local */ |
681 | 0 | allocres=(Unit *)malloc(needbytes); |
682 | 0 | if (allocres==NULL) {status|=DEC_Insufficient_storage; break;} |
683 | 0 | res=allocres; |
684 | 0 | } |
685 | 0 | } |
686 | | /* res now -> number lsu, buffer, or allocated storage for Unit array */ |
687 | | |
688 | | /* Place the coefficient into the selected Unit array */ |
689 | | /* [this is often 70% of the cost of this function when DECDPUN>1] */ |
690 | | #if DECDPUN>1 |
691 | | out=0; /* accumulator */ |
692 | | up=res+D2U(d)-1; /* -> msu */ |
693 | | cut=d-(up-res)*DECDPUN; /* digits in top unit */ |
694 | | for (c=cfirst;; c++) { /* along the digits */ |
695 | | if (*c=='.') continue; /* ignore '.' [don't decrement cut] */ |
696 | | out=X10(out)+(Int)*c-(Int)'0'; |
697 | | if (c==last) break; /* done [never get to trailing '.'] */ |
698 | | cut--; |
699 | | if (cut>0) continue; /* more for this unit */ |
700 | | *up=(Unit)out; /* write unit */ |
701 | | up--; /* prepare for unit below.. */ |
702 | | cut=DECDPUN; /* .. */ |
703 | | out=0; /* .. */ |
704 | | } /* c */ |
705 | | *up=(Unit)out; /* write lsu */ |
706 | | |
707 | | #else |
708 | | /* DECDPUN==1 */ |
709 | 0 | up=res; /* -> lsu */ |
710 | 0 | for (c=last; c>=cfirst; c--) { /* over each character, from least */ |
711 | 0 | if (*c=='.') continue; /* ignore . [don't step up] */ |
712 | 0 | *up=(Unit)((Int)*c-(Int)'0'); |
713 | 0 | up++; |
714 | 0 | } /* c */ |
715 | 0 | #endif |
716 | |
|
717 | 0 | dn->bits=bits; |
718 | 0 | dn->exponent=exponent; |
719 | 0 | dn->digits=d; |
720 | | |
721 | | /* if not in number (too long) shorten into the number */ |
722 | 0 | if (d>set->digits) { |
723 | 0 | residue=0; |
724 | 0 | decSetCoeff(dn, set, res, d, &residue, &status); |
725 | | /* always check for overflow or subnormal and round as needed */ |
726 | 0 | decFinalize(dn, set, &residue, &status); |
727 | 0 | } |
728 | 0 | else { /* no rounding, but may still have overflow or subnormal */ |
729 | | /* [these tests are just for performance; finalize repeats them] */ |
730 | 0 | if ((dn->exponent-1<set->emin-dn->digits) |
731 | 0 | || (dn->exponent-1>set->emax-set->digits)) { |
732 | 0 | residue=0; |
733 | 0 | decFinalize(dn, set, &residue, &status); |
734 | 0 | } |
735 | 0 | } |
736 | | /* decNumberShow(dn); */ |
737 | 0 | } while(0); /* [for break] */ |
738 | | |
739 | 0 | if (allocres!=NULL) free(allocres); /* drop any storage used */ |
740 | 0 | if (status!=0) decStatus(dn, status, set); |
741 | 0 | return dn; |
742 | 0 | } /* decNumberFromString */ |
743 | | |
744 | | /* ================================================================== */ |
745 | | /* Operators */ |
746 | | /* ================================================================== */ |
747 | | |
748 | | /* ------------------------------------------------------------------ */ |
749 | | /* decNumberAbs -- absolute value operator */ |
750 | | /* */ |
751 | | /* This computes C = abs(A) */ |
752 | | /* */ |
753 | | /* res is C, the result. C may be A */ |
754 | | /* rhs is A */ |
755 | | /* set is the context */ |
756 | | /* */ |
757 | | /* See also decNumberCopyAbs for a quiet bitwise version of this. */ |
758 | | /* C must have space for set->digits digits. */ |
759 | | /* ------------------------------------------------------------------ */ |
760 | | /* This has the same effect as decNumberPlus unless A is negative, */ |
761 | | /* in which case it has the same effect as decNumberMinus. */ |
762 | | /* ------------------------------------------------------------------ */ |
763 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberAbs(decNumber *res, const decNumber *rhs, |
764 | 0 | decContext *set) { |
765 | 0 | decNumber dzero; /* for 0 */ |
766 | 0 | uInt status=0; /* accumulator */ |
767 | |
|
768 | | #if DECCHECK |
769 | | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
770 | | #endif |
771 | |
|
772 | 0 | uprv_decNumberZero(&dzero); /* set 0 */ |
773 | 0 | dzero.exponent=rhs->exponent; /* [no coefficient expansion] */ |
774 | 0 | decAddOp(res, &dzero, rhs, set, (uByte)(rhs->bits & DECNEG), &status); |
775 | 0 | if (status!=0) decStatus(res, status, set); |
776 | | #if DECCHECK |
777 | | decCheckInexact(res, set); |
778 | | #endif |
779 | 0 | return res; |
780 | 0 | } /* decNumberAbs */ |
781 | | |
782 | | /* ------------------------------------------------------------------ */ |
783 | | /* decNumberAdd -- add two Numbers */ |
784 | | /* */ |
785 | | /* This computes C = A + B */ |
786 | | /* */ |
787 | | /* res is C, the result. C may be A and/or B (e.g., X=X+X) */ |
788 | | /* lhs is A */ |
789 | | /* rhs is B */ |
790 | | /* set is the context */ |
791 | | /* */ |
792 | | /* C must have space for set->digits digits. */ |
793 | | /* ------------------------------------------------------------------ */ |
794 | | /* This just calls the routine shared with Subtract */ |
795 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberAdd(decNumber *res, const decNumber *lhs, |
796 | 0 | const decNumber *rhs, decContext *set) { |
797 | 0 | uInt status=0; /* accumulator */ |
798 | 0 | decAddOp(res, lhs, rhs, set, 0, &status); |
799 | 0 | if (status!=0) decStatus(res, status, set); |
800 | | #if DECCHECK |
801 | | decCheckInexact(res, set); |
802 | | #endif |
803 | 0 | return res; |
804 | 0 | } /* decNumberAdd */ |
805 | | |
806 | | /* ------------------------------------------------------------------ */ |
807 | | /* decNumberAnd -- AND two Numbers, digitwise */ |
808 | | /* */ |
809 | | /* This computes C = A & B */ |
810 | | /* */ |
811 | | /* res is C, the result. C may be A and/or B (e.g., X=X&X) */ |
812 | | /* lhs is A */ |
813 | | /* rhs is B */ |
814 | | /* set is the context (used for result length and error report) */ |
815 | | /* */ |
816 | | /* C must have space for set->digits digits. */ |
817 | | /* */ |
818 | | /* Logical function restrictions apply (see above); a NaN is */ |
819 | | /* returned with Invalid_operation if a restriction is violated. */ |
820 | | /* ------------------------------------------------------------------ */ |
821 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberAnd(decNumber *res, const decNumber *lhs, |
822 | 0 | const decNumber *rhs, decContext *set) { |
823 | 0 | const Unit *ua, *ub; /* -> operands */ |
824 | 0 | const Unit *msua, *msub; /* -> operand msus */ |
825 | 0 | Unit *uc, *msuc; /* -> result and its msu */ |
826 | 0 | Int msudigs; /* digits in res msu */ |
827 | | #if DECCHECK |
828 | | if (decCheckOperands(res, lhs, rhs, set)) return res; |
829 | | #endif |
830 | |
|
831 | 0 | if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) |
832 | 0 | || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { |
833 | 0 | decStatus(res, DEC_Invalid_operation, set); |
834 | 0 | return res; |
835 | 0 | } |
836 | | |
837 | | /* operands are valid */ |
838 | 0 | ua=lhs->lsu; /* bottom-up */ |
839 | 0 | ub=rhs->lsu; /* .. */ |
840 | 0 | uc=res->lsu; /* .. */ |
841 | 0 | msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */ |
842 | 0 | msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */ |
843 | 0 | msuc=uc+D2U(set->digits)-1; /* -> msu of result */ |
844 | 0 | msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ |
845 | 0 | for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */ |
846 | 0 | Unit a, b; /* extract units */ |
847 | 0 | if (ua>msua) a=0; |
848 | 0 | else a=*ua; |
849 | 0 | if (ub>msub) b=0; |
850 | 0 | else b=*ub; |
851 | 0 | *uc=0; /* can now write back */ |
852 | 0 | if (a|b) { /* maybe 1 bits to examine */ |
853 | 0 | Int i, j; |
854 | 0 | *uc=0; /* can now write back */ |
855 | | /* This loop could be unrolled and/or use BIN2BCD tables */ |
856 | 0 | for (i=0; i<DECDPUN; i++) { |
857 | 0 | if (a&b&1) *uc=*uc+(Unit)powers[i]; /* effect AND */ |
858 | 0 | j=a%10; |
859 | 0 | a=a/10; |
860 | 0 | j|=b%10; |
861 | 0 | b=b/10; |
862 | 0 | if (j>1) { |
863 | 0 | decStatus(res, DEC_Invalid_operation, set); |
864 | 0 | return res; |
865 | 0 | } |
866 | 0 | if (uc==msuc && i==msudigs-1) break; /* just did final digit */ |
867 | 0 | } /* each digit */ |
868 | 0 | } /* both OK */ |
869 | 0 | } /* each unit */ |
870 | | /* [here uc-1 is the msu of the result] */ |
871 | 0 | res->digits=decGetDigits(res->lsu, static_cast<int32_t>(uc - res->lsu)); |
872 | 0 | res->exponent=0; /* integer */ |
873 | 0 | res->bits=0; /* sign=0 */ |
874 | 0 | return res; /* [no status to set] */ |
875 | 0 | } /* decNumberAnd */ |
876 | | |
877 | | /* ------------------------------------------------------------------ */ |
878 | | /* decNumberCompare -- compare two Numbers */ |
879 | | /* */ |
880 | | /* This computes C = A ? B */ |
881 | | /* */ |
882 | | /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ |
883 | | /* lhs is A */ |
884 | | /* rhs is B */ |
885 | | /* set is the context */ |
886 | | /* */ |
887 | | /* C must have space for one digit (or NaN). */ |
888 | | /* ------------------------------------------------------------------ */ |
889 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompare(decNumber *res, const decNumber *lhs, |
890 | 0 | const decNumber *rhs, decContext *set) { |
891 | 0 | uInt status=0; /* accumulator */ |
892 | 0 | decCompareOp(res, lhs, rhs, set, COMPARE, &status); |
893 | 0 | if (status!=0) decStatus(res, status, set); |
894 | 0 | return res; |
895 | 0 | } /* decNumberCompare */ |
896 | | |
897 | | /* ------------------------------------------------------------------ */ |
898 | | /* decNumberCompareSignal -- compare, signalling on all NaNs */ |
899 | | /* */ |
900 | | /* This computes C = A ? B */ |
901 | | /* */ |
902 | | /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ |
903 | | /* lhs is A */ |
904 | | /* rhs is B */ |
905 | | /* set is the context */ |
906 | | /* */ |
907 | | /* C must have space for one digit (or NaN). */ |
908 | | /* ------------------------------------------------------------------ */ |
909 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompareSignal(decNumber *res, const decNumber *lhs, |
910 | 0 | const decNumber *rhs, decContext *set) { |
911 | 0 | uInt status=0; /* accumulator */ |
912 | 0 | decCompareOp(res, lhs, rhs, set, COMPSIG, &status); |
913 | 0 | if (status!=0) decStatus(res, status, set); |
914 | 0 | return res; |
915 | 0 | } /* decNumberCompareSignal */ |
916 | | |
917 | | /* ------------------------------------------------------------------ */ |
918 | | /* decNumberCompareTotal -- compare two Numbers, using total ordering */ |
919 | | /* */ |
920 | | /* This computes C = A ? B, under total ordering */ |
921 | | /* */ |
922 | | /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ |
923 | | /* lhs is A */ |
924 | | /* rhs is B */ |
925 | | /* set is the context */ |
926 | | /* */ |
927 | | /* C must have space for one digit; the result will always be one of */ |
928 | | /* -1, 0, or 1. */ |
929 | | /* ------------------------------------------------------------------ */ |
930 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompareTotal(decNumber *res, const decNumber *lhs, |
931 | 0 | const decNumber *rhs, decContext *set) { |
932 | 0 | uInt status=0; /* accumulator */ |
933 | 0 | decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status); |
934 | 0 | if (status!=0) decStatus(res, status, set); |
935 | 0 | return res; |
936 | 0 | } /* decNumberCompareTotal */ |
937 | | |
938 | | /* ------------------------------------------------------------------ */ |
939 | | /* decNumberCompareTotalMag -- compare, total ordering of magnitudes */ |
940 | | /* */ |
941 | | /* This computes C = |A| ? |B|, under total ordering */ |
942 | | /* */ |
943 | | /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ |
944 | | /* lhs is A */ |
945 | | /* rhs is B */ |
946 | | /* set is the context */ |
947 | | /* */ |
948 | | /* C must have space for one digit; the result will always be one of */ |
949 | | /* -1, 0, or 1. */ |
950 | | /* ------------------------------------------------------------------ */ |
951 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompareTotalMag(decNumber *res, const decNumber *lhs, |
952 | 0 | const decNumber *rhs, decContext *set) { |
953 | 0 | uInt status=0; /* accumulator */ |
954 | 0 | uInt needbytes; /* for space calculations */ |
955 | 0 | decNumber bufa[D2N(DECBUFFER+1)];/* +1 in case DECBUFFER=0 */ |
956 | 0 | decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ |
957 | 0 | decNumber bufb[D2N(DECBUFFER+1)]; |
958 | 0 | decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */ |
959 | 0 | decNumber *a, *b; /* temporary pointers */ |
960 | |
|
961 | | #if DECCHECK |
962 | | if (decCheckOperands(res, lhs, rhs, set)) return res; |
963 | | #endif |
964 | |
|
965 | 0 | do { /* protect allocated storage */ |
966 | | /* if either is negative, take a copy and absolute */ |
967 | 0 | if (decNumberIsNegative(lhs)) { /* lhs<0 */ |
968 | 0 | a=bufa; |
969 | 0 | needbytes=sizeof(decNumber)+(D2U(lhs->digits)-1)*sizeof(Unit); |
970 | 0 | if (needbytes>sizeof(bufa)) { /* need malloc space */ |
971 | 0 | allocbufa=(decNumber *)malloc(needbytes); |
972 | 0 | if (allocbufa==NULL) { /* hopeless -- abandon */ |
973 | 0 | status|=DEC_Insufficient_storage; |
974 | 0 | break;} |
975 | 0 | a=allocbufa; /* use the allocated space */ |
976 | 0 | } |
977 | 0 | uprv_decNumberCopy(a, lhs); /* copy content */ |
978 | 0 | a->bits&=~DECNEG; /* .. and clear the sign */ |
979 | 0 | lhs=a; /* use copy from here on */ |
980 | 0 | } |
981 | 0 | if (decNumberIsNegative(rhs)) { /* rhs<0 */ |
982 | 0 | b=bufb; |
983 | 0 | needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); |
984 | 0 | if (needbytes>sizeof(bufb)) { /* need malloc space */ |
985 | 0 | allocbufb=(decNumber *)malloc(needbytes); |
986 | 0 | if (allocbufb==NULL) { /* hopeless -- abandon */ |
987 | 0 | status|=DEC_Insufficient_storage; |
988 | 0 | break;} |
989 | 0 | b=allocbufb; /* use the allocated space */ |
990 | 0 | } |
991 | 0 | uprv_decNumberCopy(b, rhs); /* copy content */ |
992 | 0 | b->bits&=~DECNEG; /* .. and clear the sign */ |
993 | 0 | rhs=b; /* use copy from here on */ |
994 | 0 | } |
995 | 0 | decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status); |
996 | 0 | } while(0); /* end protected */ |
997 | | |
998 | 0 | if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ |
999 | 0 | if (allocbufb!=NULL) free(allocbufb); /* .. */ |
1000 | 0 | if (status!=0) decStatus(res, status, set); |
1001 | 0 | return res; |
1002 | 0 | } /* decNumberCompareTotalMag */ |
1003 | | |
1004 | | /* ------------------------------------------------------------------ */ |
1005 | | /* decNumberDivide -- divide one number by another */ |
1006 | | /* */ |
1007 | | /* This computes C = A / B */ |
1008 | | /* */ |
1009 | | /* res is C, the result. C may be A and/or B (e.g., X=X/X) */ |
1010 | | /* lhs is A */ |
1011 | | /* rhs is B */ |
1012 | | /* set is the context */ |
1013 | | /* */ |
1014 | | /* C must have space for set->digits digits. */ |
1015 | | /* ------------------------------------------------------------------ */ |
1016 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberDivide(decNumber *res, const decNumber *lhs, |
1017 | 0 | const decNumber *rhs, decContext *set) { |
1018 | 0 | uInt status=0; /* accumulator */ |
1019 | 0 | decDivideOp(res, lhs, rhs, set, DIVIDE, &status); |
1020 | 0 | if (status!=0) decStatus(res, status, set); |
1021 | | #if DECCHECK |
1022 | | decCheckInexact(res, set); |
1023 | | #endif |
1024 | 0 | return res; |
1025 | 0 | } /* decNumberDivide */ |
1026 | | |
1027 | | /* ------------------------------------------------------------------ */ |
1028 | | /* decNumberDivideInteger -- divide and return integer quotient */ |
1029 | | /* */ |
1030 | | /* This computes C = A # B, where # is the integer divide operator */ |
1031 | | /* */ |
1032 | | /* res is C, the result. C may be A and/or B (e.g., X=X#X) */ |
1033 | | /* lhs is A */ |
1034 | | /* rhs is B */ |
1035 | | /* set is the context */ |
1036 | | /* */ |
1037 | | /* C must have space for set->digits digits. */ |
1038 | | /* ------------------------------------------------------------------ */ |
1039 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberDivideInteger(decNumber *res, const decNumber *lhs, |
1040 | 0 | const decNumber *rhs, decContext *set) { |
1041 | 0 | uInt status=0; /* accumulator */ |
1042 | 0 | decDivideOp(res, lhs, rhs, set, DIVIDEINT, &status); |
1043 | 0 | if (status!=0) decStatus(res, status, set); |
1044 | 0 | return res; |
1045 | 0 | } /* decNumberDivideInteger */ |
1046 | | |
1047 | | /* ------------------------------------------------------------------ */ |
1048 | | /* decNumberExp -- exponentiation */ |
1049 | | /* */ |
1050 | | /* This computes C = exp(A) */ |
1051 | | /* */ |
1052 | | /* res is C, the result. C may be A */ |
1053 | | /* rhs is A */ |
1054 | | /* set is the context; note that rounding mode has no effect */ |
1055 | | /* */ |
1056 | | /* C must have space for set->digits digits. */ |
1057 | | /* */ |
1058 | | /* Mathematical function restrictions apply (see above); a NaN is */ |
1059 | | /* returned with Invalid_operation if a restriction is violated. */ |
1060 | | /* */ |
1061 | | /* Finite results will always be full precision and Inexact, except */ |
1062 | | /* when A is a zero or -Infinity (giving 1 or 0 respectively). */ |
1063 | | /* */ |
1064 | | /* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ |
1065 | | /* almost always be correctly rounded, but may be up to 1 ulp in */ |
1066 | | /* error in rare cases. */ |
1067 | | /* ------------------------------------------------------------------ */ |
1068 | | /* This is a wrapper for decExpOp which can handle the slightly wider */ |
1069 | | /* (double) range needed by Ln (which has to be able to calculate */ |
1070 | | /* exp(-a) where a can be the tiniest number (Ntiny). */ |
1071 | | /* ------------------------------------------------------------------ */ |
1072 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberExp(decNumber *res, const decNumber *rhs, |
1073 | 0 | decContext *set) { |
1074 | 0 | uInt status=0; /* accumulator */ |
1075 | | #if DECSUBSET |
1076 | | decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ |
1077 | | #endif |
1078 | |
|
1079 | | #if DECCHECK |
1080 | | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
1081 | | #endif |
1082 | | |
1083 | | /* Check restrictions; these restrictions ensure that if h=8 (see */ |
1084 | | /* decExpOp) then the result will either overflow or underflow to 0. */ |
1085 | | /* Other math functions restrict the input range, too, for inverses. */ |
1086 | | /* If not violated then carry out the operation. */ |
1087 | 0 | if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */ |
1088 | | #if DECSUBSET |
1089 | | if (!set->extended) { |
1090 | | /* reduce operand and set lostDigits status, as needed */ |
1091 | | if (rhs->digits>set->digits) { |
1092 | | allocrhs=decRoundOperand(rhs, set, &status); |
1093 | | if (allocrhs==NULL) break; |
1094 | | rhs=allocrhs; |
1095 | | } |
1096 | | } |
1097 | | #endif |
1098 | 0 | decExpOp(res, rhs, set, &status); |
1099 | 0 | } while(0); /* end protected */ |
1100 | |
|
1101 | | #if DECSUBSET |
1102 | | if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */ |
1103 | | #endif |
1104 | | /* apply significant status */ |
1105 | 0 | if (status!=0) decStatus(res, status, set); |
1106 | | #if DECCHECK |
1107 | | decCheckInexact(res, set); |
1108 | | #endif |
1109 | 0 | return res; |
1110 | 0 | } /* decNumberExp */ |
1111 | | |
1112 | | /* ------------------------------------------------------------------ */ |
1113 | | /* decNumberFMA -- fused multiply add */ |
1114 | | /* */ |
1115 | | /* This computes D = (A * B) + C with only one rounding */ |
1116 | | /* */ |
1117 | | /* res is D, the result. D may be A or B or C (e.g., X=FMA(X,X,X)) */ |
1118 | | /* lhs is A */ |
1119 | | /* rhs is B */ |
1120 | | /* fhs is C [far hand side] */ |
1121 | | /* set is the context */ |
1122 | | /* */ |
1123 | | /* Mathematical function restrictions apply (see above); a NaN is */ |
1124 | | /* returned with Invalid_operation if a restriction is violated. */ |
1125 | | /* */ |
1126 | | /* C must have space for set->digits digits. */ |
1127 | | /* ------------------------------------------------------------------ */ |
1128 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberFMA(decNumber *res, const decNumber *lhs, |
1129 | | const decNumber *rhs, const decNumber *fhs, |
1130 | 0 | decContext *set) { |
1131 | 0 | uInt status=0; /* accumulator */ |
1132 | 0 | decContext dcmul; /* context for the multiplication */ |
1133 | 0 | uInt needbytes; /* for space calculations */ |
1134 | 0 | decNumber bufa[D2N(DECBUFFER*2+1)]; |
1135 | 0 | decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ |
1136 | 0 | decNumber *acc; /* accumulator pointer */ |
1137 | 0 | decNumber dzero; /* work */ |
1138 | |
|
1139 | | #if DECCHECK |
1140 | | if (decCheckOperands(res, lhs, rhs, set)) return res; |
1141 | | if (decCheckOperands(res, fhs, DECUNUSED, set)) return res; |
1142 | | #endif |
1143 | |
|
1144 | 0 | do { /* protect allocated storage */ |
1145 | | #if DECSUBSET |
1146 | | if (!set->extended) { /* [undefined if subset] */ |
1147 | | status|=DEC_Invalid_operation; |
1148 | | break;} |
1149 | | #endif |
1150 | | /* Check math restrictions [these ensure no overflow or underflow] */ |
1151 | 0 | if ((!decNumberIsSpecial(lhs) && decCheckMath(lhs, set, &status)) |
1152 | 0 | || (!decNumberIsSpecial(rhs) && decCheckMath(rhs, set, &status)) |
1153 | 0 | || (!decNumberIsSpecial(fhs) && decCheckMath(fhs, set, &status))) break; |
1154 | | /* set up context for multiply */ |
1155 | 0 | dcmul=*set; |
1156 | 0 | dcmul.digits=lhs->digits+rhs->digits; /* just enough */ |
1157 | | /* [The above may be an over-estimate for subset arithmetic, but that's OK] */ |
1158 | 0 | dcmul.emax=DEC_MAX_EMAX; /* effectively unbounded .. */ |
1159 | 0 | dcmul.emin=DEC_MIN_EMIN; /* [thanks to Math restrictions] */ |
1160 | | /* set up decNumber space to receive the result of the multiply */ |
1161 | 0 | acc=bufa; /* may fit */ |
1162 | 0 | needbytes=sizeof(decNumber)+(D2U(dcmul.digits)-1)*sizeof(Unit); |
1163 | 0 | if (needbytes>sizeof(bufa)) { /* need malloc space */ |
1164 | 0 | allocbufa=(decNumber *)malloc(needbytes); |
1165 | 0 | if (allocbufa==NULL) { /* hopeless -- abandon */ |
1166 | 0 | status|=DEC_Insufficient_storage; |
1167 | 0 | break;} |
1168 | 0 | acc=allocbufa; /* use the allocated space */ |
1169 | 0 | } |
1170 | | /* multiply with extended range and necessary precision */ |
1171 | | /*printf("emin=%ld\n", dcmul.emin); */ |
1172 | 0 | decMultiplyOp(acc, lhs, rhs, &dcmul, &status); |
1173 | | /* Only Invalid operation (from sNaN or Inf * 0) is possible in */ |
1174 | | /* status; if either is seen than ignore fhs (in case it is */ |
1175 | | /* another sNaN) and set acc to NaN unless we had an sNaN */ |
1176 | | /* [decMultiplyOp leaves that to caller] */ |
1177 | | /* Note sNaN has to go through addOp to shorten payload if */ |
1178 | | /* necessary */ |
1179 | 0 | if ((status&DEC_Invalid_operation)!=0) { |
1180 | 0 | if (!(status&DEC_sNaN)) { /* but be true invalid */ |
1181 | 0 | uprv_decNumberZero(res); /* acc not yet set */ |
1182 | 0 | res->bits=DECNAN; |
1183 | 0 | break; |
1184 | 0 | } |
1185 | 0 | uprv_decNumberZero(&dzero); /* make 0 (any non-NaN would do) */ |
1186 | 0 | fhs=&dzero; /* use that */ |
1187 | 0 | } |
1188 | | #if DECCHECK |
1189 | | else { /* multiply was OK */ |
1190 | | if (status!=0) printf("Status=%08lx after FMA multiply\n", (LI)status); |
1191 | | } |
1192 | | #endif |
1193 | | /* add the third operand and result -> res, and all is done */ |
1194 | 0 | decAddOp(res, acc, fhs, set, 0, &status); |
1195 | 0 | } while(0); /* end protected */ |
1196 | | |
1197 | 0 | if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ |
1198 | 0 | if (status!=0) decStatus(res, status, set); |
1199 | | #if DECCHECK |
1200 | | decCheckInexact(res, set); |
1201 | | #endif |
1202 | 0 | return res; |
1203 | 0 | } /* decNumberFMA */ |
1204 | | |
1205 | | /* ------------------------------------------------------------------ */ |
1206 | | /* decNumberInvert -- invert a Number, digitwise */ |
1207 | | /* */ |
1208 | | /* This computes C = ~A */ |
1209 | | /* */ |
1210 | | /* res is C, the result. C may be A (e.g., X=~X) */ |
1211 | | /* rhs is A */ |
1212 | | /* set is the context (used for result length and error report) */ |
1213 | | /* */ |
1214 | | /* C must have space for set->digits digits. */ |
1215 | | /* */ |
1216 | | /* Logical function restrictions apply (see above); a NaN is */ |
1217 | | /* returned with Invalid_operation if a restriction is violated. */ |
1218 | | /* ------------------------------------------------------------------ */ |
1219 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberInvert(decNumber *res, const decNumber *rhs, |
1220 | 0 | decContext *set) { |
1221 | 0 | const Unit *ua, *msua; /* -> operand and its msu */ |
1222 | 0 | Unit *uc, *msuc; /* -> result and its msu */ |
1223 | 0 | Int msudigs; /* digits in res msu */ |
1224 | | #if DECCHECK |
1225 | | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
1226 | | #endif |
1227 | |
|
1228 | 0 | if (rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { |
1229 | 0 | decStatus(res, DEC_Invalid_operation, set); |
1230 | 0 | return res; |
1231 | 0 | } |
1232 | | /* operand is valid */ |
1233 | 0 | ua=rhs->lsu; /* bottom-up */ |
1234 | 0 | uc=res->lsu; /* .. */ |
1235 | 0 | msua=ua+D2U(rhs->digits)-1; /* -> msu of rhs */ |
1236 | 0 | msuc=uc+D2U(set->digits)-1; /* -> msu of result */ |
1237 | 0 | msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ |
1238 | 0 | for (; uc<=msuc; ua++, uc++) { /* Unit loop */ |
1239 | 0 | Unit a; /* extract unit */ |
1240 | 0 | Int i, j; /* work */ |
1241 | 0 | if (ua>msua) a=0; |
1242 | 0 | else a=*ua; |
1243 | 0 | *uc=0; /* can now write back */ |
1244 | | /* always need to examine all bits in rhs */ |
1245 | | /* This loop could be unrolled and/or use BIN2BCD tables */ |
1246 | 0 | for (i=0; i<DECDPUN; i++) { |
1247 | 0 | if ((~a)&1) *uc=*uc+(Unit)powers[i]; /* effect INVERT */ |
1248 | 0 | j=a%10; |
1249 | 0 | a=a/10; |
1250 | 0 | if (j>1) { |
1251 | 0 | decStatus(res, DEC_Invalid_operation, set); |
1252 | 0 | return res; |
1253 | 0 | } |
1254 | 0 | if (uc==msuc && i==msudigs-1) break; /* just did final digit */ |
1255 | 0 | } /* each digit */ |
1256 | 0 | } /* each unit */ |
1257 | | /* [here uc-1 is the msu of the result] */ |
1258 | 0 | res->digits=decGetDigits(res->lsu, static_cast<int32_t>(uc - res->lsu)); |
1259 | 0 | res->exponent=0; /* integer */ |
1260 | 0 | res->bits=0; /* sign=0 */ |
1261 | 0 | return res; /* [no status to set] */ |
1262 | 0 | } /* decNumberInvert */ |
1263 | | |
1264 | | /* ------------------------------------------------------------------ */ |
1265 | | /* decNumberLn -- natural logarithm */ |
1266 | | /* */ |
1267 | | /* This computes C = ln(A) */ |
1268 | | /* */ |
1269 | | /* res is C, the result. C may be A */ |
1270 | | /* rhs is A */ |
1271 | | /* set is the context; note that rounding mode has no effect */ |
1272 | | /* */ |
1273 | | /* C must have space for set->digits digits. */ |
1274 | | /* */ |
1275 | | /* Notable cases: */ |
1276 | | /* A<0 -> Invalid */ |
1277 | | /* A=0 -> -Infinity (Exact) */ |
1278 | | /* A=+Infinity -> +Infinity (Exact) */ |
1279 | | /* A=1 exactly -> 0 (Exact) */ |
1280 | | /* */ |
1281 | | /* Mathematical function restrictions apply (see above); a NaN is */ |
1282 | | /* returned with Invalid_operation if a restriction is violated. */ |
1283 | | /* */ |
1284 | | /* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ |
1285 | | /* almost always be correctly rounded, but may be up to 1 ulp in */ |
1286 | | /* error in rare cases. */ |
1287 | | /* ------------------------------------------------------------------ */ |
1288 | | /* This is a wrapper for decLnOp which can handle the slightly wider */ |
1289 | | /* (+11) range needed by Ln, Log10, etc. (which may have to be able */ |
1290 | | /* to calculate at p+e+2). */ |
1291 | | /* ------------------------------------------------------------------ */ |
1292 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberLn(decNumber *res, const decNumber *rhs, |
1293 | 0 | decContext *set) { |
1294 | 0 | uInt status=0; /* accumulator */ |
1295 | | #if DECSUBSET |
1296 | | decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ |
1297 | | #endif |
1298 | |
|
1299 | | #if DECCHECK |
1300 | | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
1301 | | #endif |
1302 | | |
1303 | | /* Check restrictions; this is a math function; if not violated */ |
1304 | | /* then carry out the operation. */ |
1305 | 0 | if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */ |
1306 | | #if DECSUBSET |
1307 | | if (!set->extended) { |
1308 | | /* reduce operand and set lostDigits status, as needed */ |
1309 | | if (rhs->digits>set->digits) { |
1310 | | allocrhs=decRoundOperand(rhs, set, &status); |
1311 | | if (allocrhs==NULL) break; |
1312 | | rhs=allocrhs; |
1313 | | } |
1314 | | /* special check in subset for rhs=0 */ |
1315 | | if (ISZERO(rhs)) { /* +/- zeros -> error */ |
1316 | | status|=DEC_Invalid_operation; |
1317 | | break;} |
1318 | | } /* extended=0 */ |
1319 | | #endif |
1320 | 0 | decLnOp(res, rhs, set, &status); |
1321 | 0 | } while(0); /* end protected */ |
1322 | |
|
1323 | | #if DECSUBSET |
1324 | | if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */ |
1325 | | #endif |
1326 | | /* apply significant status */ |
1327 | 0 | if (status!=0) decStatus(res, status, set); |
1328 | | #if DECCHECK |
1329 | | decCheckInexact(res, set); |
1330 | | #endif |
1331 | 0 | return res; |
1332 | 0 | } /* decNumberLn */ |
1333 | | |
1334 | | /* ------------------------------------------------------------------ */ |
1335 | | /* decNumberLogB - get adjusted exponent, by 754 rules */ |
1336 | | /* */ |
1337 | | /* This computes C = adjustedexponent(A) */ |
1338 | | /* */ |
1339 | | /* res is C, the result. C may be A */ |
1340 | | /* rhs is A */ |
1341 | | /* set is the context, used only for digits and status */ |
1342 | | /* */ |
1343 | | /* C must have space for 10 digits (A might have 10**9 digits and */ |
1344 | | /* an exponent of +999999999, or one digit and an exponent of */ |
1345 | | /* -1999999999). */ |
1346 | | /* */ |
1347 | | /* This returns the adjusted exponent of A after (in theory) padding */ |
1348 | | /* with zeros on the right to set->digits digits while keeping the */ |
1349 | | /* same value. The exponent is not limited by emin/emax. */ |
1350 | | /* */ |
1351 | | /* Notable cases: */ |
1352 | | /* A<0 -> Use |A| */ |
1353 | | /* A=0 -> -Infinity (Division by zero) */ |
1354 | | /* A=Infinite -> +Infinity (Exact) */ |
1355 | | /* A=1 exactly -> 0 (Exact) */ |
1356 | | /* NaNs are propagated as usual */ |
1357 | | /* ------------------------------------------------------------------ */ |
1358 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberLogB(decNumber *res, const decNumber *rhs, |
1359 | 0 | decContext *set) { |
1360 | 0 | uInt status=0; /* accumulator */ |
1361 | |
|
1362 | | #if DECCHECK |
1363 | | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
1364 | | #endif |
1365 | | |
1366 | | /* NaNs as usual; Infinities return +Infinity; 0->oops */ |
1367 | 0 | if (decNumberIsNaN(rhs)) decNaNs(res, rhs, NULL, set, &status); |
1368 | 0 | else if (decNumberIsInfinite(rhs)) uprv_decNumberCopyAbs(res, rhs); |
1369 | 0 | else if (decNumberIsZero(rhs)) { |
1370 | 0 | uprv_decNumberZero(res); /* prepare for Infinity */ |
1371 | 0 | res->bits=DECNEG|DECINF; /* -Infinity */ |
1372 | 0 | status|=DEC_Division_by_zero; /* as per 754 */ |
1373 | 0 | } |
1374 | 0 | else { /* finite non-zero */ |
1375 | 0 | Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */ |
1376 | 0 | uprv_decNumberFromInt32(res, ae); /* lay it out */ |
1377 | 0 | } |
1378 | |
|
1379 | 0 | if (status!=0) decStatus(res, status, set); |
1380 | 0 | return res; |
1381 | 0 | } /* decNumberLogB */ |
1382 | | |
1383 | | /* ------------------------------------------------------------------ */ |
1384 | | /* decNumberLog10 -- logarithm in base 10 */ |
1385 | | /* */ |
1386 | | /* This computes C = log10(A) */ |
1387 | | /* */ |
1388 | | /* res is C, the result. C may be A */ |
1389 | | /* rhs is A */ |
1390 | | /* set is the context; note that rounding mode has no effect */ |
1391 | | /* */ |
1392 | | /* C must have space for set->digits digits. */ |
1393 | | /* */ |
1394 | | /* Notable cases: */ |
1395 | | /* A<0 -> Invalid */ |
1396 | | /* A=0 -> -Infinity (Exact) */ |
1397 | | /* A=+Infinity -> +Infinity (Exact) */ |
1398 | | /* A=10**n (if n is an integer) -> n (Exact) */ |
1399 | | /* */ |
1400 | | /* Mathematical function restrictions apply (see above); a NaN is */ |
1401 | | /* returned with Invalid_operation if a restriction is violated. */ |
1402 | | /* */ |
1403 | | /* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ |
1404 | | /* almost always be correctly rounded, but may be up to 1 ulp in */ |
1405 | | /* error in rare cases. */ |
1406 | | /* ------------------------------------------------------------------ */ |
1407 | | /* This calculates ln(A)/ln(10) using appropriate precision. For */ |
1408 | | /* ln(A) this is the max(p, rhs->digits + t) + 3, where p is the */ |
1409 | | /* requested digits and t is the number of digits in the exponent */ |
1410 | | /* (maximum 6). For ln(10) it is p + 3; this is often handled by the */ |
1411 | | /* fastpath in decLnOp. The final division is done to the requested */ |
1412 | | /* precision. */ |
1413 | | /* ------------------------------------------------------------------ */ |
1414 | | #if defined(__clang__) || U_GCC_MAJOR_MINOR >= 406 |
1415 | | #pragma GCC diagnostic push |
1416 | | #pragma GCC diagnostic ignored "-Warray-bounds" |
1417 | | #endif |
1418 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberLog10(decNumber *res, const decNumber *rhs, |
1419 | 0 | decContext *set) { |
1420 | 0 | uInt status=0, ignore=0; /* status accumulators */ |
1421 | 0 | uInt needbytes; /* for space calculations */ |
1422 | 0 | Int p; /* working precision */ |
1423 | 0 | Int t; /* digits in exponent of A */ |
1424 | | |
1425 | | /* buffers for a and b working decimals */ |
1426 | | /* (adjustment calculator, same size) */ |
1427 | 0 | decNumber bufa[D2N(DECBUFFER+2)]; |
1428 | 0 | decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ |
1429 | 0 | decNumber *a=bufa; /* temporary a */ |
1430 | 0 | decNumber bufb[D2N(DECBUFFER+2)]; |
1431 | 0 | decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */ |
1432 | 0 | decNumber *b=bufb; /* temporary b */ |
1433 | 0 | decNumber bufw[D2N(10)]; /* working 2-10 digit number */ |
1434 | 0 | decNumber *w=bufw; /* .. */ |
1435 | | #if DECSUBSET |
1436 | | decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ |
1437 | | #endif |
1438 | |
|
1439 | 0 | decContext aset; /* working context */ |
1440 | |
|
1441 | | #if DECCHECK |
1442 | | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
1443 | | #endif |
1444 | | |
1445 | | /* Check restrictions; this is a math function; if not violated */ |
1446 | | /* then carry out the operation. */ |
1447 | 0 | if (!decCheckMath(rhs, set, &status)) do { /* protect malloc */ |
1448 | | #if DECSUBSET |
1449 | | if (!set->extended) { |
1450 | | /* reduce operand and set lostDigits status, as needed */ |
1451 | | if (rhs->digits>set->digits) { |
1452 | | allocrhs=decRoundOperand(rhs, set, &status); |
1453 | | if (allocrhs==NULL) break; |
1454 | | rhs=allocrhs; |
1455 | | } |
1456 | | /* special check in subset for rhs=0 */ |
1457 | | if (ISZERO(rhs)) { /* +/- zeros -> error */ |
1458 | | status|=DEC_Invalid_operation; |
1459 | | break;} |
1460 | | } /* extended=0 */ |
1461 | | #endif |
1462 | |
|
1463 | 0 | uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */ |
1464 | | |
1465 | | /* handle exact powers of 10; only check if +ve finite */ |
1466 | 0 | if (!(rhs->bits&(DECNEG|DECSPECIAL)) && !ISZERO(rhs)) { |
1467 | 0 | Int residue=0; /* (no residue) */ |
1468 | 0 | uInt copystat=0; /* clean status */ |
1469 | | |
1470 | | /* round to a single digit... */ |
1471 | 0 | aset.digits=1; |
1472 | 0 | decCopyFit(w, rhs, &aset, &residue, ©stat); /* copy & shorten */ |
1473 | | /* if exact and the digit is 1, rhs is a power of 10 */ |
1474 | 0 | if (!(copystat&DEC_Inexact) && w->lsu[0]==1) { |
1475 | | /* the exponent, conveniently, is the power of 10; making */ |
1476 | | /* this the result needs a little care as it might not fit, */ |
1477 | | /* so first convert it into the working number, and then move */ |
1478 | | /* to res */ |
1479 | 0 | uprv_decNumberFromInt32(w, w->exponent); |
1480 | 0 | residue=0; |
1481 | 0 | decCopyFit(res, w, set, &residue, &status); /* copy & round */ |
1482 | 0 | decFinish(res, set, &residue, &status); /* cleanup/set flags */ |
1483 | 0 | break; |
1484 | 0 | } /* not a power of 10 */ |
1485 | 0 | } /* not a candidate for exact */ |
1486 | | |
1487 | | /* simplify the information-content calculation to use 'total */ |
1488 | | /* number of digits in a, including exponent' as compared to the */ |
1489 | | /* requested digits, as increasing this will only rarely cost an */ |
1490 | | /* iteration in ln(a) anyway */ |
1491 | 0 | t=6; /* it can never be >6 */ |
1492 | | |
1493 | | /* allocate space when needed... */ |
1494 | 0 | p=(rhs->digits+t>set->digits?rhs->digits+t:set->digits)+3; |
1495 | 0 | needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit); |
1496 | 0 | if (needbytes>sizeof(bufa)) { /* need malloc space */ |
1497 | 0 | allocbufa=(decNumber *)malloc(needbytes); |
1498 | 0 | if (allocbufa==NULL) { /* hopeless -- abandon */ |
1499 | 0 | status|=DEC_Insufficient_storage; |
1500 | 0 | break;} |
1501 | 0 | a=allocbufa; /* use the allocated space */ |
1502 | 0 | } |
1503 | 0 | aset.digits=p; /* as calculated */ |
1504 | 0 | aset.emax=DEC_MAX_MATH; /* usual bounds */ |
1505 | 0 | aset.emin=-DEC_MAX_MATH; /* .. */ |
1506 | 0 | aset.clamp=0; /* and no concrete format */ |
1507 | 0 | decLnOp(a, rhs, &aset, &status); /* a=ln(rhs) */ |
1508 | | |
1509 | | /* skip the division if the result so far is infinite, NaN, or */ |
1510 | | /* zero, or there was an error; note NaN from sNaN needs copy */ |
1511 | 0 | if (status&DEC_NaNs && !(status&DEC_sNaN)) break; |
1512 | 0 | if (a->bits&DECSPECIAL || ISZERO(a)) { |
1513 | 0 | uprv_decNumberCopy(res, a); /* [will fit] */ |
1514 | 0 | break;} |
1515 | | |
1516 | | /* for ln(10) an extra 3 digits of precision are needed */ |
1517 | 0 | p=set->digits+3; |
1518 | 0 | needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit); |
1519 | 0 | if (needbytes>sizeof(bufb)) { /* need malloc space */ |
1520 | 0 | allocbufb=(decNumber *)malloc(needbytes); |
1521 | 0 | if (allocbufb==NULL) { /* hopeless -- abandon */ |
1522 | 0 | status|=DEC_Insufficient_storage; |
1523 | 0 | break;} |
1524 | 0 | b=allocbufb; /* use the allocated space */ |
1525 | 0 | } |
1526 | 0 | uprv_decNumberZero(w); /* set up 10... */ |
1527 | 0 | #if DECDPUN==1 |
1528 | 0 | w->lsu[1]=1; w->lsu[0]=0; /* .. */ |
1529 | | #else |
1530 | | w->lsu[0]=10; /* .. */ |
1531 | | #endif |
1532 | 0 | w->digits=2; /* .. */ |
1533 | |
|
1534 | 0 | aset.digits=p; |
1535 | 0 | decLnOp(b, w, &aset, &ignore); /* b=ln(10) */ |
1536 | |
|
1537 | 0 | aset.digits=set->digits; /* for final divide */ |
1538 | 0 | decDivideOp(res, a, b, &aset, DIVIDE, &status); /* into result */ |
1539 | 0 | } while(0); /* [for break] */ |
1540 | | |
1541 | 0 | if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ |
1542 | 0 | if (allocbufb!=NULL) free(allocbufb); /* .. */ |
1543 | | #if DECSUBSET |
1544 | | if (allocrhs !=NULL) free(allocrhs); /* .. */ |
1545 | | #endif |
1546 | | /* apply significant status */ |
1547 | 0 | if (status!=0) decStatus(res, status, set); |
1548 | | #if DECCHECK |
1549 | | decCheckInexact(res, set); |
1550 | | #endif |
1551 | 0 | return res; |
1552 | 0 | } /* decNumberLog10 */ |
1553 | | #if defined(__clang__) || U_GCC_MAJOR_MINOR >= 406 |
1554 | | #pragma GCC diagnostic pop |
1555 | | #endif |
1556 | | |
1557 | | /* ------------------------------------------------------------------ */ |
1558 | | /* decNumberMax -- compare two Numbers and return the maximum */ |
1559 | | /* */ |
1560 | | /* This computes C = A ? B, returning the maximum by 754 rules */ |
1561 | | /* */ |
1562 | | /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ |
1563 | | /* lhs is A */ |
1564 | | /* rhs is B */ |
1565 | | /* set is the context */ |
1566 | | /* */ |
1567 | | /* C must have space for set->digits digits. */ |
1568 | | /* ------------------------------------------------------------------ */ |
1569 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberMax(decNumber *res, const decNumber *lhs, |
1570 | 0 | const decNumber *rhs, decContext *set) { |
1571 | 0 | uInt status=0; /* accumulator */ |
1572 | 0 | decCompareOp(res, lhs, rhs, set, COMPMAX, &status); |
1573 | 0 | if (status!=0) decStatus(res, status, set); |
1574 | | #if DECCHECK |
1575 | | decCheckInexact(res, set); |
1576 | | #endif |
1577 | 0 | return res; |
1578 | 0 | } /* decNumberMax */ |
1579 | | |
1580 | | /* ------------------------------------------------------------------ */ |
1581 | | /* decNumberMaxMag -- compare and return the maximum by magnitude */ |
1582 | | /* */ |
1583 | | /* This computes C = A ? B, returning the maximum by 754 rules */ |
1584 | | /* */ |
1585 | | /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ |
1586 | | /* lhs is A */ |
1587 | | /* rhs is B */ |
1588 | | /* set is the context */ |
1589 | | /* */ |
1590 | | /* C must have space for set->digits digits. */ |
1591 | | /* ------------------------------------------------------------------ */ |
1592 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberMaxMag(decNumber *res, const decNumber *lhs, |
1593 | 0 | const decNumber *rhs, decContext *set) { |
1594 | 0 | uInt status=0; /* accumulator */ |
1595 | 0 | decCompareOp(res, lhs, rhs, set, COMPMAXMAG, &status); |
1596 | 0 | if (status!=0) decStatus(res, status, set); |
1597 | | #if DECCHECK |
1598 | | decCheckInexact(res, set); |
1599 | | #endif |
1600 | 0 | return res; |
1601 | 0 | } /* decNumberMaxMag */ |
1602 | | |
1603 | | /* ------------------------------------------------------------------ */ |
1604 | | /* decNumberMin -- compare two Numbers and return the minimum */ |
1605 | | /* */ |
1606 | | /* This computes C = A ? B, returning the minimum by 754 rules */ |
1607 | | /* */ |
1608 | | /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ |
1609 | | /* lhs is A */ |
1610 | | /* rhs is B */ |
1611 | | /* set is the context */ |
1612 | | /* */ |
1613 | | /* C must have space for set->digits digits. */ |
1614 | | /* ------------------------------------------------------------------ */ |
1615 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberMin(decNumber *res, const decNumber *lhs, |
1616 | 0 | const decNumber *rhs, decContext *set) { |
1617 | 0 | uInt status=0; /* accumulator */ |
1618 | 0 | decCompareOp(res, lhs, rhs, set, COMPMIN, &status); |
1619 | 0 | if (status!=0) decStatus(res, status, set); |
1620 | | #if DECCHECK |
1621 | | decCheckInexact(res, set); |
1622 | | #endif |
1623 | 0 | return res; |
1624 | 0 | } /* decNumberMin */ |
1625 | | |
1626 | | /* ------------------------------------------------------------------ */ |
1627 | | /* decNumberMinMag -- compare and return the minimum by magnitude */ |
1628 | | /* */ |
1629 | | /* This computes C = A ? B, returning the minimum by 754 rules */ |
1630 | | /* */ |
1631 | | /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ |
1632 | | /* lhs is A */ |
1633 | | /* rhs is B */ |
1634 | | /* set is the context */ |
1635 | | /* */ |
1636 | | /* C must have space for set->digits digits. */ |
1637 | | /* ------------------------------------------------------------------ */ |
1638 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberMinMag(decNumber *res, const decNumber *lhs, |
1639 | 0 | const decNumber *rhs, decContext *set) { |
1640 | 0 | uInt status=0; /* accumulator */ |
1641 | 0 | decCompareOp(res, lhs, rhs, set, COMPMINMAG, &status); |
1642 | 0 | if (status!=0) decStatus(res, status, set); |
1643 | | #if DECCHECK |
1644 | | decCheckInexact(res, set); |
1645 | | #endif |
1646 | 0 | return res; |
1647 | 0 | } /* decNumberMinMag */ |
1648 | | |
1649 | | /* ------------------------------------------------------------------ */ |
1650 | | /* decNumberMinus -- prefix minus operator */ |
1651 | | /* */ |
1652 | | /* This computes C = 0 - A */ |
1653 | | /* */ |
1654 | | /* res is C, the result. C may be A */ |
1655 | | /* rhs is A */ |
1656 | | /* set is the context */ |
1657 | | /* */ |
1658 | | /* See also decNumberCopyNegate for a quiet bitwise version of this. */ |
1659 | | /* C must have space for set->digits digits. */ |
1660 | | /* ------------------------------------------------------------------ */ |
1661 | | /* Simply use AddOp for the subtract, which will do the necessary. */ |
1662 | | /* ------------------------------------------------------------------ */ |
1663 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberMinus(decNumber *res, const decNumber *rhs, |
1664 | 0 | decContext *set) { |
1665 | 0 | decNumber dzero; |
1666 | 0 | uInt status=0; /* accumulator */ |
1667 | |
|
1668 | | #if DECCHECK |
1669 | | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
1670 | | #endif |
1671 | |
|
1672 | 0 | uprv_decNumberZero(&dzero); /* make 0 */ |
1673 | 0 | dzero.exponent=rhs->exponent; /* [no coefficient expansion] */ |
1674 | 0 | decAddOp(res, &dzero, rhs, set, DECNEG, &status); |
1675 | 0 | if (status!=0) decStatus(res, status, set); |
1676 | | #if DECCHECK |
1677 | | decCheckInexact(res, set); |
1678 | | #endif |
1679 | 0 | return res; |
1680 | 0 | } /* decNumberMinus */ |
1681 | | |
1682 | | /* ------------------------------------------------------------------ */ |
1683 | | /* decNumberNextMinus -- next towards -Infinity */ |
1684 | | /* */ |
1685 | | /* This computes C = A - infinitesimal, rounded towards -Infinity */ |
1686 | | /* */ |
1687 | | /* res is C, the result. C may be A */ |
1688 | | /* rhs is A */ |
1689 | | /* set is the context */ |
1690 | | /* */ |
1691 | | /* This is a generalization of 754 NextDown. */ |
1692 | | /* ------------------------------------------------------------------ */ |
1693 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberNextMinus(decNumber *res, const decNumber *rhs, |
1694 | 0 | decContext *set) { |
1695 | 0 | decNumber dtiny; /* constant */ |
1696 | 0 | decContext workset=*set; /* work */ |
1697 | 0 | uInt status=0; /* accumulator */ |
1698 | | #if DECCHECK |
1699 | | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
1700 | | #endif |
1701 | | |
1702 | | /* +Infinity is the special case */ |
1703 | 0 | if ((rhs->bits&(DECINF|DECNEG))==DECINF) { |
1704 | 0 | decSetMaxValue(res, set); /* is +ve */ |
1705 | | /* there is no status to set */ |
1706 | 0 | return res; |
1707 | 0 | } |
1708 | 0 | uprv_decNumberZero(&dtiny); /* start with 0 */ |
1709 | 0 | dtiny.lsu[0]=1; /* make number that is .. */ |
1710 | 0 | dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */ |
1711 | 0 | workset.round=DEC_ROUND_FLOOR; |
1712 | 0 | decAddOp(res, rhs, &dtiny, &workset, DECNEG, &status); |
1713 | 0 | status&=DEC_Invalid_operation|DEC_sNaN; /* only sNaN Invalid please */ |
1714 | 0 | if (status!=0) decStatus(res, status, set); |
1715 | 0 | return res; |
1716 | 0 | } /* decNumberNextMinus */ |
1717 | | |
1718 | | /* ------------------------------------------------------------------ */ |
1719 | | /* decNumberNextPlus -- next towards +Infinity */ |
1720 | | /* */ |
1721 | | /* This computes C = A + infinitesimal, rounded towards +Infinity */ |
1722 | | /* */ |
1723 | | /* res is C, the result. C may be A */ |
1724 | | /* rhs is A */ |
1725 | | /* set is the context */ |
1726 | | /* */ |
1727 | | /* This is a generalization of 754 NextUp. */ |
1728 | | /* ------------------------------------------------------------------ */ |
1729 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberNextPlus(decNumber *res, const decNumber *rhs, |
1730 | 0 | decContext *set) { |
1731 | 0 | decNumber dtiny; /* constant */ |
1732 | 0 | decContext workset=*set; /* work */ |
1733 | 0 | uInt status=0; /* accumulator */ |
1734 | | #if DECCHECK |
1735 | | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
1736 | | #endif |
1737 | | |
1738 | | /* -Infinity is the special case */ |
1739 | 0 | if ((rhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) { |
1740 | 0 | decSetMaxValue(res, set); |
1741 | 0 | res->bits=DECNEG; /* negative */ |
1742 | | /* there is no status to set */ |
1743 | 0 | return res; |
1744 | 0 | } |
1745 | 0 | uprv_decNumberZero(&dtiny); /* start with 0 */ |
1746 | 0 | dtiny.lsu[0]=1; /* make number that is .. */ |
1747 | 0 | dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */ |
1748 | 0 | workset.round=DEC_ROUND_CEILING; |
1749 | 0 | decAddOp(res, rhs, &dtiny, &workset, 0, &status); |
1750 | 0 | status&=DEC_Invalid_operation|DEC_sNaN; /* only sNaN Invalid please */ |
1751 | 0 | if (status!=0) decStatus(res, status, set); |
1752 | 0 | return res; |
1753 | 0 | } /* decNumberNextPlus */ |
1754 | | |
1755 | | /* ------------------------------------------------------------------ */ |
1756 | | /* decNumberNextToward -- next towards rhs */ |
1757 | | /* */ |
1758 | | /* This computes C = A +/- infinitesimal, rounded towards */ |
1759 | | /* +/-Infinity in the direction of B, as per 754-1985 nextafter */ |
1760 | | /* modified during revision but dropped from 754-2008. */ |
1761 | | /* */ |
1762 | | /* res is C, the result. C may be A or B. */ |
1763 | | /* lhs is A */ |
1764 | | /* rhs is B */ |
1765 | | /* set is the context */ |
1766 | | /* */ |
1767 | | /* This is a generalization of 754-1985 NextAfter. */ |
1768 | | /* ------------------------------------------------------------------ */ |
1769 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberNextToward(decNumber *res, const decNumber *lhs, |
1770 | 0 | const decNumber *rhs, decContext *set) { |
1771 | 0 | decNumber dtiny; /* constant */ |
1772 | 0 | decContext workset=*set; /* work */ |
1773 | 0 | Int result; /* .. */ |
1774 | 0 | uInt status=0; /* accumulator */ |
1775 | | #if DECCHECK |
1776 | | if (decCheckOperands(res, lhs, rhs, set)) return res; |
1777 | | #endif |
1778 | |
|
1779 | 0 | if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { |
1780 | 0 | decNaNs(res, lhs, rhs, set, &status); |
1781 | 0 | } |
1782 | 0 | else { /* Is numeric, so no chance of sNaN Invalid, etc. */ |
1783 | 0 | result=decCompare(lhs, rhs, 0); /* sign matters */ |
1784 | 0 | if (result==BADINT) status|=DEC_Insufficient_storage; /* rare */ |
1785 | 0 | else { /* valid compare */ |
1786 | 0 | if (result==0) uprv_decNumberCopySign(res, lhs, rhs); /* easy */ |
1787 | 0 | else { /* differ: need NextPlus or NextMinus */ |
1788 | 0 | uByte sub; /* add or subtract */ |
1789 | 0 | if (result<0) { /* lhs<rhs, do nextplus */ |
1790 | | /* -Infinity is the special case */ |
1791 | 0 | if ((lhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) { |
1792 | 0 | decSetMaxValue(res, set); |
1793 | 0 | res->bits=DECNEG; /* negative */ |
1794 | 0 | return res; /* there is no status to set */ |
1795 | 0 | } |
1796 | 0 | workset.round=DEC_ROUND_CEILING; |
1797 | 0 | sub=0; /* add, please */ |
1798 | 0 | } /* plus */ |
1799 | 0 | else { /* lhs>rhs, do nextminus */ |
1800 | | /* +Infinity is the special case */ |
1801 | 0 | if ((lhs->bits&(DECINF|DECNEG))==DECINF) { |
1802 | 0 | decSetMaxValue(res, set); |
1803 | 0 | return res; /* there is no status to set */ |
1804 | 0 | } |
1805 | 0 | workset.round=DEC_ROUND_FLOOR; |
1806 | 0 | sub=DECNEG; /* subtract, please */ |
1807 | 0 | } /* minus */ |
1808 | 0 | uprv_decNumberZero(&dtiny); /* start with 0 */ |
1809 | 0 | dtiny.lsu[0]=1; /* make number that is .. */ |
1810 | 0 | dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */ |
1811 | 0 | decAddOp(res, lhs, &dtiny, &workset, sub, &status); /* + or - */ |
1812 | | /* turn off exceptions if the result is a normal number */ |
1813 | | /* (including Nmin), otherwise let all status through */ |
1814 | 0 | if (uprv_decNumberIsNormal(res, set)) status=0; |
1815 | 0 | } /* unequal */ |
1816 | 0 | } /* compare OK */ |
1817 | 0 | } /* numeric */ |
1818 | 0 | if (status!=0) decStatus(res, status, set); |
1819 | 0 | return res; |
1820 | 0 | } /* decNumberNextToward */ |
1821 | | |
1822 | | /* ------------------------------------------------------------------ */ |
1823 | | /* decNumberOr -- OR two Numbers, digitwise */ |
1824 | | /* */ |
1825 | | /* This computes C = A | B */ |
1826 | | /* */ |
1827 | | /* res is C, the result. C may be A and/or B (e.g., X=X|X) */ |
1828 | | /* lhs is A */ |
1829 | | /* rhs is B */ |
1830 | | /* set is the context (used for result length and error report) */ |
1831 | | /* */ |
1832 | | /* C must have space for set->digits digits. */ |
1833 | | /* */ |
1834 | | /* Logical function restrictions apply (see above); a NaN is */ |
1835 | | /* returned with Invalid_operation if a restriction is violated. */ |
1836 | | /* ------------------------------------------------------------------ */ |
1837 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberOr(decNumber *res, const decNumber *lhs, |
1838 | 0 | const decNumber *rhs, decContext *set) { |
1839 | 0 | const Unit *ua, *ub; /* -> operands */ |
1840 | 0 | const Unit *msua, *msub; /* -> operand msus */ |
1841 | 0 | Unit *uc, *msuc; /* -> result and its msu */ |
1842 | 0 | Int msudigs; /* digits in res msu */ |
1843 | | #if DECCHECK |
1844 | | if (decCheckOperands(res, lhs, rhs, set)) return res; |
1845 | | #endif |
1846 | |
|
1847 | 0 | if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) |
1848 | 0 | || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { |
1849 | 0 | decStatus(res, DEC_Invalid_operation, set); |
1850 | 0 | return res; |
1851 | 0 | } |
1852 | | /* operands are valid */ |
1853 | 0 | ua=lhs->lsu; /* bottom-up */ |
1854 | 0 | ub=rhs->lsu; /* .. */ |
1855 | 0 | uc=res->lsu; /* .. */ |
1856 | 0 | msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */ |
1857 | 0 | msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */ |
1858 | 0 | msuc=uc+D2U(set->digits)-1; /* -> msu of result */ |
1859 | 0 | msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ |
1860 | 0 | for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */ |
1861 | 0 | Unit a, b; /* extract units */ |
1862 | 0 | if (ua>msua) a=0; |
1863 | 0 | else a=*ua; |
1864 | 0 | if (ub>msub) b=0; |
1865 | 0 | else b=*ub; |
1866 | 0 | *uc=0; /* can now write back */ |
1867 | 0 | if (a|b) { /* maybe 1 bits to examine */ |
1868 | 0 | Int i, j; |
1869 | | /* This loop could be unrolled and/or use BIN2BCD tables */ |
1870 | 0 | for (i=0; i<DECDPUN; i++) { |
1871 | 0 | if ((a|b)&1) *uc=*uc+(Unit)powers[i]; /* effect OR */ |
1872 | 0 | j=a%10; |
1873 | 0 | a=a/10; |
1874 | 0 | j|=b%10; |
1875 | 0 | b=b/10; |
1876 | 0 | if (j>1) { |
1877 | 0 | decStatus(res, DEC_Invalid_operation, set); |
1878 | 0 | return res; |
1879 | 0 | } |
1880 | 0 | if (uc==msuc && i==msudigs-1) break; /* just did final digit */ |
1881 | 0 | } /* each digit */ |
1882 | 0 | } /* non-zero */ |
1883 | 0 | } /* each unit */ |
1884 | | /* [here uc-1 is the msu of the result] */ |
1885 | 0 | res->digits=decGetDigits(res->lsu, static_cast<int32_t>(uc-res->lsu)); |
1886 | 0 | res->exponent=0; /* integer */ |
1887 | 0 | res->bits=0; /* sign=0 */ |
1888 | 0 | return res; /* [no status to set] */ |
1889 | 0 | } /* decNumberOr */ |
1890 | | |
1891 | | /* ------------------------------------------------------------------ */ |
1892 | | /* decNumberPlus -- prefix plus operator */ |
1893 | | /* */ |
1894 | | /* This computes C = 0 + A */ |
1895 | | /* */ |
1896 | | /* res is C, the result. C may be A */ |
1897 | | /* rhs is A */ |
1898 | | /* set is the context */ |
1899 | | /* */ |
1900 | | /* See also decNumberCopy for a quiet bitwise version of this. */ |
1901 | | /* C must have space for set->digits digits. */ |
1902 | | /* ------------------------------------------------------------------ */ |
1903 | | /* This simply uses AddOp; Add will take fast path after preparing A. */ |
1904 | | /* Performance is a concern here, as this routine is often used to */ |
1905 | | /* check operands and apply rounding and overflow/underflow testing. */ |
1906 | | /* ------------------------------------------------------------------ */ |
1907 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberPlus(decNumber *res, const decNumber *rhs, |
1908 | 0 | decContext *set) { |
1909 | 0 | decNumber dzero; |
1910 | 0 | uInt status=0; /* accumulator */ |
1911 | | #if DECCHECK |
1912 | | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
1913 | | #endif |
1914 | |
|
1915 | 0 | uprv_decNumberZero(&dzero); /* make 0 */ |
1916 | 0 | dzero.exponent=rhs->exponent; /* [no coefficient expansion] */ |
1917 | 0 | decAddOp(res, &dzero, rhs, set, 0, &status); |
1918 | 0 | if (status!=0) decStatus(res, status, set); |
1919 | | #if DECCHECK |
1920 | | decCheckInexact(res, set); |
1921 | | #endif |
1922 | 0 | return res; |
1923 | 0 | } /* decNumberPlus */ |
1924 | | |
1925 | | /* ------------------------------------------------------------------ */ |
1926 | | /* decNumberMultiply -- multiply two Numbers */ |
1927 | | /* */ |
1928 | | /* This computes C = A x B */ |
1929 | | /* */ |
1930 | | /* res is C, the result. C may be A and/or B (e.g., X=X+X) */ |
1931 | | /* lhs is A */ |
1932 | | /* rhs is B */ |
1933 | | /* set is the context */ |
1934 | | /* */ |
1935 | | /* C must have space for set->digits digits. */ |
1936 | | /* ------------------------------------------------------------------ */ |
1937 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberMultiply(decNumber *res, const decNumber *lhs, |
1938 | 0 | const decNumber *rhs, decContext *set) { |
1939 | 0 | uInt status=0; /* accumulator */ |
1940 | 0 | decMultiplyOp(res, lhs, rhs, set, &status); |
1941 | 0 | if (status!=0) decStatus(res, status, set); |
1942 | | #if DECCHECK |
1943 | | decCheckInexact(res, set); |
1944 | | #endif |
1945 | 0 | return res; |
1946 | 0 | } /* decNumberMultiply */ |
1947 | | |
1948 | | /* ------------------------------------------------------------------ */ |
1949 | | /* decNumberPower -- raise a number to a power */ |
1950 | | /* */ |
1951 | | /* This computes C = A ** B */ |
1952 | | /* */ |
1953 | | /* res is C, the result. C may be A and/or B (e.g., X=X**X) */ |
1954 | | /* lhs is A */ |
1955 | | /* rhs is B */ |
1956 | | /* set is the context */ |
1957 | | /* */ |
1958 | | /* C must have space for set->digits digits. */ |
1959 | | /* */ |
1960 | | /* Mathematical function restrictions apply (see above); a NaN is */ |
1961 | | /* returned with Invalid_operation if a restriction is violated. */ |
1962 | | /* */ |
1963 | | /* However, if 1999999997<=B<=999999999 and B is an integer then the */ |
1964 | | /* restrictions on A and the context are relaxed to the usual bounds, */ |
1965 | | /* for compatibility with the earlier (integer power only) version */ |
1966 | | /* of this function. */ |
1967 | | /* */ |
1968 | | /* When B is an integer, the result may be exact, even if rounded. */ |
1969 | | /* */ |
1970 | | /* The final result is rounded according to the context; it will */ |
1971 | | /* almost always be correctly rounded, but may be up to 1 ulp in */ |
1972 | | /* error in rare cases. */ |
1973 | | /* ------------------------------------------------------------------ */ |
1974 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberPower(decNumber *res, const decNumber *lhs, |
1975 | 0 | const decNumber *rhs, decContext *set) { |
1976 | | #if DECSUBSET |
1977 | | decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ |
1978 | | decNumber *allocrhs=NULL; /* .., rhs */ |
1979 | | #endif |
1980 | 0 | decNumber *allocdac=NULL; /* -> allocated acc buffer, iff used */ |
1981 | 0 | decNumber *allocinv=NULL; /* -> allocated 1/x buffer, iff used */ |
1982 | 0 | Int reqdigits=set->digits; /* requested DIGITS */ |
1983 | 0 | Int n; /* rhs in binary */ |
1984 | 0 | Flag rhsint=0; /* 1 if rhs is an integer */ |
1985 | 0 | Flag useint=0; /* 1 if can use integer calculation */ |
1986 | 0 | Flag isoddint=0; /* 1 if rhs is an integer and odd */ |
1987 | 0 | Int i; /* work */ |
1988 | | #if DECSUBSET |
1989 | | Int dropped; /* .. */ |
1990 | | #endif |
1991 | 0 | uInt needbytes; /* buffer size needed */ |
1992 | 0 | Flag seenbit; /* seen a bit while powering */ |
1993 | 0 | Int residue=0; /* rounding residue */ |
1994 | 0 | uInt status=0; /* accumulators */ |
1995 | 0 | uByte bits=0; /* result sign if errors */ |
1996 | 0 | decContext aset; /* working context */ |
1997 | 0 | decNumber dnOne; /* work value 1... */ |
1998 | | /* local accumulator buffer [a decNumber, with digits+elength+1 digits] */ |
1999 | 0 | decNumber dacbuff[D2N(DECBUFFER+9)]; |
2000 | 0 | decNumber *dac=dacbuff; /* -> result accumulator */ |
2001 | | /* same again for possible 1/lhs calculation */ |
2002 | 0 | decNumber invbuff[D2N(DECBUFFER+9)]; |
2003 | |
|
2004 | | #if DECCHECK |
2005 | | if (decCheckOperands(res, lhs, rhs, set)) return res; |
2006 | | #endif |
2007 | |
|
2008 | 0 | do { /* protect allocated storage */ |
2009 | | #if DECSUBSET |
2010 | | if (!set->extended) { /* reduce operands and set status, as needed */ |
2011 | | if (lhs->digits>reqdigits) { |
2012 | | alloclhs=decRoundOperand(lhs, set, &status); |
2013 | | if (alloclhs==NULL) break; |
2014 | | lhs=alloclhs; |
2015 | | } |
2016 | | if (rhs->digits>reqdigits) { |
2017 | | allocrhs=decRoundOperand(rhs, set, &status); |
2018 | | if (allocrhs==NULL) break; |
2019 | | rhs=allocrhs; |
2020 | | } |
2021 | | } |
2022 | | #endif |
2023 | | /* [following code does not require input rounding] */ |
2024 | | |
2025 | | /* handle NaNs and rhs Infinity (lhs infinity is harder) */ |
2026 | 0 | if (SPECIALARGS) { |
2027 | 0 | if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { /* NaNs */ |
2028 | 0 | decNaNs(res, lhs, rhs, set, &status); |
2029 | 0 | break;} |
2030 | 0 | if (decNumberIsInfinite(rhs)) { /* rhs Infinity */ |
2031 | 0 | Flag rhsneg=rhs->bits&DECNEG; /* save rhs sign */ |
2032 | 0 | if (decNumberIsNegative(lhs) /* lhs<0 */ |
2033 | 0 | && !decNumberIsZero(lhs)) /* .. */ |
2034 | 0 | status|=DEC_Invalid_operation; |
2035 | 0 | else { /* lhs >=0 */ |
2036 | 0 | uprv_decNumberZero(&dnOne); /* set up 1 */ |
2037 | 0 | dnOne.lsu[0]=1; |
2038 | 0 | uprv_decNumberCompare(dac, lhs, &dnOne, set); /* lhs ? 1 */ |
2039 | 0 | uprv_decNumberZero(res); /* prepare for 0/1/Infinity */ |
2040 | 0 | if (decNumberIsNegative(dac)) { /* lhs<1 */ |
2041 | 0 | if (rhsneg) res->bits|=DECINF; /* +Infinity [else is +0] */ |
2042 | 0 | } |
2043 | 0 | else if (dac->lsu[0]==0) { /* lhs=1 */ |
2044 | | /* 1**Infinity is inexact, so return fully-padded 1.0000 */ |
2045 | 0 | Int shift=set->digits-1; |
2046 | 0 | *res->lsu=1; /* was 0, make int 1 */ |
2047 | 0 | res->digits=decShiftToMost(res->lsu, 1, shift); |
2048 | 0 | res->exponent=-shift; /* make 1.0000... */ |
2049 | 0 | status|=DEC_Inexact|DEC_Rounded; /* deemed inexact */ |
2050 | 0 | } |
2051 | 0 | else { /* lhs>1 */ |
2052 | 0 | if (!rhsneg) res->bits|=DECINF; /* +Infinity [else is +0] */ |
2053 | 0 | } |
2054 | 0 | } /* lhs>=0 */ |
2055 | 0 | break;} |
2056 | | /* [lhs infinity drops through] */ |
2057 | 0 | } /* specials */ |
2058 | | |
2059 | | /* Original rhs may be an integer that fits and is in range */ |
2060 | 0 | n=decGetInt(rhs); |
2061 | 0 | if (n!=BADINT) { /* it is an integer */ |
2062 | 0 | rhsint=1; /* record the fact for 1**n */ |
2063 | 0 | isoddint=(Flag)n&1; /* [works even if big] */ |
2064 | 0 | if (n!=BIGEVEN && n!=BIGODD) /* can use integer path? */ |
2065 | 0 | useint=1; /* looks good */ |
2066 | 0 | } |
2067 | |
|
2068 | 0 | if (decNumberIsNegative(lhs) /* -x .. */ |
2069 | 0 | && isoddint) bits=DECNEG; /* .. to an odd power */ |
2070 | | |
2071 | | /* handle LHS infinity */ |
2072 | 0 | if (decNumberIsInfinite(lhs)) { /* [NaNs already handled] */ |
2073 | 0 | uByte rbits=rhs->bits; /* save */ |
2074 | 0 | uprv_decNumberZero(res); /* prepare */ |
2075 | 0 | if (n==0) *res->lsu=1; /* [-]Inf**0 => 1 */ |
2076 | 0 | else { |
2077 | | /* -Inf**nonint -> error */ |
2078 | 0 | if (!rhsint && decNumberIsNegative(lhs)) { |
2079 | 0 | status|=DEC_Invalid_operation; /* -Inf**nonint is error */ |
2080 | 0 | break;} |
2081 | 0 | if (!(rbits & DECNEG)) bits|=DECINF; /* was not a **-n */ |
2082 | | /* [otherwise will be 0 or -0] */ |
2083 | 0 | res->bits=bits; |
2084 | 0 | } |
2085 | 0 | break;} |
2086 | | |
2087 | | /* similarly handle LHS zero */ |
2088 | 0 | if (decNumberIsZero(lhs)) { |
2089 | 0 | if (n==0) { /* 0**0 => Error */ |
2090 | | #if DECSUBSET |
2091 | | if (!set->extended) { /* [unless subset] */ |
2092 | | uprv_decNumberZero(res); |
2093 | | *res->lsu=1; /* return 1 */ |
2094 | | break;} |
2095 | | #endif |
2096 | 0 | status|=DEC_Invalid_operation; |
2097 | 0 | } |
2098 | 0 | else { /* 0**x */ |
2099 | 0 | uByte rbits=rhs->bits; /* save */ |
2100 | 0 | if (rbits & DECNEG) { /* was a 0**(-n) */ |
2101 | | #if DECSUBSET |
2102 | | if (!set->extended) { /* [bad if subset] */ |
2103 | | status|=DEC_Invalid_operation; |
2104 | | break;} |
2105 | | #endif |
2106 | 0 | bits|=DECINF; |
2107 | 0 | } |
2108 | 0 | uprv_decNumberZero(res); /* prepare */ |
2109 | | /* [otherwise will be 0 or -0] */ |
2110 | 0 | res->bits=bits; |
2111 | 0 | } |
2112 | 0 | break;} |
2113 | | |
2114 | | /* here both lhs and rhs are finite; rhs==0 is handled in the */ |
2115 | | /* integer path. Next handle the non-integer cases */ |
2116 | 0 | if (!useint) { /* non-integral rhs */ |
2117 | | /* any -ve lhs is bad, as is either operand or context out of */ |
2118 | | /* bounds */ |
2119 | 0 | if (decNumberIsNegative(lhs)) { |
2120 | 0 | status|=DEC_Invalid_operation; |
2121 | 0 | break;} |
2122 | 0 | if (decCheckMath(lhs, set, &status) |
2123 | 0 | || decCheckMath(rhs, set, &status)) break; /* variable status */ |
2124 | | |
2125 | 0 | uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */ |
2126 | 0 | aset.emax=DEC_MAX_MATH; /* usual bounds */ |
2127 | 0 | aset.emin=-DEC_MAX_MATH; /* .. */ |
2128 | 0 | aset.clamp=0; /* and no concrete format */ |
2129 | | |
2130 | | /* calculate the result using exp(ln(lhs)*rhs), which can */ |
2131 | | /* all be done into the accumulator, dac. The precision needed */ |
2132 | | /* is enough to contain the full information in the lhs (which */ |
2133 | | /* is the total digits, including exponent), or the requested */ |
2134 | | /* precision, if larger, + 4; 6 is used for the exponent */ |
2135 | | /* maximum length, and this is also used when it is shorter */ |
2136 | | /* than the requested digits as it greatly reduces the >0.5 ulp */ |
2137 | | /* cases at little cost (because Ln doubles digits each */ |
2138 | | /* iteration so a few extra digits rarely causes an extra */ |
2139 | | /* iteration) */ |
2140 | 0 | aset.digits=MAXI(lhs->digits, set->digits)+6+4; |
2141 | 0 | } /* non-integer rhs */ |
2142 | | |
2143 | 0 | else { /* rhs is in-range integer */ |
2144 | 0 | if (n==0) { /* x**0 = 1 */ |
2145 | | /* (0**0 was handled above) */ |
2146 | 0 | uprv_decNumberZero(res); /* result=1 */ |
2147 | 0 | *res->lsu=1; /* .. */ |
2148 | 0 | break;} |
2149 | | /* rhs is a non-zero integer */ |
2150 | 0 | if (n<0) n=-n; /* use abs(n) */ |
2151 | |
|
2152 | 0 | aset=*set; /* clone the context */ |
2153 | 0 | aset.round=DEC_ROUND_HALF_EVEN; /* internally use balanced */ |
2154 | | /* calculate the working DIGITS */ |
2155 | 0 | aset.digits=reqdigits+(rhs->digits+rhs->exponent)+2; |
2156 | | #if DECSUBSET |
2157 | | if (!set->extended) aset.digits--; /* use classic precision */ |
2158 | | #endif |
2159 | | /* it's an error if this is more than can be handled */ |
2160 | 0 | if (aset.digits>DECNUMMAXP) {status|=DEC_Invalid_operation; break;} |
2161 | 0 | } /* integer path */ |
2162 | | |
2163 | | /* aset.digits is the count of digits for the accumulator needed */ |
2164 | | /* if accumulator is too long for local storage, then allocate */ |
2165 | 0 | needbytes=sizeof(decNumber)+(D2U(aset.digits)-1)*sizeof(Unit); |
2166 | | /* [needbytes also used below if 1/lhs needed] */ |
2167 | 0 | if (needbytes>sizeof(dacbuff)) { |
2168 | 0 | allocdac=(decNumber *)malloc(needbytes); |
2169 | 0 | if (allocdac==NULL) { /* hopeless -- abandon */ |
2170 | 0 | status|=DEC_Insufficient_storage; |
2171 | 0 | break;} |
2172 | 0 | dac=allocdac; /* use the allocated space */ |
2173 | 0 | } |
2174 | | /* here, aset is set up and accumulator is ready for use */ |
2175 | | |
2176 | 0 | if (!useint) { /* non-integral rhs */ |
2177 | | /* x ** y; special-case x=1 here as it will otherwise always */ |
2178 | | /* reduce to integer 1; decLnOp has a fastpath which detects */ |
2179 | | /* the case of x=1 */ |
2180 | 0 | decLnOp(dac, lhs, &aset, &status); /* dac=ln(lhs) */ |
2181 | | /* [no error possible, as lhs 0 already handled] */ |
2182 | 0 | if (ISZERO(dac)) { /* x==1, 1.0, etc. */ |
2183 | | /* need to return fully-padded 1.0000 etc., but rhsint->1 */ |
2184 | 0 | *dac->lsu=1; /* was 0, make int 1 */ |
2185 | 0 | if (!rhsint) { /* add padding */ |
2186 | 0 | Int shift=set->digits-1; |
2187 | 0 | dac->digits=decShiftToMost(dac->lsu, 1, shift); |
2188 | 0 | dac->exponent=-shift; /* make 1.0000... */ |
2189 | 0 | status|=DEC_Inexact|DEC_Rounded; /* deemed inexact */ |
2190 | 0 | } |
2191 | 0 | } |
2192 | 0 | else { |
2193 | 0 | decMultiplyOp(dac, dac, rhs, &aset, &status); /* dac=dac*rhs */ |
2194 | 0 | decExpOp(dac, dac, &aset, &status); /* dac=exp(dac) */ |
2195 | 0 | } |
2196 | | /* and drop through for final rounding */ |
2197 | 0 | } /* non-integer rhs */ |
2198 | | |
2199 | 0 | else { /* carry on with integer */ |
2200 | 0 | uprv_decNumberZero(dac); /* acc=1 */ |
2201 | 0 | *dac->lsu=1; /* .. */ |
2202 | | |
2203 | | /* if a negative power the constant 1 is needed, and if not subset */ |
2204 | | /* invert the lhs now rather than inverting the result later */ |
2205 | 0 | if (decNumberIsNegative(rhs)) { /* was a **-n [hence digits>0] */ |
2206 | 0 | decNumber *inv=invbuff; /* assume use fixed buffer */ |
2207 | 0 | uprv_decNumberCopy(&dnOne, dac); /* dnOne=1; [needed now or later] */ |
2208 | | #if DECSUBSET |
2209 | | if (set->extended) { /* need to calculate 1/lhs */ |
2210 | | #endif |
2211 | | /* divide lhs into 1, putting result in dac [dac=1/dac] */ |
2212 | 0 | decDivideOp(dac, &dnOne, lhs, &aset, DIVIDE, &status); |
2213 | | /* now locate or allocate space for the inverted lhs */ |
2214 | 0 | if (needbytes>sizeof(invbuff)) { |
2215 | 0 | allocinv=(decNumber *)malloc(needbytes); |
2216 | 0 | if (allocinv==NULL) { /* hopeless -- abandon */ |
2217 | 0 | status|=DEC_Insufficient_storage; |
2218 | 0 | break;} |
2219 | 0 | inv=allocinv; /* use the allocated space */ |
2220 | 0 | } |
2221 | | /* [inv now points to big-enough buffer or allocated storage] */ |
2222 | 0 | uprv_decNumberCopy(inv, dac); /* copy the 1/lhs */ |
2223 | 0 | uprv_decNumberCopy(dac, &dnOne); /* restore acc=1 */ |
2224 | 0 | lhs=inv; /* .. and go forward with new lhs */ |
2225 | | #if DECSUBSET |
2226 | | } |
2227 | | #endif |
2228 | 0 | } |
2229 | | |
2230 | | /* Raise-to-the-power loop... */ |
2231 | 0 | seenbit=0; /* set once a 1-bit is encountered */ |
2232 | 0 | for (i=1;;i++){ /* for each bit [top bit ignored] */ |
2233 | | /* abandon if had overflow or terminal underflow */ |
2234 | 0 | if (status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */ |
2235 | 0 | if (status&DEC_Overflow || ISZERO(dac)) break; |
2236 | 0 | } |
2237 | | /* [the following two lines revealed an optimizer bug in a C++ */ |
2238 | | /* compiler, with symptom: 5**3 -> 25, when n=n+n was used] */ |
2239 | 0 | n=n<<1; /* move next bit to testable position */ |
2240 | 0 | if (n<0) { /* top bit is set */ |
2241 | 0 | seenbit=1; /* OK, significant bit seen */ |
2242 | 0 | decMultiplyOp(dac, dac, lhs, &aset, &status); /* dac=dac*x */ |
2243 | 0 | } |
2244 | 0 | if (i==31) break; /* that was the last bit */ |
2245 | 0 | if (!seenbit) continue; /* no need to square 1 */ |
2246 | 0 | decMultiplyOp(dac, dac, dac, &aset, &status); /* dac=dac*dac [square] */ |
2247 | 0 | } /*i*/ /* 32 bits */ |
2248 | | |
2249 | | /* complete internal overflow or underflow processing */ |
2250 | 0 | if (status & (DEC_Overflow|DEC_Underflow)) { |
2251 | | #if DECSUBSET |
2252 | | /* If subset, and power was negative, reverse the kind of -erflow */ |
2253 | | /* [1/x not yet done] */ |
2254 | | if (!set->extended && decNumberIsNegative(rhs)) { |
2255 | | if (status & DEC_Overflow) |
2256 | | status^=DEC_Overflow | DEC_Underflow | DEC_Subnormal; |
2257 | | else { /* trickier -- Underflow may or may not be set */ |
2258 | | status&=~(DEC_Underflow | DEC_Subnormal); /* [one or both] */ |
2259 | | status|=DEC_Overflow; |
2260 | | } |
2261 | | } |
2262 | | #endif |
2263 | 0 | dac->bits=(dac->bits & ~DECNEG) | bits; /* force correct sign */ |
2264 | | /* round subnormals [to set.digits rather than aset.digits] */ |
2265 | | /* or set overflow result similarly as required */ |
2266 | 0 | decFinalize(dac, set, &residue, &status); |
2267 | 0 | uprv_decNumberCopy(res, dac); /* copy to result (is now OK length) */ |
2268 | 0 | break; |
2269 | 0 | } |
2270 | |
|
2271 | | #if DECSUBSET |
2272 | | if (!set->extended && /* subset math */ |
2273 | | decNumberIsNegative(rhs)) { /* was a **-n [hence digits>0] */ |
2274 | | /* so divide result into 1 [dac=1/dac] */ |
2275 | | decDivideOp(dac, &dnOne, dac, &aset, DIVIDE, &status); |
2276 | | } |
2277 | | #endif |
2278 | 0 | } /* rhs integer path */ |
2279 | | |
2280 | | /* reduce result to the requested length and copy to result */ |
2281 | 0 | decCopyFit(res, dac, set, &residue, &status); |
2282 | 0 | decFinish(res, set, &residue, &status); /* final cleanup */ |
2283 | | #if DECSUBSET |
2284 | | if (!set->extended) decTrim(res, set, 0, 1, &dropped); /* trailing zeros */ |
2285 | | #endif |
2286 | 0 | } while(0); /* end protected */ |
2287 | | |
2288 | 0 | if (allocdac!=NULL) free(allocdac); /* drop any storage used */ |
2289 | 0 | if (allocinv!=NULL) free(allocinv); /* .. */ |
2290 | | #if DECSUBSET |
2291 | | if (alloclhs!=NULL) free(alloclhs); /* .. */ |
2292 | | if (allocrhs!=NULL) free(allocrhs); /* .. */ |
2293 | | #endif |
2294 | 0 | if (status!=0) decStatus(res, status, set); |
2295 | | #if DECCHECK |
2296 | | decCheckInexact(res, set); |
2297 | | #endif |
2298 | 0 | return res; |
2299 | 0 | } /* decNumberPower */ |
2300 | | |
2301 | | /* ------------------------------------------------------------------ */ |
2302 | | /* decNumberQuantize -- force exponent to requested value */ |
2303 | | /* */ |
2304 | | /* This computes C = op(A, B), where op adjusts the coefficient */ |
2305 | | /* of C (by rounding or shifting) such that the exponent (-scale) */ |
2306 | | /* of C has exponent of B. The numerical value of C will equal A, */ |
2307 | | /* except for the effects of any rounding that occurred. */ |
2308 | | /* */ |
2309 | | /* res is C, the result. C may be A or B */ |
2310 | | /* lhs is A, the number to adjust */ |
2311 | | /* rhs is B, the number with exponent to match */ |
2312 | | /* set is the context */ |
2313 | | /* */ |
2314 | | /* C must have space for set->digits digits. */ |
2315 | | /* */ |
2316 | | /* Unless there is an error or the result is infinite, the exponent */ |
2317 | | /* after the operation is guaranteed to be equal to that of B. */ |
2318 | | /* ------------------------------------------------------------------ */ |
2319 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberQuantize(decNumber *res, const decNumber *lhs, |
2320 | 0 | const decNumber *rhs, decContext *set) { |
2321 | 0 | uInt status=0; /* accumulator */ |
2322 | 0 | decQuantizeOp(res, lhs, rhs, set, 1, &status); |
2323 | 0 | if (status!=0) decStatus(res, status, set); |
2324 | 0 | return res; |
2325 | 0 | } /* decNumberQuantize */ |
2326 | | |
2327 | | /* ------------------------------------------------------------------ */ |
2328 | | /* decNumberReduce -- remove trailing zeros */ |
2329 | | /* */ |
2330 | | /* This computes C = 0 + A, and normalizes the result */ |
2331 | | /* */ |
2332 | | /* res is C, the result. C may be A */ |
2333 | | /* rhs is A */ |
2334 | | /* set is the context */ |
2335 | | /* */ |
2336 | | /* C must have space for set->digits digits. */ |
2337 | | /* ------------------------------------------------------------------ */ |
2338 | | /* Previously known as Normalize */ |
2339 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberNormalize(decNumber *res, const decNumber *rhs, |
2340 | 0 | decContext *set) { |
2341 | 0 | return uprv_decNumberReduce(res, rhs, set); |
2342 | 0 | } /* decNumberNormalize */ |
2343 | | |
2344 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberReduce(decNumber *res, const decNumber *rhs, |
2345 | 0 | decContext *set) { |
2346 | | #if DECSUBSET |
2347 | | decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ |
2348 | | #endif |
2349 | 0 | uInt status=0; /* as usual */ |
2350 | 0 | Int residue=0; /* as usual */ |
2351 | 0 | Int dropped; /* work */ |
2352 | |
|
2353 | | #if DECCHECK |
2354 | | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
2355 | | #endif |
2356 | |
|
2357 | 0 | do { /* protect allocated storage */ |
2358 | | #if DECSUBSET |
2359 | | if (!set->extended) { |
2360 | | /* reduce operand and set lostDigits status, as needed */ |
2361 | | if (rhs->digits>set->digits) { |
2362 | | allocrhs=decRoundOperand(rhs, set, &status); |
2363 | | if (allocrhs==NULL) break; |
2364 | | rhs=allocrhs; |
2365 | | } |
2366 | | } |
2367 | | #endif |
2368 | | /* [following code does not require input rounding] */ |
2369 | | |
2370 | | /* Infinities copy through; NaNs need usual treatment */ |
2371 | 0 | if (decNumberIsNaN(rhs)) { |
2372 | 0 | decNaNs(res, rhs, NULL, set, &status); |
2373 | 0 | break; |
2374 | 0 | } |
2375 | | |
2376 | | /* reduce result to the requested length and copy to result */ |
2377 | 0 | decCopyFit(res, rhs, set, &residue, &status); /* copy & round */ |
2378 | 0 | decFinish(res, set, &residue, &status); /* cleanup/set flags */ |
2379 | 0 | decTrim(res, set, 1, 0, &dropped); /* normalize in place */ |
2380 | | /* [may clamp] */ |
2381 | 0 | } while(0); /* end protected */ |
2382 | | |
2383 | | #if DECSUBSET |
2384 | | if (allocrhs !=NULL) free(allocrhs); /* .. */ |
2385 | | #endif |
2386 | 0 | if (status!=0) decStatus(res, status, set);/* then report status */ |
2387 | 0 | return res; |
2388 | 0 | } /* decNumberReduce */ |
2389 | | |
2390 | | /* ------------------------------------------------------------------ */ |
2391 | | /* decNumberRescale -- force exponent to requested value */ |
2392 | | /* */ |
2393 | | /* This computes C = op(A, B), where op adjusts the coefficient */ |
2394 | | /* of C (by rounding or shifting) such that the exponent (-scale) */ |
2395 | | /* of C has the value B. The numerical value of C will equal A, */ |
2396 | | /* except for the effects of any rounding that occurred. */ |
2397 | | /* */ |
2398 | | /* res is C, the result. C may be A or B */ |
2399 | | /* lhs is A, the number to adjust */ |
2400 | | /* rhs is B, the requested exponent */ |
2401 | | /* set is the context */ |
2402 | | /* */ |
2403 | | /* C must have space for set->digits digits. */ |
2404 | | /* */ |
2405 | | /* Unless there is an error or the result is infinite, the exponent */ |
2406 | | /* after the operation is guaranteed to be equal to B. */ |
2407 | | /* ------------------------------------------------------------------ */ |
2408 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberRescale(decNumber *res, const decNumber *lhs, |
2409 | 0 | const decNumber *rhs, decContext *set) { |
2410 | 0 | uInt status=0; /* accumulator */ |
2411 | 0 | decQuantizeOp(res, lhs, rhs, set, 0, &status); |
2412 | 0 | if (status!=0) decStatus(res, status, set); |
2413 | 0 | return res; |
2414 | 0 | } /* decNumberRescale */ |
2415 | | |
2416 | | /* ------------------------------------------------------------------ */ |
2417 | | /* decNumberRemainder -- divide and return remainder */ |
2418 | | /* */ |
2419 | | /* This computes C = A % B */ |
2420 | | /* */ |
2421 | | /* res is C, the result. C may be A and/or B (e.g., X=X%X) */ |
2422 | | /* lhs is A */ |
2423 | | /* rhs is B */ |
2424 | | /* set is the context */ |
2425 | | /* */ |
2426 | | /* C must have space for set->digits digits. */ |
2427 | | /* ------------------------------------------------------------------ */ |
2428 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberRemainder(decNumber *res, const decNumber *lhs, |
2429 | 0 | const decNumber *rhs, decContext *set) { |
2430 | 0 | uInt status=0; /* accumulator */ |
2431 | 0 | decDivideOp(res, lhs, rhs, set, REMAINDER, &status); |
2432 | 0 | if (status!=0) decStatus(res, status, set); |
2433 | | #if DECCHECK |
2434 | | decCheckInexact(res, set); |
2435 | | #endif |
2436 | 0 | return res; |
2437 | 0 | } /* decNumberRemainder */ |
2438 | | |
2439 | | /* ------------------------------------------------------------------ */ |
2440 | | /* decNumberRemainderNear -- divide and return remainder from nearest */ |
2441 | | /* */ |
2442 | | /* This computes C = A % B, where % is the IEEE remainder operator */ |
2443 | | /* */ |
2444 | | /* res is C, the result. C may be A and/or B (e.g., X=X%X) */ |
2445 | | /* lhs is A */ |
2446 | | /* rhs is B */ |
2447 | | /* set is the context */ |
2448 | | /* */ |
2449 | | /* C must have space for set->digits digits. */ |
2450 | | /* ------------------------------------------------------------------ */ |
2451 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberRemainderNear(decNumber *res, const decNumber *lhs, |
2452 | 0 | const decNumber *rhs, decContext *set) { |
2453 | 0 | uInt status=0; /* accumulator */ |
2454 | 0 | decDivideOp(res, lhs, rhs, set, REMNEAR, &status); |
2455 | 0 | if (status!=0) decStatus(res, status, set); |
2456 | | #if DECCHECK |
2457 | | decCheckInexact(res, set); |
2458 | | #endif |
2459 | 0 | return res; |
2460 | 0 | } /* decNumberRemainderNear */ |
2461 | | |
2462 | | /* ------------------------------------------------------------------ */ |
2463 | | /* decNumberRotate -- rotate the coefficient of a Number left/right */ |
2464 | | /* */ |
2465 | | /* This computes C = A rot B (in base ten and rotating set->digits */ |
2466 | | /* digits). */ |
2467 | | /* */ |
2468 | | /* res is C, the result. C may be A and/or B (e.g., X=XrotX) */ |
2469 | | /* lhs is A */ |
2470 | | /* rhs is B, the number of digits to rotate (-ve to right) */ |
2471 | | /* set is the context */ |
2472 | | /* */ |
2473 | | /* The digits of the coefficient of A are rotated to the left (if B */ |
2474 | | /* is positive) or to the right (if B is negative) without adjusting */ |
2475 | | /* the exponent or the sign of A. If lhs->digits is less than */ |
2476 | | /* set->digits the coefficient is padded with zeros on the left */ |
2477 | | /* before the rotate. Any leading zeros in the result are removed */ |
2478 | | /* as usual. */ |
2479 | | /* */ |
2480 | | /* B must be an integer (q=0) and in the range -set->digits through */ |
2481 | | /* +set->digits. */ |
2482 | | /* C must have space for set->digits digits. */ |
2483 | | /* NaNs are propagated as usual. Infinities are unaffected (but */ |
2484 | | /* B must be valid). No status is set unless B is invalid or an */ |
2485 | | /* operand is an sNaN. */ |
2486 | | /* ------------------------------------------------------------------ */ |
2487 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberRotate(decNumber *res, const decNumber *lhs, |
2488 | 0 | const decNumber *rhs, decContext *set) { |
2489 | 0 | uInt status=0; /* accumulator */ |
2490 | 0 | Int rotate; /* rhs as an Int */ |
2491 | |
|
2492 | | #if DECCHECK |
2493 | | if (decCheckOperands(res, lhs, rhs, set)) return res; |
2494 | | #endif |
2495 | | |
2496 | | /* NaNs propagate as normal */ |
2497 | 0 | if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) |
2498 | 0 | decNaNs(res, lhs, rhs, set, &status); |
2499 | | /* rhs must be an integer */ |
2500 | 0 | else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) |
2501 | 0 | status=DEC_Invalid_operation; |
2502 | 0 | else { /* both numeric, rhs is an integer */ |
2503 | 0 | rotate=decGetInt(rhs); /* [cannot fail] */ |
2504 | 0 | if (rotate==BADINT /* something bad .. */ |
2505 | 0 | || rotate==BIGODD || rotate==BIGEVEN /* .. very big .. */ |
2506 | 0 | || abs(rotate)>set->digits) /* .. or out of range */ |
2507 | 0 | status=DEC_Invalid_operation; |
2508 | 0 | else { /* rhs is OK */ |
2509 | 0 | uprv_decNumberCopy(res, lhs); |
2510 | | /* convert -ve rotate to equivalent positive rotation */ |
2511 | 0 | if (rotate<0) rotate=set->digits+rotate; |
2512 | 0 | if (rotate!=0 && rotate!=set->digits /* zero or full rotation */ |
2513 | 0 | && !decNumberIsInfinite(res)) { /* lhs was infinite */ |
2514 | | /* left-rotate to do; 0 < rotate < set->digits */ |
2515 | 0 | uInt units, shift; /* work */ |
2516 | 0 | uInt msudigits; /* digits in result msu */ |
2517 | 0 | Unit *msu=res->lsu+D2U(res->digits)-1; /* current msu */ |
2518 | 0 | Unit *msumax=res->lsu+D2U(set->digits)-1; /* rotation msu */ |
2519 | 0 | for (msu++; msu<=msumax; msu++) *msu=0; /* ensure high units=0 */ |
2520 | 0 | res->digits=set->digits; /* now full-length */ |
2521 | 0 | msudigits=MSUDIGITS(res->digits); /* actual digits in msu */ |
2522 | | |
2523 | | /* rotation here is done in-place, in three steps */ |
2524 | | /* 1. shift all to least up to one unit to unit-align final */ |
2525 | | /* lsd [any digits shifted out are rotated to the left, */ |
2526 | | /* abutted to the original msd (which may require split)] */ |
2527 | | /* */ |
2528 | | /* [if there are no whole units left to rotate, the */ |
2529 | | /* rotation is now complete] */ |
2530 | | /* */ |
2531 | | /* 2. shift to least, from below the split point only, so that */ |
2532 | | /* the final msd is in the right place in its Unit [any */ |
2533 | | /* digits shifted out will fit exactly in the current msu, */ |
2534 | | /* left aligned, no split required] */ |
2535 | | /* */ |
2536 | | /* 3. rotate all the units by reversing left part, right */ |
2537 | | /* part, and then whole */ |
2538 | | /* */ |
2539 | | /* example: rotate right 8 digits (2 units + 2), DECDPUN=3. */ |
2540 | | /* */ |
2541 | | /* start: 00a bcd efg hij klm npq */ |
2542 | | /* */ |
2543 | | /* 1a 000 0ab cde fgh|ijk lmn [pq saved] */ |
2544 | | /* 1b 00p qab cde fgh|ijk lmn */ |
2545 | | /* */ |
2546 | | /* 2a 00p qab cde fgh|00i jkl [mn saved] */ |
2547 | | /* 2b mnp qab cde fgh|00i jkl */ |
2548 | | /* */ |
2549 | | /* 3a fgh cde qab mnp|00i jkl */ |
2550 | | /* 3b fgh cde qab mnp|jkl 00i */ |
2551 | | /* 3c 00i jkl mnp qab cde fgh */ |
2552 | | |
2553 | | /* Step 1: amount to shift is the partial right-rotate count */ |
2554 | 0 | rotate=set->digits-rotate; /* make it right-rotate */ |
2555 | 0 | units=rotate/DECDPUN; /* whole units to rotate */ |
2556 | 0 | shift=rotate%DECDPUN; /* left-over digits count */ |
2557 | 0 | if (shift>0) { /* not an exact number of units */ |
2558 | 0 | uInt save=res->lsu[0]%powers[shift]; /* save low digit(s) */ |
2559 | 0 | decShiftToLeast(res->lsu, D2U(res->digits), shift); |
2560 | 0 | if (shift>msudigits) { /* msumax-1 needs >0 digits */ |
2561 | 0 | uInt rem=save%powers[shift-msudigits];/* split save */ |
2562 | 0 | *msumax=(Unit)(save/powers[shift-msudigits]); /* and insert */ |
2563 | 0 | *(msumax-1)=*(msumax-1) |
2564 | 0 | +(Unit)(rem*powers[DECDPUN-(shift-msudigits)]); /* .. */ |
2565 | 0 | } |
2566 | 0 | else { /* all fits in msumax */ |
2567 | 0 | *msumax=*msumax+(Unit)(save*powers[msudigits-shift]); /* [maybe *1] */ |
2568 | 0 | } |
2569 | 0 | } /* digits shift needed */ |
2570 | | |
2571 | | /* If whole units to rotate... */ |
2572 | 0 | if (units>0) { /* some to do */ |
2573 | | /* Step 2: the units to touch are the whole ones in rotate, */ |
2574 | | /* if any, and the shift is DECDPUN-msudigits (which may be */ |
2575 | | /* 0, again) */ |
2576 | 0 | shift=DECDPUN-msudigits; |
2577 | 0 | if (shift>0) { /* not an exact number of units */ |
2578 | 0 | uInt save=res->lsu[0]%powers[shift]; /* save low digit(s) */ |
2579 | 0 | decShiftToLeast(res->lsu, units, shift); |
2580 | 0 | *msumax=*msumax+(Unit)(save*powers[msudigits]); |
2581 | 0 | } /* partial shift needed */ |
2582 | | |
2583 | | /* Step 3: rotate the units array using triple reverse */ |
2584 | | /* (reversing is easy and fast) */ |
2585 | 0 | decReverse(res->lsu+units, msumax); /* left part */ |
2586 | 0 | decReverse(res->lsu, res->lsu+units-1); /* right part */ |
2587 | 0 | decReverse(res->lsu, msumax); /* whole */ |
2588 | 0 | } /* whole units to rotate */ |
2589 | | /* the rotation may have left an undetermined number of zeros */ |
2590 | | /* on the left, so true length needs to be calculated */ |
2591 | 0 | res->digits=decGetDigits(res->lsu, static_cast<int32_t>(msumax-res->lsu+1)); |
2592 | 0 | } /* rotate needed */ |
2593 | 0 | } /* rhs OK */ |
2594 | 0 | } /* numerics */ |
2595 | 0 | if (status!=0) decStatus(res, status, set); |
2596 | 0 | return res; |
2597 | 0 | } /* decNumberRotate */ |
2598 | | |
2599 | | /* ------------------------------------------------------------------ */ |
2600 | | /* decNumberSameQuantum -- test for equal exponents */ |
2601 | | /* */ |
2602 | | /* res is the result number, which will contain either 0 or 1 */ |
2603 | | /* lhs is a number to test */ |
2604 | | /* rhs is the second (usually a pattern) */ |
2605 | | /* */ |
2606 | | /* No errors are possible and no context is needed. */ |
2607 | | /* ------------------------------------------------------------------ */ |
2608 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberSameQuantum(decNumber *res, const decNumber *lhs, |
2609 | 0 | const decNumber *rhs) { |
2610 | 0 | Unit ret=0; /* return value */ |
2611 | |
|
2612 | | #if DECCHECK |
2613 | | if (decCheckOperands(res, lhs, rhs, DECUNCONT)) return res; |
2614 | | #endif |
2615 | |
|
2616 | 0 | if (SPECIALARGS) { |
2617 | 0 | if (decNumberIsNaN(lhs) && decNumberIsNaN(rhs)) ret=1; |
2618 | 0 | else if (decNumberIsInfinite(lhs) && decNumberIsInfinite(rhs)) ret=1; |
2619 | | /* [anything else with a special gives 0] */ |
2620 | 0 | } |
2621 | 0 | else if (lhs->exponent==rhs->exponent) ret=1; |
2622 | |
|
2623 | 0 | uprv_decNumberZero(res); /* OK to overwrite an operand now */ |
2624 | 0 | *res->lsu=ret; |
2625 | 0 | return res; |
2626 | 0 | } /* decNumberSameQuantum */ |
2627 | | |
2628 | | /* ------------------------------------------------------------------ */ |
2629 | | /* decNumberScaleB -- multiply by a power of 10 */ |
2630 | | /* */ |
2631 | | /* This computes C = A x 10**B where B is an integer (q=0) with */ |
2632 | | /* maximum magnitude 2*(emax+digits) */ |
2633 | | /* */ |
2634 | | /* res is C, the result. C may be A or B */ |
2635 | | /* lhs is A, the number to adjust */ |
2636 | | /* rhs is B, the requested power of ten to use */ |
2637 | | /* set is the context */ |
2638 | | /* */ |
2639 | | /* C must have space for set->digits digits. */ |
2640 | | /* */ |
2641 | | /* The result may underflow or overflow. */ |
2642 | | /* ------------------------------------------------------------------ */ |
2643 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberScaleB(decNumber *res, const decNumber *lhs, |
2644 | 0 | const decNumber *rhs, decContext *set) { |
2645 | 0 | Int reqexp; /* requested exponent change [B] */ |
2646 | 0 | uInt status=0; /* accumulator */ |
2647 | 0 | Int residue; /* work */ |
2648 | |
|
2649 | | #if DECCHECK |
2650 | | if (decCheckOperands(res, lhs, rhs, set)) return res; |
2651 | | #endif |
2652 | | |
2653 | | /* Handle special values except lhs infinite */ |
2654 | 0 | if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) |
2655 | 0 | decNaNs(res, lhs, rhs, set, &status); |
2656 | | /* rhs must be an integer */ |
2657 | 0 | else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) |
2658 | 0 | status=DEC_Invalid_operation; |
2659 | 0 | else { |
2660 | | /* lhs is a number; rhs is a finite with q==0 */ |
2661 | 0 | reqexp=decGetInt(rhs); /* [cannot fail] */ |
2662 | 0 | if (reqexp==BADINT /* something bad .. */ |
2663 | 0 | || reqexp==BIGODD || reqexp==BIGEVEN /* .. very big .. */ |
2664 | 0 | || abs(reqexp)>(2*(set->digits+set->emax))) /* .. or out of range */ |
2665 | 0 | status=DEC_Invalid_operation; |
2666 | 0 | else { /* rhs is OK */ |
2667 | 0 | uprv_decNumberCopy(res, lhs); /* all done if infinite lhs */ |
2668 | 0 | if (!decNumberIsInfinite(res)) { /* prepare to scale */ |
2669 | 0 | res->exponent+=reqexp; /* adjust the exponent */ |
2670 | 0 | residue=0; |
2671 | 0 | decFinalize(res, set, &residue, &status); /* .. and check */ |
2672 | 0 | } /* finite LHS */ |
2673 | 0 | } /* rhs OK */ |
2674 | 0 | } /* rhs finite */ |
2675 | 0 | if (status!=0) decStatus(res, status, set); |
2676 | 0 | return res; |
2677 | 0 | } /* decNumberScaleB */ |
2678 | | |
2679 | | /* ------------------------------------------------------------------ */ |
2680 | | /* decNumberShift -- shift the coefficient of a Number left or right */ |
2681 | | /* */ |
2682 | | /* This computes C = A << B or C = A >> -B (in base ten). */ |
2683 | | /* */ |
2684 | | /* res is C, the result. C may be A and/or B (e.g., X=X<<X) */ |
2685 | | /* lhs is A */ |
2686 | | /* rhs is B, the number of digits to shift (-ve to right) */ |
2687 | | /* set is the context */ |
2688 | | /* */ |
2689 | | /* The digits of the coefficient of A are shifted to the left (if B */ |
2690 | | /* is positive) or to the right (if B is negative) without adjusting */ |
2691 | | /* the exponent or the sign of A. */ |
2692 | | /* */ |
2693 | | /* B must be an integer (q=0) and in the range -set->digits through */ |
2694 | | /* +set->digits. */ |
2695 | | /* C must have space for set->digits digits. */ |
2696 | | /* NaNs are propagated as usual. Infinities are unaffected (but */ |
2697 | | /* B must be valid). No status is set unless B is invalid or an */ |
2698 | | /* operand is an sNaN. */ |
2699 | | /* ------------------------------------------------------------------ */ |
2700 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberShift(decNumber *res, const decNumber *lhs, |
2701 | 0 | const decNumber *rhs, decContext *set) { |
2702 | 0 | uInt status=0; /* accumulator */ |
2703 | 0 | Int shift; /* rhs as an Int */ |
2704 | |
|
2705 | | #if DECCHECK |
2706 | | if (decCheckOperands(res, lhs, rhs, set)) return res; |
2707 | | #endif |
2708 | | |
2709 | | /* NaNs propagate as normal */ |
2710 | 0 | if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) |
2711 | 0 | decNaNs(res, lhs, rhs, set, &status); |
2712 | | /* rhs must be an integer */ |
2713 | 0 | else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) |
2714 | 0 | status=DEC_Invalid_operation; |
2715 | 0 | else { /* both numeric, rhs is an integer */ |
2716 | 0 | shift=decGetInt(rhs); /* [cannot fail] */ |
2717 | 0 | if (shift==BADINT /* something bad .. */ |
2718 | 0 | || shift==BIGODD || shift==BIGEVEN /* .. very big .. */ |
2719 | 0 | || abs(shift)>set->digits) /* .. or out of range */ |
2720 | 0 | status=DEC_Invalid_operation; |
2721 | 0 | else { /* rhs is OK */ |
2722 | 0 | uprv_decNumberCopy(res, lhs); |
2723 | 0 | if (shift!=0 && !decNumberIsInfinite(res)) { /* something to do */ |
2724 | 0 | if (shift>0) { /* to left */ |
2725 | 0 | if (shift==set->digits) { /* removing all */ |
2726 | 0 | *res->lsu=0; /* so place 0 */ |
2727 | 0 | res->digits=1; /* .. */ |
2728 | 0 | } |
2729 | 0 | else { /* */ |
2730 | | /* first remove leading digits if necessary */ |
2731 | 0 | if (res->digits+shift>set->digits) { |
2732 | 0 | decDecap(res, res->digits+shift-set->digits); |
2733 | | /* that updated res->digits; may have gone to 1 (for a */ |
2734 | | /* single digit or for zero */ |
2735 | 0 | } |
2736 | 0 | if (res->digits>1 || *res->lsu) /* if non-zero.. */ |
2737 | 0 | res->digits=decShiftToMost(res->lsu, res->digits, shift); |
2738 | 0 | } /* partial left */ |
2739 | 0 | } /* left */ |
2740 | 0 | else { /* to right */ |
2741 | 0 | if (-shift>=res->digits) { /* discarding all */ |
2742 | 0 | *res->lsu=0; /* so place 0 */ |
2743 | 0 | res->digits=1; /* .. */ |
2744 | 0 | } |
2745 | 0 | else { |
2746 | 0 | decShiftToLeast(res->lsu, D2U(res->digits), -shift); |
2747 | 0 | res->digits-=(-shift); |
2748 | 0 | } |
2749 | 0 | } /* to right */ |
2750 | 0 | } /* non-0 non-Inf shift */ |
2751 | 0 | } /* rhs OK */ |
2752 | 0 | } /* numerics */ |
2753 | 0 | if (status!=0) decStatus(res, status, set); |
2754 | 0 | return res; |
2755 | 0 | } /* decNumberShift */ |
2756 | | |
2757 | | /* ------------------------------------------------------------------ */ |
2758 | | /* decNumberSquareRoot -- square root operator */ |
2759 | | /* */ |
2760 | | /* This computes C = squareroot(A) */ |
2761 | | /* */ |
2762 | | /* res is C, the result. C may be A */ |
2763 | | /* rhs is A */ |
2764 | | /* set is the context; note that rounding mode has no effect */ |
2765 | | /* */ |
2766 | | /* C must have space for set->digits digits. */ |
2767 | | /* ------------------------------------------------------------------ */ |
2768 | | /* This uses the following varying-precision algorithm in: */ |
2769 | | /* */ |
2770 | | /* Properly Rounded Variable Precision Square Root, T. E. Hull and */ |
2771 | | /* A. Abrham, ACM Transactions on Mathematical Software, Vol 11 #3, */ |
2772 | | /* pp229-237, ACM, September 1985. */ |
2773 | | /* */ |
2774 | | /* The square-root is calculated using Newton's method, after which */ |
2775 | | /* a check is made to ensure the result is correctly rounded. */ |
2776 | | /* */ |
2777 | | /* % [Reformatted original Numerical Turing source code follows.] */ |
2778 | | /* function sqrt(x : real) : real */ |
2779 | | /* % sqrt(x) returns the properly rounded approximation to the square */ |
2780 | | /* % root of x, in the precision of the calling environment, or it */ |
2781 | | /* % fails if x < 0. */ |
2782 | | /* % t e hull and a abrham, august, 1984 */ |
2783 | | /* if x <= 0 then */ |
2784 | | /* if x < 0 then */ |
2785 | | /* assert false */ |
2786 | | /* else */ |
2787 | | /* result 0 */ |
2788 | | /* end if */ |
2789 | | /* end if */ |
2790 | | /* var f := setexp(x, 0) % fraction part of x [0.1 <= x < 1] */ |
2791 | | /* var e := getexp(x) % exponent part of x */ |
2792 | | /* var approx : real */ |
2793 | | /* if e mod 2 = 0 then */ |
2794 | | /* approx := .259 + .819 * f % approx to root of f */ |
2795 | | /* else */ |
2796 | | /* f := f/l0 % adjustments */ |
2797 | | /* e := e + 1 % for odd */ |
2798 | | /* approx := .0819 + 2.59 * f % exponent */ |
2799 | | /* end if */ |
2800 | | /* */ |
2801 | | /* var p:= 3 */ |
2802 | | /* const maxp := currentprecision + 2 */ |
2803 | | /* loop */ |
2804 | | /* p := min(2*p - 2, maxp) % p = 4,6,10, . . . , maxp */ |
2805 | | /* precision p */ |
2806 | | /* approx := .5 * (approx + f/approx) */ |
2807 | | /* exit when p = maxp */ |
2808 | | /* end loop */ |
2809 | | /* */ |
2810 | | /* % approx is now within 1 ulp of the properly rounded square root */ |
2811 | | /* % of f; to ensure proper rounding, compare squares of (approx - */ |
2812 | | /* % l/2 ulp) and (approx + l/2 ulp) with f. */ |
2813 | | /* p := currentprecision */ |
2814 | | /* begin */ |
2815 | | /* precision p + 2 */ |
2816 | | /* const approxsubhalf := approx - setexp(.5, -p) */ |
2817 | | /* if mulru(approxsubhalf, approxsubhalf) > f then */ |
2818 | | /* approx := approx - setexp(.l, -p + 1) */ |
2819 | | /* else */ |
2820 | | /* const approxaddhalf := approx + setexp(.5, -p) */ |
2821 | | /* if mulrd(approxaddhalf, approxaddhalf) < f then */ |
2822 | | /* approx := approx + setexp(.l, -p + 1) */ |
2823 | | /* end if */ |
2824 | | /* end if */ |
2825 | | /* end */ |
2826 | | /* result setexp(approx, e div 2) % fix exponent */ |
2827 | | /* end sqrt */ |
2828 | | /* ------------------------------------------------------------------ */ |
2829 | | #if defined(__clang__) || U_GCC_MAJOR_MINOR >= 406 |
2830 | | #pragma GCC diagnostic push |
2831 | | #pragma GCC diagnostic ignored "-Warray-bounds" |
2832 | | #endif |
2833 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberSquareRoot(decNumber *res, const decNumber *rhs, |
2834 | 0 | decContext *set) { |
2835 | 0 | decContext workset, approxset; /* work contexts */ |
2836 | 0 | decNumber dzero; /* used for constant zero */ |
2837 | 0 | Int maxp; /* largest working precision */ |
2838 | 0 | Int workp; /* working precision */ |
2839 | 0 | Int residue=0; /* rounding residue */ |
2840 | 0 | uInt status=0, ignore=0; /* status accumulators */ |
2841 | 0 | uInt rstatus; /* .. */ |
2842 | 0 | Int exp; /* working exponent */ |
2843 | 0 | Int ideal; /* ideal (preferred) exponent */ |
2844 | 0 | Int needbytes; /* work */ |
2845 | 0 | Int dropped; /* .. */ |
2846 | |
|
2847 | | #if DECSUBSET |
2848 | | decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ |
2849 | | #endif |
2850 | | /* buffer for f [needs +1 in case DECBUFFER 0] */ |
2851 | 0 | decNumber buff[D2N(DECBUFFER+1)]; |
2852 | | /* buffer for a [needs +2 to match likely maxp] */ |
2853 | 0 | decNumber bufa[D2N(DECBUFFER+2)]; |
2854 | | /* buffer for temporary, b [must be same size as a] */ |
2855 | 0 | decNumber bufb[D2N(DECBUFFER+2)]; |
2856 | 0 | decNumber *allocbuff=NULL; /* -> allocated buff, iff allocated */ |
2857 | 0 | decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ |
2858 | 0 | decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */ |
2859 | 0 | decNumber *f=buff; /* reduced fraction */ |
2860 | 0 | decNumber *a=bufa; /* approximation to result */ |
2861 | 0 | decNumber *b=bufb; /* intermediate result */ |
2862 | | /* buffer for temporary variable, up to 3 digits */ |
2863 | 0 | decNumber buft[D2N(3)]; |
2864 | 0 | decNumber *t=buft; /* up-to-3-digit constant or work */ |
2865 | |
|
2866 | | #if DECCHECK |
2867 | | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
2868 | | #endif |
2869 | |
|
2870 | 0 | do { /* protect allocated storage */ |
2871 | | #if DECSUBSET |
2872 | | if (!set->extended) { |
2873 | | /* reduce operand and set lostDigits status, as needed */ |
2874 | | if (rhs->digits>set->digits) { |
2875 | | allocrhs=decRoundOperand(rhs, set, &status); |
2876 | | if (allocrhs==NULL) break; |
2877 | | /* [Note: 'f' allocation below could reuse this buffer if */ |
2878 | | /* used, but as this is rare they are kept separate for clarity.] */ |
2879 | | rhs=allocrhs; |
2880 | | } |
2881 | | } |
2882 | | #endif |
2883 | | /* [following code does not require input rounding] */ |
2884 | | |
2885 | | /* handle infinities and NaNs */ |
2886 | 0 | if (SPECIALARG) { |
2887 | 0 | if (decNumberIsInfinite(rhs)) { /* an infinity */ |
2888 | 0 | if (decNumberIsNegative(rhs)) status|=DEC_Invalid_operation; |
2889 | 0 | else uprv_decNumberCopy(res, rhs); /* +Infinity */ |
2890 | 0 | } |
2891 | 0 | else decNaNs(res, rhs, NULL, set, &status); /* a NaN */ |
2892 | 0 | break; |
2893 | 0 | } |
2894 | | |
2895 | | /* calculate the ideal (preferred) exponent [floor(exp/2)] */ |
2896 | | /* [It would be nicer to write: ideal=rhs->exponent>>1, but this */ |
2897 | | /* generates a compiler warning. Generated code is the same.] */ |
2898 | 0 | ideal=(rhs->exponent&~1)/2; /* target */ |
2899 | | |
2900 | | /* handle zeros */ |
2901 | 0 | if (ISZERO(rhs)) { |
2902 | 0 | uprv_decNumberCopy(res, rhs); /* could be 0 or -0 */ |
2903 | 0 | res->exponent=ideal; /* use the ideal [safe] */ |
2904 | | /* use decFinish to clamp any out-of-range exponent, etc. */ |
2905 | 0 | decFinish(res, set, &residue, &status); |
2906 | 0 | break; |
2907 | 0 | } |
2908 | | |
2909 | | /* any other -x is an oops */ |
2910 | 0 | if (decNumberIsNegative(rhs)) { |
2911 | 0 | status|=DEC_Invalid_operation; |
2912 | 0 | break; |
2913 | 0 | } |
2914 | | |
2915 | | /* space is needed for three working variables */ |
2916 | | /* f -- the same precision as the RHS, reduced to 0.01->0.99... */ |
2917 | | /* a -- Hull's approximation -- precision, when assigned, is */ |
2918 | | /* currentprecision+1 or the input argument precision, */ |
2919 | | /* whichever is larger (+2 for use as temporary) */ |
2920 | | /* b -- intermediate temporary result (same size as a) */ |
2921 | | /* if any is too long for local storage, then allocate */ |
2922 | 0 | workp=MAXI(set->digits+1, rhs->digits); /* actual rounding precision */ |
2923 | 0 | workp=MAXI(workp, 7); /* at least 7 for low cases */ |
2924 | 0 | maxp=workp+2; /* largest working precision */ |
2925 | |
|
2926 | 0 | needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); |
2927 | 0 | if (needbytes>(Int)sizeof(buff)) { |
2928 | 0 | allocbuff=(decNumber *)malloc(needbytes); |
2929 | 0 | if (allocbuff==NULL) { /* hopeless -- abandon */ |
2930 | 0 | status|=DEC_Insufficient_storage; |
2931 | 0 | break;} |
2932 | 0 | f=allocbuff; /* use the allocated space */ |
2933 | 0 | } |
2934 | | /* a and b both need to be able to hold a maxp-length number */ |
2935 | 0 | needbytes=sizeof(decNumber)+(D2U(maxp)-1)*sizeof(Unit); |
2936 | 0 | if (needbytes>(Int)sizeof(bufa)) { /* [same applies to b] */ |
2937 | 0 | allocbufa=(decNumber *)malloc(needbytes); |
2938 | 0 | allocbufb=(decNumber *)malloc(needbytes); |
2939 | 0 | if (allocbufa==NULL || allocbufb==NULL) { /* hopeless */ |
2940 | 0 | status|=DEC_Insufficient_storage; |
2941 | 0 | break;} |
2942 | 0 | a=allocbufa; /* use the allocated spaces */ |
2943 | 0 | b=allocbufb; /* .. */ |
2944 | 0 | } |
2945 | | |
2946 | | /* copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1 */ |
2947 | 0 | uprv_decNumberCopy(f, rhs); |
2948 | 0 | exp=f->exponent+f->digits; /* adjusted to Hull rules */ |
2949 | 0 | f->exponent=-(f->digits); /* to range */ |
2950 | | |
2951 | | /* set up working context */ |
2952 | 0 | uprv_decContextDefault(&workset, DEC_INIT_DECIMAL64); |
2953 | 0 | workset.emax=DEC_MAX_EMAX; |
2954 | 0 | workset.emin=DEC_MIN_EMIN; |
2955 | | |
2956 | | /* [Until further notice, no error is possible and status bits */ |
2957 | | /* (Rounded, etc.) should be ignored, not accumulated.] */ |
2958 | | |
2959 | | /* Calculate initial approximation, and allow for odd exponent */ |
2960 | 0 | workset.digits=workp; /* p for initial calculation */ |
2961 | 0 | t->bits=0; t->digits=3; |
2962 | 0 | a->bits=0; a->digits=3; |
2963 | 0 | if ((exp & 1)==0) { /* even exponent */ |
2964 | | /* Set t=0.259, a=0.819 */ |
2965 | 0 | t->exponent=-3; |
2966 | 0 | a->exponent=-3; |
2967 | | #if DECDPUN>=3 |
2968 | | t->lsu[0]=259; |
2969 | | a->lsu[0]=819; |
2970 | | #elif DECDPUN==2 |
2971 | | t->lsu[0]=59; t->lsu[1]=2; |
2972 | | a->lsu[0]=19; a->lsu[1]=8; |
2973 | | #else |
2974 | 0 | t->lsu[0]=9; t->lsu[1]=5; t->lsu[2]=2; |
2975 | 0 | a->lsu[0]=9; a->lsu[1]=1; a->lsu[2]=8; |
2976 | 0 | #endif |
2977 | 0 | } |
2978 | 0 | else { /* odd exponent */ |
2979 | | /* Set t=0.0819, a=2.59 */ |
2980 | 0 | f->exponent--; /* f=f/10 */ |
2981 | 0 | exp++; /* e=e+1 */ |
2982 | 0 | t->exponent=-4; |
2983 | 0 | a->exponent=-2; |
2984 | | #if DECDPUN>=3 |
2985 | | t->lsu[0]=819; |
2986 | | a->lsu[0]=259; |
2987 | | #elif DECDPUN==2 |
2988 | | t->lsu[0]=19; t->lsu[1]=8; |
2989 | | a->lsu[0]=59; a->lsu[1]=2; |
2990 | | #else |
2991 | 0 | t->lsu[0]=9; t->lsu[1]=1; t->lsu[2]=8; |
2992 | 0 | a->lsu[0]=9; a->lsu[1]=5; a->lsu[2]=2; |
2993 | 0 | #endif |
2994 | 0 | } |
2995 | |
|
2996 | 0 | decMultiplyOp(a, a, f, &workset, &ignore); /* a=a*f */ |
2997 | 0 | decAddOp(a, a, t, &workset, 0, &ignore); /* ..+t */ |
2998 | | /* [a is now the initial approximation for sqrt(f), calculated with */ |
2999 | | /* currentprecision, which is also a's precision.] */ |
3000 | | |
3001 | | /* the main calculation loop */ |
3002 | 0 | uprv_decNumberZero(&dzero); /* make 0 */ |
3003 | 0 | uprv_decNumberZero(t); /* set t = 0.5 */ |
3004 | 0 | t->lsu[0]=5; /* .. */ |
3005 | 0 | t->exponent=-1; /* .. */ |
3006 | 0 | workset.digits=3; /* initial p */ |
3007 | 0 | for (; workset.digits<maxp;) { |
3008 | | /* set p to min(2*p - 2, maxp) [hence 3; or: 4, 6, 10, ... , maxp] */ |
3009 | 0 | workset.digits=MINI(workset.digits*2-2, maxp); |
3010 | | /* a = 0.5 * (a + f/a) */ |
3011 | | /* [calculated at p then rounded to currentprecision] */ |
3012 | 0 | decDivideOp(b, f, a, &workset, DIVIDE, &ignore); /* b=f/a */ |
3013 | 0 | decAddOp(b, b, a, &workset, 0, &ignore); /* b=b+a */ |
3014 | 0 | decMultiplyOp(a, b, t, &workset, &ignore); /* a=b*0.5 */ |
3015 | 0 | } /* loop */ |
3016 | | |
3017 | | /* Here, 0.1 <= a < 1 [Hull], and a has maxp digits */ |
3018 | | /* now reduce to length, etc.; this needs to be done with a */ |
3019 | | /* having the correct exponent so as to handle subnormals */ |
3020 | | /* correctly */ |
3021 | 0 | approxset=*set; /* get emin, emax, etc. */ |
3022 | 0 | approxset.round=DEC_ROUND_HALF_EVEN; |
3023 | 0 | a->exponent+=exp/2; /* set correct exponent */ |
3024 | 0 | rstatus=0; /* clear status */ |
3025 | 0 | residue=0; /* .. and accumulator */ |
3026 | 0 | decCopyFit(a, a, &approxset, &residue, &rstatus); /* reduce (if needed) */ |
3027 | 0 | decFinish(a, &approxset, &residue, &rstatus); /* clean and finalize */ |
3028 | | |
3029 | | /* Overflow was possible if the input exponent was out-of-range, */ |
3030 | | /* in which case quit */ |
3031 | 0 | if (rstatus&DEC_Overflow) { |
3032 | 0 | status=rstatus; /* use the status as-is */ |
3033 | 0 | uprv_decNumberCopy(res, a); /* copy to result */ |
3034 | 0 | break; |
3035 | 0 | } |
3036 | | |
3037 | | /* Preserve status except Inexact/Rounded */ |
3038 | 0 | status|=(rstatus & ~(DEC_Rounded|DEC_Inexact)); |
3039 | | |
3040 | | /* Carry out the Hull correction */ |
3041 | 0 | a->exponent-=exp/2; /* back to 0.1->1 */ |
3042 | | |
3043 | | /* a is now at final precision and within 1 ulp of the properly */ |
3044 | | /* rounded square root of f; to ensure proper rounding, compare */ |
3045 | | /* squares of (a - l/2 ulp) and (a + l/2 ulp) with f. */ |
3046 | | /* Here workset.digits=maxp and t=0.5, and a->digits determines */ |
3047 | | /* the ulp */ |
3048 | 0 | workset.digits--; /* maxp-1 is OK now */ |
3049 | 0 | t->exponent=-a->digits-1; /* make 0.5 ulp */ |
3050 | 0 | decAddOp(b, a, t, &workset, DECNEG, &ignore); /* b = a - 0.5 ulp */ |
3051 | 0 | workset.round=DEC_ROUND_UP; |
3052 | 0 | decMultiplyOp(b, b, b, &workset, &ignore); /* b = mulru(b, b) */ |
3053 | 0 | decCompareOp(b, f, b, &workset, COMPARE, &ignore); /* b ? f, reversed */ |
3054 | 0 | if (decNumberIsNegative(b)) { /* f < b [i.e., b > f] */ |
3055 | | /* this is the more common adjustment, though both are rare */ |
3056 | 0 | t->exponent++; /* make 1.0 ulp */ |
3057 | 0 | t->lsu[0]=1; /* .. */ |
3058 | 0 | decAddOp(a, a, t, &workset, DECNEG, &ignore); /* a = a - 1 ulp */ |
3059 | | /* assign to approx [round to length] */ |
3060 | 0 | approxset.emin-=exp/2; /* adjust to match a */ |
3061 | 0 | approxset.emax-=exp/2; |
3062 | 0 | decAddOp(a, &dzero, a, &approxset, 0, &ignore); |
3063 | 0 | } |
3064 | 0 | else { |
3065 | 0 | decAddOp(b, a, t, &workset, 0, &ignore); /* b = a + 0.5 ulp */ |
3066 | 0 | workset.round=DEC_ROUND_DOWN; |
3067 | 0 | decMultiplyOp(b, b, b, &workset, &ignore); /* b = mulrd(b, b) */ |
3068 | 0 | decCompareOp(b, b, f, &workset, COMPARE, &ignore); /* b ? f */ |
3069 | 0 | if (decNumberIsNegative(b)) { /* b < f */ |
3070 | 0 | t->exponent++; /* make 1.0 ulp */ |
3071 | 0 | t->lsu[0]=1; /* .. */ |
3072 | 0 | decAddOp(a, a, t, &workset, 0, &ignore); /* a = a + 1 ulp */ |
3073 | | /* assign to approx [round to length] */ |
3074 | 0 | approxset.emin-=exp/2; /* adjust to match a */ |
3075 | 0 | approxset.emax-=exp/2; |
3076 | 0 | decAddOp(a, &dzero, a, &approxset, 0, &ignore); |
3077 | 0 | } |
3078 | 0 | } |
3079 | | /* [no errors are possible in the above, and rounding/inexact during */ |
3080 | | /* estimation are irrelevant, so status was not accumulated] */ |
3081 | | |
3082 | | /* Here, 0.1 <= a < 1 (still), so adjust back */ |
3083 | 0 | a->exponent+=exp/2; /* set correct exponent */ |
3084 | | |
3085 | | /* count droppable zeros [after any subnormal rounding] by */ |
3086 | | /* trimming a copy */ |
3087 | 0 | uprv_decNumberCopy(b, a); |
3088 | 0 | decTrim(b, set, 1, 1, &dropped); /* [drops trailing zeros] */ |
3089 | | |
3090 | | /* Set Inexact and Rounded. The answer can only be exact if */ |
3091 | | /* it is short enough so that squaring it could fit in workp */ |
3092 | | /* digits, so this is the only (relatively rare) condition that */ |
3093 | | /* a careful check is needed */ |
3094 | 0 | if (b->digits*2-1 > workp) { /* cannot fit */ |
3095 | 0 | status|=DEC_Inexact|DEC_Rounded; |
3096 | 0 | } |
3097 | 0 | else { /* could be exact/unrounded */ |
3098 | 0 | uInt mstatus=0; /* local status */ |
3099 | 0 | decMultiplyOp(b, b, b, &workset, &mstatus); /* try the multiply */ |
3100 | 0 | if (mstatus&DEC_Overflow) { /* result just won't fit */ |
3101 | 0 | status|=DEC_Inexact|DEC_Rounded; |
3102 | 0 | } |
3103 | 0 | else { /* plausible */ |
3104 | 0 | decCompareOp(t, b, rhs, &workset, COMPARE, &mstatus); /* b ? rhs */ |
3105 | 0 | if (!ISZERO(t)) status|=DEC_Inexact|DEC_Rounded; /* not equal */ |
3106 | 0 | else { /* is Exact */ |
3107 | | /* here, dropped is the count of trailing zeros in 'a' */ |
3108 | | /* use closest exponent to ideal... */ |
3109 | 0 | Int todrop=ideal-a->exponent; /* most that can be dropped */ |
3110 | 0 | if (todrop<0) status|=DEC_Rounded; /* ideally would add 0s */ |
3111 | 0 | else { /* unrounded */ |
3112 | | /* there are some to drop, but emax may not allow all */ |
3113 | 0 | Int maxexp=set->emax-set->digits+1; |
3114 | 0 | Int maxdrop=maxexp-a->exponent; |
3115 | 0 | if (todrop>maxdrop && set->clamp) { /* apply clamping */ |
3116 | 0 | todrop=maxdrop; |
3117 | 0 | status|=DEC_Clamped; |
3118 | 0 | } |
3119 | 0 | if (dropped<todrop) { /* clamp to those available */ |
3120 | 0 | todrop=dropped; |
3121 | 0 | status|=DEC_Clamped; |
3122 | 0 | } |
3123 | 0 | if (todrop>0) { /* have some to drop */ |
3124 | 0 | decShiftToLeast(a->lsu, D2U(a->digits), todrop); |
3125 | 0 | a->exponent+=todrop; /* maintain numerical value */ |
3126 | 0 | a->digits-=todrop; /* new length */ |
3127 | 0 | } |
3128 | 0 | } |
3129 | 0 | } |
3130 | 0 | } |
3131 | 0 | } |
3132 | | |
3133 | | /* double-check Underflow, as perhaps the result could not have */ |
3134 | | /* been subnormal (initial argument too big), or it is now Exact */ |
3135 | 0 | if (status&DEC_Underflow) { |
3136 | 0 | Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */ |
3137 | | /* check if truly subnormal */ |
3138 | | #if DECEXTFLAG /* DEC_Subnormal too */ |
3139 | 0 | if (ae>=set->emin*2) status&=~(DEC_Subnormal|DEC_Underflow); |
3140 | | #else |
3141 | | if (ae>=set->emin*2) status&=~DEC_Underflow; |
3142 | | #endif |
3143 | | /* check if truly inexact */ |
3144 | 0 | if (!(status&DEC_Inexact)) status&=~DEC_Underflow; |
3145 | 0 | } |
3146 | |
|
3147 | 0 | uprv_decNumberCopy(res, a); /* a is now the result */ |
3148 | 0 | } while(0); /* end protected */ |
3149 | | |
3150 | 0 | if (allocbuff!=NULL) free(allocbuff); /* drop any storage used */ |
3151 | 0 | if (allocbufa!=NULL) free(allocbufa); /* .. */ |
3152 | 0 | if (allocbufb!=NULL) free(allocbufb); /* .. */ |
3153 | | #if DECSUBSET |
3154 | | if (allocrhs !=NULL) free(allocrhs); /* .. */ |
3155 | | #endif |
3156 | 0 | if (status!=0) decStatus(res, status, set);/* then report status */ |
3157 | | #if DECCHECK |
3158 | | decCheckInexact(res, set); |
3159 | | #endif |
3160 | 0 | return res; |
3161 | 0 | } /* decNumberSquareRoot */ |
3162 | | #if defined(__clang__) || U_GCC_MAJOR_MINOR >= 406 |
3163 | | #pragma GCC diagnostic pop |
3164 | | #endif |
3165 | | |
3166 | | /* ------------------------------------------------------------------ */ |
3167 | | /* decNumberSubtract -- subtract two Numbers */ |
3168 | | /* */ |
3169 | | /* This computes C = A - B */ |
3170 | | /* */ |
3171 | | /* res is C, the result. C may be A and/or B (e.g., X=X-X) */ |
3172 | | /* lhs is A */ |
3173 | | /* rhs is B */ |
3174 | | /* set is the context */ |
3175 | | /* */ |
3176 | | /* C must have space for set->digits digits. */ |
3177 | | /* ------------------------------------------------------------------ */ |
3178 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberSubtract(decNumber *res, const decNumber *lhs, |
3179 | 0 | const decNumber *rhs, decContext *set) { |
3180 | 0 | uInt status=0; /* accumulator */ |
3181 | |
|
3182 | 0 | decAddOp(res, lhs, rhs, set, DECNEG, &status); |
3183 | 0 | if (status!=0) decStatus(res, status, set); |
3184 | | #if DECCHECK |
3185 | | decCheckInexact(res, set); |
3186 | | #endif |
3187 | 0 | return res; |
3188 | 0 | } /* decNumberSubtract */ |
3189 | | |
3190 | | /* ------------------------------------------------------------------ */ |
3191 | | /* decNumberToIntegralExact -- round-to-integral-value with InExact */ |
3192 | | /* decNumberToIntegralValue -- round-to-integral-value */ |
3193 | | /* */ |
3194 | | /* res is the result */ |
3195 | | /* rhs is input number */ |
3196 | | /* set is the context */ |
3197 | | /* */ |
3198 | | /* res must have space for any value of rhs. */ |
3199 | | /* */ |
3200 | | /* This implements the IEEE special operators and therefore treats */ |
3201 | | /* special values as valid. For finite numbers it returns */ |
3202 | | /* rescale(rhs, 0) if rhs->exponent is <0. */ |
3203 | | /* Otherwise the result is rhs (so no error is possible, except for */ |
3204 | | /* sNaN). */ |
3205 | | /* */ |
3206 | | /* The context is used for rounding mode and status after sNaN, but */ |
3207 | | /* the digits setting is ignored. The Exact version will signal */ |
3208 | | /* Inexact if the result differs numerically from rhs; the other */ |
3209 | | /* never signals Inexact. */ |
3210 | | /* ------------------------------------------------------------------ */ |
3211 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberToIntegralExact(decNumber *res, const decNumber *rhs, |
3212 | 0 | decContext *set) { |
3213 | 0 | decNumber dn; |
3214 | 0 | decContext workset; /* working context */ |
3215 | 0 | uInt status=0; /* accumulator */ |
3216 | |
|
3217 | | #if DECCHECK |
3218 | | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
3219 | | #endif |
3220 | | |
3221 | | /* handle infinities and NaNs */ |
3222 | 0 | if (SPECIALARG) { |
3223 | 0 | if (decNumberIsInfinite(rhs)) uprv_decNumberCopy(res, rhs); /* an Infinity */ |
3224 | 0 | else decNaNs(res, rhs, NULL, set, &status); /* a NaN */ |
3225 | 0 | } |
3226 | 0 | else { /* finite */ |
3227 | | /* have a finite number; no error possible (res must be big enough) */ |
3228 | 0 | if (rhs->exponent>=0) return uprv_decNumberCopy(res, rhs); |
3229 | | /* that was easy, but if negative exponent there is work to do... */ |
3230 | 0 | workset=*set; /* clone rounding, etc. */ |
3231 | 0 | workset.digits=rhs->digits; /* no length rounding */ |
3232 | 0 | workset.traps=0; /* no traps */ |
3233 | 0 | uprv_decNumberZero(&dn); /* make a number with exponent 0 */ |
3234 | 0 | uprv_decNumberQuantize(res, rhs, &dn, &workset); |
3235 | 0 | status|=workset.status; |
3236 | 0 | } |
3237 | 0 | if (status!=0) decStatus(res, status, set); |
3238 | 0 | return res; |
3239 | 0 | } /* decNumberToIntegralExact */ |
3240 | | |
3241 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberToIntegralValue(decNumber *res, const decNumber *rhs, |
3242 | 0 | decContext *set) { |
3243 | 0 | decContext workset=*set; /* working context */ |
3244 | 0 | workset.traps=0; /* no traps */ |
3245 | 0 | uprv_decNumberToIntegralExact(res, rhs, &workset); |
3246 | | /* this never affects set, except for sNaNs; NaN will have been set */ |
3247 | | /* or propagated already, so no need to call decStatus */ |
3248 | 0 | set->status|=workset.status&DEC_Invalid_operation; |
3249 | 0 | return res; |
3250 | 0 | } /* decNumberToIntegralValue */ |
3251 | | |
3252 | | /* ------------------------------------------------------------------ */ |
3253 | | /* decNumberXor -- XOR two Numbers, digitwise */ |
3254 | | /* */ |
3255 | | /* This computes C = A ^ B */ |
3256 | | /* */ |
3257 | | /* res is C, the result. C may be A and/or B (e.g., X=X^X) */ |
3258 | | /* lhs is A */ |
3259 | | /* rhs is B */ |
3260 | | /* set is the context (used for result length and error report) */ |
3261 | | /* */ |
3262 | | /* C must have space for set->digits digits. */ |
3263 | | /* */ |
3264 | | /* Logical function restrictions apply (see above); a NaN is */ |
3265 | | /* returned with Invalid_operation if a restriction is violated. */ |
3266 | | /* ------------------------------------------------------------------ */ |
3267 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberXor(decNumber *res, const decNumber *lhs, |
3268 | 0 | const decNumber *rhs, decContext *set) { |
3269 | 0 | const Unit *ua, *ub; /* -> operands */ |
3270 | 0 | const Unit *msua, *msub; /* -> operand msus */ |
3271 | 0 | Unit *uc, *msuc; /* -> result and its msu */ |
3272 | 0 | Int msudigs; /* digits in res msu */ |
3273 | | #if DECCHECK |
3274 | | if (decCheckOperands(res, lhs, rhs, set)) return res; |
3275 | | #endif |
3276 | |
|
3277 | 0 | if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) |
3278 | 0 | || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { |
3279 | 0 | decStatus(res, DEC_Invalid_operation, set); |
3280 | 0 | return res; |
3281 | 0 | } |
3282 | | /* operands are valid */ |
3283 | 0 | ua=lhs->lsu; /* bottom-up */ |
3284 | 0 | ub=rhs->lsu; /* .. */ |
3285 | 0 | uc=res->lsu; /* .. */ |
3286 | 0 | msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */ |
3287 | 0 | msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */ |
3288 | 0 | msuc=uc+D2U(set->digits)-1; /* -> msu of result */ |
3289 | 0 | msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ |
3290 | 0 | for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */ |
3291 | 0 | Unit a, b; /* extract units */ |
3292 | 0 | if (ua>msua) a=0; |
3293 | 0 | else a=*ua; |
3294 | 0 | if (ub>msub) b=0; |
3295 | 0 | else b=*ub; |
3296 | 0 | *uc=0; /* can now write back */ |
3297 | 0 | if (a|b) { /* maybe 1 bits to examine */ |
3298 | 0 | Int i, j; |
3299 | | /* This loop could be unrolled and/or use BIN2BCD tables */ |
3300 | 0 | for (i=0; i<DECDPUN; i++) { |
3301 | 0 | if ((a^b)&1) *uc=*uc+(Unit)powers[i]; /* effect XOR */ |
3302 | 0 | j=a%10; |
3303 | 0 | a=a/10; |
3304 | 0 | j|=b%10; |
3305 | 0 | b=b/10; |
3306 | 0 | if (j>1) { |
3307 | 0 | decStatus(res, DEC_Invalid_operation, set); |
3308 | 0 | return res; |
3309 | 0 | } |
3310 | 0 | if (uc==msuc && i==msudigs-1) break; /* just did final digit */ |
3311 | 0 | } /* each digit */ |
3312 | 0 | } /* non-zero */ |
3313 | 0 | } /* each unit */ |
3314 | | /* [here uc-1 is the msu of the result] */ |
3315 | 0 | res->digits=decGetDigits(res->lsu, static_cast<int32_t>(uc-res->lsu)); |
3316 | 0 | res->exponent=0; /* integer */ |
3317 | 0 | res->bits=0; /* sign=0 */ |
3318 | 0 | return res; /* [no status to set] */ |
3319 | 0 | } /* decNumberXor */ |
3320 | | |
3321 | | |
3322 | | /* ================================================================== */ |
3323 | | /* Utility routines */ |
3324 | | /* ================================================================== */ |
3325 | | |
3326 | | /* ------------------------------------------------------------------ */ |
3327 | | /* decNumberClass -- return the decClass of a decNumber */ |
3328 | | /* dn -- the decNumber to test */ |
3329 | | /* set -- the context to use for Emin */ |
3330 | | /* returns the decClass enum */ |
3331 | | /* ------------------------------------------------------------------ */ |
3332 | 0 | enum decClass uprv_decNumberClass(const decNumber *dn, decContext *set) { |
3333 | 0 | if (decNumberIsSpecial(dn)) { |
3334 | 0 | if (decNumberIsQNaN(dn)) return DEC_CLASS_QNAN; |
3335 | 0 | if (decNumberIsSNaN(dn)) return DEC_CLASS_SNAN; |
3336 | | /* must be an infinity */ |
3337 | 0 | if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_INF; |
3338 | 0 | return DEC_CLASS_POS_INF; |
3339 | 0 | } |
3340 | | /* is finite */ |
3341 | 0 | if (uprv_decNumberIsNormal(dn, set)) { /* most common */ |
3342 | 0 | if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_NORMAL; |
3343 | 0 | return DEC_CLASS_POS_NORMAL; |
3344 | 0 | } |
3345 | | /* is subnormal or zero */ |
3346 | 0 | if (decNumberIsZero(dn)) { /* most common */ |
3347 | 0 | if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_ZERO; |
3348 | 0 | return DEC_CLASS_POS_ZERO; |
3349 | 0 | } |
3350 | 0 | if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_SUBNORMAL; |
3351 | 0 | return DEC_CLASS_POS_SUBNORMAL; |
3352 | 0 | } /* decNumberClass */ |
3353 | | |
3354 | | /* ------------------------------------------------------------------ */ |
3355 | | /* decNumberClassToString -- convert decClass to a string */ |
3356 | | /* */ |
3357 | | /* eclass is a valid decClass */ |
3358 | | /* returns a constant string describing the class (max 13+1 chars) */ |
3359 | | /* ------------------------------------------------------------------ */ |
3360 | 0 | const char *uprv_decNumberClassToString(enum decClass eclass) { |
3361 | 0 | if (eclass==DEC_CLASS_POS_NORMAL) return DEC_ClassString_PN; |
3362 | 0 | if (eclass==DEC_CLASS_NEG_NORMAL) return DEC_ClassString_NN; |
3363 | 0 | if (eclass==DEC_CLASS_POS_ZERO) return DEC_ClassString_PZ; |
3364 | 0 | if (eclass==DEC_CLASS_NEG_ZERO) return DEC_ClassString_NZ; |
3365 | 0 | if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS; |
3366 | 0 | if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS; |
3367 | 0 | if (eclass==DEC_CLASS_POS_INF) return DEC_ClassString_PI; |
3368 | 0 | if (eclass==DEC_CLASS_NEG_INF) return DEC_ClassString_NI; |
3369 | 0 | if (eclass==DEC_CLASS_QNAN) return DEC_ClassString_QN; |
3370 | 0 | if (eclass==DEC_CLASS_SNAN) return DEC_ClassString_SN; |
3371 | 0 | return DEC_ClassString_UN; /* Unknown */ |
3372 | 0 | } /* decNumberClassToString */ |
3373 | | |
3374 | | /* ------------------------------------------------------------------ */ |
3375 | | /* decNumberCopy -- copy a number */ |
3376 | | /* */ |
3377 | | /* dest is the target decNumber */ |
3378 | | /* src is the source decNumber */ |
3379 | | /* returns dest */ |
3380 | | /* */ |
3381 | | /* (dest==src is allowed and is a no-op) */ |
3382 | | /* All fields are updated as required. This is a utility operation, */ |
3383 | | /* so special values are unchanged and no error is possible. */ |
3384 | | /* ------------------------------------------------------------------ */ |
3385 | 0 | U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopy(decNumber *dest, const decNumber *src) { |
3386 | |
|
3387 | | #if DECCHECK |
3388 | | if (src==NULL) return uprv_decNumberZero(dest); |
3389 | | #endif |
3390 | |
|
3391 | 0 | if (dest==src) return dest; /* no copy required */ |
3392 | | |
3393 | | /* Use explicit assignments here as structure assignment could copy */ |
3394 | | /* more than just the lsu (for small DECDPUN). This would not affect */ |
3395 | | /* the value of the results, but could disturb test harness spill */ |
3396 | | /* checking. */ |
3397 | 0 | dest->bits=src->bits; |
3398 | 0 | dest->exponent=src->exponent; |
3399 | 0 | dest->digits=src->digits; |
3400 | 0 | dest->lsu[0]=src->lsu[0]; |
3401 | 0 | if (src->digits>DECDPUN) { /* more Units to come */ |
3402 | 0 | const Unit *smsup, *s; /* work */ |
3403 | 0 | Unit *d; /* .. */ |
3404 | | /* memcpy for the remaining Units would be safe as they cannot */ |
3405 | | /* overlap. However, this explicit loop is faster in short cases. */ |
3406 | 0 | d=dest->lsu+1; /* -> first destination */ |
3407 | 0 | smsup=src->lsu+D2U(src->digits); /* -> source msu+1 */ |
3408 | 0 | for (s=src->lsu+1; s<smsup; s++, d++) *d=*s; |
3409 | 0 | } |
3410 | 0 | return dest; |
3411 | 0 | } /* decNumberCopy */ |
3412 | | |
3413 | | /* ------------------------------------------------------------------ */ |
3414 | | /* decNumberCopyAbs -- quiet absolute value operator */ |
3415 | | /* */ |
3416 | | /* This sets C = abs(A) */ |
3417 | | /* */ |
3418 | | /* res is C, the result. C may be A */ |
3419 | | /* rhs is A */ |
3420 | | /* */ |
3421 | | /* C must have space for set->digits digits. */ |
3422 | | /* No exception or error can occur; this is a quiet bitwise operation.*/ |
3423 | | /* See also decNumberAbs for a checking version of this. */ |
3424 | | /* ------------------------------------------------------------------ */ |
3425 | 0 | U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopyAbs(decNumber *res, const decNumber *rhs) { |
3426 | | #if DECCHECK |
3427 | | if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; |
3428 | | #endif |
3429 | 0 | uprv_decNumberCopy(res, rhs); |
3430 | 0 | res->bits&=~DECNEG; /* turn off sign */ |
3431 | 0 | return res; |
3432 | 0 | } /* decNumberCopyAbs */ |
3433 | | |
3434 | | /* ------------------------------------------------------------------ */ |
3435 | | /* decNumberCopyNegate -- quiet negate value operator */ |
3436 | | /* */ |
3437 | | /* This sets C = negate(A) */ |
3438 | | /* */ |
3439 | | /* res is C, the result. C may be A */ |
3440 | | /* rhs is A */ |
3441 | | /* */ |
3442 | | /* C must have space for set->digits digits. */ |
3443 | | /* No exception or error can occur; this is a quiet bitwise operation.*/ |
3444 | | /* See also decNumberMinus for a checking version of this. */ |
3445 | | /* ------------------------------------------------------------------ */ |
3446 | 0 | U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopyNegate(decNumber *res, const decNumber *rhs) { |
3447 | | #if DECCHECK |
3448 | | if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; |
3449 | | #endif |
3450 | 0 | uprv_decNumberCopy(res, rhs); |
3451 | 0 | res->bits^=DECNEG; /* invert the sign */ |
3452 | 0 | return res; |
3453 | 0 | } /* decNumberCopyNegate */ |
3454 | | |
3455 | | /* ------------------------------------------------------------------ */ |
3456 | | /* decNumberCopySign -- quiet copy and set sign operator */ |
3457 | | /* */ |
3458 | | /* This sets C = A with the sign of B */ |
3459 | | /* */ |
3460 | | /* res is C, the result. C may be A */ |
3461 | | /* lhs is A */ |
3462 | | /* rhs is B */ |
3463 | | /* */ |
3464 | | /* C must have space for set->digits digits. */ |
3465 | | /* No exception or error can occur; this is a quiet bitwise operation.*/ |
3466 | | /* ------------------------------------------------------------------ */ |
3467 | | U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopySign(decNumber *res, const decNumber *lhs, |
3468 | 0 | const decNumber *rhs) { |
3469 | 0 | uByte sign; /* rhs sign */ |
3470 | | #if DECCHECK |
3471 | | if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; |
3472 | | #endif |
3473 | 0 | sign=rhs->bits & DECNEG; /* save sign bit */ |
3474 | 0 | uprv_decNumberCopy(res, lhs); |
3475 | 0 | res->bits&=~DECNEG; /* clear the sign */ |
3476 | 0 | res->bits|=sign; /* set from rhs */ |
3477 | 0 | return res; |
3478 | 0 | } /* decNumberCopySign */ |
3479 | | |
3480 | | /* ------------------------------------------------------------------ */ |
3481 | | /* decNumberGetBCD -- get the coefficient in BCD8 */ |
3482 | | /* dn is the source decNumber */ |
3483 | | /* bcd is the uInt array that will receive dn->digits BCD bytes, */ |
3484 | | /* most-significant at offset 0 */ |
3485 | | /* returns bcd */ |
3486 | | /* */ |
3487 | | /* bcd must have at least dn->digits bytes. No error is possible; if */ |
3488 | | /* dn is a NaN or Infinite, digits must be 1 and the coefficient 0. */ |
3489 | | /* ------------------------------------------------------------------ */ |
3490 | 0 | U_CAPI uByte * U_EXPORT2 uprv_decNumberGetBCD(const decNumber *dn, uByte *bcd) { |
3491 | 0 | uByte *ub=bcd+dn->digits-1; /* -> lsd */ |
3492 | 0 | const Unit *up=dn->lsu; /* Unit pointer, -> lsu */ |
3493 | |
|
3494 | 0 | #if DECDPUN==1 /* trivial simple copy */ |
3495 | 0 | for (; ub>=bcd; ub--, up++) *ub=*up; |
3496 | | #else /* chopping needed */ |
3497 | | uInt u=*up; /* work */ |
3498 | | uInt cut=DECDPUN; /* downcounter through unit */ |
3499 | | for (; ub>=bcd; ub--) { |
3500 | | *ub=(uByte)(u%10); /* [*6554 trick inhibits, here] */ |
3501 | | u=u/10; |
3502 | | cut--; |
3503 | | if (cut>0) continue; /* more in this unit */ |
3504 | | up++; |
3505 | | u=*up; |
3506 | | cut=DECDPUN; |
3507 | | } |
3508 | | #endif |
3509 | 0 | return bcd; |
3510 | 0 | } /* decNumberGetBCD */ |
3511 | | |
3512 | | /* ------------------------------------------------------------------ */ |
3513 | | /* decNumberSetBCD -- set (replace) the coefficient from BCD8 */ |
3514 | | /* dn is the target decNumber */ |
3515 | | /* bcd is the uInt array that will source n BCD bytes, most- */ |
3516 | | /* significant at offset 0 */ |
3517 | | /* n is the number of digits in the source BCD array (bcd) */ |
3518 | | /* returns dn */ |
3519 | | /* */ |
3520 | | /* dn must have space for at least n digits. No error is possible; */ |
3521 | | /* if dn is a NaN, or Infinite, or is to become a zero, n must be 1 */ |
3522 | | /* and bcd[0] zero. */ |
3523 | | /* ------------------------------------------------------------------ */ |
3524 | 0 | U_CAPI decNumber * U_EXPORT2 uprv_decNumberSetBCD(decNumber *dn, const uByte *bcd, uInt n) { |
3525 | 0 | Unit *up=dn->lsu+D2U(dn->digits)-1; /* -> msu [target pointer] */ |
3526 | 0 | const uByte *ub=bcd; /* -> source msd */ |
3527 | |
|
3528 | 0 | #if DECDPUN==1 /* trivial simple copy */ |
3529 | 0 | for (; ub<bcd+n; ub++, up--) *up=*ub; |
3530 | | #else /* some assembly needed */ |
3531 | | /* calculate how many digits in msu, and hence first cut */ |
3532 | | Int cut=MSUDIGITS(n); /* [faster than remainder] */ |
3533 | | for (;up>=dn->lsu; up--) { /* each Unit from msu */ |
3534 | | *up=0; /* will take <=DECDPUN digits */ |
3535 | | for (; cut>0; ub++, cut--) *up=X10(*up)+*ub; |
3536 | | cut=DECDPUN; /* next Unit has all digits */ |
3537 | | } |
3538 | | #endif |
3539 | 0 | dn->digits=n; /* set digit count */ |
3540 | 0 | return dn; |
3541 | 0 | } /* decNumberSetBCD */ |
3542 | | |
3543 | | /* ------------------------------------------------------------------ */ |
3544 | | /* decNumberIsNormal -- test normality of a decNumber */ |
3545 | | /* dn is the decNumber to test */ |
3546 | | /* set is the context to use for Emin */ |
3547 | | /* returns 1 if |dn| is finite and >=Nmin, 0 otherwise */ |
3548 | | /* ------------------------------------------------------------------ */ |
3549 | 0 | Int uprv_decNumberIsNormal(const decNumber *dn, decContext *set) { |
3550 | 0 | Int ae; /* adjusted exponent */ |
3551 | | #if DECCHECK |
3552 | | if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; |
3553 | | #endif |
3554 | |
|
3555 | 0 | if (decNumberIsSpecial(dn)) return 0; /* not finite */ |
3556 | 0 | if (decNumberIsZero(dn)) return 0; /* not non-zero */ |
3557 | | |
3558 | 0 | ae=dn->exponent+dn->digits-1; /* adjusted exponent */ |
3559 | 0 | if (ae<set->emin) return 0; /* is subnormal */ |
3560 | 0 | return 1; |
3561 | 0 | } /* decNumberIsNormal */ |
3562 | | |
3563 | | /* ------------------------------------------------------------------ */ |
3564 | | /* decNumberIsSubnormal -- test subnormality of a decNumber */ |
3565 | | /* dn is the decNumber to test */ |
3566 | | /* set is the context to use for Emin */ |
3567 | | /* returns 1 if |dn| is finite, non-zero, and <Nmin, 0 otherwise */ |
3568 | | /* ------------------------------------------------------------------ */ |
3569 | 0 | Int uprv_decNumberIsSubnormal(const decNumber *dn, decContext *set) { |
3570 | 0 | Int ae; /* adjusted exponent */ |
3571 | | #if DECCHECK |
3572 | | if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; |
3573 | | #endif |
3574 | |
|
3575 | 0 | if (decNumberIsSpecial(dn)) return 0; /* not finite */ |
3576 | 0 | if (decNumberIsZero(dn)) return 0; /* not non-zero */ |
3577 | | |
3578 | 0 | ae=dn->exponent+dn->digits-1; /* adjusted exponent */ |
3579 | 0 | if (ae<set->emin) return 1; /* is subnormal */ |
3580 | 0 | return 0; |
3581 | 0 | } /* decNumberIsSubnormal */ |
3582 | | |
3583 | | /* ------------------------------------------------------------------ */ |
3584 | | /* decNumberTrim -- remove insignificant zeros */ |
3585 | | /* */ |
3586 | | /* dn is the number to trim */ |
3587 | | /* returns dn */ |
3588 | | /* */ |
3589 | | /* All fields are updated as required. This is a utility operation, */ |
3590 | | /* so special values are unchanged and no error is possible. The */ |
3591 | | /* zeros are removed unconditionally. */ |
3592 | | /* ------------------------------------------------------------------ */ |
3593 | 0 | U_CAPI decNumber * U_EXPORT2 uprv_decNumberTrim(decNumber *dn) { |
3594 | 0 | Int dropped; /* work */ |
3595 | 0 | decContext set; /* .. */ |
3596 | | #if DECCHECK |
3597 | | if (decCheckOperands(DECUNRESU, DECUNUSED, dn, DECUNCONT)) return dn; |
3598 | | #endif |
3599 | 0 | uprv_decContextDefault(&set, DEC_INIT_BASE); /* clamp=0 */ |
3600 | 0 | return decTrim(dn, &set, 0, 1, &dropped); |
3601 | 0 | } /* decNumberTrim */ |
3602 | | |
3603 | | /* ------------------------------------------------------------------ */ |
3604 | | /* decNumberVersion -- return the name and version of this module */ |
3605 | | /* */ |
3606 | | /* No error is possible. */ |
3607 | | /* ------------------------------------------------------------------ */ |
3608 | 0 | const char * uprv_decNumberVersion(void) { |
3609 | 0 | return DECVERSION; |
3610 | 0 | } /* decNumberVersion */ |
3611 | | |
3612 | | /* ------------------------------------------------------------------ */ |
3613 | | /* decNumberZero -- set a number to 0 */ |
3614 | | /* */ |
3615 | | /* dn is the number to set, with space for one digit */ |
3616 | | /* returns dn */ |
3617 | | /* */ |
3618 | | /* No error is possible. */ |
3619 | | /* ------------------------------------------------------------------ */ |
3620 | | /* Memset is not used as it is much slower in some environments. */ |
3621 | 0 | U_CAPI decNumber * U_EXPORT2 uprv_decNumberZero(decNumber *dn) { |
3622 | |
|
3623 | | #if DECCHECK |
3624 | | if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn; |
3625 | | #endif |
3626 | |
|
3627 | 0 | dn->bits=0; |
3628 | 0 | dn->exponent=0; |
3629 | 0 | dn->digits=1; |
3630 | 0 | dn->lsu[0]=0; |
3631 | 0 | return dn; |
3632 | 0 | } /* decNumberZero */ |
3633 | | |
3634 | | /* ================================================================== */ |
3635 | | /* Local routines */ |
3636 | | /* ================================================================== */ |
3637 | | |
3638 | | /* ------------------------------------------------------------------ */ |
3639 | | /* decToString -- lay out a number into a string */ |
3640 | | /* */ |
3641 | | /* dn is the number to lay out */ |
3642 | | /* string is where to lay out the number */ |
3643 | | /* eng is 1 if Engineering, 0 if Scientific */ |
3644 | | /* */ |
3645 | | /* string must be at least dn->digits+14 characters long */ |
3646 | | /* No error is possible. */ |
3647 | | /* */ |
3648 | | /* Note that this routine can generate a -0 or 0.000. These are */ |
3649 | | /* never generated in subset to-number or arithmetic, but can occur */ |
3650 | | /* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234). */ |
3651 | | /* ------------------------------------------------------------------ */ |
3652 | | /* If DECCHECK is enabled the string "?" is returned if a number is */ |
3653 | | /* invalid. */ |
3654 | 0 | static void decToString(const decNumber *dn, char *string, Flag eng) { |
3655 | 0 | Int exp=dn->exponent; /* local copy */ |
3656 | 0 | Int e; /* E-part value */ |
3657 | 0 | Int pre; /* digits before the '.' */ |
3658 | 0 | Int cut; /* for counting digits in a Unit */ |
3659 | 0 | char *c=string; /* work [output pointer] */ |
3660 | 0 | const Unit *up=dn->lsu+D2U(dn->digits)-1; /* -> msu [input pointer] */ |
3661 | 0 | uInt u, pow; /* work */ |
3662 | |
|
3663 | | #if DECCHECK |
3664 | | if (decCheckOperands(DECUNRESU, dn, DECUNUSED, DECUNCONT)) { |
3665 | | strcpy(string, "?"); |
3666 | | return;} |
3667 | | #endif |
3668 | |
|
3669 | 0 | if (decNumberIsNegative(dn)) { /* Negatives get a minus */ |
3670 | 0 | *c='-'; |
3671 | 0 | c++; |
3672 | 0 | } |
3673 | 0 | if (dn->bits&DECSPECIAL) { /* Is a special value */ |
3674 | 0 | if (decNumberIsInfinite(dn)) { |
3675 | 0 | strcpy(c, "Inf"); |
3676 | 0 | strcpy(c+3, "inity"); |
3677 | 0 | return;} |
3678 | | /* a NaN */ |
3679 | 0 | if (dn->bits&DECSNAN) { /* signalling NaN */ |
3680 | 0 | *c='s'; |
3681 | 0 | c++; |
3682 | 0 | } |
3683 | 0 | strcpy(c, "NaN"); |
3684 | 0 | c+=3; /* step past */ |
3685 | | /* if not a clean non-zero coefficient, that's all there is in a */ |
3686 | | /* NaN string */ |
3687 | 0 | if (exp!=0 || (*dn->lsu==0 && dn->digits==1)) return; |
3688 | | /* [drop through to add integer] */ |
3689 | 0 | } |
3690 | | |
3691 | | /* calculate how many digits in msu, and hence first cut */ |
3692 | 0 | cut=MSUDIGITS(dn->digits); /* [faster than remainder] */ |
3693 | 0 | cut--; /* power of ten for digit */ |
3694 | |
|
3695 | 0 | if (exp==0) { /* simple integer [common fastpath] */ |
3696 | 0 | for (;up>=dn->lsu; up--) { /* each Unit from msu */ |
3697 | 0 | u=*up; /* contains DECDPUN digits to lay out */ |
3698 | 0 | for (; cut>=0; c++, cut--) TODIGIT(u, cut, c, pow); |
3699 | 0 | cut=DECDPUN-1; /* next Unit has all digits */ |
3700 | 0 | } |
3701 | 0 | *c='\0'; /* terminate the string */ |
3702 | 0 | return;} |
3703 | | |
3704 | | /* non-0 exponent -- assume plain form */ |
3705 | 0 | pre=dn->digits+exp; /* digits before '.' */ |
3706 | 0 | e=0; /* no E */ |
3707 | 0 | if ((exp>0) || (pre<-5)) { /* need exponential form */ |
3708 | 0 | e=exp+dn->digits-1; /* calculate E value */ |
3709 | 0 | pre=1; /* assume one digit before '.' */ |
3710 | 0 | if (eng && (e!=0)) { /* engineering: may need to adjust */ |
3711 | 0 | Int adj; /* adjustment */ |
3712 | | /* The C remainder operator is undefined for negative numbers, so */ |
3713 | | /* a positive remainder calculation must be used here */ |
3714 | 0 | if (e<0) { |
3715 | 0 | adj=(-e)%3; |
3716 | 0 | if (adj!=0) adj=3-adj; |
3717 | 0 | } |
3718 | 0 | else { /* e>0 */ |
3719 | 0 | adj=e%3; |
3720 | 0 | } |
3721 | 0 | e=e-adj; |
3722 | | /* if dealing with zero still produce an exponent which is a */ |
3723 | | /* multiple of three, as expected, but there will only be the */ |
3724 | | /* one zero before the E, still. Otherwise note the padding. */ |
3725 | 0 | if (!ISZERO(dn)) pre+=adj; |
3726 | 0 | else { /* is zero */ |
3727 | 0 | if (adj!=0) { /* 0.00Esnn needed */ |
3728 | 0 | e=e+3; |
3729 | 0 | pre=-(2-adj); |
3730 | 0 | } |
3731 | 0 | } /* zero */ |
3732 | 0 | } /* eng */ |
3733 | 0 | } /* need exponent */ |
3734 | | |
3735 | | /* lay out the digits of the coefficient, adding 0s and . as needed */ |
3736 | 0 | u=*up; |
3737 | 0 | if (pre>0) { /* xxx.xxx or xx00 (engineering) form */ |
3738 | 0 | Int n=pre; |
3739 | 0 | for (; pre>0; pre--, c++, cut--) { |
3740 | 0 | if (cut<0) { /* need new Unit */ |
3741 | 0 | if (up==dn->lsu) break; /* out of input digits (pre>digits) */ |
3742 | 0 | up--; |
3743 | 0 | cut=DECDPUN-1; |
3744 | 0 | u=*up; |
3745 | 0 | } |
3746 | 0 | TODIGIT(u, cut, c, pow); |
3747 | 0 | } |
3748 | 0 | if (n<dn->digits) { /* more to come, after '.' */ |
3749 | 0 | *c='.'; c++; |
3750 | 0 | for (;; c++, cut--) { |
3751 | 0 | if (cut<0) { /* need new Unit */ |
3752 | 0 | if (up==dn->lsu) break; /* out of input digits */ |
3753 | 0 | up--; |
3754 | 0 | cut=DECDPUN-1; |
3755 | 0 | u=*up; |
3756 | 0 | } |
3757 | 0 | TODIGIT(u, cut, c, pow); |
3758 | 0 | } |
3759 | 0 | } |
3760 | 0 | else for (; pre>0; pre--, c++) *c='0'; /* 0 padding (for engineering) needed */ |
3761 | 0 | } |
3762 | 0 | else { /* 0.xxx or 0.000xxx form */ |
3763 | 0 | *c='0'; c++; |
3764 | 0 | *c='.'; c++; |
3765 | 0 | for (; pre<0; pre++, c++) *c='0'; /* add any 0's after '.' */ |
3766 | 0 | for (; ; c++, cut--) { |
3767 | 0 | if (cut<0) { /* need new Unit */ |
3768 | 0 | if (up==dn->lsu) break; /* out of input digits */ |
3769 | 0 | up--; |
3770 | 0 | cut=DECDPUN-1; |
3771 | 0 | u=*up; |
3772 | 0 | } |
3773 | 0 | TODIGIT(u, cut, c, pow); |
3774 | 0 | } |
3775 | 0 | } |
3776 | | |
3777 | | /* Finally add the E-part, if needed. It will never be 0, has a |
3778 | | base maximum and minimum of +999999999 through -999999999, but |
3779 | | could range down to -1999999998 for abnormal numbers */ |
3780 | 0 | if (e!=0) { |
3781 | 0 | Flag had=0; /* 1=had non-zero */ |
3782 | 0 | *c='E'; c++; |
3783 | 0 | *c='+'; c++; /* assume positive */ |
3784 | 0 | u=e; /* .. */ |
3785 | 0 | if (e<0) { |
3786 | 0 | *(c-1)='-'; /* oops, need - */ |
3787 | 0 | u=-e; /* uInt, please */ |
3788 | 0 | } |
3789 | | /* lay out the exponent [_itoa or equivalent is not ANSI C] */ |
3790 | 0 | for (cut=9; cut>=0; cut--) { |
3791 | 0 | TODIGIT(u, cut, c, pow); |
3792 | 0 | if (*c=='0' && !had) continue; /* skip leading zeros */ |
3793 | 0 | had=1; /* had non-0 */ |
3794 | 0 | c++; /* step for next */ |
3795 | 0 | } /* cut */ |
3796 | 0 | } |
3797 | 0 | *c='\0'; /* terminate the string (all paths) */ |
3798 | 0 | return; |
3799 | 0 | } /* decToString */ |
3800 | | |
3801 | | /* ------------------------------------------------------------------ */ |
3802 | | /* decAddOp -- add/subtract operation */ |
3803 | | /* */ |
3804 | | /* This computes C = A + B */ |
3805 | | /* */ |
3806 | | /* res is C, the result. C may be A and/or B (e.g., X=X+X) */ |
3807 | | /* lhs is A */ |
3808 | | /* rhs is B */ |
3809 | | /* set is the context */ |
3810 | | /* negate is DECNEG if rhs should be negated, or 0 otherwise */ |
3811 | | /* status accumulates status for the caller */ |
3812 | | /* */ |
3813 | | /* C must have space for set->digits digits. */ |
3814 | | /* Inexact in status must be 0 for correct Exact zero sign in result */ |
3815 | | /* ------------------------------------------------------------------ */ |
3816 | | /* If possible, the coefficient is calculated directly into C. */ |
3817 | | /* However, if: */ |
3818 | | /* -- a digits+1 calculation is needed because the numbers are */ |
3819 | | /* unaligned and span more than set->digits digits */ |
3820 | | /* -- a carry to digits+1 digits looks possible */ |
3821 | | /* -- C is the same as A or B, and the result would destructively */ |
3822 | | /* overlap the A or B coefficient */ |
3823 | | /* then the result must be calculated into a temporary buffer. In */ |
3824 | | /* this case a local (stack) buffer is used if possible, and only if */ |
3825 | | /* too long for that does malloc become the final resort. */ |
3826 | | /* */ |
3827 | | /* Misalignment is handled as follows: */ |
3828 | | /* Apad: (AExp>BExp) Swap operands and proceed as for BExp>AExp. */ |
3829 | | /* BPad: Apply the padding by a combination of shifting (whole */ |
3830 | | /* units) and multiplication (part units). */ |
3831 | | /* */ |
3832 | | /* Addition, especially x=x+1, is speed-critical. */ |
3833 | | /* The static buffer is larger than might be expected to allow for */ |
3834 | | /* calls from higher-level functions (notable exp). */ |
3835 | | /* ------------------------------------------------------------------ */ |
3836 | | static decNumber * decAddOp(decNumber *res, const decNumber *lhs, |
3837 | | const decNumber *rhs, decContext *set, |
3838 | 0 | uByte negate, uInt *status) { |
3839 | | #if DECSUBSET |
3840 | | decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ |
3841 | | decNumber *allocrhs=NULL; /* .., rhs */ |
3842 | | #endif |
3843 | 0 | Int rhsshift; /* working shift (in Units) */ |
3844 | 0 | Int maxdigits; /* longest logical length */ |
3845 | 0 | Int mult; /* multiplier */ |
3846 | 0 | Int residue; /* rounding accumulator */ |
3847 | 0 | uByte bits; /* result bits */ |
3848 | 0 | Flag diffsign; /* non-0 if arguments have different sign */ |
3849 | 0 | Unit *acc; /* accumulator for result */ |
3850 | 0 | Unit accbuff[SD2U(DECBUFFER*2+20)]; /* local buffer [*2+20 reduces many */ |
3851 | | /* allocations when called from */ |
3852 | | /* other operations, notable exp] */ |
3853 | 0 | Unit *allocacc=NULL; /* -> allocated acc buffer, iff allocated */ |
3854 | 0 | Int reqdigits=set->digits; /* local copy; requested DIGITS */ |
3855 | 0 | Int padding; /* work */ |
3856 | |
|
3857 | | #if DECCHECK |
3858 | | if (decCheckOperands(res, lhs, rhs, set)) return res; |
3859 | | #endif |
3860 | |
|
3861 | 0 | do { /* protect allocated storage */ |
3862 | | #if DECSUBSET |
3863 | | if (!set->extended) { |
3864 | | /* reduce operands and set lostDigits status, as needed */ |
3865 | | if (lhs->digits>reqdigits) { |
3866 | | alloclhs=decRoundOperand(lhs, set, status); |
3867 | | if (alloclhs==NULL) break; |
3868 | | lhs=alloclhs; |
3869 | | } |
3870 | | if (rhs->digits>reqdigits) { |
3871 | | allocrhs=decRoundOperand(rhs, set, status); |
3872 | | if (allocrhs==NULL) break; |
3873 | | rhs=allocrhs; |
3874 | | } |
3875 | | } |
3876 | | #endif |
3877 | | /* [following code does not require input rounding] */ |
3878 | | |
3879 | | /* note whether signs differ [used all paths] */ |
3880 | 0 | diffsign=(Flag)((lhs->bits^rhs->bits^negate)&DECNEG); |
3881 | | |
3882 | | /* handle infinities and NaNs */ |
3883 | 0 | if (SPECIALARGS) { /* a special bit set */ |
3884 | 0 | if (SPECIALARGS & (DECSNAN | DECNAN)) /* a NaN */ |
3885 | 0 | decNaNs(res, lhs, rhs, set, status); |
3886 | 0 | else { /* one or two infinities */ |
3887 | 0 | if (decNumberIsInfinite(lhs)) { /* LHS is infinity */ |
3888 | | /* two infinities with different signs is invalid */ |
3889 | 0 | if (decNumberIsInfinite(rhs) && diffsign) { |
3890 | 0 | *status|=DEC_Invalid_operation; |
3891 | 0 | break; |
3892 | 0 | } |
3893 | 0 | bits=lhs->bits & DECNEG; /* get sign from LHS */ |
3894 | 0 | } |
3895 | 0 | else bits=(rhs->bits^negate) & DECNEG;/* RHS must be Infinity */ |
3896 | 0 | bits|=DECINF; |
3897 | 0 | uprv_decNumberZero(res); |
3898 | 0 | res->bits=bits; /* set +/- infinity */ |
3899 | 0 | } /* an infinity */ |
3900 | 0 | break; |
3901 | 0 | } |
3902 | | |
3903 | | /* Quick exit for add 0s; return the non-0, modified as need be */ |
3904 | 0 | if (ISZERO(lhs)) { |
3905 | 0 | Int adjust; /* work */ |
3906 | 0 | Int lexp=lhs->exponent; /* save in case LHS==RES */ |
3907 | 0 | bits=lhs->bits; /* .. */ |
3908 | 0 | residue=0; /* clear accumulator */ |
3909 | 0 | decCopyFit(res, rhs, set, &residue, status); /* copy (as needed) */ |
3910 | 0 | res->bits^=negate; /* flip if rhs was negated */ |
3911 | | #if DECSUBSET |
3912 | | if (set->extended) { /* exponents on zeros count */ |
3913 | | #endif |
3914 | | /* exponent will be the lower of the two */ |
3915 | 0 | adjust=lexp-res->exponent; /* adjustment needed [if -ve] */ |
3916 | 0 | if (ISZERO(res)) { /* both 0: special IEEE 754 rules */ |
3917 | 0 | if (adjust<0) res->exponent=lexp; /* set exponent */ |
3918 | | /* 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0 */ |
3919 | 0 | if (diffsign) { |
3920 | 0 | if (set->round!=DEC_ROUND_FLOOR) res->bits=0; |
3921 | 0 | else res->bits=DECNEG; /* preserve 0 sign */ |
3922 | 0 | } |
3923 | 0 | } |
3924 | 0 | else { /* non-0 res */ |
3925 | 0 | if (adjust<0) { /* 0-padding needed */ |
3926 | 0 | if ((res->digits-adjust)>set->digits) { |
3927 | 0 | adjust=res->digits-set->digits; /* to fit exactly */ |
3928 | 0 | *status|=DEC_Rounded; /* [but exact] */ |
3929 | 0 | } |
3930 | 0 | res->digits=decShiftToMost(res->lsu, res->digits, -adjust); |
3931 | 0 | res->exponent+=adjust; /* set the exponent. */ |
3932 | 0 | } |
3933 | 0 | } /* non-0 res */ |
3934 | | #if DECSUBSET |
3935 | | } /* extended */ |
3936 | | #endif |
3937 | 0 | decFinish(res, set, &residue, status); /* clean and finalize */ |
3938 | 0 | break;} |
3939 | | |
3940 | 0 | if (ISZERO(rhs)) { /* [lhs is non-zero] */ |
3941 | 0 | Int adjust; /* work */ |
3942 | 0 | Int rexp=rhs->exponent; /* save in case RHS==RES */ |
3943 | 0 | bits=rhs->bits; /* be clean */ |
3944 | 0 | residue=0; /* clear accumulator */ |
3945 | 0 | decCopyFit(res, lhs, set, &residue, status); /* copy (as needed) */ |
3946 | | #if DECSUBSET |
3947 | | if (set->extended) { /* exponents on zeros count */ |
3948 | | #endif |
3949 | | /* exponent will be the lower of the two */ |
3950 | | /* [0-0 case handled above] */ |
3951 | 0 | adjust=rexp-res->exponent; /* adjustment needed [if -ve] */ |
3952 | 0 | if (adjust<0) { /* 0-padding needed */ |
3953 | 0 | if ((res->digits-adjust)>set->digits) { |
3954 | 0 | adjust=res->digits-set->digits; /* to fit exactly */ |
3955 | 0 | *status|=DEC_Rounded; /* [but exact] */ |
3956 | 0 | } |
3957 | 0 | res->digits=decShiftToMost(res->lsu, res->digits, -adjust); |
3958 | 0 | res->exponent+=adjust; /* set the exponent. */ |
3959 | 0 | } |
3960 | | #if DECSUBSET |
3961 | | } /* extended */ |
3962 | | #endif |
3963 | 0 | decFinish(res, set, &residue, status); /* clean and finalize */ |
3964 | 0 | break;} |
3965 | | |
3966 | | /* [NB: both fastpath and mainpath code below assume these cases */ |
3967 | | /* (notably 0-0) have already been handled] */ |
3968 | | |
3969 | | /* calculate the padding needed to align the operands */ |
3970 | 0 | padding=rhs->exponent-lhs->exponent; |
3971 | | |
3972 | | /* Fastpath cases where the numbers are aligned and normal, the RHS */ |
3973 | | /* is all in one unit, no operand rounding is needed, and no carry, */ |
3974 | | /* lengthening, or borrow is needed */ |
3975 | 0 | if (padding==0 |
3976 | 0 | && rhs->digits<=DECDPUN |
3977 | 0 | && rhs->exponent>=set->emin /* [some normals drop through] */ |
3978 | 0 | && rhs->exponent<=set->emax-set->digits+1 /* [could clamp] */ |
3979 | 0 | && rhs->digits<=reqdigits |
3980 | 0 | && lhs->digits<=reqdigits) { |
3981 | 0 | Int partial=*lhs->lsu; |
3982 | 0 | if (!diffsign) { /* adding */ |
3983 | 0 | partial+=*rhs->lsu; |
3984 | 0 | if ((partial<=DECDPUNMAX) /* result fits in unit */ |
3985 | 0 | && (lhs->digits>=DECDPUN || /* .. and no digits-count change */ |
3986 | 0 | partial<(Int)powers[lhs->digits])) { /* .. */ |
3987 | 0 | if (res!=lhs) uprv_decNumberCopy(res, lhs); /* not in place */ |
3988 | 0 | *res->lsu=(Unit)partial; /* [copy could have overwritten RHS] */ |
3989 | 0 | break; |
3990 | 0 | } |
3991 | | /* else drop out for careful add */ |
3992 | 0 | } |
3993 | 0 | else { /* signs differ */ |
3994 | 0 | partial-=*rhs->lsu; |
3995 | 0 | if (partial>0) { /* no borrow needed, and non-0 result */ |
3996 | 0 | if (res!=lhs) uprv_decNumberCopy(res, lhs); /* not in place */ |
3997 | 0 | *res->lsu=(Unit)partial; |
3998 | | /* this could have reduced digits [but result>0] */ |
3999 | 0 | res->digits=decGetDigits(res->lsu, D2U(res->digits)); |
4000 | 0 | break; |
4001 | 0 | } |
4002 | | /* else drop out for careful subtract */ |
4003 | 0 | } |
4004 | 0 | } |
4005 | | |
4006 | | /* Now align (pad) the lhs or rhs so they can be added or */ |
4007 | | /* subtracted, as necessary. If one number is much larger than */ |
4008 | | /* the other (that is, if in plain form there is a least one */ |
4009 | | /* digit between the lowest digit of one and the highest of the */ |
4010 | | /* other) padding with up to DIGITS-1 trailing zeros may be */ |
4011 | | /* needed; then apply rounding (as exotic rounding modes may be */ |
4012 | | /* affected by the residue). */ |
4013 | 0 | rhsshift=0; /* rhs shift to left (padding) in Units */ |
4014 | 0 | bits=lhs->bits; /* assume sign is that of LHS */ |
4015 | 0 | mult=1; /* likely multiplier */ |
4016 | | |
4017 | | /* [if padding==0 the operands are aligned; no padding is needed] */ |
4018 | 0 | if (padding!=0) { |
4019 | | /* some padding needed; always pad the RHS, as any required */ |
4020 | | /* padding can then be effected by a simple combination of */ |
4021 | | /* shifts and a multiply */ |
4022 | 0 | Flag swapped=0; |
4023 | 0 | if (padding<0) { /* LHS needs the padding */ |
4024 | 0 | const decNumber *t; |
4025 | 0 | padding=-padding; /* will be +ve */ |
4026 | 0 | bits=(uByte)(rhs->bits^negate); /* assumed sign is now that of RHS */ |
4027 | 0 | t=lhs; lhs=rhs; rhs=t; |
4028 | 0 | swapped=1; |
4029 | 0 | } |
4030 | | |
4031 | | /* If, after pad, rhs would be longer than lhs by digits+1 or */ |
4032 | | /* more then lhs cannot affect the answer, except as a residue, */ |
4033 | | /* so only need to pad up to a length of DIGITS+1. */ |
4034 | 0 | if (rhs->digits+padding > lhs->digits+reqdigits+1) { |
4035 | | /* The RHS is sufficient */ |
4036 | | /* for residue use the relative sign indication... */ |
4037 | 0 | Int shift=reqdigits-rhs->digits; /* left shift needed */ |
4038 | 0 | residue=1; /* residue for rounding */ |
4039 | 0 | if (diffsign) residue=-residue; /* signs differ */ |
4040 | | /* copy, shortening if necessary */ |
4041 | 0 | decCopyFit(res, rhs, set, &residue, status); |
4042 | | /* if it was already shorter, then need to pad with zeros */ |
4043 | 0 | if (shift>0) { |
4044 | 0 | res->digits=decShiftToMost(res->lsu, res->digits, shift); |
4045 | 0 | res->exponent-=shift; /* adjust the exponent. */ |
4046 | 0 | } |
4047 | | /* flip the result sign if unswapped and rhs was negated */ |
4048 | 0 | if (!swapped) res->bits^=negate; |
4049 | 0 | decFinish(res, set, &residue, status); /* done */ |
4050 | 0 | break;} |
4051 | | |
4052 | | /* LHS digits may affect result */ |
4053 | 0 | rhsshift=D2U(padding+1)-1; /* this much by Unit shift .. */ |
4054 | 0 | mult=powers[padding-(rhsshift*DECDPUN)]; /* .. this by multiplication */ |
4055 | 0 | } /* padding needed */ |
4056 | | |
4057 | 0 | if (diffsign) mult=-mult; /* signs differ */ |
4058 | | |
4059 | | /* determine the longer operand */ |
4060 | 0 | maxdigits=rhs->digits+padding; /* virtual length of RHS */ |
4061 | 0 | if (lhs->digits>maxdigits) maxdigits=lhs->digits; |
4062 | | |
4063 | | /* Decide on the result buffer to use; if possible place directly */ |
4064 | | /* into result. */ |
4065 | 0 | acc=res->lsu; /* assume add direct to result */ |
4066 | | /* If destructive overlap, or the number is too long, or a carry or */ |
4067 | | /* borrow to DIGITS+1 might be possible, a buffer must be used. */ |
4068 | | /* [Might be worth more sophisticated tests when maxdigits==reqdigits] */ |
4069 | 0 | if ((maxdigits>=reqdigits) /* is, or could be, too large */ |
4070 | 0 | || (res==rhs && rhsshift>0)) { /* destructive overlap */ |
4071 | | /* buffer needed, choose it; units for maxdigits digits will be */ |
4072 | | /* needed, +1 Unit for carry or borrow */ |
4073 | 0 | Int need=D2U(maxdigits)+1; |
4074 | 0 | acc=accbuff; /* assume use local buffer */ |
4075 | 0 | if (need*sizeof(Unit)>sizeof(accbuff)) { |
4076 | | /* printf("malloc add %ld %ld\n", need, sizeof(accbuff)); */ |
4077 | 0 | allocacc=(Unit *)malloc(need*sizeof(Unit)); |
4078 | 0 | if (allocacc==NULL) { /* hopeless -- abandon */ |
4079 | 0 | *status|=DEC_Insufficient_storage; |
4080 | 0 | break;} |
4081 | 0 | acc=allocacc; |
4082 | 0 | } |
4083 | 0 | } |
4084 | | |
4085 | 0 | res->bits=(uByte)(bits&DECNEG); /* it's now safe to overwrite.. */ |
4086 | 0 | res->exponent=lhs->exponent; /* .. operands (even if aliased) */ |
4087 | |
|
4088 | | #if DECTRACE |
4089 | | decDumpAr('A', lhs->lsu, D2U(lhs->digits)); |
4090 | | decDumpAr('B', rhs->lsu, D2U(rhs->digits)); |
4091 | | printf(" :h: %ld %ld\n", rhsshift, mult); |
4092 | | #endif |
4093 | | |
4094 | | /* add [A+B*m] or subtract [A+B*(-m)] */ |
4095 | 0 | U_ASSERT(rhs->digits > 0); |
4096 | 0 | U_ASSERT(lhs->digits > 0); |
4097 | 0 | res->digits=decUnitAddSub(lhs->lsu, D2U(lhs->digits), |
4098 | 0 | rhs->lsu, D2U(rhs->digits), |
4099 | 0 | rhsshift, acc, mult) |
4100 | 0 | *DECDPUN; /* [units -> digits] */ |
4101 | 0 | if (res->digits<0) { /* borrowed... */ |
4102 | 0 | res->digits=-res->digits; |
4103 | 0 | res->bits^=DECNEG; /* flip the sign */ |
4104 | 0 | } |
4105 | | #if DECTRACE |
4106 | | decDumpAr('+', acc, D2U(res->digits)); |
4107 | | #endif |
4108 | | |
4109 | | /* If a buffer was used the result must be copied back, possibly */ |
4110 | | /* shortening. (If no buffer was used then the result must have */ |
4111 | | /* fit, so can't need rounding and residue must be 0.) */ |
4112 | 0 | residue=0; /* clear accumulator */ |
4113 | 0 | if (acc!=res->lsu) { |
4114 | | #if DECSUBSET |
4115 | | if (set->extended) { /* round from first significant digit */ |
4116 | | #endif |
4117 | | /* remove leading zeros that were added due to rounding up to */ |
4118 | | /* integral Units -- before the test for rounding. */ |
4119 | 0 | if (res->digits>reqdigits) |
4120 | 0 | res->digits=decGetDigits(acc, D2U(res->digits)); |
4121 | 0 | decSetCoeff(res, set, acc, res->digits, &residue, status); |
4122 | | #if DECSUBSET |
4123 | | } |
4124 | | else { /* subset arithmetic rounds from original significant digit */ |
4125 | | /* May have an underestimate. This only occurs when both */ |
4126 | | /* numbers fit in DECDPUN digits and are padding with a */ |
4127 | | /* negative multiple (-10, -100...) and the top digit(s) become */ |
4128 | | /* 0. (This only matters when using X3.274 rules where the */ |
4129 | | /* leading zero could be included in the rounding.) */ |
4130 | | if (res->digits<maxdigits) { |
4131 | | *(acc+D2U(res->digits))=0; /* ensure leading 0 is there */ |
4132 | | res->digits=maxdigits; |
4133 | | } |
4134 | | else { |
4135 | | /* remove leading zeros that added due to rounding up to */ |
4136 | | /* integral Units (but only those in excess of the original */ |
4137 | | /* maxdigits length, unless extended) before test for rounding. */ |
4138 | | if (res->digits>reqdigits) { |
4139 | | res->digits=decGetDigits(acc, D2U(res->digits)); |
4140 | | if (res->digits<maxdigits) res->digits=maxdigits; |
4141 | | } |
4142 | | } |
4143 | | decSetCoeff(res, set, acc, res->digits, &residue, status); |
4144 | | /* Now apply rounding if needed before removing leading zeros. */ |
4145 | | /* This is safe because subnormals are not a possibility */ |
4146 | | if (residue!=0) { |
4147 | | decApplyRound(res, set, residue, status); |
4148 | | residue=0; /* did what needed to be done */ |
4149 | | } |
4150 | | } /* subset */ |
4151 | | #endif |
4152 | 0 | } /* used buffer */ |
4153 | | |
4154 | | /* strip leading zeros [these were left on in case of subset subtract] */ |
4155 | 0 | res->digits=decGetDigits(res->lsu, D2U(res->digits)); |
4156 | | |
4157 | | /* apply checks and rounding */ |
4158 | 0 | decFinish(res, set, &residue, status); |
4159 | | |
4160 | | /* "When the sum of two operands with opposite signs is exactly */ |
4161 | | /* zero, the sign of that sum shall be '+' in all rounding modes */ |
4162 | | /* except round toward -Infinity, in which mode that sign shall be */ |
4163 | | /* '-'." [Subset zeros also never have '-', set by decFinish.] */ |
4164 | 0 | if (ISZERO(res) && diffsign |
4165 | | #if DECSUBSET |
4166 | | && set->extended |
4167 | | #endif |
4168 | 0 | && (*status&DEC_Inexact)==0) { |
4169 | 0 | if (set->round==DEC_ROUND_FLOOR) res->bits|=DECNEG; /* sign - */ |
4170 | 0 | else res->bits&=~DECNEG; /* sign + */ |
4171 | 0 | } |
4172 | 0 | } while(0); /* end protected */ |
4173 | | |
4174 | 0 | if (allocacc!=NULL) free(allocacc); /* drop any storage used */ |
4175 | | #if DECSUBSET |
4176 | | if (allocrhs!=NULL) free(allocrhs); /* .. */ |
4177 | | if (alloclhs!=NULL) free(alloclhs); /* .. */ |
4178 | | #endif |
4179 | 0 | return res; |
4180 | 0 | } /* decAddOp */ |
4181 | | |
4182 | | /* ------------------------------------------------------------------ */ |
4183 | | /* decDivideOp -- division operation */ |
4184 | | /* */ |
4185 | | /* This routine performs the calculations for all four division */ |
4186 | | /* operators (divide, divideInteger, remainder, remainderNear). */ |
4187 | | /* */ |
4188 | | /* C=A op B */ |
4189 | | /* */ |
4190 | | /* res is C, the result. C may be A and/or B (e.g., X=X/X) */ |
4191 | | /* lhs is A */ |
4192 | | /* rhs is B */ |
4193 | | /* set is the context */ |
4194 | | /* op is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively. */ |
4195 | | /* status is the usual accumulator */ |
4196 | | /* */ |
4197 | | /* C must have space for set->digits digits. */ |
4198 | | /* */ |
4199 | | /* ------------------------------------------------------------------ */ |
4200 | | /* The underlying algorithm of this routine is the same as in the */ |
4201 | | /* 1981 S/370 implementation, that is, non-restoring long division */ |
4202 | | /* with bi-unit (rather than bi-digit) estimation for each unit */ |
4203 | | /* multiplier. In this pseudocode overview, complications for the */ |
4204 | | /* Remainder operators and division residues for exact rounding are */ |
4205 | | /* omitted for clarity. */ |
4206 | | /* */ |
4207 | | /* Prepare operands and handle special values */ |
4208 | | /* Test for x/0 and then 0/x */ |
4209 | | /* Exp =Exp1 - Exp2 */ |
4210 | | /* Exp =Exp +len(var1) -len(var2) */ |
4211 | | /* Sign=Sign1 * Sign2 */ |
4212 | | /* Pad accumulator (Var1) to double-length with 0's (pad1) */ |
4213 | | /* Pad Var2 to same length as Var1 */ |
4214 | | /* msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round */ |
4215 | | /* have=0 */ |
4216 | | /* Do until (have=digits+1 OR residue=0) */ |
4217 | | /* if exp<0 then if integer divide/residue then leave */ |
4218 | | /* this_unit=0 */ |
4219 | | /* Do forever */ |
4220 | | /* compare numbers */ |
4221 | | /* if <0 then leave inner_loop */ |
4222 | | /* if =0 then (* quick exit without subtract *) do */ |
4223 | | /* this_unit=this_unit+1; output this_unit */ |
4224 | | /* leave outer_loop; end */ |
4225 | | /* Compare lengths of numbers (mantissae): */ |
4226 | | /* If same then tops2=msu2pair -- {units 1&2 of var2} */ |
4227 | | /* else tops2=msu2plus -- {0, unit 1 of var2} */ |
4228 | | /* tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */ |
4229 | | /* mult=tops1/tops2 -- Good and safe guess at divisor */ |
4230 | | /* if mult=0 then mult=1 */ |
4231 | | /* this_unit=this_unit+mult */ |
4232 | | /* subtract */ |
4233 | | /* end inner_loop */ |
4234 | | /* if have\=0 | this_unit\=0 then do */ |
4235 | | /* output this_unit */ |
4236 | | /* have=have+1; end */ |
4237 | | /* var2=var2/10 */ |
4238 | | /* exp=exp-1 */ |
4239 | | /* end outer_loop */ |
4240 | | /* exp=exp+1 -- set the proper exponent */ |
4241 | | /* if have=0 then generate answer=0 */ |
4242 | | /* Return (Result is defined by Var1) */ |
4243 | | /* */ |
4244 | | /* ------------------------------------------------------------------ */ |
4245 | | /* Two working buffers are needed during the division; one (digits+ */ |
4246 | | /* 1) to accumulate the result, and the other (up to 2*digits+1) for */ |
4247 | | /* long subtractions. These are acc and var1 respectively. */ |
4248 | | /* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/ |
4249 | | /* The static buffers may be larger than might be expected to allow */ |
4250 | | /* for calls from higher-level functions (notable exp). */ |
4251 | | /* ------------------------------------------------------------------ */ |
4252 | | static decNumber * decDivideOp(decNumber *res, |
4253 | | const decNumber *lhs, const decNumber *rhs, |
4254 | 0 | decContext *set, Flag op, uInt *status) { |
4255 | | #if DECSUBSET |
4256 | | decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ |
4257 | | decNumber *allocrhs=NULL; /* .., rhs */ |
4258 | | #endif |
4259 | 0 | Unit accbuff[SD2U(DECBUFFER+DECDPUN+10)]; /* local buffer */ |
4260 | 0 | Unit *acc=accbuff; /* -> accumulator array for result */ |
4261 | 0 | Unit *allocacc=NULL; /* -> allocated buffer, iff allocated */ |
4262 | 0 | Unit *accnext; /* -> where next digit will go */ |
4263 | 0 | Int acclength; /* length of acc needed [Units] */ |
4264 | 0 | Int accunits; /* count of units accumulated */ |
4265 | 0 | Int accdigits; /* count of digits accumulated */ |
4266 | |
|
4267 | 0 | Unit varbuff[SD2U(DECBUFFER*2+DECDPUN)]; /* buffer for var1 */ |
4268 | 0 | Unit *var1=varbuff; /* -> var1 array for long subtraction */ |
4269 | 0 | Unit *varalloc=NULL; /* -> allocated buffer, iff used */ |
4270 | 0 | Unit *msu1; /* -> msu of var1 */ |
4271 | |
|
4272 | 0 | const Unit *var2; /* -> var2 array */ |
4273 | 0 | const Unit *msu2; /* -> msu of var2 */ |
4274 | 0 | Int msu2plus; /* msu2 plus one [does not vary] */ |
4275 | 0 | eInt msu2pair; /* msu2 pair plus one [does not vary] */ |
4276 | |
|
4277 | 0 | Int var1units, var2units; /* actual lengths */ |
4278 | 0 | Int var2ulen; /* logical length (units) */ |
4279 | 0 | Int var1initpad=0; /* var1 initial padding (digits) */ |
4280 | 0 | Int maxdigits; /* longest LHS or required acc length */ |
4281 | 0 | Int mult; /* multiplier for subtraction */ |
4282 | 0 | Unit thisunit; /* current unit being accumulated */ |
4283 | 0 | Int residue; /* for rounding */ |
4284 | 0 | Int reqdigits=set->digits; /* requested DIGITS */ |
4285 | 0 | Int exponent; /* working exponent */ |
4286 | 0 | Int maxexponent=0; /* DIVIDE maximum exponent if unrounded */ |
4287 | 0 | uByte bits; /* working sign */ |
4288 | 0 | Unit *target; /* work */ |
4289 | 0 | const Unit *source; /* .. */ |
4290 | 0 | uInt const *pow; /* .. */ |
4291 | 0 | Int shift, cut; /* .. */ |
4292 | | #if DECSUBSET |
4293 | | Int dropped; /* work */ |
4294 | | #endif |
4295 | |
|
4296 | | #if DECCHECK |
4297 | | if (decCheckOperands(res, lhs, rhs, set)) return res; |
4298 | | #endif |
4299 | |
|
4300 | 0 | do { /* protect allocated storage */ |
4301 | | #if DECSUBSET |
4302 | | if (!set->extended) { |
4303 | | /* reduce operands and set lostDigits status, as needed */ |
4304 | | if (lhs->digits>reqdigits) { |
4305 | | alloclhs=decRoundOperand(lhs, set, status); |
4306 | | if (alloclhs==NULL) break; |
4307 | | lhs=alloclhs; |
4308 | | } |
4309 | | if (rhs->digits>reqdigits) { |
4310 | | allocrhs=decRoundOperand(rhs, set, status); |
4311 | | if (allocrhs==NULL) break; |
4312 | | rhs=allocrhs; |
4313 | | } |
4314 | | } |
4315 | | #endif |
4316 | | /* [following code does not require input rounding] */ |
4317 | |
|
4318 | 0 | bits=(lhs->bits^rhs->bits)&DECNEG; /* assumed sign for divisions */ |
4319 | | |
4320 | | /* handle infinities and NaNs */ |
4321 | 0 | if (SPECIALARGS) { /* a special bit set */ |
4322 | 0 | if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */ |
4323 | 0 | decNaNs(res, lhs, rhs, set, status); |
4324 | 0 | break; |
4325 | 0 | } |
4326 | | /* one or two infinities */ |
4327 | 0 | if (decNumberIsInfinite(lhs)) { /* LHS (dividend) is infinite */ |
4328 | 0 | if (decNumberIsInfinite(rhs) || /* two infinities are invalid .. */ |
4329 | 0 | op & (REMAINDER | REMNEAR)) { /* as is remainder of infinity */ |
4330 | 0 | *status|=DEC_Invalid_operation; |
4331 | 0 | break; |
4332 | 0 | } |
4333 | | /* [Note that infinity/0 raises no exceptions] */ |
4334 | 0 | uprv_decNumberZero(res); |
4335 | 0 | res->bits=bits|DECINF; /* set +/- infinity */ |
4336 | 0 | break; |
4337 | 0 | } |
4338 | 0 | else { /* RHS (divisor) is infinite */ |
4339 | 0 | residue=0; |
4340 | 0 | if (op&(REMAINDER|REMNEAR)) { |
4341 | | /* result is [finished clone of] lhs */ |
4342 | 0 | decCopyFit(res, lhs, set, &residue, status); |
4343 | 0 | } |
4344 | 0 | else { /* a division */ |
4345 | 0 | uprv_decNumberZero(res); |
4346 | 0 | res->bits=bits; /* set +/- zero */ |
4347 | | /* for DIVIDEINT the exponent is always 0. For DIVIDE, result */ |
4348 | | /* is a 0 with infinitely negative exponent, clamped to minimum */ |
4349 | 0 | if (op&DIVIDE) { |
4350 | 0 | res->exponent=set->emin-set->digits+1; |
4351 | 0 | *status|=DEC_Clamped; |
4352 | 0 | } |
4353 | 0 | } |
4354 | 0 | decFinish(res, set, &residue, status); |
4355 | 0 | break; |
4356 | 0 | } |
4357 | 0 | } |
4358 | | |
4359 | | /* handle 0 rhs (x/0) */ |
4360 | 0 | if (ISZERO(rhs)) { /* x/0 is always exceptional */ |
4361 | 0 | if (ISZERO(lhs)) { |
4362 | 0 | uprv_decNumberZero(res); /* [after lhs test] */ |
4363 | 0 | *status|=DEC_Division_undefined;/* 0/0 will become NaN */ |
4364 | 0 | } |
4365 | 0 | else { |
4366 | 0 | uprv_decNumberZero(res); |
4367 | 0 | if (op&(REMAINDER|REMNEAR)) *status|=DEC_Invalid_operation; |
4368 | 0 | else { |
4369 | 0 | *status|=DEC_Division_by_zero; /* x/0 */ |
4370 | 0 | res->bits=bits|DECINF; /* .. is +/- Infinity */ |
4371 | 0 | } |
4372 | 0 | } |
4373 | 0 | break;} |
4374 | | |
4375 | | /* handle 0 lhs (0/x) */ |
4376 | 0 | if (ISZERO(lhs)) { /* 0/x [x!=0] */ |
4377 | | #if DECSUBSET |
4378 | | if (!set->extended) uprv_decNumberZero(res); |
4379 | | else { |
4380 | | #endif |
4381 | 0 | if (op&DIVIDE) { |
4382 | 0 | residue=0; |
4383 | 0 | exponent=lhs->exponent-rhs->exponent; /* ideal exponent */ |
4384 | 0 | uprv_decNumberCopy(res, lhs); /* [zeros always fit] */ |
4385 | 0 | res->bits=bits; /* sign as computed */ |
4386 | 0 | res->exponent=exponent; /* exponent, too */ |
4387 | 0 | decFinalize(res, set, &residue, status); /* check exponent */ |
4388 | 0 | } |
4389 | 0 | else if (op&DIVIDEINT) { |
4390 | 0 | uprv_decNumberZero(res); /* integer 0 */ |
4391 | 0 | res->bits=bits; /* sign as computed */ |
4392 | 0 | } |
4393 | 0 | else { /* a remainder */ |
4394 | 0 | exponent=rhs->exponent; /* [save in case overwrite] */ |
4395 | 0 | uprv_decNumberCopy(res, lhs); /* [zeros always fit] */ |
4396 | 0 | if (exponent<res->exponent) res->exponent=exponent; /* use lower */ |
4397 | 0 | } |
4398 | | #if DECSUBSET |
4399 | | } |
4400 | | #endif |
4401 | 0 | break;} |
4402 | | |
4403 | | /* Precalculate exponent. This starts off adjusted (and hence fits */ |
4404 | | /* in 31 bits) and becomes the usual unadjusted exponent as the */ |
4405 | | /* division proceeds. The order of evaluation is important, here, */ |
4406 | | /* to avoid wrap. */ |
4407 | 0 | exponent=(lhs->exponent+lhs->digits)-(rhs->exponent+rhs->digits); |
4408 | | |
4409 | | /* If the working exponent is -ve, then some quick exits are */ |
4410 | | /* possible because the quotient is known to be <1 */ |
4411 | | /* [for REMNEAR, it needs to be < -1, as -0.5 could need work] */ |
4412 | 0 | if (exponent<0 && !(op==DIVIDE)) { |
4413 | 0 | if (op&DIVIDEINT) { |
4414 | 0 | uprv_decNumberZero(res); /* integer part is 0 */ |
4415 | | #if DECSUBSET |
4416 | | if (set->extended) |
4417 | | #endif |
4418 | 0 | res->bits=bits; /* set +/- zero */ |
4419 | 0 | break;} |
4420 | | /* fastpath remainders so long as the lhs has the smaller */ |
4421 | | /* (or equal) exponent */ |
4422 | 0 | if (lhs->exponent<=rhs->exponent) { |
4423 | 0 | if (op&REMAINDER || exponent<-1) { |
4424 | | /* It is REMAINDER or safe REMNEAR; result is [finished */ |
4425 | | /* clone of] lhs (r = x - 0*y) */ |
4426 | 0 | residue=0; |
4427 | 0 | decCopyFit(res, lhs, set, &residue, status); |
4428 | 0 | decFinish(res, set, &residue, status); |
4429 | 0 | break; |
4430 | 0 | } |
4431 | | /* [unsafe REMNEAR drops through] */ |
4432 | 0 | } |
4433 | 0 | } /* fastpaths */ |
4434 | | |
4435 | | /* Long (slow) division is needed; roll up the sleeves... */ |
4436 | | |
4437 | | /* The accumulator will hold the quotient of the division. */ |
4438 | | /* If it needs to be too long for stack storage, then allocate. */ |
4439 | 0 | acclength=D2U(reqdigits+DECDPUN); /* in Units */ |
4440 | 0 | if (acclength*sizeof(Unit)>sizeof(accbuff)) { |
4441 | | /* printf("malloc dvacc %ld units\n", acclength); */ |
4442 | 0 | allocacc=(Unit *)malloc(acclength*sizeof(Unit)); |
4443 | 0 | if (allocacc==NULL) { /* hopeless -- abandon */ |
4444 | 0 | *status|=DEC_Insufficient_storage; |
4445 | 0 | break;} |
4446 | 0 | acc=allocacc; /* use the allocated space */ |
4447 | 0 | } |
4448 | | |
4449 | | /* var1 is the padded LHS ready for subtractions. */ |
4450 | | /* If it needs to be too long for stack storage, then allocate. */ |
4451 | | /* The maximum units needed for var1 (long subtraction) is: */ |
4452 | | /* Enough for */ |
4453 | | /* (rhs->digits+reqdigits-1) -- to allow full slide to right */ |
4454 | | /* or (lhs->digits) -- to allow for long lhs */ |
4455 | | /* whichever is larger */ |
4456 | | /* +1 -- for rounding of slide to right */ |
4457 | | /* +1 -- for leading 0s */ |
4458 | | /* +1 -- for pre-adjust if a remainder or DIVIDEINT */ |
4459 | | /* [Note: unused units do not participate in decUnitAddSub data] */ |
4460 | 0 | maxdigits=rhs->digits+reqdigits-1; |
4461 | 0 | if (lhs->digits>maxdigits) maxdigits=lhs->digits; |
4462 | 0 | var1units=D2U(maxdigits)+2; |
4463 | | /* allocate a guard unit above msu1 for REMAINDERNEAR */ |
4464 | 0 | if (!(op&DIVIDE)) var1units++; |
4465 | 0 | if ((var1units+1)*sizeof(Unit)>sizeof(varbuff)) { |
4466 | | /* printf("malloc dvvar %ld units\n", var1units+1); */ |
4467 | 0 | varalloc=(Unit *)malloc((var1units+1)*sizeof(Unit)); |
4468 | 0 | if (varalloc==NULL) { /* hopeless -- abandon */ |
4469 | 0 | *status|=DEC_Insufficient_storage; |
4470 | 0 | break;} |
4471 | 0 | var1=varalloc; /* use the allocated space */ |
4472 | 0 | } |
4473 | | |
4474 | | /* Extend the lhs and rhs to full long subtraction length. The lhs */ |
4475 | | /* is truly extended into the var1 buffer, with 0 padding, so a */ |
4476 | | /* subtract in place is always possible. The rhs (var2) has */ |
4477 | | /* virtual padding (implemented by decUnitAddSub). */ |
4478 | | /* One guard unit was allocated above msu1 for rem=rem+rem in */ |
4479 | | /* REMAINDERNEAR. */ |
4480 | 0 | msu1=var1+var1units-1; /* msu of var1 */ |
4481 | 0 | source=lhs->lsu+D2U(lhs->digits)-1; /* msu of input array */ |
4482 | 0 | for (target=msu1; source>=lhs->lsu; source--, target--) *target=*source; |
4483 | 0 | for (; target>=var1; target--) *target=0; |
4484 | | |
4485 | | /* rhs (var2) is left-aligned with var1 at the start */ |
4486 | 0 | var2ulen=var1units; /* rhs logical length (units) */ |
4487 | 0 | var2units=D2U(rhs->digits); /* rhs actual length (units) */ |
4488 | 0 | var2=rhs->lsu; /* -> rhs array */ |
4489 | 0 | msu2=var2+var2units-1; /* -> msu of var2 [never changes] */ |
4490 | | /* now set up the variables which will be used for estimating the */ |
4491 | | /* multiplication factor. If these variables are not exact, add */ |
4492 | | /* 1 to make sure that the multiplier is never overestimated. */ |
4493 | 0 | msu2plus=*msu2; /* it's value .. */ |
4494 | 0 | if (var2units>1) msu2plus++; /* .. +1 if any more */ |
4495 | 0 | msu2pair=(eInt)*msu2*(DECDPUNMAX+1);/* top two pair .. */ |
4496 | 0 | if (var2units>1) { /* .. [else treat 2nd as 0] */ |
4497 | 0 | msu2pair+=*(msu2-1); /* .. */ |
4498 | 0 | if (var2units>2) msu2pair++; /* .. +1 if any more */ |
4499 | 0 | } |
4500 | | |
4501 | | /* The calculation is working in units, which may have leading zeros, */ |
4502 | | /* but the exponent was calculated on the assumption that they are */ |
4503 | | /* both left-aligned. Adjust the exponent to compensate: add the */ |
4504 | | /* number of leading zeros in var1 msu and subtract those in var2 msu. */ |
4505 | | /* [This is actually done by counting the digits and negating, as */ |
4506 | | /* lead1=DECDPUN-digits1, and similarly for lead2.] */ |
4507 | 0 | for (pow=&powers[1]; *msu1>=*pow; pow++) exponent--; |
4508 | 0 | for (pow=&powers[1]; *msu2>=*pow; pow++) exponent++; |
4509 | | |
4510 | | /* Now, if doing an integer divide or remainder, ensure that */ |
4511 | | /* the result will be Unit-aligned. To do this, shift the var1 */ |
4512 | | /* accumulator towards least if need be. (It's much easier to */ |
4513 | | /* do this now than to reassemble the residue afterwards, if */ |
4514 | | /* doing a remainder.) Also ensure the exponent is not negative. */ |
4515 | 0 | if (!(op&DIVIDE)) { |
4516 | 0 | Unit *u; /* work */ |
4517 | | /* save the initial 'false' padding of var1, in digits */ |
4518 | 0 | var1initpad=(var1units-D2U(lhs->digits))*DECDPUN; |
4519 | | /* Determine the shift to do. */ |
4520 | 0 | if (exponent<0) cut=-exponent; |
4521 | 0 | else cut=DECDPUN-exponent%DECDPUN; |
4522 | 0 | decShiftToLeast(var1, var1units, cut); |
4523 | 0 | exponent+=cut; /* maintain numerical value */ |
4524 | 0 | var1initpad-=cut; /* .. and reduce padding */ |
4525 | | /* clean any most-significant units which were just emptied */ |
4526 | 0 | for (u=msu1; cut>=DECDPUN; cut-=DECDPUN, u--) *u=0; |
4527 | 0 | } /* align */ |
4528 | 0 | else { /* is DIVIDE */ |
4529 | 0 | maxexponent=lhs->exponent-rhs->exponent; /* save */ |
4530 | | /* optimization: if the first iteration will just produce 0, */ |
4531 | | /* preadjust to skip it [valid for DIVIDE only] */ |
4532 | 0 | if (*msu1<*msu2) { |
4533 | 0 | var2ulen--; /* shift down */ |
4534 | 0 | exponent-=DECDPUN; /* update the exponent */ |
4535 | 0 | } |
4536 | 0 | } |
4537 | | |
4538 | | /* ---- start the long-division loops ------------------------------ */ |
4539 | 0 | accunits=0; /* no units accumulated yet */ |
4540 | 0 | accdigits=0; /* .. or digits */ |
4541 | 0 | accnext=acc+acclength-1; /* -> msu of acc [NB: allows digits+1] */ |
4542 | 0 | for (;;) { /* outer forever loop */ |
4543 | 0 | thisunit=0; /* current unit assumed 0 */ |
4544 | | /* find the next unit */ |
4545 | 0 | for (;;) { /* inner forever loop */ |
4546 | | /* strip leading zero units [from either pre-adjust or from */ |
4547 | | /* subtract last time around]. Leave at least one unit. */ |
4548 | 0 | for (; *msu1==0 && msu1>var1; msu1--) var1units--; |
4549 | |
|
4550 | 0 | if (var1units<var2ulen) break; /* var1 too low for subtract */ |
4551 | 0 | if (var1units==var2ulen) { /* unit-by-unit compare needed */ |
4552 | | /* compare the two numbers, from msu */ |
4553 | 0 | const Unit *pv1, *pv2; |
4554 | 0 | Unit v2; /* units to compare */ |
4555 | 0 | pv2=msu2; /* -> msu */ |
4556 | 0 | for (pv1=msu1; ; pv1--, pv2--) { |
4557 | | /* v1=*pv1 -- always OK */ |
4558 | 0 | v2=0; /* assume in padding */ |
4559 | 0 | if (pv2>=var2) v2=*pv2; /* in range */ |
4560 | 0 | if (*pv1!=v2) break; /* no longer the same */ |
4561 | 0 | if (pv1==var1) break; /* done; leave pv1 as is */ |
4562 | 0 | } |
4563 | | /* here when all inspected or a difference seen */ |
4564 | 0 | if (*pv1<v2) break; /* var1 too low to subtract */ |
4565 | 0 | if (*pv1==v2) { /* var1 == var2 */ |
4566 | | /* reach here if var1 and var2 are identical; subtraction */ |
4567 | | /* would increase digit by one, and the residue will be 0 so */ |
4568 | | /* the calculation is done; leave the loop with residue=0. */ |
4569 | 0 | thisunit++; /* as though subtracted */ |
4570 | 0 | *var1=0; /* set var1 to 0 */ |
4571 | 0 | var1units=1; /* .. */ |
4572 | 0 | break; /* from inner */ |
4573 | 0 | } /* var1 == var2 */ |
4574 | | /* *pv1>v2. Prepare for real subtraction; the lengths are equal */ |
4575 | | /* Estimate the multiplier (there's always a msu1-1)... */ |
4576 | | /* Bring in two units of var2 to provide a good estimate. */ |
4577 | 0 | mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2pair); |
4578 | 0 | } /* lengths the same */ |
4579 | 0 | else { /* var1units > var2ulen, so subtraction is safe */ |
4580 | | /* The var2 msu is one unit towards the lsu of the var1 msu, */ |
4581 | | /* so only one unit for var2 can be used. */ |
4582 | 0 | mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2plus); |
4583 | 0 | } |
4584 | 0 | if (mult==0) mult=1; /* must always be at least 1 */ |
4585 | | /* subtraction needed; var1 is > var2 */ |
4586 | 0 | thisunit=(Unit)(thisunit+mult); /* accumulate */ |
4587 | | /* subtract var1-var2, into var1; only the overlap needs */ |
4588 | | /* processing, as this is an in-place calculation */ |
4589 | 0 | shift=var2ulen-var2units; |
4590 | | #if DECTRACE |
4591 | | decDumpAr('1', &var1[shift], var1units-shift); |
4592 | | decDumpAr('2', var2, var2units); |
4593 | | printf("m=%ld\n", -mult); |
4594 | | #endif |
4595 | 0 | decUnitAddSub(&var1[shift], var1units-shift, |
4596 | 0 | var2, var2units, 0, |
4597 | 0 | &var1[shift], -mult); |
4598 | | #if DECTRACE |
4599 | | decDumpAr('#', &var1[shift], var1units-shift); |
4600 | | #endif |
4601 | | /* var1 now probably has leading zeros; these are removed at the */ |
4602 | | /* top of the inner loop. */ |
4603 | 0 | } /* inner loop */ |
4604 | | |
4605 | | /* The next unit has been calculated in full; unless it's a */ |
4606 | | /* leading zero, add to acc */ |
4607 | 0 | if (accunits!=0 || thisunit!=0) { /* is first or non-zero */ |
4608 | 0 | *accnext=thisunit; /* store in accumulator */ |
4609 | | /* account exactly for the new digits */ |
4610 | 0 | if (accunits==0) { |
4611 | 0 | accdigits++; /* at least one */ |
4612 | 0 | for (pow=&powers[1]; thisunit>=*pow; pow++) accdigits++; |
4613 | 0 | } |
4614 | 0 | else accdigits+=DECDPUN; |
4615 | 0 | accunits++; /* update count */ |
4616 | 0 | accnext--; /* ready for next */ |
4617 | 0 | if (accdigits>reqdigits) break; /* have enough digits */ |
4618 | 0 | } |
4619 | | |
4620 | | /* if the residue is zero, the operation is done (unless divide */ |
4621 | | /* or divideInteger and still not enough digits yet) */ |
4622 | 0 | if (*var1==0 && var1units==1) { /* residue is 0 */ |
4623 | 0 | if (op&(REMAINDER|REMNEAR)) break; |
4624 | 0 | if ((op&DIVIDE) && (exponent<=maxexponent)) break; |
4625 | | /* [drop through if divideInteger] */ |
4626 | 0 | } |
4627 | | /* also done enough if calculating remainder or integer */ |
4628 | | /* divide and just did the last ('units') unit */ |
4629 | 0 | if (exponent==0 && !(op&DIVIDE)) break; |
4630 | | |
4631 | | /* to get here, var1 is less than var2, so divide var2 by the per- */ |
4632 | | /* Unit power of ten and go for the next digit */ |
4633 | 0 | var2ulen--; /* shift down */ |
4634 | 0 | exponent-=DECDPUN; /* update the exponent */ |
4635 | 0 | } /* outer loop */ |
4636 | | |
4637 | | /* ---- division is complete --------------------------------------- */ |
4638 | | /* here: acc has at least reqdigits+1 of good results (or fewer */ |
4639 | | /* if early stop), starting at accnext+1 (its lsu) */ |
4640 | | /* var1 has any residue at the stopping point */ |
4641 | | /* accunits is the number of digits collected in acc */ |
4642 | 0 | if (accunits==0) { /* acc is 0 */ |
4643 | 0 | accunits=1; /* show have a unit .. */ |
4644 | 0 | accdigits=1; /* .. */ |
4645 | 0 | *accnext=0; /* .. whose value is 0 */ |
4646 | 0 | } |
4647 | 0 | else accnext++; /* back to last placed */ |
4648 | | /* accnext now -> lowest unit of result */ |
4649 | |
|
4650 | 0 | residue=0; /* assume no residue */ |
4651 | 0 | if (op&DIVIDE) { |
4652 | | /* record the presence of any residue, for rounding */ |
4653 | 0 | if (*var1!=0 || var1units>1) residue=1; |
4654 | 0 | else { /* no residue */ |
4655 | | /* Had an exact division; clean up spurious trailing 0s. */ |
4656 | | /* There will be at most DECDPUN-1, from the final multiply, */ |
4657 | | /* and then only if the result is non-0 (and even) and the */ |
4658 | | /* exponent is 'loose'. */ |
4659 | | #if DECDPUN>1 |
4660 | | Unit lsu=*accnext; |
4661 | | if (!(lsu&0x01) && (lsu!=0)) { |
4662 | | /* count the trailing zeros */ |
4663 | | Int drop=0; |
4664 | | for (;; drop++) { /* [will terminate because lsu!=0] */ |
4665 | | if (exponent>=maxexponent) break; /* don't chop real 0s */ |
4666 | | #if DECDPUN<=4 |
4667 | | if ((lsu-QUOT10(lsu, drop+1) |
4668 | | *powers[drop+1])!=0) break; /* found non-0 digit */ |
4669 | | #else |
4670 | | if (lsu%powers[drop+1]!=0) break; /* found non-0 digit */ |
4671 | | #endif |
4672 | | exponent++; |
4673 | | } |
4674 | | if (drop>0) { |
4675 | | accunits=decShiftToLeast(accnext, accunits, drop); |
4676 | | accdigits=decGetDigits(accnext, accunits); |
4677 | | accunits=D2U(accdigits); |
4678 | | /* [exponent was adjusted in the loop] */ |
4679 | | } |
4680 | | } /* neither odd nor 0 */ |
4681 | | #endif |
4682 | 0 | } /* exact divide */ |
4683 | 0 | } /* divide */ |
4684 | 0 | else /* op!=DIVIDE */ { |
4685 | | /* check for coefficient overflow */ |
4686 | 0 | if (accdigits+exponent>reqdigits) { |
4687 | 0 | *status|=DEC_Division_impossible; |
4688 | 0 | break; |
4689 | 0 | } |
4690 | 0 | if (op & (REMAINDER|REMNEAR)) { |
4691 | | /* [Here, the exponent will be 0, because var1 was adjusted */ |
4692 | | /* appropriately.] */ |
4693 | 0 | Int postshift; /* work */ |
4694 | 0 | Flag wasodd=0; /* integer was odd */ |
4695 | 0 | Unit *quotlsu; /* for save */ |
4696 | 0 | Int quotdigits; /* .. */ |
4697 | |
|
4698 | 0 | bits=lhs->bits; /* remainder sign is always as lhs */ |
4699 | | |
4700 | | /* Fastpath when residue is truly 0 is worthwhile [and */ |
4701 | | /* simplifies the code below] */ |
4702 | 0 | if (*var1==0 && var1units==1) { /* residue is 0 */ |
4703 | 0 | Int exp=lhs->exponent; /* save min(exponents) */ |
4704 | 0 | if (rhs->exponent<exp) exp=rhs->exponent; |
4705 | 0 | uprv_decNumberZero(res); /* 0 coefficient */ |
4706 | | #if DECSUBSET |
4707 | | if (set->extended) |
4708 | | #endif |
4709 | 0 | res->exponent=exp; /* .. with proper exponent */ |
4710 | 0 | res->bits=(uByte)(bits&DECNEG); /* [cleaned] */ |
4711 | 0 | decFinish(res, set, &residue, status); /* might clamp */ |
4712 | 0 | break; |
4713 | 0 | } |
4714 | | /* note if the quotient was odd */ |
4715 | 0 | if (*accnext & 0x01) wasodd=1; /* acc is odd */ |
4716 | 0 | quotlsu=accnext; /* save in case need to reinspect */ |
4717 | 0 | quotdigits=accdigits; /* .. */ |
4718 | | |
4719 | | /* treat the residue, in var1, as the value to return, via acc */ |
4720 | | /* calculate the unused zero digits. This is the smaller of: */ |
4721 | | /* var1 initial padding (saved above) */ |
4722 | | /* var2 residual padding, which happens to be given by: */ |
4723 | 0 | postshift=var1initpad+exponent-lhs->exponent+rhs->exponent; |
4724 | | /* [the 'exponent' term accounts for the shifts during divide] */ |
4725 | 0 | if (var1initpad<postshift) postshift=var1initpad; |
4726 | | |
4727 | | /* shift var1 the requested amount, and adjust its digits */ |
4728 | 0 | var1units=decShiftToLeast(var1, var1units, postshift); |
4729 | 0 | accnext=var1; |
4730 | 0 | accdigits=decGetDigits(var1, var1units); |
4731 | 0 | accunits=D2U(accdigits); |
4732 | |
|
4733 | 0 | exponent=lhs->exponent; /* exponent is smaller of lhs & rhs */ |
4734 | 0 | if (rhs->exponent<exponent) exponent=rhs->exponent; |
4735 | | |
4736 | | /* Now correct the result if doing remainderNear; if it */ |
4737 | | /* (looking just at coefficients) is > rhs/2, or == rhs/2 and */ |
4738 | | /* the integer was odd then the result should be rem-rhs. */ |
4739 | 0 | if (op&REMNEAR) { |
4740 | 0 | Int compare, tarunits; /* work */ |
4741 | 0 | Unit *up; /* .. */ |
4742 | | /* calculate remainder*2 into the var1 buffer (which has */ |
4743 | | /* 'headroom' of an extra unit and hence enough space) */ |
4744 | | /* [a dedicated 'double' loop would be faster, here] */ |
4745 | 0 | tarunits=decUnitAddSub(accnext, accunits, accnext, accunits, |
4746 | 0 | 0, accnext, 1); |
4747 | | /* decDumpAr('r', accnext, tarunits); */ |
4748 | | |
4749 | | /* Here, accnext (var1) holds tarunits Units with twice the */ |
4750 | | /* remainder's coefficient, which must now be compared to the */ |
4751 | | /* RHS. The remainder's exponent may be smaller than the RHS's. */ |
4752 | 0 | compare=decUnitCompare(accnext, tarunits, rhs->lsu, D2U(rhs->digits), |
4753 | 0 | rhs->exponent-exponent); |
4754 | 0 | if (compare==BADINT) { /* deep trouble */ |
4755 | 0 | *status|=DEC_Insufficient_storage; |
4756 | 0 | break;} |
4757 | | |
4758 | | /* now restore the remainder by dividing by two; the lsu */ |
4759 | | /* is known to be even. */ |
4760 | 0 | for (up=accnext; up<accnext+tarunits; up++) { |
4761 | 0 | Int half; /* half to add to lower unit */ |
4762 | 0 | half=*up & 0x01; |
4763 | 0 | *up/=2; /* [shift] */ |
4764 | 0 | if (!half) continue; |
4765 | 0 | *(up-1)+=(DECDPUNMAX+1)/2; |
4766 | 0 | } |
4767 | | /* [accunits still describes the original remainder length] */ |
4768 | |
|
4769 | 0 | if (compare>0 || (compare==0 && wasodd)) { /* adjustment needed */ |
4770 | 0 | Int exp, expunits, exprem; /* work */ |
4771 | | /* This is effectively causing round-up of the quotient, */ |
4772 | | /* so if it was the rare case where it was full and all */ |
4773 | | /* nines, it would overflow and hence division-impossible */ |
4774 | | /* should be raised */ |
4775 | 0 | Flag allnines=0; /* 1 if quotient all nines */ |
4776 | 0 | if (quotdigits==reqdigits) { /* could be borderline */ |
4777 | 0 | for (up=quotlsu; ; up++) { |
4778 | 0 | if (quotdigits>DECDPUN) { |
4779 | 0 | if (*up!=DECDPUNMAX) break;/* non-nines */ |
4780 | 0 | } |
4781 | 0 | else { /* this is the last Unit */ |
4782 | 0 | if (*up==powers[quotdigits]-1) allnines=1; |
4783 | 0 | break; |
4784 | 0 | } |
4785 | 0 | quotdigits-=DECDPUN; /* checked those digits */ |
4786 | 0 | } /* up */ |
4787 | 0 | } /* borderline check */ |
4788 | 0 | if (allnines) { |
4789 | 0 | *status|=DEC_Division_impossible; |
4790 | 0 | break;} |
4791 | | |
4792 | | /* rem-rhs is needed; the sign will invert. Again, var1 */ |
4793 | | /* can safely be used for the working Units array. */ |
4794 | 0 | exp=rhs->exponent-exponent; /* RHS padding needed */ |
4795 | | /* Calculate units and remainder from exponent. */ |
4796 | 0 | expunits=exp/DECDPUN; |
4797 | 0 | exprem=exp%DECDPUN; |
4798 | | /* subtract [A+B*(-m)]; the result will always be negative */ |
4799 | 0 | accunits=-decUnitAddSub(accnext, accunits, |
4800 | 0 | rhs->lsu, D2U(rhs->digits), |
4801 | 0 | expunits, accnext, -(Int)powers[exprem]); |
4802 | 0 | accdigits=decGetDigits(accnext, accunits); /* count digits exactly */ |
4803 | 0 | accunits=D2U(accdigits); /* and recalculate the units for copy */ |
4804 | | /* [exponent is as for original remainder] */ |
4805 | 0 | bits^=DECNEG; /* flip the sign */ |
4806 | 0 | } |
4807 | 0 | } /* REMNEAR */ |
4808 | 0 | } /* REMAINDER or REMNEAR */ |
4809 | 0 | } /* not DIVIDE */ |
4810 | | |
4811 | | /* Set exponent and bits */ |
4812 | 0 | res->exponent=exponent; |
4813 | 0 | res->bits=(uByte)(bits&DECNEG); /* [cleaned] */ |
4814 | | |
4815 | | /* Now the coefficient. */ |
4816 | 0 | decSetCoeff(res, set, accnext, accdigits, &residue, status); |
4817 | |
|
4818 | 0 | decFinish(res, set, &residue, status); /* final cleanup */ |
4819 | |
|
4820 | | #if DECSUBSET |
4821 | | /* If a divide then strip trailing zeros if subset [after round] */ |
4822 | | if (!set->extended && (op==DIVIDE)) decTrim(res, set, 0, 1, &dropped); |
4823 | | #endif |
4824 | 0 | } while(0); /* end protected */ |
4825 | | |
4826 | 0 | if (varalloc!=NULL) free(varalloc); /* drop any storage used */ |
4827 | 0 | if (allocacc!=NULL) free(allocacc); /* .. */ |
4828 | | #if DECSUBSET |
4829 | | if (allocrhs!=NULL) free(allocrhs); /* .. */ |
4830 | | if (alloclhs!=NULL) free(alloclhs); /* .. */ |
4831 | | #endif |
4832 | 0 | return res; |
4833 | 0 | } /* decDivideOp */ |
4834 | | |
4835 | | /* ------------------------------------------------------------------ */ |
4836 | | /* decMultiplyOp -- multiplication operation */ |
4837 | | /* */ |
4838 | | /* This routine performs the multiplication C=A x B. */ |
4839 | | /* */ |
4840 | | /* res is C, the result. C may be A and/or B (e.g., X=X*X) */ |
4841 | | /* lhs is A */ |
4842 | | /* rhs is B */ |
4843 | | /* set is the context */ |
4844 | | /* status is the usual accumulator */ |
4845 | | /* */ |
4846 | | /* C must have space for set->digits digits. */ |
4847 | | /* */ |
4848 | | /* ------------------------------------------------------------------ */ |
4849 | | /* 'Classic' multiplication is used rather than Karatsuba, as the */ |
4850 | | /* latter would give only a minor improvement for the short numbers */ |
4851 | | /* expected to be handled most (and uses much more memory). */ |
4852 | | /* */ |
4853 | | /* There are two major paths here: the general-purpose ('old code') */ |
4854 | | /* path which handles all DECDPUN values, and a fastpath version */ |
4855 | | /* which is used if 64-bit ints are available, DECDPUN<=4, and more */ |
4856 | | /* than two calls to decUnitAddSub would be made. */ |
4857 | | /* */ |
4858 | | /* The fastpath version lumps units together into 8-digit or 9-digit */ |
4859 | | /* chunks, and also uses a lazy carry strategy to minimise expensive */ |
4860 | | /* 64-bit divisions. The chunks are then broken apart again into */ |
4861 | | /* units for continuing processing. Despite this overhead, the */ |
4862 | | /* fastpath can speed up some 16-digit operations by 10x (and much */ |
4863 | | /* more for higher-precision calculations). */ |
4864 | | /* */ |
4865 | | /* A buffer always has to be used for the accumulator; in the */ |
4866 | | /* fastpath, buffers are also always needed for the chunked copies of */ |
4867 | | /* of the operand coefficients. */ |
4868 | | /* Static buffers are larger than needed just for multiply, to allow */ |
4869 | | /* for calls from other operations (notably exp). */ |
4870 | | /* ------------------------------------------------------------------ */ |
4871 | | #define FASTMUL (DECUSE64 && DECDPUN<5) |
4872 | | static decNumber * decMultiplyOp(decNumber *res, const decNumber *lhs, |
4873 | | const decNumber *rhs, decContext *set, |
4874 | 0 | uInt *status) { |
4875 | 0 | Int accunits; /* Units of accumulator in use */ |
4876 | 0 | Int exponent; /* work */ |
4877 | 0 | Int residue=0; /* rounding residue */ |
4878 | 0 | uByte bits; /* result sign */ |
4879 | 0 | Unit *acc; /* -> accumulator Unit array */ |
4880 | 0 | Int needbytes; /* size calculator */ |
4881 | 0 | void *allocacc=NULL; /* -> allocated accumulator, iff allocated */ |
4882 | 0 | Unit accbuff[SD2U(DECBUFFER*4+1)]; /* buffer (+1 for DECBUFFER==0, */ |
4883 | | /* *4 for calls from other operations) */ |
4884 | 0 | const Unit *mer, *mermsup; /* work */ |
4885 | 0 | Int madlength; /* Units in multiplicand */ |
4886 | 0 | Int shift; /* Units to shift multiplicand by */ |
4887 | |
|
4888 | 0 | #if FASTMUL |
4889 | | /* if DECDPUN is 1 or 3 work in base 10**9, otherwise */ |
4890 | | /* (DECDPUN is 2 or 4) then work in base 10**8 */ |
4891 | 0 | #if DECDPUN & 1 /* odd */ |
4892 | 0 | #define FASTBASE 1000000000 /* base */ |
4893 | 0 | #define FASTDIGS 9 /* digits in base */ |
4894 | 0 | #define FASTLAZY 18 /* carry resolution point [1->18] */ |
4895 | | #else |
4896 | | #define FASTBASE 100000000 |
4897 | | #define FASTDIGS 8 |
4898 | | #define FASTLAZY 1844 /* carry resolution point [1->1844] */ |
4899 | | #endif |
4900 | | /* three buffers are used, two for chunked copies of the operands */ |
4901 | | /* (base 10**8 or base 10**9) and one base 2**64 accumulator with */ |
4902 | | /* lazy carry evaluation */ |
4903 | 0 | uInt zlhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */ |
4904 | 0 | uInt *zlhi=zlhibuff; /* -> lhs array */ |
4905 | 0 | uInt *alloclhi=NULL; /* -> allocated buffer, iff allocated */ |
4906 | 0 | uInt zrhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */ |
4907 | 0 | uInt *zrhi=zrhibuff; /* -> rhs array */ |
4908 | 0 | uInt *allocrhi=NULL; /* -> allocated buffer, iff allocated */ |
4909 | 0 | uLong zaccbuff[(DECBUFFER*2+1)/4+2]; /* buffer (+1 for DECBUFFER==0) */ |
4910 | | /* [allocacc is shared for both paths, as only one will run] */ |
4911 | 0 | uLong *zacc=zaccbuff; /* -> accumulator array for exact result */ |
4912 | 0 | #if DECDPUN==1 |
4913 | 0 | Int zoff; /* accumulator offset */ |
4914 | 0 | #endif |
4915 | 0 | uInt *lip, *rip; /* item pointers */ |
4916 | 0 | uInt *lmsi, *rmsi; /* most significant items */ |
4917 | 0 | Int ilhs, irhs, iacc; /* item counts in the arrays */ |
4918 | 0 | Int lazy; /* lazy carry counter */ |
4919 | 0 | uLong lcarry; /* uLong carry */ |
4920 | 0 | uInt carry; /* carry (NB not uLong) */ |
4921 | 0 | Int count; /* work */ |
4922 | 0 | const Unit *cup; /* .. */ |
4923 | 0 | Unit *up; /* .. */ |
4924 | 0 | uLong *lp; /* .. */ |
4925 | 0 | Int p; /* .. */ |
4926 | 0 | #endif |
4927 | |
|
4928 | | #if DECSUBSET |
4929 | | decNumber *alloclhs=NULL; /* -> allocated buffer, iff allocated */ |
4930 | | decNumber *allocrhs=NULL; /* -> allocated buffer, iff allocated */ |
4931 | | #endif |
4932 | |
|
4933 | | #if DECCHECK |
4934 | | if (decCheckOperands(res, lhs, rhs, set)) return res; |
4935 | | #endif |
4936 | | |
4937 | | /* precalculate result sign */ |
4938 | 0 | bits=(uByte)((lhs->bits^rhs->bits)&DECNEG); |
4939 | | |
4940 | | /* handle infinities and NaNs */ |
4941 | 0 | if (SPECIALARGS) { /* a special bit set */ |
4942 | 0 | if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */ |
4943 | 0 | decNaNs(res, lhs, rhs, set, status); |
4944 | 0 | return res;} |
4945 | | /* one or two infinities; Infinity * 0 is invalid */ |
4946 | 0 | if (((lhs->bits & DECINF)==0 && ISZERO(lhs)) |
4947 | 0 | ||((rhs->bits & DECINF)==0 && ISZERO(rhs))) { |
4948 | 0 | *status|=DEC_Invalid_operation; |
4949 | 0 | return res;} |
4950 | 0 | uprv_decNumberZero(res); |
4951 | 0 | res->bits=bits|DECINF; /* infinity */ |
4952 | 0 | return res;} |
4953 | | |
4954 | | /* For best speed, as in DMSRCN [the original Rexx numerics */ |
4955 | | /* module], use the shorter number as the multiplier (rhs) and */ |
4956 | | /* the longer as the multiplicand (lhs) to minimise the number of */ |
4957 | | /* adds (partial products) */ |
4958 | 0 | if (lhs->digits<rhs->digits) { /* swap... */ |
4959 | 0 | const decNumber *hold=lhs; |
4960 | 0 | lhs=rhs; |
4961 | 0 | rhs=hold; |
4962 | 0 | } |
4963 | |
|
4964 | 0 | do { /* protect allocated storage */ |
4965 | | #if DECSUBSET |
4966 | | if (!set->extended) { |
4967 | | /* reduce operands and set lostDigits status, as needed */ |
4968 | | if (lhs->digits>set->digits) { |
4969 | | alloclhs=decRoundOperand(lhs, set, status); |
4970 | | if (alloclhs==NULL) break; |
4971 | | lhs=alloclhs; |
4972 | | } |
4973 | | if (rhs->digits>set->digits) { |
4974 | | allocrhs=decRoundOperand(rhs, set, status); |
4975 | | if (allocrhs==NULL) break; |
4976 | | rhs=allocrhs; |
4977 | | } |
4978 | | } |
4979 | | #endif |
4980 | | /* [following code does not require input rounding] */ |
4981 | |
|
4982 | | #if FASTMUL /* fastpath can be used */ |
4983 | | /* use the fast path if there are enough digits in the shorter */ |
4984 | | /* operand to make the setup and takedown worthwhile */ |
4985 | 0 | #define NEEDTWO (DECDPUN*2) /* within two decUnitAddSub calls */ |
4986 | 0 | if (rhs->digits>NEEDTWO) { /* use fastpath... */ |
4987 | | /* calculate the number of elements in each array */ |
4988 | 0 | ilhs=(lhs->digits+FASTDIGS-1)/FASTDIGS; /* [ceiling] */ |
4989 | 0 | irhs=(rhs->digits+FASTDIGS-1)/FASTDIGS; /* .. */ |
4990 | 0 | iacc=ilhs+irhs; |
4991 | | |
4992 | | /* allocate buffers if required, as usual */ |
4993 | 0 | needbytes=ilhs*sizeof(uInt); |
4994 | 0 | if (needbytes>(Int)sizeof(zlhibuff)) { |
4995 | 0 | alloclhi=(uInt *)malloc(needbytes); |
4996 | 0 | zlhi=alloclhi;} |
4997 | 0 | needbytes=irhs*sizeof(uInt); |
4998 | 0 | if (needbytes>(Int)sizeof(zrhibuff)) { |
4999 | 0 | allocrhi=(uInt *)malloc(needbytes); |
5000 | 0 | zrhi=allocrhi;} |
5001 | | |
5002 | | /* Allocating the accumulator space needs a special case when */ |
5003 | | /* DECDPUN=1 because when converting the accumulator to Units */ |
5004 | | /* after the multiplication each 8-byte item becomes 9 1-byte */ |
5005 | | /* units. Therefore iacc extra bytes are needed at the front */ |
5006 | | /* (rounded up to a multiple of 8 bytes), and the uLong */ |
5007 | | /* accumulator starts offset the appropriate number of units */ |
5008 | | /* to the right to avoid overwrite during the unchunking. */ |
5009 | | |
5010 | | /* Make sure no signed int overflow below. This is always true */ |
5011 | | /* if the given numbers have less digits than DEC_MAX_DIGITS. */ |
5012 | 0 | U_ASSERT((uint32_t)iacc <= INT32_MAX/sizeof(uLong)); |
5013 | 0 | needbytes=iacc*sizeof(uLong); |
5014 | 0 | #if DECDPUN==1 |
5015 | 0 | zoff=(iacc+7)/8; /* items to offset by */ |
5016 | 0 | needbytes+=zoff*8; |
5017 | 0 | #endif |
5018 | 0 | if (needbytes>(Int)sizeof(zaccbuff)) { |
5019 | 0 | allocacc=(uLong *)malloc(needbytes); |
5020 | 0 | zacc=(uLong *)allocacc;} |
5021 | 0 | if (zlhi==NULL||zrhi==NULL||zacc==NULL) { |
5022 | 0 | *status|=DEC_Insufficient_storage; |
5023 | 0 | break;} |
5024 | | |
5025 | 0 | acc=(Unit *)zacc; /* -> target Unit array */ |
5026 | 0 | #if DECDPUN==1 |
5027 | 0 | zacc+=zoff; /* start uLong accumulator to right */ |
5028 | 0 | #endif |
5029 | | |
5030 | | /* assemble the chunked copies of the left and right sides */ |
5031 | 0 | for (count=lhs->digits, cup=lhs->lsu, lip=zlhi; count>0; lip++) |
5032 | 0 | for (p=0, *lip=0; p<FASTDIGS && count>0; |
5033 | 0 | p+=DECDPUN, cup++, count-=DECDPUN) |
5034 | 0 | *lip+=*cup*powers[p]; |
5035 | 0 | lmsi=lip-1; /* save -> msi */ |
5036 | 0 | for (count=rhs->digits, cup=rhs->lsu, rip=zrhi; count>0; rip++) |
5037 | 0 | for (p=0, *rip=0; p<FASTDIGS && count>0; |
5038 | 0 | p+=DECDPUN, cup++, count-=DECDPUN) |
5039 | 0 | *rip+=*cup*powers[p]; |
5040 | 0 | rmsi=rip-1; /* save -> msi */ |
5041 | | |
5042 | | /* zero the accumulator */ |
5043 | 0 | for (lp=zacc; lp<zacc+iacc; lp++) *lp=0; |
5044 | | |
5045 | | /* Start the multiplication */ |
5046 | | /* Resolving carries can dominate the cost of accumulating the */ |
5047 | | /* partial products, so this is only done when necessary. */ |
5048 | | /* Each uLong item in the accumulator can hold values up to */ |
5049 | | /* 2**64-1, and each partial product can be as large as */ |
5050 | | /* (10**FASTDIGS-1)**2. When FASTDIGS=9, this can be added to */ |
5051 | | /* itself 18.4 times in a uLong without overflowing, so during */ |
5052 | | /* the main calculation resolution is carried out every 18th */ |
5053 | | /* add -- every 162 digits. Similarly, when FASTDIGS=8, the */ |
5054 | | /* partial products can be added to themselves 1844.6 times in */ |
5055 | | /* a uLong without overflowing, so intermediate carry */ |
5056 | | /* resolution occurs only every 14752 digits. Hence for common */ |
5057 | | /* short numbers usually only the one final carry resolution */ |
5058 | | /* occurs. */ |
5059 | | /* (The count is set via FASTLAZY to simplify experiments to */ |
5060 | | /* measure the value of this approach: a 35% improvement on a */ |
5061 | | /* [34x34] multiply.) */ |
5062 | 0 | lazy=FASTLAZY; /* carry delay count */ |
5063 | 0 | for (rip=zrhi; rip<=rmsi; rip++) { /* over each item in rhs */ |
5064 | 0 | lp=zacc+(rip-zrhi); /* where to add the lhs */ |
5065 | 0 | for (lip=zlhi; lip<=lmsi; lip++, lp++) { /* over each item in lhs */ |
5066 | 0 | *lp+=(uLong)(*lip)*(*rip); /* [this should in-line] */ |
5067 | 0 | } /* lip loop */ |
5068 | 0 | lazy--; |
5069 | 0 | if (lazy>0 && rip!=rmsi) continue; |
5070 | 0 | lazy=FASTLAZY; /* reset delay count */ |
5071 | | /* spin up the accumulator resolving overflows */ |
5072 | 0 | for (lp=zacc; lp<zacc+iacc; lp++) { |
5073 | 0 | if (*lp<FASTBASE) continue; /* it fits */ |
5074 | 0 | lcarry=*lp/FASTBASE; /* top part [slow divide] */ |
5075 | | /* lcarry can exceed 2**32-1, so check again; this check */ |
5076 | | /* and occasional extra divide (slow) is well worth it, as */ |
5077 | | /* it allows FASTLAZY to be increased to 18 rather than 4 */ |
5078 | | /* in the FASTDIGS=9 case */ |
5079 | 0 | if (lcarry<FASTBASE) carry=(uInt)lcarry; /* [usual] */ |
5080 | 0 | else { /* two-place carry [fairly rare] */ |
5081 | 0 | uInt carry2=(uInt)(lcarry/FASTBASE); /* top top part */ |
5082 | 0 | *(lp+2)+=carry2; /* add to item+2 */ |
5083 | 0 | *lp-=((uLong)FASTBASE*FASTBASE*carry2); /* [slow] */ |
5084 | 0 | carry=(uInt)(lcarry-((uLong)FASTBASE*carry2)); /* [inline] */ |
5085 | 0 | } |
5086 | 0 | *(lp+1)+=carry; /* add to item above [inline] */ |
5087 | 0 | *lp-=((uLong)FASTBASE*carry); /* [inline] */ |
5088 | 0 | } /* carry resolution */ |
5089 | 0 | } /* rip loop */ |
5090 | | |
5091 | | /* The multiplication is complete; time to convert back into */ |
5092 | | /* units. This can be done in-place in the accumulator and in */ |
5093 | | /* 32-bit operations, because carries were resolved after the */ |
5094 | | /* final add. This needs N-1 divides and multiplies for */ |
5095 | | /* each item in the accumulator (which will become up to N */ |
5096 | | /* units, where 2<=N<=9). */ |
5097 | 0 | for (lp=zacc, up=acc; lp<zacc+iacc; lp++) { |
5098 | 0 | uInt item=(uInt)*lp; /* decapitate to uInt */ |
5099 | 0 | for (p=0; p<FASTDIGS-DECDPUN; p+=DECDPUN, up++) { |
5100 | 0 | uInt part=item/(DECDPUNMAX+1); |
5101 | 0 | *up=(Unit)(item-(part*(DECDPUNMAX+1))); |
5102 | 0 | item=part; |
5103 | 0 | } /* p */ |
5104 | 0 | *up=(Unit)item; up++; /* [final needs no division] */ |
5105 | 0 | } /* lp */ |
5106 | 0 | accunits = static_cast<int32_t>(up-acc); /* count of units */ |
5107 | 0 | } |
5108 | 0 | else { /* here to use units directly, without chunking ['old code'] */ |
5109 | 0 | #endif |
5110 | | |
5111 | | /* if accumulator will be too long for local storage, then allocate */ |
5112 | 0 | acc=accbuff; /* -> assume buffer for accumulator */ |
5113 | 0 | needbytes=(D2U(lhs->digits)+D2U(rhs->digits))*sizeof(Unit); |
5114 | 0 | if (needbytes>(Int)sizeof(accbuff)) { |
5115 | 0 | allocacc=(Unit *)malloc(needbytes); |
5116 | 0 | if (allocacc==NULL) {*status|=DEC_Insufficient_storage; break;} |
5117 | 0 | acc=(Unit *)allocacc; /* use the allocated space */ |
5118 | 0 | } |
5119 | | |
5120 | | /* Now the main long multiplication loop */ |
5121 | | /* Unlike the equivalent in the IBM Java implementation, there */ |
5122 | | /* is no advantage in calculating from msu to lsu. So, do it */ |
5123 | | /* by the book, as it were. */ |
5124 | | /* Each iteration calculates ACC=ACC+MULTAND*MULT */ |
5125 | 0 | accunits=1; /* accumulator starts at '0' */ |
5126 | 0 | *acc=0; /* .. (lsu=0) */ |
5127 | 0 | shift=0; /* no multiplicand shift at first */ |
5128 | 0 | madlength=D2U(lhs->digits); /* this won't change */ |
5129 | 0 | mermsup=rhs->lsu+D2U(rhs->digits); /* -> msu+1 of multiplier */ |
5130 | |
|
5131 | 0 | for (mer=rhs->lsu; mer<mermsup; mer++) { |
5132 | | /* Here, *mer is the next Unit in the multiplier to use */ |
5133 | | /* If non-zero [optimization] add it... */ |
5134 | 0 | if (*mer!=0) accunits=decUnitAddSub(&acc[shift], accunits-shift, |
5135 | 0 | lhs->lsu, madlength, 0, |
5136 | 0 | &acc[shift], *mer) |
5137 | 0 | + shift; |
5138 | 0 | else { /* extend acc with a 0; it will be used shortly */ |
5139 | 0 | *(acc+accunits)=0; /* [this avoids length of <=0 later] */ |
5140 | 0 | accunits++; |
5141 | 0 | } |
5142 | | /* multiply multiplicand by 10**DECDPUN for next Unit to left */ |
5143 | 0 | shift++; /* add this for 'logical length' */ |
5144 | 0 | } /* n */ |
5145 | 0 | #if FASTMUL |
5146 | 0 | } /* unchunked units */ |
5147 | 0 | #endif |
5148 | | /* common end-path */ |
5149 | | #if DECTRACE |
5150 | | decDumpAr('*', acc, accunits); /* Show exact result */ |
5151 | | #endif |
5152 | | |
5153 | | /* acc now contains the exact result of the multiplication, */ |
5154 | | /* possibly with a leading zero unit; build the decNumber from */ |
5155 | | /* it, noting if any residue */ |
5156 | 0 | res->bits=bits; /* set sign */ |
5157 | 0 | res->digits=decGetDigits(acc, accunits); /* count digits exactly */ |
5158 | | |
5159 | | /* There can be a 31-bit wrap in calculating the exponent. */ |
5160 | | /* This can only happen if both input exponents are negative and */ |
5161 | | /* both their magnitudes are large. If there was a wrap, set a */ |
5162 | | /* safe very negative exponent, from which decFinalize() will */ |
5163 | | /* raise a hard underflow shortly. */ |
5164 | 0 | exponent=lhs->exponent+rhs->exponent; /* calculate exponent */ |
5165 | 0 | if (lhs->exponent<0 && rhs->exponent<0 && exponent>0) |
5166 | 0 | exponent=-2*DECNUMMAXE; /* force underflow */ |
5167 | 0 | res->exponent=exponent; /* OK to overwrite now */ |
5168 | | |
5169 | | |
5170 | | /* Set the coefficient. If any rounding, residue records */ |
5171 | 0 | decSetCoeff(res, set, acc, res->digits, &residue, status); |
5172 | 0 | decFinish(res, set, &residue, status); /* final cleanup */ |
5173 | 0 | } while(0); /* end protected */ |
5174 | | |
5175 | 0 | if (allocacc!=NULL) free(allocacc); /* drop any storage used */ |
5176 | | #if DECSUBSET |
5177 | | if (allocrhs!=NULL) free(allocrhs); /* .. */ |
5178 | | if (alloclhs!=NULL) free(alloclhs); /* .. */ |
5179 | | #endif |
5180 | 0 | #if FASTMUL |
5181 | 0 | if (allocrhi!=NULL) free(allocrhi); /* .. */ |
5182 | 0 | if (alloclhi!=NULL) free(alloclhi); /* .. */ |
5183 | 0 | #endif |
5184 | 0 | return res; |
5185 | 0 | } /* decMultiplyOp */ |
5186 | | |
5187 | | /* ------------------------------------------------------------------ */ |
5188 | | /* decExpOp -- effect exponentiation */ |
5189 | | /* */ |
5190 | | /* This computes C = exp(A) */ |
5191 | | /* */ |
5192 | | /* res is C, the result. C may be A */ |
5193 | | /* rhs is A */ |
5194 | | /* set is the context; note that rounding mode has no effect */ |
5195 | | /* */ |
5196 | | /* C must have space for set->digits digits. status is updated but */ |
5197 | | /* not set. */ |
5198 | | /* */ |
5199 | | /* Restrictions: */ |
5200 | | /* */ |
5201 | | /* digits, emax, and -emin in the context must be less than */ |
5202 | | /* 2*DEC_MAX_MATH (1999998), and the rhs must be within these */ |
5203 | | /* bounds or a zero. This is an internal routine, so these */ |
5204 | | /* restrictions are contractual and not enforced. */ |
5205 | | /* */ |
5206 | | /* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */ |
5207 | | /* almost always be correctly rounded, but may be up to 1 ulp in */ |
5208 | | /* error in rare cases. */ |
5209 | | /* */ |
5210 | | /* Finite results will always be full precision and Inexact, except */ |
5211 | | /* when A is a zero or -Infinity (giving 1 or 0 respectively). */ |
5212 | | /* ------------------------------------------------------------------ */ |
5213 | | /* This approach used here is similar to the algorithm described in */ |
5214 | | /* */ |
5215 | | /* Variable Precision Exponential Function, T. E. Hull and */ |
5216 | | /* A. Abrham, ACM Transactions on Mathematical Software, Vol 12 #2, */ |
5217 | | /* pp79-91, ACM, June 1986. */ |
5218 | | /* */ |
5219 | | /* with the main difference being that the iterations in the series */ |
5220 | | /* evaluation are terminated dynamically (which does not require the */ |
5221 | | /* extra variable-precision variables which are expensive in this */ |
5222 | | /* context). */ |
5223 | | /* */ |
5224 | | /* The error analysis in Hull & Abrham's paper applies except for the */ |
5225 | | /* round-off error accumulation during the series evaluation. This */ |
5226 | | /* code does not precalculate the number of iterations and so cannot */ |
5227 | | /* use Horner's scheme. Instead, the accumulation is done at double- */ |
5228 | | /* precision, which ensures that the additions of the terms are exact */ |
5229 | | /* and do not accumulate round-off (and any round-off errors in the */ |
5230 | | /* terms themselves move 'to the right' faster than they can */ |
5231 | | /* accumulate). This code also extends the calculation by allowing, */ |
5232 | | /* in the spirit of other decNumber operators, the input to be more */ |
5233 | | /* precise than the result (the precision used is based on the more */ |
5234 | | /* precise of the input or requested result). */ |
5235 | | /* */ |
5236 | | /* Implementation notes: */ |
5237 | | /* */ |
5238 | | /* 1. This is separated out as decExpOp so it can be called from */ |
5239 | | /* other Mathematical functions (notably Ln) with a wider range */ |
5240 | | /* than normal. In particular, it can handle the slightly wider */ |
5241 | | /* (double) range needed by Ln (which has to be able to calculate */ |
5242 | | /* exp(-x) where x can be the tiniest number (Ntiny). */ |
5243 | | /* */ |
5244 | | /* 2. Normalizing x to be <=0.1 (instead of <=1) reduces loop */ |
5245 | | /* iterations by approximately a third with additional (although */ |
5246 | | /* diminishing) returns as the range is reduced to even smaller */ |
5247 | | /* fractions. However, h (the power of 10 used to correct the */ |
5248 | | /* result at the end, see below) must be kept <=8 as otherwise */ |
5249 | | /* the final result cannot be computed. Hence the leverage is a */ |
5250 | | /* sliding value (8-h), where potentially the range is reduced */ |
5251 | | /* more for smaller values. */ |
5252 | | /* */ |
5253 | | /* The leverage that can be applied in this way is severely */ |
5254 | | /* limited by the cost of the raise-to-the power at the end, */ |
5255 | | /* which dominates when the number of iterations is small (less */ |
5256 | | /* than ten) or when rhs is short. As an example, the adjustment */ |
5257 | | /* x**10,000,000 needs 31 multiplications, all but one full-width. */ |
5258 | | /* */ |
5259 | | /* 3. The restrictions (especially precision) could be raised with */ |
5260 | | /* care, but the full decNumber range seems very hard within the */ |
5261 | | /* 32-bit limits. */ |
5262 | | /* */ |
5263 | | /* 4. The working precisions for the static buffers are twice the */ |
5264 | | /* obvious size to allow for calls from decNumberPower. */ |
5265 | | /* ------------------------------------------------------------------ */ |
5266 | | decNumber * decExpOp(decNumber *res, const decNumber *rhs, |
5267 | 0 | decContext *set, uInt *status) { |
5268 | 0 | uInt ignore=0; /* working status */ |
5269 | 0 | Int h; /* adjusted exponent for 0.xxxx */ |
5270 | 0 | Int p; /* working precision */ |
5271 | 0 | Int residue; /* rounding residue */ |
5272 | 0 | uInt needbytes; /* for space calculations */ |
5273 | 0 | const decNumber *x=rhs; /* (may point to safe copy later) */ |
5274 | 0 | decContext aset, tset, dset; /* working contexts */ |
5275 | 0 | Int comp; /* work */ |
5276 | | |
5277 | | /* the argument is often copied to normalize it, so (unusually) it */ |
5278 | | /* is treated like other buffers, using DECBUFFER, +1 in case */ |
5279 | | /* DECBUFFER is 0 */ |
5280 | 0 | decNumber bufr[D2N(DECBUFFER*2+1)]; |
5281 | 0 | decNumber *allocrhs=NULL; /* non-NULL if rhs buffer allocated */ |
5282 | | |
5283 | | /* the working precision will be no more than set->digits+8+1 */ |
5284 | | /* so for on-stack buffers DECBUFFER+9 is used, +1 in case DECBUFFER */ |
5285 | | /* is 0 (and twice that for the accumulator) */ |
5286 | | |
5287 | | /* buffer for t, term (working precision plus) */ |
5288 | 0 | decNumber buft[D2N(DECBUFFER*2+9+1)]; |
5289 | 0 | decNumber *allocbuft=NULL; /* -> allocated buft, iff allocated */ |
5290 | 0 | decNumber *t=buft; /* term */ |
5291 | | /* buffer for a, accumulator (working precision * 2), at least 9 */ |
5292 | 0 | decNumber bufa[D2N(DECBUFFER*4+18+1)]; |
5293 | 0 | decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ |
5294 | 0 | decNumber *a=bufa; /* accumulator */ |
5295 | | /* decNumber for the divisor term; this needs at most 9 digits */ |
5296 | | /* and so can be fixed size [16 so can use standard context] */ |
5297 | 0 | decNumber bufd[D2N(16)]; |
5298 | 0 | decNumber *d=bufd; /* divisor */ |
5299 | 0 | decNumber numone; /* constant 1 */ |
5300 | |
|
5301 | | #if DECCHECK |
5302 | | Int iterations=0; /* for later sanity check */ |
5303 | | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
5304 | | #endif |
5305 | |
|
5306 | 0 | do { /* protect allocated storage */ |
5307 | 0 | if (SPECIALARG) { /* handle infinities and NaNs */ |
5308 | 0 | if (decNumberIsInfinite(rhs)) { /* an infinity */ |
5309 | 0 | if (decNumberIsNegative(rhs)) /* -Infinity -> +0 */ |
5310 | 0 | uprv_decNumberZero(res); |
5311 | 0 | else uprv_decNumberCopy(res, rhs); /* +Infinity -> self */ |
5312 | 0 | } |
5313 | 0 | else decNaNs(res, rhs, NULL, set, status); /* a NaN */ |
5314 | 0 | break;} |
5315 | | |
5316 | 0 | if (ISZERO(rhs)) { /* zeros -> exact 1 */ |
5317 | 0 | uprv_decNumberZero(res); /* make clean 1 */ |
5318 | 0 | *res->lsu=1; /* .. */ |
5319 | 0 | break;} /* [no status to set] */ |
5320 | | |
5321 | | /* e**x when 0 < x < 0.66 is < 1+3x/2, hence can fast-path */ |
5322 | | /* positive and negative tiny cases which will result in inexact */ |
5323 | | /* 1. This also allows the later add-accumulate to always be */ |
5324 | | /* exact (because its length will never be more than twice the */ |
5325 | | /* working precision). */ |
5326 | | /* The comparator (tiny) needs just one digit, so use the */ |
5327 | | /* decNumber d for it (reused as the divisor, etc., below); its */ |
5328 | | /* exponent is such that if x is positive it will have */ |
5329 | | /* set->digits-1 zeros between the decimal point and the digit, */ |
5330 | | /* which is 4, and if x is negative one more zero there as the */ |
5331 | | /* more precise result will be of the form 0.9999999 rather than */ |
5332 | | /* 1.0000001. Hence, tiny will be 0.0000004 if digits=7 and x>0 */ |
5333 | | /* or 0.00000004 if digits=7 and x<0. If RHS not larger than */ |
5334 | | /* this then the result will be 1.000000 */ |
5335 | 0 | uprv_decNumberZero(d); /* clean */ |
5336 | 0 | *d->lsu=4; /* set 4 .. */ |
5337 | 0 | d->exponent=-set->digits; /* * 10**(-d) */ |
5338 | 0 | if (decNumberIsNegative(rhs)) d->exponent--; /* negative case */ |
5339 | 0 | comp=decCompare(d, rhs, 1); /* signless compare */ |
5340 | 0 | if (comp==BADINT) { |
5341 | 0 | *status|=DEC_Insufficient_storage; |
5342 | 0 | break;} |
5343 | 0 | if (comp>=0) { /* rhs < d */ |
5344 | 0 | Int shift=set->digits-1; |
5345 | 0 | uprv_decNumberZero(res); /* set 1 */ |
5346 | 0 | *res->lsu=1; /* .. */ |
5347 | 0 | res->digits=decShiftToMost(res->lsu, 1, shift); |
5348 | 0 | res->exponent=-shift; /* make 1.0000... */ |
5349 | 0 | *status|=DEC_Inexact | DEC_Rounded; /* .. inexactly */ |
5350 | 0 | break;} /* tiny */ |
5351 | | |
5352 | | /* set up the context to be used for calculating a, as this is */ |
5353 | | /* used on both paths below */ |
5354 | 0 | uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64); |
5355 | | /* accumulator bounds are as requested (could underflow) */ |
5356 | 0 | aset.emax=set->emax; /* usual bounds */ |
5357 | 0 | aset.emin=set->emin; /* .. */ |
5358 | 0 | aset.clamp=0; /* and no concrete format */ |
5359 | | |
5360 | | /* calculate the adjusted (Hull & Abrham) exponent (where the */ |
5361 | | /* decimal point is just to the left of the coefficient msd) */ |
5362 | 0 | h=rhs->exponent+rhs->digits; |
5363 | | /* if h>8 then 10**h cannot be calculated safely; however, when */ |
5364 | | /* h=8 then exp(|rhs|) will be at least exp(1E+7) which is at */ |
5365 | | /* least 6.59E+4342944, so (due to the restriction on Emax/Emin) */ |
5366 | | /* overflow (or underflow to 0) is guaranteed -- so this case can */ |
5367 | | /* be handled by simply forcing the appropriate excess */ |
5368 | 0 | if (h>8) { /* overflow/underflow */ |
5369 | | /* set up here so Power call below will over or underflow to */ |
5370 | | /* zero; set accumulator to either 2 or 0.02 */ |
5371 | | /* [stack buffer for a is always big enough for this] */ |
5372 | 0 | uprv_decNumberZero(a); |
5373 | 0 | *a->lsu=2; /* not 1 but < exp(1) */ |
5374 | 0 | if (decNumberIsNegative(rhs)) a->exponent=-2; /* make 0.02 */ |
5375 | 0 | h=8; /* clamp so 10**h computable */ |
5376 | 0 | p=9; /* set a working precision */ |
5377 | 0 | } |
5378 | 0 | else { /* h<=8 */ |
5379 | 0 | Int maxlever=(rhs->digits>8?1:0); |
5380 | | /* [could/should increase this for precisions >40 or so, too] */ |
5381 | | |
5382 | | /* if h is 8, cannot normalize to a lower upper limit because */ |
5383 | | /* the final result will not be computable (see notes above), */ |
5384 | | /* but leverage can be applied whenever h is less than 8. */ |
5385 | | /* Apply as much as possible, up to a MAXLEVER digits, which */ |
5386 | | /* sets the tradeoff against the cost of the later a**(10**h). */ |
5387 | | /* As h is increased, the working precision below also */ |
5388 | | /* increases to compensate for the "constant digits at the */ |
5389 | | /* front" effect. */ |
5390 | 0 | Int lever=MINI(8-h, maxlever); /* leverage attainable */ |
5391 | 0 | Int use=-rhs->digits-lever; /* exponent to use for RHS */ |
5392 | 0 | h+=lever; /* apply leverage selected */ |
5393 | 0 | if (h<0) { /* clamp */ |
5394 | 0 | use+=h; /* [may end up subnormal] */ |
5395 | 0 | h=0; |
5396 | 0 | } |
5397 | | /* Take a copy of RHS if it needs normalization (true whenever x>=1) */ |
5398 | 0 | if (rhs->exponent!=use) { |
5399 | 0 | decNumber *newrhs=bufr; /* assume will fit on stack */ |
5400 | 0 | needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); |
5401 | 0 | if (needbytes>sizeof(bufr)) { /* need malloc space */ |
5402 | 0 | allocrhs=(decNumber *)malloc(needbytes); |
5403 | 0 | if (allocrhs==NULL) { /* hopeless -- abandon */ |
5404 | 0 | *status|=DEC_Insufficient_storage; |
5405 | 0 | break;} |
5406 | 0 | newrhs=allocrhs; /* use the allocated space */ |
5407 | 0 | } |
5408 | 0 | uprv_decNumberCopy(newrhs, rhs); /* copy to safe space */ |
5409 | 0 | newrhs->exponent=use; /* normalize; now <1 */ |
5410 | 0 | x=newrhs; /* ready for use */ |
5411 | | /* decNumberShow(x); */ |
5412 | 0 | } |
5413 | | |
5414 | | /* Now use the usual power series to evaluate exp(x). The */ |
5415 | | /* series starts as 1 + x + x^2/2 ... so prime ready for the */ |
5416 | | /* third term by setting the term variable t=x, the accumulator */ |
5417 | | /* a=1, and the divisor d=2. */ |
5418 | | |
5419 | | /* First determine the working precision. From Hull & Abrham */ |
5420 | | /* this is set->digits+h+2. However, if x is 'over-precise' we */ |
5421 | | /* need to allow for all its digits to potentially participate */ |
5422 | | /* (consider an x where all the excess digits are 9s) so in */ |
5423 | | /* this case use x->digits+h+2 */ |
5424 | 0 | p=MAXI(x->digits, set->digits)+h+2; /* [h<=8] */ |
5425 | | |
5426 | | /* a and t are variable precision, and depend on p, so space */ |
5427 | | /* must be allocated for them if necessary */ |
5428 | | |
5429 | | /* the accumulator needs to be able to hold 2p digits so that */ |
5430 | | /* the additions on the second and subsequent iterations are */ |
5431 | | /* sufficiently exact. */ |
5432 | 0 | needbytes=sizeof(decNumber)+(D2U(p*2)-1)*sizeof(Unit); |
5433 | 0 | if (needbytes>sizeof(bufa)) { /* need malloc space */ |
5434 | 0 | allocbufa=(decNumber *)malloc(needbytes); |
5435 | 0 | if (allocbufa==NULL) { /* hopeless -- abandon */ |
5436 | 0 | *status|=DEC_Insufficient_storage; |
5437 | 0 | break;} |
5438 | 0 | a=allocbufa; /* use the allocated space */ |
5439 | 0 | } |
5440 | | /* the term needs to be able to hold p digits (which is */ |
5441 | | /* guaranteed to be larger than x->digits, so the initial copy */ |
5442 | | /* is safe); it may also be used for the raise-to-power */ |
5443 | | /* calculation below, which needs an extra two digits */ |
5444 | 0 | needbytes=sizeof(decNumber)+(D2U(p+2)-1)*sizeof(Unit); |
5445 | 0 | if (needbytes>sizeof(buft)) { /* need malloc space */ |
5446 | 0 | allocbuft=(decNumber *)malloc(needbytes); |
5447 | 0 | if (allocbuft==NULL) { /* hopeless -- abandon */ |
5448 | 0 | *status|=DEC_Insufficient_storage; |
5449 | 0 | break;} |
5450 | 0 | t=allocbuft; /* use the allocated space */ |
5451 | 0 | } |
5452 | | |
5453 | 0 | uprv_decNumberCopy(t, x); /* term=x */ |
5454 | 0 | uprv_decNumberZero(a); *a->lsu=1; /* accumulator=1 */ |
5455 | 0 | uprv_decNumberZero(d); *d->lsu=2; /* divisor=2 */ |
5456 | 0 | uprv_decNumberZero(&numone); *numone.lsu=1; /* constant 1 for increment */ |
5457 | | |
5458 | | /* set up the contexts for calculating a, t, and d */ |
5459 | 0 | uprv_decContextDefault(&tset, DEC_INIT_DECIMAL64); |
5460 | 0 | dset=tset; |
5461 | | /* accumulator bounds are set above, set precision now */ |
5462 | 0 | aset.digits=p*2; /* double */ |
5463 | | /* term bounds avoid any underflow or overflow */ |
5464 | 0 | tset.digits=p; |
5465 | 0 | tset.emin=DEC_MIN_EMIN; /* [emax is plenty] */ |
5466 | | /* [dset.digits=16, etc., are sufficient] */ |
5467 | | |
5468 | | /* finally ready to roll */ |
5469 | 0 | for (;;) { |
5470 | | #if DECCHECK |
5471 | | iterations++; |
5472 | | #endif |
5473 | | /* only the status from the accumulation is interesting */ |
5474 | | /* [but it should remain unchanged after first add] */ |
5475 | 0 | decAddOp(a, a, t, &aset, 0, status); /* a=a+t */ |
5476 | 0 | decMultiplyOp(t, t, x, &tset, &ignore); /* t=t*x */ |
5477 | 0 | decDivideOp(t, t, d, &tset, DIVIDE, &ignore); /* t=t/d */ |
5478 | | /* the iteration ends when the term cannot affect the result, */ |
5479 | | /* if rounded to p digits, which is when its value is smaller */ |
5480 | | /* than the accumulator by p+1 digits. There must also be */ |
5481 | | /* full precision in a. */ |
5482 | 0 | if (((a->digits+a->exponent)>=(t->digits+t->exponent+p+1)) |
5483 | 0 | && (a->digits>=p)) break; |
5484 | 0 | decAddOp(d, d, &numone, &dset, 0, &ignore); /* d=d+1 */ |
5485 | 0 | } /* iterate */ |
5486 | |
|
5487 | | #if DECCHECK |
5488 | | /* just a sanity check; comment out test to show always */ |
5489 | | if (iterations>p+3) |
5490 | | printf("Exp iterations=%ld, status=%08lx, p=%ld, d=%ld\n", |
5491 | | (LI)iterations, (LI)*status, (LI)p, (LI)x->digits); |
5492 | | #endif |
5493 | 0 | } /* h<=8 */ |
5494 | | |
5495 | | /* apply postconditioning: a=a**(10**h) -- this is calculated */ |
5496 | | /* at a slightly higher precision than Hull & Abrham suggest */ |
5497 | 0 | if (h>0) { |
5498 | 0 | Int seenbit=0; /* set once a 1-bit is seen */ |
5499 | 0 | Int i; /* counter */ |
5500 | 0 | Int n=powers[h]; /* always positive */ |
5501 | 0 | aset.digits=p+2; /* sufficient precision */ |
5502 | | /* avoid the overhead and many extra digits of decNumberPower */ |
5503 | | /* as all that is needed is the short 'multipliers' loop; here */ |
5504 | | /* accumulate the answer into t */ |
5505 | 0 | uprv_decNumberZero(t); *t->lsu=1; /* acc=1 */ |
5506 | 0 | for (i=1;;i++){ /* for each bit [top bit ignored] */ |
5507 | | /* abandon if have had overflow or terminal underflow */ |
5508 | 0 | if (*status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */ |
5509 | 0 | if (*status&DEC_Overflow || ISZERO(t)) break;} |
5510 | 0 | n=n<<1; /* move next bit to testable position */ |
5511 | 0 | if (n<0) { /* top bit is set */ |
5512 | 0 | seenbit=1; /* OK, have a significant bit */ |
5513 | 0 | decMultiplyOp(t, t, a, &aset, status); /* acc=acc*x */ |
5514 | 0 | } |
5515 | 0 | if (i==31) break; /* that was the last bit */ |
5516 | 0 | if (!seenbit) continue; /* no need to square 1 */ |
5517 | 0 | decMultiplyOp(t, t, t, &aset, status); /* acc=acc*acc [square] */ |
5518 | 0 | } /*i*/ /* 32 bits */ |
5519 | | /* decNumberShow(t); */ |
5520 | 0 | a=t; /* and carry on using t instead of a */ |
5521 | 0 | } |
5522 | | |
5523 | | /* Copy and round the result to res */ |
5524 | 0 | residue=1; /* indicate dirt to right .. */ |
5525 | 0 | if (ISZERO(a)) residue=0; /* .. unless underflowed to 0 */ |
5526 | 0 | aset.digits=set->digits; /* [use default rounding] */ |
5527 | 0 | decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */ |
5528 | 0 | decFinish(res, set, &residue, status); /* cleanup/set flags */ |
5529 | 0 | } while(0); /* end protected */ |
5530 | | |
5531 | 0 | if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */ |
5532 | 0 | if (allocbufa!=NULL) free(allocbufa); /* .. */ |
5533 | 0 | if (allocbuft!=NULL) free(allocbuft); /* .. */ |
5534 | | /* [status is handled by caller] */ |
5535 | 0 | return res; |
5536 | 0 | } /* decExpOp */ |
5537 | | |
5538 | | /* ------------------------------------------------------------------ */ |
5539 | | /* Initial-estimate natural logarithm table */ |
5540 | | /* */ |
5541 | | /* LNnn -- 90-entry 16-bit table for values from .10 through .99. */ |
5542 | | /* The result is a 4-digit encode of the coefficient (c=the */ |
5543 | | /* top 14 bits encoding 0-9999) and a 2-digit encode of the */ |
5544 | | /* exponent (e=the bottom 2 bits encoding 0-3) */ |
5545 | | /* */ |
5546 | | /* The resulting value is given by: */ |
5547 | | /* */ |
5548 | | /* v = -c * 10**(-e-3) */ |
5549 | | /* */ |
5550 | | /* where e and c are extracted from entry k = LNnn[x-10] */ |
5551 | | /* where x is truncated (NB) into the range 10 through 99, */ |
5552 | | /* and then c = k>>2 and e = k&3. */ |
5553 | | /* ------------------------------------------------------------------ */ |
5554 | | static const uShort LNnn[90]={9016, 8652, 8316, 8008, 7724, 7456, 7208, |
5555 | | 6972, 6748, 6540, 6340, 6148, 5968, 5792, 5628, 5464, 5312, |
5556 | | 5164, 5020, 4884, 4748, 4620, 4496, 4376, 4256, 4144, 4032, |
5557 | | 39233, 38181, 37157, 36157, 35181, 34229, 33297, 32389, 31501, 30629, |
5558 | | 29777, 28945, 28129, 27329, 26545, 25777, 25021, 24281, 23553, 22837, |
5559 | | 22137, 21445, 20769, 20101, 19445, 18801, 18165, 17541, 16925, 16321, |
5560 | | 15721, 15133, 14553, 13985, 13421, 12865, 12317, 11777, 11241, 10717, |
5561 | | 10197, 9685, 9177, 8677, 8185, 7697, 7213, 6737, 6269, 5801, |
5562 | | 5341, 4889, 4437, 39930, 35534, 31186, 26886, 22630, 18418, 14254, |
5563 | | 10130, 6046, 20055}; |
5564 | | |
5565 | | /* ------------------------------------------------------------------ */ |
5566 | | /* decLnOp -- effect natural logarithm */ |
5567 | | /* */ |
5568 | | /* This computes C = ln(A) */ |
5569 | | /* */ |
5570 | | /* res is C, the result. C may be A */ |
5571 | | /* rhs is A */ |
5572 | | /* set is the context; note that rounding mode has no effect */ |
5573 | | /* */ |
5574 | | /* C must have space for set->digits digits. */ |
5575 | | /* */ |
5576 | | /* Notable cases: */ |
5577 | | /* A<0 -> Invalid */ |
5578 | | /* A=0 -> -Infinity (Exact) */ |
5579 | | /* A=+Infinity -> +Infinity (Exact) */ |
5580 | | /* A=1 exactly -> 0 (Exact) */ |
5581 | | /* */ |
5582 | | /* Restrictions (as for Exp): */ |
5583 | | /* */ |
5584 | | /* digits, emax, and -emin in the context must be less than */ |
5585 | | /* DEC_MAX_MATH+11 (1000010), and the rhs must be within these */ |
5586 | | /* bounds or a zero. This is an internal routine, so these */ |
5587 | | /* restrictions are contractual and not enforced. */ |
5588 | | /* */ |
5589 | | /* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */ |
5590 | | /* almost always be correctly rounded, but may be up to 1 ulp in */ |
5591 | | /* error in rare cases. */ |
5592 | | /* ------------------------------------------------------------------ */ |
5593 | | /* The result is calculated using Newton's method, with each */ |
5594 | | /* iteration calculating a' = a + x * exp(-a) - 1. See, for example, */ |
5595 | | /* Epperson 1989. */ |
5596 | | /* */ |
5597 | | /* The iteration ends when the adjustment x*exp(-a)-1 is tiny enough. */ |
5598 | | /* This has to be calculated at the sum of the precision of x and the */ |
5599 | | /* working precision. */ |
5600 | | /* */ |
5601 | | /* Implementation notes: */ |
5602 | | /* */ |
5603 | | /* 1. This is separated out as decLnOp so it can be called from */ |
5604 | | /* other Mathematical functions (e.g., Log 10) with a wider range */ |
5605 | | /* than normal. In particular, it can handle the slightly wider */ |
5606 | | /* (+9+2) range needed by a power function. */ |
5607 | | /* */ |
5608 | | /* 2. The speed of this function is about 10x slower than exp, as */ |
5609 | | /* it typically needs 4-6 iterations for short numbers, and the */ |
5610 | | /* extra precision needed adds a squaring effect, twice. */ |
5611 | | /* */ |
5612 | | /* 3. Fastpaths are included for ln(10) and ln(2), up to length 40, */ |
5613 | | /* as these are common requests. ln(10) is used by log10(x). */ |
5614 | | /* */ |
5615 | | /* 4. An iteration might be saved by widening the LNnn table, and */ |
5616 | | /* would certainly save at least one if it were made ten times */ |
5617 | | /* bigger, too (for truncated fractions 0.100 through 0.999). */ |
5618 | | /* However, for most practical evaluations, at least four or five */ |
5619 | | /* iterations will be needed -- so this would only speed up by */ |
5620 | | /* 20-25% and that probably does not justify increasing the table */ |
5621 | | /* size. */ |
5622 | | /* */ |
5623 | | /* 5. The static buffers are larger than might be expected to allow */ |
5624 | | /* for calls from decNumberPower. */ |
5625 | | /* ------------------------------------------------------------------ */ |
5626 | | #if defined(__clang__) || U_GCC_MAJOR_MINOR >= 406 |
5627 | | #pragma GCC diagnostic push |
5628 | | #pragma GCC diagnostic ignored "-Warray-bounds" |
5629 | | #endif |
5630 | | decNumber * decLnOp(decNumber *res, const decNumber *rhs, |
5631 | 0 | decContext *set, uInt *status) { |
5632 | 0 | uInt ignore=0; /* working status accumulator */ |
5633 | 0 | uInt needbytes; /* for space calculations */ |
5634 | 0 | Int residue; /* rounding residue */ |
5635 | 0 | Int r; /* rhs=f*10**r [see below] */ |
5636 | 0 | Int p; /* working precision */ |
5637 | 0 | Int pp; /* precision for iteration */ |
5638 | 0 | Int t; /* work */ |
5639 | | |
5640 | | /* buffers for a (accumulator, typically precision+2) and b */ |
5641 | | /* (adjustment calculator, same size) */ |
5642 | 0 | decNumber bufa[D2N(DECBUFFER+12)]; |
5643 | 0 | decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ |
5644 | 0 | decNumber *a=bufa; /* accumulator/work */ |
5645 | 0 | decNumber bufb[D2N(DECBUFFER*2+2)]; |
5646 | 0 | decNumber *allocbufb=NULL; /* -> allocated bufa, iff allocated */ |
5647 | 0 | decNumber *b=bufb; /* adjustment/work */ |
5648 | |
|
5649 | 0 | decNumber numone; /* constant 1 */ |
5650 | 0 | decNumber cmp; /* work */ |
5651 | 0 | decContext aset, bset; /* working contexts */ |
5652 | |
|
5653 | | #if DECCHECK |
5654 | | Int iterations=0; /* for later sanity check */ |
5655 | | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
5656 | | #endif |
5657 | |
|
5658 | 0 | do { /* protect allocated storage */ |
5659 | 0 | if (SPECIALARG) { /* handle infinities and NaNs */ |
5660 | 0 | if (decNumberIsInfinite(rhs)) { /* an infinity */ |
5661 | 0 | if (decNumberIsNegative(rhs)) /* -Infinity -> error */ |
5662 | 0 | *status|=DEC_Invalid_operation; |
5663 | 0 | else uprv_decNumberCopy(res, rhs); /* +Infinity -> self */ |
5664 | 0 | } |
5665 | 0 | else decNaNs(res, rhs, NULL, set, status); /* a NaN */ |
5666 | 0 | break;} |
5667 | | |
5668 | 0 | if (ISZERO(rhs)) { /* +/- zeros -> -Infinity */ |
5669 | 0 | uprv_decNumberZero(res); /* make clean */ |
5670 | 0 | res->bits=DECINF|DECNEG; /* set - infinity */ |
5671 | 0 | break;} /* [no status to set] */ |
5672 | | |
5673 | | /* Non-zero negatives are bad... */ |
5674 | 0 | if (decNumberIsNegative(rhs)) { /* -x -> error */ |
5675 | 0 | *status|=DEC_Invalid_operation; |
5676 | 0 | break;} |
5677 | | |
5678 | | /* Here, rhs is positive, finite, and in range */ |
5679 | | |
5680 | | /* lookaside fastpath code for ln(2) and ln(10) at common lengths */ |
5681 | 0 | if (rhs->exponent==0 && set->digits<=40) { |
5682 | 0 | #if DECDPUN==1 |
5683 | 0 | if (rhs->lsu[0]==0 && rhs->lsu[1]==1 && rhs->digits==2) { /* ln(10) */ |
5684 | | #else |
5685 | | if (rhs->lsu[0]==10 && rhs->digits==2) { /* ln(10) */ |
5686 | | #endif |
5687 | 0 | aset=*set; aset.round=DEC_ROUND_HALF_EVEN; |
5688 | 0 | #define LN10 "2.302585092994045684017991454684364207601" |
5689 | 0 | uprv_decNumberFromString(res, LN10, &aset); |
5690 | 0 | *status|=(DEC_Inexact | DEC_Rounded); /* is inexact */ |
5691 | 0 | break;} |
5692 | 0 | if (rhs->lsu[0]==2 && rhs->digits==1) { /* ln(2) */ |
5693 | 0 | aset=*set; aset.round=DEC_ROUND_HALF_EVEN; |
5694 | 0 | #define LN2 "0.6931471805599453094172321214581765680755" |
5695 | 0 | uprv_decNumberFromString(res, LN2, &aset); |
5696 | 0 | *status|=(DEC_Inexact | DEC_Rounded); |
5697 | 0 | break;} |
5698 | 0 | } /* integer and short */ |
5699 | | |
5700 | | /* Determine the working precision. This is normally the */ |
5701 | | /* requested precision + 2, with a minimum of 9. However, if */ |
5702 | | /* the rhs is 'over-precise' then allow for all its digits to */ |
5703 | | /* potentially participate (consider an rhs where all the excess */ |
5704 | | /* digits are 9s) so in this case use rhs->digits+2. */ |
5705 | 0 | p=MAXI(rhs->digits, MAXI(set->digits, 7))+2; |
5706 | | |
5707 | | /* Allocate space for the accumulator and the high-precision */ |
5708 | | /* adjustment calculator, if necessary. The accumulator must */ |
5709 | | /* be able to hold p digits, and the adjustment up to */ |
5710 | | /* rhs->digits+p digits. They are also made big enough for 16 */ |
5711 | | /* digits so that they can be used for calculating the initial */ |
5712 | | /* estimate. */ |
5713 | 0 | needbytes=sizeof(decNumber)+(D2U(MAXI(p,16))-1)*sizeof(Unit); |
5714 | 0 | if (needbytes>sizeof(bufa)) { /* need malloc space */ |
5715 | 0 | allocbufa=(decNumber *)malloc(needbytes); |
5716 | 0 | if (allocbufa==NULL) { /* hopeless -- abandon */ |
5717 | 0 | *status|=DEC_Insufficient_storage; |
5718 | 0 | break;} |
5719 | 0 | a=allocbufa; /* use the allocated space */ |
5720 | 0 | } |
5721 | 0 | pp=p+rhs->digits; |
5722 | 0 | needbytes=sizeof(decNumber)+(D2U(MAXI(pp,16))-1)*sizeof(Unit); |
5723 | 0 | if (needbytes>sizeof(bufb)) { /* need malloc space */ |
5724 | 0 | allocbufb=(decNumber *)malloc(needbytes); |
5725 | 0 | if (allocbufb==NULL) { /* hopeless -- abandon */ |
5726 | 0 | *status|=DEC_Insufficient_storage; |
5727 | 0 | break;} |
5728 | 0 | b=allocbufb; /* use the allocated space */ |
5729 | 0 | } |
5730 | | |
5731 | | /* Prepare an initial estimate in acc. Calculate this by */ |
5732 | | /* considering the coefficient of x to be a normalized fraction, */ |
5733 | | /* f, with the decimal point at far left and multiplied by */ |
5734 | | /* 10**r. Then, rhs=f*10**r and 0.1<=f<1, and */ |
5735 | | /* ln(x) = ln(f) + ln(10)*r */ |
5736 | | /* Get the initial estimate for ln(f) from a small lookup */ |
5737 | | /* table (see above) indexed by the first two digits of f, */ |
5738 | | /* truncated. */ |
5739 | | |
5740 | 0 | uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64); /* 16-digit extended */ |
5741 | 0 | r=rhs->exponent+rhs->digits; /* 'normalised' exponent */ |
5742 | 0 | uprv_decNumberFromInt32(a, r); /* a=r */ |
5743 | 0 | uprv_decNumberFromInt32(b, 2302585); /* b=ln(10) (2.302585) */ |
5744 | 0 | b->exponent=-6; /* .. */ |
5745 | 0 | decMultiplyOp(a, a, b, &aset, &ignore); /* a=a*b */ |
5746 | | /* now get top two digits of rhs into b by simple truncate and */ |
5747 | | /* force to integer */ |
5748 | 0 | residue=0; /* (no residue) */ |
5749 | 0 | aset.digits=2; aset.round=DEC_ROUND_DOWN; |
5750 | 0 | decCopyFit(b, rhs, &aset, &residue, &ignore); /* copy & shorten */ |
5751 | 0 | b->exponent=0; /* make integer */ |
5752 | 0 | t=decGetInt(b); /* [cannot fail] */ |
5753 | 0 | if (t<10) t=X10(t); /* adjust single-digit b */ |
5754 | 0 | t=LNnn[t-10]; /* look up ln(b) */ |
5755 | 0 | uprv_decNumberFromInt32(b, t>>2); /* b=ln(b) coefficient */ |
5756 | 0 | b->exponent=-(t&3)-3; /* set exponent */ |
5757 | 0 | b->bits=DECNEG; /* ln(0.10)->ln(0.99) always -ve */ |
5758 | 0 | aset.digits=16; aset.round=DEC_ROUND_HALF_EVEN; /* restore */ |
5759 | 0 | decAddOp(a, a, b, &aset, 0, &ignore); /* acc=a+b */ |
5760 | | /* the initial estimate is now in a, with up to 4 digits correct. */ |
5761 | | /* When rhs is at or near Nmax the estimate will be low, so we */ |
5762 | | /* will approach it from below, avoiding overflow when calling exp. */ |
5763 | |
|
5764 | 0 | uprv_decNumberZero(&numone); *numone.lsu=1; /* constant 1 for adjustment */ |
5765 | | |
5766 | | /* accumulator bounds are as requested (could underflow, but */ |
5767 | | /* cannot overflow) */ |
5768 | 0 | aset.emax=set->emax; |
5769 | 0 | aset.emin=set->emin; |
5770 | 0 | aset.clamp=0; /* no concrete format */ |
5771 | | /* set up a context to be used for the multiply and subtract */ |
5772 | 0 | bset=aset; |
5773 | 0 | bset.emax=DEC_MAX_MATH*2; /* use double bounds for the */ |
5774 | 0 | bset.emin=-DEC_MAX_MATH*2; /* adjustment calculation */ |
5775 | | /* [see decExpOp call below] */ |
5776 | | /* for each iteration double the number of digits to calculate, */ |
5777 | | /* up to a maximum of p */ |
5778 | 0 | pp=9; /* initial precision */ |
5779 | | /* [initially 9 as then the sequence starts 7+2, 16+2, and */ |
5780 | | /* 34+2, which is ideal for standard-sized numbers] */ |
5781 | 0 | aset.digits=pp; /* working context */ |
5782 | 0 | bset.digits=pp+rhs->digits; /* wider context */ |
5783 | 0 | for (;;) { /* iterate */ |
5784 | | #if DECCHECK |
5785 | | iterations++; |
5786 | | if (iterations>24) break; /* consider 9 * 2**24 */ |
5787 | | #endif |
5788 | | /* calculate the adjustment (exp(-a)*x-1) into b. This is a */ |
5789 | | /* catastrophic subtraction but it really is the difference */ |
5790 | | /* from 1 that is of interest. */ |
5791 | | /* Use the internal entry point to Exp as it allows the double */ |
5792 | | /* range for calculating exp(-a) when a is the tiniest subnormal. */ |
5793 | 0 | a->bits^=DECNEG; /* make -a */ |
5794 | 0 | decExpOp(b, a, &bset, &ignore); /* b=exp(-a) */ |
5795 | 0 | a->bits^=DECNEG; /* restore sign of a */ |
5796 | | /* now multiply by rhs and subtract 1, at the wider precision */ |
5797 | 0 | decMultiplyOp(b, b, rhs, &bset, &ignore); /* b=b*rhs */ |
5798 | 0 | decAddOp(b, b, &numone, &bset, DECNEG, &ignore); /* b=b-1 */ |
5799 | | |
5800 | | /* the iteration ends when the adjustment cannot affect the */ |
5801 | | /* result by >=0.5 ulp (at the requested digits), which */ |
5802 | | /* is when its value is smaller than the accumulator by */ |
5803 | | /* set->digits+1 digits (or it is zero) -- this is a looser */ |
5804 | | /* requirement than for Exp because all that happens to the */ |
5805 | | /* accumulator after this is the final rounding (but note that */ |
5806 | | /* there must also be full precision in a, or a=0). */ |
5807 | |
|
5808 | 0 | if (decNumberIsZero(b) || |
5809 | 0 | (a->digits+a->exponent)>=(b->digits+b->exponent+set->digits+1)) { |
5810 | 0 | if (a->digits==p) break; |
5811 | 0 | if (decNumberIsZero(a)) { |
5812 | 0 | decCompareOp(&cmp, rhs, &numone, &aset, COMPARE, &ignore); /* rhs=1 ? */ |
5813 | 0 | if (cmp.lsu[0]==0) a->exponent=0; /* yes, exact 0 */ |
5814 | 0 | else *status|=(DEC_Inexact | DEC_Rounded); /* no, inexact */ |
5815 | 0 | break; |
5816 | 0 | } |
5817 | | /* force padding if adjustment has gone to 0 before full length */ |
5818 | 0 | if (decNumberIsZero(b)) b->exponent=a->exponent-p; |
5819 | 0 | } |
5820 | | |
5821 | | /* not done yet ... */ |
5822 | 0 | decAddOp(a, a, b, &aset, 0, &ignore); /* a=a+b for next estimate */ |
5823 | 0 | if (pp==p) continue; /* precision is at maximum */ |
5824 | | /* lengthen the next calculation */ |
5825 | 0 | pp=pp*2; /* double precision */ |
5826 | 0 | if (pp>p) pp=p; /* clamp to maximum */ |
5827 | 0 | aset.digits=pp; /* working context */ |
5828 | 0 | bset.digits=pp+rhs->digits; /* wider context */ |
5829 | 0 | } /* Newton's iteration */ |
5830 | |
|
5831 | | #if DECCHECK |
5832 | | /* just a sanity check; remove the test to show always */ |
5833 | | if (iterations>24) |
5834 | | printf("Ln iterations=%ld, status=%08lx, p=%ld, d=%ld\n", |
5835 | | (LI)iterations, (LI)*status, (LI)p, (LI)rhs->digits); |
5836 | | #endif |
5837 | | |
5838 | | /* Copy and round the result to res */ |
5839 | 0 | residue=1; /* indicate dirt to right */ |
5840 | 0 | if (ISZERO(a)) residue=0; /* .. unless underflowed to 0 */ |
5841 | 0 | aset.digits=set->digits; /* [use default rounding] */ |
5842 | 0 | decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */ |
5843 | 0 | decFinish(res, set, &residue, status); /* cleanup/set flags */ |
5844 | 0 | } while(0); /* end protected */ |
5845 | | |
5846 | 0 | if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ |
5847 | 0 | if (allocbufb!=NULL) free(allocbufb); /* .. */ |
5848 | | /* [status is handled by caller] */ |
5849 | 0 | return res; |
5850 | 0 | } /* decLnOp */ |
5851 | | #if defined(__clang__) || U_GCC_MAJOR_MINOR >= 406 |
5852 | | #pragma GCC diagnostic pop |
5853 | | #endif |
5854 | | |
5855 | | /* ------------------------------------------------------------------ */ |
5856 | | /* decQuantizeOp -- force exponent to requested value */ |
5857 | | /* */ |
5858 | | /* This computes C = op(A, B), where op adjusts the coefficient */ |
5859 | | /* of C (by rounding or shifting) such that the exponent (-scale) */ |
5860 | | /* of C has the value B or matches the exponent of B. */ |
5861 | | /* The numerical value of C will equal A, except for the effects of */ |
5862 | | /* any rounding that occurred. */ |
5863 | | /* */ |
5864 | | /* res is C, the result. C may be A or B */ |
5865 | | /* lhs is A, the number to adjust */ |
5866 | | /* rhs is B, the requested exponent */ |
5867 | | /* set is the context */ |
5868 | | /* quant is 1 for quantize or 0 for rescale */ |
5869 | | /* status is the status accumulator (this can be called without */ |
5870 | | /* risk of control loss) */ |
5871 | | /* */ |
5872 | | /* C must have space for set->digits digits. */ |
5873 | | /* */ |
5874 | | /* Unless there is an error or the result is infinite, the exponent */ |
5875 | | /* after the operation is guaranteed to be that requested. */ |
5876 | | /* ------------------------------------------------------------------ */ |
5877 | | static decNumber * decQuantizeOp(decNumber *res, const decNumber *lhs, |
5878 | | const decNumber *rhs, decContext *set, |
5879 | 0 | Flag quant, uInt *status) { |
5880 | | #if DECSUBSET |
5881 | | decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ |
5882 | | decNumber *allocrhs=NULL; /* .., rhs */ |
5883 | | #endif |
5884 | 0 | const decNumber *inrhs=rhs; /* save original rhs */ |
5885 | 0 | Int reqdigits=set->digits; /* requested DIGITS */ |
5886 | 0 | Int reqexp; /* requested exponent [-scale] */ |
5887 | 0 | Int residue=0; /* rounding residue */ |
5888 | 0 | Int etiny=set->emin-(reqdigits-1); |
5889 | |
|
5890 | | #if DECCHECK |
5891 | | if (decCheckOperands(res, lhs, rhs, set)) return res; |
5892 | | #endif |
5893 | |
|
5894 | 0 | do { /* protect allocated storage */ |
5895 | | #if DECSUBSET |
5896 | | if (!set->extended) { |
5897 | | /* reduce operands and set lostDigits status, as needed */ |
5898 | | if (lhs->digits>reqdigits) { |
5899 | | alloclhs=decRoundOperand(lhs, set, status); |
5900 | | if (alloclhs==NULL) break; |
5901 | | lhs=alloclhs; |
5902 | | } |
5903 | | if (rhs->digits>reqdigits) { /* [this only checks lostDigits] */ |
5904 | | allocrhs=decRoundOperand(rhs, set, status); |
5905 | | if (allocrhs==NULL) break; |
5906 | | rhs=allocrhs; |
5907 | | } |
5908 | | } |
5909 | | #endif |
5910 | | /* [following code does not require input rounding] */ |
5911 | | |
5912 | | /* Handle special values */ |
5913 | 0 | if (SPECIALARGS) { |
5914 | | /* NaNs get usual processing */ |
5915 | 0 | if (SPECIALARGS & (DECSNAN | DECNAN)) |
5916 | 0 | decNaNs(res, lhs, rhs, set, status); |
5917 | | /* one infinity but not both is bad */ |
5918 | 0 | else if ((lhs->bits ^ rhs->bits) & DECINF) |
5919 | 0 | *status|=DEC_Invalid_operation; |
5920 | | /* both infinity: return lhs */ |
5921 | 0 | else uprv_decNumberCopy(res, lhs); /* [nop if in place] */ |
5922 | 0 | break; |
5923 | 0 | } |
5924 | | |
5925 | | /* set requested exponent */ |
5926 | 0 | if (quant) reqexp=inrhs->exponent; /* quantize -- match exponents */ |
5927 | 0 | else { /* rescale -- use value of rhs */ |
5928 | | /* Original rhs must be an integer that fits and is in range, */ |
5929 | | /* which could be from -1999999997 to +999999999, thanks to */ |
5930 | | /* subnormals */ |
5931 | 0 | reqexp=decGetInt(inrhs); /* [cannot fail] */ |
5932 | 0 | } |
5933 | |
|
5934 | | #if DECSUBSET |
5935 | | if (!set->extended) etiny=set->emin; /* no subnormals */ |
5936 | | #endif |
5937 | |
|
5938 | 0 | if (reqexp==BADINT /* bad (rescale only) or .. */ |
5939 | 0 | || reqexp==BIGODD || reqexp==BIGEVEN /* very big (ditto) or .. */ |
5940 | 0 | || (reqexp<etiny) /* < lowest */ |
5941 | 0 | || (reqexp>set->emax)) { /* > emax */ |
5942 | 0 | *status|=DEC_Invalid_operation; |
5943 | 0 | break;} |
5944 | | |
5945 | | /* the RHS has been processed, so it can be overwritten now if necessary */ |
5946 | 0 | if (ISZERO(lhs)) { /* zero coefficient unchanged */ |
5947 | 0 | uprv_decNumberCopy(res, lhs); /* [nop if in place] */ |
5948 | 0 | res->exponent=reqexp; /* .. just set exponent */ |
5949 | | #if DECSUBSET |
5950 | | if (!set->extended) res->bits=0; /* subset specification; no -0 */ |
5951 | | #endif |
5952 | 0 | } |
5953 | 0 | else { /* non-zero lhs */ |
5954 | 0 | Int adjust=reqexp-lhs->exponent; /* digit adjustment needed */ |
5955 | | /* if adjusted coefficient will definitely not fit, give up now */ |
5956 | 0 | if ((lhs->digits-adjust)>reqdigits) { |
5957 | 0 | *status|=DEC_Invalid_operation; |
5958 | 0 | break; |
5959 | 0 | } |
5960 | | |
5961 | 0 | if (adjust>0) { /* increasing exponent */ |
5962 | | /* this will decrease the length of the coefficient by adjust */ |
5963 | | /* digits, and must round as it does so */ |
5964 | 0 | decContext workset; /* work */ |
5965 | 0 | workset=*set; /* clone rounding, etc. */ |
5966 | 0 | workset.digits=lhs->digits-adjust; /* set requested length */ |
5967 | | /* [note that the latter can be <1, here] */ |
5968 | 0 | decCopyFit(res, lhs, &workset, &residue, status); /* fit to result */ |
5969 | 0 | decApplyRound(res, &workset, residue, status); /* .. and round */ |
5970 | 0 | residue=0; /* [used] */ |
5971 | | /* If just rounded a 999s case, exponent will be off by one; */ |
5972 | | /* adjust back (after checking space), if so. */ |
5973 | 0 | if (res->exponent>reqexp) { |
5974 | | /* re-check needed, e.g., for quantize(0.9999, 0.001) under */ |
5975 | | /* set->digits==3 */ |
5976 | 0 | if (res->digits==reqdigits) { /* cannot shift by 1 */ |
5977 | 0 | *status&=~(DEC_Inexact | DEC_Rounded); /* [clean these] */ |
5978 | 0 | *status|=DEC_Invalid_operation; |
5979 | 0 | break; |
5980 | 0 | } |
5981 | 0 | res->digits=decShiftToMost(res->lsu, res->digits, 1); /* shift */ |
5982 | 0 | res->exponent--; /* (re)adjust the exponent. */ |
5983 | 0 | } |
5984 | | #if DECSUBSET |
5985 | | if (ISZERO(res) && !set->extended) res->bits=0; /* subset; no -0 */ |
5986 | | #endif |
5987 | 0 | } /* increase */ |
5988 | 0 | else /* adjust<=0 */ { /* decreasing or = exponent */ |
5989 | | /* this will increase the length of the coefficient by -adjust */ |
5990 | | /* digits, by adding zero or more trailing zeros; this is */ |
5991 | | /* already checked for fit, above */ |
5992 | 0 | uprv_decNumberCopy(res, lhs); /* [it will fit] */ |
5993 | | /* if padding needed (adjust<0), add it now... */ |
5994 | 0 | if (adjust<0) { |
5995 | 0 | res->digits=decShiftToMost(res->lsu, res->digits, -adjust); |
5996 | 0 | res->exponent+=adjust; /* adjust the exponent */ |
5997 | 0 | } |
5998 | 0 | } /* decrease */ |
5999 | 0 | } /* non-zero */ |
6000 | | |
6001 | | /* Check for overflow [do not use Finalize in this case, as an */ |
6002 | | /* overflow here is a "don't fit" situation] */ |
6003 | 0 | if (res->exponent>set->emax-res->digits+1) { /* too big */ |
6004 | 0 | *status|=DEC_Invalid_operation; |
6005 | 0 | break; |
6006 | 0 | } |
6007 | 0 | else { |
6008 | 0 | decFinalize(res, set, &residue, status); /* set subnormal flags */ |
6009 | 0 | *status&=~DEC_Underflow; /* suppress Underflow [as per 754] */ |
6010 | 0 | } |
6011 | 0 | } while(0); /* end protected */ |
6012 | | |
6013 | | #if DECSUBSET |
6014 | | if (allocrhs!=NULL) free(allocrhs); /* drop any storage used */ |
6015 | | if (alloclhs!=NULL) free(alloclhs); /* .. */ |
6016 | | #endif |
6017 | 0 | return res; |
6018 | 0 | } /* decQuantizeOp */ |
6019 | | |
6020 | | /* ------------------------------------------------------------------ */ |
6021 | | /* decCompareOp -- compare, min, or max two Numbers */ |
6022 | | /* */ |
6023 | | /* This computes C = A ? B and carries out one of four operations: */ |
6024 | | /* COMPARE -- returns the signum (as a number) giving the */ |
6025 | | /* result of a comparison unless one or both */ |
6026 | | /* operands is a NaN (in which case a NaN results) */ |
6027 | | /* COMPSIG -- as COMPARE except that a quiet NaN raises */ |
6028 | | /* Invalid operation. */ |
6029 | | /* COMPMAX -- returns the larger of the operands, using the */ |
6030 | | /* 754 maxnum operation */ |
6031 | | /* COMPMAXMAG -- ditto, comparing absolute values */ |
6032 | | /* COMPMIN -- the 754 minnum operation */ |
6033 | | /* COMPMINMAG -- ditto, comparing absolute values */ |
6034 | | /* COMTOTAL -- returns the signum (as a number) giving the */ |
6035 | | /* result of a comparison using 754 total ordering */ |
6036 | | /* */ |
6037 | | /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ |
6038 | | /* lhs is A */ |
6039 | | /* rhs is B */ |
6040 | | /* set is the context */ |
6041 | | /* op is the operation flag */ |
6042 | | /* status is the usual accumulator */ |
6043 | | /* */ |
6044 | | /* C must have space for one digit for COMPARE or set->digits for */ |
6045 | | /* COMPMAX, COMPMIN, COMPMAXMAG, or COMPMINMAG. */ |
6046 | | /* ------------------------------------------------------------------ */ |
6047 | | /* The emphasis here is on speed for common cases, and avoiding */ |
6048 | | /* coefficient comparison if possible. */ |
6049 | | /* ------------------------------------------------------------------ */ |
6050 | | static decNumber * decCompareOp(decNumber *res, const decNumber *lhs, |
6051 | | const decNumber *rhs, decContext *set, |
6052 | 0 | Flag op, uInt *status) { |
6053 | | #if DECSUBSET |
6054 | | decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ |
6055 | | decNumber *allocrhs=NULL; /* .., rhs */ |
6056 | | #endif |
6057 | 0 | Int result=0; /* default result value */ |
6058 | 0 | uByte merged; /* work */ |
6059 | |
|
6060 | | #if DECCHECK |
6061 | | if (decCheckOperands(res, lhs, rhs, set)) return res; |
6062 | | #endif |
6063 | |
|
6064 | 0 | do { /* protect allocated storage */ |
6065 | | #if DECSUBSET |
6066 | | if (!set->extended) { |
6067 | | /* reduce operands and set lostDigits status, as needed */ |
6068 | | if (lhs->digits>set->digits) { |
6069 | | alloclhs=decRoundOperand(lhs, set, status); |
6070 | | if (alloclhs==NULL) {result=BADINT; break;} |
6071 | | lhs=alloclhs; |
6072 | | } |
6073 | | if (rhs->digits>set->digits) { |
6074 | | allocrhs=decRoundOperand(rhs, set, status); |
6075 | | if (allocrhs==NULL) {result=BADINT; break;} |
6076 | | rhs=allocrhs; |
6077 | | } |
6078 | | } |
6079 | | #endif |
6080 | | /* [following code does not require input rounding] */ |
6081 | | |
6082 | | /* If total ordering then handle differing signs 'up front' */ |
6083 | 0 | if (op==COMPTOTAL) { /* total ordering */ |
6084 | 0 | if (decNumberIsNegative(lhs) && !decNumberIsNegative(rhs)) { |
6085 | 0 | result=-1; |
6086 | 0 | break; |
6087 | 0 | } |
6088 | 0 | if (!decNumberIsNegative(lhs) && decNumberIsNegative(rhs)) { |
6089 | 0 | result=+1; |
6090 | 0 | break; |
6091 | 0 | } |
6092 | 0 | } |
6093 | | |
6094 | | /* handle NaNs specially; let infinities drop through */ |
6095 | | /* This assumes sNaN (even just one) leads to NaN. */ |
6096 | 0 | merged=(lhs->bits | rhs->bits) & (DECSNAN | DECNAN); |
6097 | 0 | if (merged) { /* a NaN bit set */ |
6098 | 0 | if (op==COMPARE); /* result will be NaN */ |
6099 | 0 | else if (op==COMPSIG) /* treat qNaN as sNaN */ |
6100 | 0 | *status|=DEC_Invalid_operation | DEC_sNaN; |
6101 | 0 | else if (op==COMPTOTAL) { /* total ordering, always finite */ |
6102 | | /* signs are known to be the same; compute the ordering here */ |
6103 | | /* as if the signs are both positive, then invert for negatives */ |
6104 | 0 | if (!decNumberIsNaN(lhs)) result=-1; |
6105 | 0 | else if (!decNumberIsNaN(rhs)) result=+1; |
6106 | | /* here if both NaNs */ |
6107 | 0 | else if (decNumberIsSNaN(lhs) && decNumberIsQNaN(rhs)) result=-1; |
6108 | 0 | else if (decNumberIsQNaN(lhs) && decNumberIsSNaN(rhs)) result=+1; |
6109 | 0 | else { /* both NaN or both sNaN */ |
6110 | | /* now it just depends on the payload */ |
6111 | 0 | result=decUnitCompare(lhs->lsu, D2U(lhs->digits), |
6112 | 0 | rhs->lsu, D2U(rhs->digits), 0); |
6113 | | /* [Error not possible, as these are 'aligned'] */ |
6114 | 0 | } /* both same NaNs */ |
6115 | 0 | if (decNumberIsNegative(lhs)) result=-result; |
6116 | 0 | break; |
6117 | 0 | } /* total order */ |
6118 | | |
6119 | 0 | else if (merged & DECSNAN); /* sNaN -> qNaN */ |
6120 | 0 | else { /* here if MIN or MAX and one or two quiet NaNs */ |
6121 | | /* min or max -- 754 rules ignore single NaN */ |
6122 | 0 | if (!decNumberIsNaN(lhs) || !decNumberIsNaN(rhs)) { |
6123 | | /* just one NaN; force choice to be the non-NaN operand */ |
6124 | 0 | op=COMPMAX; |
6125 | 0 | if (lhs->bits & DECNAN) result=-1; /* pick rhs */ |
6126 | 0 | else result=+1; /* pick lhs */ |
6127 | 0 | break; |
6128 | 0 | } |
6129 | 0 | } /* max or min */ |
6130 | 0 | op=COMPNAN; /* use special path */ |
6131 | 0 | decNaNs(res, lhs, rhs, set, status); /* propagate NaN */ |
6132 | 0 | break; |
6133 | 0 | } |
6134 | | /* have numbers */ |
6135 | 0 | if (op==COMPMAXMAG || op==COMPMINMAG) result=decCompare(lhs, rhs, 1); |
6136 | 0 | else result=decCompare(lhs, rhs, 0); /* sign matters */ |
6137 | 0 | } while(0); /* end protected */ |
6138 | | |
6139 | 0 | if (result==BADINT) *status|=DEC_Insufficient_storage; /* rare */ |
6140 | 0 | else { |
6141 | 0 | if (op==COMPARE || op==COMPSIG ||op==COMPTOTAL) { /* returning signum */ |
6142 | 0 | if (op==COMPTOTAL && result==0) { |
6143 | | /* operands are numerically equal or same NaN (and same sign, */ |
6144 | | /* tested first); if identical, leave result 0 */ |
6145 | 0 | if (lhs->exponent!=rhs->exponent) { |
6146 | 0 | if (lhs->exponent<rhs->exponent) result=-1; |
6147 | 0 | else result=+1; |
6148 | 0 | if (decNumberIsNegative(lhs)) result=-result; |
6149 | 0 | } /* lexp!=rexp */ |
6150 | 0 | } /* total-order by exponent */ |
6151 | 0 | uprv_decNumberZero(res); /* [always a valid result] */ |
6152 | 0 | if (result!=0) { /* must be -1 or +1 */ |
6153 | 0 | *res->lsu=1; |
6154 | 0 | if (result<0) res->bits=DECNEG; |
6155 | 0 | } |
6156 | 0 | } |
6157 | 0 | else if (op==COMPNAN); /* special, drop through */ |
6158 | 0 | else { /* MAX or MIN, non-NaN result */ |
6159 | 0 | Int residue=0; /* rounding accumulator */ |
6160 | | /* choose the operand for the result */ |
6161 | 0 | const decNumber *choice; |
6162 | 0 | if (result==0) { /* operands are numerically equal */ |
6163 | | /* choose according to sign then exponent (see 754) */ |
6164 | 0 | uByte slhs=(lhs->bits & DECNEG); |
6165 | 0 | uByte srhs=(rhs->bits & DECNEG); |
6166 | | #if DECSUBSET |
6167 | | if (!set->extended) { /* subset: force left-hand */ |
6168 | | op=COMPMAX; |
6169 | | result=+1; |
6170 | | } |
6171 | | else |
6172 | | #endif |
6173 | 0 | if (slhs!=srhs) { /* signs differ */ |
6174 | 0 | if (slhs) result=-1; /* rhs is max */ |
6175 | 0 | else result=+1; /* lhs is max */ |
6176 | 0 | } |
6177 | 0 | else if (slhs && srhs) { /* both negative */ |
6178 | 0 | if (lhs->exponent<rhs->exponent) result=+1; |
6179 | 0 | else result=-1; |
6180 | | /* [if equal, use lhs, technically identical] */ |
6181 | 0 | } |
6182 | 0 | else { /* both positive */ |
6183 | 0 | if (lhs->exponent>rhs->exponent) result=+1; |
6184 | 0 | else result=-1; |
6185 | | /* [ditto] */ |
6186 | 0 | } |
6187 | 0 | } /* numerically equal */ |
6188 | | /* here result will be non-0; reverse if looking for MIN */ |
6189 | 0 | if (op==COMPMIN || op==COMPMINMAG) result=-result; |
6190 | 0 | choice=(result>0 ? lhs : rhs); /* choose */ |
6191 | | /* copy chosen to result, rounding if need be */ |
6192 | 0 | decCopyFit(res, choice, set, &residue, status); |
6193 | 0 | decFinish(res, set, &residue, status); |
6194 | 0 | } |
6195 | 0 | } |
6196 | | #if DECSUBSET |
6197 | | if (allocrhs!=NULL) free(allocrhs); /* free any storage used */ |
6198 | | if (alloclhs!=NULL) free(alloclhs); /* .. */ |
6199 | | #endif |
6200 | 0 | return res; |
6201 | 0 | } /* decCompareOp */ |
6202 | | |
6203 | | /* ------------------------------------------------------------------ */ |
6204 | | /* decCompare -- compare two decNumbers by numerical value */ |
6205 | | /* */ |
6206 | | /* This routine compares A ? B without altering them. */ |
6207 | | /* */ |
6208 | | /* Arg1 is A, a decNumber which is not a NaN */ |
6209 | | /* Arg2 is B, a decNumber which is not a NaN */ |
6210 | | /* Arg3 is 1 for a sign-independent compare, 0 otherwise */ |
6211 | | /* */ |
6212 | | /* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */ |
6213 | | /* (the only possible failure is an allocation error) */ |
6214 | | /* ------------------------------------------------------------------ */ |
6215 | | static Int decCompare(const decNumber *lhs, const decNumber *rhs, |
6216 | 0 | Flag abs_c) { |
6217 | 0 | Int result; /* result value */ |
6218 | 0 | Int sigr; /* rhs signum */ |
6219 | 0 | Int compare; /* work */ |
6220 | |
|
6221 | 0 | result=1; /* assume signum(lhs) */ |
6222 | 0 | if (ISZERO(lhs)) result=0; |
6223 | 0 | if (abs_c) { |
6224 | 0 | if (ISZERO(rhs)) return result; /* LHS wins or both 0 */ |
6225 | | /* RHS is non-zero */ |
6226 | 0 | if (result==0) return -1; /* LHS is 0; RHS wins */ |
6227 | | /* [here, both non-zero, result=1] */ |
6228 | 0 | } |
6229 | 0 | else { /* signs matter */ |
6230 | 0 | if (result && decNumberIsNegative(lhs)) result=-1; |
6231 | 0 | sigr=1; /* compute signum(rhs) */ |
6232 | 0 | if (ISZERO(rhs)) sigr=0; |
6233 | 0 | else if (decNumberIsNegative(rhs)) sigr=-1; |
6234 | 0 | if (result > sigr) return +1; /* L > R, return 1 */ |
6235 | 0 | if (result < sigr) return -1; /* L < R, return -1 */ |
6236 | 0 | if (result==0) return 0; /* both 0 */ |
6237 | 0 | } |
6238 | | |
6239 | | /* signums are the same; both are non-zero */ |
6240 | 0 | if ((lhs->bits | rhs->bits) & DECINF) { /* one or more infinities */ |
6241 | 0 | if (decNumberIsInfinite(rhs)) { |
6242 | 0 | if (decNumberIsInfinite(lhs)) result=0;/* both infinite */ |
6243 | 0 | else result=-result; /* only rhs infinite */ |
6244 | 0 | } |
6245 | 0 | return result; |
6246 | 0 | } |
6247 | | /* must compare the coefficients, allowing for exponents */ |
6248 | 0 | if (lhs->exponent>rhs->exponent) { /* LHS exponent larger */ |
6249 | | /* swap sides, and sign */ |
6250 | 0 | const decNumber *temp=lhs; |
6251 | 0 | lhs=rhs; |
6252 | 0 | rhs=temp; |
6253 | 0 | result=-result; |
6254 | 0 | } |
6255 | 0 | compare=decUnitCompare(lhs->lsu, D2U(lhs->digits), |
6256 | 0 | rhs->lsu, D2U(rhs->digits), |
6257 | 0 | rhs->exponent-lhs->exponent); |
6258 | 0 | if (compare!=BADINT) compare*=result; /* comparison succeeded */ |
6259 | 0 | return compare; |
6260 | 0 | } /* decCompare */ |
6261 | | |
6262 | | /* ------------------------------------------------------------------ */ |
6263 | | /* decUnitCompare -- compare two >=0 integers in Unit arrays */ |
6264 | | /* */ |
6265 | | /* This routine compares A ? B*10**E where A and B are unit arrays */ |
6266 | | /* A is a plain integer */ |
6267 | | /* B has an exponent of E (which must be non-negative) */ |
6268 | | /* */ |
6269 | | /* Arg1 is A first Unit (lsu) */ |
6270 | | /* Arg2 is A length in Units */ |
6271 | | /* Arg3 is B first Unit (lsu) */ |
6272 | | /* Arg4 is B length in Units */ |
6273 | | /* Arg5 is E (0 if the units are aligned) */ |
6274 | | /* */ |
6275 | | /* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */ |
6276 | | /* (the only possible failure is an allocation error, which can */ |
6277 | | /* only occur if E!=0) */ |
6278 | | /* ------------------------------------------------------------------ */ |
6279 | | static Int decUnitCompare(const Unit *a, Int alength, |
6280 | 0 | const Unit *b, Int blength, Int exp) { |
6281 | 0 | Unit *acc; /* accumulator for result */ |
6282 | 0 | Unit accbuff[SD2U(DECBUFFER*2+1)]; /* local buffer */ |
6283 | 0 | Unit *allocacc=NULL; /* -> allocated acc buffer, iff allocated */ |
6284 | 0 | Int accunits, need; /* units in use or needed for acc */ |
6285 | 0 | const Unit *l, *r, *u; /* work */ |
6286 | 0 | Int expunits, exprem, result; /* .. */ |
6287 | |
|
6288 | 0 | if (exp==0) { /* aligned; fastpath */ |
6289 | 0 | if (alength>blength) return 1; |
6290 | 0 | if (alength<blength) return -1; |
6291 | | /* same number of units in both -- need unit-by-unit compare */ |
6292 | 0 | l=a+alength-1; |
6293 | 0 | r=b+alength-1; |
6294 | 0 | for (;l>=a; l--, r--) { |
6295 | 0 | if (*l>*r) return 1; |
6296 | 0 | if (*l<*r) return -1; |
6297 | 0 | } |
6298 | 0 | return 0; /* all units match */ |
6299 | 0 | } /* aligned */ |
6300 | | |
6301 | | /* Unaligned. If one is >1 unit longer than the other, padded */ |
6302 | | /* approximately, then can return easily */ |
6303 | 0 | if (alength>blength+(Int)D2U(exp)) return 1; |
6304 | 0 | if (alength+1<blength+(Int)D2U(exp)) return -1; |
6305 | | |
6306 | | /* Need to do a real subtract. For this, a result buffer is needed */ |
6307 | | /* even though only the sign is of interest. Its length needs */ |
6308 | | /* to be the larger of alength and padded blength, +2 */ |
6309 | 0 | need=blength+D2U(exp); /* maximum real length of B */ |
6310 | 0 | if (need<alength) need=alength; |
6311 | 0 | need+=2; |
6312 | 0 | acc=accbuff; /* assume use local buffer */ |
6313 | 0 | if (need*sizeof(Unit)>sizeof(accbuff)) { |
6314 | 0 | allocacc=(Unit *)malloc(need*sizeof(Unit)); |
6315 | 0 | if (allocacc==NULL) return BADINT; /* hopeless -- abandon */ |
6316 | 0 | acc=allocacc; |
6317 | 0 | } |
6318 | | /* Calculate units and remainder from exponent. */ |
6319 | 0 | expunits=exp/DECDPUN; |
6320 | 0 | exprem=exp%DECDPUN; |
6321 | | /* subtract [A+B*(-m)] */ |
6322 | 0 | accunits=decUnitAddSub(a, alength, b, blength, expunits, acc, |
6323 | 0 | -(Int)powers[exprem]); |
6324 | | /* [UnitAddSub result may have leading zeros, even on zero] */ |
6325 | 0 | if (accunits<0) result=-1; /* negative result */ |
6326 | 0 | else { /* non-negative result */ |
6327 | | /* check units of the result before freeing any storage */ |
6328 | 0 | for (u=acc; u<acc+accunits-1 && *u==0;) u++; |
6329 | 0 | result=(*u==0 ? 0 : +1); |
6330 | 0 | } |
6331 | | /* clean up and return the result */ |
6332 | 0 | if (allocacc!=NULL) free(allocacc); /* drop any storage used */ |
6333 | 0 | return result; |
6334 | 0 | } /* decUnitCompare */ |
6335 | | |
6336 | | /* ------------------------------------------------------------------ */ |
6337 | | /* decUnitAddSub -- add or subtract two >=0 integers in Unit arrays */ |
6338 | | /* */ |
6339 | | /* This routine performs the calculation: */ |
6340 | | /* */ |
6341 | | /* C=A+(B*M) */ |
6342 | | /* */ |
6343 | | /* Where M is in the range -DECDPUNMAX through +DECDPUNMAX. */ |
6344 | | /* */ |
6345 | | /* A may be shorter or longer than B. */ |
6346 | | /* */ |
6347 | | /* Leading zeros are not removed after a calculation. The result is */ |
6348 | | /* either the same length as the longer of A and B (adding any */ |
6349 | | /* shift), or one Unit longer than that (if a Unit carry occurred). */ |
6350 | | /* */ |
6351 | | /* A and B content are not altered unless C is also A or B. */ |
6352 | | /* C may be the same array as A or B, but only if no zero padding is */ |
6353 | | /* requested (that is, C may be B only if bshift==0). */ |
6354 | | /* C is filled from the lsu; only those units necessary to complete */ |
6355 | | /* the calculation are referenced. */ |
6356 | | /* */ |
6357 | | /* Arg1 is A first Unit (lsu) */ |
6358 | | /* Arg2 is A length in Units */ |
6359 | | /* Arg3 is B first Unit (lsu) */ |
6360 | | /* Arg4 is B length in Units */ |
6361 | | /* Arg5 is B shift in Units (>=0; pads with 0 units if positive) */ |
6362 | | /* Arg6 is C first Unit (lsu) */ |
6363 | | /* Arg7 is M, the multiplier */ |
6364 | | /* */ |
6365 | | /* returns the count of Units written to C, which will be non-zero */ |
6366 | | /* and negated if the result is negative. That is, the sign of the */ |
6367 | | /* returned Int is the sign of the result (positive for zero) and */ |
6368 | | /* the absolute value of the Int is the count of Units. */ |
6369 | | /* */ |
6370 | | /* It is the caller's responsibility to make sure that C size is */ |
6371 | | /* safe, allowing space if necessary for a one-Unit carry. */ |
6372 | | /* */ |
6373 | | /* This routine is severely performance-critical; *any* change here */ |
6374 | | /* must be measured (timed) to assure no performance degradation. */ |
6375 | | /* In particular, trickery here tends to be counter-productive, as */ |
6376 | | /* increased complexity of code hurts register optimizations on */ |
6377 | | /* register-poor architectures. Avoiding divisions is nearly */ |
6378 | | /* always a Good Idea, however. */ |
6379 | | /* */ |
6380 | | /* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark */ |
6381 | | /* (IBM Warwick, UK) for some of the ideas used in this routine. */ |
6382 | | /* ------------------------------------------------------------------ */ |
6383 | | static Int decUnitAddSub(const Unit *a, Int alength, |
6384 | | const Unit *b, Int blength, Int bshift, |
6385 | 0 | Unit *c, Int m) { |
6386 | 0 | const Unit *alsu=a; /* A lsu [need to remember it] */ |
6387 | 0 | Unit *clsu=c; /* C ditto */ |
6388 | 0 | Unit *minC; /* low water mark for C */ |
6389 | 0 | Unit *maxC; /* high water mark for C */ |
6390 | 0 | eInt carry=0; /* carry integer (could be Long) */ |
6391 | 0 | Int add; /* work */ |
6392 | 0 | #if DECDPUN<=4 /* myriadal, millenary, etc. */ |
6393 | 0 | Int est; /* estimated quotient */ |
6394 | 0 | #endif |
6395 | |
|
6396 | | #if DECTRACE |
6397 | | if (alength<1 || blength<1) |
6398 | | printf("decUnitAddSub: alen blen m %ld %ld [%ld]\n", alength, blength, m); |
6399 | | #endif |
6400 | |
|
6401 | 0 | maxC=c+alength; /* A is usually the longer */ |
6402 | 0 | minC=c+blength; /* .. and B the shorter */ |
6403 | 0 | if (bshift!=0) { /* B is shifted; low As copy across */ |
6404 | 0 | minC+=bshift; |
6405 | | /* if in place [common], skip copy unless there's a gap [rare] */ |
6406 | 0 | if (a==c && bshift<=alength) { |
6407 | 0 | c+=bshift; |
6408 | 0 | a+=bshift; |
6409 | 0 | } |
6410 | 0 | else for (; c<clsu+bshift; a++, c++) { /* copy needed */ |
6411 | 0 | if (a<alsu+alength) *c=*a; |
6412 | 0 | else *c=0; |
6413 | 0 | } |
6414 | 0 | } |
6415 | 0 | if (minC>maxC) { /* swap */ |
6416 | 0 | Unit *hold=minC; |
6417 | 0 | minC=maxC; |
6418 | 0 | maxC=hold; |
6419 | 0 | } |
6420 | | |
6421 | | /* For speed, do the addition as two loops; the first where both A */ |
6422 | | /* and B contribute, and the second (if necessary) where only one or */ |
6423 | | /* other of the numbers contribute. */ |
6424 | | /* Carry handling is the same (i.e., duplicated) in each case. */ |
6425 | 0 | for (; c<minC; c++) { |
6426 | 0 | carry+=*a; |
6427 | 0 | a++; |
6428 | 0 | carry+=((eInt)*b)*m; /* [special-casing m=1/-1 */ |
6429 | 0 | b++; /* here is not a win] */ |
6430 | | /* here carry is new Unit of digits; it could be +ve or -ve */ |
6431 | 0 | if ((ueInt)carry<=DECDPUNMAX) { /* fastpath 0-DECDPUNMAX */ |
6432 | 0 | *c=(Unit)carry; |
6433 | 0 | carry=0; |
6434 | 0 | continue; |
6435 | 0 | } |
6436 | | #if DECDPUN==4 /* use divide-by-multiply */ |
6437 | | if (carry>=0) { |
6438 | | est=(((ueInt)carry>>11)*53687)>>18; |
6439 | | *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ |
6440 | | carry=est; /* likely quotient [89%] */ |
6441 | | if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ |
6442 | | carry++; |
6443 | | *c-=DECDPUNMAX+1; |
6444 | | continue; |
6445 | | } |
6446 | | /* negative case */ |
6447 | | carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ |
6448 | | est=(((ueInt)carry>>11)*53687)>>18; |
6449 | | *c=(Unit)(carry-est*(DECDPUNMAX+1)); |
6450 | | carry=est-(DECDPUNMAX+1); /* correctly negative */ |
6451 | | if (*c<DECDPUNMAX+1) continue; /* was OK */ |
6452 | | carry++; |
6453 | | *c-=DECDPUNMAX+1; |
6454 | | #elif DECDPUN==3 |
6455 | | if (carry>=0) { |
6456 | | est=(((ueInt)carry>>3)*16777)>>21; |
6457 | | *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ |
6458 | | carry=est; /* likely quotient [99%] */ |
6459 | | if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ |
6460 | | carry++; |
6461 | | *c-=DECDPUNMAX+1; |
6462 | | continue; |
6463 | | } |
6464 | | /* negative case */ |
6465 | | carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ |
6466 | | est=(((ueInt)carry>>3)*16777)>>21; |
6467 | | *c=(Unit)(carry-est*(DECDPUNMAX+1)); |
6468 | | carry=est-(DECDPUNMAX+1); /* correctly negative */ |
6469 | | if (*c<DECDPUNMAX+1) continue; /* was OK */ |
6470 | | carry++; |
6471 | | *c-=DECDPUNMAX+1; |
6472 | | #elif DECDPUN<=2 |
6473 | | /* Can use QUOT10 as carry <= 4 digits */ |
6474 | 0 | if (carry>=0) { |
6475 | 0 | est=QUOT10(carry, DECDPUN); |
6476 | 0 | *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ |
6477 | 0 | carry=est; /* quotient */ |
6478 | 0 | continue; |
6479 | 0 | } |
6480 | | /* negative case */ |
6481 | 0 | carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ |
6482 | 0 | est=QUOT10(carry, DECDPUN); |
6483 | 0 | *c=(Unit)(carry-est*(DECDPUNMAX+1)); |
6484 | 0 | carry=est-(DECDPUNMAX+1); /* correctly negative */ |
6485 | | #else |
6486 | | /* remainder operator is undefined if negative, so must test */ |
6487 | | if ((ueInt)carry<(DECDPUNMAX+1)*2) { /* fastpath carry +1 */ |
6488 | | *c=(Unit)(carry-(DECDPUNMAX+1)); /* [helps additions] */ |
6489 | | carry=1; |
6490 | | continue; |
6491 | | } |
6492 | | if (carry>=0) { |
6493 | | *c=(Unit)(carry%(DECDPUNMAX+1)); |
6494 | | carry=carry/(DECDPUNMAX+1); |
6495 | | continue; |
6496 | | } |
6497 | | /* negative case */ |
6498 | | carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ |
6499 | | *c=(Unit)(carry%(DECDPUNMAX+1)); |
6500 | | carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1); |
6501 | | #endif |
6502 | 0 | } /* c */ |
6503 | | |
6504 | | /* now may have one or other to complete */ |
6505 | | /* [pretest to avoid loop setup/shutdown] */ |
6506 | 0 | if (c<maxC) for (; c<maxC; c++) { |
6507 | 0 | if (a<alsu+alength) { /* still in A */ |
6508 | 0 | carry+=*a; |
6509 | 0 | a++; |
6510 | 0 | } |
6511 | 0 | else { /* inside B */ |
6512 | 0 | carry+=((eInt)*b)*m; |
6513 | 0 | b++; |
6514 | 0 | } |
6515 | | /* here carry is new Unit of digits; it could be +ve or -ve and */ |
6516 | | /* magnitude up to DECDPUNMAX squared */ |
6517 | 0 | if ((ueInt)carry<=DECDPUNMAX) { /* fastpath 0-DECDPUNMAX */ |
6518 | 0 | *c=(Unit)carry; |
6519 | 0 | carry=0; |
6520 | 0 | continue; |
6521 | 0 | } |
6522 | | /* result for this unit is negative or >DECDPUNMAX */ |
6523 | | #if DECDPUN==4 /* use divide-by-multiply */ |
6524 | | if (carry>=0) { |
6525 | | est=(((ueInt)carry>>11)*53687)>>18; |
6526 | | *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ |
6527 | | carry=est; /* likely quotient [79.7%] */ |
6528 | | if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ |
6529 | | carry++; |
6530 | | *c-=DECDPUNMAX+1; |
6531 | | continue; |
6532 | | } |
6533 | | /* negative case */ |
6534 | | carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ |
6535 | | est=(((ueInt)carry>>11)*53687)>>18; |
6536 | | *c=(Unit)(carry-est*(DECDPUNMAX+1)); |
6537 | | carry=est-(DECDPUNMAX+1); /* correctly negative */ |
6538 | | if (*c<DECDPUNMAX+1) continue; /* was OK */ |
6539 | | carry++; |
6540 | | *c-=DECDPUNMAX+1; |
6541 | | #elif DECDPUN==3 |
6542 | | if (carry>=0) { |
6543 | | est=(((ueInt)carry>>3)*16777)>>21; |
6544 | | *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ |
6545 | | carry=est; /* likely quotient [99%] */ |
6546 | | if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ |
6547 | | carry++; |
6548 | | *c-=DECDPUNMAX+1; |
6549 | | continue; |
6550 | | } |
6551 | | /* negative case */ |
6552 | | carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ |
6553 | | est=(((ueInt)carry>>3)*16777)>>21; |
6554 | | *c=(Unit)(carry-est*(DECDPUNMAX+1)); |
6555 | | carry=est-(DECDPUNMAX+1); /* correctly negative */ |
6556 | | if (*c<DECDPUNMAX+1) continue; /* was OK */ |
6557 | | carry++; |
6558 | | *c-=DECDPUNMAX+1; |
6559 | | #elif DECDPUN<=2 |
6560 | 0 | if (carry>=0) { |
6561 | 0 | est=QUOT10(carry, DECDPUN); |
6562 | 0 | *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ |
6563 | 0 | carry=est; /* quotient */ |
6564 | 0 | continue; |
6565 | 0 | } |
6566 | | /* negative case */ |
6567 | 0 | carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ |
6568 | 0 | est=QUOT10(carry, DECDPUN); |
6569 | 0 | *c=(Unit)(carry-est*(DECDPUNMAX+1)); |
6570 | 0 | carry=est-(DECDPUNMAX+1); /* correctly negative */ |
6571 | | #else |
6572 | | if ((ueInt)carry<(DECDPUNMAX+1)*2){ /* fastpath carry 1 */ |
6573 | | *c=(Unit)(carry-(DECDPUNMAX+1)); |
6574 | | carry=1; |
6575 | | continue; |
6576 | | } |
6577 | | /* remainder operator is undefined if negative, so must test */ |
6578 | | if (carry>=0) { |
6579 | | *c=(Unit)(carry%(DECDPUNMAX+1)); |
6580 | | carry=carry/(DECDPUNMAX+1); |
6581 | | continue; |
6582 | | } |
6583 | | /* negative case */ |
6584 | | carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ |
6585 | | *c=(Unit)(carry%(DECDPUNMAX+1)); |
6586 | | carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1); |
6587 | | #endif |
6588 | 0 | } /* c */ |
6589 | | |
6590 | | /* OK, all A and B processed; might still have carry or borrow */ |
6591 | | /* return number of Units in the result, negated if a borrow */ |
6592 | 0 | if (carry==0) return static_cast<int32_t>(c-clsu); /* no carry, so no more to do */ |
6593 | 0 | if (carry>0) { /* positive carry */ |
6594 | 0 | *c=(Unit)carry; /* place as new unit */ |
6595 | 0 | c++; /* .. */ |
6596 | 0 | return static_cast<int32_t>(c-clsu); |
6597 | 0 | } |
6598 | | /* -ve carry: it's a borrow; complement needed */ |
6599 | 0 | add=1; /* temporary carry... */ |
6600 | 0 | for (c=clsu; c<maxC; c++) { |
6601 | 0 | add=DECDPUNMAX+add-*c; |
6602 | 0 | if (add<=DECDPUNMAX) { |
6603 | 0 | *c=(Unit)add; |
6604 | 0 | add=0; |
6605 | 0 | } |
6606 | 0 | else { |
6607 | 0 | *c=0; |
6608 | 0 | add=1; |
6609 | 0 | } |
6610 | 0 | } |
6611 | | /* add an extra unit iff it would be non-zero */ |
6612 | | #if DECTRACE |
6613 | | printf("UAS borrow: add %ld, carry %ld\n", add, carry); |
6614 | | #endif |
6615 | 0 | if ((add-carry-1)!=0) { |
6616 | 0 | *c=(Unit)(add-carry-1); |
6617 | 0 | c++; /* interesting, include it */ |
6618 | 0 | } |
6619 | 0 | return static_cast<int32_t>(clsu-c); /* -ve result indicates borrowed */ |
6620 | 0 | } /* decUnitAddSub */ |
6621 | | |
6622 | | /* ------------------------------------------------------------------ */ |
6623 | | /* decTrim -- trim trailing zeros or normalize */ |
6624 | | /* */ |
6625 | | /* dn is the number to trim or normalize */ |
6626 | | /* set is the context to use to check for clamp */ |
6627 | | /* all is 1 to remove all trailing zeros, 0 for just fraction ones */ |
6628 | | /* noclamp is 1 to unconditional (unclamped) trim */ |
6629 | | /* dropped returns the number of discarded trailing zeros */ |
6630 | | /* returns dn */ |
6631 | | /* */ |
6632 | | /* If clamp is set in the context then the number of zeros trimmed */ |
6633 | | /* may be limited if the exponent is high. */ |
6634 | | /* All fields are updated as required. This is a utility operation, */ |
6635 | | /* so special values are unchanged and no error is possible. */ |
6636 | | /* ------------------------------------------------------------------ */ |
6637 | | static decNumber * decTrim(decNumber *dn, decContext *set, Flag all, |
6638 | 0 | Flag noclamp, Int *dropped) { |
6639 | 0 | Int d, exp; /* work */ |
6640 | 0 | uInt cut; /* .. */ |
6641 | 0 | Unit *up; /* -> current Unit */ |
6642 | |
|
6643 | | #if DECCHECK |
6644 | | if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn; |
6645 | | #endif |
6646 | |
|
6647 | 0 | *dropped=0; /* assume no zeros dropped */ |
6648 | 0 | if ((dn->bits & DECSPECIAL) /* fast exit if special .. */ |
6649 | 0 | || (*dn->lsu & 0x01)) return dn; /* .. or odd */ |
6650 | 0 | if (ISZERO(dn)) { /* .. or 0 */ |
6651 | 0 | dn->exponent=0; /* (sign is preserved) */ |
6652 | 0 | return dn; |
6653 | 0 | } |
6654 | | |
6655 | | /* have a finite number which is even */ |
6656 | 0 | exp=dn->exponent; |
6657 | 0 | cut=1; /* digit (1-DECDPUN) in Unit */ |
6658 | 0 | up=dn->lsu; /* -> current Unit */ |
6659 | 0 | for (d=0; d<dn->digits-1; d++) { /* [don't strip the final digit] */ |
6660 | | /* slice by powers */ |
6661 | 0 | #if DECDPUN<=4 |
6662 | 0 | uInt quot=QUOT10(*up, cut); |
6663 | 0 | if ((*up-quot*powers[cut])!=0) break; /* found non-0 digit */ |
6664 | | #else |
6665 | | if (*up%powers[cut]!=0) break; /* found non-0 digit */ |
6666 | | #endif |
6667 | | /* have a trailing 0 */ |
6668 | 0 | if (!all) { /* trimming */ |
6669 | | /* [if exp>0 then all trailing 0s are significant for trim] */ |
6670 | 0 | if (exp<=0) { /* if digit might be significant */ |
6671 | 0 | if (exp==0) break; /* then quit */ |
6672 | 0 | exp++; /* next digit might be significant */ |
6673 | 0 | } |
6674 | 0 | } |
6675 | 0 | cut++; /* next power */ |
6676 | 0 | if (cut>DECDPUN) { /* need new Unit */ |
6677 | 0 | up++; |
6678 | 0 | cut=1; |
6679 | 0 | } |
6680 | 0 | } /* d */ |
6681 | 0 | if (d==0) return dn; /* none to drop */ |
6682 | | |
6683 | | /* may need to limit drop if clamping */ |
6684 | 0 | if (set->clamp && !noclamp) { |
6685 | 0 | Int maxd=set->emax-set->digits+1-dn->exponent; |
6686 | 0 | if (maxd<=0) return dn; /* nothing possible */ |
6687 | 0 | if (d>maxd) d=maxd; |
6688 | 0 | } |
6689 | | |
6690 | | /* effect the drop */ |
6691 | 0 | decShiftToLeast(dn->lsu, D2U(dn->digits), d); |
6692 | 0 | dn->exponent+=d; /* maintain numerical value */ |
6693 | 0 | dn->digits-=d; /* new length */ |
6694 | 0 | *dropped=d; /* report the count */ |
6695 | 0 | return dn; |
6696 | 0 | } /* decTrim */ |
6697 | | |
6698 | | /* ------------------------------------------------------------------ */ |
6699 | | /* decReverse -- reverse a Unit array in place */ |
6700 | | /* */ |
6701 | | /* ulo is the start of the array */ |
6702 | | /* uhi is the end of the array (highest Unit to include) */ |
6703 | | /* */ |
6704 | | /* The units ulo through uhi are reversed in place (if the number */ |
6705 | | /* of units is odd, the middle one is untouched). Note that the */ |
6706 | | /* digit(s) in each unit are unaffected. */ |
6707 | | /* ------------------------------------------------------------------ */ |
6708 | 0 | static void decReverse(Unit *ulo, Unit *uhi) { |
6709 | 0 | Unit temp; |
6710 | 0 | for (; ulo<uhi; ulo++, uhi--) { |
6711 | 0 | temp=*ulo; |
6712 | 0 | *ulo=*uhi; |
6713 | 0 | *uhi=temp; |
6714 | 0 | } |
6715 | 0 | return; |
6716 | 0 | } /* decReverse */ |
6717 | | |
6718 | | /* ------------------------------------------------------------------ */ |
6719 | | /* decShiftToMost -- shift digits in array towards most significant */ |
6720 | | /* */ |
6721 | | /* uar is the array */ |
6722 | | /* digits is the count of digits in use in the array */ |
6723 | | /* shift is the number of zeros to pad with (least significant); */ |
6724 | | /* it must be zero or positive */ |
6725 | | /* */ |
6726 | | /* returns the new length of the integer in the array, in digits */ |
6727 | | /* */ |
6728 | | /* No overflow is permitted (that is, the uar array must be known to */ |
6729 | | /* be large enough to hold the result, after shifting). */ |
6730 | | /* ------------------------------------------------------------------ */ |
6731 | 0 | static Int decShiftToMost(Unit *uar, Int digits, Int shift) { |
6732 | 0 | Unit *target, *source, *first; /* work */ |
6733 | 0 | Int cut; /* odd 0's to add */ |
6734 | 0 | uInt next; /* work */ |
6735 | |
|
6736 | 0 | if (shift==0) return digits; /* [fastpath] nothing to do */ |
6737 | 0 | if ((digits+shift)<=DECDPUN) { /* [fastpath] single-unit case */ |
6738 | 0 | *uar=(Unit)(*uar*powers[shift]); |
6739 | 0 | return digits+shift; |
6740 | 0 | } |
6741 | | |
6742 | 0 | next=0; /* all paths */ |
6743 | 0 | source=uar+D2U(digits)-1; /* where msu comes from */ |
6744 | 0 | target=source+D2U(shift); /* where upper part of first cut goes */ |
6745 | 0 | cut=DECDPUN-MSUDIGITS(shift); /* where to slice */ |
6746 | 0 | if (cut==0) { /* unit-boundary case */ |
6747 | 0 | for (; source>=uar; source--, target--) *target=*source; |
6748 | 0 | } |
6749 | 0 | else { |
6750 | 0 | first=uar+D2U(digits+shift)-1; /* where msu of source will end up */ |
6751 | 0 | for (; source>=uar; source--, target--) { |
6752 | | /* split the source Unit and accumulate remainder for next */ |
6753 | 0 | #if DECDPUN<=4 |
6754 | 0 | uInt quot=QUOT10(*source, cut); |
6755 | 0 | uInt rem=*source-quot*powers[cut]; |
6756 | 0 | next+=quot; |
6757 | | #else |
6758 | | uInt rem=*source%powers[cut]; |
6759 | | next+=*source/powers[cut]; |
6760 | | #endif |
6761 | 0 | if (target<=first) *target=(Unit)next; /* write to target iff valid */ |
6762 | 0 | next=rem*powers[DECDPUN-cut]; /* save remainder for next Unit */ |
6763 | 0 | } |
6764 | 0 | } /* shift-move */ |
6765 | | |
6766 | | /* propagate any partial unit to one below and clear the rest */ |
6767 | 0 | for (; target>=uar; target--) { |
6768 | 0 | *target=(Unit)next; |
6769 | 0 | next=0; |
6770 | 0 | } |
6771 | 0 | return digits+shift; |
6772 | 0 | } /* decShiftToMost */ |
6773 | | |
6774 | | /* ------------------------------------------------------------------ */ |
6775 | | /* decShiftToLeast -- shift digits in array towards least significant */ |
6776 | | /* */ |
6777 | | /* uar is the array */ |
6778 | | /* units is length of the array, in units */ |
6779 | | /* shift is the number of digits to remove from the lsu end; it */ |
6780 | | /* must be zero or positive and <= than units*DECDPUN. */ |
6781 | | /* */ |
6782 | | /* returns the new length of the integer in the array, in units */ |
6783 | | /* */ |
6784 | | /* Removed digits are discarded (lost). Units not required to hold */ |
6785 | | /* the final result are unchanged. */ |
6786 | | /* ------------------------------------------------------------------ */ |
6787 | 0 | static Int decShiftToLeast(Unit *uar, Int units, Int shift) { |
6788 | 0 | Unit *target, *up; /* work */ |
6789 | 0 | Int cut, count; /* work */ |
6790 | 0 | Int quot, rem; /* for division */ |
6791 | |
|
6792 | 0 | if (shift==0) return units; /* [fastpath] nothing to do */ |
6793 | 0 | if (shift==units*DECDPUN) { /* [fastpath] little to do */ |
6794 | 0 | *uar=0; /* all digits cleared gives zero */ |
6795 | 0 | return 1; /* leaves just the one */ |
6796 | 0 | } |
6797 | | |
6798 | 0 | target=uar; /* both paths */ |
6799 | 0 | cut=MSUDIGITS(shift); |
6800 | 0 | if (cut==DECDPUN) { /* unit-boundary case; easy */ |
6801 | 0 | up=uar+D2U(shift); |
6802 | 0 | for (; up<uar+units; target++, up++) *target=*up; |
6803 | 0 | return static_cast<int32_t>(target-uar); |
6804 | 0 | } |
6805 | | |
6806 | | /* messier */ |
6807 | 0 | up=uar+D2U(shift-cut); /* source; correct to whole Units */ |
6808 | 0 | count=units*DECDPUN-shift; /* the maximum new length */ |
6809 | 0 | #if DECDPUN<=4 |
6810 | 0 | quot=QUOT10(*up, cut); |
6811 | | #else |
6812 | | quot=*up/powers[cut]; |
6813 | | #endif |
6814 | 0 | for (; ; target++) { |
6815 | 0 | *target=(Unit)quot; |
6816 | 0 | count-=(DECDPUN-cut); |
6817 | 0 | if (count<=0) break; |
6818 | 0 | up++; |
6819 | 0 | quot=*up; |
6820 | 0 | #if DECDPUN<=4 |
6821 | 0 | quot=QUOT10(quot, cut); |
6822 | 0 | rem=*up-quot*powers[cut]; |
6823 | | #else |
6824 | | rem=quot%powers[cut]; |
6825 | | quot=quot/powers[cut]; |
6826 | | #endif |
6827 | 0 | *target=(Unit)(*target+rem*powers[DECDPUN-cut]); |
6828 | 0 | count-=cut; |
6829 | 0 | if (count<=0) break; |
6830 | 0 | } |
6831 | 0 | return static_cast<int32_t>(target-uar+1); |
6832 | 0 | } /* decShiftToLeast */ |
6833 | | |
6834 | | #if DECSUBSET |
6835 | | /* ------------------------------------------------------------------ */ |
6836 | | /* decRoundOperand -- round an operand [used for subset only] */ |
6837 | | /* */ |
6838 | | /* dn is the number to round (dn->digits is > set->digits) */ |
6839 | | /* set is the relevant context */ |
6840 | | /* status is the status accumulator */ |
6841 | | /* */ |
6842 | | /* returns an allocated decNumber with the rounded result. */ |
6843 | | /* */ |
6844 | | /* lostDigits and other status may be set by this. */ |
6845 | | /* */ |
6846 | | /* Since the input is an operand, it must not be modified. */ |
6847 | | /* Instead, return an allocated decNumber, rounded as required. */ |
6848 | | /* It is the caller's responsibility to free the allocated storage. */ |
6849 | | /* */ |
6850 | | /* If no storage is available then the result cannot be used, so NULL */ |
6851 | | /* is returned. */ |
6852 | | /* ------------------------------------------------------------------ */ |
6853 | | static decNumber *decRoundOperand(const decNumber *dn, decContext *set, |
6854 | | uInt *status) { |
6855 | | decNumber *res; /* result structure */ |
6856 | | uInt newstatus=0; /* status from round */ |
6857 | | Int residue=0; /* rounding accumulator */ |
6858 | | |
6859 | | /* Allocate storage for the returned decNumber, big enough for the */ |
6860 | | /* length specified by the context */ |
6861 | | res=(decNumber *)malloc(sizeof(decNumber) |
6862 | | +(D2U(set->digits)-1)*sizeof(Unit)); |
6863 | | if (res==NULL) { |
6864 | | *status|=DEC_Insufficient_storage; |
6865 | | return NULL; |
6866 | | } |
6867 | | decCopyFit(res, dn, set, &residue, &newstatus); |
6868 | | decApplyRound(res, set, residue, &newstatus); |
6869 | | |
6870 | | /* If that set Inexact then "lost digits" is raised... */ |
6871 | | if (newstatus & DEC_Inexact) newstatus|=DEC_Lost_digits; |
6872 | | *status|=newstatus; |
6873 | | return res; |
6874 | | } /* decRoundOperand */ |
6875 | | #endif |
6876 | | |
6877 | | /* ------------------------------------------------------------------ */ |
6878 | | /* decCopyFit -- copy a number, truncating the coefficient if needed */ |
6879 | | /* */ |
6880 | | /* dest is the target decNumber */ |
6881 | | /* src is the source decNumber */ |
6882 | | /* set is the context [used for length (digits) and rounding mode] */ |
6883 | | /* residue is the residue accumulator */ |
6884 | | /* status contains the current status to be updated */ |
6885 | | /* */ |
6886 | | /* (dest==src is allowed and will be a no-op if fits) */ |
6887 | | /* All fields are updated as required. */ |
6888 | | /* ------------------------------------------------------------------ */ |
6889 | | static void decCopyFit(decNumber *dest, const decNumber *src, |
6890 | 0 | decContext *set, Int *residue, uInt *status) { |
6891 | 0 | dest->bits=src->bits; |
6892 | 0 | dest->exponent=src->exponent; |
6893 | 0 | decSetCoeff(dest, set, src->lsu, src->digits, residue, status); |
6894 | 0 | } /* decCopyFit */ |
6895 | | |
6896 | | /* ------------------------------------------------------------------ */ |
6897 | | /* decSetCoeff -- set the coefficient of a number */ |
6898 | | /* */ |
6899 | | /* dn is the number whose coefficient array is to be set. */ |
6900 | | /* It must have space for set->digits digits */ |
6901 | | /* set is the context [for size] */ |
6902 | | /* lsu -> lsu of the source coefficient [may be dn->lsu] */ |
6903 | | /* len is digits in the source coefficient [may be dn->digits] */ |
6904 | | /* residue is the residue accumulator. This has values as in */ |
6905 | | /* decApplyRound, and will be unchanged unless the */ |
6906 | | /* target size is less than len. In this case, the */ |
6907 | | /* coefficient is truncated and the residue is updated to */ |
6908 | | /* reflect the previous residue and the dropped digits. */ |
6909 | | /* status is the status accumulator, as usual */ |
6910 | | /* */ |
6911 | | /* The coefficient may already be in the number, or it can be an */ |
6912 | | /* external intermediate array. If it is in the number, lsu must == */ |
6913 | | /* dn->lsu and len must == dn->digits. */ |
6914 | | /* */ |
6915 | | /* Note that the coefficient length (len) may be < set->digits, and */ |
6916 | | /* in this case this merely copies the coefficient (or is a no-op */ |
6917 | | /* if dn->lsu==lsu). */ |
6918 | | /* */ |
6919 | | /* Note also that (only internally, from decQuantizeOp and */ |
6920 | | /* decSetSubnormal) the value of set->digits may be less than one, */ |
6921 | | /* indicating a round to left. This routine handles that case */ |
6922 | | /* correctly; caller ensures space. */ |
6923 | | /* */ |
6924 | | /* dn->digits, dn->lsu (and as required), and dn->exponent are */ |
6925 | | /* updated as necessary. dn->bits (sign) is unchanged. */ |
6926 | | /* */ |
6927 | | /* DEC_Rounded status is set if any digits are discarded. */ |
6928 | | /* DEC_Inexact status is set if any non-zero digits are discarded, or */ |
6929 | | /* incoming residue was non-0 (implies rounded) */ |
6930 | | /* ------------------------------------------------------------------ */ |
6931 | | /* mapping array: maps 0-9 to canonical residues, so that a residue */ |
6932 | | /* can be adjusted in the range [-1, +1] and achieve correct rounding */ |
6933 | | /* 0 1 2 3 4 5 6 7 8 9 */ |
6934 | | static const uByte resmap[10]={0, 3, 3, 3, 3, 5, 7, 7, 7, 7}; |
6935 | | static void decSetCoeff(decNumber *dn, decContext *set, const Unit *lsu, |
6936 | 0 | Int len, Int *residue, uInt *status) { |
6937 | 0 | Int discard; /* number of digits to discard */ |
6938 | 0 | uInt cut; /* cut point in Unit */ |
6939 | 0 | const Unit *up; /* work */ |
6940 | 0 | Unit *target; /* .. */ |
6941 | 0 | Int count; /* .. */ |
6942 | 0 | #if DECDPUN<=4 |
6943 | 0 | uInt temp; /* .. */ |
6944 | 0 | #endif |
6945 | |
|
6946 | 0 | discard=len-set->digits; /* digits to discard */ |
6947 | 0 | if (discard<=0) { /* no digits are being discarded */ |
6948 | 0 | if (dn->lsu!=lsu) { /* copy needed */ |
6949 | | /* copy the coefficient array to the result number; no shift needed */ |
6950 | 0 | count=len; /* avoids D2U */ |
6951 | 0 | up=lsu; |
6952 | 0 | for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN) |
6953 | 0 | *target=*up; |
6954 | 0 | dn->digits=len; /* set the new length */ |
6955 | 0 | } |
6956 | | /* dn->exponent and residue are unchanged, record any inexactitude */ |
6957 | 0 | if (*residue!=0) *status|=(DEC_Inexact | DEC_Rounded); |
6958 | 0 | return; |
6959 | 0 | } |
6960 | | |
6961 | | /* some digits must be discarded ... */ |
6962 | 0 | dn->exponent+=discard; /* maintain numerical value */ |
6963 | 0 | *status|=DEC_Rounded; /* accumulate Rounded status */ |
6964 | 0 | if (*residue>1) *residue=1; /* previous residue now to right, so reduce */ |
6965 | |
|
6966 | 0 | if (discard>len) { /* everything, +1, is being discarded */ |
6967 | | /* guard digit is 0 */ |
6968 | | /* residue is all the number [NB could be all 0s] */ |
6969 | 0 | if (*residue<=0) { /* not already positive */ |
6970 | 0 | count=len; /* avoids D2U */ |
6971 | 0 | for (up=lsu; count>0; up++, count-=DECDPUN) if (*up!=0) { /* found non-0 */ |
6972 | 0 | *residue=1; |
6973 | 0 | break; /* no need to check any others */ |
6974 | 0 | } |
6975 | 0 | } |
6976 | 0 | if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */ |
6977 | 0 | *dn->lsu=0; /* coefficient will now be 0 */ |
6978 | 0 | dn->digits=1; /* .. */ |
6979 | 0 | return; |
6980 | 0 | } /* total discard */ |
6981 | | |
6982 | | /* partial discard [most common case] */ |
6983 | | /* here, at least the first (most significant) discarded digit exists */ |
6984 | | |
6985 | | /* spin up the number, noting residue during the spin, until get to */ |
6986 | | /* the Unit with the first discarded digit. When reach it, extract */ |
6987 | | /* it and remember its position */ |
6988 | 0 | count=0; |
6989 | 0 | for (up=lsu;; up++) { |
6990 | 0 | count+=DECDPUN; |
6991 | 0 | if (count>=discard) break; /* full ones all checked */ |
6992 | 0 | if (*up!=0) *residue=1; |
6993 | 0 | } /* up */ |
6994 | | |
6995 | | /* here up -> Unit with first discarded digit */ |
6996 | 0 | cut=discard-(count-DECDPUN)-1; |
6997 | 0 | if (cut==DECDPUN-1) { /* unit-boundary case (fast) */ |
6998 | 0 | Unit half=(Unit)powers[DECDPUN]>>1; |
6999 | | /* set residue directly */ |
7000 | 0 | if (*up>=half) { |
7001 | 0 | if (*up>half) *residue=7; |
7002 | 0 | else *residue+=5; /* add sticky bit */ |
7003 | 0 | } |
7004 | 0 | else { /* <half */ |
7005 | 0 | if (*up!=0) *residue=3; /* [else is 0, leave as sticky bit] */ |
7006 | 0 | } |
7007 | 0 | if (set->digits<=0) { /* special for Quantize/Subnormal :-( */ |
7008 | 0 | *dn->lsu=0; /* .. result is 0 */ |
7009 | 0 | dn->digits=1; /* .. */ |
7010 | 0 | } |
7011 | 0 | else { /* shift to least */ |
7012 | 0 | count=set->digits; /* now digits to end up with */ |
7013 | 0 | dn->digits=count; /* set the new length */ |
7014 | 0 | up++; /* move to next */ |
7015 | | /* on unit boundary, so shift-down copy loop is simple */ |
7016 | 0 | for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN) |
7017 | 0 | *target=*up; |
7018 | 0 | } |
7019 | 0 | } /* unit-boundary case */ |
7020 | | |
7021 | 0 | else { /* discard digit is in low digit(s), and not top digit */ |
7022 | 0 | uInt discard1; /* first discarded digit */ |
7023 | 0 | uInt quot, rem; /* for divisions */ |
7024 | 0 | if (cut==0) quot=*up; /* is at bottom of unit */ |
7025 | 0 | else /* cut>0 */ { /* it's not at bottom of unit */ |
7026 | 0 | #if DECDPUN<=4 |
7027 | 0 | U_ASSERT(/* cut >= 0 &&*/ cut <= 4); |
7028 | 0 | quot=QUOT10(*up, cut); |
7029 | 0 | rem=*up-quot*powers[cut]; |
7030 | | #else |
7031 | | rem=*up%powers[cut]; |
7032 | | quot=*up/powers[cut]; |
7033 | | #endif |
7034 | 0 | if (rem!=0) *residue=1; |
7035 | 0 | } |
7036 | | /* discard digit is now at bottom of quot */ |
7037 | 0 | #if DECDPUN<=4 |
7038 | 0 | temp=(quot*6554)>>16; /* fast /10 */ |
7039 | | /* Vowels algorithm here not a win (9 instructions) */ |
7040 | 0 | discard1=quot-X10(temp); |
7041 | 0 | quot=temp; |
7042 | | #else |
7043 | | discard1=quot%10; |
7044 | | quot=quot/10; |
7045 | | #endif |
7046 | | /* here, discard1 is the guard digit, and residue is everything */ |
7047 | | /* else [use mapping array to accumulate residue safely] */ |
7048 | 0 | *residue+=resmap[discard1]; |
7049 | 0 | cut++; /* update cut */ |
7050 | | /* here: up -> Unit of the array with bottom digit */ |
7051 | | /* cut is the division point for each Unit */ |
7052 | | /* quot holds the uncut high-order digits for the current unit */ |
7053 | 0 | if (set->digits<=0) { /* special for Quantize/Subnormal :-( */ |
7054 | 0 | *dn->lsu=0; /* .. result is 0 */ |
7055 | 0 | dn->digits=1; /* .. */ |
7056 | 0 | } |
7057 | 0 | else { /* shift to least needed */ |
7058 | 0 | count=set->digits; /* now digits to end up with */ |
7059 | 0 | dn->digits=count; /* set the new length */ |
7060 | | /* shift-copy the coefficient array to the result number */ |
7061 | 0 | for (target=dn->lsu; ; target++) { |
7062 | 0 | *target=(Unit)quot; |
7063 | 0 | count-=(DECDPUN-cut); |
7064 | 0 | if (count<=0) break; |
7065 | 0 | up++; |
7066 | 0 | quot=*up; |
7067 | 0 | #if DECDPUN<=4 |
7068 | 0 | quot=QUOT10(quot, cut); |
7069 | 0 | rem=*up-quot*powers[cut]; |
7070 | | #else |
7071 | | rem=quot%powers[cut]; |
7072 | | quot=quot/powers[cut]; |
7073 | | #endif |
7074 | 0 | *target=(Unit)(*target+rem*powers[DECDPUN-cut]); |
7075 | 0 | count-=cut; |
7076 | 0 | if (count<=0) break; |
7077 | 0 | } /* shift-copy loop */ |
7078 | 0 | } /* shift to least */ |
7079 | 0 | } /* not unit boundary */ |
7080 | |
|
7081 | 0 | if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */ |
7082 | 0 | return; |
7083 | 0 | } /* decSetCoeff */ |
7084 | | |
7085 | | /* ------------------------------------------------------------------ */ |
7086 | | /* decApplyRound -- apply pending rounding to a number */ |
7087 | | /* */ |
7088 | | /* dn is the number, with space for set->digits digits */ |
7089 | | /* set is the context [for size and rounding mode] */ |
7090 | | /* residue indicates pending rounding, being any accumulated */ |
7091 | | /* guard and sticky information. It may be: */ |
7092 | | /* 6-9: rounding digit is >5 */ |
7093 | | /* 5: rounding digit is exactly half-way */ |
7094 | | /* 1-4: rounding digit is <5 and >0 */ |
7095 | | /* 0: the coefficient is exact */ |
7096 | | /* -1: as 1, but the hidden digits are subtractive, that */ |
7097 | | /* is, of the opposite sign to dn. In this case the */ |
7098 | | /* coefficient must be non-0. This case occurs when */ |
7099 | | /* subtracting a small number (which can be reduced to */ |
7100 | | /* a sticky bit); see decAddOp. */ |
7101 | | /* status is the status accumulator, as usual */ |
7102 | | /* */ |
7103 | | /* This routine applies rounding while keeping the length of the */ |
7104 | | /* coefficient constant. The exponent and status are unchanged */ |
7105 | | /* except if: */ |
7106 | | /* */ |
7107 | | /* -- the coefficient was increased and is all nines (in which */ |
7108 | | /* case Overflow could occur, and is handled directly here so */ |
7109 | | /* the caller does not need to re-test for overflow) */ |
7110 | | /* */ |
7111 | | /* -- the coefficient was decreased and becomes all nines (in which */ |
7112 | | /* case Underflow could occur, and is also handled directly). */ |
7113 | | /* */ |
7114 | | /* All fields in dn are updated as required. */ |
7115 | | /* */ |
7116 | | /* ------------------------------------------------------------------ */ |
7117 | | static void decApplyRound(decNumber *dn, decContext *set, Int residue, |
7118 | 0 | uInt *status) { |
7119 | 0 | Int bump; /* 1 if coefficient needs to be incremented */ |
7120 | | /* -1 if coefficient needs to be decremented */ |
7121 | |
|
7122 | 0 | if (residue==0) return; /* nothing to apply */ |
7123 | | |
7124 | 0 | bump=0; /* assume a smooth ride */ |
7125 | | |
7126 | | /* now decide whether, and how, to round, depending on mode */ |
7127 | 0 | switch (set->round) { |
7128 | 0 | case DEC_ROUND_05UP: { /* round zero or five up (for reround) */ |
7129 | | /* This is the same as DEC_ROUND_DOWN unless there is a */ |
7130 | | /* positive residue and the lsd of dn is 0 or 5, in which case */ |
7131 | | /* it is bumped; when residue is <0, the number is therefore */ |
7132 | | /* bumped down unless the final digit was 1 or 6 (in which */ |
7133 | | /* case it is bumped down and then up -- a no-op) */ |
7134 | 0 | Int lsd5=*dn->lsu%5; /* get lsd and quintate */ |
7135 | 0 | if (residue<0 && lsd5!=1) bump=-1; |
7136 | 0 | else if (residue>0 && lsd5==0) bump=1; |
7137 | | /* [bump==1 could be applied directly; use common path for clarity] */ |
7138 | 0 | break;} /* r-05 */ |
7139 | | |
7140 | 0 | case DEC_ROUND_DOWN: { |
7141 | | /* no change, except if negative residue */ |
7142 | 0 | if (residue<0) bump=-1; |
7143 | 0 | break;} /* r-d */ |
7144 | | |
7145 | 0 | case DEC_ROUND_HALF_DOWN: { |
7146 | 0 | if (residue>5) bump=1; |
7147 | 0 | break;} /* r-h-d */ |
7148 | | |
7149 | 0 | case DEC_ROUND_HALF_EVEN: { |
7150 | 0 | if (residue>5) bump=1; /* >0.5 goes up */ |
7151 | 0 | else if (residue==5) { /* exactly 0.5000... */ |
7152 | | /* 0.5 goes up iff [new] lsd is odd */ |
7153 | 0 | if (*dn->lsu & 0x01) bump=1; |
7154 | 0 | } |
7155 | 0 | break;} /* r-h-e */ |
7156 | | |
7157 | 0 | case DEC_ROUND_HALF_UP: { |
7158 | 0 | if (residue>=5) bump=1; |
7159 | 0 | break;} /* r-h-u */ |
7160 | | |
7161 | 0 | case DEC_ROUND_UP: { |
7162 | 0 | if (residue>0) bump=1; |
7163 | 0 | break;} /* r-u */ |
7164 | | |
7165 | 0 | case DEC_ROUND_CEILING: { |
7166 | | /* same as _UP for positive numbers, and as _DOWN for negatives */ |
7167 | | /* [negative residue cannot occur on 0] */ |
7168 | 0 | if (decNumberIsNegative(dn)) { |
7169 | 0 | if (residue<0) bump=-1; |
7170 | 0 | } |
7171 | 0 | else { |
7172 | 0 | if (residue>0) bump=1; |
7173 | 0 | } |
7174 | 0 | break;} /* r-c */ |
7175 | | |
7176 | 0 | case DEC_ROUND_FLOOR: { |
7177 | | /* same as _UP for negative numbers, and as _DOWN for positive */ |
7178 | | /* [negative residue cannot occur on 0] */ |
7179 | 0 | if (!decNumberIsNegative(dn)) { |
7180 | 0 | if (residue<0) bump=-1; |
7181 | 0 | } |
7182 | 0 | else { |
7183 | 0 | if (residue>0) bump=1; |
7184 | 0 | } |
7185 | 0 | break;} /* r-f */ |
7186 | | |
7187 | 0 | default: { /* e.g., DEC_ROUND_MAX */ |
7188 | 0 | *status|=DEC_Invalid_context; |
7189 | | #if DECTRACE || (DECCHECK && DECVERB) |
7190 | | printf("Unknown rounding mode: %d\n", set->round); |
7191 | | #endif |
7192 | 0 | break;} |
7193 | 0 | } /* switch */ |
7194 | | |
7195 | | /* now bump the number, up or down, if need be */ |
7196 | 0 | if (bump==0) return; /* no action required */ |
7197 | | |
7198 | | /* Simply use decUnitAddSub unless bumping up and the number is */ |
7199 | | /* all nines. In this special case set to 100... explicitly */ |
7200 | | /* and adjust the exponent by one (as otherwise could overflow */ |
7201 | | /* the array) */ |
7202 | | /* Similarly handle all-nines result if bumping down. */ |
7203 | 0 | if (bump>0) { |
7204 | 0 | Unit *up; /* work */ |
7205 | 0 | uInt count=dn->digits; /* digits to be checked */ |
7206 | 0 | for (up=dn->lsu; ; up++) { |
7207 | 0 | if (count<=DECDPUN) { |
7208 | | /* this is the last Unit (the msu) */ |
7209 | 0 | if (*up!=powers[count]-1) break; /* not still 9s */ |
7210 | | /* here if it, too, is all nines */ |
7211 | 0 | *up=(Unit)powers[count-1]; /* here 999 -> 100 etc. */ |
7212 | 0 | for (up=up-1; up>=dn->lsu; up--) *up=0; /* others all to 0 */ |
7213 | 0 | dn->exponent++; /* and bump exponent */ |
7214 | | /* [which, very rarely, could cause Overflow...] */ |
7215 | 0 | if ((dn->exponent+dn->digits)>set->emax+1) { |
7216 | 0 | decSetOverflow(dn, set, status); |
7217 | 0 | } |
7218 | 0 | return; /* done */ |
7219 | 0 | } |
7220 | | /* a full unit to check, with more to come */ |
7221 | 0 | if (*up!=DECDPUNMAX) break; /* not still 9s */ |
7222 | 0 | count-=DECDPUN; |
7223 | 0 | } /* up */ |
7224 | 0 | } /* bump>0 */ |
7225 | 0 | else { /* -1 */ |
7226 | | /* here checking for a pre-bump of 1000... (leading 1, all */ |
7227 | | /* other digits zero) */ |
7228 | 0 | Unit *up, *sup; /* work */ |
7229 | 0 | uInt count=dn->digits; /* digits to be checked */ |
7230 | 0 | for (up=dn->lsu; ; up++) { |
7231 | 0 | if (count<=DECDPUN) { |
7232 | | /* this is the last Unit (the msu) */ |
7233 | 0 | if (*up!=powers[count-1]) break; /* not 100.. */ |
7234 | | /* here if have the 1000... case */ |
7235 | 0 | sup=up; /* save msu pointer */ |
7236 | 0 | *up=(Unit)powers[count]-1; /* here 100 in msu -> 999 */ |
7237 | | /* others all to all-nines, too */ |
7238 | 0 | for (up=up-1; up>=dn->lsu; up--) *up=(Unit)powers[DECDPUN]-1; |
7239 | 0 | dn->exponent--; /* and bump exponent */ |
7240 | | |
7241 | | /* iff the number was at the subnormal boundary (exponent=etiny) */ |
7242 | | /* then the exponent is now out of range, so it will in fact get */ |
7243 | | /* clamped to etiny and the final 9 dropped. */ |
7244 | | /* printf(">> emin=%d exp=%d sdig=%d\n", set->emin, */ |
7245 | | /* dn->exponent, set->digits); */ |
7246 | 0 | if (dn->exponent+1==set->emin-set->digits+1) { |
7247 | 0 | if (count==1 && dn->digits==1) *sup=0; /* here 9 -> 0[.9] */ |
7248 | 0 | else { |
7249 | 0 | *sup=(Unit)powers[count-1]-1; /* here 999.. in msu -> 99.. */ |
7250 | 0 | dn->digits--; |
7251 | 0 | } |
7252 | 0 | dn->exponent++; |
7253 | 0 | *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded; |
7254 | 0 | } |
7255 | 0 | return; /* done */ |
7256 | 0 | } |
7257 | | |
7258 | | /* a full unit to check, with more to come */ |
7259 | 0 | if (*up!=0) break; /* not still 0s */ |
7260 | 0 | count-=DECDPUN; |
7261 | 0 | } /* up */ |
7262 | |
|
7263 | 0 | } /* bump<0 */ |
7264 | | |
7265 | | /* Actual bump needed. Do it. */ |
7266 | 0 | decUnitAddSub(dn->lsu, D2U(dn->digits), uarrone, 1, 0, dn->lsu, bump); |
7267 | 0 | } /* decApplyRound */ |
7268 | | |
7269 | | #if DECSUBSET |
7270 | | /* ------------------------------------------------------------------ */ |
7271 | | /* decFinish -- finish processing a number */ |
7272 | | /* */ |
7273 | | /* dn is the number */ |
7274 | | /* set is the context */ |
7275 | | /* residue is the rounding accumulator (as in decApplyRound) */ |
7276 | | /* status is the accumulator */ |
7277 | | /* */ |
7278 | | /* This finishes off the current number by: */ |
7279 | | /* 1. If not extended: */ |
7280 | | /* a. Converting a zero result to clean '0' */ |
7281 | | /* b. Reducing positive exponents to 0, if would fit in digits */ |
7282 | | /* 2. Checking for overflow and subnormals (always) */ |
7283 | | /* Note this is just Finalize when no subset arithmetic. */ |
7284 | | /* All fields are updated as required. */ |
7285 | | /* ------------------------------------------------------------------ */ |
7286 | | static void decFinish(decNumber *dn, decContext *set, Int *residue, |
7287 | | uInt *status) { |
7288 | | if (!set->extended) { |
7289 | | if ISZERO(dn) { /* value is zero */ |
7290 | | dn->exponent=0; /* clean exponent .. */ |
7291 | | dn->bits=0; /* .. and sign */ |
7292 | | return; /* no error possible */ |
7293 | | } |
7294 | | if (dn->exponent>=0) { /* non-negative exponent */ |
7295 | | /* >0; reduce to integer if possible */ |
7296 | | if (set->digits >= (dn->exponent+dn->digits)) { |
7297 | | dn->digits=decShiftToMost(dn->lsu, dn->digits, dn->exponent); |
7298 | | dn->exponent=0; |
7299 | | } |
7300 | | } |
7301 | | } /* !extended */ |
7302 | | |
7303 | | decFinalize(dn, set, residue, status); |
7304 | | } /* decFinish */ |
7305 | | #endif |
7306 | | |
7307 | | /* ------------------------------------------------------------------ */ |
7308 | | /* decFinalize -- final check, clamp, and round of a number */ |
7309 | | /* */ |
7310 | | /* dn is the number */ |
7311 | | /* set is the context */ |
7312 | | /* residue is the rounding accumulator (as in decApplyRound) */ |
7313 | | /* status is the status accumulator */ |
7314 | | /* */ |
7315 | | /* This finishes off the current number by checking for subnormal */ |
7316 | | /* results, applying any pending rounding, checking for overflow, */ |
7317 | | /* and applying any clamping. */ |
7318 | | /* Underflow and overflow conditions are raised as appropriate. */ |
7319 | | /* All fields are updated as required. */ |
7320 | | /* ------------------------------------------------------------------ */ |
7321 | | static void decFinalize(decNumber *dn, decContext *set, Int *residue, |
7322 | 0 | uInt *status) { |
7323 | 0 | Int shift; /* shift needed if clamping */ |
7324 | 0 | Int tinyexp=set->emin-dn->digits+1; /* precalculate subnormal boundary */ |
7325 | | |
7326 | | /* Must be careful, here, when checking the exponent as the */ |
7327 | | /* adjusted exponent could overflow 31 bits [because it may already */ |
7328 | | /* be up to twice the expected]. */ |
7329 | | |
7330 | | /* First test for subnormal. This must be done before any final */ |
7331 | | /* round as the result could be rounded to Nmin or 0. */ |
7332 | 0 | if (dn->exponent<=tinyexp) { /* prefilter */ |
7333 | 0 | Int comp; |
7334 | 0 | decNumber nmin; |
7335 | | /* A very nasty case here is dn == Nmin and residue<0 */ |
7336 | 0 | if (dn->exponent<tinyexp) { |
7337 | | /* Go handle subnormals; this will apply round if needed. */ |
7338 | 0 | decSetSubnormal(dn, set, residue, status); |
7339 | 0 | return; |
7340 | 0 | } |
7341 | | /* Equals case: only subnormal if dn=Nmin and negative residue */ |
7342 | 0 | uprv_decNumberZero(&nmin); |
7343 | 0 | nmin.lsu[0]=1; |
7344 | 0 | nmin.exponent=set->emin; |
7345 | 0 | comp=decCompare(dn, &nmin, 1); /* (signless compare) */ |
7346 | 0 | if (comp==BADINT) { /* oops */ |
7347 | 0 | *status|=DEC_Insufficient_storage; /* abandon... */ |
7348 | 0 | return; |
7349 | 0 | } |
7350 | 0 | if (*residue<0 && comp==0) { /* neg residue and dn==Nmin */ |
7351 | 0 | decApplyRound(dn, set, *residue, status); /* might force down */ |
7352 | 0 | decSetSubnormal(dn, set, residue, status); |
7353 | 0 | return; |
7354 | 0 | } |
7355 | 0 | } |
7356 | | |
7357 | | /* now apply any pending round (this could raise overflow). */ |
7358 | 0 | if (*residue!=0) decApplyRound(dn, set, *residue, status); |
7359 | | |
7360 | | /* Check for overflow [redundant in the 'rare' case] or clamp */ |
7361 | 0 | if (dn->exponent<=set->emax-set->digits+1) return; /* neither needed */ |
7362 | | |
7363 | | |
7364 | | /* here when might have an overflow or clamp to do */ |
7365 | 0 | if (dn->exponent>set->emax-dn->digits+1) { /* too big */ |
7366 | 0 | decSetOverflow(dn, set, status); |
7367 | 0 | return; |
7368 | 0 | } |
7369 | | /* here when the result is normal but in clamp range */ |
7370 | 0 | if (!set->clamp) return; |
7371 | | |
7372 | | /* here when need to apply the IEEE exponent clamp (fold-down) */ |
7373 | 0 | shift=dn->exponent-(set->emax-set->digits+1); |
7374 | | |
7375 | | /* shift coefficient (if non-zero) */ |
7376 | 0 | if (!ISZERO(dn)) { |
7377 | 0 | dn->digits=decShiftToMost(dn->lsu, dn->digits, shift); |
7378 | 0 | } |
7379 | 0 | dn->exponent-=shift; /* adjust the exponent to match */ |
7380 | 0 | *status|=DEC_Clamped; /* and record the dirty deed */ |
7381 | 0 | return; |
7382 | 0 | } /* decFinalize */ |
7383 | | |
7384 | | /* ------------------------------------------------------------------ */ |
7385 | | /* decSetOverflow -- set number to proper overflow value */ |
7386 | | /* */ |
7387 | | /* dn is the number (used for sign [only] and result) */ |
7388 | | /* set is the context [used for the rounding mode, etc.] */ |
7389 | | /* status contains the current status to be updated */ |
7390 | | /* */ |
7391 | | /* This sets the sign of a number and sets its value to either */ |
7392 | | /* Infinity or the maximum finite value, depending on the sign of */ |
7393 | | /* dn and the rounding mode, following IEEE 754 rules. */ |
7394 | | /* ------------------------------------------------------------------ */ |
7395 | 0 | static void decSetOverflow(decNumber *dn, decContext *set, uInt *status) { |
7396 | 0 | Flag needmax=0; /* result is maximum finite value */ |
7397 | 0 | uByte sign=dn->bits&DECNEG; /* clean and save sign bit */ |
7398 | |
|
7399 | 0 | if (ISZERO(dn)) { /* zero does not overflow magnitude */ |
7400 | 0 | Int emax=set->emax; /* limit value */ |
7401 | 0 | if (set->clamp) emax-=set->digits-1; /* lower if clamping */ |
7402 | 0 | if (dn->exponent>emax) { /* clamp required */ |
7403 | 0 | dn->exponent=emax; |
7404 | 0 | *status|=DEC_Clamped; |
7405 | 0 | } |
7406 | 0 | return; |
7407 | 0 | } |
7408 | | |
7409 | 0 | uprv_decNumberZero(dn); |
7410 | 0 | switch (set->round) { |
7411 | 0 | case DEC_ROUND_DOWN: { |
7412 | 0 | needmax=1; /* never Infinity */ |
7413 | 0 | break;} /* r-d */ |
7414 | 0 | case DEC_ROUND_05UP: { |
7415 | 0 | needmax=1; /* never Infinity */ |
7416 | 0 | break;} /* r-05 */ |
7417 | 0 | case DEC_ROUND_CEILING: { |
7418 | 0 | if (sign) needmax=1; /* Infinity if non-negative */ |
7419 | 0 | break;} /* r-c */ |
7420 | 0 | case DEC_ROUND_FLOOR: { |
7421 | 0 | if (!sign) needmax=1; /* Infinity if negative */ |
7422 | 0 | break;} /* r-f */ |
7423 | 0 | default: break; /* Infinity in all other cases */ |
7424 | 0 | } |
7425 | 0 | if (needmax) { |
7426 | 0 | decSetMaxValue(dn, set); |
7427 | 0 | dn->bits=sign; /* set sign */ |
7428 | 0 | } |
7429 | 0 | else dn->bits=sign|DECINF; /* Value is +/-Infinity */ |
7430 | 0 | *status|=DEC_Overflow | DEC_Inexact | DEC_Rounded; |
7431 | 0 | } /* decSetOverflow */ |
7432 | | |
7433 | | /* ------------------------------------------------------------------ */ |
7434 | | /* decSetMaxValue -- set number to +Nmax (maximum normal value) */ |
7435 | | /* */ |
7436 | | /* dn is the number to set */ |
7437 | | /* set is the context [used for digits and emax] */ |
7438 | | /* */ |
7439 | | /* This sets the number to the maximum positive value. */ |
7440 | | /* ------------------------------------------------------------------ */ |
7441 | 0 | static void decSetMaxValue(decNumber *dn, decContext *set) { |
7442 | 0 | Unit *up; /* work */ |
7443 | 0 | Int count=set->digits; /* nines to add */ |
7444 | 0 | dn->digits=count; |
7445 | | /* fill in all nines to set maximum value */ |
7446 | 0 | for (up=dn->lsu; ; up++) { |
7447 | 0 | if (count>DECDPUN) *up=DECDPUNMAX; /* unit full o'nines */ |
7448 | 0 | else { /* this is the msu */ |
7449 | 0 | *up=(Unit)(powers[count]-1); |
7450 | 0 | break; |
7451 | 0 | } |
7452 | 0 | count-=DECDPUN; /* filled those digits */ |
7453 | 0 | } /* up */ |
7454 | 0 | dn->bits=0; /* + sign */ |
7455 | 0 | dn->exponent=set->emax-set->digits+1; |
7456 | 0 | } /* decSetMaxValue */ |
7457 | | |
7458 | | /* ------------------------------------------------------------------ */ |
7459 | | /* decSetSubnormal -- process value whose exponent is <Emin */ |
7460 | | /* */ |
7461 | | /* dn is the number (used as input as well as output; it may have */ |
7462 | | /* an allowed subnormal value, which may need to be rounded) */ |
7463 | | /* set is the context [used for the rounding mode] */ |
7464 | | /* residue is any pending residue */ |
7465 | | /* status contains the current status to be updated */ |
7466 | | /* */ |
7467 | | /* If subset mode, set result to zero and set Underflow flags. */ |
7468 | | /* */ |
7469 | | /* Value may be zero with a low exponent; this does not set Subnormal */ |
7470 | | /* but the exponent will be clamped to Etiny. */ |
7471 | | /* */ |
7472 | | /* Otherwise ensure exponent is not out of range, and round as */ |
7473 | | /* necessary. Underflow is set if the result is Inexact. */ |
7474 | | /* ------------------------------------------------------------------ */ |
7475 | | static void decSetSubnormal(decNumber *dn, decContext *set, Int *residue, |
7476 | 0 | uInt *status) { |
7477 | 0 | decContext workset; /* work */ |
7478 | 0 | Int etiny, adjust; /* .. */ |
7479 | |
|
7480 | | #if DECSUBSET |
7481 | | /* simple set to zero and 'hard underflow' for subset */ |
7482 | | if (!set->extended) { |
7483 | | uprv_decNumberZero(dn); |
7484 | | /* always full overflow */ |
7485 | | *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded; |
7486 | | return; |
7487 | | } |
7488 | | #endif |
7489 | | |
7490 | | /* Full arithmetic -- allow subnormals, rounded to minimum exponent */ |
7491 | | /* (Etiny) if needed */ |
7492 | 0 | etiny=set->emin-(set->digits-1); /* smallest allowed exponent */ |
7493 | |
|
7494 | 0 | if ISZERO(dn) { /* value is zero */ |
7495 | | /* residue can never be non-zero here */ |
7496 | | #if DECCHECK |
7497 | | if (*residue!=0) { |
7498 | | printf("++ Subnormal 0 residue %ld\n", (LI)*residue); |
7499 | | *status|=DEC_Invalid_operation; |
7500 | | } |
7501 | | #endif |
7502 | 0 | if (dn->exponent<etiny) { /* clamp required */ |
7503 | 0 | dn->exponent=etiny; |
7504 | 0 | *status|=DEC_Clamped; |
7505 | 0 | } |
7506 | 0 | return; |
7507 | 0 | } |
7508 | | |
7509 | 0 | *status|=DEC_Subnormal; /* have a non-zero subnormal */ |
7510 | 0 | adjust=etiny-dn->exponent; /* calculate digits to remove */ |
7511 | 0 | if (adjust<=0) { /* not out of range; unrounded */ |
7512 | | /* residue can never be non-zero here, except in the Nmin-residue */ |
7513 | | /* case (which is a subnormal result), so can take fast-path here */ |
7514 | | /* it may already be inexact (from setting the coefficient) */ |
7515 | 0 | if (*status&DEC_Inexact) *status|=DEC_Underflow; |
7516 | 0 | return; |
7517 | 0 | } |
7518 | | |
7519 | | /* adjust>0, so need to rescale the result so exponent becomes Etiny */ |
7520 | | /* [this code is similar to that in rescale] */ |
7521 | 0 | workset=*set; /* clone rounding, etc. */ |
7522 | 0 | workset.digits=dn->digits-adjust; /* set requested length */ |
7523 | 0 | workset.emin-=adjust; /* and adjust emin to match */ |
7524 | | /* [note that the latter can be <1, here, similar to Rescale case] */ |
7525 | 0 | decSetCoeff(dn, &workset, dn->lsu, dn->digits, residue, status); |
7526 | 0 | decApplyRound(dn, &workset, *residue, status); |
7527 | | |
7528 | | /* Use 754 default rule: Underflow is set iff Inexact */ |
7529 | | /* [independent of whether trapped] */ |
7530 | 0 | if (*status&DEC_Inexact) *status|=DEC_Underflow; |
7531 | | |
7532 | | /* if rounded up a 999s case, exponent will be off by one; adjust */ |
7533 | | /* back if so [it will fit, because it was shortened earlier] */ |
7534 | 0 | if (dn->exponent>etiny) { |
7535 | 0 | dn->digits=decShiftToMost(dn->lsu, dn->digits, 1); |
7536 | 0 | dn->exponent--; /* (re)adjust the exponent. */ |
7537 | 0 | } |
7538 | | |
7539 | | /* if rounded to zero, it is by definition clamped... */ |
7540 | 0 | if (ISZERO(dn)) *status|=DEC_Clamped; |
7541 | 0 | } /* decSetSubnormal */ |
7542 | | |
7543 | | /* ------------------------------------------------------------------ */ |
7544 | | /* decCheckMath - check entry conditions for a math function */ |
7545 | | /* */ |
7546 | | /* This checks the context and the operand */ |
7547 | | /* */ |
7548 | | /* rhs is the operand to check */ |
7549 | | /* set is the context to check */ |
7550 | | /* status is unchanged if both are good */ |
7551 | | /* */ |
7552 | | /* returns non-zero if status is changed, 0 otherwise */ |
7553 | | /* */ |
7554 | | /* Restrictions enforced: */ |
7555 | | /* */ |
7556 | | /* digits, emax, and -emin in the context must be less than */ |
7557 | | /* DEC_MAX_MATH (999999), and A must be within these bounds if */ |
7558 | | /* non-zero. Invalid_operation is set in the status if a */ |
7559 | | /* restriction is violated. */ |
7560 | | /* ------------------------------------------------------------------ */ |
7561 | | static uInt decCheckMath(const decNumber *rhs, decContext *set, |
7562 | 0 | uInt *status) { |
7563 | 0 | uInt save=*status; /* record */ |
7564 | 0 | if (set->digits>DEC_MAX_MATH |
7565 | 0 | || set->emax>DEC_MAX_MATH |
7566 | 0 | || -set->emin>DEC_MAX_MATH) *status|=DEC_Invalid_context; |
7567 | 0 | else if ((rhs->digits>DEC_MAX_MATH |
7568 | 0 | || rhs->exponent+rhs->digits>DEC_MAX_MATH+1 |
7569 | 0 | || rhs->exponent+rhs->digits<2*(1-DEC_MAX_MATH)) |
7570 | 0 | && !ISZERO(rhs)) *status|=DEC_Invalid_operation; |
7571 | 0 | return (*status!=save); |
7572 | 0 | } /* decCheckMath */ |
7573 | | |
7574 | | /* ------------------------------------------------------------------ */ |
7575 | | /* decGetInt -- get integer from a number */ |
7576 | | /* */ |
7577 | | /* dn is the number [which will not be altered] */ |
7578 | | /* */ |
7579 | | /* returns one of: */ |
7580 | | /* BADINT if there is a non-zero fraction */ |
7581 | | /* the converted integer */ |
7582 | | /* BIGEVEN if the integer is even and magnitude > 2*10**9 */ |
7583 | | /* BIGODD if the integer is odd and magnitude > 2*10**9 */ |
7584 | | /* */ |
7585 | | /* This checks and gets a whole number from the input decNumber. */ |
7586 | | /* The sign can be determined from dn by the caller when BIGEVEN or */ |
7587 | | /* BIGODD is returned. */ |
7588 | | /* ------------------------------------------------------------------ */ |
7589 | 0 | static Int decGetInt(const decNumber *dn) { |
7590 | 0 | Int theInt; /* result accumulator */ |
7591 | 0 | const Unit *up; /* work */ |
7592 | 0 | Int got; /* digits (real or not) processed */ |
7593 | 0 | Int ilength=dn->digits+dn->exponent; /* integral length */ |
7594 | 0 | Flag neg=decNumberIsNegative(dn); /* 1 if -ve */ |
7595 | | |
7596 | | /* The number must be an integer that fits in 10 digits */ |
7597 | | /* Assert, here, that 10 is enough for any rescale Etiny */ |
7598 | | #if DEC_MAX_EMAX > 999999999 |
7599 | | #error GetInt may need updating [for Emax] |
7600 | | #endif |
7601 | | #if DEC_MIN_EMIN < -999999999 |
7602 | | #error GetInt may need updating [for Emin] |
7603 | | #endif |
7604 | 0 | if (ISZERO(dn)) return 0; /* zeros are OK, with any exponent */ |
7605 | | |
7606 | 0 | up=dn->lsu; /* ready for lsu */ |
7607 | 0 | theInt=0; /* ready to accumulate */ |
7608 | 0 | if (dn->exponent>=0) { /* relatively easy */ |
7609 | | /* no fractional part [usual]; allow for positive exponent */ |
7610 | 0 | got=dn->exponent; |
7611 | 0 | } |
7612 | 0 | else { /* -ve exponent; some fractional part to check and discard */ |
7613 | 0 | Int count=-dn->exponent; /* digits to discard */ |
7614 | | /* spin up whole units until reach the Unit with the unit digit */ |
7615 | 0 | for (; count>=DECDPUN; up++) { |
7616 | 0 | if (*up!=0) return BADINT; /* non-zero Unit to discard */ |
7617 | 0 | count-=DECDPUN; |
7618 | 0 | } |
7619 | 0 | if (count==0) got=0; /* [a multiple of DECDPUN] */ |
7620 | 0 | else { /* [not multiple of DECDPUN] */ |
7621 | 0 | Int rem; /* work */ |
7622 | | /* slice off fraction digits and check for non-zero */ |
7623 | 0 | #if DECDPUN<=4 |
7624 | 0 | theInt=QUOT10(*up, count); |
7625 | 0 | rem=*up-theInt*powers[count]; |
7626 | | #else |
7627 | | rem=*up%powers[count]; /* slice off discards */ |
7628 | | theInt=*up/powers[count]; |
7629 | | #endif |
7630 | 0 | if (rem!=0) return BADINT; /* non-zero fraction */ |
7631 | | /* it looks good */ |
7632 | 0 | got=DECDPUN-count; /* number of digits so far */ |
7633 | 0 | up++; /* ready for next */ |
7634 | 0 | } |
7635 | 0 | } |
7636 | | /* now it's known there's no fractional part */ |
7637 | | |
7638 | | /* tricky code now, to accumulate up to 9.3 digits */ |
7639 | 0 | if (got==0) {theInt=*up; got+=DECDPUN; up++;} /* ensure lsu is there */ |
7640 | |
|
7641 | 0 | if (ilength<11) { |
7642 | 0 | Int save=theInt; |
7643 | | /* collect any remaining unit(s) */ |
7644 | 0 | for (; got<ilength; up++) { |
7645 | 0 | theInt+=*up*powers[got]; |
7646 | 0 | got+=DECDPUN; |
7647 | 0 | } |
7648 | 0 | if (ilength==10) { /* need to check for wrap */ |
7649 | 0 | if (theInt/(Int)powers[got-DECDPUN]!=(Int)*(up-1)) ilength=11; |
7650 | | /* [that test also disallows the BADINT result case] */ |
7651 | 0 | else if (neg && theInt>1999999997) ilength=11; |
7652 | 0 | else if (!neg && theInt>999999999) ilength=11; |
7653 | 0 | if (ilength==11) theInt=save; /* restore correct low bit */ |
7654 | 0 | } |
7655 | 0 | } |
7656 | |
|
7657 | 0 | if (ilength>10) { /* too big */ |
7658 | 0 | if (theInt&1) return BIGODD; /* bottom bit 1 */ |
7659 | 0 | return BIGEVEN; /* bottom bit 0 */ |
7660 | 0 | } |
7661 | | |
7662 | 0 | if (neg) theInt=-theInt; /* apply sign */ |
7663 | 0 | return theInt; |
7664 | 0 | } /* decGetInt */ |
7665 | | |
7666 | | /* ------------------------------------------------------------------ */ |
7667 | | /* decDecap -- decapitate the coefficient of a number */ |
7668 | | /* */ |
7669 | | /* dn is the number to be decapitated */ |
7670 | | /* drop is the number of digits to be removed from the left of dn; */ |
7671 | | /* this must be <= dn->digits (if equal, the coefficient is */ |
7672 | | /* set to 0) */ |
7673 | | /* */ |
7674 | | /* Returns dn; dn->digits will be <= the initial digits less drop */ |
7675 | | /* (after removing drop digits there may be leading zero digits */ |
7676 | | /* which will also be removed). Only dn->lsu and dn->digits change. */ |
7677 | | /* ------------------------------------------------------------------ */ |
7678 | 0 | static decNumber *decDecap(decNumber *dn, Int drop) { |
7679 | 0 | Unit *msu; /* -> target cut point */ |
7680 | 0 | Int cut; /* work */ |
7681 | 0 | if (drop>=dn->digits) { /* losing the whole thing */ |
7682 | | #if DECCHECK |
7683 | | if (drop>dn->digits) |
7684 | | printf("decDecap called with drop>digits [%ld>%ld]\n", |
7685 | | (LI)drop, (LI)dn->digits); |
7686 | | #endif |
7687 | 0 | dn->lsu[0]=0; |
7688 | 0 | dn->digits=1; |
7689 | 0 | return dn; |
7690 | 0 | } |
7691 | 0 | msu=dn->lsu+D2U(dn->digits-drop)-1; /* -> likely msu */ |
7692 | 0 | cut=MSUDIGITS(dn->digits-drop); /* digits to be in use in msu */ |
7693 | 0 | if (cut!=DECDPUN) *msu%=powers[cut]; /* clear left digits */ |
7694 | | /* that may have left leading zero digits, so do a proper count... */ |
7695 | 0 | dn->digits=decGetDigits(dn->lsu, static_cast<int32_t>(msu-dn->lsu+1)); |
7696 | 0 | return dn; |
7697 | 0 | } /* decDecap */ |
7698 | | |
7699 | | /* ------------------------------------------------------------------ */ |
7700 | | /* decBiStr -- compare string with pairwise options */ |
7701 | | /* */ |
7702 | | /* targ is the string to compare */ |
7703 | | /* str1 is one of the strings to compare against (length may be 0) */ |
7704 | | /* str2 is the other; it must be the same length as str1 */ |
7705 | | /* */ |
7706 | | /* returns 1 if strings compare equal, (that is, it is the same */ |
7707 | | /* length as str1 and str2, and each character of targ is in either */ |
7708 | | /* str1 or str2 in the corresponding position), or 0 otherwise */ |
7709 | | /* */ |
7710 | | /* This is used for generic caseless compare, including the awkward */ |
7711 | | /* case of the Turkish dotted and dotless Is. Use as (for example): */ |
7712 | | /* if (decBiStr(test, "mike", "MIKE")) ... */ |
7713 | | /* ------------------------------------------------------------------ */ |
7714 | 0 | static Flag decBiStr(const char *targ, const char *str1, const char *str2) { |
7715 | 0 | for (;;targ++, str1++, str2++) { |
7716 | 0 | if (*targ!=*str1 && *targ!=*str2) return 0; |
7717 | | /* *targ has a match in one (or both, if terminator) */ |
7718 | 0 | if (*targ=='\0') break; |
7719 | 0 | } /* forever */ |
7720 | 0 | return 1; |
7721 | 0 | } /* decBiStr */ |
7722 | | |
7723 | | /* ------------------------------------------------------------------ */ |
7724 | | /* decNaNs -- handle NaN operand or operands */ |
7725 | | /* */ |
7726 | | /* res is the result number */ |
7727 | | /* lhs is the first operand */ |
7728 | | /* rhs is the second operand, or NULL if none */ |
7729 | | /* context is used to limit payload length */ |
7730 | | /* status contains the current status */ |
7731 | | /* returns res in case convenient */ |
7732 | | /* */ |
7733 | | /* Called when one or both operands is a NaN, and propagates the */ |
7734 | | /* appropriate result to res. When an sNaN is found, it is changed */ |
7735 | | /* to a qNaN and Invalid operation is set. */ |
7736 | | /* ------------------------------------------------------------------ */ |
7737 | | static decNumber * decNaNs(decNumber *res, const decNumber *lhs, |
7738 | | const decNumber *rhs, decContext *set, |
7739 | 0 | uInt *status) { |
7740 | | /* This decision tree ends up with LHS being the source pointer, */ |
7741 | | /* and status updated if need be */ |
7742 | 0 | if (lhs->bits & DECSNAN) |
7743 | 0 | *status|=DEC_Invalid_operation | DEC_sNaN; |
7744 | 0 | else if (rhs==NULL); |
7745 | 0 | else if (rhs->bits & DECSNAN) { |
7746 | 0 | lhs=rhs; |
7747 | 0 | *status|=DEC_Invalid_operation | DEC_sNaN; |
7748 | 0 | } |
7749 | 0 | else if (lhs->bits & DECNAN); |
7750 | 0 | else lhs=rhs; |
7751 | | |
7752 | | /* propagate the payload */ |
7753 | 0 | if (lhs->digits<=set->digits) uprv_decNumberCopy(res, lhs); /* easy */ |
7754 | 0 | else { /* too long */ |
7755 | 0 | const Unit *ul; |
7756 | 0 | Unit *ur, *uresp1; |
7757 | | /* copy safe number of units, then decapitate */ |
7758 | 0 | res->bits=lhs->bits; /* need sign etc. */ |
7759 | 0 | uresp1=res->lsu+D2U(set->digits); |
7760 | 0 | for (ur=res->lsu, ul=lhs->lsu; ur<uresp1; ur++, ul++) *ur=*ul; |
7761 | 0 | res->digits=D2U(set->digits)*DECDPUN; |
7762 | | /* maybe still too long */ |
7763 | 0 | if (res->digits>set->digits) decDecap(res, res->digits-set->digits); |
7764 | 0 | } |
7765 | |
|
7766 | 0 | res->bits&=~DECSNAN; /* convert any sNaN to NaN, while */ |
7767 | 0 | res->bits|=DECNAN; /* .. preserving sign */ |
7768 | 0 | res->exponent=0; /* clean exponent */ |
7769 | | /* [coefficient was copied/decapitated] */ |
7770 | 0 | return res; |
7771 | 0 | } /* decNaNs */ |
7772 | | |
7773 | | /* ------------------------------------------------------------------ */ |
7774 | | /* decStatus -- apply non-zero status */ |
7775 | | /* */ |
7776 | | /* dn is the number to set if error */ |
7777 | | /* status contains the current status (not yet in context) */ |
7778 | | /* set is the context */ |
7779 | | /* */ |
7780 | | /* If the status is an error status, the number is set to a NaN, */ |
7781 | | /* unless the error was an overflow, divide-by-zero, or underflow, */ |
7782 | | /* in which case the number will have already been set. */ |
7783 | | /* */ |
7784 | | /* The context status is then updated with the new status. Note that */ |
7785 | | /* this may raise a signal, so control may never return from this */ |
7786 | | /* routine (hence resources must be recovered before it is called). */ |
7787 | | /* ------------------------------------------------------------------ */ |
7788 | 0 | static void decStatus(decNumber *dn, uInt status, decContext *set) { |
7789 | 0 | if (status & DEC_NaNs) { /* error status -> NaN */ |
7790 | | /* if cause was an sNaN, clear and propagate [NaN is already set up] */ |
7791 | 0 | if (status & DEC_sNaN) status&=~DEC_sNaN; |
7792 | 0 | else { |
7793 | 0 | uprv_decNumberZero(dn); /* other error: clean throughout */ |
7794 | 0 | dn->bits=DECNAN; /* and make a quiet NaN */ |
7795 | 0 | } |
7796 | 0 | } |
7797 | 0 | uprv_decContextSetStatus(set, status); /* [may not return] */ |
7798 | 0 | return; |
7799 | 0 | } /* decStatus */ |
7800 | | |
7801 | | /* ------------------------------------------------------------------ */ |
7802 | | /* decGetDigits -- count digits in a Units array */ |
7803 | | /* */ |
7804 | | /* uar is the Unit array holding the number (this is often an */ |
7805 | | /* accumulator of some sort) */ |
7806 | | /* len is the length of the array in units [>=1] */ |
7807 | | /* */ |
7808 | | /* returns the number of (significant) digits in the array */ |
7809 | | /* */ |
7810 | | /* All leading zeros are excluded, except the last if the array has */ |
7811 | | /* only zero Units. */ |
7812 | | /* ------------------------------------------------------------------ */ |
7813 | | /* This may be called twice during some operations. */ |
7814 | 0 | static Int decGetDigits(Unit *uar, Int len) { |
7815 | 0 | Unit *up=uar+(len-1); /* -> msu */ |
7816 | 0 | Int digits=(len-1)*DECDPUN+1; /* possible digits excluding msu */ |
7817 | | #if DECDPUN>4 |
7818 | | uInt const *pow; /* work */ |
7819 | | #endif |
7820 | | /* (at least 1 in final msu) */ |
7821 | | #if DECCHECK |
7822 | | if (len<1) printf("decGetDigits called with len<1 [%ld]\n", (LI)len); |
7823 | | #endif |
7824 | |
|
7825 | 0 | for (; up>=uar; up--) { |
7826 | 0 | if (*up==0) { /* unit is all 0s */ |
7827 | 0 | if (digits==1) break; /* a zero has one digit */ |
7828 | 0 | digits-=DECDPUN; /* adjust for 0 unit */ |
7829 | 0 | continue;} |
7830 | | /* found the first (most significant) non-zero Unit */ |
7831 | | #if DECDPUN>1 /* not done yet */ |
7832 | | if (*up<10) break; /* is 1-9 */ |
7833 | | digits++; |
7834 | | #if DECDPUN>2 /* not done yet */ |
7835 | | if (*up<100) break; /* is 10-99 */ |
7836 | | digits++; |
7837 | | #if DECDPUN>3 /* not done yet */ |
7838 | | if (*up<1000) break; /* is 100-999 */ |
7839 | | digits++; |
7840 | | #if DECDPUN>4 /* count the rest ... */ |
7841 | | for (pow=&powers[4]; *up>=*pow; pow++) digits++; |
7842 | | #endif |
7843 | | #endif |
7844 | | #endif |
7845 | | #endif |
7846 | 0 | break; |
7847 | 0 | } /* up */ |
7848 | 0 | return digits; |
7849 | 0 | } /* decGetDigits */ |
7850 | | |
7851 | | #if DECTRACE | DECCHECK |
7852 | | /* ------------------------------------------------------------------ */ |
7853 | | /* decNumberShow -- display a number [debug aid] */ |
7854 | | /* dn is the number to show */ |
7855 | | /* */ |
7856 | | /* Shows: sign, exponent, coefficient (msu first), digits */ |
7857 | | /* or: sign, special-value */ |
7858 | | /* ------------------------------------------------------------------ */ |
7859 | | /* this is public so other modules can use it */ |
7860 | | void uprv_decNumberShow(const decNumber *dn) { |
7861 | | const Unit *up; /* work */ |
7862 | | uInt u, d; /* .. */ |
7863 | | Int cut; /* .. */ |
7864 | | char isign='+'; /* main sign */ |
7865 | | if (dn==NULL) { |
7866 | | printf("NULL\n"); |
7867 | | return;} |
7868 | | if (decNumberIsNegative(dn)) isign='-'; |
7869 | | printf(" >> %c ", isign); |
7870 | | if (dn->bits&DECSPECIAL) { /* Is a special value */ |
7871 | | if (decNumberIsInfinite(dn)) printf("Infinity"); |
7872 | | else { /* a NaN */ |
7873 | | if (dn->bits&DECSNAN) printf("sNaN"); /* signalling NaN */ |
7874 | | else printf("NaN"); |
7875 | | } |
7876 | | /* if coefficient and exponent are 0, no more to do */ |
7877 | | if (dn->exponent==0 && dn->digits==1 && *dn->lsu==0) { |
7878 | | printf("\n"); |
7879 | | return;} |
7880 | | /* drop through to report other information */ |
7881 | | printf(" "); |
7882 | | } |
7883 | | |
7884 | | /* now carefully display the coefficient */ |
7885 | | up=dn->lsu+D2U(dn->digits)-1; /* msu */ |
7886 | | printf("%ld", (LI)*up); |
7887 | | for (up=up-1; up>=dn->lsu; up--) { |
7888 | | u=*up; |
7889 | | printf(":"); |
7890 | | for (cut=DECDPUN-1; cut>=0; cut--) { |
7891 | | d=u/powers[cut]; |
7892 | | u-=d*powers[cut]; |
7893 | | printf("%ld", (LI)d); |
7894 | | } /* cut */ |
7895 | | } /* up */ |
7896 | | if (dn->exponent!=0) { |
7897 | | char esign='+'; |
7898 | | if (dn->exponent<0) esign='-'; |
7899 | | printf(" E%c%ld", esign, (LI)abs(dn->exponent)); |
7900 | | } |
7901 | | printf(" [%ld]\n", (LI)dn->digits); |
7902 | | } /* decNumberShow */ |
7903 | | #endif |
7904 | | |
7905 | | #if DECTRACE || DECCHECK |
7906 | | /* ------------------------------------------------------------------ */ |
7907 | | /* decDumpAr -- display a unit array [debug/check aid] */ |
7908 | | /* name is a single-character tag name */ |
7909 | | /* ar is the array to display */ |
7910 | | /* len is the length of the array in Units */ |
7911 | | /* ------------------------------------------------------------------ */ |
7912 | | static void decDumpAr(char name, const Unit *ar, Int len) { |
7913 | | Int i; |
7914 | | const char *spec; |
7915 | | #if DECDPUN==9 |
7916 | | spec="%09d "; |
7917 | | #elif DECDPUN==8 |
7918 | | spec="%08d "; |
7919 | | #elif DECDPUN==7 |
7920 | | spec="%07d "; |
7921 | | #elif DECDPUN==6 |
7922 | | spec="%06d "; |
7923 | | #elif DECDPUN==5 |
7924 | | spec="%05d "; |
7925 | | #elif DECDPUN==4 |
7926 | | spec="%04d "; |
7927 | | #elif DECDPUN==3 |
7928 | | spec="%03d "; |
7929 | | #elif DECDPUN==2 |
7930 | | spec="%02d "; |
7931 | | #else |
7932 | | spec="%d "; |
7933 | | #endif |
7934 | | printf(" :%c: ", name); |
7935 | | for (i=len-1; i>=0; i--) { |
7936 | | if (i==len-1) printf("%ld ", (LI)ar[i]); |
7937 | | else printf(spec, ar[i]); |
7938 | | } |
7939 | | printf("\n"); |
7940 | | return;} |
7941 | | #endif |
7942 | | |
7943 | | #if DECCHECK |
7944 | | /* ------------------------------------------------------------------ */ |
7945 | | /* decCheckOperands -- check operand(s) to a routine */ |
7946 | | /* res is the result structure (not checked; it will be set to */ |
7947 | | /* quiet NaN if error found (and it is not NULL)) */ |
7948 | | /* lhs is the first operand (may be DECUNRESU) */ |
7949 | | /* rhs is the second (may be DECUNUSED) */ |
7950 | | /* set is the context (may be DECUNCONT) */ |
7951 | | /* returns 0 if both operands, and the context are clean, or 1 */ |
7952 | | /* otherwise (in which case the context will show an error, */ |
7953 | | /* unless NULL). Note that res is not cleaned; caller should */ |
7954 | | /* handle this so res=NULL case is safe. */ |
7955 | | /* The caller is expected to abandon immediately if 1 is returned. */ |
7956 | | /* ------------------------------------------------------------------ */ |
7957 | | static Flag decCheckOperands(decNumber *res, const decNumber *lhs, |
7958 | | const decNumber *rhs, decContext *set) { |
7959 | | Flag bad=0; |
7960 | | if (set==NULL) { /* oops; hopeless */ |
7961 | | #if DECTRACE || DECVERB |
7962 | | printf("Reference to context is NULL.\n"); |
7963 | | #endif |
7964 | | bad=1; |
7965 | | return 1;} |
7966 | | else if (set!=DECUNCONT |
7967 | | && (set->digits<1 || set->round>=DEC_ROUND_MAX)) { |
7968 | | bad=1; |
7969 | | #if DECTRACE || DECVERB |
7970 | | printf("Bad context [digits=%ld round=%ld].\n", |
7971 | | (LI)set->digits, (LI)set->round); |
7972 | | #endif |
7973 | | } |
7974 | | else { |
7975 | | if (res==NULL) { |
7976 | | bad=1; |
7977 | | #if DECTRACE |
7978 | | /* this one not DECVERB as standard tests include NULL */ |
7979 | | printf("Reference to result is NULL.\n"); |
7980 | | #endif |
7981 | | } |
7982 | | if (!bad && lhs!=DECUNUSED) bad=(decCheckNumber(lhs)); |
7983 | | if (!bad && rhs!=DECUNUSED) bad=(decCheckNumber(rhs)); |
7984 | | } |
7985 | | if (bad) { |
7986 | | if (set!=DECUNCONT) uprv_decContextSetStatus(set, DEC_Invalid_operation); |
7987 | | if (res!=DECUNRESU && res!=NULL) { |
7988 | | uprv_decNumberZero(res); |
7989 | | res->bits=DECNAN; /* qNaN */ |
7990 | | } |
7991 | | } |
7992 | | return bad; |
7993 | | } /* decCheckOperands */ |
7994 | | |
7995 | | /* ------------------------------------------------------------------ */ |
7996 | | /* decCheckNumber -- check a number */ |
7997 | | /* dn is the number to check */ |
7998 | | /* returns 0 if the number is clean, or 1 otherwise */ |
7999 | | /* */ |
8000 | | /* The number is considered valid if it could be a result from some */ |
8001 | | /* operation in some valid context. */ |
8002 | | /* ------------------------------------------------------------------ */ |
8003 | | static Flag decCheckNumber(const decNumber *dn) { |
8004 | | const Unit *up; /* work */ |
8005 | | uInt maxuint; /* .. */ |
8006 | | Int ae, d, digits; /* .. */ |
8007 | | Int emin, emax; /* .. */ |
8008 | | |
8009 | | if (dn==NULL) { /* hopeless */ |
8010 | | #if DECTRACE |
8011 | | /* this one not DECVERB as standard tests include NULL */ |
8012 | | printf("Reference to decNumber is NULL.\n"); |
8013 | | #endif |
8014 | | return 1;} |
8015 | | |
8016 | | /* check special values */ |
8017 | | if (dn->bits & DECSPECIAL) { |
8018 | | if (dn->exponent!=0) { |
8019 | | #if DECTRACE || DECVERB |
8020 | | printf("Exponent %ld (not 0) for a special value [%02x].\n", |
8021 | | (LI)dn->exponent, dn->bits); |
8022 | | #endif |
8023 | | return 1;} |
8024 | | |
8025 | | /* 2003.09.08: NaNs may now have coefficients, so next tests Inf only */ |
8026 | | if (decNumberIsInfinite(dn)) { |
8027 | | if (dn->digits!=1) { |
8028 | | #if DECTRACE || DECVERB |
8029 | | printf("Digits %ld (not 1) for an infinity.\n", (LI)dn->digits); |
8030 | | #endif |
8031 | | return 1;} |
8032 | | if (*dn->lsu!=0) { |
8033 | | #if DECTRACE || DECVERB |
8034 | | printf("LSU %ld (not 0) for an infinity.\n", (LI)*dn->lsu); |
8035 | | #endif |
8036 | | decDumpAr('I', dn->lsu, D2U(dn->digits)); |
8037 | | return 1;} |
8038 | | } /* Inf */ |
8039 | | /* 2002.12.26: negative NaNs can now appear through proposed IEEE */ |
8040 | | /* concrete formats (decimal64, etc.). */ |
8041 | | return 0; |
8042 | | } |
8043 | | |
8044 | | /* check the coefficient */ |
8045 | | if (dn->digits<1 || dn->digits>DECNUMMAXP) { |
8046 | | #if DECTRACE || DECVERB |
8047 | | printf("Digits %ld in number.\n", (LI)dn->digits); |
8048 | | #endif |
8049 | | return 1;} |
8050 | | |
8051 | | d=dn->digits; |
8052 | | |
8053 | | for (up=dn->lsu; d>0; up++) { |
8054 | | if (d>DECDPUN) maxuint=DECDPUNMAX; |
8055 | | else { /* reached the msu */ |
8056 | | maxuint=powers[d]-1; |
8057 | | if (dn->digits>1 && *up<powers[d-1]) { |
8058 | | #if DECTRACE || DECVERB |
8059 | | printf("Leading 0 in number.\n"); |
8060 | | uprv_decNumberShow(dn); |
8061 | | #endif |
8062 | | return 1;} |
8063 | | } |
8064 | | if (*up>maxuint) { |
8065 | | #if DECTRACE || DECVERB |
8066 | | printf("Bad Unit [%08lx] in %ld-digit number at offset %ld [maxuint %ld].\n", |
8067 | | (LI)*up, (LI)dn->digits, (LI)(up-dn->lsu), (LI)maxuint); |
8068 | | #endif |
8069 | | return 1;} |
8070 | | d-=DECDPUN; |
8071 | | } |
8072 | | |
8073 | | /* check the exponent. Note that input operands can have exponents */ |
8074 | | /* which are out of the set->emin/set->emax and set->digits range */ |
8075 | | /* (just as they can have more digits than set->digits). */ |
8076 | | ae=dn->exponent+dn->digits-1; /* adjusted exponent */ |
8077 | | emax=DECNUMMAXE; |
8078 | | emin=DECNUMMINE; |
8079 | | digits=DECNUMMAXP; |
8080 | | if (ae<emin-(digits-1)) { |
8081 | | #if DECTRACE || DECVERB |
8082 | | printf("Adjusted exponent underflow [%ld].\n", (LI)ae); |
8083 | | uprv_decNumberShow(dn); |
8084 | | #endif |
8085 | | return 1;} |
8086 | | if (ae>+emax) { |
8087 | | #if DECTRACE || DECVERB |
8088 | | printf("Adjusted exponent overflow [%ld].\n", (LI)ae); |
8089 | | uprv_decNumberShow(dn); |
8090 | | #endif |
8091 | | return 1;} |
8092 | | |
8093 | | return 0; /* it's OK */ |
8094 | | } /* decCheckNumber */ |
8095 | | |
8096 | | /* ------------------------------------------------------------------ */ |
8097 | | /* decCheckInexact -- check a normal finite inexact result has digits */ |
8098 | | /* dn is the number to check */ |
8099 | | /* set is the context (for status and precision) */ |
8100 | | /* sets Invalid operation, etc., if some digits are missing */ |
8101 | | /* [this check is not made for DECSUBSET compilation or when */ |
8102 | | /* subnormal is not set] */ |
8103 | | /* ------------------------------------------------------------------ */ |
8104 | | static void decCheckInexact(const decNumber *dn, decContext *set) { |
8105 | | #if !DECSUBSET && DECEXTFLAG |
8106 | | if ((set->status & (DEC_Inexact|DEC_Subnormal))==DEC_Inexact |
8107 | | && (set->digits!=dn->digits) && !(dn->bits & DECSPECIAL)) { |
8108 | | #if DECTRACE || DECVERB |
8109 | | printf("Insufficient digits [%ld] on normal Inexact result.\n", |
8110 | | (LI)dn->digits); |
8111 | | uprv_decNumberShow(dn); |
8112 | | #endif |
8113 | | uprv_decContextSetStatus(set, DEC_Invalid_operation); |
8114 | | } |
8115 | | #else |
8116 | | /* next is a noop for quiet compiler */ |
8117 | | if (dn!=NULL && dn->digits==0) set->status|=DEC_Invalid_operation; |
8118 | | #endif |
8119 | | return; |
8120 | | } /* decCheckInexact */ |
8121 | | #endif |
8122 | | |
8123 | | #if DECALLOC |
8124 | | #undef malloc |
8125 | | #undef free |
8126 | | /* ------------------------------------------------------------------ */ |
8127 | | /* decMalloc -- accountable allocation routine */ |
8128 | | /* n is the number of bytes to allocate */ |
8129 | | /* */ |
8130 | | /* Semantics is the same as the stdlib malloc routine, but bytes */ |
8131 | | /* allocated are accounted for globally, and corruption fences are */ |
8132 | | /* added before and after the 'actual' storage. */ |
8133 | | /* ------------------------------------------------------------------ */ |
8134 | | /* This routine allocates storage with an extra twelve bytes; 8 are */ |
8135 | | /* at the start and hold: */ |
8136 | | /* 0-3 the original length requested */ |
8137 | | /* 4-7 buffer corruption detection fence (DECFENCE, x4) */ |
8138 | | /* The 4 bytes at the end also hold a corruption fence (DECFENCE, x4) */ |
8139 | | /* ------------------------------------------------------------------ */ |
8140 | | static void *decMalloc(size_t n) { |
8141 | | uInt size=n+12; /* true size */ |
8142 | | void *alloc; /* -> allocated storage */ |
8143 | | uByte *b, *b0; /* work */ |
8144 | | uInt uiwork; /* for macros */ |
8145 | | |
8146 | | alloc=malloc(size); /* -> allocated storage */ |
8147 | | if (alloc==NULL) return NULL; /* out of strorage */ |
8148 | | b0=(uByte *)alloc; /* as bytes */ |
8149 | | decAllocBytes+=n; /* account for storage */ |
8150 | | UBFROMUI(alloc, n); /* save n */ |
8151 | | /* printf(" alloc ++ dAB: %ld (%ld)\n", (LI)decAllocBytes, (LI)n); */ |
8152 | | for (b=b0+4; b<b0+8; b++) *b=DECFENCE; |
8153 | | for (b=b0+n+8; b<b0+n+12; b++) *b=DECFENCE; |
8154 | | return b0+8; /* -> play area */ |
8155 | | } /* decMalloc */ |
8156 | | |
8157 | | /* ------------------------------------------------------------------ */ |
8158 | | /* decFree -- accountable free routine */ |
8159 | | /* alloc is the storage to free */ |
8160 | | /* */ |
8161 | | /* Semantics is the same as the stdlib malloc routine, except that */ |
8162 | | /* the global storage accounting is updated and the fences are */ |
8163 | | /* checked to ensure that no routine has written 'out of bounds'. */ |
8164 | | /* ------------------------------------------------------------------ */ |
8165 | | /* This routine first checks that the fences have not been corrupted. */ |
8166 | | /* It then frees the storage using the 'truw' storage address (that */ |
8167 | | /* is, offset by 8). */ |
8168 | | /* ------------------------------------------------------------------ */ |
8169 | | static void decFree(void *alloc) { |
8170 | | uInt n; /* original length */ |
8171 | | uByte *b, *b0; /* work */ |
8172 | | uInt uiwork; /* for macros */ |
8173 | | |
8174 | | if (alloc==NULL) return; /* allowed; it's a nop */ |
8175 | | b0=(uByte *)alloc; /* as bytes */ |
8176 | | b0-=8; /* -> true start of storage */ |
8177 | | n=UBTOUI(b0); /* lift length */ |
8178 | | for (b=b0+4; b<b0+8; b++) if (*b!=DECFENCE) |
8179 | | printf("=== Corrupt byte [%02x] at offset %d from %ld ===\n", *b, |
8180 | | b-b0-8, (LI)b0); |
8181 | | for (b=b0+n+8; b<b0+n+12; b++) if (*b!=DECFENCE) |
8182 | | printf("=== Corrupt byte [%02x] at offset +%d from %ld, n=%ld ===\n", *b, |
8183 | | b-b0-8, (LI)b0, (LI)n); |
8184 | | free(b0); /* drop the storage */ |
8185 | | decAllocBytes-=n; /* account for storage */ |
8186 | | /* printf(" free -- dAB: %d (%d)\n", decAllocBytes, -n); */ |
8187 | | } /* decFree */ |
8188 | | #define malloc(a) decMalloc(a) |
8189 | | #define free(a) decFree(a) |
8190 | | #endif |