Coverage Report

Created: 2024-11-21 06:47

/src/libgmp/mpn/get_str.c
Line
Count
Source (jump to first uncovered line)
1
/* mpn_get_str -- Convert {UP,USIZE} to a base BASE string in STR.
2
3
   Contributed to the GNU project by Torbjorn Granlund.
4
5
   THE FUNCTIONS IN THIS FILE, EXCEPT mpn_get_str, ARE INTERNAL WITH MUTABLE
6
   INTERFACES.  IT IS ONLY SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES.
7
   IN FACT, IT IS ALMOST GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A
8
   FUTURE GNU MP RELEASE.
9
10
Copyright 1991-2017 Free Software Foundation, Inc.
11
12
This file is part of the GNU MP Library.
13
14
The GNU MP Library is free software; you can redistribute it and/or modify
15
it under the terms of either:
16
17
  * the GNU Lesser General Public License as published by the Free
18
    Software Foundation; either version 3 of the License, or (at your
19
    option) any later version.
20
21
or
22
23
  * the GNU General Public License as published by the Free Software
24
    Foundation; either version 2 of the License, or (at your option) any
25
    later version.
26
27
or both in parallel, as here.
28
29
The GNU MP Library is distributed in the hope that it will be useful, but
30
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
31
or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
32
for more details.
33
34
You should have received copies of the GNU General Public License and the
35
GNU Lesser General Public License along with the GNU MP Library.  If not,
36
see https://www.gnu.org/licenses/.  */
37
38
#include "gmp-impl.h"
39
#include "longlong.h"
40
41
/* Conversion of U {up,un} to a string in base b.  Internally, we convert to
42
   base B = b^m, the largest power of b that fits a limb.  Basic algorithms:
43
44
  A) Divide U repeatedly by B, generating a quotient and remainder, until the
45
     quotient becomes zero.  The remainders hold the converted digits.  Digits
46
     come out from right to left.  (Used in mpn_bc_get_str.)
47
48
  B) Divide U by b^g, for g such that 1/b <= U/b^g < 1, generating a fraction.
49
     Then develop digits by multiplying the fraction repeatedly by b.  Digits
50
     come out from left to right.  (Currently not used herein, except for in
51
     code for converting single limbs to individual digits.)
52
53
  C) Compute B^1, B^2, B^4, ..., B^s, for s such that B^s is just above
54
     sqrt(U).  Then divide U by B^s, generating quotient and remainder.
55
     Recursively convert the quotient, then the remainder, using the
56
     precomputed powers.  Digits come out from left to right.  (Used in
57
     mpn_dc_get_str.)
58
59
  When using algorithm C, algorithm B might be suitable for basecase code,
60
  since the required b^g power will be readily accessible.
61
62
  Optimization ideas:
63
  1. The recursive function of (C) could use less temporary memory.  The powtab
64
     allocation could be trimmed with some computation, and the tmp area could
65
     be reduced, or perhaps eliminated if up is reused for both quotient and
66
     remainder (it is currently used just for remainder).
67
  2. Store the powers of (C) in normalized form, with the normalization count.
68
     Quotients will usually need to be left-shifted before each divide, and
69
     remainders will either need to be left-shifted of right-shifted.
70
  3. In the code for developing digits from a single limb, we could avoid using
71
     a full umul_ppmm except for the first (or first few) digits, provided base
72
     is even.  Subsequent digits can be developed using plain multiplication.
73
     (This saves on register-starved machines (read x86) and on all machines
74
     that generate the upper product half using a separate instruction (alpha,
75
     powerpc, IA-64) or lacks such support altogether (sparc64, hppa64).
76
  4. Separate mpn_dc_get_str basecase code from code for small conversions. The
77
     former code will have the exact right power readily available in the
78
     powtab parameter for dividing the current number into a fraction.  Convert
79
     that using algorithm B.
80
  5. Completely avoid division.  Compute the inverses of the powers now in
81
     powtab instead of the actual powers.
82
  6. Decrease powtab allocation for even bases.  E.g. for base 10 we could save
83
     about 30% (1-log(5)/log(10)).
84
85
  Basic structure of (C):
86
    mpn_get_str:
87
      if POW2_P (n)
88
  ...
89
      else
90
  if (un < GET_STR_PRECOMPUTE_THRESHOLD)
91
    mpn_bx_get_str (str, base, up, un);
92
  else
93
    precompute_power_tables
94
    mpn_dc_get_str
95
96
    mpn_dc_get_str:
97
  mpn_tdiv_qr
98
  if (qn < GET_STR_DC_THRESHOLD)
99
    mpn_bc_get_str
100
  else
101
    mpn_dc_get_str
102
  if (rn < GET_STR_DC_THRESHOLD)
103
    mpn_bc_get_str
104
  else
105
    mpn_dc_get_str
106
107
108
  The reason for the two threshold values is the cost of
109
  precompute_power_tables.  GET_STR_PRECOMPUTE_THRESHOLD will be
110
  considerably larger than GET_STR_DC_THRESHOLD.  */
111
112
113
/* The x86s and m68020 have a quotient and remainder "div" instruction and
114
   gcc recognises an adjacent "/" and "%" can be combined using that.
115
   Elsewhere "/" and "%" are either separate instructions, or separate
116
   libgcc calls (which unfortunately gcc as of version 3.0 doesn't combine).
117
   A multiply and subtract should be faster than a "%" in those cases.  */
118
#if HAVE_HOST_CPU_FAMILY_x86            \
119
  || HAVE_HOST_CPU_m68020               \
120
  || HAVE_HOST_CPU_m68030               \
121
  || HAVE_HOST_CPU_m68040               \
122
  || HAVE_HOST_CPU_m68060               \
123
  || HAVE_HOST_CPU_m68360 /* CPU32 */
124
#define udiv_qrnd_unnorm(q,r,n,d)       \
125
  do {                                  \
126
    mp_limb_t  __q = (n) / (d);         \
127
    mp_limb_t  __r = (n) % (d);         \
128
    (q) = __q;                          \
129
    (r) = __r;                          \
130
  } while (0)
131
#else
132
#define udiv_qrnd_unnorm(q,r,n,d)       \
133
16.0M
  do {                                  \
134
16.0M
    mp_limb_t  __q = (n) / (d);         \
135
16.0M
    mp_limb_t  __r = (n) - __q*(d);     \
136
16.0M
    (q) = __q;                          \
137
16.0M
    (r) = __r;                          \
138
16.0M
  } while (0)
139
#endif
140
141

142
/* Convert {up,un} to a string in base base, and put the result in str.
143
   Generate len characters, possibly padding with zeros to the left.  If len is
144
   zero, generate as many characters as required.  Return a pointer immediately
145
   after the last digit of the result string.  Complexity is O(un^2); intended
146
   for small conversions.  */
147
static unsigned char *
148
mpn_bc_get_str (unsigned char *str, size_t len,
149
    mp_ptr up, mp_size_t un, int base)
150
1.97M
{
151
1.97M
  mp_limb_t rl, ul;
152
1.97M
  unsigned char *s;
153
1.97M
  size_t l;
154
  /* Allocate memory for largest possible string, given that we only get here
155
     for operands with un < GET_STR_PRECOMPUTE_THRESHOLD and that the smallest
156
     base is 3.  7/11 is an approximation to 1/log2(3).  */
157
#if TUNE_PROGRAM_BUILD
158
#define BUF_ALLOC (GET_STR_THRESHOLD_LIMIT * GMP_LIMB_BITS * 7 / 11)
159
#else
160
3.95M
#define BUF_ALLOC (GET_STR_PRECOMPUTE_THRESHOLD * GMP_LIMB_BITS * 7 / 11)
161
1.97M
#endif
162
1.97M
  unsigned char buf[BUF_ALLOC];
163
#if TUNE_PROGRAM_BUILD
164
  mp_limb_t rp[GET_STR_THRESHOLD_LIMIT];
165
#else
166
1.97M
  mp_limb_t rp[GET_STR_PRECOMPUTE_THRESHOLD];
167
1.97M
#endif
168
169
1.97M
  if (base == 10)
170
1.97M
    {
171
      /* Special case code for base==10 so that the compiler has a chance to
172
   optimize things.  */
173
174
1.97M
      MPN_COPY (rp + 1, up, un);
175
176
1.97M
      s = buf + BUF_ALLOC;
177
20.2M
      while (un > 1)
178
18.2M
  {
179
18.2M
    int i;
180
18.2M
    mp_limb_t frac, digit;
181
18.2M
    MPN_DIVREM_OR_PREINV_DIVREM_1 (rp, (mp_size_t) 1, rp + 1, un,
182
18.2M
           MP_BASES_BIG_BASE_10,
183
18.2M
           MP_BASES_BIG_BASE_INVERTED_10,
184
18.2M
           MP_BASES_NORMALIZATION_STEPS_10);
185
18.2M
    un -= rp[un] == 0;
186
18.2M
    frac = (rp[0] + 1) << GMP_NAIL_BITS;
187
18.2M
    s -= MP_BASES_CHARS_PER_LIMB_10;
188
#if HAVE_HOST_CPU_FAMILY_x86
189
    /* The code below turns out to be a bit slower for x86 using gcc.
190
       Use plain code.  */
191
    i = MP_BASES_CHARS_PER_LIMB_10;
192
    do
193
      {
194
        umul_ppmm (digit, frac, frac, 10);
195
        *s++ = digit;
196
      }
197
    while (--i);
198
#else
199
    /* Use the fact that 10 in binary is 1010, with the lowest bit 0.
200
       After a few umul_ppmm, we will have accumulated enough low zeros
201
       to use a plain multiply.  */
202
18.2M
    if (MP_BASES_NORMALIZATION_STEPS_10 == 0)
203
18.2M
      {
204
18.2M
        umul_ppmm (digit, frac, frac, 10);
205
18.2M
        *s++ = digit;
206
18.2M
      }
207
18.2M
    if (MP_BASES_NORMALIZATION_STEPS_10 <= 1)
208
18.2M
      {
209
18.2M
        umul_ppmm (digit, frac, frac, 10);
210
18.2M
        *s++ = digit;
211
18.2M
      }
212
18.2M
    if (MP_BASES_NORMALIZATION_STEPS_10 <= 2)
213
18.2M
      {
214
18.2M
        umul_ppmm (digit, frac, frac, 10);
215
18.2M
        *s++ = digit;
216
18.2M
      }
217
18.2M
    if (MP_BASES_NORMALIZATION_STEPS_10 <= 3)
218
18.2M
      {
219
18.2M
        umul_ppmm (digit, frac, frac, 10);
220
18.2M
        *s++ = digit;
221
18.2M
      }
222
18.2M
    i = (MP_BASES_CHARS_PER_LIMB_10 - ((MP_BASES_NORMALIZATION_STEPS_10 < 4)
223
18.2M
               ? (4-MP_BASES_NORMALIZATION_STEPS_10)
224
18.2M
               : 0));
225
18.2M
    frac = (frac + 0xf) >> 4;
226
18.2M
    do
227
274M
      {
228
274M
        frac *= 10;
229
274M
        digit = frac >> (GMP_LIMB_BITS - 4);
230
274M
        *s++ = digit;
231
274M
        frac &= (~(mp_limb_t) 0) >> 4;
232
274M
      }
233
274M
    while (--i);
234
18.2M
#endif
235
18.2M
    s -= MP_BASES_CHARS_PER_LIMB_10;
236
18.2M
  }
237
238
1.97M
      ul = rp[1];
239
18.0M
      while (ul != 0)
240
16.0M
  {
241
16.0M
    udiv_qrnd_unnorm (ul, rl, ul, 10);
242
16.0M
    *--s = rl;
243
16.0M
  }
244
1.97M
    }
245
0
  else /* not base 10 */
246
0
    {
247
0
      unsigned chars_per_limb;
248
0
      mp_limb_t big_base, big_base_inverted;
249
0
      unsigned normalization_steps;
250
251
0
      chars_per_limb = mp_bases[base].chars_per_limb;
252
0
      big_base = mp_bases[base].big_base;
253
0
      big_base_inverted = mp_bases[base].big_base_inverted;
254
0
      count_leading_zeros (normalization_steps, big_base);
255
256
0
      MPN_COPY (rp + 1, up, un);
257
258
0
      s = buf + BUF_ALLOC;
259
0
      while (un > 1)
260
0
  {
261
0
    int i;
262
0
    mp_limb_t frac;
263
0
    MPN_DIVREM_OR_PREINV_DIVREM_1 (rp, (mp_size_t) 1, rp + 1, un,
264
0
           big_base, big_base_inverted,
265
0
           normalization_steps);
266
0
    un -= rp[un] == 0;
267
0
    frac = (rp[0] + 1) << GMP_NAIL_BITS;
268
0
    s -= chars_per_limb;
269
0
    i = chars_per_limb;
270
0
    do
271
0
      {
272
0
        mp_limb_t digit;
273
0
        umul_ppmm (digit, frac, frac, base);
274
0
        *s++ = digit;
275
0
      }
276
0
    while (--i);
277
0
    s -= chars_per_limb;
278
0
  }
279
280
0
      ul = rp[1];
281
0
      while (ul != 0)
282
0
  {
283
0
    udiv_qrnd_unnorm (ul, rl, ul, base);
284
0
    *--s = rl;
285
0
  }
286
0
    }
287
288
1.97M
  l = buf + BUF_ALLOC - s;
289
18.3M
  while (l < len)
290
16.3M
    {
291
16.3M
      *str++ = 0;
292
16.3M
      len--;
293
16.3M
    }
294
365M
  while (l != 0)
295
363M
    {
296
363M
      *str++ = *s++;
297
363M
      l--;
298
363M
    }
299
1.97M
  return str;
300
1.97M
}
301
302

303
/* Convert {UP,UN} to a string with a base as represented in POWTAB, and put
304
   the string in STR.  Generate LEN characters, possibly padding with zeros to
305
   the left.  If LEN is zero, generate as many characters as required.
306
   Return a pointer immediately after the last digit of the result string.
307
   This uses divide-and-conquer and is intended for large conversions.  */
308
static unsigned char *
309
mpn_dc_get_str (unsigned char *str, size_t len,
310
    mp_ptr up, mp_size_t un,
311
    const powers_t *powtab, mp_ptr tmp)
312
3.31M
{
313
3.31M
  if (BELOW_THRESHOLD (un, GET_STR_DC_THRESHOLD))
314
1.83M
    {
315
1.83M
      if (un != 0)
316
1.83M
  str = mpn_bc_get_str (str, len, up, un, powtab->base);
317
0
      else
318
0
  {
319
0
    while (len != 0)
320
0
      {
321
0
        *str++ = 0;
322
0
        len--;
323
0
      }
324
0
  }
325
1.83M
    }
326
1.47M
  else
327
1.47M
    {
328
1.47M
      mp_ptr pwp, qp, rp;
329
1.47M
      mp_size_t pwn, qn;
330
1.47M
      mp_size_t sn;
331
332
1.47M
      pwp = powtab->p;
333
1.47M
      pwn = powtab->n;
334
1.47M
      sn = powtab->shift;
335
336
1.47M
      if (un < pwn + sn || (un == pwn + sn && mpn_cmp (up + sn, pwp, un - sn) < 0))
337
0
  {
338
0
    str = mpn_dc_get_str (str, len, up, un, powtab - 1, tmp);
339
0
  }
340
1.47M
      else
341
1.47M
  {
342
1.47M
    qp = tmp;   /* (un - pwn + 1) limbs for qp */
343
1.47M
    rp = up;    /* pwn limbs for rp; overwrite up area */
344
345
1.47M
    mpn_tdiv_qr (qp, rp + sn, 0L, up + sn, un - sn, pwp, pwn);
346
1.47M
    qn = un - sn - pwn; qn += qp[qn] != 0;    /* quotient size */
347
348
1.47M
    ASSERT (qn < pwn + sn || (qn == pwn + sn && mpn_cmp (qp + sn, pwp, pwn) < 0));
349
350
1.47M
    if (len != 0)
351
780k
      len = len - powtab->digits_in_base;
352
353
1.47M
    str = mpn_dc_get_str (str, len, qp, qn, powtab - 1, tmp + qn);
354
1.47M
    str = mpn_dc_get_str (str, powtab->digits_in_base, rp, pwn + sn, powtab - 1, tmp);
355
1.47M
  }
356
1.47M
    }
357
3.31M
  return str;
358
3.31M
}
359
360
/* There are no leading zeros on the digits generated at str, but that's not
361
   currently a documented feature.  The current mpz_out_str and mpz_get_str
362
   rely on it.  */
363
364
size_t
365
mpn_get_str (unsigned char *str, int base, mp_ptr up, mp_size_t un)
366
507k
{
367
507k
  mp_ptr powtab_mem;
368
507k
  powers_t powtab[GMP_LIMB_BITS];
369
507k
  int pi;
370
507k
  size_t out_len;
371
507k
  mp_ptr tmp;
372
507k
  TMP_DECL;
373
374
  /* Special case zero, as the code below doesn't handle it.  */
375
507k
  if (un == 0)
376
10.9k
    {
377
10.9k
      str[0] = 0;
378
10.9k
      return 1;
379
10.9k
    }
380
381
496k
  if (POW2_P (base))
382
0
    {
383
      /* The base is a power of 2.  Convert from most significant end.  */
384
0
      mp_limb_t n1, n0;
385
0
      int bits_per_digit = mp_bases[base].big_base;
386
0
      int cnt;
387
0
      int bit_pos;
388
0
      mp_size_t i;
389
0
      unsigned char *s = str;
390
0
      mp_bitcnt_t bits;
391
392
0
      n1 = up[un - 1];
393
0
      count_leading_zeros (cnt, n1);
394
395
      /* BIT_POS should be R when input ends in least significant nibble,
396
   R + bits_per_digit * n when input ends in nth least significant
397
   nibble. */
398
399
0
      bits = (mp_bitcnt_t) GMP_NUMB_BITS * un - cnt + GMP_NAIL_BITS;
400
0
      cnt = bits % bits_per_digit;
401
0
      if (cnt != 0)
402
0
  bits += bits_per_digit - cnt;
403
0
      bit_pos = bits - (mp_bitcnt_t) (un - 1) * GMP_NUMB_BITS;
404
405
      /* Fast loop for bit output.  */
406
0
      i = un - 1;
407
0
      for (;;)
408
0
  {
409
0
    bit_pos -= bits_per_digit;
410
0
    while (bit_pos >= 0)
411
0
      {
412
0
        *s++ = (n1 >> bit_pos) & ((1 << bits_per_digit) - 1);
413
0
        bit_pos -= bits_per_digit;
414
0
      }
415
0
    i--;
416
0
    if (i < 0)
417
0
      break;
418
0
    n0 = (n1 << -bit_pos) & ((1 << bits_per_digit) - 1);
419
0
    n1 = up[i];
420
0
    bit_pos += GMP_NUMB_BITS;
421
0
    *s++ = n0 | (n1 >> bit_pos);
422
0
  }
423
424
0
      return s - str;
425
0
    }
426
427
  /* General case.  The base is not a power of 2.  */
428
429
496k
  if (BELOW_THRESHOLD (un, GET_STR_PRECOMPUTE_THRESHOLD))
430
137k
    return mpn_bc_get_str (str, (size_t) 0, up, un, base) - str;
431
432
359k
  TMP_MARK;
433
434
  /* Allocate one large block for the powers of big_base.  */
435
359k
  powtab_mem = TMP_BALLOC_LIMBS (mpn_str_powtab_alloc (un));
436
437
  /* Compute a table of powers, were the largest power is >= sqrt(U).  */
438
359k
  size_t ndig;
439
359k
  mp_size_t xn;
440
359k
  DIGITS_IN_BASE_PER_LIMB (ndig, un, base);
441
359k
  xn = 1 + ndig / mp_bases[base].chars_per_limb; /* FIXME: scalar integer division */
442
443
359k
  pi = 1 + mpn_compute_powtab (powtab, powtab_mem, xn, base);
444
445
  /* Using our precomputed powers, now in powtab[], convert our number.  */
446
359k
  tmp = TMP_BALLOC_LIMBS (mpn_dc_get_str_itch (un));
447
359k
  out_len = mpn_dc_get_str (str, 0, up, un, powtab + (pi - 1), tmp) - str;
448
359k
  TMP_FREE;
449
450
359k
  return out_len;
451
496k
}