Coverage Report

Created: 2023-02-22 06:39

/src/gmp-6.2.1/mpn/get_str.c
Line
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Source (jump to first uncovered line)
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/* 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.
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10
Copyright 1991-2017 Free Software Foundation, Inc.
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12
This file is part of the GNU MP Library.
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14
The GNU MP Library is free software; you can redistribute it and/or modify
15
it under the terms of either:
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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.
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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
145k
  do {                                  \
134
145k
    mp_limb_t  __q = (n) / (d);         \
135
145k
    mp_limb_t  __r = (n) - __q*(d);     \
136
145k
    (q) = __q;                          \
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145k
    (r) = __r;                          \
138
145k
  } 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
13.1k
{
151
13.1k
  mp_limb_t rl, ul;
152
13.1k
  unsigned char *s;
153
13.1k
  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
26.3k
#define BUF_ALLOC (GET_STR_PRECOMPUTE_THRESHOLD * GMP_LIMB_BITS * 7 / 11)
161
13.1k
#endif
162
13.1k
  unsigned char buf[BUF_ALLOC];
163
#if TUNE_PROGRAM_BUILD
164
  mp_limb_t rp[GET_STR_THRESHOLD_LIMIT];
165
#else
166
13.1k
  mp_limb_t rp[GET_STR_PRECOMPUTE_THRESHOLD];
167
13.1k
#endif
168
169
13.1k
  if (base == 10)
170
13.1k
    {
171
      /* Special case code for base==10 so that the compiler has a chance to
172
   optimize things.  */
173
174
13.1k
      MPN_COPY (rp + 1, up, un);
175
176
13.1k
      s = buf + BUF_ALLOC;
177
132k
      while (un > 1)
178
119k
  {
179
119k
    int i;
180
119k
    mp_limb_t frac, digit;
181
119k
    MPN_DIVREM_OR_PREINV_DIVREM_1 (rp, (mp_size_t) 1, rp + 1, un,
182
119k
           MP_BASES_BIG_BASE_10,
183
119k
           MP_BASES_BIG_BASE_INVERTED_10,
184
119k
           MP_BASES_NORMALIZATION_STEPS_10);
185
119k
    un -= rp[un] == 0;
186
119k
    frac = (rp[0] + 1) << GMP_NAIL_BITS;
187
119k
    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
119k
    if (MP_BASES_NORMALIZATION_STEPS_10 == 0)
203
119k
      {
204
119k
        umul_ppmm (digit, frac, frac, 10);
205
119k
        *s++ = digit;
206
119k
      }
207
119k
    if (MP_BASES_NORMALIZATION_STEPS_10 <= 1)
208
119k
      {
209
119k
        umul_ppmm (digit, frac, frac, 10);
210
119k
        *s++ = digit;
211
119k
      }
212
119k
    if (MP_BASES_NORMALIZATION_STEPS_10 <= 2)
213
119k
      {
214
119k
        umul_ppmm (digit, frac, frac, 10);
215
119k
        *s++ = digit;
216
119k
      }
217
119k
    if (MP_BASES_NORMALIZATION_STEPS_10 <= 3)
218
119k
      {
219
119k
        umul_ppmm (digit, frac, frac, 10);
220
119k
        *s++ = digit;
221
119k
      }
222
119k
    i = (MP_BASES_CHARS_PER_LIMB_10 - ((MP_BASES_NORMALIZATION_STEPS_10 < 4)
223
119k
               ? (4-MP_BASES_NORMALIZATION_STEPS_10)
224
119k
               : 0));
225
119k
    frac = (frac + 0xf) >> 4;
226
119k
    do
227
1.78M
      {
228
1.78M
        frac *= 10;
229
1.78M
        digit = frac >> (GMP_LIMB_BITS - 4);
230
1.78M
        *s++ = digit;
231
1.78M
        frac &= (~(mp_limb_t) 0) >> 4;
232
1.78M
      }
233
1.78M
    while (--i);
234
119k
#endif
235
119k
    s -= MP_BASES_CHARS_PER_LIMB_10;
236
119k
  }
237
238
13.1k
      ul = rp[1];
239
158k
      while (ul != 0)
240
145k
  {
241
145k
    udiv_qrnd_unnorm (ul, rl, ul, 10);
242
145k
    *--s = rl;
243
145k
  }
244
13.1k
    }
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
13.1k
  l = buf + BUF_ALLOC - s;
289
91.3k
  while (l < len)
290
78.1k
    {
291
78.1k
      *str++ = 0;
292
78.1k
      len--;
293
78.1k
    }
294
2.42M
  while (l != 0)
295
2.41M
    {
296
2.41M
      *str++ = *s++;
297
2.41M
      l--;
298
2.41M
    }
299
13.1k
  return str;
300
13.1k
}
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
21.3k
{
313
21.3k
  if (BELOW_THRESHOLD (un, GET_STR_DC_THRESHOLD))
314
11.0k
    {
315
11.0k
      if (un != 0)
316
11.0k
  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
11.0k
    }
326
10.3k
  else
327
10.3k
    {
328
10.3k
      mp_ptr pwp, qp, rp;
329
10.3k
      mp_size_t pwn, qn;
330
10.3k
      mp_size_t sn;
331
332
10.3k
      pwp = powtab->p;
333
10.3k
      pwn = powtab->n;
334
10.3k
      sn = powtab->shift;
335
336
10.3k
      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
10.3k
      else
341
10.3k
  {
342
10.3k
    qp = tmp;   /* (un - pwn + 1) limbs for qp */
343
10.3k
    rp = up;    /* pwn limbs for rp; overwrite up area */
344
345
10.3k
    mpn_tdiv_qr (qp, rp + sn, 0L, up + sn, un - sn, pwp, pwn);
346
10.3k
    qn = un - sn - pwn; qn += qp[qn] != 0;    /* quotient size */
347
348
10.3k
    ASSERT (qn < pwn + sn || (qn == pwn + sn && mpn_cmp (qp + sn, pwp, pwn) < 0));
349
350
10.3k
    if (len != 0)
351
7.84k
      len = len - powtab->digits_in_base;
352
353
10.3k
    str = mpn_dc_get_str (str, len, qp, qn, powtab - 1, tmp + qn);
354
10.3k
    str = mpn_dc_get_str (str, powtab->digits_in_base, rp, pwn + sn, powtab - 1, tmp);
355
10.3k
  }
356
10.3k
    }
357
21.3k
  return str;
358
21.3k
}
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
3.92k
{
367
3.92k
  mp_ptr powtab_mem;
368
3.92k
  powers_t powtab[GMP_LIMB_BITS];
369
3.92k
  int pi;
370
3.92k
  size_t out_len;
371
3.92k
  mp_ptr tmp;
372
3.92k
  size_t ndig;
373
3.92k
  mp_size_t xn;
374
3.92k
  TMP_DECL;
375
376
  /* Special case zero, as the code below doesn't handle it.  */
377
3.92k
  if (un == 0)
378
1.03k
    {
379
1.03k
      str[0] = 0;
380
1.03k
      return 1;
381
1.03k
    }
382
383
2.88k
  if (POW2_P (base))
384
0
    {
385
      /* The base is a power of 2.  Convert from most significant end.  */
386
0
      mp_limb_t n1, n0;
387
0
      int bits_per_digit = mp_bases[base].big_base;
388
0
      int cnt;
389
0
      int bit_pos;
390
0
      mp_size_t i;
391
0
      unsigned char *s = str;
392
0
      mp_bitcnt_t bits;
393
394
0
      n1 = up[un - 1];
395
0
      count_leading_zeros (cnt, n1);
396
397
      /* BIT_POS should be R when input ends in least significant nibble,
398
   R + bits_per_digit * n when input ends in nth least significant
399
   nibble. */
400
401
0
      bits = (mp_bitcnt_t) GMP_NUMB_BITS * un - cnt + GMP_NAIL_BITS;
402
0
      cnt = bits % bits_per_digit;
403
0
      if (cnt != 0)
404
0
  bits += bits_per_digit - cnt;
405
0
      bit_pos = bits - (mp_bitcnt_t) (un - 1) * GMP_NUMB_BITS;
406
407
      /* Fast loop for bit output.  */
408
0
      i = un - 1;
409
0
      for (;;)
410
0
  {
411
0
    bit_pos -= bits_per_digit;
412
0
    while (bit_pos >= 0)
413
0
      {
414
0
        *s++ = (n1 >> bit_pos) & ((1 << bits_per_digit) - 1);
415
0
        bit_pos -= bits_per_digit;
416
0
      }
417
0
    i--;
418
0
    if (i < 0)
419
0
      break;
420
0
    n0 = (n1 << -bit_pos) & ((1 << bits_per_digit) - 1);
421
0
    n1 = up[i];
422
0
    bit_pos += GMP_NUMB_BITS;
423
0
    *s++ = n0 | (n1 >> bit_pos);
424
0
  }
425
426
0
      return s - str;
427
0
    }
428
429
  /* General case.  The base is not a power of 2.  */
430
431
2.88k
  if (BELOW_THRESHOLD (un, GET_STR_PRECOMPUTE_THRESHOLD))
432
2.13k
    return mpn_bc_get_str (str, (size_t) 0, up, un, base) - str;
433
434
748
  TMP_MARK;
435
436
  /* Allocate one large block for the powers of big_base.  */
437
748
  powtab_mem = TMP_BALLOC_LIMBS (mpn_str_powtab_alloc (un));
438
439
  /* Compute a table of powers, were the largest power is >= sqrt(U).  */
440
748
  DIGITS_IN_BASE_PER_LIMB (ndig, un, base);
441
748
  xn = 1 + ndig / mp_bases[base].chars_per_limb; /* FIXME: scalar integer division */
442
443
748
  pi = 1 + mpn_compute_powtab (powtab, powtab_mem, xn, base);
444
445
  /* Using our precomputed powers, now in powtab[], convert our number.  */
446
748
  tmp = TMP_BALLOC_LIMBS (mpn_dc_get_str_itch (un));
447
748
  out_len = mpn_dc_get_str (str, 0, up, un, powtab + (pi - 1), tmp) - str;
448
748
  TMP_FREE;
449
450
748
  return out_len;
451
2.88k
}