Coverage Report

Created: 2024-11-21 07:03

/src/libgmp/mpn/get_str.c
Line
Count
Source (jump to first uncovered line)
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/* mpn_get_str -- Convert {UP,USIZE} to a base BASE string in STR.
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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.
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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
408k
  do {                                  \
134
408k
    mp_limb_t  __q = (n) / (d);         \
135
408k
    mp_limb_t  __r = (n) - __q*(d);     \
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408k
    (q) = __q;                          \
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408k
    (r) = __r;                          \
138
408k
  } 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
28.2k
{
151
28.2k
  mp_limb_t rl, ul;
152
28.2k
  unsigned char *s;
153
28.2k
  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
56.5k
#define BUF_ALLOC (GET_STR_PRECOMPUTE_THRESHOLD * GMP_LIMB_BITS * 7 / 11)
161
28.2k
#endif
162
28.2k
  unsigned char buf[BUF_ALLOC];
163
#if TUNE_PROGRAM_BUILD
164
  mp_limb_t rp[GET_STR_THRESHOLD_LIMIT];
165
#else
166
28.2k
  mp_limb_t rp[GET_STR_PRECOMPUTE_THRESHOLD];
167
28.2k
#endif
168
169
28.2k
  if (base == 10)
170
28.2k
    {
171
      /* Special case code for base==10 so that the compiler has a chance to
172
   optimize things.  */
173
174
28.2k
      MPN_COPY (rp + 1, up, un);
175
176
28.2k
      s = buf + BUF_ALLOC;
177
261k
      while (un > 1)
178
232k
  {
179
232k
    int i;
180
232k
    mp_limb_t frac, digit;
181
232k
    MPN_DIVREM_OR_PREINV_DIVREM_1 (rp, (mp_size_t) 1, rp + 1, un,
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232k
           MP_BASES_BIG_BASE_10,
183
232k
           MP_BASES_BIG_BASE_INVERTED_10,
184
232k
           MP_BASES_NORMALIZATION_STEPS_10);
185
232k
    un -= rp[un] == 0;
186
232k
    frac = (rp[0] + 1) << GMP_NAIL_BITS;
187
232k
    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
232k
    if (MP_BASES_NORMALIZATION_STEPS_10 == 0)
203
232k
      {
204
232k
        umul_ppmm (digit, frac, frac, 10);
205
232k
        *s++ = digit;
206
232k
      }
207
232k
    if (MP_BASES_NORMALIZATION_STEPS_10 <= 1)
208
232k
      {
209
232k
        umul_ppmm (digit, frac, frac, 10);
210
232k
        *s++ = digit;
211
232k
      }
212
232k
    if (MP_BASES_NORMALIZATION_STEPS_10 <= 2)
213
232k
      {
214
232k
        umul_ppmm (digit, frac, frac, 10);
215
232k
        *s++ = digit;
216
232k
      }
217
232k
    if (MP_BASES_NORMALIZATION_STEPS_10 <= 3)
218
232k
      {
219
232k
        umul_ppmm (digit, frac, frac, 10);
220
232k
        *s++ = digit;
221
232k
      }
222
232k
    i = (MP_BASES_CHARS_PER_LIMB_10 - ((MP_BASES_NORMALIZATION_STEPS_10 < 4)
223
232k
               ? (4-MP_BASES_NORMALIZATION_STEPS_10)
224
232k
               : 0));
225
232k
    frac = (frac + 0xf) >> 4;
226
232k
    do
227
3.49M
      {
228
3.49M
        frac *= 10;
229
3.49M
        digit = frac >> (GMP_LIMB_BITS - 4);
230
3.49M
        *s++ = digit;
231
3.49M
        frac &= (~(mp_limb_t) 0) >> 4;
232
3.49M
      }
233
3.49M
    while (--i);
234
232k
#endif
235
232k
    s -= MP_BASES_CHARS_PER_LIMB_10;
236
232k
  }
237
238
28.2k
      ul = rp[1];
239
436k
      while (ul != 0)
240
408k
  {
241
408k
    udiv_qrnd_unnorm (ul, rl, ul, 10);
242
408k
    *--s = rl;
243
408k
  }
244
28.2k
    }
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
28.2k
  l = buf + BUF_ALLOC - s;
289
47.2k
  while (l < len)
290
18.9k
    {
291
18.9k
      *str++ = 0;
292
18.9k
      len--;
293
18.9k
    }
294
4.86M
  while (l != 0)
295
4.83M
    {
296
4.83M
      *str++ = *s++;
297
4.83M
      l--;
298
4.83M
    }
299
28.2k
  return str;
300
28.2k
}
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
39.5k
{
313
39.5k
  if (BELOW_THRESHOLD (un, GET_STR_DC_THRESHOLD))
314
21.1k
    {
315
21.1k
      if (un != 0)
316
21.1k
  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
21.1k
    }
326
18.3k
  else
327
18.3k
    {
328
18.3k
      mp_ptr pwp, qp, rp;
329
18.3k
      mp_size_t pwn, qn;
330
18.3k
      mp_size_t sn;
331
332
18.3k
      pwp = powtab->p;
333
18.3k
      pwn = powtab->n;
334
18.3k
      sn = powtab->shift;
335
336
18.3k
      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
18.3k
      else
341
18.3k
  {
342
18.3k
    qp = tmp;   /* (un - pwn + 1) limbs for qp */
343
18.3k
    rp = up;    /* pwn limbs for rp; overwrite up area */
344
345
18.3k
    mpn_tdiv_qr (qp, rp + sn, 0L, up + sn, un - sn, pwp, pwn);
346
18.3k
    qn = un - sn - pwn; qn += qp[qn] != 0;    /* quotient size */
347
348
18.3k
    ASSERT (qn < pwn + sn || (qn == pwn + sn && mpn_cmp (qp + sn, pwp, pwn) < 0));
349
350
18.3k
    if (len != 0)
351
11.5k
      len = len - powtab->digits_in_base;
352
353
18.3k
    str = mpn_dc_get_str (str, len, qp, qn, powtab - 1, tmp + qn);
354
18.3k
    str = mpn_dc_get_str (str, powtab->digits_in_base, rp, pwn + sn, powtab - 1, tmp);
355
18.3k
  }
356
18.3k
    }
357
39.5k
  return str;
358
39.5k
}
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
11.9k
{
367
11.9k
  mp_ptr powtab_mem;
368
11.9k
  powers_t powtab[GMP_LIMB_BITS];
369
11.9k
  int pi;
370
11.9k
  size_t out_len;
371
11.9k
  mp_ptr tmp;
372
11.9k
  TMP_DECL;
373
374
  /* Special case zero, as the code below doesn't handle it.  */
375
11.9k
  if (un == 0)
376
1.99k
    {
377
1.99k
      str[0] = 0;
378
1.99k
      return 1;
379
1.99k
    }
380
381
9.97k
  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
9.97k
  if (BELOW_THRESHOLD (un, GET_STR_PRECOMPUTE_THRESHOLD))
430
7.10k
    return mpn_bc_get_str (str, (size_t) 0, up, un, base) - str;
431
432
2.87k
  TMP_MARK;
433
434
  /* Allocate one large block for the powers of big_base.  */
435
2.87k
  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
2.87k
  size_t ndig;
439
2.87k
  mp_size_t xn;
440
2.87k
  DIGITS_IN_BASE_PER_LIMB (ndig, un, base);
441
2.87k
  xn = 1 + ndig / mp_bases[base].chars_per_limb; /* FIXME: scalar integer division */
442
443
2.87k
  pi = 1 + mpn_compute_powtab (powtab, powtab_mem, xn, base);
444
445
  /* Using our precomputed powers, now in powtab[], convert our number.  */
446
2.87k
  tmp = TMP_BALLOC_LIMBS (mpn_dc_get_str_itch (un));
447
2.87k
  out_len = mpn_dc_get_str (str, 0, up, un, powtab + (pi - 1), tmp) - str;
448
2.87k
  TMP_FREE;
449
450
2.87k
  return out_len;
451
9.97k
}