Coverage Report

Created: 2024-11-21 06:47

/src/libgmp/mpz/n_pow_ui.c
Line
Count
Source (jump to first uncovered line)
1
/* mpz_n_pow_ui -- mpn raised to ulong.
2
3
   THE FUNCTIONS IN THIS FILE ARE FOR INTERNAL USE ONLY.  THEY'RE ALMOST
4
   CERTAIN TO BE SUBJECT TO INCOMPATIBLE CHANGES OR DISAPPEAR COMPLETELY IN
5
   FUTURE GNU MP RELEASES.
6
7
Copyright 2001, 2002, 2005, 2012, 2015 Free Software Foundation, Inc.
8
9
This file is part of the GNU MP Library.
10
11
The GNU MP Library is free software; you can redistribute it and/or modify
12
it under the terms of either:
13
14
  * the GNU Lesser General Public License as published by the Free
15
    Software Foundation; either version 3 of the License, or (at your
16
    option) any later version.
17
18
or
19
20
  * the GNU General Public License as published by the Free Software
21
    Foundation; either version 2 of the License, or (at your option) any
22
    later version.
23
24
or both in parallel, as here.
25
26
The GNU MP Library is distributed in the hope that it will be useful, but
27
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
28
or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
29
for more details.
30
31
You should have received copies of the GNU General Public License and the
32
GNU Lesser General Public License along with the GNU MP Library.  If not,
33
see https://www.gnu.org/licenses/.  */
34
35
#include "gmp-impl.h"
36
#include "longlong.h"
37
38
39
/* Change this to "#define TRACE(x) x" for some traces. */
40
#define TRACE(x)
41
42
43
/* Use this to test the mul_2 code on a CPU without a native version of that
44
   routine.  */
45
#if 0
46
#define mpn_mul_2  refmpn_mul_2
47
#define HAVE_NATIVE_mpn_mul_2  1
48
#endif
49
50
51
/* mpz_pow_ui and mpz_ui_pow_ui want to share almost all of this code.
52
   ui_pow_ui doesn't need the mpn_mul based powering loop or the tests on
53
   bsize==2 or >2, but separating that isn't easy because there's shared
54
   code both before and after (the size calculations and the powers of 2
55
   handling).
56
57
   Alternatives:
58
59
   It would work to just use the mpn_mul powering loop for 1 and 2 limb
60
   bases, but the current separate loop allows mul_1 and mul_2 to be done
61
   in-place, which might help cache locality a bit.  If mpn_mul was relaxed
62
   to allow source==dest when vn==1 or 2 then some pointer twiddling might
63
   let us get the same effect in one loop.
64
65
   The initial powering for bsize==1 into blimb or blimb:blimb_low doesn't
66
   form the biggest possible power of b that fits, only the biggest power of
67
   2 power, ie. b^(2^n).  It'd be possible to choose a bigger power, perhaps
68
   using mp_bases[b].big_base for small b, and thereby get better value
69
   from mpn_mul_1 or mpn_mul_2 in the bignum powering.  It's felt that doing
70
   so would be more complicated than it's worth, and could well end up being
71
   a slowdown for small e.  For big e on the other hand the algorithm is
72
   dominated by mpn_sqr so there wouldn't much of a saving.  The current
73
   code can be viewed as simply doing the first few steps of the powering in
74
   a single or double limb where possible.
75
76
   If r==b, and blow_twos==0, and r must be realloc'ed, then the temporary
77
   copy made of b is unnecessary.  We could just use the old alloc'ed block
78
   and free it at the end.  But arranging this seems like a lot more trouble
79
   than it's worth.  */
80
81
82
/* floor(sqrt(GMP_NUMB_MAX)), ie. the biggest value that can be squared in
83
   a limb without overflowing.
84
   FIXME: This formula is an underestimate when GMP_NUMB_BITS is odd. */
85
86
0
#define GMP_NUMB_HALFMAX  (((mp_limb_t) 1 << GMP_NUMB_BITS/2) - 1)
87
88
89
/* The following are for convenience, they update the size and check the
90
   alloc.  */
91
92
#define MPN_SQR(dst, alloc, src, size)          \
93
0
  do {                                          \
94
0
    ASSERT (2*(size) <= (alloc));               \
95
0
    mpn_sqr (dst, src, size);                   \
96
0
    (size) *= 2;                                \
97
0
    (size) -= ((dst)[(size)-1] == 0);           \
98
0
  } while (0)
99
100
#define MPN_MUL(dst, alloc, src, size, src2, size2)     \
101
0
  do {                                                  \
102
0
    mp_limb_t  cy;                                      \
103
0
    ASSERT ((size) + (size2) <= (alloc));               \
104
0
    cy = mpn_mul (dst, src, size, src2, size2);         \
105
0
    (size) += (size2) - (cy == 0);                      \
106
0
  } while (0)
107
108
#define MPN_MUL_2(ptr, size, alloc, mult)       \
109
0
  do {                                          \
110
0
    mp_limb_t  cy;                              \
111
0
    ASSERT ((size)+2 <= (alloc));               \
112
0
    cy = mpn_mul_2 (ptr, ptr, size, mult);      \
113
0
    (size)++;                                   \
114
0
    (ptr)[(size)] = cy;                         \
115
0
    (size) += (cy != 0);                        \
116
0
  } while (0)
117
118
#define MPN_MUL_1(ptr, size, alloc, limb)       \
119
0
  do {                                          \
120
0
    mp_limb_t  cy;                              \
121
0
    ASSERT ((size)+1 <= (alloc));               \
122
0
    cy = mpn_mul_1 (ptr, ptr, size, limb);      \
123
0
    (ptr)[size] = cy;                           \
124
0
    (size) += (cy != 0);                        \
125
0
  } while (0)
126
127
#define MPN_LSHIFT(ptr, size, alloc, shift)     \
128
0
  do {                                          \
129
0
    mp_limb_t  cy;                              \
130
0
    ASSERT ((size)+1 <= (alloc));               \
131
0
    cy = mpn_lshift (ptr, ptr, size, shift);    \
132
0
    (ptr)[size] = cy;                           \
133
0
    (size) += (cy != 0);                        \
134
0
  } while (0)
135
136
#define MPN_RSHIFT_OR_COPY(dst, src, size, shift)       \
137
0
  do {                                                  \
138
0
    if ((shift) == 0)                                   \
139
0
      MPN_COPY (dst, src, size);                        \
140
0
    else                                                \
141
0
      {                                                 \
142
0
        mpn_rshift (dst, src, size, shift);             \
143
0
        (size) -= ((dst)[(size)-1] == 0);               \
144
0
      }                                                 \
145
0
  } while (0)
146
147
148
/* ralloc and talloc are only wanted for ASSERTs, after the initial space
149
   allocations.  Avoid writing values to them in a normal build, to ensure
150
   the compiler lets them go dead.  gcc already figures this out itself
151
   actually.  */
152
153
#define SWAP_RP_TP                                      \
154
0
  do {                                                  \
155
0
    MP_PTR_SWAP (rp, tp);                               \
156
0
    ASSERT_CODE (MP_SIZE_T_SWAP (ralloc, talloc));      \
157
0
  } while (0)
158
159
160
void
161
mpz_n_pow_ui (mpz_ptr r, mp_srcptr bp, mp_size_t bsize, unsigned long int e)
162
0
{
163
0
  mp_ptr         rp;
164
0
  mp_size_t      rtwos_limbs, ralloc, rsize;
165
0
  int            rneg, i, cnt, btwos, r_bp_overlap;
166
0
  mp_limb_t      blimb, rl;
167
0
  mp_bitcnt_t    rtwos_bits;
168
0
#if HAVE_NATIVE_mpn_mul_2
169
0
  mp_limb_t      blimb_low, rl_high;
170
#else
171
  mp_limb_t      b_twolimbs[2];
172
#endif
173
0
  TMP_DECL;
174
175
0
  TRACE (printf ("mpz_n_pow_ui rp=0x%lX bp=0x%lX bsize=%ld e=%lu (0x%lX)\n",
176
0
     PTR(r), bp, bsize, e, e);
177
0
   mpn_trace ("b", bp, bsize));
178
179
0
  ASSERT (bsize == 0 || bp[ABS(bsize)-1] != 0);
180
0
  ASSERT (MPN_SAME_OR_SEPARATE2_P (PTR(r), ALLOC(r), bp, ABS(bsize)));
181
182
  /* b^0 == 1, including 0^0 == 1 */
183
0
  if (e == 0)
184
0
    {
185
0
      MPZ_NEWALLOC (r, 1)[0] = 1;
186
0
      SIZ(r) = 1;
187
0
      return;
188
0
    }
189
190
  /* 0^e == 0 apart from 0^0 above */
191
0
  if (bsize == 0)
192
0
    {
193
0
      SIZ(r) = 0;
194
0
      return;
195
0
    }
196
197
  /* Sign of the final result. */
198
0
  rneg = (bsize < 0 && (e & 1) != 0);
199
0
  bsize = ABS (bsize);
200
0
  TRACE (printf ("rneg %d\n", rneg));
201
202
0
  r_bp_overlap = (PTR(r) == bp);
203
204
  /* Strip low zero limbs from b. */
205
0
  rtwos_limbs = 0;
206
0
  for (blimb = *bp; blimb == 0; blimb = *++bp)
207
0
    {
208
0
      rtwos_limbs += e;
209
0
      bsize--; ASSERT (bsize >= 1);
210
0
    }
211
0
  TRACE (printf ("trailing zero rtwos_limbs=%ld\n", rtwos_limbs));
212
213
  /* Strip low zero bits from b. */
214
0
  count_trailing_zeros (btwos, blimb);
215
0
  blimb >>= btwos;
216
0
  rtwos_bits = e * btwos;
217
0
  rtwos_limbs += rtwos_bits / GMP_NUMB_BITS;
218
0
  rtwos_bits %= GMP_NUMB_BITS;
219
0
  TRACE (printf ("trailing zero btwos=%d rtwos_limbs=%ld rtwos_bits=%lu\n",
220
0
     btwos, rtwos_limbs, rtwos_bits));
221
222
0
  TMP_MARK;
223
224
0
  rl = 1;
225
0
#if HAVE_NATIVE_mpn_mul_2
226
0
  rl_high = 0;
227
0
#endif
228
229
0
  if (bsize == 1)
230
0
    {
231
0
    bsize_1:
232
      /* Power up as far as possible within blimb.  We start here with e!=0,
233
   but if e is small then we might reach e==0 and the whole b^e in rl.
234
   Notice this code works when blimb==1 too, reaching e==0.  */
235
236
0
      while (blimb <= GMP_NUMB_HALFMAX)
237
0
  {
238
0
    TRACE (printf ("small e=0x%lX blimb=0x%lX rl=0x%lX\n",
239
0
       e, blimb, rl));
240
0
    ASSERT (e != 0);
241
0
    if ((e & 1) != 0)
242
0
      rl *= blimb;
243
0
    e >>= 1;
244
0
    if (e == 0)
245
0
      goto got_rl;
246
0
    blimb *= blimb;
247
0
  }
248
249
0
#if HAVE_NATIVE_mpn_mul_2
250
0
      TRACE (printf ("single power, e=0x%lX b=0x%lX rl=0x%lX\n",
251
0
         e, blimb, rl));
252
253
      /* Can power b once more into blimb:blimb_low */
254
0
      bsize = 2;
255
0
      ASSERT (e != 0);
256
0
      if ((e & 1) != 0)
257
0
  {
258
0
    umul_ppmm (rl_high, rl, rl, blimb << GMP_NAIL_BITS);
259
0
    rl >>= GMP_NAIL_BITS;
260
0
  }
261
0
      e >>= 1;
262
0
      umul_ppmm (blimb, blimb_low, blimb, blimb << GMP_NAIL_BITS);
263
0
      blimb_low >>= GMP_NAIL_BITS;
264
265
0
    got_rl:
266
0
      TRACE (printf ("double power e=0x%lX blimb=0x%lX:0x%lX rl=0x%lX:%lX\n",
267
0
         e, blimb, blimb_low, rl_high, rl));
268
269
      /* Combine left-over rtwos_bits into rl_high:rl to be handled by the
270
   final mul_1 or mul_2 rather than a separate lshift.
271
   - rl_high:rl mustn't be 1 (since then there's no final mul)
272
   - rl_high mustn't overflow
273
   - rl_high mustn't change to non-zero, since mul_1+lshift is
274
   probably faster than mul_2 (FIXME: is this true?)  */
275
276
0
      if (rtwos_bits != 0
277
0
    && ! (rl_high == 0 && rl == 1)
278
0
    && (rl_high >> (GMP_NUMB_BITS-rtwos_bits)) == 0)
279
0
  {
280
0
    mp_limb_t  new_rl_high = (rl_high << rtwos_bits)
281
0
      | (rl >> (GMP_NUMB_BITS-rtwos_bits));
282
0
    if (! (rl_high == 0 && new_rl_high != 0))
283
0
      {
284
0
        rl_high = new_rl_high;
285
0
        rl <<= rtwos_bits;
286
0
        rtwos_bits = 0;
287
0
        TRACE (printf ("merged rtwos_bits, rl=0x%lX:%lX\n",
288
0
           rl_high, rl));
289
0
      }
290
0
  }
291
#else
292
    got_rl:
293
      TRACE (printf ("small power e=0x%lX blimb=0x%lX rl=0x%lX\n",
294
         e, blimb, rl));
295
296
      /* Combine left-over rtwos_bits into rl to be handled by the final
297
   mul_1 rather than a separate lshift.
298
   - rl mustn't be 1 (since then there's no final mul)
299
   - rl mustn't overflow  */
300
301
      if (rtwos_bits != 0
302
    && rl != 1
303
    && (rl >> (GMP_NUMB_BITS-rtwos_bits)) == 0)
304
  {
305
    rl <<= rtwos_bits;
306
    rtwos_bits = 0;
307
    TRACE (printf ("merged rtwos_bits, rl=0x%lX\n", rl));
308
  }
309
#endif
310
0
    }
311
0
  else if (bsize == 2)
312
0
    {
313
0
      mp_limb_t  bsecond = bp[1];
314
0
      if (btwos != 0)
315
0
  blimb |= (bsecond << (GMP_NUMB_BITS - btwos)) & GMP_NUMB_MASK;
316
0
      bsecond >>= btwos;
317
0
      if (bsecond == 0)
318
0
  {
319
    /* Two limbs became one after rshift. */
320
0
    bsize = 1;
321
0
    goto bsize_1;
322
0
  }
323
324
0
      TRACE (printf ("bsize==2 using b=0x%lX:%lX", bsecond, blimb));
325
0
#if HAVE_NATIVE_mpn_mul_2
326
0
      blimb_low = blimb;
327
#else
328
      bp = b_twolimbs;
329
      b_twolimbs[0] = blimb;
330
      b_twolimbs[1] = bsecond;
331
#endif
332
0
      blimb = bsecond;
333
0
    }
334
0
  else
335
0
    {
336
0
      if (r_bp_overlap || btwos != 0)
337
0
  {
338
0
    mp_ptr tp = TMP_ALLOC_LIMBS (bsize);
339
0
    MPN_RSHIFT_OR_COPY (tp, bp, bsize, btwos);
340
0
    bp = tp;
341
0
    TRACE (printf ("rshift or copy bp,bsize, new bsize=%ld\n", bsize));
342
0
  }
343
0
#if HAVE_NATIVE_mpn_mul_2
344
      /* in case 3 limbs rshift to 2 and hence use the mul_2 loop below */
345
0
      blimb_low = bp[0];
346
0
#endif
347
0
      blimb = bp[bsize-1];
348
349
0
      TRACE (printf ("big bsize=%ld  ", bsize);
350
0
       mpn_trace ("b", bp, bsize));
351
0
    }
352
353
  /* At this point blimb is the most significant limb of the base to use.
354
355
     Each factor of b takes (bsize*BPML-cnt) bits and there's e of them; +1
356
     limb to round up the division; +1 for multiplies all using an extra
357
     limb over the true size; +2 for rl at the end; +1 for lshift at the
358
     end.
359
360
     The size calculation here is reasonably accurate.  The base is at least
361
     half a limb, so in 32 bits the worst case is 2^16+1 treated as 17 bits
362
     when it will power up as just over 16, an overestimate of 17/16 =
363
     6.25%.  For a 64-bit limb it's half that.
364
365
     If e==0 then blimb won't be anything useful (though it will be
366
     non-zero), but that doesn't matter since we just end up with ralloc==5,
367
     and that's fine for 2 limbs of rl and 1 of lshift.  */
368
369
0
  ASSERT (blimb != 0);
370
0
  count_leading_zeros (cnt, blimb);
371
0
  ralloc = (bsize*GMP_NUMB_BITS - cnt + GMP_NAIL_BITS) * e / GMP_NUMB_BITS + 5;
372
0
  TRACE (printf ("ralloc %ld, from bsize=%ld blimb=0x%lX cnt=%d\n",
373
0
     ralloc, bsize, blimb, cnt));
374
0
  rp = MPZ_NEWALLOC (r, ralloc + rtwos_limbs);
375
376
  /* Low zero limbs resulting from powers of 2. */
377
0
  MPN_ZERO (rp, rtwos_limbs);
378
0
  rp += rtwos_limbs;
379
380
0
  if (e == 0)
381
0
    {
382
      /* Any e==0 other than via bsize==1 or bsize==2 is covered at the
383
   start. */
384
0
      rp[0] = rl;
385
0
      rsize = 1;
386
0
#if HAVE_NATIVE_mpn_mul_2
387
0
      rp[1] = rl_high;
388
0
      rsize += (rl_high != 0);
389
0
#endif
390
0
      ASSERT (rp[rsize-1] != 0);
391
0
    }
392
0
  else
393
0
    {
394
0
      mp_ptr     tp;
395
0
      mp_size_t  talloc;
396
397
      /* In the mpn_mul_1 or mpn_mul_2 loops or in the mpn_mul loop when the
398
   low bit of e is zero, tp only has to hold the second last power
399
   step, which is half the size of the final result.  There's no need
400
   to round up the divide by 2, since ralloc includes a +2 for rl
401
   which not needed by tp.  In the mpn_mul loop when the low bit of e
402
   is 1, tp must hold nearly the full result, so just size it the same
403
   as rp.  */
404
405
0
      talloc = ralloc;
406
0
#if HAVE_NATIVE_mpn_mul_2
407
0
      if (bsize <= 2 || (e & 1) == 0)
408
0
  talloc /= 2;
409
#else
410
      if (bsize <= 1 || (e & 1) == 0)
411
  talloc /= 2;
412
#endif
413
0
      TRACE (printf ("talloc %ld\n", talloc));
414
0
      tp = TMP_ALLOC_LIMBS (talloc);
415
416
      /* Go from high to low over the bits of e, starting with i pointing at
417
   the bit below the highest 1 (which will mean i==-1 if e==1).  */
418
0
      count_leading_zeros (cnt, (mp_limb_t) e);
419
0
      i = GMP_LIMB_BITS - cnt - 2;
420
421
0
#if HAVE_NATIVE_mpn_mul_2
422
0
      if (bsize <= 2)
423
0
  {
424
0
    mp_limb_t  mult[2];
425
426
    /* Any bsize==1 will have been powered above to be two limbs. */
427
0
    ASSERT (bsize == 2);
428
0
    ASSERT (blimb != 0);
429
430
    /* Arrange the final result ends up in r, not in the temp space */
431
0
    if ((i & 1) == 0)
432
0
      SWAP_RP_TP;
433
434
0
    rp[0] = blimb_low;
435
0
    rp[1] = blimb;
436
0
    rsize = 2;
437
438
0
    mult[0] = blimb_low;
439
0
    mult[1] = blimb;
440
441
0
    for ( ; i >= 0; i--)
442
0
      {
443
0
        TRACE (printf ("mul_2 loop i=%d e=0x%lX, rsize=%ld ralloc=%ld talloc=%ld\n",
444
0
           i, e, rsize, ralloc, talloc);
445
0
         mpn_trace ("r", rp, rsize));
446
447
0
        MPN_SQR (tp, talloc, rp, rsize);
448
0
        SWAP_RP_TP;
449
0
        if ((e & (1L << i)) != 0)
450
0
    MPN_MUL_2 (rp, rsize, ralloc, mult);
451
0
      }
452
453
0
    TRACE (mpn_trace ("mul_2 before rl, r", rp, rsize));
454
0
    if (rl_high != 0)
455
0
      {
456
0
        mult[0] = rl;
457
0
        mult[1] = rl_high;
458
0
        MPN_MUL_2 (rp, rsize, ralloc, mult);
459
0
      }
460
0
    else if (rl != 1)
461
0
      MPN_MUL_1 (rp, rsize, ralloc, rl);
462
0
  }
463
#else
464
      if (bsize == 1)
465
  {
466
    /* Arrange the final result ends up in r, not in the temp space */
467
    if ((i & 1) == 0)
468
      SWAP_RP_TP;
469
470
    rp[0] = blimb;
471
    rsize = 1;
472
473
    for ( ; i >= 0; i--)
474
      {
475
        TRACE (printf ("mul_1 loop i=%d e=0x%lX, rsize=%ld ralloc=%ld talloc=%ld\n",
476
           i, e, rsize, ralloc, talloc);
477
         mpn_trace ("r", rp, rsize));
478
479
        MPN_SQR (tp, talloc, rp, rsize);
480
        SWAP_RP_TP;
481
        if ((e & (1L << i)) != 0)
482
    MPN_MUL_1 (rp, rsize, ralloc, blimb);
483
      }
484
485
    TRACE (mpn_trace ("mul_1 before rl, r", rp, rsize));
486
    if (rl != 1)
487
      MPN_MUL_1 (rp, rsize, ralloc, rl);
488
  }
489
#endif
490
0
      else
491
0
  {
492
0
    int  parity;
493
494
    /* Arrange the final result ends up in r, not in the temp space */
495
0
    ULONG_PARITY (parity, e);
496
0
    if (((parity ^ i) & 1) != 0)
497
0
      SWAP_RP_TP;
498
499
0
    MPN_COPY (rp, bp, bsize);
500
0
    rsize = bsize;
501
502
0
    for ( ; i >= 0; i--)
503
0
      {
504
0
        TRACE (printf ("mul loop i=%d e=0x%lX, rsize=%ld ralloc=%ld talloc=%ld\n",
505
0
           i, e, rsize, ralloc, talloc);
506
0
         mpn_trace ("r", rp, rsize));
507
508
0
        MPN_SQR (tp, talloc, rp, rsize);
509
0
        SWAP_RP_TP;
510
0
        if ((e & (1L << i)) != 0)
511
0
    {
512
0
      MPN_MUL (tp, talloc, rp, rsize, bp, bsize);
513
0
      SWAP_RP_TP;
514
0
    }
515
0
      }
516
0
  }
517
0
    }
518
519
0
  ASSERT (rp == PTR(r) + rtwos_limbs);
520
0
  TRACE (mpn_trace ("end loop r", rp, rsize));
521
0
  TMP_FREE;
522
523
  /* Apply any partial limb factors of 2. */
524
0
  if (rtwos_bits != 0)
525
0
    {
526
0
      MPN_LSHIFT (rp, rsize, ralloc, (unsigned) rtwos_bits);
527
0
      TRACE (mpn_trace ("lshift r", rp, rsize));
528
0
    }
529
530
0
  rsize += rtwos_limbs;
531
0
  SIZ(r) = (rneg ? -rsize : rsize);
532
0
}