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1 684 jeremybenn
/* Operations with long integers.
2
   Copyright (C) 2006, 2007, 2009, 2010 Free Software Foundation, Inc.
3
 
4
This file is part of GCC.
5
 
6
GCC is free software; you can redistribute it and/or modify it
7
under the terms of the GNU General Public License as published by the
8
Free Software Foundation; either version 3, or (at your option) any
9
later version.
10
 
11
GCC is distributed in the hope that it will be useful, but WITHOUT
12
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
14
for more details.
15
 
16
You should have received a copy of the GNU General Public License
17
along with GCC; see the file COPYING3.  If not see
18
<http://www.gnu.org/licenses/>.  */
19
 
20
#include "config.h"
21
#include "system.h"
22
#include "coretypes.h"
23
#include "tm.h"                 /* For SHIFT_COUNT_TRUNCATED.  */
24
#include "tree.h"
25
 
26
/* We know that A1 + B1 = SUM1, using 2's complement arithmetic and ignoring
27
   overflow.  Suppose A, B and SUM have the same respective signs as A1, B1,
28
   and SUM1.  Then this yields nonzero if overflow occurred during the
29
   addition.
30
 
31
   Overflow occurs if A and B have the same sign, but A and SUM differ in
32
   sign.  Use `^' to test whether signs differ, and `< 0' to isolate the
33
   sign.  */
34
#define OVERFLOW_SUM_SIGN(a, b, sum) ((~((a) ^ (b)) & ((a) ^ (sum))) < 0)
35
 
36
/* To do constant folding on INTEGER_CST nodes requires two-word arithmetic.
37
   We do that by representing the two-word integer in 4 words, with only
38
   HOST_BITS_PER_WIDE_INT / 2 bits stored in each word, as a positive
39
   number.  The value of the word is LOWPART + HIGHPART * BASE.  */
40
 
41
#define LOWPART(x) \
42
  ((x) & (((unsigned HOST_WIDE_INT) 1 << (HOST_BITS_PER_WIDE_INT / 2)) - 1))
43
#define HIGHPART(x) \
44
  ((unsigned HOST_WIDE_INT) (x) >> HOST_BITS_PER_WIDE_INT / 2)
45
#define BASE ((unsigned HOST_WIDE_INT) 1 << HOST_BITS_PER_WIDE_INT / 2)
46
 
47
/* Unpack a two-word integer into 4 words.
48
   LOW and HI are the integer, as two `HOST_WIDE_INT' pieces.
49
   WORDS points to the array of HOST_WIDE_INTs.  */
50
 
51
static void
52
encode (HOST_WIDE_INT *words, unsigned HOST_WIDE_INT low, HOST_WIDE_INT hi)
53
{
54
  words[0] = LOWPART (low);
55
  words[1] = HIGHPART (low);
56
  words[2] = LOWPART (hi);
57
  words[3] = HIGHPART (hi);
58
}
59
 
60
/* Pack an array of 4 words into a two-word integer.
61
   WORDS points to the array of words.
62
   The integer is stored into *LOW and *HI as two `HOST_WIDE_INT' pieces.  */
63
 
64
static void
65
decode (HOST_WIDE_INT *words, unsigned HOST_WIDE_INT *low,
66
        HOST_WIDE_INT *hi)
67
{
68
  *low = words[0] + words[1] * BASE;
69
  *hi = words[2] + words[3] * BASE;
70
}
71
 
72
/* Add two doubleword integers with doubleword result.
73
   Return nonzero if the operation overflows according to UNSIGNED_P.
74
   Each argument is given as two `HOST_WIDE_INT' pieces.
75
   One argument is L1 and H1; the other, L2 and H2.
76
   The value is stored as two `HOST_WIDE_INT' pieces in *LV and *HV.  */
77
 
78
int
79
add_double_with_sign (unsigned HOST_WIDE_INT l1, HOST_WIDE_INT h1,
80
                      unsigned HOST_WIDE_INT l2, HOST_WIDE_INT h2,
81
                      unsigned HOST_WIDE_INT *lv, HOST_WIDE_INT *hv,
82
                      bool unsigned_p)
83
{
84
  unsigned HOST_WIDE_INT l;
85
  HOST_WIDE_INT h;
86
 
87
  l = l1 + l2;
88
  h = (HOST_WIDE_INT) ((unsigned HOST_WIDE_INT) h1
89
                       + (unsigned HOST_WIDE_INT) h2
90
                       + (l < l1));
91
 
92
  *lv = l;
93
  *hv = h;
94
 
95
  if (unsigned_p)
96
    return ((unsigned HOST_WIDE_INT) h < (unsigned HOST_WIDE_INT) h1
97
            || (h == h1
98
                && l < l1));
99
  else
100
    return OVERFLOW_SUM_SIGN (h1, h2, h);
101
}
102
 
103
/* Negate a doubleword integer with doubleword result.
104
   Return nonzero if the operation overflows, assuming it's signed.
105
   The argument is given as two `HOST_WIDE_INT' pieces in L1 and H1.
106
   The value is stored as two `HOST_WIDE_INT' pieces in *LV and *HV.  */
107
 
108
int
109
neg_double (unsigned HOST_WIDE_INT l1, HOST_WIDE_INT h1,
110
            unsigned HOST_WIDE_INT *lv, HOST_WIDE_INT *hv)
111
{
112
  if (l1 == 0)
113
    {
114
      *lv = 0;
115
      *hv = - h1;
116
      return (*hv & h1) < 0;
117
    }
118
  else
119
    {
120
      *lv = -l1;
121
      *hv = ~h1;
122
      return 0;
123
    }
124
}
125
 
126
/* Multiply two doubleword integers with doubleword result.
127
   Return nonzero if the operation overflows according to UNSIGNED_P.
128
   Each argument is given as two `HOST_WIDE_INT' pieces.
129
   One argument is L1 and H1; the other, L2 and H2.
130
   The value is stored as two `HOST_WIDE_INT' pieces in *LV and *HV.  */
131
 
132
int
133
mul_double_with_sign (unsigned HOST_WIDE_INT l1, HOST_WIDE_INT h1,
134
                      unsigned HOST_WIDE_INT l2, HOST_WIDE_INT h2,
135
                      unsigned HOST_WIDE_INT *lv, HOST_WIDE_INT *hv,
136
                      bool unsigned_p)
137
{
138
  HOST_WIDE_INT arg1[4];
139
  HOST_WIDE_INT arg2[4];
140
  HOST_WIDE_INT prod[4 * 2];
141
  unsigned HOST_WIDE_INT carry;
142
  int i, j, k;
143
  unsigned HOST_WIDE_INT toplow, neglow;
144
  HOST_WIDE_INT tophigh, neghigh;
145
 
146
  encode (arg1, l1, h1);
147
  encode (arg2, l2, h2);
148
 
149
  memset (prod, 0, sizeof prod);
150
 
151
  for (i = 0; i < 4; i++)
152
    {
153
      carry = 0;
154
      for (j = 0; j < 4; j++)
155
        {
156
          k = i + j;
157
          /* This product is <= 0xFFFE0001, the sum <= 0xFFFF0000.  */
158
          carry += arg1[i] * arg2[j];
159
          /* Since prod[p] < 0xFFFF, this sum <= 0xFFFFFFFF.  */
160
          carry += prod[k];
161
          prod[k] = LOWPART (carry);
162
          carry = HIGHPART (carry);
163
        }
164
      prod[i + 4] = carry;
165
    }
166
 
167
  decode (prod, lv, hv);
168
  decode (prod + 4, &toplow, &tophigh);
169
 
170
  /* Unsigned overflow is immediate.  */
171
  if (unsigned_p)
172
    return (toplow | tophigh) != 0;
173
 
174
  /* Check for signed overflow by calculating the signed representation of the
175
     top half of the result; it should agree with the low half's sign bit.  */
176
  if (h1 < 0)
177
    {
178
      neg_double (l2, h2, &neglow, &neghigh);
179
      add_double (neglow, neghigh, toplow, tophigh, &toplow, &tophigh);
180
    }
181
  if (h2 < 0)
182
    {
183
      neg_double (l1, h1, &neglow, &neghigh);
184
      add_double (neglow, neghigh, toplow, tophigh, &toplow, &tophigh);
185
    }
186
  return (*hv < 0 ? ~(toplow & tophigh) : toplow | tophigh) != 0;
187
}
188
 
189
/* Shift the doubleword integer in L1, H1 left by COUNT places
190
   keeping only PREC bits of result.
191
   Shift right if COUNT is negative.
192
   ARITH nonzero specifies arithmetic shifting; otherwise use logical shift.
193
   Store the value as two `HOST_WIDE_INT' pieces in *LV and *HV.  */
194
 
195
void
196
lshift_double (unsigned HOST_WIDE_INT l1, HOST_WIDE_INT h1,
197
               HOST_WIDE_INT count, unsigned int prec,
198
               unsigned HOST_WIDE_INT *lv, HOST_WIDE_INT *hv, bool arith)
199
{
200
  unsigned HOST_WIDE_INT signmask;
201
 
202
  if (count < 0)
203
    {
204
      rshift_double (l1, h1, -count, prec, lv, hv, arith);
205
      return;
206
    }
207
 
208
  if (SHIFT_COUNT_TRUNCATED)
209
    count %= prec;
210
 
211
  if (count >= 2 * HOST_BITS_PER_WIDE_INT)
212
    {
213
      /* Shifting by the host word size is undefined according to the
214
         ANSI standard, so we must handle this as a special case.  */
215
      *hv = 0;
216
      *lv = 0;
217
    }
218
  else if (count >= HOST_BITS_PER_WIDE_INT)
219
    {
220
      *hv = l1 << (count - HOST_BITS_PER_WIDE_INT);
221
      *lv = 0;
222
    }
223
  else
224
    {
225
      *hv = (((unsigned HOST_WIDE_INT) h1 << count)
226
             | (l1 >> (HOST_BITS_PER_WIDE_INT - count - 1) >> 1));
227
      *lv = l1 << count;
228
    }
229
 
230
  /* Sign extend all bits that are beyond the precision.  */
231
 
232
  signmask = -((prec > HOST_BITS_PER_WIDE_INT
233
                ? ((unsigned HOST_WIDE_INT) *hv
234
                   >> (prec - HOST_BITS_PER_WIDE_INT - 1))
235
                : (*lv >> (prec - 1))) & 1);
236
 
237
  if (prec >= 2 * HOST_BITS_PER_WIDE_INT)
238
    ;
239
  else if (prec >= HOST_BITS_PER_WIDE_INT)
240
    {
241
      *hv &= ~((HOST_WIDE_INT) (-1) << (prec - HOST_BITS_PER_WIDE_INT));
242
      *hv |= signmask << (prec - HOST_BITS_PER_WIDE_INT);
243
    }
244
  else
245
    {
246
      *hv = signmask;
247
      *lv &= ~((unsigned HOST_WIDE_INT) (-1) << prec);
248
      *lv |= signmask << prec;
249
    }
250
}
251
 
252
/* Shift the doubleword integer in L1, H1 right by COUNT places
253
   keeping only PREC bits of result.  Shift left if COUNT is negative.
254
   ARITH nonzero specifies arithmetic shifting; otherwise use logical shift.
255
   Store the value as two `HOST_WIDE_INT' pieces in *LV and *HV.  */
256
 
257
void
258
rshift_double (unsigned HOST_WIDE_INT l1, HOST_WIDE_INT h1,
259
               HOST_WIDE_INT count, unsigned int prec,
260
               unsigned HOST_WIDE_INT *lv, HOST_WIDE_INT *hv,
261
               bool arith)
262
{
263
  unsigned HOST_WIDE_INT signmask;
264
 
265
  if (count < 0)
266
    {
267
      lshift_double (l1, h1, -count, prec, lv, hv, arith);
268
      return;
269
    }
270
 
271
  signmask = (arith
272
              ? -((unsigned HOST_WIDE_INT) h1 >> (HOST_BITS_PER_WIDE_INT - 1))
273
              : 0);
274
 
275
  if (SHIFT_COUNT_TRUNCATED)
276
    count %= prec;
277
 
278
  if (count >= 2 * HOST_BITS_PER_WIDE_INT)
279
    {
280
      /* Shifting by the host word size is undefined according to the
281
         ANSI standard, so we must handle this as a special case.  */
282
      *hv = 0;
283
      *lv = 0;
284
    }
285
  else if (count >= HOST_BITS_PER_WIDE_INT)
286
    {
287
      *hv = 0;
288
      *lv = (unsigned HOST_WIDE_INT) h1 >> (count - HOST_BITS_PER_WIDE_INT);
289
    }
290
  else
291
    {
292
      *hv = (unsigned HOST_WIDE_INT) h1 >> count;
293
      *lv = ((l1 >> count)
294
             | ((unsigned HOST_WIDE_INT) h1
295
                << (HOST_BITS_PER_WIDE_INT - count - 1) << 1));
296
    }
297
 
298
  /* Zero / sign extend all bits that are beyond the precision.  */
299
 
300
  if (count >= (HOST_WIDE_INT)prec)
301
    {
302
      *hv = signmask;
303
      *lv = signmask;
304
    }
305
  else if ((prec - count) >= 2 * HOST_BITS_PER_WIDE_INT)
306
    ;
307
  else if ((prec - count) >= HOST_BITS_PER_WIDE_INT)
308
    {
309
      *hv &= ~((HOST_WIDE_INT) (-1) << (prec - count - HOST_BITS_PER_WIDE_INT));
310
      *hv |= signmask << (prec - count - HOST_BITS_PER_WIDE_INT);
311
    }
312
  else
313
    {
314
      *hv = signmask;
315
      *lv &= ~((unsigned HOST_WIDE_INT) (-1) << (prec - count));
316
      *lv |= signmask << (prec - count);
317
    }
318
}
319
 
320
/* Divide doubleword integer LNUM, HNUM by doubleword integer LDEN, HDEN
321
   for a quotient (stored in *LQUO, *HQUO) and remainder (in *LREM, *HREM).
322
   CODE is a tree code for a kind of division, one of
323
   TRUNC_DIV_EXPR, FLOOR_DIV_EXPR, CEIL_DIV_EXPR, ROUND_DIV_EXPR
324
   or EXACT_DIV_EXPR
325
   It controls how the quotient is rounded to an integer.
326
   Return nonzero if the operation overflows.
327
   UNS nonzero says do unsigned division.  */
328
 
329
int
330
div_and_round_double (unsigned code, int uns,
331
                      /* num == numerator == dividend */
332
                      unsigned HOST_WIDE_INT lnum_orig,
333
                      HOST_WIDE_INT hnum_orig,
334
                      /* den == denominator == divisor */
335
                      unsigned HOST_WIDE_INT lden_orig,
336
                      HOST_WIDE_INT hden_orig,
337
                      unsigned HOST_WIDE_INT *lquo,
338
                      HOST_WIDE_INT *hquo, unsigned HOST_WIDE_INT *lrem,
339
                      HOST_WIDE_INT *hrem)
340
{
341
  int quo_neg = 0;
342
  HOST_WIDE_INT num[4 + 1];     /* extra element for scaling.  */
343
  HOST_WIDE_INT den[4], quo[4];
344
  int i, j;
345
  unsigned HOST_WIDE_INT work;
346
  unsigned HOST_WIDE_INT carry = 0;
347
  unsigned HOST_WIDE_INT lnum = lnum_orig;
348
  HOST_WIDE_INT hnum = hnum_orig;
349
  unsigned HOST_WIDE_INT lden = lden_orig;
350
  HOST_WIDE_INT hden = hden_orig;
351
  int overflow = 0;
352
 
353
  if (hden == 0 && lden == 0)
354
    overflow = 1, lden = 1;
355
 
356
  /* Calculate quotient sign and convert operands to unsigned.  */
357
  if (!uns)
358
    {
359
      if (hnum < 0)
360
        {
361
          quo_neg = ~ quo_neg;
362
          /* (minimum integer) / (-1) is the only overflow case.  */
363
          if (neg_double (lnum, hnum, &lnum, &hnum)
364
              && ((HOST_WIDE_INT) lden & hden) == -1)
365
            overflow = 1;
366
        }
367
      if (hden < 0)
368
        {
369
          quo_neg = ~ quo_neg;
370
          neg_double (lden, hden, &lden, &hden);
371
        }
372
    }
373
 
374
  if (hnum == 0 && hden == 0)
375
    {                           /* single precision */
376
      *hquo = *hrem = 0;
377
      /* This unsigned division rounds toward zero.  */
378
      *lquo = lnum / lden;
379
      goto finish_up;
380
    }
381
 
382
  if (hnum == 0)
383
    {                           /* trivial case: dividend < divisor */
384
      /* hden != 0 already checked.  */
385
      *hquo = *lquo = 0;
386
      *hrem = hnum;
387
      *lrem = lnum;
388
      goto finish_up;
389
    }
390
 
391
  memset (quo, 0, sizeof quo);
392
 
393
  memset (num, 0, sizeof num);   /* to zero 9th element */
394
  memset (den, 0, sizeof den);
395
 
396
  encode (num, lnum, hnum);
397
  encode (den, lden, hden);
398
 
399
  /* Special code for when the divisor < BASE.  */
400
  if (hden == 0 && lden < (unsigned HOST_WIDE_INT) BASE)
401
    {
402
      /* hnum != 0 already checked.  */
403
      for (i = 4 - 1; i >= 0; i--)
404
        {
405
          work = num[i] + carry * BASE;
406
          quo[i] = work / lden;
407
          carry = work % lden;
408
        }
409
    }
410
  else
411
    {
412
      /* Full double precision division,
413
         with thanks to Don Knuth's "Seminumerical Algorithms".  */
414
      int num_hi_sig, den_hi_sig;
415
      unsigned HOST_WIDE_INT quo_est, scale;
416
 
417
      /* Find the highest nonzero divisor digit.  */
418
      for (i = 4 - 1;; i--)
419
        if (den[i] != 0)
420
          {
421
            den_hi_sig = i;
422
            break;
423
          }
424
 
425
      /* Insure that the first digit of the divisor is at least BASE/2.
426
         This is required by the quotient digit estimation algorithm.  */
427
 
428
      scale = BASE / (den[den_hi_sig] + 1);
429
      if (scale > 1)
430
        {               /* scale divisor and dividend */
431
          carry = 0;
432
          for (i = 0; i <= 4 - 1; i++)
433
            {
434
              work = (num[i] * scale) + carry;
435
              num[i] = LOWPART (work);
436
              carry = HIGHPART (work);
437
            }
438
 
439
          num[4] = carry;
440
          carry = 0;
441
          for (i = 0; i <= 4 - 1; i++)
442
            {
443
              work = (den[i] * scale) + carry;
444
              den[i] = LOWPART (work);
445
              carry = HIGHPART (work);
446
              if (den[i] != 0) den_hi_sig = i;
447
            }
448
        }
449
 
450
      num_hi_sig = 4;
451
 
452
      /* Main loop */
453
      for (i = num_hi_sig - den_hi_sig - 1; i >= 0; i--)
454
        {
455
          /* Guess the next quotient digit, quo_est, by dividing the first
456
             two remaining dividend digits by the high order quotient digit.
457
             quo_est is never low and is at most 2 high.  */
458
          unsigned HOST_WIDE_INT tmp;
459
 
460
          num_hi_sig = i + den_hi_sig + 1;
461
          work = num[num_hi_sig] * BASE + num[num_hi_sig - 1];
462
          if (num[num_hi_sig] != den[den_hi_sig])
463
            quo_est = work / den[den_hi_sig];
464
          else
465
            quo_est = BASE - 1;
466
 
467
          /* Refine quo_est so it's usually correct, and at most one high.  */
468
          tmp = work - quo_est * den[den_hi_sig];
469
          if (tmp < BASE
470
              && (den[den_hi_sig - 1] * quo_est
471
                  > (tmp * BASE + num[num_hi_sig - 2])))
472
            quo_est--;
473
 
474
          /* Try QUO_EST as the quotient digit, by multiplying the
475
             divisor by QUO_EST and subtracting from the remaining dividend.
476
             Keep in mind that QUO_EST is the I - 1st digit.  */
477
 
478
          carry = 0;
479
          for (j = 0; j <= den_hi_sig; j++)
480
            {
481
              work = quo_est * den[j] + carry;
482
              carry = HIGHPART (work);
483
              work = num[i + j] - LOWPART (work);
484
              num[i + j] = LOWPART (work);
485
              carry += HIGHPART (work) != 0;
486
            }
487
 
488
          /* If quo_est was high by one, then num[i] went negative and
489
             we need to correct things.  */
490
          if (num[num_hi_sig] < (HOST_WIDE_INT) carry)
491
            {
492
              quo_est--;
493
              carry = 0;         /* add divisor back in */
494
              for (j = 0; j <= den_hi_sig; j++)
495
                {
496
                  work = num[i + j] + den[j] + carry;
497
                  carry = HIGHPART (work);
498
                  num[i + j] = LOWPART (work);
499
                }
500
 
501
              num [num_hi_sig] += carry;
502
            }
503
 
504
          /* Store the quotient digit.  */
505
          quo[i] = quo_est;
506
        }
507
    }
508
 
509
  decode (quo, lquo, hquo);
510
 
511
 finish_up:
512
  /* If result is negative, make it so.  */
513
  if (quo_neg)
514
    neg_double (*lquo, *hquo, lquo, hquo);
515
 
516
  /* Compute trial remainder:  rem = num - (quo * den)  */
517
  mul_double (*lquo, *hquo, lden_orig, hden_orig, lrem, hrem);
518
  neg_double (*lrem, *hrem, lrem, hrem);
519
  add_double (lnum_orig, hnum_orig, *lrem, *hrem, lrem, hrem);
520
 
521
  switch (code)
522
    {
523
    case TRUNC_DIV_EXPR:
524
    case TRUNC_MOD_EXPR:        /* round toward zero */
525
    case EXACT_DIV_EXPR:        /* for this one, it shouldn't matter */
526
      return overflow;
527
 
528
    case FLOOR_DIV_EXPR:
529
    case FLOOR_MOD_EXPR:        /* round toward negative infinity */
530
      if (quo_neg && (*lrem != 0 || *hrem != 0))   /* ratio < 0 && rem != 0 */
531
        {
532
          /* quo = quo - 1;  */
533
          add_double (*lquo, *hquo, (HOST_WIDE_INT) -1, (HOST_WIDE_INT)  -1,
534
                      lquo, hquo);
535
        }
536
      else
537
        return overflow;
538
      break;
539
 
540
    case CEIL_DIV_EXPR:
541
    case CEIL_MOD_EXPR:         /* round toward positive infinity */
542
      if (!quo_neg && (*lrem != 0 || *hrem != 0))  /* ratio > 0 && rem != 0 */
543
        {
544
          add_double (*lquo, *hquo, (HOST_WIDE_INT) 1, (HOST_WIDE_INT) 0,
545
                      lquo, hquo);
546
        }
547
      else
548
        return overflow;
549
      break;
550
 
551
    case ROUND_DIV_EXPR:
552
    case ROUND_MOD_EXPR:        /* round to closest integer */
553
      {
554
        unsigned HOST_WIDE_INT labs_rem = *lrem;
555
        HOST_WIDE_INT habs_rem = *hrem;
556
        unsigned HOST_WIDE_INT labs_den = lden, ltwice;
557
        HOST_WIDE_INT habs_den = hden, htwice;
558
 
559
        /* Get absolute values.  */
560
        if (*hrem < 0)
561
          neg_double (*lrem, *hrem, &labs_rem, &habs_rem);
562
        if (hden < 0)
563
          neg_double (lden, hden, &labs_den, &habs_den);
564
 
565
        /* If (2 * abs (lrem) >= abs (lden)), adjust the quotient.  */
566
        mul_double ((HOST_WIDE_INT) 2, (HOST_WIDE_INT) 0,
567
                    labs_rem, habs_rem, &ltwice, &htwice);
568
 
569
        if (((unsigned HOST_WIDE_INT) habs_den
570
             < (unsigned HOST_WIDE_INT) htwice)
571
            || (((unsigned HOST_WIDE_INT) habs_den
572
                 == (unsigned HOST_WIDE_INT) htwice)
573
                && (labs_den <= ltwice)))
574
          {
575
            if (*hquo < 0)
576
              /* quo = quo - 1;  */
577
              add_double (*lquo, *hquo,
578
                          (HOST_WIDE_INT) -1, (HOST_WIDE_INT) -1, lquo, hquo);
579
            else
580
              /* quo = quo + 1; */
581
              add_double (*lquo, *hquo, (HOST_WIDE_INT) 1, (HOST_WIDE_INT) 0,
582
                          lquo, hquo);
583
          }
584
        else
585
          return overflow;
586
      }
587
      break;
588
 
589
    default:
590
      gcc_unreachable ();
591
    }
592
 
593
  /* Compute true remainder:  rem = num - (quo * den)  */
594
  mul_double (*lquo, *hquo, lden_orig, hden_orig, lrem, hrem);
595
  neg_double (*lrem, *hrem, lrem, hrem);
596
  add_double (lnum_orig, hnum_orig, *lrem, *hrem, lrem, hrem);
597
  return overflow;
598
}
599
 
600
 
601
/* Returns mask for PREC bits.  */
602
 
603
double_int
604
double_int_mask (unsigned prec)
605
{
606
  unsigned HOST_WIDE_INT m;
607
  double_int mask;
608
 
609
  if (prec > HOST_BITS_PER_WIDE_INT)
610
    {
611
      prec -= HOST_BITS_PER_WIDE_INT;
612
      m = ((unsigned HOST_WIDE_INT) 2 << (prec - 1)) - 1;
613
      mask.high = (HOST_WIDE_INT) m;
614
      mask.low = ALL_ONES;
615
    }
616
  else
617
    {
618
      mask.high = 0;
619
      mask.low = ((unsigned HOST_WIDE_INT) 2 << (prec - 1)) - 1;
620
    }
621
 
622
  return mask;
623
}
624
 
625
/* Clears the bits of CST over the precision PREC.  If UNS is false, the bits
626
   outside of the precision are set to the sign bit (i.e., the PREC-th one),
627
   otherwise they are set to zero.
628
 
629
   This corresponds to returning the value represented by PREC lowermost bits
630
   of CST, with the given signedness.  */
631
 
632
double_int
633
double_int_ext (double_int cst, unsigned prec, bool uns)
634
{
635
  if (uns)
636
    return double_int_zext (cst, prec);
637
  else
638
    return double_int_sext (cst, prec);
639
}
640
 
641
/* The same as double_int_ext with UNS = true.  */
642
 
643
double_int
644
double_int_zext (double_int cst, unsigned prec)
645
{
646
  double_int mask = double_int_mask (prec);
647
  double_int r;
648
 
649
  r.low = cst.low & mask.low;
650
  r.high = cst.high & mask.high;
651
 
652
  return r;
653
}
654
 
655
/* The same as double_int_ext with UNS = false.  */
656
 
657
double_int
658
double_int_sext (double_int cst, unsigned prec)
659
{
660
  double_int mask = double_int_mask (prec);
661
  double_int r;
662
  unsigned HOST_WIDE_INT snum;
663
 
664
  if (prec <= HOST_BITS_PER_WIDE_INT)
665
    snum = cst.low;
666
  else
667
    {
668
      prec -= HOST_BITS_PER_WIDE_INT;
669
      snum = (unsigned HOST_WIDE_INT) cst.high;
670
    }
671
  if (((snum >> (prec - 1)) & 1) == 1)
672
    {
673
      r.low = cst.low | ~mask.low;
674
      r.high = cst.high | ~mask.high;
675
    }
676
  else
677
    {
678
      r.low = cst.low & mask.low;
679
      r.high = cst.high & mask.high;
680
    }
681
 
682
  return r;
683
}
684
 
685
/* Returns true if CST fits in signed HOST_WIDE_INT.  */
686
 
687
bool
688
double_int_fits_in_shwi_p (double_int cst)
689
{
690
  if (cst.high == 0)
691
    return (HOST_WIDE_INT) cst.low >= 0;
692
  else if (cst.high == -1)
693
    return (HOST_WIDE_INT) cst.low < 0;
694
  else
695
    return false;
696
}
697
 
698
/* Returns true if CST fits in HOST_WIDE_INT if UNS is false, or in
699
   unsigned HOST_WIDE_INT if UNS is true.  */
700
 
701
bool
702
double_int_fits_in_hwi_p (double_int cst, bool uns)
703
{
704
  if (uns)
705
    return double_int_fits_in_uhwi_p (cst);
706
  else
707
    return double_int_fits_in_shwi_p (cst);
708
}
709
 
710
/* Returns A * B.  */
711
 
712
double_int
713
double_int_mul (double_int a, double_int b)
714
{
715
  double_int ret;
716
  mul_double (a.low, a.high, b.low, b.high, &ret.low, &ret.high);
717
  return ret;
718
}
719
 
720
/* Returns A * B. If the operation overflows according to UNSIGNED_P,
721
   *OVERFLOW is set to nonzero.  */
722
 
723
double_int
724
double_int_mul_with_sign (double_int a, double_int b,
725
                          bool unsigned_p, int *overflow)
726
{
727
  double_int ret;
728
  *overflow = mul_double_with_sign (a.low, a.high, b.low, b.high,
729
                                    &ret.low, &ret.high, unsigned_p);
730
  return ret;
731
}
732
 
733
/* Returns A + B.  */
734
 
735
double_int
736
double_int_add (double_int a, double_int b)
737
{
738
  double_int ret;
739
  add_double (a.low, a.high, b.low, b.high, &ret.low, &ret.high);
740
  return ret;
741
}
742
 
743
/* Returns A - B.  */
744
 
745
double_int
746
double_int_sub (double_int a, double_int b)
747
{
748
  double_int ret;
749
  neg_double (b.low, b.high, &b.low, &b.high);
750
  add_double (a.low, a.high, b.low, b.high, &ret.low, &ret.high);
751
  return ret;
752
}
753
 
754
/* Returns -A.  */
755
 
756
double_int
757
double_int_neg (double_int a)
758
{
759
  double_int ret;
760
  neg_double (a.low, a.high, &ret.low, &ret.high);
761
  return ret;
762
}
763
 
764
/* Returns A / B (computed as unsigned depending on UNS, and rounded as
765
   specified by CODE).  CODE is enum tree_code in fact, but double_int.h
766
   must be included before tree.h.  The remainder after the division is
767
   stored to MOD.  */
768
 
769
double_int
770
double_int_divmod (double_int a, double_int b, bool uns, unsigned code,
771
                   double_int *mod)
772
{
773
  double_int ret;
774
 
775
  div_and_round_double (code, uns, a.low, a.high,
776
                        b.low, b.high, &ret.low, &ret.high,
777
                        &mod->low, &mod->high);
778
  return ret;
779
}
780
 
781
/* The same as double_int_divmod with UNS = false.  */
782
 
783
double_int
784
double_int_sdivmod (double_int a, double_int b, unsigned code, double_int *mod)
785
{
786
  return double_int_divmod (a, b, false, code, mod);
787
}
788
 
789
/* The same as double_int_divmod with UNS = true.  */
790
 
791
double_int
792
double_int_udivmod (double_int a, double_int b, unsigned code, double_int *mod)
793
{
794
  return double_int_divmod (a, b, true, code, mod);
795
}
796
 
797
/* Returns A / B (computed as unsigned depending on UNS, and rounded as
798
   specified by CODE).  CODE is enum tree_code in fact, but double_int.h
799
   must be included before tree.h.  */
800
 
801
double_int
802
double_int_div (double_int a, double_int b, bool uns, unsigned code)
803
{
804
  double_int mod;
805
 
806
  return double_int_divmod (a, b, uns, code, &mod);
807
}
808
 
809
/* The same as double_int_div with UNS = false.  */
810
 
811
double_int
812
double_int_sdiv (double_int a, double_int b, unsigned code)
813
{
814
  return double_int_div (a, b, false, code);
815
}
816
 
817
/* The same as double_int_div with UNS = true.  */
818
 
819
double_int
820
double_int_udiv (double_int a, double_int b, unsigned code)
821
{
822
  return double_int_div (a, b, true, code);
823
}
824
 
825
/* Returns A % B (computed as unsigned depending on UNS, and rounded as
826
   specified by CODE).  CODE is enum tree_code in fact, but double_int.h
827
   must be included before tree.h.  */
828
 
829
double_int
830
double_int_mod (double_int a, double_int b, bool uns, unsigned code)
831
{
832
  double_int mod;
833
 
834
  double_int_divmod (a, b, uns, code, &mod);
835
  return mod;
836
}
837
 
838
/* The same as double_int_mod with UNS = false.  */
839
 
840
double_int
841
double_int_smod (double_int a, double_int b, unsigned code)
842
{
843
  return double_int_mod (a, b, false, code);
844
}
845
 
846
/* The same as double_int_mod with UNS = true.  */
847
 
848
double_int
849
double_int_umod (double_int a, double_int b, unsigned code)
850
{
851
  return double_int_mod (a, b, true, code);
852
}
853
 
854
/* Set BITPOS bit in A.  */
855
double_int
856
double_int_setbit (double_int a, unsigned bitpos)
857
{
858
  if (bitpos < HOST_BITS_PER_WIDE_INT)
859
    a.low |= (unsigned HOST_WIDE_INT) 1 << bitpos;
860
  else
861
    a.high |= (HOST_WIDE_INT) 1 <<  (bitpos - HOST_BITS_PER_WIDE_INT);
862
 
863
  return a;
864
}
865
 
866
/* Count trailing zeros in A.  */
867
int
868
double_int_ctz (double_int a)
869
{
870
  unsigned HOST_WIDE_INT w = a.low ? a.low : (unsigned HOST_WIDE_INT) a.high;
871
  unsigned bits = a.low ? 0 : HOST_BITS_PER_WIDE_INT;
872
  if (!w)
873
    return HOST_BITS_PER_DOUBLE_INT;
874
  bits += ctz_hwi (w);
875
  return bits;
876
}
877
 
878
/* Shift A left by COUNT places keeping only PREC bits of result.  Shift
879
   right if COUNT is negative.  ARITH true specifies arithmetic shifting;
880
   otherwise use logical shift.  */
881
 
882
double_int
883
double_int_lshift (double_int a, HOST_WIDE_INT count, unsigned int prec, bool arith)
884
{
885
  double_int ret;
886
  lshift_double (a.low, a.high, count, prec, &ret.low, &ret.high, arith);
887
  return ret;
888
}
889
 
890
/* Shift A rigth by COUNT places keeping only PREC bits of result.  Shift
891
   left if COUNT is negative.  ARITH true specifies arithmetic shifting;
892
   otherwise use logical shift.  */
893
 
894
double_int
895
double_int_rshift (double_int a, HOST_WIDE_INT count, unsigned int prec, bool arith)
896
{
897
  double_int ret;
898
  rshift_double (a.low, a.high, count, prec, &ret.low, &ret.high, arith);
899
  return ret;
900
}
901
 
902
/* Rotate  A left by COUNT places keeping only PREC bits of result.
903
   Rotate right if COUNT is negative.  */
904
 
905
double_int
906
double_int_lrotate (double_int a, HOST_WIDE_INT count, unsigned int prec)
907
{
908
  double_int t1, t2;
909
 
910
  count %= prec;
911
  if (count < 0)
912
    count += prec;
913
 
914
  t1 = double_int_lshift (a, count, prec, false);
915
  t2 = double_int_rshift (a, prec - count, prec, false);
916
 
917
  return double_int_ior (t1, t2);
918
}
919
 
920
/* Rotate A rigth by COUNT places keeping only PREC bits of result.
921
   Rotate right if COUNT is negative.  */
922
 
923
double_int
924
double_int_rrotate (double_int a, HOST_WIDE_INT count, unsigned int prec)
925
{
926
  double_int t1, t2;
927
 
928
  count %= prec;
929
  if (count < 0)
930
    count += prec;
931
 
932
  t1 = double_int_rshift (a, count, prec, false);
933
  t2 = double_int_lshift (a, prec - count, prec, false);
934
 
935
  return double_int_ior (t1, t2);
936
}
937
 
938
/* Returns -1 if A < B, 0 if A == B and 1 if A > B.  Signedness of the
939
   comparison is given by UNS.  */
940
 
941
int
942
double_int_cmp (double_int a, double_int b, bool uns)
943
{
944
  if (uns)
945
    return double_int_ucmp (a, b);
946
  else
947
    return double_int_scmp (a, b);
948
}
949
 
950
/* Compares two unsigned values A and B.  Returns -1 if A < B, 0 if A == B,
951
   and 1 if A > B.  */
952
 
953
int
954
double_int_ucmp (double_int a, double_int b)
955
{
956
  if ((unsigned HOST_WIDE_INT) a.high < (unsigned HOST_WIDE_INT) b.high)
957
    return -1;
958
  if ((unsigned HOST_WIDE_INT) a.high > (unsigned HOST_WIDE_INT) b.high)
959
    return 1;
960
  if (a.low < b.low)
961
    return -1;
962
  if (a.low > b.low)
963
    return 1;
964
 
965
  return 0;
966
}
967
 
968
/* Compares two signed values A and B.  Returns -1 if A < B, 0 if A == B,
969
   and 1 if A > B.  */
970
 
971
int
972
double_int_scmp (double_int a, double_int b)
973
{
974
  if (a.high < b.high)
975
    return -1;
976
  if (a.high > b.high)
977
    return 1;
978
  if (a.low < b.low)
979
    return -1;
980
  if (a.low > b.low)
981
    return 1;
982
 
983
  return 0;
984
}
985
 
986
/* Compares two values A and B.  Returns max value.  Signedness of the
987
   comparison is given by UNS.  */
988
 
989
double_int
990
double_int_max (double_int a, double_int b, bool uns)
991
{
992
  return (double_int_cmp (a, b, uns) == 1) ? a : b;
993
}
994
 
995
/* Compares two signed values A and B.  Returns max value.  */
996
 
997
double_int double_int_smax (double_int a, double_int b)
998
{
999
  return (double_int_scmp (a, b) == 1) ? a : b;
1000
}
1001
 
1002
/* Compares two unsigned values A and B.  Returns max value.  */
1003
 
1004
double_int double_int_umax (double_int a, double_int b)
1005
{
1006
  return (double_int_ucmp (a, b) == 1) ? a : b;
1007
}
1008
 
1009
/* Compares two values A and B.  Returns mix value.  Signedness of the
1010
   comparison is given by UNS.  */
1011
 
1012
double_int double_int_min (double_int a, double_int b, bool uns)
1013
{
1014
  return (double_int_cmp (a, b, uns) == -1) ? a : b;
1015
}
1016
 
1017
/* Compares two signed values A and B.  Returns min value.  */
1018
 
1019
double_int double_int_smin (double_int a, double_int b)
1020
{
1021
  return (double_int_scmp (a, b) == -1) ? a : b;
1022
}
1023
 
1024
/* Compares two unsigned values A and B.  Returns min value.  */
1025
 
1026
double_int double_int_umin (double_int a, double_int b)
1027
{
1028
  return (double_int_ucmp (a, b) == -1) ? a : b;
1029
}
1030
 
1031
/* Splits last digit of *CST (taken as unsigned) in BASE and returns it.  */
1032
 
1033
static unsigned
1034
double_int_split_digit (double_int *cst, unsigned base)
1035
{
1036
  unsigned HOST_WIDE_INT resl, reml;
1037
  HOST_WIDE_INT resh, remh;
1038
 
1039
  div_and_round_double (FLOOR_DIV_EXPR, true, cst->low, cst->high, base, 0,
1040
                        &resl, &resh, &reml, &remh);
1041
  cst->high = resh;
1042
  cst->low = resl;
1043
 
1044
  return reml;
1045
}
1046
 
1047
/* Dumps CST to FILE.  If UNS is true, CST is considered to be unsigned,
1048
   otherwise it is signed.  */
1049
 
1050
void
1051
dump_double_int (FILE *file, double_int cst, bool uns)
1052
{
1053
  unsigned digits[100], n;
1054
  int i;
1055
 
1056
  if (double_int_zero_p (cst))
1057
    {
1058
      fprintf (file, "0");
1059
      return;
1060
    }
1061
 
1062
  if (!uns && double_int_negative_p (cst))
1063
    {
1064
      fprintf (file, "-");
1065
      cst = double_int_neg (cst);
1066
    }
1067
 
1068
  for (n = 0; !double_int_zero_p (cst); n++)
1069
    digits[n] = double_int_split_digit (&cst, 10);
1070
  for (i = n - 1; i >= 0; i--)
1071
    fprintf (file, "%u", digits[i]);
1072
}
1073
 
1074
 
1075
/* Sets RESULT to VAL, taken unsigned if UNS is true and as signed
1076
   otherwise.  */
1077
 
1078
void
1079
mpz_set_double_int (mpz_t result, double_int val, bool uns)
1080
{
1081
  bool negate = false;
1082
  unsigned HOST_WIDE_INT vp[2];
1083
 
1084
  if (!uns && double_int_negative_p (val))
1085
    {
1086
      negate = true;
1087
      val = double_int_neg (val);
1088
    }
1089
 
1090
  vp[0] = val.low;
1091
  vp[1] = (unsigned HOST_WIDE_INT) val.high;
1092
  mpz_import (result, 2, -1, sizeof (HOST_WIDE_INT), 0, 0, vp);
1093
 
1094
  if (negate)
1095
    mpz_neg (result, result);
1096
}
1097
 
1098
/* Returns VAL converted to TYPE.  If WRAP is true, then out-of-range
1099
   values of VAL will be wrapped; otherwise, they will be set to the
1100
   appropriate minimum or maximum TYPE bound.  */
1101
 
1102
double_int
1103
mpz_get_double_int (const_tree type, mpz_t val, bool wrap)
1104
{
1105
  unsigned HOST_WIDE_INT *vp;
1106
  size_t count, numb;
1107
  double_int res;
1108
 
1109
  if (!wrap)
1110
    {
1111
      mpz_t min, max;
1112
 
1113
      mpz_init (min);
1114
      mpz_init (max);
1115
      get_type_static_bounds (type, min, max);
1116
 
1117
      if (mpz_cmp (val, min) < 0)
1118
        mpz_set (val, min);
1119
      else if (mpz_cmp (val, max) > 0)
1120
        mpz_set (val, max);
1121
 
1122
      mpz_clear (min);
1123
      mpz_clear (max);
1124
    }
1125
 
1126
  /* Determine the number of unsigned HOST_WIDE_INT that are required
1127
     for representing the value.  The code to calculate count is
1128
     extracted from the GMP manual, section "Integer Import and Export":
1129
     http://gmplib.org/manual/Integer-Import-and-Export.html  */
1130
  numb = 8*sizeof(HOST_WIDE_INT);
1131
  count = (mpz_sizeinbase (val, 2) + numb-1) / numb;
1132
  if (count < 2)
1133
    count = 2;
1134
  vp = (unsigned HOST_WIDE_INT *) alloca (count * sizeof(HOST_WIDE_INT));
1135
 
1136
  vp[0] = 0;
1137
  vp[1] = 0;
1138
  mpz_export (vp, &count, -1, sizeof (HOST_WIDE_INT), 0, 0, val);
1139
 
1140
  gcc_assert (wrap || count <= 2);
1141
 
1142
  res.low = vp[0];
1143
  res.high = (HOST_WIDE_INT) vp[1];
1144
 
1145
  res = double_int_ext (res, TYPE_PRECISION (type), TYPE_UNSIGNED (type));
1146
  if (mpz_sgn (val) < 0)
1147
    res = double_int_neg (res);
1148
 
1149
  return res;
1150
}

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