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[/] [openrisc/] [trunk/] [gnu-src/] [newlib-1.18.0/] [newlib/] [libc/] [stdlib/] [mprec.c] - Blame information for rev 297

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Line No. Rev Author Line
1 207 jeremybenn
/****************************************************************
2
 *
3
 * The author of this software is David M. Gay.
4
 *
5
 * Copyright (c) 1991 by AT&T.
6
 *
7
 * Permission to use, copy, modify, and distribute this software for any
8
 * purpose without fee is hereby granted, provided that this entire notice
9
 * is included in all copies of any software which is or includes a copy
10
 * or modification of this software and in all copies of the supporting
11
 * documentation for such software.
12
 *
13
 * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
14
 * WARRANTY.  IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY
15
 * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
16
 * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
17
 *
18
 ***************************************************************/
19
 
20
/* Please send bug reports to
21
        David M. Gay
22
        AT&T Bell Laboratories, Room 2C-463
23
        600 Mountain Avenue
24
        Murray Hill, NJ 07974-2070
25
        U.S.A.
26
        dmg@research.att.com or research!dmg
27
 */
28
 
29
/* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
30
 *
31
 * This strtod returns a nearest machine number to the input decimal
32
 * string (or sets errno to ERANGE).  With IEEE arithmetic, ties are
33
 * broken by the IEEE round-even rule.  Otherwise ties are broken by
34
 * biased rounding (add half and chop).
35
 *
36
 * Inspired loosely by William D. Clinger's paper "How to Read Floating
37
 * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
38
 *
39
 * Modifications:
40
 *
41
 *      1. We only require IEEE, IBM, or VAX double-precision
42
 *              arithmetic (not IEEE double-extended).
43
 *      2. We get by with floating-point arithmetic in a case that
44
 *              Clinger missed -- when we're computing d * 10^n
45
 *              for a small integer d and the integer n is not too
46
 *              much larger than 22 (the maximum integer k for which
47
 *              we can represent 10^k exactly), we may be able to
48
 *              compute (d*10^k) * 10^(e-k) with just one roundoff.
49
 *      3. Rather than a bit-at-a-time adjustment of the binary
50
 *              result in the hard case, we use floating-point
51
 *              arithmetic to determine the adjustment to within
52
 *              one bit; only in really hard cases do we need to
53
 *              compute a second residual.
54
 *      4. Because of 3., we don't need a large table of powers of 10
55
 *              for ten-to-e (just some small tables, e.g. of 10^k
56
 *              for 0 <= k <= 22).
57
 */
58
 
59
/*
60
 * #define IEEE_8087 for IEEE-arithmetic machines where the least
61
 *      significant byte has the lowest address.
62
 * #define IEEE_MC68k for IEEE-arithmetic machines where the most
63
 *      significant byte has the lowest address.
64
 * #define Sudden_Underflow for IEEE-format machines without gradual
65
 *      underflow (i.e., that flush to zero on underflow).
66
 * #define IBM for IBM mainframe-style floating-point arithmetic.
67
 * #define VAX for VAX-style floating-point arithmetic.
68
 * #define Unsigned_Shifts if >> does treats its left operand as unsigned.
69
 * #define No_leftright to omit left-right logic in fast floating-point
70
 *      computation of dtoa.
71
 * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3.
72
 * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
73
 *      that use extended-precision instructions to compute rounded
74
 *      products and quotients) with IBM.
75
 * #define ROUND_BIASED for IEEE-format with biased rounding.
76
 * #define Inaccurate_Divide for IEEE-format with correctly rounded
77
 *      products but inaccurate quotients, e.g., for Intel i860.
78
 * #define Just_16 to store 16 bits per 32-bit long when doing high-precision
79
 *      integer arithmetic.  Whether this speeds things up or slows things
80
 *      down depends on the machine and the number being converted.
81
 */
82
 
83
#include <_ansi.h>
84
#include <stdlib.h>
85
#include <string.h>
86
#include <reent.h>
87
#include "mprec.h"
88
 
89
/* This is defined in sys/reent.h as (sizeof (size_t) << 3) now, as in NetBSD.
90
   The old value of 15 was wrong and made newlib vulnerable against buffer
91
   overrun attacks (CVE-2009-0689), same as other implementations of gdtoa
92
   based on BSD code.
93
#define _Kmax 15
94
*/
95
 
96
_Bigint *
97
_DEFUN (Balloc, (ptr, k), struct _reent *ptr _AND int k)
98
{
99
  int x;
100
  _Bigint *rv ;
101
 
102
  _REENT_CHECK_MP(ptr);
103
  if (_REENT_MP_FREELIST(ptr) == NULL)
104
    {
105
      /* Allocate a list of pointers to the mprec objects */
106
      _REENT_MP_FREELIST(ptr) = (struct _Bigint **) _calloc_r (ptr,
107
                                                      sizeof (struct _Bigint *),
108
                                                      _Kmax + 1);
109
      if (_REENT_MP_FREELIST(ptr) == NULL)
110
        {
111
          return NULL;
112
        }
113
    }
114
 
115
  if ((rv = _REENT_MP_FREELIST(ptr)[k]) != 0)
116
    {
117
      _REENT_MP_FREELIST(ptr)[k] = rv->_next;
118
    }
119
  else
120
    {
121
      x = 1 << k;
122
      /* Allocate an mprec Bigint and stick in in the freelist */
123
      rv = (_Bigint *) _calloc_r (ptr,
124
                                  1,
125
                                  sizeof (_Bigint) +
126
                                  (x-1) * sizeof(rv->_x));
127
      if (rv == NULL) return NULL;
128
      rv->_k = k;
129
      rv->_maxwds = x;
130
    }
131
  rv->_sign = rv->_wds = 0;
132
  return rv;
133
}
134
 
135
void
136
_DEFUN (Bfree, (ptr, v), struct _reent *ptr _AND _Bigint * v)
137
{
138
  _REENT_CHECK_MP(ptr);
139
  if (v)
140
    {
141
      v->_next = _REENT_MP_FREELIST(ptr)[v->_k];
142
      _REENT_MP_FREELIST(ptr)[v->_k] = v;
143
    }
144
}
145
 
146
_Bigint *
147
_DEFUN (multadd, (ptr, b, m, a),
148
        struct _reent *ptr _AND
149
        _Bigint * b _AND
150
        int m _AND
151
        int a)
152
{
153
  int i, wds;
154
  __ULong *x, y;
155
#ifdef Pack_32
156
  __ULong xi, z;
157
#endif
158
  _Bigint *b1;
159
 
160
  wds = b->_wds;
161
  x = b->_x;
162
  i = 0;
163
  do
164
    {
165
#ifdef Pack_32
166
      xi = *x;
167
      y = (xi & 0xffff) * m + a;
168
      z = (xi >> 16) * m + (y >> 16);
169
      a = (int) (z >> 16);
170
      *x++ = (z << 16) + (y & 0xffff);
171
#else
172
      y = *x * m + a;
173
      a = (int) (y >> 16);
174
      *x++ = y & 0xffff;
175
#endif
176
    }
177
  while (++i < wds);
178
  if (a)
179
    {
180
      if (wds >= b->_maxwds)
181
        {
182
          b1 = Balloc (ptr, b->_k + 1);
183
          Bcopy (b1, b);
184
          Bfree (ptr, b);
185
          b = b1;
186
        }
187
      b->_x[wds++] = a;
188
      b->_wds = wds;
189
    }
190
  return b;
191
}
192
 
193
_Bigint *
194
_DEFUN (s2b, (ptr, s, nd0, nd, y9),
195
        struct _reent * ptr _AND
196
        _CONST char *s _AND
197
        int nd0 _AND
198
        int nd _AND
199
        __ULong y9)
200
{
201
  _Bigint *b;
202
  int i, k;
203
  __Long x, y;
204
 
205
  x = (nd + 8) / 9;
206
  for (k = 0, y = 1; x > y; y <<= 1, k++);
207
#ifdef Pack_32
208
  b = Balloc (ptr, k);
209
  b->_x[0] = y9;
210
  b->_wds = 1;
211
#else
212
  b = Balloc (ptr, k + 1);
213
  b->_x[0] = y9 & 0xffff;
214
  b->_wds = (b->_x[1] = y9 >> 16) ? 2 : 1;
215
#endif
216
 
217
  i = 9;
218
  if (9 < nd0)
219
    {
220
      s += 9;
221
      do
222
        b = multadd (ptr, b, 10, *s++ - '0');
223
      while (++i < nd0);
224
      s++;
225
    }
226
  else
227
    s += 10;
228
  for (; i < nd; i++)
229
    b = multadd (ptr, b, 10, *s++ - '0');
230
  return b;
231
}
232
 
233
int
234
_DEFUN (hi0bits,
235
        (x), register __ULong x)
236
{
237
  register int k = 0;
238
 
239
  if (!(x & 0xffff0000))
240
    {
241
      k = 16;
242
      x <<= 16;
243
    }
244
  if (!(x & 0xff000000))
245
    {
246
      k += 8;
247
      x <<= 8;
248
    }
249
  if (!(x & 0xf0000000))
250
    {
251
      k += 4;
252
      x <<= 4;
253
    }
254
  if (!(x & 0xc0000000))
255
    {
256
      k += 2;
257
      x <<= 2;
258
    }
259
  if (!(x & 0x80000000))
260
    {
261
      k++;
262
      if (!(x & 0x40000000))
263
        return 32;
264
    }
265
  return k;
266
}
267
 
268
int
269
_DEFUN (lo0bits, (y), __ULong *y)
270
{
271
  register int k;
272
  register __ULong x = *y;
273
 
274
  if (x & 7)
275
    {
276
      if (x & 1)
277
        return 0;
278
      if (x & 2)
279
        {
280
          *y = x >> 1;
281
          return 1;
282
        }
283
      *y = x >> 2;
284
      return 2;
285
    }
286
  k = 0;
287
  if (!(x & 0xffff))
288
    {
289
      k = 16;
290
      x >>= 16;
291
    }
292
  if (!(x & 0xff))
293
    {
294
      k += 8;
295
      x >>= 8;
296
    }
297
  if (!(x & 0xf))
298
    {
299
      k += 4;
300
      x >>= 4;
301
    }
302
  if (!(x & 0x3))
303
    {
304
      k += 2;
305
      x >>= 2;
306
    }
307
  if (!(x & 1))
308
    {
309
      k++;
310
      x >>= 1;
311
      if (!x & 1)
312
        return 32;
313
    }
314
  *y = x;
315
  return k;
316
}
317
 
318
_Bigint *
319
_DEFUN (i2b, (ptr, i), struct _reent * ptr _AND int i)
320
{
321
  _Bigint *b;
322
 
323
  b = Balloc (ptr, 1);
324
  b->_x[0] = i;
325
  b->_wds = 1;
326
  return b;
327
}
328
 
329
_Bigint *
330
_DEFUN (mult, (ptr, a, b), struct _reent * ptr _AND _Bigint * a _AND _Bigint * b)
331
{
332
  _Bigint *c;
333
  int k, wa, wb, wc;
334
  __ULong carry, y, z;
335
  __ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
336
#ifdef Pack_32
337
  __ULong z2;
338
#endif
339
 
340
  if (a->_wds < b->_wds)
341
    {
342
      c = a;
343
      a = b;
344
      b = c;
345
    }
346
  k = a->_k;
347
  wa = a->_wds;
348
  wb = b->_wds;
349
  wc = wa + wb;
350
  if (wc > a->_maxwds)
351
    k++;
352
  c = Balloc (ptr, k);
353
  for (x = c->_x, xa = x + wc; x < xa; x++)
354
    *x = 0;
355
  xa = a->_x;
356
  xae = xa + wa;
357
  xb = b->_x;
358
  xbe = xb + wb;
359
  xc0 = c->_x;
360
#ifdef Pack_32
361
  for (; xb < xbe; xb++, xc0++)
362
    {
363
      if ((y = *xb & 0xffff) != 0)
364
        {
365
          x = xa;
366
          xc = xc0;
367
          carry = 0;
368
          do
369
            {
370
              z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
371
              carry = z >> 16;
372
              z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
373
              carry = z2 >> 16;
374
              Storeinc (xc, z2, z);
375
            }
376
          while (x < xae);
377
          *xc = carry;
378
        }
379
      if ((y = *xb >> 16) != 0)
380
        {
381
          x = xa;
382
          xc = xc0;
383
          carry = 0;
384
          z2 = *xc;
385
          do
386
            {
387
              z = (*x & 0xffff) * y + (*xc >> 16) + carry;
388
              carry = z >> 16;
389
              Storeinc (xc, z, z2);
390
              z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
391
              carry = z2 >> 16;
392
            }
393
          while (x < xae);
394
          *xc = z2;
395
        }
396
    }
397
#else
398
  for (; xb < xbe; xc0++)
399
    {
400
      if (y = *xb++)
401
        {
402
          x = xa;
403
          xc = xc0;
404
          carry = 0;
405
          do
406
            {
407
              z = *x++ * y + *xc + carry;
408
              carry = z >> 16;
409
              *xc++ = z & 0xffff;
410
            }
411
          while (x < xae);
412
          *xc = carry;
413
        }
414
    }
415
#endif
416
  for (xc0 = c->_x, xc = xc0 + wc; wc > 0 && !*--xc; --wc);
417
  c->_wds = wc;
418
  return c;
419
}
420
 
421
_Bigint *
422
_DEFUN (pow5mult,
423
        (ptr, b, k), struct _reent * ptr _AND _Bigint * b _AND int k)
424
{
425
  _Bigint *b1, *p5, *p51;
426
  int i;
427
  static _CONST int p05[3] = {5, 25, 125};
428
 
429
  if ((i = k & 3) != 0)
430
    b = multadd (ptr, b, p05[i - 1], 0);
431
 
432
  if (!(k >>= 2))
433
    return b;
434
  _REENT_CHECK_MP(ptr);
435
  if (!(p5 = _REENT_MP_P5S(ptr)))
436
    {
437
      /* first time */
438
      p5 = _REENT_MP_P5S(ptr) = i2b (ptr, 625);
439
      p5->_next = 0;
440
    }
441
  for (;;)
442
    {
443
      if (k & 1)
444
        {
445
          b1 = mult (ptr, b, p5);
446
          Bfree (ptr, b);
447
          b = b1;
448
        }
449
      if (!(k >>= 1))
450
        break;
451
      if (!(p51 = p5->_next))
452
        {
453
          p51 = p5->_next = mult (ptr, p5, p5);
454
          p51->_next = 0;
455
        }
456
      p5 = p51;
457
    }
458
  return b;
459
}
460
 
461
_Bigint *
462
_DEFUN (lshift, (ptr, b, k), struct _reent * ptr _AND _Bigint * b _AND int k)
463
{
464
  int i, k1, n, n1;
465
  _Bigint *b1;
466
  __ULong *x, *x1, *xe, z;
467
 
468
#ifdef Pack_32
469
  n = k >> 5;
470
#else
471
  n = k >> 4;
472
#endif
473
  k1 = b->_k;
474
  n1 = n + b->_wds + 1;
475
  for (i = b->_maxwds; n1 > i; i <<= 1)
476
    k1++;
477
  b1 = Balloc (ptr, k1);
478
  x1 = b1->_x;
479
  for (i = 0; i < n; i++)
480
    *x1++ = 0;
481
  x = b->_x;
482
  xe = x + b->_wds;
483
#ifdef Pack_32
484
  if (k &= 0x1f)
485
    {
486
      k1 = 32 - k;
487
      z = 0;
488
      do
489
        {
490
          *x1++ = *x << k | z;
491
          z = *x++ >> k1;
492
        }
493
      while (x < xe);
494
      if ((*x1 = z) != 0)
495
        ++n1;
496
    }
497
#else
498
  if (k &= 0xf)
499
    {
500
      k1 = 16 - k;
501
      z = 0;
502
      do
503
        {
504
          *x1++ = *x << k & 0xffff | z;
505
          z = *x++ >> k1;
506
        }
507
      while (x < xe);
508
      if (*x1 = z)
509
        ++n1;
510
    }
511
#endif
512
  else
513
    do
514
      *x1++ = *x++;
515
    while (x < xe);
516
  b1->_wds = n1 - 1;
517
  Bfree (ptr, b);
518
  return b1;
519
}
520
 
521
int
522
_DEFUN (cmp, (a, b), _Bigint * a _AND _Bigint * b)
523
{
524
  __ULong *xa, *xa0, *xb, *xb0;
525
  int i, j;
526
 
527
  i = a->_wds;
528
  j = b->_wds;
529
#ifdef DEBUG
530
  if (i > 1 && !a->_x[i - 1])
531
    Bug ("cmp called with a->_x[a->_wds-1] == 0");
532
  if (j > 1 && !b->_x[j - 1])
533
    Bug ("cmp called with b->_x[b->_wds-1] == 0");
534
#endif
535
  if (i -= j)
536
    return i;
537
  xa0 = a->_x;
538
  xa = xa0 + j;
539
  xb0 = b->_x;
540
  xb = xb0 + j;
541
  for (;;)
542
    {
543
      if (*--xa != *--xb)
544
        return *xa < *xb ? -1 : 1;
545
      if (xa <= xa0)
546
        break;
547
    }
548
  return 0;
549
}
550
 
551
_Bigint *
552
_DEFUN (diff, (ptr, a, b), struct _reent * ptr _AND
553
        _Bigint * a _AND _Bigint * b)
554
{
555
  _Bigint *c;
556
  int i, wa, wb;
557
  __Long borrow, y;             /* We need signed shifts here. */
558
  __ULong *xa, *xae, *xb, *xbe, *xc;
559
#ifdef Pack_32
560
  __Long z;
561
#endif
562
 
563
  i = cmp (a, b);
564
  if (!i)
565
    {
566
      c = Balloc (ptr, 0);
567
      c->_wds = 1;
568
      c->_x[0] = 0;
569
      return c;
570
    }
571
  if (i < 0)
572
    {
573
      c = a;
574
      a = b;
575
      b = c;
576
      i = 1;
577
    }
578
  else
579
    i = 0;
580
  c = Balloc (ptr, a->_k);
581
  c->_sign = i;
582
  wa = a->_wds;
583
  xa = a->_x;
584
  xae = xa + wa;
585
  wb = b->_wds;
586
  xb = b->_x;
587
  xbe = xb + wb;
588
  xc = c->_x;
589
  borrow = 0;
590
#ifdef Pack_32
591
  do
592
    {
593
      y = (*xa & 0xffff) - (*xb & 0xffff) + borrow;
594
      borrow = y >> 16;
595
      Sign_Extend (borrow, y);
596
      z = (*xa++ >> 16) - (*xb++ >> 16) + borrow;
597
      borrow = z >> 16;
598
      Sign_Extend (borrow, z);
599
      Storeinc (xc, z, y);
600
    }
601
  while (xb < xbe);
602
  while (xa < xae)
603
    {
604
      y = (*xa & 0xffff) + borrow;
605
      borrow = y >> 16;
606
      Sign_Extend (borrow, y);
607
      z = (*xa++ >> 16) + borrow;
608
      borrow = z >> 16;
609
      Sign_Extend (borrow, z);
610
      Storeinc (xc, z, y);
611
    }
612
#else
613
  do
614
    {
615
      y = *xa++ - *xb++ + borrow;
616
      borrow = y >> 16;
617
      Sign_Extend (borrow, y);
618
      *xc++ = y & 0xffff;
619
    }
620
  while (xb < xbe);
621
  while (xa < xae)
622
    {
623
      y = *xa++ + borrow;
624
      borrow = y >> 16;
625
      Sign_Extend (borrow, y);
626
      *xc++ = y & 0xffff;
627
    }
628
#endif
629
  while (!*--xc)
630
    wa--;
631
  c->_wds = wa;
632
  return c;
633
}
634
 
635
double
636
_DEFUN (ulp, (_x), double _x)
637
{
638
  union double_union x, a;
639
  register __Long L;
640
 
641
  x.d = _x;
642
 
643
  L = (word0 (x) & Exp_mask) - (P - 1) * Exp_msk1;
644
#ifndef Sudden_Underflow
645
  if (L > 0)
646
    {
647
#endif
648
#ifdef IBM
649
      L |= Exp_msk1 >> 4;
650
#endif
651
      word0 (a) = L;
652
#ifndef _DOUBLE_IS_32BITS
653
      word1 (a) = 0;
654
#endif
655
 
656
#ifndef Sudden_Underflow
657
    }
658
  else
659
    {
660
      L = -L >> Exp_shift;
661
      if (L < Exp_shift)
662
        {
663
          word0 (a) = 0x80000 >> L;
664
#ifndef _DOUBLE_IS_32BITS
665
          word1 (a) = 0;
666
#endif
667
        }
668
      else
669
        {
670
          word0 (a) = 0;
671
          L -= Exp_shift;
672
#ifndef _DOUBLE_IS_32BITS
673
         word1 (a) = L >= 31 ? 1 : 1 << (31 - L);
674
#endif
675
        }
676
    }
677
#endif
678
  return a.d;
679
}
680
 
681
double
682
_DEFUN (b2d, (a, e),
683
        _Bigint * a _AND int *e)
684
{
685
  __ULong *xa, *xa0, w, y, z;
686
  int k;
687
  union double_union d;
688
#ifdef VAX
689
  __ULong d0, d1;
690
#else
691
#define d0 word0(d)
692
#define d1 word1(d)
693
#endif
694
 
695
  xa0 = a->_x;
696
  xa = xa0 + a->_wds;
697
  y = *--xa;
698
#ifdef DEBUG
699
  if (!y)
700
    Bug ("zero y in b2d");
701
#endif
702
  k = hi0bits (y);
703
  *e = 32 - k;
704
#ifdef Pack_32
705
  if (k < Ebits)
706
    {
707
      d0 = Exp_1 | y >> (Ebits - k);
708
      w = xa > xa0 ? *--xa : 0;
709
#ifndef _DOUBLE_IS_32BITS
710
      d1 = y << ((32 - Ebits) + k) | w >> (Ebits - k);
711
#endif
712
      goto ret_d;
713
    }
714
  z = xa > xa0 ? *--xa : 0;
715
  if (k -= Ebits)
716
    {
717
      d0 = Exp_1 | y << k | z >> (32 - k);
718
      y = xa > xa0 ? *--xa : 0;
719
#ifndef _DOUBLE_IS_32BITS
720
      d1 = z << k | y >> (32 - k);
721
#endif
722
    }
723
  else
724
    {
725
      d0 = Exp_1 | y;
726
#ifndef _DOUBLE_IS_32BITS
727
      d1 = z;
728
#endif
729
    }
730
#else
731
  if (k < Ebits + 16)
732
    {
733
      z = xa > xa0 ? *--xa : 0;
734
      d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
735
      w = xa > xa0 ? *--xa : 0;
736
      y = xa > xa0 ? *--xa : 0;
737
      d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
738
      goto ret_d;
739
    }
740
  z = xa > xa0 ? *--xa : 0;
741
  w = xa > xa0 ? *--xa : 0;
742
  k -= Ebits + 16;
743
  d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
744
  y = xa > xa0 ? *--xa : 0;
745
  d1 = w << k + 16 | y << k;
746
#endif
747
ret_d:
748
#ifdef VAX
749
  word0 (d) = d0 >> 16 | d0 << 16;
750
  word1 (d) = d1 >> 16 | d1 << 16;
751
#else
752
#undef d0
753
#undef d1
754
#endif
755
  return d.d;
756
}
757
 
758
_Bigint *
759
_DEFUN (d2b,
760
        (ptr, _d, e, bits),
761
        struct _reent * ptr _AND
762
        double _d _AND
763
        int *e _AND
764
        int *bits)
765
 
766
{
767
  union double_union d;
768
  _Bigint *b;
769
  int de, i, k;
770
  __ULong *x, y, z;
771
#ifdef VAX
772
  __ULong d0, d1;
773
#endif
774
  d.d = _d;
775
#ifdef VAX
776
  d0 = word0 (d) >> 16 | word0 (d) << 16;
777
  d1 = word1 (d) >> 16 | word1 (d) << 16;
778
#else
779
#define d0 word0(d)
780
#define d1 word1(d)
781
  d.d = _d;
782
#endif
783
 
784
#ifdef Pack_32
785
  b = Balloc (ptr, 1);
786
#else
787
  b = Balloc (ptr, 2);
788
#endif
789
  x = b->_x;
790
 
791
  z = d0 & Frac_mask;
792
  d0 &= 0x7fffffff;             /* clear sign bit, which we ignore */
793
#ifdef Sudden_Underflow
794
  de = (int) (d0 >> Exp_shift);
795
#ifndef IBM
796
  z |= Exp_msk11;
797
#endif
798
#else
799
  if ((de = (int) (d0 >> Exp_shift)) != 0)
800
    z |= Exp_msk1;
801
#endif
802
#ifdef Pack_32
803
#ifndef _DOUBLE_IS_32BITS
804
  if (d1)
805
    {
806
      y = d1;
807
      k = lo0bits (&y);
808
      if (k)
809
        {
810
         x[0] = y | z << (32 - k);
811
          z >>= k;
812
        }
813
      else
814
        x[0] = y;
815
      i = b->_wds = (x[1] = z) ? 2 : 1;
816
    }
817
  else
818
#endif
819
    {
820
#ifdef DEBUG
821
      if (!z)
822
        Bug ("Zero passed to d2b");
823
#endif
824
      k = lo0bits (&z);
825
      x[0] = z;
826
      i = b->_wds = 1;
827
#ifndef _DOUBLE_IS_32BITS
828
      k += 32;
829
#endif
830
    }
831
#else
832
  if (d1)
833
    {
834
      y = d1;
835
      k = lo0bits (&y);
836
      if (k)
837
        if (k >= 16)
838
          {
839
            x[0] = y | z << 32 - k & 0xffff;
840
            x[1] = z >> k - 16 & 0xffff;
841
            x[2] = z >> k;
842
            i = 2;
843
          }
844
        else
845
          {
846
            x[0] = y & 0xffff;
847
            x[1] = y >> 16 | z << 16 - k & 0xffff;
848
            x[2] = z >> k & 0xffff;
849
            x[3] = z >> k + 16;
850
            i = 3;
851
          }
852
      else
853
        {
854
          x[0] = y & 0xffff;
855
          x[1] = y >> 16;
856
          x[2] = z & 0xffff;
857
          x[3] = z >> 16;
858
          i = 3;
859
        }
860
    }
861
  else
862
    {
863
#ifdef DEBUG
864
      if (!z)
865
        Bug ("Zero passed to d2b");
866
#endif
867
      k = lo0bits (&z);
868
      if (k >= 16)
869
        {
870
          x[0] = z;
871
          i = 0;
872
        }
873
      else
874
        {
875
          x[0] = z & 0xffff;
876
          x[1] = z >> 16;
877
          i = 1;
878
        }
879
      k += 32;
880
    }
881
  while (!x[i])
882
    --i;
883
  b->_wds = i + 1;
884
#endif
885
#ifndef Sudden_Underflow
886
  if (de)
887
    {
888
#endif
889
#ifdef IBM
890
      *e = (de - Bias - (P - 1) << 2) + k;
891
      *bits = 4 * P + 8 - k - hi0bits (word0 (d) & Frac_mask);
892
#else
893
      *e = de - Bias - (P - 1) + k;
894
      *bits = P - k;
895
#endif
896
#ifndef Sudden_Underflow
897
    }
898
  else
899
    {
900
      *e = de - Bias - (P - 1) + 1 + k;
901
#ifdef Pack_32
902
      *bits = 32 * i - hi0bits (x[i - 1]);
903
#else
904
      *bits = (i + 2) * 16 - hi0bits (x[i]);
905
#endif
906
    }
907
#endif
908
  return b;
909
}
910
#undef d0
911
#undef d1
912
 
913
double
914
_DEFUN (ratio, (a, b), _Bigint * a _AND _Bigint * b)
915
 
916
{
917
  union double_union da, db;
918
  int k, ka, kb;
919
 
920
  da.d = b2d (a, &ka);
921
  db.d = b2d (b, &kb);
922
#ifdef Pack_32
923
  k = ka - kb + 32 * (a->_wds - b->_wds);
924
#else
925
  k = ka - kb + 16 * (a->_wds - b->_wds);
926
#endif
927
#ifdef IBM
928
  if (k > 0)
929
    {
930
      word0 (da) += (k >> 2) * Exp_msk1;
931
      if (k &= 3)
932
        da.d *= 1 << k;
933
    }
934
  else
935
    {
936
      k = -k;
937
      word0 (db) += (k >> 2) * Exp_msk1;
938
      if (k &= 3)
939
        db.d *= 1 << k;
940
    }
941
#else
942
  if (k > 0)
943
    word0 (da) += k * Exp_msk1;
944
  else
945
    {
946
      k = -k;
947
      word0 (db) += k * Exp_msk1;
948
    }
949
#endif
950
  return da.d / db.d;
951
}
952
 
953
 
954
_CONST double
955
  tens[] =
956
{
957
  1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
958
  1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
959
  1e20, 1e21, 1e22, 1e23, 1e24
960
 
961
};
962
 
963
#if !defined(_DOUBLE_IS_32BITS) && !defined(__v800)
964
_CONST double bigtens[] =
965
{1e16, 1e32, 1e64, 1e128, 1e256};
966
 
967
_CONST double tinytens[] =
968
{1e-16, 1e-32, 1e-64, 1e-128, 1e-256};
969
#else
970
_CONST double bigtens[] =
971
{1e16, 1e32};
972
 
973
_CONST double tinytens[] =
974
{1e-16, 1e-32};
975
#endif
976
 
977
 
978
double
979
_DEFUN (_mprec_log10, (dig),
980
        int dig)
981
{
982
  double v = 1.0;
983
  if (dig < 24)
984
    return tens[dig];
985
  while (dig > 0)
986
    {
987
      v *= 10;
988
      dig--;
989
    }
990
  return v;
991
}
992
 
993
void
994
_DEFUN (copybits, (c, n, b),
995
        __ULong *c _AND
996
        int n _AND
997
        _Bigint *b)
998
{
999
        __ULong *ce, *x, *xe;
1000
#ifdef Pack_16
1001
        int nw, nw1;
1002
#endif
1003
 
1004
        ce = c + ((n-1) >> kshift) + 1;
1005
        x = b->_x;
1006
#ifdef Pack_32
1007
        xe = x + b->_wds;
1008
        while(x < xe)
1009
                *c++ = *x++;
1010
#else
1011
        nw = b->_wds;
1012
        nw1 = nw & 1;
1013
        for(xe = x + (nw - nw1); x < xe; x += 2)
1014
                Storeinc(c, x[1], x[0]);
1015
        if (nw1)
1016
                *c++ = *x;
1017
#endif
1018
        while(c < ce)
1019
                *c++ = 0;
1020
}
1021
 
1022
__ULong
1023
_DEFUN (any_on, (b, k),
1024
        _Bigint *b _AND
1025
        int k)
1026
{
1027
        int n, nwds;
1028
        __ULong *x, *x0, x1, x2;
1029
 
1030
        x = b->_x;
1031
        nwds = b->_wds;
1032
        n = k >> kshift;
1033
        if (n > nwds)
1034
                n = nwds;
1035
        else if (n < nwds && (k &= kmask)) {
1036
                x1 = x2 = x[n];
1037
                x1 >>= k;
1038
                x1 <<= k;
1039
                if (x1 != x2)
1040
                        return 1;
1041
                }
1042
        x0 = x;
1043
        x += n;
1044
        while(x > x0)
1045
                if (*--x)
1046
                        return 1;
1047
        return 0;
1048
}
1049
 

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