1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
|
/****************************************************************
*
* The author of this software is David M. Gay.
*
* Copyright (c) 1991 by AT&T.
*
* Permission to use, copy, modify, and distribute this software for any
* purpose without fee is hereby granted, provided that this entire notice
* is included in all copies of any software which is or includes a copy
* or modification of this software and in all copies of the supporting
* documentation for such software.
*
* THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
* WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY
* REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
* OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
*
***************************************************************/
/* Please send bug reports to
David M. Gay
AT&T Bell Laboratories, Room 2C-463
600 Mountain Avenue
Murray Hill, NJ 07974-2070
U.S.A.
dmg@research.att.com or research!dmg
*/
#include <_ansi.h>
#include <stdlib.h>
#include <reent.h>
#include <string.h>
#include "mprec.h"
#ifdef _REENT_THREAD_LOCAL
_Thread_local struct _Bigint *_tls_mp_result;
_Thread_local int _tls_mp_result_k;
#endif
static int
quorem (_Bigint * b, _Bigint * S)
{
int n;
__Long borrow, y;
__ULong carry, q, ys;
__ULong *bx, *bxe, *sx, *sxe;
#ifdef Pack_32
__Long z;
__ULong si, zs;
#endif
n = S->_wds;
#ifdef DEBUG
/*debug*/ if (b->_wds > n)
/*debug*/ Bug ("oversize b in quorem");
#endif
if (b->_wds < n)
return 0;
sx = S->_x;
sxe = sx + --n;
bx = b->_x;
bxe = bx + n;
q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
#ifdef DEBUG
/*debug*/ if (q > 9)
/*debug*/ Bug ("oversized quotient in quorem");
#endif
if (q)
{
borrow = 0;
carry = 0;
do
{
#ifdef Pack_32
si = *sx++;
ys = (si & 0xffff) * q + carry;
zs = (si >> 16) * q + (ys >> 16);
carry = zs >> 16;
y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
borrow = y >> 16;
Sign_Extend (borrow, y);
z = (*bx >> 16) - (zs & 0xffff) + borrow;
borrow = z >> 16;
Sign_Extend (borrow, z);
Storeinc (bx, z, y);
#else
ys = *sx++ * q + carry;
carry = ys >> 16;
y = *bx - (ys & 0xffff) + borrow;
borrow = y >> 16;
Sign_Extend (borrow, y);
*bx++ = y & 0xffff;
#endif
}
while (sx <= sxe);
if (!*bxe)
{
bx = b->_x;
while (--bxe > bx && !*bxe)
--n;
b->_wds = n;
}
}
if (cmp (b, S) >= 0)
{
q++;
borrow = 0;
carry = 0;
bx = b->_x;
sx = S->_x;
do
{
#ifdef Pack_32
si = *sx++;
ys = (si & 0xffff) + carry;
zs = (si >> 16) + (ys >> 16);
carry = zs >> 16;
y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
borrow = y >> 16;
Sign_Extend (borrow, y);
z = (*bx >> 16) - (zs & 0xffff) + borrow;
borrow = z >> 16;
Sign_Extend (borrow, z);
Storeinc (bx, z, y);
#else
ys = *sx++ + carry;
carry = ys >> 16;
y = *bx - (ys & 0xffff) + borrow;
borrow = y >> 16;
Sign_Extend (borrow, y);
*bx++ = y & 0xffff;
#endif
}
while (sx <= sxe);
bx = b->_x;
bxe = bx + n;
if (!*bxe)
{
while (--bxe > bx && !*bxe)
--n;
b->_wds = n;
}
}
return q;
}
/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
*
* Inspired by "How to Print Floating-Point Numbers Accurately" by
* Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
*
* Modifications:
* 1. Rather than iterating, we use a simple numeric overestimate
* to determine k = floor(log10(d)). We scale relevant
* quantities using O(log2(k)) rather than O(k) multiplications.
* 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
* try to generate digits strictly left to right. Instead, we
* compute with fewer bits and propagate the carry if necessary
* when rounding the final digit up. This is often faster.
* 3. Under the assumption that input will be rounded nearest,
* mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
* That is, we allow equality in stopping tests when the
* round-nearest rule will give the same floating-point value
* as would satisfaction of the stopping test with strict
* inequality.
* 4. We remove common factors of powers of 2 from relevant
* quantities.
* 5. When converting floating-point integers less than 1e16,
* we use floating-point arithmetic rather than resorting
* to multiple-precision integers.
* 6. When asked to produce fewer than 15 digits, we first try
* to get by with floating-point arithmetic; we resort to
* multiple-precision integer arithmetic only if we cannot
* guarantee that the floating-point calculation has given
* the correctly rounded result. For k requested digits and
* "uniformly" distributed input, the probability is
* something like 10^(k-15) that we must resort to the long
* calculation.
*/
char *
_dtoa_r (struct _reent *ptr,
double _d,
int mode,
int ndigits,
int *decpt,
int *sign,
char **rve)
{
/* Arguments ndigits, decpt, sign are similar to those
of ecvt and fcvt; trailing zeros are suppressed from
the returned string. If not null, *rve is set to point
to the end of the return value. If d is +-Infinity or NaN,
then *decpt is set to 9999.
mode:
0 ==> shortest string that yields d when read in
and rounded to nearest.
1 ==> like 0, but with Steele & White stopping rule;
e.g. with IEEE P754 arithmetic , mode 0 gives
1e23 whereas mode 1 gives 9.999999999999999e22.
2 ==> max(1,ndigits) significant digits. This gives a
return value similar to that of ecvt, except
that trailing zeros are suppressed.
3 ==> through ndigits past the decimal point. This
gives a return value similar to that from fcvt,
except that trailing zeros are suppressed, and
ndigits can be negative.
4-9 should give the same return values as 2-3, i.e.,
4 <= mode <= 9 ==> same return as mode
2 + (mode & 1). These modes are mainly for
debugging; often they run slower but sometimes
faster than modes 2-3.
4,5,8,9 ==> left-to-right digit generation.
6-9 ==> don't try fast floating-point estimate
(if applicable).
Values of mode other than 0-9 are treated as mode 0.
Sufficient space is allocated to the return value
to hold the suppressed trailing zeros.
*/
int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1, j, j1, k, k0,
k_check, leftright, m2, m5, s2, s5, spec_case, try_quick;
union double_union d, d2, eps;
__Long L;
#ifndef Sudden_Underflow
int denorm;
__ULong x;
#endif
_Bigint *b, *b1, *delta, *mlo = NULL, *mhi, *S;
double ds;
char *s, *s0;
d.d = _d;
_REENT_CHECK_MP(ptr);
if (_REENT_MP_RESULT(ptr))
{
_REENT_MP_RESULT(ptr)->_k = _REENT_MP_RESULT_K(ptr);
_REENT_MP_RESULT(ptr)->_maxwds = 1 << _REENT_MP_RESULT_K(ptr);
Bfree (ptr, _REENT_MP_RESULT(ptr));
_REENT_MP_RESULT(ptr) = 0;
}
if (word0 (d) & Sign_bit)
{
/* set sign for everything, including 0's and NaNs */
*sign = 1;
word0 (d) &= ~Sign_bit; /* clear sign bit */
}
else
*sign = 0;
#if defined(IEEE_Arith) + defined(VAX)
#ifdef IEEE_Arith
if ((word0 (d) & Exp_mask) == Exp_mask)
#else
if (word0 (d) == 0x8000)
#endif
{
/* Infinity or NaN */
*decpt = 9999;
s =
#ifdef IEEE_Arith
!word1 (d) && !(word0 (d) & 0xfffff) ? "Infinity" :
#endif
"NaN";
if (rve)
*rve =
#ifdef IEEE_Arith
s[3] ? s + 8 :
#endif
s + 3;
return s;
}
#endif
#ifdef IBM
d.d += 0; /* normalize */
#endif
if (!d.d)
{
*decpt = 1;
s = "0";
if (rve)
*rve = s + 1;
return s;
}
b = d2b (ptr, d.d, &be, &bbits);
#ifdef Sudden_Underflow
i = (int) (word0 (d) >> Exp_shift1 & (Exp_mask >> Exp_shift1));
#else
if ((i = (int) (word0 (d) >> Exp_shift1 & (Exp_mask >> Exp_shift1))) != 0)
{
#endif
d2.d = d.d;
word0 (d2) &= Frac_mask1;
word0 (d2) |= Exp_11;
#ifdef IBM
if (j = 11 - hi0bits (word0 (d2) & Frac_mask))
d2.d /= 1 << j;
#endif
/* log(x) ~=~ log(1.5) + (x-1.5)/1.5
* log10(x) = log(x) / log(10)
* ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
* log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
*
* This suggests computing an approximation k to log10(d) by
*
* k = (i - Bias)*0.301029995663981
* + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
*
* We want k to be too large rather than too small.
* The error in the first-order Taylor series approximation
* is in our favor, so we just round up the constant enough
* to compensate for any error in the multiplication of
* (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
* and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
* adding 1e-13 to the constant term more than suffices.
* Hence we adjust the constant term to 0.1760912590558.
* (We could get a more accurate k by invoking log10,
* but this is probably not worthwhile.)
*/
i -= Bias;
#ifdef IBM
i <<= 2;
i += j;
#endif
#ifndef Sudden_Underflow
denorm = 0;
}
else
{
/* d is denormalized */
i = bbits + be + (Bias + (P - 1) - 1);
#if defined (_DOUBLE_IS_32BITS)
x = word0 (d) << (32 - i);
#else
x = (i > 32) ? (word0 (d) << (64 - i)) | (word1 (d) >> (i - 32))
: (word1 (d) << (32 - i));
#endif
d2.d = x;
word0 (d2) -= 31 * Exp_msk1; /* adjust exponent */
i -= (Bias + (P - 1) - 1) + 1;
denorm = 1;
}
#endif
#if defined (_DOUBLE_IS_32BITS)
ds = (d2.d - 1.5) * 0.289529651 + 0.176091269 + i * 0.30103001;
#else
ds = (d2.d - 1.5) * 0.289529654602168 + 0.1760912590558 + i * 0.301029995663981;
#endif
k = (int) ds;
if (ds < 0. && ds != k)
k--; /* want k = floor(ds) */
k_check = 1;
if (k >= 0 && k <= Ten_pmax)
{
if (d.d < tens[k])
k--;
k_check = 0;
}
j = bbits - i - 1;
if (j >= 0)
{
b2 = 0;
s2 = j;
}
else
{
b2 = -j;
s2 = 0;
}
if (k >= 0)
{
b5 = 0;
s5 = k;
s2 += k;
}
else
{
b2 -= k;
b5 = -k;
s5 = 0;
}
if (mode < 0 || mode > 9)
mode = 0;
try_quick = 1;
if (mode > 5)
{
mode -= 4;
try_quick = 0;
}
leftright = 1;
ilim = ilim1 = -1;
switch (mode)
{
case 0:
case 1:
i = 18;
ndigits = 0;
break;
case 2:
leftright = 0;
/* no break */
case 4:
if (ndigits <= 0)
ndigits = 1;
ilim = ilim1 = i = ndigits;
break;
case 3:
leftright = 0;
/* no break */
case 5:
i = ndigits + k + 1;
ilim = i;
ilim1 = i - 1;
if (i <= 0)
i = 1;
}
j = sizeof (__ULong);
for (_REENT_MP_RESULT_K(ptr) = 0; sizeof (_Bigint) - sizeof (__ULong) + j <= i;
j <<= 1)
_REENT_MP_RESULT_K(ptr)++;
_REENT_MP_RESULT(ptr) = eBalloc (ptr, _REENT_MP_RESULT_K(ptr));
s = s0 = (char *) _REENT_MP_RESULT(ptr);
if (ilim >= 0 && ilim <= Quick_max && try_quick)
{
/* Try to get by with floating-point arithmetic. */
i = 0;
d2.d = d.d;
k0 = k;
ilim0 = ilim;
ieps = 2; /* conservative */
if (k > 0)
{
ds = tens[k & 0xf];
j = k >> 4;
if (j & Bletch)
{
/* prevent overflows */
j &= Bletch - 1;
d.d /= bigtens[n_bigtens - 1];
ieps++;
}
for (; j; j >>= 1, i++)
if (j & 1)
{
ieps++;
ds *= bigtens[i];
}
d.d /= ds;
}
else if ((j1 = -k) != 0)
{
d.d *= tens[j1 & 0xf];
for (j = j1 >> 4; j; j >>= 1, i++)
if (j & 1)
{
ieps++;
d.d *= bigtens[i];
}
}
if (k_check && d.d < 1. && ilim > 0)
{
if (ilim1 <= 0)
goto fast_failed;
ilim = ilim1;
k--;
d.d *= 10.;
ieps++;
}
eps.d = ieps * d.d + 7.;
word0 (eps) -= (P - 1) * Exp_msk1;
if (ilim == 0)
{
S = mhi = 0;
d.d -= 5.;
if (d.d > eps.d)
goto one_digit;
if (d.d < -eps.d)
goto no_digits;
goto fast_failed;
}
#ifndef No_leftright
if (leftright)
{
/* Use Steele & White method of only
* generating digits needed.
*/
eps.d = 0.5 / tens[ilim - 1] - eps.d;
for (i = 0;;)
{
L = d.d;
d.d -= L;
*s++ = '0' + (int) L;
if (d.d < eps.d)
goto ret1;
if (1. - d.d < eps.d)
goto bump_up;
if (++i >= ilim)
break;
eps.d *= 10.;
d.d *= 10.;
}
}
else
{
#endif
/* Generate ilim digits, then fix them up. */
eps.d *= tens[ilim - 1];
for (i = 1;; i++, d.d *= 10.)
{
L = d.d;
d.d -= L;
*s++ = '0' + (int) L;
if (i == ilim)
{
if (d.d > 0.5 + eps.d)
goto bump_up;
else if (d.d < 0.5 - eps.d)
{
while (*--s == '0');
s++;
goto ret1;
}
break;
}
}
#ifndef No_leftright
}
#endif
fast_failed:
s = s0;
d.d = d2.d;
k = k0;
ilim = ilim0;
}
/* Do we have a "small" integer? */
if (be >= 0 && k <= Int_max)
{
/* Yes. */
ds = tens[k];
if (ndigits < 0 && ilim <= 0)
{
S = mhi = 0;
if (ilim < 0 || d.d <= 5 * ds)
goto no_digits;
goto one_digit;
}
for (i = 1;; i++)
{
L = d.d / ds;
d.d -= L * ds;
#ifdef Check_FLT_ROUNDS
/* If FLT_ROUNDS == 2, L will usually be high by 1 */
if (d.d < 0)
{
L--;
d.d += ds;
}
#endif
*s++ = '0' + (int) L;
if (i == ilim)
{
d.d += d.d;
if ((d.d > ds) || ((d.d == ds) && (L & 1)))
{
bump_up:
while (*--s == '9')
if (s == s0)
{
k++;
*s = '0';
break;
}
++*s++;
}
break;
}
if (!(d.d *= 10.))
break;
}
goto ret1;
}
m2 = b2;
m5 = b5;
mhi = mlo = 0;
if (leftright)
{
if (mode < 2)
{
i =
#ifndef Sudden_Underflow
denorm ? be + (Bias + (P - 1) - 1 + 1) :
#endif
#ifdef IBM
1 + 4 * P - 3 - bbits + ((bbits + be - 1) & 3);
#else
1 + P - bbits;
#endif
}
else
{
j = ilim - 1;
if (m5 >= j)
m5 -= j;
else
{
s5 += j -= m5;
b5 += j;
m5 = 0;
}
if ((i = ilim) < 0)
{
m2 -= i;
i = 0;
}
}
b2 += i;
s2 += i;
mhi = i2b (ptr, 1);
}
if (m2 > 0 && s2 > 0)
{
i = m2 < s2 ? m2 : s2;
b2 -= i;
m2 -= i;
s2 -= i;
}
if (b5 > 0)
{
if (leftright)
{
if (m5 > 0)
{
mhi = pow5mult (ptr, mhi, m5);
b1 = mult (ptr, mhi, b);
Bfree (ptr, b);
b = b1;
}
if ((j = b5 - m5) != 0)
b = pow5mult (ptr, b, j);
}
else
b = pow5mult (ptr, b, b5);
}
S = i2b (ptr, 1);
if (s5 > 0)
S = pow5mult (ptr, S, s5);
/* Check for special case that d is a normalized power of 2. */
spec_case = 0;
if (mode < 2)
{
if (!word1 (d) && !(word0 (d) & Bndry_mask)
#ifndef Sudden_Underflow
&& word0 (d) & Exp_mask
#endif
)
{
/* The special case */
b2 += Log2P;
s2 += Log2P;
spec_case = 1;
}
}
/* Arrange for convenient computation of quotients:
* shift left if necessary so divisor has 4 leading 0 bits.
*
* Perhaps we should just compute leading 28 bits of S once
* and for all and pass them and a shift to quorem, so it
* can do shifts and ors to compute the numerator for q.
*/
#ifdef Pack_32
if ((i = ((s5 ? 32 - hi0bits (S->_x[S->_wds - 1]) : 1) + s2) & 0x1f) != 0)
i = 32 - i;
#else
if ((i = ((s5 ? 32 - hi0bits (S->_x[S->_wds - 1]) : 1) + s2) & 0xf) != 0)
i = 16 - i;
#endif
if (i > 4)
{
i -= 4;
b2 += i;
m2 += i;
s2 += i;
}
else if (i < 4)
{
i += 28;
b2 += i;
m2 += i;
s2 += i;
}
if (b2 > 0)
b = lshift (ptr, b, b2);
if (s2 > 0)
S = lshift (ptr, S, s2);
if (k_check)
{
if (cmp (b, S) < 0)
{
k--;
b = multadd (ptr, b, 10, 0); /* we botched the k estimate */
if (leftright)
mhi = multadd (ptr, mhi, 10, 0);
ilim = ilim1;
}
}
if (ilim <= 0 && mode > 2)
{
if (ilim < 0 || cmp (b, S = multadd (ptr, S, 5, 0)) <= 0)
{
/* no digits, fcvt style */
no_digits:
k = -1 - ndigits;
goto ret;
}
one_digit:
*s++ = '1';
k++;
goto ret;
}
if (leftright)
{
if (m2 > 0)
mhi = lshift (ptr, mhi, m2);
/* Compute mlo -- check for special case
* that d is a normalized power of 2.
*/
mlo = mhi;
if (spec_case)
{
mhi = eBalloc (ptr, mhi->_k);
Bcopy (mhi, mlo);
mhi = lshift (ptr, mhi, Log2P);
}
for (i = 1;; i++)
{
dig = quorem (b, S) + '0';
/* Do we yet have the shortest decimal string
* that will round to d?
*/
j = cmp (b, mlo);
delta = diff (ptr, S, mhi);
j1 = delta->_sign ? 1 : cmp (b, delta);
Bfree (ptr, delta);
#ifndef ROUND_BIASED
if (j1 == 0 && !mode && !(word1 (d) & 1))
{
if (dig == '9')
goto round_9_up;
if (j > 0)
dig++;
*s++ = dig;
goto ret;
}
#endif
if ((j < 0) || ((j == 0) && !mode
#ifndef ROUND_BIASED
&& !(word1 (d) & 1)
#endif
))
{
if (j1 > 0)
{
b = lshift (ptr, b, 1);
j1 = cmp (b, S);
if (((j1 > 0) || ((j1 == 0) && (dig & 1)))
&& dig++ == '9')
goto round_9_up;
}
*s++ = dig;
goto ret;
}
if (j1 > 0)
{
if (dig == '9')
{ /* possible if i == 1 */
round_9_up:
*s++ = '9';
goto roundoff;
}
*s++ = dig + 1;
goto ret;
}
*s++ = dig;
if (i == ilim)
break;
b = multadd (ptr, b, 10, 0);
if (mlo == mhi)
mlo = mhi = multadd (ptr, mhi, 10, 0);
else
{
mlo = multadd (ptr, mlo, 10, 0);
mhi = multadd (ptr, mhi, 10, 0);
}
}
}
else
for (i = 1;; i++)
{
*s++ = dig = quorem (b, S) + '0';
if (i >= ilim)
break;
b = multadd (ptr, b, 10, 0);
}
/* Round off last digit */
b = lshift (ptr, b, 1);
j = cmp (b, S);
if ((j > 0) || ((j == 0) && (dig & 1)))
{
roundoff:
while (*--s == '9')
if (s == s0)
{
k++;
*s++ = '1';
goto ret;
}
++*s++;
}
else
{
while (*--s == '0');
s++;
}
ret:
Bfree (ptr, S);
if (mhi)
{
if (mlo && mlo != mhi)
Bfree (ptr, mlo);
Bfree (ptr, mhi);
}
ret1:
Bfree (ptr, b);
*s = 0;
*decpt = k + 1;
if (rve)
*rve = s;
return s0;
}
|