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1 /* $NetBSD: gdtoa.c,v 1.1.1.1.4.1.4.1 2008/04/08 21:10:55 jdc Exp $ */
3 /****************************************************************
5 The author of this software is David M. Gay.
7 Copyright (C) 1998, 1999 by Lucent Technologies
10 Permission to use, copy, modify, and distribute this software and
11 its documentation for any purpose and without fee is hereby
12 granted, provided that the above copyright notice appear in all
13 copies and that both that the copyright notice and this
14 permission notice and warranty disclaimer appear in supporting
15 documentation, and that the name of Lucent or any of its entities
16 not be used in advertising or publicity pertaining to
17 distribution of the software without specific, written prior
20 LUCENT DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE,
21 INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS.
22 IN NO EVENT SHALL LUCENT OR ANY OF ITS ENTITIES BE LIABLE FOR ANY
23 SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
24 WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER
25 IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION,
26 ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF
29 ****************************************************************/
31 /* Please send bug reports to David M. Gay (dmg at acm dot org,
32 * with " at " changed at "@" and " dot " changed to "."). */
33 #include <LibConfig.h>
38 /* Disable warnings about conversions to narrower data types. */
39 #pragma warning ( disable : 4244 )
40 // Squelch bogus warnings about uninitialized variable use.
41 #pragma warning ( disable : 4701 )
45 bitstob(ULong
*bits
, int nbits
, int *bbits
)
64 be
= bits
+ (((unsigned int)nbits
- 1) >> kshift
);
67 *x
++ = *bits
& ALL_ON
;
69 *x
++ = (*bits
>> 16) & ALL_ON
;
71 } while(++bits
<= be
);
80 *bbits
= i
*ULbits
+ 32 - hi0bits(b
->x
[i
]);
85 /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
87 * Inspired by "How to Print Floating-Point Numbers Accurately" by
88 * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
91 * 1. Rather than iterating, we use a simple numeric overestimate
92 * to determine k = floor(log10(d)). We scale relevant
93 * quantities using O(log2(k)) rather than O(k) multiplications.
94 * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
95 * try to generate digits strictly left to right. Instead, we
96 * compute with fewer bits and propagate the carry if necessary
97 * when rounding the final digit up. This is often faster.
98 * 3. Under the assumption that input will be rounded nearest,
99 * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
100 * That is, we allow equality in stopping tests when the
101 * round-nearest rule will give the same floating-point value
102 * as would satisfaction of the stopping test with strict
104 * 4. We remove common factors of powers of 2 from relevant
106 * 5. When converting floating-point integers less than 1e16,
107 * we use floating-point arithmetic rather than resorting
108 * to multiple-precision integers.
109 * 6. When asked to produce fewer than 15 digits, we first try
110 * to get by with floating-point arithmetic; we resort to
111 * multiple-precision integer arithmetic only if we cannot
112 * guarantee that the floating-point calculation has given
113 * the correctly rounded result. For k requested digits and
114 * "uniformly" distributed input, the probability is
115 * something like 10^(k-15) that we must resort to the Long
121 (FPI
*fpi
, int be
, ULong
*bits
, int *kindp
, int mode
, int ndigits
, int *decpt
, char **rve
)
123 /* Arguments ndigits and decpt are similar to the second and third
124 arguments of ecvt and fcvt; trailing zeros are suppressed from
125 the returned string. If not null, *rve is set to point
126 to the end of the return value. If d is +-Infinity or NaN,
127 then *decpt is set to 9999.
130 0 ==> shortest string that yields d when read in
131 and rounded to nearest.
132 1 ==> like 0, but with Steele & White stopping rule;
133 e.g. with IEEE P754 arithmetic , mode 0 gives
134 1e23 whereas mode 1 gives 9.999999999999999e22.
135 2 ==> max(1,ndigits) significant digits. This gives a
136 return value similar to that of ecvt, except
137 that trailing zeros are suppressed.
138 3 ==> through ndigits past the decimal point. This
139 gives a return value similar to that from fcvt,
140 except that trailing zeros are suppressed, and
141 ndigits can be negative.
142 4-9 should give the same return values as 2-3, i.e.,
143 4 <= mode <= 9 ==> same return as mode
144 2 + (mode & 1). These modes are mainly for
145 debugging; often they run slower but sometimes
146 faster than modes 2-3.
147 4,5,8,9 ==> left-to-right digit generation.
148 6-9 ==> don't try fast floating-point estimate
151 Values of mode other than 0-9 are treated as mode 0.
153 Sufficient space is allocated to the return value
154 to hold the suppressed trailing zeros.
157 int bbits
, b2
, b5
, be0
, dig
, i
, ieps
, ilim
= 0, ilim0
, ilim1
= 0, inex
;
158 int j
, jj1
, k
, k0
, k_check
, kind
, leftright
, m2
, m5
, nbits
;
159 int rdir
, s2
, s5
, spec_case
, try_quick
;
161 Bigint
*b
, *b1
, *delta
, *mlo
, *mhi
, *mhi1
, *S
;
162 double d
, d2
, ds
, eps
;
165 #ifndef MULTIPLE_THREADS
167 freedtoa(dtoa_result
);
172 if (*kindp
& STRTOG_NoMemory
)
174 kind
= *kindp
&= ~STRTOG_Inexact
;
175 switch(kind
& STRTOG_Retmask
) {
179 case STRTOG_Denormal
:
181 case STRTOG_Infinite
:
183 return nrv_alloc("Infinity", rve
, 8);
186 return nrv_alloc("NaN", rve
, 3);
190 b
= bitstob(bits
, nbits
= fpi
->nbits
, &bbits
);
194 if ( (i
= trailz(b
)) !=0) {
203 return nrv_alloc("0", rve
, 1);
206 dval(d
) = b2d(b
, &i
);
208 word0(d
) &= Frac_mask1
;
211 if ( (j
= 11 - hi0bits(word0(d
) & Frac_mask
)) !=0)
215 /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
216 * log10(x) = log(x) / log(10)
217 * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
218 * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
220 * This suggests computing an approximation k to log10(d) by
222 * k = (i - Bias)*0.301029995663981
223 * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
225 * We want k to be too large rather than too small.
226 * The error in the first-order Taylor series approximation
227 * is in our favor, so we just round up the constant enough
228 * to compensate for any error in the multiplication of
229 * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
230 * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
231 * adding 1e-13 to the constant term more than suffices.
232 * Hence we adjust the constant term to 0.1760912590558.
233 * (We could get a more accurate k by invoking log10,
234 * but this is probably not worthwhile.)
240 ds
= (dval(d
)-1.5)*0.289529654602168 + 0.1760912590558 + i
*0.301029995663981;
242 /* correct assumption about exponent range */
249 if (ds
< 0. && ds
!= k
)
250 k
--; /* want k = floor(ds) */
254 if ( (jj1
= j
& 3) !=0)
256 word0(d
) += j
<< Exp_shift
- 2 & Exp_mask
;
258 word0(d
) += (be
+ bbits
- 1) << Exp_shift
;
260 if (k
>= 0 && k
<= Ten_pmax
) {
261 if (dval(d
) < tens
[k
])
284 if (mode
< 0 || mode
> 9)
296 i
= (int)(nbits
* .30103) + 3;
305 ilim
= ilim1
= i
= ndigits
;
317 s
= s0
= rv_alloc((size_t)i
);
321 if ( (rdir
= fpi
->rounding
- 1) !=0) {
324 if (kind
& STRTOG_Neg
)
328 /* Now rdir = 0 ==> round near, 1 ==> round up, 2 ==> round down. */
330 if (ilim
>= 0 && ilim
<= Quick_max
&& try_quick
&& !rdir
331 #ifndef IMPRECISE_INEXACT
336 /* Try to get by with floating-point arithmetic. */
341 if ( (j
= 11 - hi0bits(word0(d
) & Frac_mask
)) !=0)
346 ieps
= 2; /* conservative */
349 j
= (unsigned int)k
>> 4;
351 /* prevent overflows */
353 dval(d
) /= bigtens
[n_bigtens
-1];
356 for(; j
; j
/= 2, i
++)
364 if ( (jj1
= -k
) !=0) {
365 dval(d
) *= tens
[jj1
& 0xf];
366 for(j
= jj1
>> 4; j
; j
>>= 1, i
++)
369 dval(d
) *= bigtens
[i
];
373 if (k_check
&& dval(d
) < 1. && ilim
> 0) {
381 dval(eps
) = ieps
*dval(d
) + 7.;
382 word0(eps
) -= (P
-1)*Exp_msk1
;
386 if (dval(d
) > dval(eps
))
388 if (dval(d
) < -dval(eps
))
394 /* Use Steele & White method of only
395 * generating digits needed.
397 dval(eps
) = ds
*0.5/tens
[ilim
-1] - dval(eps
);
399 L
= (Long
)(dval(d
)/ds
);
402 if (dval(d
) < dval(eps
)) {
404 inex
= STRTOG_Inexlo
;
407 if (ds
- dval(d
) < dval(eps
))
417 /* Generate ilim digits, then fix them up. */
418 dval(eps
) *= tens
[ilim
-1];
419 for(i
= 1;; i
++, dval(d
) *= 10.) {
420 if ( (L
= (Long
)(dval(d
)/ds
)) !=0)
425 if (dval(d
) > ds
+ dval(eps
))
427 else if (dval(d
) < ds
- dval(eps
)) {
431 inex
= STRTOG_Inexlo
;
447 /* Do we have a "small" integer? */
449 if (be
>= 0 && k
<= Int_max
) {
452 if (ndigits
< 0 && ilim
<= 0) {
454 if (ilim
< 0 || dval(d
) <= 5*ds
)
458 for(i
= 1;; i
++, dval(d
) *= 10.) {
461 #ifdef Check_FLT_ROUNDS
462 /* If FLT_ROUNDS == 2, L will usually be high by 1 */
475 inex
= STRTOG_Inexlo
;
479 if (dval(d
) > ds
|| (dval(d
) == ds
&& L
& 1)) {
481 inex
= STRTOG_Inexhi
;
491 inex
= STRTOG_Inexlo
;
504 if (be
- i
++ < fpi
->emin
)
506 i
= be
- fpi
->emin
+ 1;
517 if ((i
= ilim
) < 0) {
526 if (m2
> 0 && s2
> 0) {
527 i
= m2
< s2
? m2
: s2
;
535 mhi
= pow5mult(mhi
, m5
);
544 if ( (j
= b5
- m5
) !=0) {
565 /* Check for special case that d is a normalized power of 2. */
569 if (bbits
== 1 && be0
> fpi
->emin
+ 1) {
570 /* The special case */
577 /* Arrange for convenient computation of quotients:
578 * shift left if necessary so divisor has 4 leading 0 bits.
580 * Perhaps we should just compute leading 28 bits of S once
581 * and for all and pass them and a shift to quorem, so it
582 * can do shifts and ors to compute the numerator for q.
585 if ( (i
= ((s5
? 32 - hi0bits(S
->x
[S
->wds
-1]) : 1) + s2
) & 0x1f) !=0)
588 if ( (i
= ((s5
? 32 - hi0bits(S
->x
[S
->wds
-1]) : 1) + s2
) & 0xf) !=0)
610 b
= multadd(b
, 10, 0); /* we botched the k estimate */
614 mhi
= multadd(mhi
, 10, 0);
621 if (ilim
<= 0 && mode
> 2) {
622 if (ilim
< 0 || cmp(b
,S
= multadd(S
,5,0)) <= 0) {
623 /* no digits, fcvt style */
626 inex
= STRTOG_Inexlo
;
630 inex
= STRTOG_Inexhi
;
637 mhi
= lshift(mhi
, m2
);
642 /* Compute mlo -- check for special case
643 * that d is a normalized power of 2.
648 mhi
= Balloc(mhi
->k
);
652 mhi
= lshift(mhi
, 1);
658 dig
= quorem(b
,S
) + '0';
659 /* Do we yet have the shortest decimal string
660 * that will round to d?
663 delta
= diff(S
, mhi
);
666 jj1
= delta
->sign
? 1 : cmp(b
, delta
);
669 if (jj1
== 0 && !mode
&& !(bits
[0] & 1) && !rdir
) {
673 if (b
->wds
> 1 || b
->x
[0])
674 inex
= STRTOG_Inexlo
;
678 inex
= STRTOG_Inexhi
;
684 if (j
< 0 || (j
== 0 && !mode
689 if (rdir
&& (b
->wds
> 1 || b
->x
[0])) {
691 inex
= STRTOG_Inexlo
;
694 while (cmp(S
,mhi
) > 0) {
696 mhi1
= multadd(mhi
, 10, 0);
702 b
= multadd(b
, 10, 0);
705 dig
= quorem(b
,S
) + '0';
709 inex
= STRTOG_Inexhi
;
717 if ((jj1
> 0 || (jj1
== 0 && dig
& 1))
720 inex
= STRTOG_Inexhi
;
722 if (b
->wds
> 1 || b
->x
[0])
723 inex
= STRTOG_Inexlo
;
728 if (jj1
> 0 && rdir
!= 2) {
729 if (dig
== '9') { /* possible if i == 1 */
732 inex
= STRTOG_Inexhi
;
735 inex
= STRTOG_Inexhi
;
742 b
= multadd(b
, 10, 0);
746 mlo
= mhi
= multadd(mhi
, 10, 0);
751 mlo
= multadd(mlo
, 10, 0);
754 mhi
= multadd(mhi
, 10, 0);
762 *s
++ = dig
= quorem(b
,S
) + '0';
765 b
= multadd(b
, 10, 0);
770 /* Round off last digit */
773 if (rdir
== 2 || (b
->wds
<= 1 && !b
->x
[0]))
781 if (j
> 0 || (j
== 0 && dig
& 1)) {
783 inex
= STRTOG_Inexhi
;
794 if (b
->wds
> 1 || b
->x
[0])
795 inex
= STRTOG_Inexlo
;
802 if (mlo
&& mlo
!= mhi
)