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98994639
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1/* numeric.c
2 *
3 * Copyright (c) 2001, Larry Wall
4 *
5 * You may distribute under the terms of either the GNU General Public
6 * License or the Artistic License, as specified in the README file.
7 *
8 */
9
10/*
11 * "That only makes eleven (plus one mislaid) and not fourteen, unless
12 * wizards count differently to other people."
13 */
14
15#include "EXTERN.h"
16#define PERL_IN_NUMERIC_C
17#include "perl.h"
18
19U32
20Perl_cast_ulong(pTHX_ NV f)
21{
22 if (f < 0.0)
23 return f < I32_MIN ? (U32) I32_MIN : (U32)(I32) f;
24 if (f < U32_MAX_P1) {
25#if CASTFLAGS & 2
26 if (f < U32_MAX_P1_HALF)
27 return (U32) f;
28 f -= U32_MAX_P1_HALF;
29 return ((U32) f) | (1 + U32_MAX >> 1);
30#else
31 return (U32) f;
32#endif
33 }
34 return f > 0 ? U32_MAX : 0 /* NaN */;
35}
36
37I32
38Perl_cast_i32(pTHX_ NV f)
39{
40 if (f < I32_MAX_P1)
41 return f < I32_MIN ? I32_MIN : (I32) f;
42 if (f < U32_MAX_P1) {
43#if CASTFLAGS & 2
44 if (f < U32_MAX_P1_HALF)
45 return (I32)(U32) f;
46 f -= U32_MAX_P1_HALF;
47 return (I32)(((U32) f) | (1 + U32_MAX >> 1));
48#else
49 return (I32)(U32) f;
50#endif
51 }
52 return f > 0 ? (I32)U32_MAX : 0 /* NaN */;
53}
54
55IV
56Perl_cast_iv(pTHX_ NV f)
57{
58 if (f < IV_MAX_P1)
59 return f < IV_MIN ? IV_MIN : (IV) f;
60 if (f < UV_MAX_P1) {
61#if CASTFLAGS & 2
62 /* For future flexibility allowing for sizeof(UV) >= sizeof(IV) */
63 if (f < UV_MAX_P1_HALF)
64 return (IV)(UV) f;
65 f -= UV_MAX_P1_HALF;
66 return (IV)(((UV) f) | (1 + UV_MAX >> 1));
67#else
68 return (IV)(UV) f;
69#endif
70 }
71 return f > 0 ? (IV)UV_MAX : 0 /* NaN */;
72}
73
74UV
75Perl_cast_uv(pTHX_ NV f)
76{
77 if (f < 0.0)
78 return f < IV_MIN ? (UV) IV_MIN : (UV)(IV) f;
79 if (f < UV_MAX_P1) {
80#if CASTFLAGS & 2
81 if (f < UV_MAX_P1_HALF)
82 return (UV) f;
83 f -= UV_MAX_P1_HALF;
84 return ((UV) f) | (1 + UV_MAX >> 1);
85#else
86 return (UV) f;
87#endif
88 }
89 return f > 0 ? UV_MAX : 0 /* NaN */;
90}
91
92#if defined(HUGE_VAL) || (defined(USE_LONG_DOUBLE) && defined(HUGE_VALL))
93/*
94 * This hack is to force load of "huge" support from libm.a
95 * So it is in perl for (say) POSIX to use.
96 * Needed for SunOS with Sun's 'acc' for example.
97 */
98NV
99Perl_huge(void)
100{
101# if defined(USE_LONG_DOUBLE) && defined(HUGE_VALL)
102 return HUGE_VALL;
103# endif
104 return HUGE_VAL;
105}
106#endif
107
108NV
109Perl_scan_bin(pTHX_ char *start, STRLEN len, STRLEN *retlen)
110{
111 register char *s = start;
112 register NV rnv = 0.0;
113 register UV ruv = 0;
114 register bool seenb = FALSE;
115 register bool overflowed = FALSE;
116
117 for (; len-- && *s; s++) {
118 if (!(*s == '0' || *s == '1')) {
119 if (*s == '_' && len && *retlen
120 && (s[1] == '0' || s[1] == '1'))
121 {
122 --len;
123 ++s;
124 }
125 else if (seenb == FALSE && *s == 'b' && ruv == 0) {
126 /* Disallow 0bbb0b0bbb... */
127 seenb = TRUE;
128 continue;
129 }
130 else {
131 if (ckWARN(WARN_DIGIT))
132 Perl_warner(aTHX_ WARN_DIGIT,
133 "Illegal binary digit '%c' ignored", *s);
134 break;
135 }
136 }
137 if (!overflowed) {
138 register UV xuv = ruv << 1;
139
140 if ((xuv >> 1) != ruv) {
141 overflowed = TRUE;
142 rnv = (NV) ruv;
143 if (ckWARN_d(WARN_OVERFLOW))
144 Perl_warner(aTHX_ WARN_OVERFLOW,
145 "Integer overflow in binary number");
146 }
147 else
148 ruv = xuv | (*s - '0');
149 }
150 if (overflowed) {
151 rnv *= 2;
152 /* If an NV has not enough bits in its mantissa to
153 * represent an UV this summing of small low-order numbers
154 * is a waste of time (because the NV cannot preserve
155 * the low-order bits anyway): we could just remember when
156 * did we overflow and in the end just multiply rnv by the
157 * right amount. */
158 rnv += (*s - '0');
159 }
160 }
161 if (!overflowed)
162 rnv = (NV) ruv;
163 if ( ( overflowed && rnv > 4294967295.0)
164#if UVSIZE > 4
165 || (!overflowed && ruv > 0xffffffff )
166#endif
167 ) {
168 if (ckWARN(WARN_PORTABLE))
169 Perl_warner(aTHX_ WARN_PORTABLE,
170 "Binary number > 0b11111111111111111111111111111111 non-portable");
171 }
172 *retlen = s - start;
173 return rnv;
174}
175
176NV
177Perl_scan_oct(pTHX_ char *start, STRLEN len, STRLEN *retlen)
178{
179 register char *s = start;
180 register NV rnv = 0.0;
181 register UV ruv = 0;
182 register bool overflowed = FALSE;
183
184 for (; len-- && *s; s++) {
185 if (!(*s >= '0' && *s <= '7')) {
186 if (*s == '_' && len && *retlen
187 && (s[1] >= '0' && s[1] <= '7'))
188 {
189 --len;
190 ++s;
191 }
192 else {
193 /* Allow \octal to work the DWIM way (that is, stop scanning
194 * as soon as non-octal characters are seen, complain only iff
195 * someone seems to want to use the digits eight and nine). */
196 if (*s == '8' || *s == '9') {
197 if (ckWARN(WARN_DIGIT))
198 Perl_warner(aTHX_ WARN_DIGIT,
199 "Illegal octal digit '%c' ignored", *s);
200 }
201 break;
202 }
203 }
204 if (!overflowed) {
205 register UV xuv = ruv << 3;
206
207 if ((xuv >> 3) != ruv) {
208 overflowed = TRUE;
209 rnv = (NV) ruv;
210 if (ckWARN_d(WARN_OVERFLOW))
211 Perl_warner(aTHX_ WARN_OVERFLOW,
212 "Integer overflow in octal number");
213 }
214 else
215 ruv = xuv | (*s - '0');
216 }
217 if (overflowed) {
218 rnv *= 8.0;
219 /* If an NV has not enough bits in its mantissa to
220 * represent an UV this summing of small low-order numbers
221 * is a waste of time (because the NV cannot preserve
222 * the low-order bits anyway): we could just remember when
223 * did we overflow and in the end just multiply rnv by the
224 * right amount of 8-tuples. */
225 rnv += (NV)(*s - '0');
226 }
227 }
228 if (!overflowed)
229 rnv = (NV) ruv;
230 if ( ( overflowed && rnv > 4294967295.0)
231#if UVSIZE > 4
232 || (!overflowed && ruv > 0xffffffff )
233#endif
234 ) {
235 if (ckWARN(WARN_PORTABLE))
236 Perl_warner(aTHX_ WARN_PORTABLE,
237 "Octal number > 037777777777 non-portable");
238 }
239 *retlen = s - start;
240 return rnv;
241}
242
243NV
244Perl_scan_hex(pTHX_ char *start, STRLEN len, STRLEN *retlen)
245{
246 register char *s = start;
247 register NV rnv = 0.0;
248 register UV ruv = 0;
249 register bool overflowed = FALSE;
250 char *hexdigit;
251
252 if (len > 2) {
253 if (s[0] == 'x') {
254 s++;
255 len--;
256 }
257 else if (len > 3 && s[0] == '0' && s[1] == 'x') {
258 s+=2;
259 len-=2;
260 }
261 }
262
263 for (; len-- && *s; s++) {
264 hexdigit = strchr((char *) PL_hexdigit, *s);
265 if (!hexdigit) {
266 if (*s == '_' && len && *retlen && s[1]
267 && (hexdigit = strchr((char *) PL_hexdigit, s[1])))
268 {
269 --len;
270 ++s;
271 }
272 else {
273 if (ckWARN(WARN_DIGIT))
274 Perl_warner(aTHX_ WARN_DIGIT,
275 "Illegal hexadecimal digit '%c' ignored", *s);
276 break;
277 }
278 }
279 if (!overflowed) {
280 register UV xuv = ruv << 4;
281
282 if ((xuv >> 4) != ruv) {
283 overflowed = TRUE;
284 rnv = (NV) ruv;
285 if (ckWARN_d(WARN_OVERFLOW))
286 Perl_warner(aTHX_ WARN_OVERFLOW,
287 "Integer overflow in hexadecimal number");
288 }
289 else
290 ruv = xuv | ((hexdigit - PL_hexdigit) & 15);
291 }
292 if (overflowed) {
293 rnv *= 16.0;
294 /* If an NV has not enough bits in its mantissa to
295 * represent an UV this summing of small low-order numbers
296 * is a waste of time (because the NV cannot preserve
297 * the low-order bits anyway): we could just remember when
298 * did we overflow and in the end just multiply rnv by the
299 * right amount of 16-tuples. */
300 rnv += (NV)((hexdigit - PL_hexdigit) & 15);
301 }
302 }
303 if (!overflowed)
304 rnv = (NV) ruv;
305 if ( ( overflowed && rnv > 4294967295.0)
306#if UVSIZE > 4
307 || (!overflowed && ruv > 0xffffffff )
308#endif
309 ) {
310 if (ckWARN(WARN_PORTABLE))
311 Perl_warner(aTHX_ WARN_PORTABLE,
312 "Hexadecimal number > 0xffffffff non-portable");
313 }
314 *retlen = s - start;
315 return rnv;
316}
317
318/*
319=for apidoc grok_numeric_radix
320
321Scan and skip for a numeric decimal separator (radix).
322
323=cut
324 */
325bool
326Perl_grok_numeric_radix(pTHX_ const char **sp, const char *send)
327{
328#ifdef USE_LOCALE_NUMERIC
329 if (PL_numeric_radix_sv && IN_LOCALE) {
330 STRLEN len;
331 char* radix = SvPV(PL_numeric_radix_sv, len);
332 if (*sp + len <= send && memEQ(*sp, radix, len)) {
333 *sp += len;
334 return TRUE;
335 }
336 }
337 /* always try "." if numeric radix didn't match because
338 * we may have data from different locales mixed */
339#endif
340 if (*sp < send && **sp == '.') {
341 ++*sp;
342 return TRUE;
343 }
344 return FALSE;
345}
346
347/*
348=for apidoc grok_number
349
350Recognise (or not) a number. The type of the number is returned
351(0 if unrecognised), otherwise it is a bit-ORed combination of
352IS_NUMBER_IN_UV, IS_NUMBER_GREATER_THAN_UV_MAX, IS_NUMBER_NOT_INT,
60939fb8
NC
353IS_NUMBER_NEG, IS_NUMBER_INFINITY (defined in perl.h).
354
355If the value of the number can fit an in UV, it is returned in the *valuep
356IS_NUMBER_IN_UV will be set to indicate that *valuep is valid, IS_NUMBER_IN_UV
357will never be set unless *valuep is valid, but *valuep may have been assigned
358to during processing even though IS_NUMBER_IN_UV is not set on return.
359If valuep is NULL, IS_NUMBER_IN_UV will be set for the same cases as when
360valuep is non-NULL, but no actual assignment (or SEGV) will occur.
361
362IS_NUMBER_NOT_INT will be set with IS_NUMBER_IN_UV if trailing decimals were
363seen (in which case *valuep gives the true value truncated to an integer), and
364IS_NUMBER_NEG if the number is negative (in which case *valuep holds the
365absolute value). IS_NUMBER_IN_UV is not set if e notation was used or the
366number is larger than a UV.
98994639
HS
367
368=cut
369 */
370int
371Perl_grok_number(pTHX_ const char *pv, STRLEN len, UV *valuep)
372{
60939fb8
NC
373 const char *s = pv;
374 const char *send = pv + len;
375 const UV max_div_10 = UV_MAX / 10;
376 const char max_mod_10 = UV_MAX % 10;
377 int numtype = 0;
378 int sawinf = 0;
379
380 while (s < send && isSPACE(*s))
381 s++;
382 if (s == send) {
383 return 0;
384 } else if (*s == '-') {
385 s++;
386 numtype = IS_NUMBER_NEG;
387 }
388 else if (*s == '+')
389 s++;
390
391 if (s == send)
392 return 0;
393
394 /* next must be digit or the radix separator or beginning of infinity */
395 if (isDIGIT(*s)) {
396 /* UVs are at least 32 bits, so the first 9 decimal digits cannot
397 overflow. */
398 UV value = *s - '0';
399 /* This construction seems to be more optimiser friendly.
400 (without it gcc does the isDIGIT test and the *s - '0' separately)
401 With it gcc on arm is managing 6 instructions (6 cycles) per digit.
402 In theory the optimiser could deduce how far to unroll the loop
403 before checking for overflow. */
58bb9ec3
NC
404 if (++s < send) {
405 int digit = *s - '0';
60939fb8
NC
406 if (digit >= 0 && digit <= 9) {
407 value = value * 10 + digit;
58bb9ec3
NC
408 if (++s < send) {
409 digit = *s - '0';
60939fb8
NC
410 if (digit >= 0 && digit <= 9) {
411 value = value * 10 + digit;
58bb9ec3
NC
412 if (++s < send) {
413 digit = *s - '0';
60939fb8
NC
414 if (digit >= 0 && digit <= 9) {
415 value = value * 10 + digit;
58bb9ec3
NC
416 if (++s < send) {
417 digit = *s - '0';
60939fb8
NC
418 if (digit >= 0 && digit <= 9) {
419 value = value * 10 + digit;
58bb9ec3
NC
420 if (++s < send) {
421 digit = *s - '0';
60939fb8
NC
422 if (digit >= 0 && digit <= 9) {
423 value = value * 10 + digit;
58bb9ec3
NC
424 if (++s < send) {
425 digit = *s - '0';
60939fb8
NC
426 if (digit >= 0 && digit <= 9) {
427 value = value * 10 + digit;
58bb9ec3
NC
428 if (++s < send) {
429 digit = *s - '0';
60939fb8
NC
430 if (digit >= 0 && digit <= 9) {
431 value = value * 10 + digit;
58bb9ec3
NC
432 if (++s < send) {
433 digit = *s - '0';
60939fb8
NC
434 if (digit >= 0 && digit <= 9) {
435 value = value * 10 + digit;
58bb9ec3 436 if (++s < send) {
60939fb8
NC
437 /* Now got 9 digits, so need to check
438 each time for overflow. */
58bb9ec3 439 digit = *s - '0';
60939fb8
NC
440 while (digit >= 0 && digit <= 9
441 && (value < max_div_10
442 || (value == max_div_10
443 && digit <= max_mod_10))) {
444 value = value * 10 + digit;
58bb9ec3
NC
445 if (++s < send)
446 digit = *s - '0';
60939fb8
NC
447 else
448 break;
449 }
450 if (digit >= 0 && digit <= 9
51bd16da 451 && (s < send)) {
60939fb8
NC
452 /* value overflowed.
453 skip the remaining digits, don't
454 worry about setting *valuep. */
455 do {
456 s++;
457 } while (s < send && isDIGIT(*s));
458 numtype |=
459 IS_NUMBER_GREATER_THAN_UV_MAX;
460 goto skip_value;
461 }
462 }
463 }
98994639 464 }
60939fb8
NC
465 }
466 }
467 }
468 }
469 }
470 }
471 }
472 }
473 }
474 }
475 }
98994639 476 }
60939fb8 477 }
98994639 478 }
60939fb8
NC
479 numtype |= IS_NUMBER_IN_UV;
480 if (valuep)
481 *valuep = value;
482
483 skip_value:
484 if (GROK_NUMERIC_RADIX(&s, send)) {
485 numtype |= IS_NUMBER_NOT_INT;
486 while (s < send && isDIGIT(*s)) /* optional digits after the radix */
487 s++;
98994639 488 }
60939fb8
NC
489 }
490 else if (GROK_NUMERIC_RADIX(&s, send)) {
491 numtype |= IS_NUMBER_NOT_INT | IS_NUMBER_IN_UV; /* valuep assigned below */
492 /* no digits before the radix means we need digits after it */
493 if (s < send && isDIGIT(*s)) {
494 do {
495 s++;
496 } while (s < send && isDIGIT(*s));
497 if (valuep) {
498 /* integer approximation is valid - it's 0. */
499 *valuep = 0;
500 }
98994639 501 }
60939fb8
NC
502 else
503 return 0;
504 } else if (*s == 'I' || *s == 'i') {
505 s++; if (s == send || (*s != 'N' && *s != 'n')) return 0;
506 s++; if (s == send || (*s != 'F' && *s != 'f')) return 0;
507 s++; if (s < send && (*s == 'I' || *s == 'i')) {
508 s++; if (s == send || (*s != 'N' && *s != 'n')) return 0;
509 s++; if (s == send || (*s != 'I' && *s != 'i')) return 0;
510 s++; if (s == send || (*s != 'T' && *s != 't')) return 0;
511 s++; if (s == send || (*s != 'Y' && *s != 'y')) return 0;
512 s++;
98994639 513 }
60939fb8
NC
514 sawinf = 1;
515 } else /* Add test for NaN here. */
98994639 516 return 0;
60939fb8
NC
517
518 if (sawinf) {
519 numtype &= IS_NUMBER_NEG; /* Keep track of sign */
520 numtype |= IS_NUMBER_INFINITY | IS_NUMBER_NOT_INT;
521 } else if (s < send) {
522 /* we can have an optional exponent part */
523 if (*s == 'e' || *s == 'E') {
524 /* The only flag we keep is sign. Blow away any "it's UV" */
525 numtype &= IS_NUMBER_NEG;
526 numtype |= IS_NUMBER_NOT_INT;
527 s++;
528 if (s < send && (*s == '-' || *s == '+'))
529 s++;
530 if (s < send && isDIGIT(*s)) {
531 do {
532 s++;
533 } while (s < send && isDIGIT(*s));
534 }
535 else
536 return 0;
537 }
538 }
539 while (s < send && isSPACE(*s))
540 s++;
541 if (s >= send)
542 return numtype;
543 if (len == 10 && memEQ(pv, "0 but true", 10)) {
544 if (valuep)
545 *valuep = 0;
546 return IS_NUMBER_IN_UV;
547 }
548 return 0;
98994639
HS
549}
550
551NV
552S_mulexp10(NV value, I32 exponent)
553{
554 NV result = 1.0;
555 NV power = 10.0;
556 bool negative = 0;
557 I32 bit;
558
559 if (exponent == 0)
560 return value;
561 else if (exponent < 0) {
562 negative = 1;
563 exponent = -exponent;
564 }
a333faaf
PP
565#ifdef __VAX /* avoid %SYSTEM-F-FLTOVF_F sans VAXC$ESTABLISH */
566# if defined(__DECC_VER) && __DECC_VER <= 50390006
567 /* __F_FLT_MAX_10_EXP - 5 == 33 */
568 if (!negative &&
569 (log10(value) + exponent) >= (__F_FLT_MAX_10_EXP - 5))
570 return NV_MAX;
571# endif
572#endif
98994639
HS
573 for (bit = 1; exponent; bit <<= 1) {
574 if (exponent & bit) {
575 exponent ^= bit;
576 result *= power;
577 }
578 power *= power;
579 }
580 return negative ? value / result : value * result;
581}
582
583NV
584Perl_my_atof(pTHX_ const char* s)
585{
586 NV x = 0.0;
587#ifdef USE_LOCALE_NUMERIC
588 if (PL_numeric_local && IN_LOCALE) {
589 NV y;
590
591 /* Scan the number twice; once using locale and once without;
592 * choose the larger result (in absolute value). */
593 Perl_atof2(aTHX_ s, &x);
594 SET_NUMERIC_STANDARD();
595 Perl_atof2(aTHX_ s, &y);
596 SET_NUMERIC_LOCAL();
597 if ((y < 0.0 && y < x) || (y > 0.0 && y > x))
598 return y;
599 }
600 else
601 Perl_atof2(aTHX_ s, &x);
602#else
603 Perl_atof2(aTHX_ s, &x);
604#endif
605 return x;
606}
607
608char*
609Perl_my_atof2(pTHX_ const char* orig, NV* value)
610{
611 NV result = 0.0;
612 bool negative = 0;
613 char* s = (char*)orig;
614 char* send = s + strlen(orig) - 1;
615 bool seendigit = 0;
616 I32 expextra = 0;
617 I32 exponent = 0;
618 I32 i;
619/* this is arbitrary */
620#define PARTLIM 6
621/* we want the largest integers we can usefully use */
622#if defined(HAS_QUAD) && defined(USE_64_BIT_INT)
623# define PARTSIZE ((int)TYPE_DIGITS(U64)-1)
624 U64 part[PARTLIM];
625#else
626# define PARTSIZE ((int)TYPE_DIGITS(U32)-1)
627 U32 part[PARTLIM];
628#endif
629 I32 ipart = 0; /* index into part[] */
630 I32 offcount; /* number of digits in least significant part */
631
96a05aee
HS
632 /* leading whitespace */
633 while (isSPACE(*s))
634 ++s;
635
98994639
HS
636 /* sign */
637 switch (*s) {
638 case '-':
639 negative = 1;
640 /* fall through */
641 case '+':
642 ++s;
643 }
644
645 part[0] = offcount = 0;
646 if (isDIGIT(*s)) {
647 seendigit = 1; /* get this over with */
648
649 /* skip leading zeros */
650 while (*s == '0')
651 ++s;
652 }
653
654 /* integer digits */
655 while (isDIGIT(*s)) {
656 if (++offcount > PARTSIZE) {
657 if (++ipart < PARTLIM) {
658 part[ipart] = 0;
659 offcount = 1; /* ++0 */
660 }
661 else {
662 /* limits of precision reached */
663 --ipart;
664 --offcount;
665 if (*s >= '5')
666 ++part[ipart];
667 while (isDIGIT(*s)) {
668 ++expextra;
669 ++s;
670 }
671 /* warn of loss of precision? */
672 break;
673 }
674 }
675 part[ipart] = part[ipart] * 10 + (*s++ - '0');
676 }
677
678 /* decimal point */
679 if (GROK_NUMERIC_RADIX((const char **)&s, send)) {
680 if (isDIGIT(*s))
681 seendigit = 1; /* get this over with */
682
683 /* decimal digits */
684 while (isDIGIT(*s)) {
685 if (++offcount > PARTSIZE) {
686 if (++ipart < PARTLIM) {
687 part[ipart] = 0;
688 offcount = 1; /* ++0 */
689 }
690 else {
691 /* limits of precision reached */
692 --ipart;
693 --offcount;
694 if (*s >= '5')
695 ++part[ipart];
696 while (isDIGIT(*s))
697 ++s;
698 /* warn of loss of precision? */
699 break;
700 }
701 }
702 --expextra;
703 part[ipart] = part[ipart] * 10 + (*s++ - '0');
704 }
705 }
706
707 /* combine components of mantissa */
708 for (i = 0; i <= ipart; ++i)
709 result += S_mulexp10((NV)part[ipart - i],
710 i ? offcount + (i - 1) * PARTSIZE : 0);
711
712 if (seendigit && (*s == 'e' || *s == 'E')) {
713 bool expnegative = 0;
714
715 ++s;
716 switch (*s) {
717 case '-':
718 expnegative = 1;
719 /* fall through */
720 case '+':
721 ++s;
722 }
723 while (isDIGIT(*s))
724 exponent = exponent * 10 + (*s++ - '0');
725 if (expnegative)
726 exponent = -exponent;
727 }
728
729 /* now apply the exponent */
730 exponent += expextra;
731 result = S_mulexp10(result, exponent);
732
733 /* now apply the sign */
734 if (negative)
735 result = -result;
736 *value = result;
737 return s;
738}
739