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grok_atoUV: allow non-C strings and document
[perl5.git] / numeric.c
CommitLineData
98994639
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1/* numeric.c
2 *
663f364b 3 * Copyright (C) 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001,
1129b882 4 * 2002, 2003, 2004, 2005, 2006, 2007, 2008 by Larry Wall and others
98994639
HS
5 *
6 * You may distribute under the terms of either the GNU General Public
7 * License or the Artistic License, as specified in the README file.
8 *
9 */
10
11/*
4ac71550
TC
12 * "That only makes eleven (plus one mislaid) and not fourteen,
13 * unless wizards count differently to other people." --Beorn
14 *
15 * [p.115 of _The Hobbit_: "Queer Lodgings"]
98994639
HS
16 */
17
ccfc67b7
JH
18/*
19=head1 Numeric functions
166f8a29 20
7fefc6c1
KW
21=cut
22
166f8a29
DM
23This file contains all the stuff needed by perl for manipulating numeric
24values, including such things as replacements for the OS's atof() function
25
ccfc67b7
JH
26*/
27
98994639
HS
28#include "EXTERN.h"
29#define PERL_IN_NUMERIC_C
30#include "perl.h"
31
32U32
ddeaf645 33Perl_cast_ulong(NV f)
98994639
HS
34{
35 if (f < 0.0)
36 return f < I32_MIN ? (U32) I32_MIN : (U32)(I32) f;
37 if (f < U32_MAX_P1) {
38#if CASTFLAGS & 2
39 if (f < U32_MAX_P1_HALF)
40 return (U32) f;
41 f -= U32_MAX_P1_HALF;
071db91b 42 return ((U32) f) | (1 + (U32_MAX >> 1));
98994639
HS
43#else
44 return (U32) f;
45#endif
46 }
47 return f > 0 ? U32_MAX : 0 /* NaN */;
48}
49
50I32
ddeaf645 51Perl_cast_i32(NV f)
98994639
HS
52{
53 if (f < I32_MAX_P1)
54 return f < I32_MIN ? I32_MIN : (I32) f;
55 if (f < U32_MAX_P1) {
56#if CASTFLAGS & 2
57 if (f < U32_MAX_P1_HALF)
58 return (I32)(U32) f;
59 f -= U32_MAX_P1_HALF;
071db91b 60 return (I32)(((U32) f) | (1 + (U32_MAX >> 1)));
98994639
HS
61#else
62 return (I32)(U32) f;
63#endif
64 }
65 return f > 0 ? (I32)U32_MAX : 0 /* NaN */;
66}
67
68IV
ddeaf645 69Perl_cast_iv(NV f)
98994639
HS
70{
71 if (f < IV_MAX_P1)
72 return f < IV_MIN ? IV_MIN : (IV) f;
73 if (f < UV_MAX_P1) {
74#if CASTFLAGS & 2
75 /* For future flexibility allowing for sizeof(UV) >= sizeof(IV) */
76 if (f < UV_MAX_P1_HALF)
77 return (IV)(UV) f;
78 f -= UV_MAX_P1_HALF;
071db91b 79 return (IV)(((UV) f) | (1 + (UV_MAX >> 1)));
98994639
HS
80#else
81 return (IV)(UV) f;
82#endif
83 }
84 return f > 0 ? (IV)UV_MAX : 0 /* NaN */;
85}
86
87UV
ddeaf645 88Perl_cast_uv(NV f)
98994639
HS
89{
90 if (f < 0.0)
91 return f < IV_MIN ? (UV) IV_MIN : (UV)(IV) f;
92 if (f < UV_MAX_P1) {
93#if CASTFLAGS & 2
94 if (f < UV_MAX_P1_HALF)
95 return (UV) f;
96 f -= UV_MAX_P1_HALF;
071db91b 97 return ((UV) f) | (1 + (UV_MAX >> 1));
98994639
HS
98#else
99 return (UV) f;
100#endif
101 }
102 return f > 0 ? UV_MAX : 0 /* NaN */;
103}
104
53305cf1
NC
105/*
106=for apidoc grok_bin
98994639 107
53305cf1
NC
108converts a string representing a binary number to numeric form.
109
2d7f6611 110On entry C<start> and C<*len> give the string to scan, C<*flags> gives
796b6530 111conversion flags, and C<result> should be C<NULL> or a pointer to an NV.
53305cf1 112The scan stops at the end of the string, or the first invalid character.
2d7f6611 113Unless C<PERL_SCAN_SILENT_ILLDIGIT> is set in C<*flags>, encountering an
7b667b5f 114invalid character will also trigger a warning.
2d7f6611
KW
115On return C<*len> is set to the length of the scanned string,
116and C<*flags> gives output flags.
53305cf1 117
7fc63493 118If the value is <= C<UV_MAX> it is returned as a UV, the output flags are clear,
796b6530
KW
119and nothing is written to C<*result>. If the value is > C<UV_MAX>, C<grok_bin>
120returns C<UV_MAX>, sets C<PERL_SCAN_GREATER_THAN_UV_MAX> in the output flags,
2d7f6611 121and writes the value to C<*result> (or the value is discarded if C<result>
53305cf1
NC
122is NULL).
123
796b6530 124The binary number may optionally be prefixed with C<"0b"> or C<"b"> unless
2d7f6611
KW
125C<PERL_SCAN_DISALLOW_PREFIX> is set in C<*flags> on entry. If
126C<PERL_SCAN_ALLOW_UNDERSCORES> is set in C<*flags> then the binary
796b6530 127number may use C<"_"> characters to separate digits.
53305cf1
NC
128
129=cut
02470786
KW
130
131Not documented yet because experimental is C<PERL_SCAN_SILENT_NON_PORTABLE
132which suppresses any message for non-portable numbers that are still valid
133on this platform.
53305cf1
NC
134 */
135
136UV
7918f24d
NC
137Perl_grok_bin(pTHX_ const char *start, STRLEN *len_p, I32 *flags, NV *result)
138{
53305cf1
NC
139 const char *s = start;
140 STRLEN len = *len_p;
141 UV value = 0;
142 NV value_nv = 0;
143
144 const UV max_div_2 = UV_MAX / 2;
f2338a2e 145 const bool allow_underscores = cBOOL(*flags & PERL_SCAN_ALLOW_UNDERSCORES);
53305cf1 146 bool overflowed = FALSE;
7fc63493 147 char bit;
53305cf1 148
7918f24d
NC
149 PERL_ARGS_ASSERT_GROK_BIN;
150
a4c04bdc
NC
151 if (!(*flags & PERL_SCAN_DISALLOW_PREFIX)) {
152 /* strip off leading b or 0b.
153 for compatibility silently suffer "b" and "0b" as valid binary
154 numbers. */
155 if (len >= 1) {
305b8651 156 if (isALPHA_FOLD_EQ(s[0], 'b')) {
a4c04bdc
NC
157 s++;
158 len--;
159 }
305b8651 160 else if (len >= 2 && s[0] == '0' && (isALPHA_FOLD_EQ(s[1], 'b'))) {
a4c04bdc
NC
161 s+=2;
162 len-=2;
163 }
164 }
53305cf1
NC
165 }
166
7fc63493 167 for (; len-- && (bit = *s); s++) {
53305cf1
NC
168 if (bit == '0' || bit == '1') {
169 /* Write it in this wonky order with a goto to attempt to get the
170 compiler to make the common case integer-only loop pretty tight.
171 With gcc seems to be much straighter code than old scan_bin. */
172 redo:
173 if (!overflowed) {
174 if (value <= max_div_2) {
175 value = (value << 1) | (bit - '0');
176 continue;
177 }
178 /* Bah. We're just overflowed. */
dcbac5bb 179 /* diag_listed_as: Integer overflow in %s number */
9b387841
NC
180 Perl_ck_warner_d(aTHX_ packWARN(WARN_OVERFLOW),
181 "Integer overflow in binary number");
53305cf1
NC
182 overflowed = TRUE;
183 value_nv = (NV) value;
184 }
185 value_nv *= 2.0;
98994639 186 /* If an NV has not enough bits in its mantissa to
d1be9408 187 * represent a UV this summing of small low-order numbers
98994639
HS
188 * is a waste of time (because the NV cannot preserve
189 * the low-order bits anyway): we could just remember when
53305cf1 190 * did we overflow and in the end just multiply value_nv by the
98994639 191 * right amount. */
53305cf1
NC
192 value_nv += (NV)(bit - '0');
193 continue;
194 }
195 if (bit == '_' && len && allow_underscores && (bit = s[1])
196 && (bit == '0' || bit == '1'))
98994639
HS
197 {
198 --len;
199 ++s;
53305cf1 200 goto redo;
98994639 201 }
a2a5de95
NC
202 if (!(*flags & PERL_SCAN_SILENT_ILLDIGIT))
203 Perl_ck_warner(aTHX_ packWARN(WARN_DIGIT),
204 "Illegal binary digit '%c' ignored", *s);
53305cf1 205 break;
98994639 206 }
53305cf1
NC
207
208 if ( ( overflowed && value_nv > 4294967295.0)
98994639 209#if UVSIZE > 4
02470786
KW
210 || (!overflowed && value > 0xffffffff
211 && ! (*flags & PERL_SCAN_SILENT_NON_PORTABLE))
98994639
HS
212#endif
213 ) {
a2a5de95
NC
214 Perl_ck_warner(aTHX_ packWARN(WARN_PORTABLE),
215 "Binary number > 0b11111111111111111111111111111111 non-portable");
53305cf1
NC
216 }
217 *len_p = s - start;
218 if (!overflowed) {
219 *flags = 0;
220 return value;
98994639 221 }
53305cf1
NC
222 *flags = PERL_SCAN_GREATER_THAN_UV_MAX;
223 if (result)
224 *result = value_nv;
225 return UV_MAX;
98994639
HS
226}
227
53305cf1
NC
228/*
229=for apidoc grok_hex
230
231converts a string representing a hex number to numeric form.
232
2d7f6611 233On entry C<start> and C<*len_p> give the string to scan, C<*flags> gives
796b6530 234conversion flags, and C<result> should be C<NULL> or a pointer to an NV.
7b667b5f 235The scan stops at the end of the string, or the first invalid character.
2d7f6611 236Unless C<PERL_SCAN_SILENT_ILLDIGIT> is set in C<*flags>, encountering an
7b667b5f 237invalid character will also trigger a warning.
2d7f6611
KW
238On return C<*len> is set to the length of the scanned string,
239and C<*flags> gives output flags.
53305cf1 240
796b6530
KW
241If the value is <= C<UV_MAX> it is returned as a UV, the output flags are clear,
242and nothing is written to C<*result>. If the value is > C<UV_MAX>, C<grok_hex>
243returns C<UV_MAX>, sets C<PERL_SCAN_GREATER_THAN_UV_MAX> in the output flags,
2d7f6611 244and writes the value to C<*result> (or the value is discarded if C<result>
796b6530 245is C<NULL>).
53305cf1 246
796b6530 247The hex number may optionally be prefixed with C<"0x"> or C<"x"> unless
2d7f6611
KW
248C<PERL_SCAN_DISALLOW_PREFIX> is set in C<*flags> on entry. If
249C<PERL_SCAN_ALLOW_UNDERSCORES> is set in C<*flags> then the hex
796b6530 250number may use C<"_"> characters to separate digits.
53305cf1
NC
251
252=cut
02470786
KW
253
254Not documented yet because experimental is C<PERL_SCAN_SILENT_NON_PORTABLE
baf48926 255which suppresses any message for non-portable numbers, but which are valid
02470786 256on this platform.
53305cf1
NC
257 */
258
259UV
7918f24d
NC
260Perl_grok_hex(pTHX_ const char *start, STRLEN *len_p, I32 *flags, NV *result)
261{
53305cf1
NC
262 const char *s = start;
263 STRLEN len = *len_p;
264 UV value = 0;
265 NV value_nv = 0;
53305cf1 266 const UV max_div_16 = UV_MAX / 16;
f2338a2e 267 const bool allow_underscores = cBOOL(*flags & PERL_SCAN_ALLOW_UNDERSCORES);
53305cf1 268 bool overflowed = FALSE;
98994639 269
7918f24d
NC
270 PERL_ARGS_ASSERT_GROK_HEX;
271
a4c04bdc
NC
272 if (!(*flags & PERL_SCAN_DISALLOW_PREFIX)) {
273 /* strip off leading x or 0x.
274 for compatibility silently suffer "x" and "0x" as valid hex numbers.
275 */
276 if (len >= 1) {
305b8651 277 if (isALPHA_FOLD_EQ(s[0], 'x')) {
a4c04bdc
NC
278 s++;
279 len--;
280 }
305b8651 281 else if (len >= 2 && s[0] == '0' && (isALPHA_FOLD_EQ(s[1], 'x'))) {
a4c04bdc
NC
282 s+=2;
283 len-=2;
284 }
285 }
98994639
HS
286 }
287
288 for (; len-- && *s; s++) {
626ef089 289 if (isXDIGIT(*s)) {
53305cf1
NC
290 /* Write it in this wonky order with a goto to attempt to get the
291 compiler to make the common case integer-only loop pretty tight.
292 With gcc seems to be much straighter code than old scan_hex. */
293 redo:
294 if (!overflowed) {
295 if (value <= max_div_16) {
626ef089 296 value = (value << 4) | XDIGIT_VALUE(*s);
53305cf1
NC
297 continue;
298 }
299 /* Bah. We're just overflowed. */
dcbac5bb 300 /* diag_listed_as: Integer overflow in %s number */
9b387841
NC
301 Perl_ck_warner_d(aTHX_ packWARN(WARN_OVERFLOW),
302 "Integer overflow in hexadecimal number");
53305cf1
NC
303 overflowed = TRUE;
304 value_nv = (NV) value;
305 }
306 value_nv *= 16.0;
307 /* If an NV has not enough bits in its mantissa to
d1be9408 308 * represent a UV this summing of small low-order numbers
53305cf1
NC
309 * is a waste of time (because the NV cannot preserve
310 * the low-order bits anyway): we could just remember when
311 * did we overflow and in the end just multiply value_nv by the
312 * right amount of 16-tuples. */
626ef089 313 value_nv += (NV) XDIGIT_VALUE(*s);
53305cf1
NC
314 continue;
315 }
316 if (*s == '_' && len && allow_underscores && s[1]
626ef089 317 && isXDIGIT(s[1]))
98994639
HS
318 {
319 --len;
320 ++s;
53305cf1 321 goto redo;
98994639 322 }
a2a5de95
NC
323 if (!(*flags & PERL_SCAN_SILENT_ILLDIGIT))
324 Perl_ck_warner(aTHX_ packWARN(WARN_DIGIT),
53305cf1
NC
325 "Illegal hexadecimal digit '%c' ignored", *s);
326 break;
327 }
328
329 if ( ( overflowed && value_nv > 4294967295.0)
330#if UVSIZE > 4
02470786
KW
331 || (!overflowed && value > 0xffffffff
332 && ! (*flags & PERL_SCAN_SILENT_NON_PORTABLE))
53305cf1
NC
333#endif
334 ) {
a2a5de95
NC
335 Perl_ck_warner(aTHX_ packWARN(WARN_PORTABLE),
336 "Hexadecimal number > 0xffffffff non-portable");
53305cf1
NC
337 }
338 *len_p = s - start;
339 if (!overflowed) {
340 *flags = 0;
341 return value;
342 }
343 *flags = PERL_SCAN_GREATER_THAN_UV_MAX;
344 if (result)
345 *result = value_nv;
346 return UV_MAX;
347}
348
349/*
350=for apidoc grok_oct
351
7b667b5f
MHM
352converts a string representing an octal number to numeric form.
353
2d7f6611 354On entry C<start> and C<*len> give the string to scan, C<*flags> gives
796b6530 355conversion flags, and C<result> should be C<NULL> or a pointer to an NV.
7b667b5f 356The scan stops at the end of the string, or the first invalid character.
2d7f6611 357Unless C<PERL_SCAN_SILENT_ILLDIGIT> is set in C<*flags>, encountering an
154bd527 3588 or 9 will also trigger a warning.
2d7f6611
KW
359On return C<*len> is set to the length of the scanned string,
360and C<*flags> gives output flags.
7b667b5f 361
796b6530
KW
362If the value is <= C<UV_MAX> it is returned as a UV, the output flags are clear,
363and nothing is written to C<*result>. If the value is > C<UV_MAX>, C<grok_oct>
364returns C<UV_MAX>, sets C<PERL_SCAN_GREATER_THAN_UV_MAX> in the output flags,
2d7f6611 365and writes the value to C<*result> (or the value is discarded if C<result>
796b6530 366is C<NULL>).
7b667b5f 367
2d7f6611 368If C<PERL_SCAN_ALLOW_UNDERSCORES> is set in C<*flags> then the octal
796b6530 369number may use C<"_"> characters to separate digits.
53305cf1
NC
370
371=cut
02470786 372
333ae27c
KW
373Not documented yet because experimental is C<PERL_SCAN_SILENT_NON_PORTABLE>
374which suppresses any message for non-portable numbers, but which are valid
02470786 375on this platform.
53305cf1
NC
376 */
377
378UV
7918f24d
NC
379Perl_grok_oct(pTHX_ const char *start, STRLEN *len_p, I32 *flags, NV *result)
380{
53305cf1
NC
381 const char *s = start;
382 STRLEN len = *len_p;
383 UV value = 0;
384 NV value_nv = 0;
53305cf1 385 const UV max_div_8 = UV_MAX / 8;
f2338a2e 386 const bool allow_underscores = cBOOL(*flags & PERL_SCAN_ALLOW_UNDERSCORES);
53305cf1
NC
387 bool overflowed = FALSE;
388
7918f24d
NC
389 PERL_ARGS_ASSERT_GROK_OCT;
390
53305cf1 391 for (; len-- && *s; s++) {
626ef089 392 if (isOCTAL(*s)) {
53305cf1
NC
393 /* Write it in this wonky order with a goto to attempt to get the
394 compiler to make the common case integer-only loop pretty tight.
395 */
396 redo:
397 if (!overflowed) {
398 if (value <= max_div_8) {
626ef089 399 value = (value << 3) | OCTAL_VALUE(*s);
53305cf1
NC
400 continue;
401 }
402 /* Bah. We're just overflowed. */
dcbac5bb 403 /* diag_listed_as: Integer overflow in %s number */
9b387841
NC
404 Perl_ck_warner_d(aTHX_ packWARN(WARN_OVERFLOW),
405 "Integer overflow in octal number");
53305cf1
NC
406 overflowed = TRUE;
407 value_nv = (NV) value;
408 }
409 value_nv *= 8.0;
98994639 410 /* If an NV has not enough bits in its mantissa to
d1be9408 411 * represent a UV this summing of small low-order numbers
98994639
HS
412 * is a waste of time (because the NV cannot preserve
413 * the low-order bits anyway): we could just remember when
53305cf1
NC
414 * did we overflow and in the end just multiply value_nv by the
415 * right amount of 8-tuples. */
626ef089 416 value_nv += (NV) OCTAL_VALUE(*s);
53305cf1
NC
417 continue;
418 }
626ef089
KW
419 if (*s == '_' && len && allow_underscores && isOCTAL(s[1])) {
420 --len;
421 ++s;
422 goto redo;
423 }
53305cf1 424 /* Allow \octal to work the DWIM way (that is, stop scanning
7b667b5f 425 * as soon as non-octal characters are seen, complain only if
626ef089
KW
426 * someone seems to want to use the digits eight and nine. Since we
427 * know it is not octal, then if isDIGIT, must be an 8 or 9). */
428 if (isDIGIT(*s)) {
a2a5de95
NC
429 if (!(*flags & PERL_SCAN_SILENT_ILLDIGIT))
430 Perl_ck_warner(aTHX_ packWARN(WARN_DIGIT),
431 "Illegal octal digit '%c' ignored", *s);
53305cf1
NC
432 }
433 break;
98994639 434 }
53305cf1
NC
435
436 if ( ( overflowed && value_nv > 4294967295.0)
98994639 437#if UVSIZE > 4
02470786
KW
438 || (!overflowed && value > 0xffffffff
439 && ! (*flags & PERL_SCAN_SILENT_NON_PORTABLE))
98994639
HS
440#endif
441 ) {
a2a5de95
NC
442 Perl_ck_warner(aTHX_ packWARN(WARN_PORTABLE),
443 "Octal number > 037777777777 non-portable");
53305cf1
NC
444 }
445 *len_p = s - start;
446 if (!overflowed) {
447 *flags = 0;
448 return value;
98994639 449 }
53305cf1
NC
450 *flags = PERL_SCAN_GREATER_THAN_UV_MAX;
451 if (result)
452 *result = value_nv;
453 return UV_MAX;
454}
455
456/*
457=for apidoc scan_bin
458
72d33970 459For backwards compatibility. Use C<grok_bin> instead.
53305cf1
NC
460
461=for apidoc scan_hex
462
72d33970 463For backwards compatibility. Use C<grok_hex> instead.
53305cf1
NC
464
465=for apidoc scan_oct
466
72d33970 467For backwards compatibility. Use C<grok_oct> instead.
53305cf1
NC
468
469=cut
470 */
471
472NV
73d840c0 473Perl_scan_bin(pTHX_ const char *start, STRLEN len, STRLEN *retlen)
53305cf1
NC
474{
475 NV rnv;
476 I32 flags = *retlen ? PERL_SCAN_ALLOW_UNDERSCORES : 0;
73d840c0 477 const UV ruv = grok_bin (start, &len, &flags, &rnv);
53305cf1 478
7918f24d
NC
479 PERL_ARGS_ASSERT_SCAN_BIN;
480
53305cf1
NC
481 *retlen = len;
482 return (flags & PERL_SCAN_GREATER_THAN_UV_MAX) ? rnv : (NV)ruv;
483}
484
485NV
73d840c0 486Perl_scan_oct(pTHX_ const char *start, STRLEN len, STRLEN *retlen)
53305cf1
NC
487{
488 NV rnv;
489 I32 flags = *retlen ? PERL_SCAN_ALLOW_UNDERSCORES : 0;
73d840c0 490 const UV ruv = grok_oct (start, &len, &flags, &rnv);
53305cf1 491
7918f24d
NC
492 PERL_ARGS_ASSERT_SCAN_OCT;
493
53305cf1
NC
494 *retlen = len;
495 return (flags & PERL_SCAN_GREATER_THAN_UV_MAX) ? rnv : (NV)ruv;
496}
497
498NV
73d840c0 499Perl_scan_hex(pTHX_ const char *start, STRLEN len, STRLEN *retlen)
53305cf1
NC
500{
501 NV rnv;
502 I32 flags = *retlen ? PERL_SCAN_ALLOW_UNDERSCORES : 0;
73d840c0 503 const UV ruv = grok_hex (start, &len, &flags, &rnv);
53305cf1 504
7918f24d
NC
505 PERL_ARGS_ASSERT_SCAN_HEX;
506
53305cf1
NC
507 *retlen = len;
508 return (flags & PERL_SCAN_GREATER_THAN_UV_MAX) ? rnv : (NV)ruv;
98994639
HS
509}
510
511/*
512=for apidoc grok_numeric_radix
513
514Scan and skip for a numeric decimal separator (radix).
515
516=cut
517 */
518bool
519Perl_grok_numeric_radix(pTHX_ const char **sp, const char *send)
520{
7918f24d
NC
521 PERL_ARGS_ASSERT_GROK_NUMERIC_RADIX;
522
7ea85fa8
KW
523#ifdef USE_LOCALE_NUMERIC
524
d6ded950 525 if (IN_LC(LC_NUMERIC)) {
f0dafd73
KW
526 STRLEN len;
527 char * radix;
528 bool matches_radix = FALSE;
67d796ae 529 DECLARATION_FOR_LC_NUMERIC_MANIPULATION;
f0dafd73 530
a1395eaf 531 STORE_LC_NUMERIC_FORCE_TO_UNDERLYING();
f0dafd73
KW
532
533 radix = SvPV(PL_numeric_radix_sv, len);
534 radix = savepvn(radix, len);
535
21431899 536 RESTORE_LC_NUMERIC();
f0dafd73
KW
537
538 if (*sp + len <= send) {
539 matches_radix = memEQ(*sp, radix, len);
540 }
541
542 Safefree(radix);
543
544 if (matches_radix) {
545 *sp += len;
546 return TRUE;
547 }
98994639 548 }
f0dafd73 549
98994639 550#endif
7918f24d 551
f0dafd73
KW
552 /* always try "." if numeric radix didn't match because
553 * we may have data from different locales mixed */
98994639
HS
554 if (*sp < send && **sp == '.') {
555 ++*sp;
556 return TRUE;
557 }
f0dafd73 558
98994639
HS
559 return FALSE;
560}
561
569f27e5 562/*
ff4eb398
JH
563=for apidoc grok_infnan
564
796b6530 565Helper for C<grok_number()>, accepts various ways of spelling "infinity"
ff4eb398
JH
566or "not a number", and returns one of the following flag combinations:
567
568 IS_NUMBER_INFINITE
569 IS_NUMBER_NAN
570 IS_NUMBER_INFINITE | IS_NUMBER_NEG
571 IS_NUMBER_NAN | IS_NUMBER_NEG
572 0
573
796b6530 574possibly |-ed with C<IS_NUMBER_TRAILING>.
b489e20f 575
796b6530 576If an infinity or a not-a-number is recognized, C<*sp> will point to
62bdc035 577one byte past the end of the recognized string. If the recognition fails,
796b6530 578zero is returned, and C<*sp> will not move.
ff4eb398
JH
579
580=cut
581*/
582
583int
3823048b 584Perl_grok_infnan(pTHX_ const char** sp, const char* send)
ff4eb398
JH
585{
586 const char* s = *sp;
587 int flags = 0;
a5dc2484 588#if defined(NV_INF) || defined(NV_NAN)
62bdc035 589 bool odh = FALSE; /* one-dot-hash: 1.#INF */
ff4eb398
JH
590
591 PERL_ARGS_ASSERT_GROK_INFNAN;
592
8c12dc63
JH
593 if (*s == '+') {
594 s++; if (s == send) return 0;
595 }
596 else if (*s == '-') {
ff4eb398
JH
597 flags |= IS_NUMBER_NEG; /* Yes, -NaN happens. Incorrect but happens. */
598 s++; if (s == send) return 0;
599 }
600
601 if (*s == '1') {
62bdc035
JH
602 /* Visual C: 1.#SNAN, -1.#QNAN, 1#INF, 1.#IND (maybe also 1.#NAN)
603 * Let's keep the dot optional. */
ff4eb398
JH
604 s++; if (s == send) return 0;
605 if (*s == '.') {
606 s++; if (s == send) return 0;
607 }
608 if (*s == '#') {
609 s++; if (s == send) return 0;
610 } else
611 return 0;
e855f543 612 odh = TRUE;
ff4eb398
JH
613 }
614
305b8651 615 if (isALPHA_FOLD_EQ(*s, 'I')) {
62bdc035
JH
616 /* INF or IND (1.#IND is "indeterminate", a certain type of NAN) */
617
305b8651 618 s++; if (s == send || isALPHA_FOLD_NE(*s, 'N')) return 0;
ff4eb398 619 s++; if (s == send) return 0;
305b8651 620 if (isALPHA_FOLD_EQ(*s, 'F')) {
ff4eb398 621 s++;
b8974fcb
JH
622 if (s < send && (isALPHA_FOLD_EQ(*s, 'I'))) {
623 int fail =
624 flags | IS_NUMBER_INFINITY | IS_NUMBER_NOT_INT | IS_NUMBER_TRAILING;
625 s++; if (s == send || isALPHA_FOLD_NE(*s, 'N')) return fail;
626 s++; if (s == send || isALPHA_FOLD_NE(*s, 'I')) return fail;
627 s++; if (s == send || isALPHA_FOLD_NE(*s, 'T')) return fail;
628 s++; if (s == send || isALPHA_FOLD_NE(*s, 'Y')) return fail;
3396ed30 629 s++;
b8974fcb
JH
630 } else if (odh) {
631 while (*s == '0') { /* 1.#INF00 */
632 s++;
633 }
3396ed30 634 }
b489e20f
JH
635 while (s < send && isSPACE(*s))
636 s++;
637 if (s < send && *s) {
3396ed30 638 flags |= IS_NUMBER_TRAILING;
fae4db12 639 }
ff4eb398
JH
640 flags |= IS_NUMBER_INFINITY | IS_NUMBER_NOT_INT;
641 }
e855f543 642 else if (isALPHA_FOLD_EQ(*s, 'D') && odh) { /* 1.#IND */
ff4eb398
JH
643 s++;
644 flags |= IS_NUMBER_NAN | IS_NUMBER_NOT_INT;
fae4db12
JH
645 while (*s == '0') { /* 1.#IND00 */
646 s++;
647 }
1e9aa12f
JH
648 if (*s) {
649 flags |= IS_NUMBER_TRAILING;
650 }
ff4eb398
JH
651 } else
652 return 0;
ff4eb398
JH
653 }
654 else {
62bdc035 655 /* Maybe NAN of some sort */
3823048b
JH
656
657 if (isALPHA_FOLD_EQ(*s, 'S') || isALPHA_FOLD_EQ(*s, 'Q')) {
658 /* snan, qNaN */
659 /* XXX do something with the snan/qnan difference */
660 s++; if (s == send) return 0;
661 }
662
663 if (isALPHA_FOLD_EQ(*s, 'N')) {
664 s++; if (s == send || isALPHA_FOLD_NE(*s, 'A')) return 0;
665 s++; if (s == send || isALPHA_FOLD_NE(*s, 'N')) return 0;
666 s++;
667
668 flags |= IS_NUMBER_NAN | IS_NUMBER_NOT_INT;
669
670 /* NaN can be followed by various stuff (NaNQ, NaNS), but
671 * there are also multiple different NaN values, and some
672 * implementations output the "payload" values,
673 * e.g. NaN123, NAN(abc), while some legacy implementations
674 * have weird stuff like NaN%. */
675 if (isALPHA_FOLD_EQ(*s, 'q') ||
676 isALPHA_FOLD_EQ(*s, 's')) {
677 /* "nanq" or "nans" are ok, though generating
678 * these portably is tricky. */
679 s++;
680 }
681 if (*s == '(') {
682 /* C99 style "nan(123)" or Perlish equivalent "nan($uv)". */
683 const char *t;
684 s++;
685 if (s == send) {
686 return flags | IS_NUMBER_TRAILING;
687 }
688 t = s + 1;
689 while (t < send && *t && *t != ')') {
690 t++;
691 }
692 if (t == send) {
693 return flags | IS_NUMBER_TRAILING;
694 }
695 if (*t == ')') {
696 int nantype;
697 UV nanval;
698 if (s[0] == '0' && s + 2 < t &&
699 isALPHA_FOLD_EQ(s[1], 'x') &&
700 isXDIGIT(s[2])) {
701 STRLEN len = t - s;
702 I32 flags = PERL_SCAN_ALLOW_UNDERSCORES;
703 nanval = grok_hex(s, &len, &flags, NULL);
704 if ((flags & PERL_SCAN_GREATER_THAN_UV_MAX)) {
705 nantype = 0;
706 } else {
707 nantype = IS_NUMBER_IN_UV;
708 }
709 s += len;
710 } else if (s[0] == '0' && s + 2 < t &&
711 isALPHA_FOLD_EQ(s[1], 'b') &&
712 (s[2] == '0' || s[2] == '1')) {
713 STRLEN len = t - s;
714 I32 flags = PERL_SCAN_ALLOW_UNDERSCORES;
715 nanval = grok_bin(s, &len, &flags, NULL);
716 if ((flags & PERL_SCAN_GREATER_THAN_UV_MAX)) {
717 nantype = 0;
718 } else {
719 nantype = IS_NUMBER_IN_UV;
720 }
721 s += len;
722 } else {
723 const char *u;
724 nantype =
725 grok_number_flags(s, t - s, &nanval,
726 PERL_SCAN_TRAILING |
727 PERL_SCAN_ALLOW_UNDERSCORES);
728 /* Unfortunately grok_number_flags() doesn't
729 * tell how far we got and the ')' will always
730 * be "trailing", so we need to double-check
731 * whether we had something dubious. */
732 for (u = s; u < t; u++) {
733 if (!isDIGIT(*u)) {
734 flags |= IS_NUMBER_TRAILING;
735 break;
736 }
737 }
738 s = u;
739 }
740
741 /* XXX Doesn't do octal: nan("0123").
742 * Probably not a big loss. */
743
744 if ((nantype & IS_NUMBER_NOT_INT) ||
745 !(nantype && IS_NUMBER_IN_UV)) {
746 /* XXX the nanval is currently unused, that is,
747 * not inserted as the NaN payload of the NV.
748 * But the above code already parses the C99
749 * nan(...) format. See below, and see also
750 * the nan() in POSIX.xs.
751 *
752 * Certain configuration combinations where
753 * NVSIZE is greater than UVSIZE mean that
754 * a single UV cannot contain all the possible
755 * NaN payload bits. There would need to be
756 * some more generic syntax than "nan($uv)".
757 *
758 * Issues to keep in mind:
759 *
760 * (1) In most common cases there would
761 * not be an integral number of bytes that
762 * could be set, only a certain number of bits.
763 * For example for the common case of
764 * NVSIZE == UVSIZE == 8 there is room for 52
765 * bits in the payload, but the most significant
766 * bit is commonly reserved for the
767 * signaling/quiet bit, leaving 51 bits.
768 * Furthermore, the C99 nan() is supposed
769 * to generate quiet NaNs, so it is doubtful
770 * whether it should be able to generate
771 * signaling NaNs. For the x86 80-bit doubles
772 * (if building a long double Perl) there would
773 * be 62 bits (s/q bit being the 63rd).
774 *
775 * (2) Endianness of the payload bits. If the
776 * payload is specified as an UV, the low-order
777 * bits of the UV are naturally little-endianed
778 * (rightmost) bits of the payload. The endianness
779 * of UVs and NVs can be different. */
780 return 0;
781 }
782 if (s < t) {
783 flags |= IS_NUMBER_TRAILING;
784 }
785 } else {
786 /* Looked like nan(...), but no close paren. */
787 flags |= IS_NUMBER_TRAILING;
788 }
789 } else {
790 while (s < send && isSPACE(*s))
791 s++;
792 if (s < send && *s) {
793 /* Note that we here implicitly accept (parse as
794 * "nan", but with warnings) also any other weird
795 * trailing stuff for "nan". In the above we just
796 * check that if we got the C99-style "nan(...)",
797 * the "..." looks sane.
798 * If in future we accept more ways of specifying
799 * the nan payload, the accepting would happen around
800 * here. */
801 flags |= IS_NUMBER_TRAILING;
802 }
803 }
804 s = send;
805 }
806 else
807 return 0;
ff4eb398
JH
808 }
809
b489e20f
JH
810 while (s < send && isSPACE(*s))
811 s++;
812
a5dc2484
JH
813#else
814 PERL_UNUSED_ARG(send);
815#endif /* #if defined(NV_INF) || defined(NV_NAN) */
a1fe7cea
JH
816 *sp = s;
817 return flags;
ff4eb398
JH
818}
819
13393a5e 820/*
3823048b 821=for apidoc grok_number_flags
13393a5e
JH
822
823Recognise (or not) a number. The type of the number is returned
824(0 if unrecognised), otherwise it is a bit-ORed combination of
796b6530
KW
825C<IS_NUMBER_IN_UV>, C<IS_NUMBER_GREATER_THAN_UV_MAX>, C<IS_NUMBER_NOT_INT>,
826C<IS_NUMBER_NEG>, C<IS_NUMBER_INFINITY>, C<IS_NUMBER_NAN> (defined in perl.h).
827
828If the value of the number can fit in a UV, it is returned in C<*valuep>.
829C<IS_NUMBER_IN_UV> will be set to indicate that C<*valuep> is valid, C<IS_NUMBER_IN_UV>
830will never be set unless C<*valuep> is valid, but C<*valuep> may have been assigned
831to during processing even though C<IS_NUMBER_IN_UV> is not set on return.
832If C<valuep> is C<NULL>, C<IS_NUMBER_IN_UV> will be set for the same cases as when
833C<valuep> is non-C<NULL>, but no actual assignment (or SEGV) will occur.
834
835C<IS_NUMBER_NOT_INT> will be set with C<IS_NUMBER_IN_UV> if trailing decimals were
836seen (in which case C<*valuep> gives the true value truncated to an integer), and
837C<IS_NUMBER_NEG> if the number is negative (in which case C<*valuep> holds the
838absolute value). C<IS_NUMBER_IN_UV> is not set if e notation was used or the
13393a5e
JH
839number is larger than a UV.
840
841C<flags> allows only C<PERL_SCAN_TRAILING>, which allows for trailing
842non-numeric text on an otherwise successful I<grok>, setting
843C<IS_NUMBER_TRAILING> on the result.
844
845=for apidoc grok_number
846
796b6530 847Identical to C<grok_number_flags()> with C<flags> set to zero.
13393a5e
JH
848
849=cut
850 */
851int
852Perl_grok_number(pTHX_ const char *pv, STRLEN len, UV *valuep)
853{
854 PERL_ARGS_ASSERT_GROK_NUMBER;
855
856 return grok_number_flags(pv, len, valuep, 0);
857}
858
945b524a
JH
859static const UV uv_max_div_10 = UV_MAX / 10;
860static const U8 uv_max_mod_10 = UV_MAX % 10;
861
3f7602fa 862int
3823048b 863Perl_grok_number_flags(pTHX_ const char *pv, STRLEN len, UV *valuep, U32 flags)
3f7602fa 864{
60939fb8 865 const char *s = pv;
c4420975 866 const char * const send = pv + len;
ae776a2c 867 const char *d;
60939fb8 868 int numtype = 0;
60939fb8 869
3823048b 870 PERL_ARGS_ASSERT_GROK_NUMBER_FLAGS;
7918f24d 871
60939fb8
NC
872 while (s < send && isSPACE(*s))
873 s++;
874 if (s == send) {
875 return 0;
876 } else if (*s == '-') {
877 s++;
878 numtype = IS_NUMBER_NEG;
879 }
880 else if (*s == '+')
aa42a541 881 s++;
60939fb8
NC
882
883 if (s == send)
884 return 0;
885
ae776a2c 886 /* The first digit (after optional sign): note that might
8c12dc63 887 * also point to "infinity" or "nan", or "1.#INF". */
ae776a2c
JH
888 d = s;
889
8c12dc63 890 /* next must be digit or the radix separator or beginning of infinity/nan */
60939fb8
NC
891 if (isDIGIT(*s)) {
892 /* UVs are at least 32 bits, so the first 9 decimal digits cannot
893 overflow. */
894 UV value = *s - '0';
895 /* This construction seems to be more optimiser friendly.
896 (without it gcc does the isDIGIT test and the *s - '0' separately)
897 With it gcc on arm is managing 6 instructions (6 cycles) per digit.
898 In theory the optimiser could deduce how far to unroll the loop
899 before checking for overflow. */
58bb9ec3
NC
900 if (++s < send) {
901 int digit = *s - '0';
60939fb8
NC
902 if (digit >= 0 && digit <= 9) {
903 value = value * 10 + digit;
58bb9ec3
NC
904 if (++s < send) {
905 digit = *s - '0';
60939fb8
NC
906 if (digit >= 0 && digit <= 9) {
907 value = value * 10 + digit;
58bb9ec3
NC
908 if (++s < send) {
909 digit = *s - '0';
60939fb8
NC
910 if (digit >= 0 && digit <= 9) {
911 value = value * 10 + digit;
58bb9ec3
NC
912 if (++s < send) {
913 digit = *s - '0';
60939fb8
NC
914 if (digit >= 0 && digit <= 9) {
915 value = value * 10 + digit;
58bb9ec3
NC
916 if (++s < send) {
917 digit = *s - '0';
60939fb8
NC
918 if (digit >= 0 && digit <= 9) {
919 value = value * 10 + digit;
58bb9ec3
NC
920 if (++s < send) {
921 digit = *s - '0';
60939fb8
NC
922 if (digit >= 0 && digit <= 9) {
923 value = value * 10 + digit;
58bb9ec3
NC
924 if (++s < send) {
925 digit = *s - '0';
60939fb8
NC
926 if (digit >= 0 && digit <= 9) {
927 value = value * 10 + digit;
58bb9ec3
NC
928 if (++s < send) {
929 digit = *s - '0';
60939fb8
NC
930 if (digit >= 0 && digit <= 9) {
931 value = value * 10 + digit;
58bb9ec3 932 if (++s < send) {
60939fb8
NC
933 /* Now got 9 digits, so need to check
934 each time for overflow. */
58bb9ec3 935 digit = *s - '0';
60939fb8 936 while (digit >= 0 && digit <= 9
945b524a
JH
937 && (value < uv_max_div_10
938 || (value == uv_max_div_10
939 && digit <= uv_max_mod_10))) {
60939fb8 940 value = value * 10 + digit;
58bb9ec3
NC
941 if (++s < send)
942 digit = *s - '0';
60939fb8
NC
943 else
944 break;
945 }
946 if (digit >= 0 && digit <= 9
51bd16da 947 && (s < send)) {
60939fb8
NC
948 /* value overflowed.
949 skip the remaining digits, don't
950 worry about setting *valuep. */
951 do {
952 s++;
953 } while (s < send && isDIGIT(*s));
954 numtype |=
955 IS_NUMBER_GREATER_THAN_UV_MAX;
956 goto skip_value;
957 }
958 }
959 }
98994639 960 }
60939fb8
NC
961 }
962 }
963 }
964 }
965 }
966 }
967 }
968 }
969 }
970 }
971 }
98994639 972 }
60939fb8 973 }
98994639 974 }
60939fb8
NC
975 numtype |= IS_NUMBER_IN_UV;
976 if (valuep)
977 *valuep = value;
978
979 skip_value:
980 if (GROK_NUMERIC_RADIX(&s, send)) {
981 numtype |= IS_NUMBER_NOT_INT;
982 while (s < send && isDIGIT(*s)) /* optional digits after the radix */
983 s++;
98994639 984 }
60939fb8
NC
985 }
986 else if (GROK_NUMERIC_RADIX(&s, send)) {
987 numtype |= IS_NUMBER_NOT_INT | IS_NUMBER_IN_UV; /* valuep assigned below */
988 /* no digits before the radix means we need digits after it */
989 if (s < send && isDIGIT(*s)) {
990 do {
991 s++;
992 } while (s < send && isDIGIT(*s));
993 if (valuep) {
994 /* integer approximation is valid - it's 0. */
995 *valuep = 0;
996 }
98994639 997 }
60939fb8 998 else
ae776a2c 999 return 0;
ff4eb398 1000 }
60939fb8 1001
926f5fc6 1002 if (s > d && s < send) {
60939fb8 1003 /* we can have an optional exponent part */
305b8651 1004 if (isALPHA_FOLD_EQ(*s, 'e')) {
60939fb8
NC
1005 s++;
1006 if (s < send && (*s == '-' || *s == '+'))
1007 s++;
1008 if (s < send && isDIGIT(*s)) {
1009 do {
1010 s++;
1011 } while (s < send && isDIGIT(*s));
1012 }
3f7602fa
TC
1013 else if (flags & PERL_SCAN_TRAILING)
1014 return numtype | IS_NUMBER_TRAILING;
60939fb8 1015 else
3f7602fa
TC
1016 return 0;
1017
1018 /* The only flag we keep is sign. Blow away any "it's UV" */
1019 numtype &= IS_NUMBER_NEG;
1020 numtype |= IS_NUMBER_NOT_INT;
60939fb8
NC
1021 }
1022 }
1023 while (s < send && isSPACE(*s))
1024 s++;
1025 if (s >= send)
aa8b85de 1026 return numtype;
b59bf0b2 1027 if (memEQs(pv, len, "0 but true")) {
60939fb8
NC
1028 if (valuep)
1029 *valuep = 0;
1030 return IS_NUMBER_IN_UV;
1031 }
8c12dc63
JH
1032 /* We could be e.g. at "Inf" or "NaN", or at the "#" of "1.#INF". */
1033 if ((s + 2 < send) && strchr("inqs#", toFOLD(*s))) {
1034 /* Really detect inf/nan. Start at d, not s, since the above
1035 * code might have already consumed the "1." or "1". */
7eff3d39 1036 const int infnan = Perl_grok_infnan(aTHX_ &d, send);
8c12dc63
JH
1037 if ((infnan & IS_NUMBER_INFINITY)) {
1038 return (numtype | infnan); /* Keep sign for infinity. */
1039 }
1040 else if ((infnan & IS_NUMBER_NAN)) {
1041 return (numtype | infnan) & ~IS_NUMBER_NEG; /* Clear sign for nan. */
1042 }
1043 }
3f7602fa
TC
1044 else if (flags & PERL_SCAN_TRAILING) {
1045 return numtype | IS_NUMBER_TRAILING;
1046 }
1047
60939fb8 1048 return 0;
98994639
HS
1049}
1050
6313e544 1051/*
5d4a52b5 1052=for apidoc grok_atoUV
6313e544 1053
5d4a52b5 1054parse a string, looking for a decimal unsigned integer.
338aa8b0 1055
5d4a52b5
KW
1056On entry, C<pv> points to the beginning of the string;
1057C<valptr> points to a UV that will receive the converted value, if found;
1058C<endptr> is either NULL or points to a variable that points to one byte
1059beyond the point in C<pv> that this routine should examine.
1060If C<endptr> is NULL, C<pv> is assumed to be NUL-terminated.
f4379102 1061
5d4a52b5
KW
1062Returns FALSE if C<pv> doesn't represent a valid unsigned integer value (with
1063no leading zeros). Otherwise it returns TRUE, and sets C<*valptr> to that
1064value.
6313e544 1065
5d4a52b5
KW
1066If you constrain the portion of C<pv> that is looked at by this function (by
1067passing a non-NULL C<endptr>), and if the intial bytes of that portion form a
1068valid value, it will return TRUE, setting C<*endptr> to the byte following the
1069final digit of the value. But if there is no constraint at what's looked at,
1070all of C<pv> must be valid in order for TRUE to be returned.
6313e544 1071
5d4a52b5 1072The only characters this accepts are the decimal digits '0'..'9'.
338aa8b0 1073
5d4a52b5
KW
1074As opposed to L<atoi(3)> or L<strtol(3)>, C<grok_atoUV> does NOT allow optional
1075leading whitespace, nor negative inputs. If such features are required, the
1076calling code needs to explicitly implement those.
6313e544 1077
5d4a52b5
KW
1078Note that this function returns FALSE for inputs that would overflow a UV,
1079or have leading zeros. Thus a single C<0> is accepted, but not C<00> nor
1080C<01>, C<002>, I<etc>.
1081
1082Background: C<atoi> has severe problems with illegal inputs, it cannot be
d62b8c6a 1083used for incremental parsing, and therefore should be avoided
5d4a52b5 1084C<atoi> and C<strtol> are also affected by locale settings, which can also be
d62b8c6a
JH
1085seen as a bug (global state controlled by user environment).
1086
6313e544
JH
1087*/
1088
22ff3130
HS
1089bool
1090Perl_grok_atoUV(const char *pv, UV *valptr, const char** endptr)
6313e544
JH
1091{
1092 const char* s = pv;
1093 const char** eptr;
1094 const char* end2; /* Used in case endptr is NULL. */
22ff3130 1095 UV val = 0; /* The parsed value. */
6313e544 1096
22ff3130 1097 PERL_ARGS_ASSERT_GROK_ATOUV;
6313e544 1098
5d4a52b5
KW
1099 if (endptr) {
1100 eptr = endptr;
1101 }
1102 else {
1103 end2 = s + strlen(s);
1104 eptr = &end2;
1105 }
1106
1107 if ( *eptr <= s
1108 || ! isDIGIT(*s))
1109 {
1110 return FALSE;
1111 }
1112
75feedba 1113 /* Single-digit inputs are quite common. */
6313e544 1114 val = *s++ - '0';
5d4a52b5 1115 if (s < *eptr && isDIGIT(*s)) {
22ff3130
HS
1116 /* Fail on extra leading zeros. */
1117 if (val == 0)
1118 return FALSE;
5d4a52b5 1119 while (s < *eptr && isDIGIT(*s)) {
75feedba
JH
1120 /* This could be unrolled like in grok_number(), but
1121 * the expected uses of this are not speed-needy, and
1122 * unlikely to need full 64-bitness. */
7eff3d39 1123 const U8 digit = *s++ - '0';
945b524a
JH
1124 if (val < uv_max_div_10 ||
1125 (val == uv_max_div_10 && digit <= uv_max_mod_10)) {
75feedba
JH
1126 val = val * 10 + digit;
1127 } else {
22ff3130 1128 return FALSE;
6313e544 1129 }
6313e544
JH
1130 }
1131 }
5d4a52b5
KW
1132 if (endptr == NULL) {
1133 if (*s) {
1134 return FALSE; /* If endptr is NULL, no trailing non-digits allowed. */
1135 }
1136 }
1137 else {
1138 *endptr = s;
75feedba 1139 }
22ff3130
HS
1140 *valptr = val;
1141 return TRUE;
6313e544
JH
1142}
1143
a4eca1d4 1144#ifndef USE_QUADMATH
4801ca72 1145STATIC NV
98994639
HS
1146S_mulexp10(NV value, I32 exponent)
1147{
1148 NV result = 1.0;
1149 NV power = 10.0;
1150 bool negative = 0;
1151 I32 bit;
1152
1153 if (exponent == 0)
1154 return value;
659c4b96
DM
1155 if (value == 0)
1156 return (NV)0;
87032ba1 1157
24866caa 1158 /* On OpenVMS VAX we by default use the D_FLOAT double format,
67597c89 1159 * and that format does not have *easy* capabilities [1] for
24866caa
CB
1160 * overflowing doubles 'silently' as IEEE fp does. We also need
1161 * to support G_FLOAT on both VAX and Alpha, and though the exponent
1162 * range is much larger than D_FLOAT it still doesn't do silent
1163 * overflow. Therefore we need to detect early whether we would
1164 * overflow (this is the behaviour of the native string-to-float
1165 * conversion routines, and therefore of native applications, too).
67597c89 1166 *
24866caa
CB
1167 * [1] Trying to establish a condition handler to trap floating point
1168 * exceptions is not a good idea. */
87032ba1
JH
1169
1170 /* In UNICOS and in certain Cray models (such as T90) there is no
1171 * IEEE fp, and no way at all from C to catch fp overflows gracefully.
1172 * There is something you can do if you are willing to use some
1173 * inline assembler: the instruction is called DFI-- but that will
1174 * disable *all* floating point interrupts, a little bit too large
1175 * a hammer. Therefore we need to catch potential overflows before
1176 * it's too late. */
353813d9 1177
a7157111 1178#if ((defined(VMS) && !defined(_IEEE_FP)) || defined(_UNICOS) || defined(DOUBLE_IS_VAX_FLOAT)) && defined(NV_MAX_10_EXP)
353813d9 1179 STMT_START {
c4420975 1180 const NV exp_v = log10(value);
353813d9
HS
1181 if (exponent >= NV_MAX_10_EXP || exponent + exp_v >= NV_MAX_10_EXP)
1182 return NV_MAX;
1183 if (exponent < 0) {
1184 if (-(exponent + exp_v) >= NV_MAX_10_EXP)
1185 return 0.0;
1186 while (-exponent >= NV_MAX_10_EXP) {
1187 /* combination does not overflow, but 10^(-exponent) does */
1188 value /= 10;
1189 ++exponent;
1190 }
1191 }
1192 } STMT_END;
87032ba1
JH
1193#endif
1194
353813d9
HS
1195 if (exponent < 0) {
1196 negative = 1;
1197 exponent = -exponent;
b27804d8
DM
1198#ifdef NV_MAX_10_EXP
1199 /* for something like 1234 x 10^-309, the action of calculating
1200 * the intermediate value 10^309 then returning 1234 / (10^309)
1201 * will fail, since 10^309 becomes infinity. In this case try to
1202 * refactor it as 123 / (10^308) etc.
1203 */
1204 while (value && exponent > NV_MAX_10_EXP) {
1205 exponent--;
1206 value /= 10;
1207 }
48853916
JH
1208 if (value == 0.0)
1209 return value;
b27804d8 1210#endif
353813d9 1211 }
c62e754c
JH
1212#if defined(__osf__)
1213 /* Even with cc -ieee + ieee_set_fp_control(IEEE_TRAP_ENABLE_INV)
1214 * Tru64 fp behavior on inf/nan is somewhat broken. Another way
1215 * to do this would be ieee_set_fp_control(IEEE_TRAP_ENABLE_OVF)
1216 * but that breaks another set of infnan.t tests. */
1217# define FP_OVERFLOWS_TO_ZERO
1218#endif
98994639
HS
1219 for (bit = 1; exponent; bit <<= 1) {
1220 if (exponent & bit) {
1221 exponent ^= bit;
1222 result *= power;
c62e754c
JH
1223#ifdef FP_OVERFLOWS_TO_ZERO
1224 if (result == 0)
a7157111 1225# ifdef NV_INF
c62e754c 1226 return value < 0 ? -NV_INF : NV_INF;
a7157111
JH
1227# else
1228 return value < 0 ? -FLT_MAX : FLT_MAX;
1229# endif
c62e754c 1230#endif
236f0012
CB
1231 /* Floating point exceptions are supposed to be turned off,
1232 * but if we're obviously done, don't risk another iteration.
1233 */
1234 if (exponent == 0) break;
98994639
HS
1235 }
1236 power *= power;
1237 }
1238 return negative ? value / result : value * result;
1239}
a4eca1d4 1240#endif /* #ifndef USE_QUADMATH */
98994639
HS
1241
1242NV
1243Perl_my_atof(pTHX_ const char* s)
1244{
f720c878
KW
1245 /* 's' must be NUL terminated */
1246
98994639 1247 NV x = 0.0;
9eda1ea6
KW
1248
1249 PERL_ARGS_ASSERT_MY_ATOF;
1250
a4eca1d4 1251#ifdef USE_QUADMATH
9eda1ea6 1252
6928bedc 1253 my_atof2(s, &x);
9eda1ea6
KW
1254
1255#elif ! defined(USE_LOCALE_NUMERIC)
1256
1257 Perl_atof2(s, x);
1258
1259#else
7918f24d 1260
a2287a13 1261 {
67d796ae
KW
1262 DECLARATION_FOR_LC_NUMERIC_MANIPULATION;
1263 STORE_LC_NUMERIC_SET_TO_NEEDED();
d6ded950 1264 if (PL_numeric_radix_sv && IN_LC(LC_NUMERIC)) {
e4850248
KW
1265 /* Look through the string for the first thing that looks like a
1266 * decimal point: either the value in the current locale or the
1267 * standard fallback of '.'. The one which appears earliest in the
1268 * input string is the one that we should have atof look for. Note
1269 * that we have to determine this beforehand because on some
1270 * systems, Perl_atof2 is just a wrapper around the system's atof.
1271 * */
1ae85f6c
KW
1272 const char * const standard_pos = strchr(s, '.');
1273 const char * const local_pos
1274 = strstr(s, SvPV_nolen(PL_numeric_radix_sv));
1275 const bool use_standard_radix
1276 = standard_pos && (!local_pos || standard_pos < local_pos);
78787052 1277
665873e9 1278 if (use_standard_radix) {
e4850248 1279 SET_NUMERIC_STANDARD();
665873e9
KW
1280 LOCK_LC_NUMERIC_STANDARD();
1281 }
78787052 1282
e4850248 1283 Perl_atof2(s, x);
78787052 1284
665873e9
KW
1285 if (use_standard_radix) {
1286 UNLOCK_LC_NUMERIC_STANDARD();
67d796ae 1287 SET_NUMERIC_UNDERLYING();
665873e9 1288 }
e4850248
KW
1289 }
1290 else
1291 Perl_atof2(s, x);
a2287a13
KW
1292 RESTORE_LC_NUMERIC();
1293 }
9eda1ea6 1294
98994639 1295#endif
9eda1ea6 1296
98994639
HS
1297 return x;
1298}
1299
a7157111 1300#if defined(NV_INF) || defined(NV_NAN)
3c81f0b3
DD
1301
1302#ifdef USING_MSVC6
1303# pragma warning(push)
1304# pragma warning(disable:4756;disable:4056)
1305#endif
829757a4 1306static char*
5563f457 1307S_my_atof_infnan(pTHX_ const char* s, bool negative, const char* send, NV* value)
829757a4
JH
1308{
1309 const char *p0 = negative ? s - 1 : s;
1310 const char *p = p0;
7eff3d39 1311 const int infnan = grok_infnan(&p, send);
829757a4
JH
1312 if (infnan && p != p0) {
1313 /* If we can generate inf/nan directly, let's do so. */
1314#ifdef NV_INF
1315 if ((infnan & IS_NUMBER_INFINITY)) {
3823048b 1316 *value = (infnan & IS_NUMBER_NEG) ? -NV_INF: NV_INF;
829757a4
JH
1317 return (char*)p;
1318 }
1319#endif
1320#ifdef NV_NAN
1321 if ((infnan & IS_NUMBER_NAN)) {
3823048b 1322 *value = NV_NAN;
829757a4
JH
1323 return (char*)p;
1324 }
1325#endif
1326#ifdef Perl_strtod
68611e6f 1327 /* If still here, we didn't have either NV_INF or NV_NAN,
829757a4
JH
1328 * and can try falling back to native strtod/strtold.
1329 *
1330 * The native interface might not recognize all the possible
1331 * inf/nan strings Perl recognizes. What we can try
1332 * is to try faking the input. We will try inf/-inf/nan
1333 * as the most promising/portable input. */
1334 {
1335 const char* fake = NULL;
1336 char* endp;
1337 NV nv;
a7157111 1338#ifdef NV_INF
829757a4
JH
1339 if ((infnan & IS_NUMBER_INFINITY)) {
1340 fake = ((infnan & IS_NUMBER_NEG)) ? "-inf" : "inf";
1341 }
a7157111
JH
1342#endif
1343#ifdef NV_NAN
1344 if ((infnan & IS_NUMBER_NAN)) {
829757a4
JH
1345 fake = "nan";
1346 }
a7157111 1347#endif
829757a4
JH
1348 assert(fake);
1349 nv = Perl_strtod(fake, &endp);
1350 if (fake != endp) {
a7157111 1351#ifdef NV_INF
829757a4 1352 if ((infnan & IS_NUMBER_INFINITY)) {
a7157111 1353# ifdef Perl_isinf
829757a4
JH
1354 if (Perl_isinf(nv))
1355 *value = nv;
a7157111 1356# else
829757a4
JH
1357 /* last resort, may generate SIGFPE */
1358 *value = Perl_exp((NV)1e9);
1359 if ((infnan & IS_NUMBER_NEG))
1360 *value = -*value;
a7157111 1361# endif
829757a4
JH
1362 return (char*)p; /* p, not endp */
1363 }
a7157111
JH
1364#endif
1365#ifdef NV_NAN
1366 if ((infnan & IS_NUMBER_NAN)) {
1367# ifdef Perl_isnan
829757a4
JH
1368 if (Perl_isnan(nv))
1369 *value = nv;
a7157111 1370# else
829757a4
JH
1371 /* last resort, may generate SIGFPE */
1372 *value = Perl_log((NV)-1.0);
a7157111 1373# endif
829757a4 1374 return (char*)p; /* p, not endp */
a7157111 1375#endif
829757a4
JH
1376 }
1377 }
1378 }
1379#endif /* #ifdef Perl_strtod */
1380 }
1381 return NULL;
1382}
3c81f0b3
DD
1383#ifdef USING_MSVC6
1384# pragma warning(pop)
1385#endif
829757a4 1386
a7157111
JH
1387#endif /* if defined(NV_INF) || defined(NV_NAN) */
1388
98994639
HS
1389char*
1390Perl_my_atof2(pTHX_ const char* orig, NV* value)
1391{
6928bedc
KW
1392 PERL_ARGS_ASSERT_MY_ATOF2;
1393 return my_atof3(orig, value, 0);
1394}
1395
1396char*
1397Perl_my_atof3(pTHX_ const char* orig, NV* value, STRLEN len)
1398{
e1ec3a88 1399 const char* s = orig;
a4eca1d4
JH
1400 NV result[3] = {0.0, 0.0, 0.0};
1401#if defined(USE_PERL_ATOF) || defined(USE_QUADMATH)
6928bedc
KW
1402 const char* send = s + ((len != 0)
1403 ? len
1404 : strlen(orig)); /* one past the last */
a4eca1d4
JH
1405 bool negative = 0;
1406#endif
1407#if defined(USE_PERL_ATOF) && !defined(USE_QUADMATH)
1408 UV accumulator[2] = {0,0}; /* before/after dp */
8194bf88 1409 bool seen_digit = 0;
20f6aaab
AS
1410 I32 exp_adjust[2] = {0,0};
1411 I32 exp_acc[2] = {-1, -1};
1412 /* the current exponent adjust for the accumulators */
98994639 1413 I32 exponent = 0;
8194bf88 1414 I32 seen_dp = 0;
20f6aaab
AS
1415 I32 digit = 0;
1416 I32 old_digit = 0;
8194bf88 1417 I32 sig_digits = 0; /* noof significant digits seen so far */
a4eca1d4 1418#endif
8194bf88 1419
a4eca1d4 1420#if defined(USE_PERL_ATOF) || defined(USE_QUADMATH)
6928bedc 1421 PERL_ARGS_ASSERT_MY_ATOF3;
7918f24d 1422
a4eca1d4 1423 /* leading whitespace */
6928bedc 1424 while (s < send && isSPACE(*s))
a4eca1d4
JH
1425 ++s;
1426
1427 /* sign */
1428 switch (*s) {
1429 case '-':
1430 negative = 1;
1431 /* FALLTHROUGH */
1432 case '+':
1433 ++s;
1434 }
1435#endif
1436
1437#ifdef USE_QUADMATH
1438 {
1439 char* endp;
adc55e02 1440 if ((endp = S_my_atof_infnan(aTHX_ s, negative, send, value)))
a4eca1d4 1441 return endp;
6928bedc 1442 endp = send;
a4eca1d4
JH
1443 result[2] = strtoflt128(s, &endp);
1444 if (s != endp) {
1445 *value = negative ? -result[2] : result[2];
1446 return endp;
1447 }
1448 return NULL;
1449 }
1450#elif defined(USE_PERL_ATOF)
1451
8194bf88
DM
1452/* There is no point in processing more significant digits
1453 * than the NV can hold. Note that NV_DIG is a lower-bound value,
1454 * while we need an upper-bound value. We add 2 to account for this;
1455 * since it will have been conservative on both the first and last digit.
1456 * For example a 32-bit mantissa with an exponent of 4 would have
1457 * exact values in the set
1458 * 4
1459 * 8
1460 * ..
1461 * 17179869172
1462 * 17179869176
1463 * 17179869180
1464 *
1465 * where for the purposes of calculating NV_DIG we would have to discount
1466 * both the first and last digit, since neither can hold all values from
1467 * 0..9; but for calculating the value we must examine those two digits.
1468 */
ffa277e5
EAS
1469#ifdef MAX_SIG_DIG_PLUS
1470 /* It is not necessarily the case that adding 2 to NV_DIG gets all the
1471 possible digits in a NV, especially if NVs are not IEEE compliant
1472 (e.g., long doubles on IRIX) - Allen <allens@cpan.org> */
1473# define MAX_SIG_DIGITS (NV_DIG+MAX_SIG_DIG_PLUS)
1474#else
1475# define MAX_SIG_DIGITS (NV_DIG+2)
1476#endif
8194bf88
DM
1477
1478/* the max number we can accumulate in a UV, and still safely do 10*N+9 */
1479#define MAX_ACCUMULATE ( (UV) ((UV_MAX - 9)/10))
98994639 1480
a5dc2484 1481#if defined(NV_INF) || defined(NV_NAN)
ae776a2c 1482 {
7eff3d39 1483 char* endp;
5563f457 1484 if ((endp = S_my_atof_infnan(aTHX_ s, negative, send, value)))
7eff3d39 1485 return endp;
ae776a2c 1486 }
a5dc2484 1487#endif
2b54f59f 1488
8194bf88
DM
1489 /* we accumulate digits into an integer; when this becomes too
1490 * large, we add the total to NV and start again */
98994639 1491
6928bedc 1492 while (s < send) {
8194bf88
DM
1493 if (isDIGIT(*s)) {
1494 seen_digit = 1;
20f6aaab 1495 old_digit = digit;
8194bf88 1496 digit = *s++ - '0';
20f6aaab
AS
1497 if (seen_dp)
1498 exp_adjust[1]++;
98994639 1499
8194bf88
DM
1500 /* don't start counting until we see the first significant
1501 * digit, eg the 5 in 0.00005... */
1502 if (!sig_digits && digit == 0)
1503 continue;
1504
1505 if (++sig_digits > MAX_SIG_DIGITS) {
98994639 1506 /* limits of precision reached */
20f6aaab
AS
1507 if (digit > 5) {
1508 ++accumulator[seen_dp];
1509 } else if (digit == 5) {
1510 if (old_digit % 2) { /* round to even - Allen */
1511 ++accumulator[seen_dp];
1512 }
1513 }
1514 if (seen_dp) {
1515 exp_adjust[1]--;
1516 } else {
1517 exp_adjust[0]++;
1518 }
8194bf88 1519 /* skip remaining digits */
6928bedc 1520 while (s < send && isDIGIT(*s)) {
98994639 1521 ++s;
20f6aaab
AS
1522 if (! seen_dp) {
1523 exp_adjust[0]++;
1524 }
98994639
HS
1525 }
1526 /* warn of loss of precision? */
98994639 1527 }
8194bf88 1528 else {
20f6aaab 1529 if (accumulator[seen_dp] > MAX_ACCUMULATE) {
8194bf88 1530 /* add accumulator to result and start again */
20f6aaab
AS
1531 result[seen_dp] = S_mulexp10(result[seen_dp],
1532 exp_acc[seen_dp])
1533 + (NV)accumulator[seen_dp];
1534 accumulator[seen_dp] = 0;
1535 exp_acc[seen_dp] = 0;
98994639 1536 }
20f6aaab
AS
1537 accumulator[seen_dp] = accumulator[seen_dp] * 10 + digit;
1538 ++exp_acc[seen_dp];
98994639 1539 }
8194bf88 1540 }
e1ec3a88 1541 else if (!seen_dp && GROK_NUMERIC_RADIX(&s, send)) {
8194bf88 1542 seen_dp = 1;
20f6aaab 1543 if (sig_digits > MAX_SIG_DIGITS) {
6928bedc 1544 while (s < send && isDIGIT(*s)) {
20f6aaab 1545 ++s;
9604fbf0 1546 }
20f6aaab
AS
1547 break;
1548 }
8194bf88
DM
1549 }
1550 else {
1551 break;
98994639
HS
1552 }
1553 }
1554
20f6aaab
AS
1555 result[0] = S_mulexp10(result[0], exp_acc[0]) + (NV)accumulator[0];
1556 if (seen_dp) {
1557 result[1] = S_mulexp10(result[1], exp_acc[1]) + (NV)accumulator[1];
1558 }
98994639 1559
6928bedc 1560 if (s < send && seen_digit && (isALPHA_FOLD_EQ(*s, 'e'))) {
98994639
HS
1561 bool expnegative = 0;
1562
1563 ++s;
1564 switch (*s) {
1565 case '-':
1566 expnegative = 1;
924ba076 1567 /* FALLTHROUGH */
98994639
HS
1568 case '+':
1569 ++s;
1570 }
6928bedc 1571 while (s < send && isDIGIT(*s))
98994639
HS
1572 exponent = exponent * 10 + (*s++ - '0');
1573 if (expnegative)
1574 exponent = -exponent;
1575 }
1576
1577 /* now apply the exponent */
20f6aaab
AS
1578
1579 if (seen_dp) {
1580 result[2] = S_mulexp10(result[0],exponent+exp_adjust[0])
1581 + S_mulexp10(result[1],exponent-exp_adjust[1]);
1582 } else {
1583 result[2] = S_mulexp10(result[0],exponent+exp_adjust[0]);
1584 }
98994639
HS
1585
1586 /* now apply the sign */
1587 if (negative)
20f6aaab 1588 result[2] = -result[2];
a36244b7 1589#endif /* USE_PERL_ATOF */
20f6aaab 1590 *value = result[2];
73d840c0 1591 return (char *)s;
98994639
HS
1592}
1593
5d34af89 1594/*
3d9d9213 1595=for apidoc isinfnan
5d34af89 1596
796b6530
KW
1597C<Perl_isinfnan()> is utility function that returns true if the NV
1598argument is either an infinity or a C<NaN>, false otherwise. To test
1599in more detail, use C<Perl_isinf()> and C<Perl_isnan()>.
5d34af89 1600
68611e6f
JH
1601This is also the logical inverse of Perl_isfinite().
1602
5d34af89
JH
1603=cut
1604*/
1cd88304
JH
1605bool
1606Perl_isinfnan(NV nv)
1607{
a5dc2484 1608 PERL_UNUSED_ARG(nv);
1cd88304
JH
1609#ifdef Perl_isinf
1610 if (Perl_isinf(nv))
1611 return TRUE;
1612#endif
1613#ifdef Perl_isnan
1614 if (Perl_isnan(nv))
1615 return TRUE;
1616#endif
1617 return FALSE;
1618}
1619
354b74ae
FC
1620/*
1621=for apidoc
1622
796b6530 1623Checks whether the argument would be either an infinity or C<NaN> when used
354b74ae 1624as a number, but is careful not to trigger non-numeric or uninitialized
796b6530 1625warnings. it assumes the caller has done C<SvGETMAGIC(sv)> already.
354b74ae
FC
1626
1627=cut
1628*/
1629
1630bool
1631Perl_isinfnansv(pTHX_ SV *sv)
1632{
1633 PERL_ARGS_ASSERT_ISINFNANSV;
1634 if (!SvOK(sv))
1635 return FALSE;
1636 if (SvNOKp(sv))
1637 return Perl_isinfnan(SvNVX(sv));
1638 if (SvIOKp(sv))
1639 return FALSE;
1640 {
1641 STRLEN len;
1642 const char *s = SvPV_nomg_const(sv, len);
3823048b 1643 return cBOOL(grok_infnan(&s, s+len));
354b74ae
FC
1644 }
1645}
1646
d67dac15 1647#ifndef HAS_MODFL
68611e6f
JH
1648/* C99 has truncl, pre-C99 Solaris had aintl. We can use either with
1649 * copysignl to emulate modfl, which is in some platforms missing or
1650 * broken. */
d67dac15
JH
1651# if defined(HAS_TRUNCL) && defined(HAS_COPYSIGNL)
1652long double
1653Perl_my_modfl(long double x, long double *ip)
1654{
68611e6f
JH
1655 *ip = truncl(x);
1656 return (x == *ip ? copysignl(0.0L, x) : x - *ip);
d67dac15
JH
1657}
1658# elif defined(HAS_AINTL) && defined(HAS_COPYSIGNL)
55954f19
JH
1659long double
1660Perl_my_modfl(long double x, long double *ip)
1661{
68611e6f
JH
1662 *ip = aintl(x);
1663 return (x == *ip ? copysignl(0.0L, x) : x - *ip);
55954f19 1664}
d67dac15 1665# endif
55954f19
JH
1666#endif
1667
7b9b7dff 1668/* Similarly, with ilogbl and scalbnl we can emulate frexpl. */
55954f19
JH
1669#if ! defined(HAS_FREXPL) && defined(HAS_ILOGBL) && defined(HAS_SCALBNL)
1670long double
1671Perl_my_frexpl(long double x, int *e) {
68611e6f
JH
1672 *e = x == 0.0L ? 0 : ilogbl(x) + 1;
1673 return (scalbnl(x, -*e));
55954f19
JH
1674}
1675#endif
66610fdd
RGS
1676
1677/*
ed140128
AD
1678=for apidoc Perl_signbit
1679
1680Return a non-zero integer if the sign bit on an NV is set, and 0 if
1681it is not.
1682
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1683If F<Configure> detects this system has a C<signbit()> that will work with
1684our NVs, then we just use it via the C<#define> in F<perl.h>. Otherwise,
8b7fad81 1685fall back on this implementation. The main use of this function
796b6530 1686is catching C<-0.0>.
ed140128 1687
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1688C<Configure> notes: This function is called C<'Perl_signbit'> instead of a
1689plain C<'signbit'> because it is easy to imagine a system having a C<signbit()>
ed140128 1690function or macro that doesn't happen to work with our particular choice
796b6530 1691of NVs. We shouldn't just re-C<#define> C<signbit> as C<Perl_signbit> and expect
ed140128 1692the standard system headers to be happy. Also, this is a no-context
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1693function (no C<pTHX_>) because C<Perl_signbit()> is usually re-C<#defined> in
1694F<perl.h> as a simple macro call to the system's C<signbit()>.
1695Users should just always call C<Perl_signbit()>.
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1696
1697=cut
1698*/
1699#if !defined(HAS_SIGNBIT)
1700int
1701Perl_signbit(NV x) {
8b7fad81 1702# ifdef Perl_fp_class_nzero
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1703 return Perl_fp_class_nzero(x);
1704 /* Try finding the high byte, and assume it's highest bit
1705 * is the sign. This assumption is probably wrong somewhere. */
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1706# elif defined(USE_LONG_DOUBLE) && LONG_DOUBLEKIND == LONG_DOUBLE_IS_X86_80_BIT_LITTLE_ENDIAN
1707 return (((unsigned char *)&x)[9] & 0x80);
1708# elif defined(NV_LITTLE_ENDIAN)
1709 /* Note that NVSIZE is sizeof(NV), which would make the below be
1710 * wrong if the end bytes are unused, which happens with the x86
1711 * 80-bit long doubles, which is why take care of that above. */
1712 return (((unsigned char *)&x)[NVSIZE - 1] & 0x80);
1713# elif defined(NV_BIG_ENDIAN)
1714 return (((unsigned char *)&x)[0] & 0x80);
1715# else
406d5545 1716 /* This last resort fallback is wrong for the negative zero. */
3585840c 1717 return (x < 0.0) ? 1 : 0;
572cd850 1718# endif
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1719}
1720#endif
1721
1722/*
14d04a33 1723 * ex: set ts=8 sts=4 sw=4 et:
37442d52 1724 */