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comparison: js/src/jsmath.cpp

js/src/jsmath.cpp

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1 /* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
2 * vim: set ts=8 sts=4 et sw=4 tw=99:
3 * This Source Code Form is subject to the terms of the Mozilla Public
4 * License, v. 2.0. If a copy of the MPL was not distributed with this
5 * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
6
7 /*
8 * JS math package.
9 */
10
11 #include "jsmath.h"
12
13 #include "mozilla/Constants.h"
14 #include "mozilla/FloatingPoint.h"
15 #include "mozilla/MathAlgorithms.h"
16 #include "mozilla/MemoryReporting.h"
17
18 #include <algorithm> // for std::max
19 #include <fcntl.h>
20
21 #ifdef XP_UNIX
22 # include <unistd.h>
23 #endif
24
25 #include "jsapi.h"
26 #include "jsatom.h"
27 #include "jscntxt.h"
28 #include "jscompartment.h"
29 #include "jslibmath.h"
30 #include "jstypes.h"
31 #include "prmjtime.h"
32
33 #include "jsobjinlines.h"
34
35 using namespace js;
36
37 using mozilla::Abs;
38 using mozilla::NumberEqualsInt32;
39 using mozilla::NumberIsInt32;
40 using mozilla::ExponentComponent;
41 using mozilla::FloatingPoint;
42 using mozilla::IsFinite;
43 using mozilla::IsInfinite;
44 using mozilla::IsNaN;
45 using mozilla::IsNegative;
46 using mozilla::IsNegativeZero;
47 using mozilla::PositiveInfinity;
48 using mozilla::NegativeInfinity;
49 using JS::ToNumber;
50 using JS::GenericNaN;
51
52 static const JSConstDoubleSpec math_constants[] = {
53 {M_E, "E", 0, {0,0,0}},
54 {M_LOG2E, "LOG2E", 0, {0,0,0}},
55 {M_LOG10E, "LOG10E", 0, {0,0,0}},
56 {M_LN2, "LN2", 0, {0,0,0}},
57 {M_LN10, "LN10", 0, {0,0,0}},
58 {M_PI, "PI", 0, {0,0,0}},
59 {M_SQRT2, "SQRT2", 0, {0,0,0}},
60 {M_SQRT1_2, "SQRT1_2", 0, {0,0,0}},
61 {0,0,0,{0,0,0}}
62 };
63
64 MathCache::MathCache() {
65 memset(table, 0, sizeof(table));
66
67 /* See comments in lookup(). */
68 JS_ASSERT(IsNegativeZero(-0.0));
69 JS_ASSERT(!IsNegativeZero(+0.0));
70 JS_ASSERT(hash(-0.0) != hash(+0.0));
71 }
72
73 size_t
74 MathCache::sizeOfIncludingThis(mozilla::MallocSizeOf mallocSizeOf)
75 {
76 return mallocSizeOf(this);
77 }
78
79 const Class js::MathClass = {
80 js_Math_str,
81 JSCLASS_HAS_CACHED_PROTO(JSProto_Math),
82 JS_PropertyStub, /* addProperty */
83 JS_DeletePropertyStub, /* delProperty */
84 JS_PropertyStub, /* getProperty */
85 JS_StrictPropertyStub, /* setProperty */
86 JS_EnumerateStub,
87 JS_ResolveStub,
88 JS_ConvertStub
89 };
90
91 bool
92 js_math_abs(JSContext *cx, unsigned argc, Value *vp)
93 {
94 CallArgs args = CallArgsFromVp(argc, vp);
95
96 if (args.length() == 0) {
97 args.rval().setNaN();
98 return true;
99 }
100
101 double x;
102 if (!ToNumber(cx, args[0], &x))
103 return false;
104
105 double z = Abs(x);
106 args.rval().setNumber(z);
107 return true;
108 }
109
110 #if defined(SOLARIS) && defined(__GNUC__)
111 #define ACOS_IF_OUT_OF_RANGE(x) if (x < -1 || 1 < x) return GenericNaN();
112 #else
113 #define ACOS_IF_OUT_OF_RANGE(x)
114 #endif
115
116 double
117 js::math_acos_impl(MathCache *cache, double x)
118 {
119 ACOS_IF_OUT_OF_RANGE(x);
120 return cache->lookup(acos, x);
121 }
122
123 double
124 js::math_acos_uncached(double x)
125 {
126 ACOS_IF_OUT_OF_RANGE(x);
127 return acos(x);
128 }
129
130 #undef ACOS_IF_OUT_OF_RANGE
131
132 bool
133 js::math_acos(JSContext *cx, unsigned argc, Value *vp)
134 {
135 CallArgs args = CallArgsFromVp(argc, vp);
136
137 if (args.length() == 0) {
138 args.rval().setNaN();
139 return true;
140 }
141
142 double x;
143 if (!ToNumber(cx, args[0], &x))
144 return false;
145
146 MathCache *mathCache = cx->runtime()->getMathCache(cx);
147 if (!mathCache)
148 return false;
149
150 double z = math_acos_impl(mathCache, x);
151 args.rval().setDouble(z);
152 return true;
153 }
154
155 #if defined(SOLARIS) && defined(__GNUC__)
156 #define ASIN_IF_OUT_OF_RANGE(x) if (x < -1 || 1 < x) return GenericNaN();
157 #else
158 #define ASIN_IF_OUT_OF_RANGE(x)
159 #endif
160
161 double
162 js::math_asin_impl(MathCache *cache, double x)
163 {
164 ASIN_IF_OUT_OF_RANGE(x);
165 return cache->lookup(asin, x);
166 }
167
168 double
169 js::math_asin_uncached(double x)
170 {
171 ASIN_IF_OUT_OF_RANGE(x);
172 return asin(x);
173 }
174
175 #undef ASIN_IF_OUT_OF_RANGE
176
177 bool
178 js::math_asin(JSContext *cx, unsigned argc, Value *vp)
179 {
180 CallArgs args = CallArgsFromVp(argc, vp);
181
182 if (args.length() == 0) {
183 args.rval().setNaN();
184 return true;
185 }
186
187 double x;
188 if (!ToNumber(cx, args[0], &x))
189 return false;
190
191 MathCache *mathCache = cx->runtime()->getMathCache(cx);
192 if (!mathCache)
193 return false;
194
195 double z = math_asin_impl(mathCache, x);
196 args.rval().setDouble(z);
197 return true;
198 }
199
200 double
201 js::math_atan_impl(MathCache *cache, double x)
202 {
203 return cache->lookup(atan, x);
204 }
205
206 double
207 js::math_atan_uncached(double x)
208 {
209 return atan(x);
210 }
211
212 bool
213 js::math_atan(JSContext *cx, unsigned argc, Value *vp)
214 {
215 CallArgs args = CallArgsFromVp(argc, vp);
216
217 if (args.length() == 0) {
218 args.rval().setNaN();
219 return true;
220 }
221
222 double x;
223 if (!ToNumber(cx, args[0], &x))
224 return false;
225
226 MathCache *mathCache = cx->runtime()->getMathCache(cx);
227 if (!mathCache)
228 return false;
229
230 double z = math_atan_impl(mathCache, x);
231 args.rval().setDouble(z);
232 return true;
233 }
234
235 double
236 js::ecmaAtan2(double y, double x)
237 {
238 #if defined(_MSC_VER)
239 /*
240 * MSVC's atan2 does not yield the result demanded by ECMA when both x
241 * and y are infinite.
242 * - The result is a multiple of pi/4.
243 * - The sign of y determines the sign of the result.
244 * - The sign of x determines the multiplicator, 1 or 3.
245 */
246 if (IsInfinite(y) && IsInfinite(x)) {
247 double z = js_copysign(M_PI / 4, y);
248 if (x < 0)
249 z *= 3;
250 return z;
251 }
252 #endif
253
254 #if defined(SOLARIS) && defined(__GNUC__)
255 if (y == 0) {
256 if (IsNegativeZero(x))
257 return js_copysign(M_PI, y);
258 if (x == 0)
259 return y;
260 }
261 #endif
262 return atan2(y, x);
263 }
264
265 bool
266 js::math_atan2(JSContext *cx, unsigned argc, Value *vp)
267 {
268 CallArgs args = CallArgsFromVp(argc, vp);
269
270 double y;
271 if (!ToNumber(cx, args.get(0), &y))
272 return false;
273
274 double x;
275 if (!ToNumber(cx, args.get(1), &x))
276 return false;
277
278 double z = ecmaAtan2(y, x);
279 args.rval().setDouble(z);
280 return true;
281 }
282
283 double
284 js::math_ceil_impl(double x)
285 {
286 #ifdef __APPLE__
287 if (x < 0 && x > -1.0)
288 return js_copysign(0, -1);
289 #endif
290 return ceil(x);
291 }
292
293 bool
294 js::math_ceil(JSContext *cx, unsigned argc, Value *vp)
295 {
296 CallArgs args = CallArgsFromVp(argc, vp);
297
298 if (args.length() == 0) {
299 args.rval().setNaN();
300 return true;
301 }
302
303 double x;
304 if (!ToNumber(cx, args[0], &x))
305 return false;
306
307 double z = math_ceil_impl(x);
308 args.rval().setNumber(z);
309 return true;
310 }
311
312 bool
313 js::math_clz32(JSContext *cx, unsigned argc, Value *vp)
314 {
315 CallArgs args = CallArgsFromVp(argc, vp);
316
317 if (args.length() == 0) {
318 args.rval().setInt32(32);
319 return true;
320 }
321
322 uint32_t n;
323 if (!ToUint32(cx, args[0], &n))
324 return false;
325
326 if (n == 0) {
327 args.rval().setInt32(32);
328 return true;
329 }
330
331 args.rval().setInt32(mozilla::CountLeadingZeroes32(n));
332 return true;
333 }
334
335 double
336 js::math_cos_impl(MathCache *cache, double x)
337 {
338 return cache->lookup(cos, x);
339 }
340
341 double
342 js::math_cos_uncached(double x)
343 {
344 return cos(x);
345 }
346
347 bool
348 js::math_cos(JSContext *cx, unsigned argc, Value *vp)
349 {
350 CallArgs args = CallArgsFromVp(argc, vp);
351
352 if (args.length() == 0) {
353 args.rval().setNaN();
354 return true;
355 }
356
357 double x;
358 if (!ToNumber(cx, args[0], &x))
359 return false;
360
361 MathCache *mathCache = cx->runtime()->getMathCache(cx);
362 if (!mathCache)
363 return false;
364
365 double z = math_cos_impl(mathCache, x);
366 args.rval().setDouble(z);
367 return true;
368 }
369
370 #ifdef _WIN32
371 #define EXP_IF_OUT_OF_RANGE(x) \
372 if (!IsNaN(x)) { \
373 if (x == PositiveInfinity<double>()) \
374 return PositiveInfinity<double>(); \
375 if (x == NegativeInfinity<double>()) \
376 return 0.0; \
377 }
378 #else
379 #define EXP_IF_OUT_OF_RANGE(x)
380 #endif
381
382 double
383 js::math_exp_impl(MathCache *cache, double x)
384 {
385 EXP_IF_OUT_OF_RANGE(x);
386 return cache->lookup(exp, x);
387 }
388
389 double
390 js::math_exp_uncached(double x)
391 {
392 EXP_IF_OUT_OF_RANGE(x);
393 return exp(x);
394 }
395
396 #undef EXP_IF_OUT_OF_RANGE
397
398 bool
399 js::math_exp(JSContext *cx, unsigned argc, Value *vp)
400 {
401 CallArgs args = CallArgsFromVp(argc, vp);
402
403 if (args.length() == 0) {
404 args.rval().setNaN();
405 return true;
406 }
407
408 double x;
409 if (!ToNumber(cx, args[0], &x))
410 return false;
411
412 MathCache *mathCache = cx->runtime()->getMathCache(cx);
413 if (!mathCache)
414 return false;
415
416 double z = math_exp_impl(mathCache, x);
417 args.rval().setNumber(z);
418 return true;
419 }
420
421 double
422 js::math_floor_impl(double x)
423 {
424 return floor(x);
425 }
426
427 bool
428 js::math_floor(JSContext *cx, unsigned argc, Value *vp)
429 {
430 CallArgs args = CallArgsFromVp(argc, vp);
431
432 if (args.length() == 0) {
433 args.rval().setNaN();
434 return true;
435 }
436
437 double x;
438 if (!ToNumber(cx, args[0], &x))
439 return false;
440
441 double z = math_floor_impl(x);
442 args.rval().setNumber(z);
443 return true;
444 }
445
446 bool
447 js::math_imul(JSContext *cx, unsigned argc, Value *vp)
448 {
449 CallArgs args = CallArgsFromVp(argc, vp);
450
451 uint32_t a = 0, b = 0;
452 if (args.hasDefined(0) && !ToUint32(cx, args[0], &a))
453 return false;
454 if (args.hasDefined(1) && !ToUint32(cx, args[1], &b))
455 return false;
456
457 uint32_t product = a * b;
458 args.rval().setInt32(product > INT32_MAX
459 ? int32_t(INT32_MIN + (product - INT32_MAX - 1))
460 : int32_t(product));
461 return true;
462 }
463
464 // Implements Math.fround (20.2.2.16) up to step 3
465 bool
466 js::RoundFloat32(JSContext *cx, Handle<Value> v, float *out)
467 {
468 double d;
469 bool success = ToNumber(cx, v, &d);
470 *out = static_cast<float>(d);
471 return success;
472 }
473
474 bool
475 js::math_fround(JSContext *cx, unsigned argc, Value *vp)
476 {
477 CallArgs args = CallArgsFromVp(argc, vp);
478
479 if (args.length() == 0) {
480 args.rval().setNaN();
481 return true;
482 }
483
484 float f;
485 if (!RoundFloat32(cx, args[0], &f))
486 return false;
487
488 args.rval().setDouble(static_cast<double>(f));
489 return true;
490 }
491
492 #if defined(SOLARIS) && defined(__GNUC__)
493 #define LOG_IF_OUT_OF_RANGE(x) if (x < 0) return GenericNaN();
494 #else
495 #define LOG_IF_OUT_OF_RANGE(x)
496 #endif
497
498 double
499 js::math_log_impl(MathCache *cache, double x)
500 {
501 LOG_IF_OUT_OF_RANGE(x);
502 return cache->lookup(log, x);
503 }
504
505 double
506 js::math_log_uncached(double x)
507 {
508 LOG_IF_OUT_OF_RANGE(x);
509 return log(x);
510 }
511
512 #undef LOG_IF_OUT_OF_RANGE
513
514 bool
515 js::math_log(JSContext *cx, unsigned argc, Value *vp)
516 {
517 CallArgs args = CallArgsFromVp(argc, vp);
518
519 if (args.length() == 0) {
520 args.rval().setNaN();
521 return true;
522 }
523
524 double x;
525 if (!ToNumber(cx, args[0], &x))
526 return false;
527
528 MathCache *mathCache = cx->runtime()->getMathCache(cx);
529 if (!mathCache)
530 return false;
531
532 double z = math_log_impl(mathCache, x);
533 args.rval().setNumber(z);
534 return true;
535 }
536
537 bool
538 js_math_max(JSContext *cx, unsigned argc, Value *vp)
539 {
540 CallArgs args = CallArgsFromVp(argc, vp);
541
542 double maxval = NegativeInfinity<double>();
543 for (unsigned i = 0; i < args.length(); i++) {
544 double x;
545 if (!ToNumber(cx, args[i], &x))
546 return false;
547 // Math.max(num, NaN) => NaN, Math.max(-0, +0) => +0
548 if (x > maxval || IsNaN(x) || (x == maxval && IsNegative(maxval)))
549 maxval = x;
550 }
551 args.rval().setNumber(maxval);
552 return true;
553 }
554
555 bool
556 js_math_min(JSContext *cx, unsigned argc, Value *vp)
557 {
558 CallArgs args = CallArgsFromVp(argc, vp);
559
560 double minval = PositiveInfinity<double>();
561 for (unsigned i = 0; i < args.length(); i++) {
562 double x;
563 if (!ToNumber(cx, args[i], &x))
564 return false;
565 // Math.min(num, NaN) => NaN, Math.min(-0, +0) => -0
566 if (x < minval || IsNaN(x) || (x == minval && IsNegativeZero(x)))
567 minval = x;
568 }
569 args.rval().setNumber(minval);
570 return true;
571 }
572
573 // Disable PGO for Math.pow() and related functions (see bug 791214).
574 #if defined(_MSC_VER)
575 # pragma optimize("g", off)
576 #endif
577 double
578 js::powi(double x, int y)
579 {
580 unsigned n = (y < 0) ? -y : y;
581 double m = x;
582 double p = 1;
583 while (true) {
584 if ((n & 1) != 0) p *= m;
585 n >>= 1;
586 if (n == 0) {
587 if (y < 0) {
588 // Unfortunately, we have to be careful when p has reached
589 // infinity in the computation, because sometimes the higher
590 // internal precision in the pow() implementation would have
591 // given us a finite p. This happens very rarely.
592
593 double result = 1.0 / p;
594 return (result == 0 && IsInfinite(p))
595 ? pow(x, static_cast<double>(y)) // Avoid pow(double, int).
596 : result;
597 }
598
599 return p;
600 }
601 m *= m;
602 }
603 }
604 #if defined(_MSC_VER)
605 # pragma optimize("", on)
606 #endif
607
608 // Disable PGO for Math.pow() and related functions (see bug 791214).
609 #if defined(_MSC_VER)
610 # pragma optimize("g", off)
611 #endif
612 double
613 js::ecmaPow(double x, double y)
614 {
615 /*
616 * Use powi if the exponent is an integer-valued double. We don't have to
617 * check for NaN since a comparison with NaN is always false.
618 */
619 int32_t yi;
620 if (NumberEqualsInt32(y, &yi))
621 return powi(x, yi);
622
623 /*
624 * Because C99 and ECMA specify different behavior for pow(),
625 * we need to wrap the libm call to make it ECMA compliant.
626 */
627 if (!IsFinite(y) && (x == 1.0 || x == -1.0))
628 return GenericNaN();
629
630 /* pow(x, +-0) is always 1, even for x = NaN (MSVC gets this wrong). */
631 if (y == 0)
632 return 1;
633
634 /*
635 * Special case for square roots. Note that pow(x, 0.5) != sqrt(x)
636 * when x = -0.0, so we have to guard for this.
637 */
638 if (IsFinite(x) && x != 0.0) {
639 if (y == 0.5)
640 return sqrt(x);
641 if (y == -0.5)
642 return 1.0 / sqrt(x);
643 }
644 return pow(x, y);
645 }
646 #if defined(_MSC_VER)
647 # pragma optimize("", on)
648 #endif
649
650 // Disable PGO for Math.pow() and related functions (see bug 791214).
651 #if defined(_MSC_VER)
652 # pragma optimize("g", off)
653 #endif
654 bool
655 js_math_pow(JSContext *cx, unsigned argc, Value *vp)
656 {
657 CallArgs args = CallArgsFromVp(argc, vp);
658
659 double x;
660 if (!ToNumber(cx, args.get(0), &x))
661 return false;
662
663 double y;
664 if (!ToNumber(cx, args.get(1), &y))
665 return false;
666
667 double z = ecmaPow(x, y);
668 args.rval().setNumber(z);
669 return true;
670 }
671 #if defined(_MSC_VER)
672 # pragma optimize("", on)
673 #endif
674
675 static uint64_t
676 random_generateSeed()
677 {
678 union {
679 uint8_t u8[8];
680 uint32_t u32[2];
681 uint64_t u64;
682 } seed;
683 seed.u64 = 0;
684
685 #if defined(XP_WIN)
686 /*
687 * Our PRNG only uses 48 bits, so calling rand_s() twice to get 64 bits is
688 * probably overkill.
689 */
690 rand_s(&seed.u32[0]);
691 #elif defined(XP_UNIX)
692 /*
693 * In the unlikely event we can't read /dev/urandom, there's not much we can
694 * do, so just mix in the fd error code and the current time.
695 */
696 int fd = open("/dev/urandom", O_RDONLY);
697 MOZ_ASSERT(fd >= 0, "Can't open /dev/urandom");
698 if (fd >= 0) {
699 read(fd, seed.u8, mozilla::ArrayLength(seed.u8));
700 close(fd);
701 }
702 seed.u32[0] ^= fd;
703 #else
704 # error "Platform needs to implement random_generateSeed()"
705 #endif
706
707 seed.u32[1] ^= PRMJ_Now();
708 return seed.u64;
709 }
710
711 static const uint64_t RNG_MULTIPLIER = 0x5DEECE66DLL;
712 static const uint64_t RNG_ADDEND = 0xBLL;
713 static const uint64_t RNG_MASK = (1LL << 48) - 1;
714 static const double RNG_DSCALE = double(1LL << 53);
715
716 /*
717 * Math.random() support, lifted from java.util.Random.java.
718 */
719 static void
720 random_initState(uint64_t *rngState)
721 {
722 /* Our PRNG only uses 48 bits, so squeeze our entropy into those bits. */
723 uint64_t seed = random_generateSeed();
724 seed ^= (seed >> 16);
725 *rngState = (seed ^ RNG_MULTIPLIER) & RNG_MASK;
726 }
727
728 uint64_t
729 random_next(uint64_t *rngState, int bits)
730 {
731 MOZ_ASSERT((*rngState & 0xffff000000000000ULL) == 0, "Bad rngState");
732 MOZ_ASSERT(bits > 0 && bits <= 48, "bits is out of range");
733
734 if (*rngState == 0) {
735 random_initState(rngState);
736 }
737
738 uint64_t nextstate = *rngState * RNG_MULTIPLIER;
739 nextstate += RNG_ADDEND;
740 nextstate &= RNG_MASK;
741 *rngState = nextstate;
742 return nextstate >> (48 - bits);
743 }
744
745 static inline double
746 random_nextDouble(JSContext *cx)
747 {
748 uint64_t *rng = &cx->compartment()->rngState;
749 return double((random_next(rng, 26) << 27) + random_next(rng, 27)) / RNG_DSCALE;
750 }
751
752 double
753 math_random_no_outparam(JSContext *cx)
754 {
755 /* Calculate random without memory traffic, for use in the JITs. */
756 return random_nextDouble(cx);
757 }
758
759 bool
760 js_math_random(JSContext *cx, unsigned argc, Value *vp)
761 {
762 CallArgs args = CallArgsFromVp(argc, vp);
763 double z = random_nextDouble(cx);
764 args.rval().setDouble(z);
765 return true;
766 }
767
768 double
769 js::math_round_impl(double x)
770 {
771 int32_t ignored;
772 if (NumberIsInt32(x, &ignored))
773 return x;
774
775 /* Some numbers are so big that adding 0.5 would give the wrong number. */
776 if (ExponentComponent(x) >= int_fast16_t(FloatingPoint<double>::ExponentShift))
777 return x;
778
779 return js_copysign(floor(x + 0.5), x);
780 }
781
782 float
783 js::math_roundf_impl(float x)
784 {
785 int32_t ignored;
786 if (NumberIsInt32(x, &ignored))
787 return x;
788
789 /* Some numbers are so big that adding 0.5 would give the wrong number. */
790 if (ExponentComponent(x) >= int_fast16_t(FloatingPoint<float>::ExponentShift))
791 return x;
792
793 return js_copysign(floorf(x + 0.5f), x);
794 }
795
796 bool /* ES5 15.8.2.15. */
797 js::math_round(JSContext *cx, unsigned argc, Value *vp)
798 {
799 CallArgs args = CallArgsFromVp(argc, vp);
800
801 if (args.length() == 0) {
802 args.rval().setNaN();
803 return true;
804 }
805
806 double x;
807 if (!ToNumber(cx, args[0], &x))
808 return false;
809
810 double z = math_round_impl(x);
811 args.rval().setNumber(z);
812 return true;
813 }
814
815 double
816 js::math_sin_impl(MathCache *cache, double x)
817 {
818 return cache->lookup(sin, x);
819 }
820
821 double
822 js::math_sin_uncached(double x)
823 {
824 return sin(x);
825 }
826
827 bool
828 js::math_sin(JSContext *cx, unsigned argc, Value *vp)
829 {
830 CallArgs args = CallArgsFromVp(argc, vp);
831
832 if (args.length() == 0) {
833 args.rval().setNaN();
834 return true;
835 }
836
837 double x;
838 if (!ToNumber(cx, args[0], &x))
839 return false;
840
841 MathCache *mathCache = cx->runtime()->getMathCache(cx);
842 if (!mathCache)
843 return false;
844
845 double z = math_sin_impl(mathCache, x);
846 args.rval().setDouble(z);
847 return true;
848 }
849
850 bool
851 js_math_sqrt(JSContext *cx, unsigned argc, Value *vp)
852 {
853 CallArgs args = CallArgsFromVp(argc, vp);
854
855 if (args.length() == 0) {
856 args.rval().setNaN();
857 return true;
858 }
859
860 double x;
861 if (!ToNumber(cx, args[0], &x))
862 return false;
863
864 MathCache *mathCache = cx->runtime()->getMathCache(cx);
865 if (!mathCache)
866 return false;
867
868 double z = mathCache->lookup(sqrt, x);
869 args.rval().setDouble(z);
870 return true;
871 }
872
873 double
874 js::math_tan_impl(MathCache *cache, double x)
875 {
876 return cache->lookup(tan, x);
877 }
878
879 double
880 js::math_tan_uncached(double x)
881 {
882 return tan(x);
883 }
884
885 bool
886 js::math_tan(JSContext *cx, unsigned argc, Value *vp)
887 {
888 CallArgs args = CallArgsFromVp(argc, vp);
889
890 if (args.length() == 0) {
891 args.rval().setNaN();
892 return true;
893 }
894
895 double x;
896 if (!ToNumber(cx, args[0], &x))
897 return false;
898
899 MathCache *mathCache = cx->runtime()->getMathCache(cx);
900 if (!mathCache)
901 return false;
902
903 double z = math_tan_impl(mathCache, x);
904 args.rval().setDouble(z);
905 return true;
906 }
907
908
909 typedef double (*UnaryMathFunctionType)(MathCache *cache, double);
910
911 template <UnaryMathFunctionType F>
912 static bool math_function(JSContext *cx, unsigned argc, Value *vp)
913 {
914 CallArgs args = CallArgsFromVp(argc, vp);
915 if (args.length() == 0) {
916 args.rval().setNumber(GenericNaN());
917 return true;
918 }
919
920 double x;
921 if (!ToNumber(cx, args[0], &x))
922 return false;
923
924 MathCache *mathCache = cx->runtime()->getMathCache(cx);
925 if (!mathCache)
926 return false;
927 double z = F(mathCache, x);
928 args.rval().setNumber(z);
929
930 return true;
931 }
932
933
934
935 double
936 js::math_log10_impl(MathCache *cache, double x)
937 {
938 return cache->lookup(log10, x);
939 }
940
941 double
942 js::math_log10_uncached(double x)
943 {
944 return log10(x);
945 }
946
947 bool
948 js::math_log10(JSContext *cx, unsigned argc, Value *vp)
949 {
950 return math_function<math_log10_impl>(cx, argc, vp);
951 }
952
953 #if !HAVE_LOG2
954 double log2(double x)
955 {
956 return log(x) / M_LN2;
957 }
958 #endif
959
960 double
961 js::math_log2_impl(MathCache *cache, double x)
962 {
963 return cache->lookup(log2, x);
964 }
965
966 double
967 js::math_log2_uncached(double x)
968 {
969 return log2(x);
970 }
971
972 bool
973 js::math_log2(JSContext *cx, unsigned argc, Value *vp)
974 {
975 return math_function<math_log2_impl>(cx, argc, vp);
976 }
977
978 #if !HAVE_LOG1P
979 double log1p(double x)
980 {
981 if (fabs(x) < 1e-4) {
982 /*
983 * Use Taylor approx. log(1 + x) = x - x^2 / 2 + x^3 / 3 - x^4 / 4 with error x^5 / 5
984 * Since |x| < 10^-4, |x|^5 < 10^-20, relative error less than 10^-16
985 */
986 double z = -(x * x * x * x) / 4 + (x * x * x) / 3 - (x * x) / 2 + x;
987 return z;
988 } else {
989 /* For other large enough values of x use direct computation */
990 return log(1.0 + x);
991 }
992 }
993 #endif
994
995 #ifdef __APPLE__
996 // Ensure that log1p(-0) is -0.
997 #define LOG1P_IF_OUT_OF_RANGE(x) if (x == 0) return x;
998 #else
999 #define LOG1P_IF_OUT_OF_RANGE(x)
1000 #endif
1001
1002 double
1003 js::math_log1p_impl(MathCache *cache, double x)
1004 {
1005 LOG1P_IF_OUT_OF_RANGE(x);
1006 return cache->lookup(log1p, x);
1007 }
1008
1009 double
1010 js::math_log1p_uncached(double x)
1011 {
1012 LOG1P_IF_OUT_OF_RANGE(x);
1013 return log1p(x);
1014 }
1015
1016 #undef LOG1P_IF_OUT_OF_RANGE
1017
1018 bool
1019 js::math_log1p(JSContext *cx, unsigned argc, Value *vp)
1020 {
1021 return math_function<math_log1p_impl>(cx, argc, vp);
1022 }
1023
1024 #if !HAVE_EXPM1
1025 double expm1(double x)
1026 {
1027 /* Special handling for -0 */
1028 if (x == 0.0)
1029 return x;
1030
1031 if (fabs(x) < 1e-5) {
1032 /*
1033 * Use Taylor approx. exp(x) - 1 = x + x^2 / 2 + x^3 / 6 with error x^4 / 24
1034 * Since |x| < 10^-5, |x|^4 < 10^-20, relative error less than 10^-15
1035 */
1036 double z = (x * x * x) / 6 + (x * x) / 2 + x;
1037 return z;
1038 } else {
1039 /* For other large enough values of x use direct computation */
1040 return exp(x) - 1.0;
1041 }
1042 }
1043 #endif
1044
1045 double
1046 js::math_expm1_impl(MathCache *cache, double x)
1047 {
1048 return cache->lookup(expm1, x);
1049 }
1050
1051 double
1052 js::math_expm1_uncached(double x)
1053 {
1054 return expm1(x);
1055 }
1056
1057 bool
1058 js::math_expm1(JSContext *cx, unsigned argc, Value *vp)
1059 {
1060 return math_function<math_expm1_impl>(cx, argc, vp);
1061 }
1062
1063 #if !HAVE_SQRT1PM1
1064 /* This algorithm computes sqrt(1+x)-1 for small x */
1065 double sqrt1pm1(double x)
1066 {
1067 if (fabs(x) > 0.75)
1068 return sqrt(1 + x) - 1;
1069
1070 return expm1(log1p(x) / 2);
1071 }
1072 #endif
1073
1074
1075 double
1076 js::math_cosh_impl(MathCache *cache, double x)
1077 {
1078 return cache->lookup(cosh, x);
1079 }
1080
1081 double
1082 js::math_cosh_uncached(double x)
1083 {
1084 return cosh(x);
1085 }
1086
1087 bool
1088 js::math_cosh(JSContext *cx, unsigned argc, Value *vp)
1089 {
1090 return math_function<math_cosh_impl>(cx, argc, vp);
1091 }
1092
1093 double
1094 js::math_sinh_impl(MathCache *cache, double x)
1095 {
1096 return cache->lookup(sinh, x);
1097 }
1098
1099 double
1100 js::math_sinh_uncached(double x)
1101 {
1102 return sinh(x);
1103 }
1104
1105 bool
1106 js::math_sinh(JSContext *cx, unsigned argc, Value *vp)
1107 {
1108 return math_function<math_sinh_impl>(cx, argc, vp);
1109 }
1110
1111 double
1112 js::math_tanh_impl(MathCache *cache, double x)
1113 {
1114 return cache->lookup(tanh, x);
1115 }
1116
1117 double
1118 js::math_tanh_uncached(double x)
1119 {
1120 return tanh(x);
1121 }
1122
1123 bool
1124 js::math_tanh(JSContext *cx, unsigned argc, Value *vp)
1125 {
1126 return math_function<math_tanh_impl>(cx, argc, vp);
1127 }
1128
1129 #if !HAVE_ACOSH
1130 double acosh(double x)
1131 {
1132 const double SQUARE_ROOT_EPSILON = sqrt(std::numeric_limits<double>::epsilon());
1133
1134 if ((x - 1) >= SQUARE_ROOT_EPSILON) {
1135 if (x > 1 / SQUARE_ROOT_EPSILON) {
1136 /*
1137 * http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/06/01/0001/
1138 * approximation by laurent series in 1/x at 0+ order from -1 to 0
1139 */
1140 return log(x) + M_LN2;
1141 } else if (x < 1.5) {
1142 // This is just a rearrangement of the standard form below
1143 // devised to minimize loss of precision when x ~ 1:
1144 double y = x - 1;
1145 return log1p(y + sqrt(y * y + 2 * y));
1146 } else {
1147 // http://functions.wolfram.com/ElementaryFunctions/ArcCosh/02/
1148 return log(x + sqrt(x * x - 1));
1149 }
1150 } else {
1151 // see http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/04/01/0001/
1152 double y = x - 1;
1153 // approximation by taylor series in y at 0 up to order 2.
1154 // If x is less than 1, sqrt(2 * y) is NaN and the result is NaN.
1155 return sqrt(2 * y) * (1 - y / 12 + 3 * y * y / 160);
1156 }
1157 }
1158 #endif
1159
1160 double
1161 js::math_acosh_impl(MathCache *cache, double x)
1162 {
1163 return cache->lookup(acosh, x);
1164 }
1165
1166 double
1167 js::math_acosh_uncached(double x)
1168 {
1169 return acosh(x);
1170 }
1171
1172 bool
1173 js::math_acosh(JSContext *cx, unsigned argc, Value *vp)
1174 {
1175 return math_function<math_acosh_impl>(cx, argc, vp);
1176 }
1177
1178 #if !HAVE_ASINH
1179 // Bug 899712 - gcc incorrectly rewrites -asinh(-x) to asinh(x) when overriding
1180 // asinh.
1181 static double my_asinh(double x)
1182 {
1183 const double SQUARE_ROOT_EPSILON = sqrt(std::numeric_limits<double>::epsilon());
1184 const double FOURTH_ROOT_EPSILON = sqrt(SQUARE_ROOT_EPSILON);
1185
1186 if (x >= FOURTH_ROOT_EPSILON) {
1187 if (x > 1 / SQUARE_ROOT_EPSILON)
1188 // http://functions.wolfram.com/ElementaryFunctions/ArcSinh/06/01/06/01/0001/
1189 // approximation by laurent series in 1/x at 0+ order from -1 to 1
1190 return M_LN2 + log(x) + 1 / (4 * x * x);
1191 else if (x < 0.5)
1192 return log1p(x + sqrt1pm1(x * x));
1193 else
1194 return log(x + sqrt(x * x + 1));
1195 } else if (x <= -FOURTH_ROOT_EPSILON) {
1196 return -my_asinh(-x);
1197 } else {
1198 // http://functions.wolfram.com/ElementaryFunctions/ArcSinh/06/01/03/01/0001/
1199 // approximation by taylor series in x at 0 up to order 2
1200 double result = x;
1201
1202 if (fabs(x) >= SQUARE_ROOT_EPSILON) {
1203 double x3 = x * x * x;
1204 // approximation by taylor series in x at 0 up to order 4
1205 result -= x3 / 6;
1206 }
1207
1208 return result;
1209 }
1210 }
1211 #endif
1212
1213 double
1214 js::math_asinh_impl(MathCache *cache, double x)
1215 {
1216 #ifdef HAVE_ASINH
1217 return cache->lookup(asinh, x);
1218 #else
1219 return cache->lookup(my_asinh, x);
1220 #endif
1221 }
1222
1223 double
1224 js::math_asinh_uncached(double x)
1225 {
1226 #ifdef HAVE_ASINH
1227 return asinh(x);
1228 #else
1229 return my_asinh(x);
1230 #endif
1231 }
1232
1233 bool
1234 js::math_asinh(JSContext *cx, unsigned argc, Value *vp)
1235 {
1236 return math_function<math_asinh_impl>(cx, argc, vp);
1237 }
1238
1239 #if !HAVE_ATANH
1240 double atanh(double x)
1241 {
1242 const double EPSILON = std::numeric_limits<double>::epsilon();
1243 const double SQUARE_ROOT_EPSILON = sqrt(EPSILON);
1244 const double FOURTH_ROOT_EPSILON = sqrt(SQUARE_ROOT_EPSILON);
1245
1246 if (fabs(x) >= FOURTH_ROOT_EPSILON) {
1247 // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/02/
1248 if (fabs(x) < 0.5)
1249 return (log1p(x) - log1p(-x)) / 2;
1250
1251 return log((1 + x) / (1 - x)) / 2;
1252 } else {
1253 // http://functions.wolfram.com/ElementaryFunctions/ArcTanh/06/01/03/01/
1254 // approximation by taylor series in x at 0 up to order 2
1255 double result = x;
1256
1257 if (fabs(x) >= SQUARE_ROOT_EPSILON) {
1258 double x3 = x * x * x;
1259 result += x3 / 3;
1260 }
1261
1262 return result;
1263 }
1264 }
1265 #endif
1266
1267 double
1268 js::math_atanh_impl(MathCache *cache, double x)
1269 {
1270 return cache->lookup(atanh, x);
1271 }
1272
1273 double
1274 js::math_atanh_uncached(double x)
1275 {
1276 return atanh(x);
1277 }
1278
1279 bool
1280 js::math_atanh(JSContext *cx, unsigned argc, Value *vp)
1281 {
1282 return math_function<math_atanh_impl>(cx, argc, vp);
1283 }
1284
1285 /* Consistency wrapper for platform deviations in hypot() */
1286 double
1287 js::ecmaHypot(double x, double y)
1288 {
1289 #ifdef XP_WIN
1290 /*
1291 * Workaround MS hypot bug, where hypot(Infinity, NaN or Math.MIN_VALUE)
1292 * is NaN, not Infinity.
1293 */
1294 if (mozilla::IsInfinite(x) || mozilla::IsInfinite(y)) {
1295 return mozilla::PositiveInfinity<double>();
1296 }
1297 #endif
1298 return hypot(x, y);
1299 }
1300
1301 bool
1302 js::math_hypot(JSContext *cx, unsigned argc, Value *vp)
1303 {
1304 CallArgs args = CallArgsFromVp(argc, vp);
1305
1306 // IonMonkey calls the system hypot function directly if two arguments are
1307 // given. Do that here as well to get the same results.
1308 if (args.length() == 2) {
1309 double x, y;
1310 if (!ToNumber(cx, args[0], &x))
1311 return false;
1312 if (!ToNumber(cx, args[1], &y))
1313 return false;
1314
1315 double result = ecmaHypot(x, y);
1316 args.rval().setNumber(result);
1317 return true;
1318 }
1319
1320 bool isInfinite = false;
1321 bool isNaN = false;
1322
1323 double scale = 0;
1324 double sumsq = 1;
1325
1326 for (unsigned i = 0; i < args.length(); i++) {
1327 double x;
1328 if (!ToNumber(cx, args[i], &x))
1329 return false;
1330
1331 isInfinite |= mozilla::IsInfinite(x);
1332 isNaN |= mozilla::IsNaN(x);
1333
1334 double xabs = mozilla::Abs(x);
1335
1336 if (scale < xabs) {
1337 sumsq = 1 + sumsq * (scale / xabs) * (scale / xabs);
1338 scale = xabs;
1339 } else if (scale != 0) {
1340 sumsq += (xabs / scale) * (xabs / scale);
1341 }
1342 }
1343
1344 double result = isInfinite ? PositiveInfinity<double>() :
1345 isNaN ? GenericNaN() :
1346 scale * sqrt(sumsq);
1347 args.rval().setNumber(result);
1348 return true;
1349 }
1350
1351 #if !HAVE_TRUNC
1352 double trunc(double x)
1353 {
1354 return x > 0 ? floor(x) : ceil(x);
1355 }
1356 #endif
1357
1358 double
1359 js::math_trunc_impl(MathCache *cache, double x)
1360 {
1361 return cache->lookup(trunc, x);
1362 }
1363
1364 double
1365 js::math_trunc_uncached(double x)
1366 {
1367 return trunc(x);
1368 }
1369
1370 bool
1371 js::math_trunc(JSContext *cx, unsigned argc, Value *vp)
1372 {
1373 return math_function<math_trunc_impl>(cx, argc, vp);
1374 }
1375
1376 static double sign(double x)
1377 {
1378 if (mozilla::IsNaN(x))
1379 return GenericNaN();
1380
1381 return x == 0 ? x : x < 0 ? -1 : 1;
1382 }
1383
1384 double
1385 js::math_sign_impl(MathCache *cache, double x)
1386 {
1387 return cache->lookup(sign, x);
1388 }
1389
1390 double
1391 js::math_sign_uncached(double x)
1392 {
1393 return sign(x);
1394 }
1395
1396 bool
1397 js::math_sign(JSContext *cx, unsigned argc, Value *vp)
1398 {
1399 return math_function<math_sign_impl>(cx, argc, vp);
1400 }
1401
1402 #if !HAVE_CBRT
1403 double cbrt(double x)
1404 {
1405 if (x > 0) {
1406 return pow(x, 1.0 / 3.0);
1407 } else if (x == 0) {
1408 return x;
1409 } else {
1410 return -pow(-x, 1.0 / 3.0);
1411 }
1412 }
1413 #endif
1414
1415 double
1416 js::math_cbrt_impl(MathCache *cache, double x)
1417 {
1418 return cache->lookup(cbrt, x);
1419 }
1420
1421 double
1422 js::math_cbrt_uncached(double x)
1423 {
1424 return cbrt(x);
1425 }
1426
1427 bool
1428 js::math_cbrt(JSContext *cx, unsigned argc, Value *vp)
1429 {
1430 return math_function<math_cbrt_impl>(cx, argc, vp);
1431 }
1432
1433 #if JS_HAS_TOSOURCE
1434 static bool
1435 math_toSource(JSContext *cx, unsigned argc, Value *vp)
1436 {
1437 CallArgs args = CallArgsFromVp(argc, vp);
1438 args.rval().setString(cx->names().Math);
1439 return true;
1440 }
1441 #endif
1442
1443 static const JSFunctionSpec math_static_methods[] = {
1444 #if JS_HAS_TOSOURCE
1445 JS_FN(js_toSource_str, math_toSource, 0, 0),
1446 #endif
1447 JS_FN("abs", js_math_abs, 1, 0),
1448 JS_FN("acos", math_acos, 1, 0),
1449 JS_FN("asin", math_asin, 1, 0),
1450 JS_FN("atan", math_atan, 1, 0),
1451 JS_FN("atan2", math_atan2, 2, 0),
1452 JS_FN("ceil", math_ceil, 1, 0),
1453 JS_FN("clz32", math_clz32, 1, 0),
1454 JS_FN("cos", math_cos, 1, 0),
1455 JS_FN("exp", math_exp, 1, 0),
1456 JS_FN("floor", math_floor, 1, 0),
1457 JS_FN("imul", math_imul, 2, 0),
1458 JS_FN("fround", math_fround, 1, 0),
1459 JS_FN("log", math_log, 1, 0),
1460 JS_FN("max", js_math_max, 2, 0),
1461 JS_FN("min", js_math_min, 2, 0),
1462 JS_FN("pow", js_math_pow, 2, 0),
1463 JS_FN("random", js_math_random, 0, 0),
1464 JS_FN("round", math_round, 1, 0),
1465 JS_FN("sin", math_sin, 1, 0),
1466 JS_FN("sqrt", js_math_sqrt, 1, 0),
1467 JS_FN("tan", math_tan, 1, 0),
1468 JS_FN("log10", math_log10, 1, 0),
1469 JS_FN("log2", math_log2, 1, 0),
1470 JS_FN("log1p", math_log1p, 1, 0),
1471 JS_FN("expm1", math_expm1, 1, 0),
1472 JS_FN("cosh", math_cosh, 1, 0),
1473 JS_FN("sinh", math_sinh, 1, 0),
1474 JS_FN("tanh", math_tanh, 1, 0),
1475 JS_FN("acosh", math_acosh, 1, 0),
1476 JS_FN("asinh", math_asinh, 1, 0),
1477 JS_FN("atanh", math_atanh, 1, 0),
1478 JS_FN("hypot", math_hypot, 2, 0),
1479 JS_FN("trunc", math_trunc, 1, 0),
1480 JS_FN("sign", math_sign, 1, 0),
1481 JS_FN("cbrt", math_cbrt, 1, 0),
1482 JS_FS_END
1483 };
1484
1485 JSObject *
1486 js_InitMathClass(JSContext *cx, HandleObject obj)
1487 {
1488 RootedObject proto(cx, obj->as<GlobalObject>().getOrCreateObjectPrototype(cx));
1489 if (!proto)
1490 return nullptr;
1491 RootedObject Math(cx, NewObjectWithGivenProto(cx, &MathClass, proto, obj, SingletonObject));
1492 if (!Math)
1493 return nullptr;
1494
1495 if (!JS_DefineProperty(cx, obj, js_Math_str, Math, 0,
1496 JS_PropertyStub, JS_StrictPropertyStub))
1497 {
1498 return nullptr;
1499 }
1500
1501 if (!JS_DefineFunctions(cx, Math, math_static_methods))
1502 return nullptr;
1503 if (!JS_DefineConstDoubles(cx, Math, math_constants))
1504 return nullptr;
1505
1506 obj->as<GlobalObject>().setConstructor(JSProto_Math, ObjectValue(*Math));
1507
1508 return Math;
1509 }

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