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/* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
* vim: set ts=8 sts=4 et sw=4 tw=99:
* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
/*
* JS math package.
*/
#include "jsmath.h"
#include "mozilla/FloatingPoint.h"
#include "mozilla/MathAlgorithms.h"
#include "mozilla/MemoryReporting.h"
#include <algorithm> // for std::max
#include <fcntl.h>
#if defined(STARBOARD)
#include "starboard/system.h"
#endif
#ifdef XP_UNIX
# include <unistd.h>
#endif
#ifdef XP_WIN
# include "jswin.h"
#endif
#include "jsapi.h"
#include "jsatom.h"
#include "jscntxt.h"
#include "jscompartment.h"
#include "jslibmath.h"
#include "jstypes.h"
#include "jit/InlinableNatives.h"
#include "js/Class.h"
#include "vm/Time.h"
#include "jsobjinlines.h"
#if defined(XP_WIN)
// #define needed to link in RtlGenRandom(), a.k.a. SystemFunction036. See the
// "Community Additions" comment on MSDN here:
// https://msdn.microsoft.com/en-us/library/windows/desktop/aa387694.aspx
# define SystemFunction036 NTAPI SystemFunction036
# include <NTSecAPI.h>
# undef SystemFunction036
#endif
#if defined(ANDROID) || defined(XP_DARWIN) || defined(__DragonFly__) || \
defined(__FreeBSD__) || defined(__NetBSD__) || defined(__OpenBSD__)
# include <stdlib.h>
# define HAVE_ARC4RANDOM
#endif
#if defined(STARBOARD)
#undef HAVE_ARC4RANDOM
#define HAVE_LOG2 1
#endif
using namespace js;
using mozilla::Abs;
using mozilla::NumberEqualsInt32;
using mozilla::NumberIsInt32;
using mozilla::ExponentComponent;
using mozilla::FloatingPoint;
using mozilla::IsFinite;
using mozilla::IsInfinite;
using mozilla::IsNaN;
using mozilla::IsNegative;
using mozilla::IsNegativeZero;
using mozilla::PositiveInfinity;
using mozilla::NegativeInfinity;
using JS::ToNumber;
using JS::GenericNaN;
static const JSConstDoubleSpec math_constants[] = {
{"E" , M_E },
{"LOG2E" , M_LOG2E },
{"LOG10E" , M_LOG10E },
{"LN2" , M_LN2 },
{"LN10" , M_LN10 },
{"PI" , M_PI },
{"SQRT2" , M_SQRT2 },
{"SQRT1_2", M_SQRT1_2 },
{0,0}
};
MathCache::MathCache() {
memset(table, 0, sizeof(table));
/* See comments in lookup(). */
MOZ_ASSERT(IsNegativeZero(-0.0));
MOZ_ASSERT(!IsNegativeZero(+0.0));
MOZ_ASSERT(hash(-0.0, MathCache::Sin) != hash(+0.0, MathCache::Sin));
}
size_t
MathCache::sizeOfIncludingThis(mozilla::MallocSizeOf mallocSizeOf)
{
return mallocSizeOf(this);
}
const Class js::MathClass = {
js_Math_str,
JSCLASS_HAS_CACHED_PROTO(JSProto_Math)
};
bool
js::math_abs_handle(JSContext* cx, js::HandleValue v, js::MutableHandleValue r)
{
double x;
if (!ToNumber(cx, v, &x))
return false;
double z = Abs(x);
r.setNumber(z);
return true;
}
bool
js::math_abs(JSContext* cx, unsigned argc, Value* vp)
{
CallArgs args = CallArgsFromVp(argc, vp);
if (args.length() == 0) {
args.rval().setNaN();
return true;
}
return math_abs_handle(cx, args[0], args.rval());
}
#if defined(SOLARIS) && defined(__GNUC__)
#define ACOS_IF_OUT_OF_RANGE(x) if (x < -1 || 1 < x) return GenericNaN();
#else
#define ACOS_IF_OUT_OF_RANGE(x)
#endif
double
js::math_acos_impl(MathCache* cache, double x)
{
ACOS_IF_OUT_OF_RANGE(x);
return cache->lookup(acos, x, MathCache::Acos);
}
double
js::math_acos_uncached(double x)
{
ACOS_IF_OUT_OF_RANGE(x);
return acos(x);
}
#undef ACOS_IF_OUT_OF_RANGE
bool
js::math_acos(JSContext* cx, unsigned argc, Value* vp)
{
CallArgs args = CallArgsFromVp(argc, vp);
if (args.length() == 0) {
args.rval().setNaN();
return true;
}
double x;
if (!ToNumber(cx, args[0], &x))
return false;
MathCache* mathCache = cx->runtime()->getMathCache(cx);
if (!mathCache)
return false;
double z = math_acos_impl(mathCache, x);
args.rval().setDouble(z);
return true;
}
#if defined(SOLARIS) && defined(__GNUC__)
#define ASIN_IF_OUT_OF_RANGE(x) if (x < -1 || 1 < x) return GenericNaN();
#else
#define ASIN_IF_OUT_OF_RANGE(x)
#endif
double
js::math_asin_impl(MathCache* cache, double x)
{
ASIN_IF_OUT_OF_RANGE(x);
return cache->lookup(asin, x, MathCache::Asin);
}
double
js::math_asin_uncached(double x)
{
ASIN_IF_OUT_OF_RANGE(x);
return asin(x);
}
#undef ASIN_IF_OUT_OF_RANGE
bool
js::math_asin(JSContext* cx, unsigned argc, Value* vp)
{
CallArgs args = CallArgsFromVp(argc, vp);
if (args.length() == 0) {
args.rval().setNaN();
return true;
}
double x;
if (!ToNumber(cx, args[0], &x))
return false;
MathCache* mathCache = cx->runtime()->getMathCache(cx);
if (!mathCache)
return false;
double z = math_asin_impl(mathCache, x);
args.rval().setDouble(z);
return true;
}
double
js::math_atan_impl(MathCache* cache, double x)
{
return cache->lookup(atan, x, MathCache::Atan);
}
double
js::math_atan_uncached(double x)
{
return atan(x);
}
bool
js::math_atan(JSContext* cx, unsigned argc, Value* vp)
{
CallArgs args = CallArgsFromVp(argc, vp);
if (args.length() == 0) {
args.rval().setNaN();
return true;
}
double x;
if (!ToNumber(cx, args[0], &x))
return false;
MathCache* mathCache = cx->runtime()->getMathCache(cx);
if (!mathCache)
return false;
double z = math_atan_impl(mathCache, x);
args.rval().setDouble(z);
return true;
}
double
js::ecmaAtan2(double y, double x)
{
#if defined(_MSC_VER)
/*
* MSVC's atan2 does not yield the result demanded by ECMA when both x
* and y are infinite.
* - The result is a multiple of pi/4.
* - The sign of y determines the sign of the result.
* - The sign of x determines the multiplicator, 1 or 3.
*/
if (IsInfinite(y) && IsInfinite(x)) {
double z = js_copysign(M_PI / 4, y);
if (x < 0)
z *= 3;
return z;
}
#endif
#if defined(SOLARIS) && defined(__GNUC__)
if (y == 0) {
if (IsNegativeZero(x))
return js_copysign(M_PI, y);
if (x == 0)
return y;
}
#endif
return atan2(y, x);
}
bool
js::math_atan2_handle(JSContext* cx, HandleValue y, HandleValue x, MutableHandleValue res)
{
double dy;
if (!ToNumber(cx, y, &dy))
return false;
double dx;
if (!ToNumber(cx, x, &dx))
return false;
double z = ecmaAtan2(dy, dx);
res.setDouble(z);
return true;
}
bool
js::math_atan2(JSContext* cx, unsigned argc, Value* vp)
{
CallArgs args = CallArgsFromVp(argc, vp);
return math_atan2_handle(cx, args.get(0), args.get(1), args.rval());
}
double
js::math_ceil_impl(double x)
{
#ifdef __APPLE__
if (x < 0 && x > -1.0)
return js_copysign(0, -1);
#endif
return ceil(x);
}
bool
js::math_ceil_handle(JSContext* cx, HandleValue v, MutableHandleValue res)
{
double d;
if(!ToNumber(cx, v, &d))
return false;
double result = math_ceil_impl(d);
res.setNumber(result);
return true;
}
bool
js::math_ceil(JSContext* cx, unsigned argc, Value* vp)
{
CallArgs args = CallArgsFromVp(argc, vp);
if (args.length() == 0) {
args.rval().setNaN();
return true;
}
return math_ceil_handle(cx, args[0], args.rval());
}
bool
js::math_clz32(JSContext* cx, unsigned argc, Value* vp)
{
CallArgs args = CallArgsFromVp(argc, vp);
if (args.length() == 0) {
args.rval().setInt32(32);
return true;
}
uint32_t n;
if (!ToUint32(cx, args[0], &n))
return false;
if (n == 0) {
args.rval().setInt32(32);
return true;
}
args.rval().setInt32(mozilla::CountLeadingZeroes32(n));
return true;
}
double
js::math_cos_impl(MathCache* cache, double x)
{
return cache->lookup(cos, x, MathCache::Cos);
}
double
js::math_cos_uncached(double x)
{
return cos(x);
}
bool
js::math_cos(JSContext* cx, unsigned argc, Value* vp)
{
CallArgs args = CallArgsFromVp(argc, vp);
if (args.length() == 0) {
args.rval().setNaN();
return true;
}
double x;
if (!ToNumber(cx, args[0], &x))
return false;
MathCache* mathCache = cx->runtime()->getMathCache(cx);
if (!mathCache)
return false;
double z = math_cos_impl(mathCache, x);
args.rval().setDouble(z);
return true;
}
#ifdef _WIN32
#define EXP_IF_OUT_OF_RANGE(x) \
if (!IsNaN(x)) { \
if (x == PositiveInfinity<double>()) \
return PositiveInfinity<double>(); \
if (x == NegativeInfinity<double>()) \
return 0.0; \
}
#else
#define EXP_IF_OUT_OF_RANGE(x)
#endif
double
js::math_exp_impl(MathCache* cache, double x)
{
EXP_IF_OUT_OF_RANGE(x);
return cache->lookup(exp, x, MathCache::Exp);
}
double
js::math_exp_uncached(double x)
{
EXP_IF_OUT_OF_RANGE(x);
return exp(x);
}
#undef EXP_IF_OUT_OF_RANGE
bool
js::math_exp(JSContext* cx, unsigned argc, Value* vp)
{
CallArgs args = CallArgsFromVp(argc, vp);
if (args.length() == 0) {
args.rval().setNaN();
return true;
}
double x;
if (!ToNumber(cx, args[0], &x))
return false;
MathCache* mathCache = cx->runtime()->getMathCache(cx);
if (!mathCache)
return false;
double z = math_exp_impl(mathCache, x);
args.rval().setNumber(z);
return true;
}
double
js::math_floor_impl(double x)
{
return floor(x);
}
bool
js::math_floor_handle(JSContext* cx, HandleValue v, MutableHandleValue r)
{
double d;
if (!ToNumber(cx, v, &d))
return false;
double z = math_floor_impl(d);
r.setNumber(z);
return true;
}
bool
js::math_floor(JSContext* cx, unsigned argc, Value* vp)
{
CallArgs args = CallArgsFromVp(argc, vp);
if (args.length() == 0) {
args.rval().setNaN();
return true;
}
return math_floor_handle(cx, args[0], args.rval());
}
bool
js::math_imul_handle(JSContext* cx, HandleValue lhs, HandleValue rhs, MutableHandleValue res)
{
uint32_t a = 0, b = 0;
if (!lhs.isUndefined() && !ToUint32(cx, lhs, &a))
return false;
if (!rhs.isUndefined() && !ToUint32(cx, rhs, &b))
return false;
uint32_t product = a * b;
res.setInt32(product > INT32_MAX
? int32_t(INT32_MIN + (product - INT32_MAX - 1))
: int32_t(product));
return true;
}
bool
js::math_imul(JSContext* cx, unsigned argc, Value* vp)
{
CallArgs args = CallArgsFromVp(argc, vp);
return math_imul_handle(cx, args.get(0), args.get(1), args.rval());
}
// Implements Math.fround (20.2.2.16) up to step 3
bool
js::RoundFloat32(JSContext* cx, HandleValue v, float* out)
{
double d;
bool success = ToNumber(cx, v, &d);
*out = static_cast<float>(d);
return success;
}
bool
js::RoundFloat32(JSContext* cx, HandleValue arg, MutableHandleValue res)
{
float f;
if (!RoundFloat32(cx, arg, &f))
return false;
res.setDouble(static_cast<double>(f));
return true;
}
bool
js::math_fround(JSContext* cx, unsigned argc, Value* vp)
{
CallArgs args = CallArgsFromVp(argc, vp);
if (args.length() == 0) {
args.rval().setNaN();
return true;
}
return RoundFloat32(cx, args[0], args.rval());
}
#if defined(SOLARIS) && defined(__GNUC__)
#define LOG_IF_OUT_OF_RANGE(x) if (x < 0) return GenericNaN();
#else
#define LOG_IF_OUT_OF_RANGE(x)
#endif
double
js::math_log_impl(MathCache* cache, double x)
{
LOG_IF_OUT_OF_RANGE(x);
return cache->lookup(math_log_uncached, x, MathCache::Log);
}
double
js::math_log_uncached(double x)
{
LOG_IF_OUT_OF_RANGE(x);
return log(x);
}
#undef LOG_IF_OUT_OF_RANGE
bool
js::math_log_handle(JSContext* cx, HandleValue val, MutableHandleValue res)
{
double in;
if (!ToNumber(cx, val, &in))
return false;
MathCache* mathCache = cx->runtime()->getMathCache(cx);
if (!mathCache)
return false;
double out = math_log_impl(mathCache, in);
res.setNumber(out);
return true;
}
bool
js::math_log(JSContext* cx, unsigned argc, Value* vp)
{
CallArgs args = CallArgsFromVp(argc, vp);
if (args.length() == 0) {
args.rval().setNaN();
return true;
}
return math_log_handle(cx, args[0], args.rval());
}
double
js::math_max_impl(double x, double y)
{
// Math.max(num, NaN) => NaN, Math.max(-0, +0) => +0
if (x > y || IsNaN(x) || (x == y && IsNegative(y)))
return x;
return y;
}
bool
js::math_max(JSContext* cx, unsigned argc, Value* vp)
{
CallArgs args = CallArgsFromVp(argc, vp);
double maxval = NegativeInfinity<double>();
for (unsigned i = 0; i < args.length(); i++) {
double x;
if (!ToNumber(cx, args[i], &x))
return false;
maxval = math_max_impl(x, maxval);
}
args.rval().setNumber(maxval);
return true;
}
double
js::math_min_impl(double x, double y)
{
// Math.min(num, NaN) => NaN, Math.min(-0, +0) => -0
if (x < y || IsNaN(x) || (x == y && IsNegativeZero(x)))
return x;
return y;
}
bool
js::math_min(JSContext* cx, unsigned argc, Value* vp)
{
CallArgs args = CallArgsFromVp(argc, vp);
double minval = PositiveInfinity<double>();
for (unsigned i = 0; i < args.length(); i++) {
double x;
if (!ToNumber(cx, args[i], &x))
return false;
minval = math_min_impl(x, minval);
}
args.rval().setNumber(minval);
return true;
}
bool
js::minmax_impl(JSContext* cx, bool max, HandleValue a, HandleValue b, MutableHandleValue res)
{
double x, y;
if (!ToNumber(cx, a, &x))
return false;
if (!ToNumber(cx, b, &y))
return false;
if (max)
res.setNumber(math_max_impl(x, y));
else
res.setNumber(math_min_impl(x, y));
return true;
}
double
js::powi(double x, int y)
{
unsigned n = (y < 0) ? -y : y;
double m = x;
double p = 1;
while (true) {
if ((n & 1) != 0) p *= m;
n >>= 1;
if (n == 0) {
if (y < 0) {
// Unfortunately, we have to be careful when p has reached
// infinity in the computation, because sometimes the higher
// internal precision in the pow() implementation would have
// given us a finite p. This happens very rarely.
double result = 1.0 / p;
return (result == 0 && IsInfinite(p))
? pow(x, static_cast<double>(y)) // Avoid pow(double, int).
: result;
}
return p;
}
m *= m;
}
}
double
js::ecmaPow(double x, double y)
{
/*
* Use powi if the exponent is an integer-valued double. We don't have to
* check for NaN since a comparison with NaN is always false.
*/
int32_t yi;
if (NumberEqualsInt32(y, &yi))
return powi(x, yi);
/*
* Because C99 and ECMA specify different behavior for pow(),
* we need to wrap the libm call to make it ECMA compliant.
*/
if (!IsFinite(y) && (x == 1.0 || x == -1.0))
return GenericNaN();
/* pow(x, +-0) is always 1, even for x = NaN (MSVC gets this wrong). */
if (y == 0)
return 1;
/*
* Special case for square roots. Note that pow(x, 0.5) != sqrt(x)
* when x = -0.0, so we have to guard for this.
*/
if (IsFinite(x) && x != 0.0) {
if (y == 0.5)
return sqrt(x);
if (y == -0.5)
return 1.0 / sqrt(x);
}
return pow(x, y);
}
bool
js::math_pow_handle(JSContext* cx, HandleValue base, HandleValue power, MutableHandleValue result)
{
double x;
if (!ToNumber(cx, base, &x))
return false;
double y;
if (!ToNumber(cx, power, &y))
return false;
double z = ecmaPow(x, y);
result.setNumber(z);
return true;
}
bool
js::math_pow(JSContext* cx, unsigned argc, Value* vp)
{
CallArgs args = CallArgsFromVp(argc, vp);
return math_pow_handle(cx, args.get(0), args.get(1), args.rval());
}
static uint64_t
GenerateSeed()
{
uint64_t seed = 0;
#if defined(XP_WIN)
MOZ_ALWAYS_TRUE(RtlGenRandom(&seed, sizeof(seed)));
#elif defined(HAVE_ARC4RANDOM)
seed = (static_cast<uint64_t>(arc4random()) << 32) | arc4random();
#elif defined(XP_UNIX)
int fd = open("/dev/urandom", O_RDONLY);
if (fd >= 0) {
read(fd, static_cast<void*>(&seed), sizeof(seed));
close(fd);
}
#elif defined(STARBOARD)
seed = SbSystemGetRandomUInt64();
#else
# error "Platform needs to implement GenerateSeed()"
#endif
// Also mix in PRMJ_Now() in case we couldn't read random bits from the OS.
return seed ^ PRMJ_Now();
}
void
js::GenerateXorShift128PlusSeed(mozilla::Array<uint64_t, 2>& seed)
{
// XorShift128PlusRNG must be initialized with a non-zero seed.
do {
seed[0] = GenerateSeed();
seed[1] = GenerateSeed();
} while (seed[0] == 0 && seed[1] == 0);
}
void
JSCompartment::ensureRandomNumberGenerator()
{
if (randomNumberGenerator.isNothing()) {
mozilla::Array<uint64_t, 2> seed;
GenerateXorShift128PlusSeed(seed);
randomNumberGenerator.emplace(seed[0], seed[1]);
}
}
bool
js::math_random(JSContext* cx, unsigned argc, Value* vp)
{
CallArgs args = CallArgsFromVp(argc, vp);
JSCompartment* comp = cx->compartment();
comp->ensureRandomNumberGenerator();
double z = comp->randomNumberGenerator.ref().nextDouble();
args.rval().setDouble(z);
return true;
}
bool
js::math_round_handle(JSContext* cx, HandleValue arg, MutableHandleValue res)
{
double d;
if (!ToNumber(cx, arg, &d))
return false;
d = math_round_impl(d);
res.setNumber(d);
return true;
}
template<typename T>
T
js::GetBiggestNumberLessThan(T x)
{
MOZ_ASSERT(!IsNegative(x));
MOZ_ASSERT(IsFinite(x));
typedef typename mozilla::FloatingPoint<T>::Bits Bits;
Bits bits = mozilla::BitwiseCast<Bits>(x);
MOZ_ASSERT(bits > 0, "will underflow");
return mozilla::BitwiseCast<T>(bits - 1);
}
template double js::GetBiggestNumberLessThan<>(double x);
template float js::GetBiggestNumberLessThan<>(float x);
double
js::math_round_impl(double x)
{
int32_t ignored;
if (NumberIsInt32(x, &ignored))
return x;
/* Some numbers are so big that adding 0.5 would give the wrong number. */
if (ExponentComponent(x) >= int_fast16_t(FloatingPoint<double>::kExponentShift))
return x;
double add = (x >= 0) ? GetBiggestNumberLessThan(0.5) : 0.5;
return js_copysign(floor(x + add), x);
}
float
js::math_roundf_impl(float x)
{
int32_t ignored;
if (NumberIsInt32(x, &ignored))
return x;
/* Some numbers are so big that adding 0.5 would give the wrong number. */
if (ExponentComponent(x) >= int_fast16_t(FloatingPoint<float>::kExponentShift))
return x;
float add = (x >= 0) ? GetBiggestNumberLessThan(0.5f) : 0.5f;
return js_copysign(floorf(x + add), x);
}
bool /* ES5 15.8.2.15. */
js::math_round(JSContext* cx, unsigned argc, Value* vp)
{
CallArgs args = CallArgsFromVp(argc, vp);
if (args.length() == 0) {
args.rval().setNaN();
return true;
}
return math_round_handle(cx, args[0], args.rval());
}
double
js::math_sin_impl(MathCache* cache, double x)
{
return cache->lookup(math_sin_uncached, x, MathCache::Sin);
}
double
js::math_sin_uncached(double x)
{
#ifdef _WIN64
// Workaround MSVC bug where sin(-0) is +0 instead of -0 on x64 on
// CPUs without FMA3 (pre-Haswell). See bug 1076670.
if (IsNegativeZero(x))
return -0.0;
#endif
return sin(x);
}
bool
js::math_sin_handle(JSContext* cx, HandleValue val, MutableHandleValue res)
{
double in;
if (!ToNumber(cx, val, &in))
return false;
MathCache* mathCache = cx->runtime()->getMathCache(cx);
if (!mathCache)
return false;
double out = math_sin_impl(mathCache, in);
res.setDouble(out);
return true;
}
bool
js::math_sin(JSContext* cx, unsigned argc, Value* vp)
{
CallArgs args = CallArgsFromVp(argc, vp);
if (args.length() == 0) {
args.rval().setNaN();
return true;
}
return math_sin_handle(cx, args[0], args.rval());
}
void
js::math_sincos_uncached(double x, double *sin, double *cos)
{
#if defined(__GLIBC__)
sincos(x, sin, cos);
#elif defined(HAVE_SINCOS)
__sincos(x, sin, cos);
#else
*sin = js::math_sin_uncached(x);
*cos = js::math_cos_uncached(x);
#endif
}
void
js::math_sincos_impl(MathCache* mathCache, double x, double *sin, double *cos)
{
unsigned indexSin;
unsigned indexCos;
bool hasSin = mathCache->isCached(x, MathCache::Sin, sin, &indexSin);
bool hasCos = mathCache->isCached(x, MathCache::Cos, cos, &indexCos);
if (!(hasSin || hasCos)) {
js::math_sincos_uncached(x, sin, cos);
mathCache->store(MathCache::Sin, x, *sin, indexSin);
mathCache->store(MathCache::Cos, x, *cos, indexCos);
return;
}
if (!hasSin)
*sin = js::math_sin_impl(mathCache, x);
if (!hasCos)
*cos = js::math_cos_impl(mathCache, x);
}
bool
js::math_sqrt_handle(JSContext* cx, HandleValue number, MutableHandleValue result)
{
double x;
if (!ToNumber(cx, number, &x))
return false;
MathCache* mathCache = cx->runtime()->getMathCache(cx);
if (!mathCache)
return false;
double z = mathCache->lookup(sqrt, x, MathCache::Sqrt);
result.setDouble(z);
return true;
}
bool
js::math_sqrt(JSContext* cx, unsigned argc, Value* vp)
{
CallArgs args = CallArgsFromVp(argc, vp);
if (args.length() == 0) {
args.rval().setNaN();
return true;
}
return math_sqrt_handle(cx, args[0], args.rval());
}
double
js::math_tan_impl(MathCache* cache, double x)
{
return cache->lookup(tan, x, MathCache::Tan);
}
double
js::math_tan_uncached(double x)
{
return tan(x);
}
bool
js::math_tan(JSContext* cx, unsigned argc, Value* vp)
{
CallArgs args = CallArgsFromVp(argc, vp);
if (args.length() == 0) {
args.rval().setNaN();
return true;
}
double x;
if (!ToNumber(cx, args[0], &x))
return false;
MathCache* mathCache = cx->runtime()->getMathCache(cx);
if (!mathCache)
return false;
double z = math_tan_impl(mathCache, x);
args.rval().setDouble(z);
return true;
}
typedef double (*UnaryMathFunctionType)(MathCache* cache, double);
template <UnaryMathFunctionType F>
static bool math_function(JSContext* cx, unsigned argc, Value* vp)
{
CallArgs args = CallArgsFromVp(argc, vp);
if (args.length() == 0) {
args.rval().setNumber(GenericNaN());
return true;
}
double x;
if (!ToNumber(cx, args[0], &x))
return false;
MathCache* mathCache = cx->runtime()->getMathCache(cx);
if (!mathCache)
return false;
double z = F(mathCache, x);
args.rval().setNumber(z);
return true;
}
double
js::math_log10_impl(MathCache* cache, double x)
{
return cache->lookup(log10, x, MathCache::Log10);
}
double
js::math_log10_uncached(double x)
{
return log10(x);
}
bool
js::math_log10(JSContext* cx, unsigned argc, Value* vp)
{
return math_function<math_log10_impl>(cx, argc, vp);
}
#if !HAVE_LOG2
double log2(double x)
{
return log(x) / M_LN2;
}
#endif
double
js::math_log2_impl(MathCache* cache, double x)
{
return cache->lookup(log2, x, MathCache::Log2);
}
double
js::math_log2_uncached(double x)
{
return log2(x);
}
bool
js::math_log2(JSContext* cx, unsigned argc, Value* vp)
{
return math_function<math_log2_impl>(cx, argc, vp);
}
#if !HAVE_LOG1P
double log1p(double x)
{
if (fabs(x) < 1e-4) {
/*
* Use Taylor approx. log(1 + x) = x - x^2 / 2 + x^3 / 3 - x^4 / 4 with error x^5 / 5
* Since |x| < 10^-4, |x|^5 < 10^-20, relative error less than 10^-16
*/
double z = -(x * x * x * x) / 4 + (x * x * x) / 3 - (x * x) / 2 + x;
return z;
} else {
/* For other large enough values of x use direct computation */
return log(1.0 + x);
}
}
#endif
#ifdef __APPLE__
// Ensure that log1p(-0) is -0.
#define LOG1P_IF_OUT_OF_RANGE(x) if (x == 0) return x;
#else
#define LOG1P_IF_OUT_OF_RANGE(x)
#endif
double
js::math_log1p_impl(MathCache* cache, double x)
{
LOG1P_IF_OUT_OF_RANGE(x);
return cache->lookup(log1p, x, MathCache::Log1p);
}
double
js::math_log1p_uncached(double x)
{
LOG1P_IF_OUT_OF_RANGE(x);
return log1p(x);
}
#undef LOG1P_IF_OUT_OF_RANGE
bool
js::math_log1p(JSContext* cx, unsigned argc, Value* vp)
{
return math_function<math_log1p_impl>(cx, argc, vp);
}
#if !HAVE_EXPM1
double expm1(double x)
{
/* Special handling for -0 */
if (x == 0.0)
return x;
if (fabs(x) < 1e-5) {
/*
* Use Taylor approx. exp(x) - 1 = x + x^2 / 2 + x^3 / 6 with error x^4 / 24
* Since |x| < 10^-5, |x|^4 < 10^-20, relative error less than 10^-15
*/
double z = (x * x * x) / 6 + (x * x) / 2 + x;
return z;
} else {
/* For other large enough values of x use direct computation */
return exp(x) - 1.0;
}
}
#endif
double
js::math_expm1_impl(MathCache* cache, double x)
{
return cache->lookup(expm1, x, MathCache::Expm1);
}
double
js::math_expm1_uncached(double x)
{
return expm1(x);
}
bool
js::math_expm1(JSContext* cx, unsigned argc, Value* vp)
{
return math_function<math_expm1_impl>(cx, argc, vp);
}
#if !HAVE_SQRT1PM1
/* This algorithm computes sqrt(1+x)-1 for small x */
double sqrt1pm1(double x)
{
if (fabs(x) > 0.75)
return sqrt(1 + x) - 1;
return expm1(log1p(x) / 2);
}
#endif
double
js::math_cosh_impl(MathCache* cache, double x)
{
return cache->lookup(cosh, x, MathCache::Cosh);
}
double
js::math_cosh_uncached(double x)
{
return cosh(x);
}
bool
js::math_cosh(JSContext* cx, unsigned argc, Value* vp)
{
return math_function<math_cosh_impl>(cx, argc, vp);
}
double
js::math_sinh_impl(MathCache* cache, double x)
{
return cache->lookup(sinh, x, MathCache::Sinh);
}
double
js::math_sinh_uncached(double x)
{
return sinh(x);
}
bool
js::math_sinh(JSContext* cx, unsigned argc, Value* vp)
{
return math_function<math_sinh_impl>(cx, argc, vp);
}
double
js::math_tanh_impl(MathCache* cache, double x)
{
return cache->lookup(tanh, x, MathCache::Tanh);
}
double
js::math_tanh_uncached(double x)
{
return tanh(x);
}
bool
js::math_tanh(JSContext* cx, unsigned argc, Value* vp)
{
return math_function<math_tanh_impl>(cx, argc, vp);
}
#if !HAVE_ACOSH
double acosh(double x)
{
const double SQUARE_ROOT_EPSILON = sqrt(std::numeric_limits<double>::epsilon());
if ((x - 1) >= SQUARE_ROOT_EPSILON) {
if (x > 1 / SQUARE_ROOT_EPSILON) {
/*
* http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/06/01/0001/
* approximation by laurent series in 1/x at 0+ order from -1 to 0
*/
return log(x) + M_LN2;
} else if (x < 1.5) {
// This is just a rearrangement of the standard form below
// devised to minimize loss of precision when x ~ 1:
double y = x - 1;
return log1p(y + sqrt(y * y + 2 * y));
} else {
// http://functions.wolfram.com/ElementaryFunctions/ArcCosh/02/
return log(x + sqrt(x * x - 1));
}
} else {
// see http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/04/01/0001/
double y = x - 1;
// approximation by taylor series in y at 0 up to order 2.
// If x is less than 1, sqrt(2 * y) is NaN and the result is NaN.
return sqrt(2 * y) * (1 - y / 12 + 3 * y * y / 160);
}
}
#endif
double
js::math_acosh_impl(MathCache* cache, double x)
{
return cache->lookup(acosh, x, MathCache::Acosh);
}
double
js::math_acosh_uncached(double x)
{
return acosh(x);
}
bool
js::math_acosh(JSContext* cx, unsigned argc, Value* vp)
{
return math_function<math_acosh_impl>(cx, argc, vp);
}
#if !HAVE_ASINH
// Bug 899712 - gcc incorrectly rewrites -asinh(-x) to asinh(x) when overriding
// asinh.
static double my_asinh(double x)
{
const double SQUARE_ROOT_EPSILON = sqrt(std::numeric_limits<double>::epsilon());
const double FOURTH_ROOT_EPSILON = sqrt(SQUARE_ROOT_EPSILON);
if (x >= FOURTH_ROOT_EPSILON) {
if (x > 1 / SQUARE_ROOT_EPSILON)
// http://functions.wolfram.com/ElementaryFunctions/ArcSinh/06/01/06/01/0001/
// approximation by laurent series in 1/x at 0+ order from -1 to 1
return M_LN2 + log(x) + 1 / (4 * x * x);
else if (x < 0.5)
return log1p(x + sqrt1pm1(x * x));
else
return log(x + sqrt(x * x + 1));
} else if (x <= -FOURTH_ROOT_EPSILON) {
return -my_asinh(-x);
} else {
// http://functions.wolfram.com/ElementaryFunctions/ArcSinh/06/01/03/01/0001/
// approximation by taylor series in x at 0 up to order 2
double result = x;
if (fabs(x) >= SQUARE_ROOT_EPSILON) {
double x3 = x * x * x;
// approximation by taylor series in x at 0 up to order 4
result -= x3 / 6;
}
return result;
}
}
#endif
double
js::math_asinh_impl(MathCache* cache, double x)
{
#ifdef HAVE_ASINH
return cache->lookup(asinh, x, MathCache::Asinh);
#else
return cache->lookup(my_asinh, x, MathCache::Asinh);
#endif
}
double
js::math_asinh_uncached(double x)
{
#ifdef HAVE_ASINH
return asinh(x);
#else
return my_asinh(x);
#endif
}
bool
js::math_asinh(JSContext* cx, unsigned argc, Value* vp)
{
return math_function<math_asinh_impl>(cx, argc, vp);
}
#if !HAVE_ATANH
double atanh(double x)
{
const double EPSILON = std::numeric_limits<double>::epsilon();
const double SQUARE_ROOT_EPSILON = sqrt(EPSILON);
const double FOURTH_ROOT_EPSILON = sqrt(SQUARE_ROOT_EPSILON);
if (fabs(x) >= FOURTH_ROOT_EPSILON) {
// http://functions.wolfram.com/ElementaryFunctions/ArcTanh/02/
if (fabs(x) < 0.5)
return (log1p(x) - log1p(-x)) / 2;
return log((1 + x) / (1 - x)) / 2;
} else {
// http://functions.wolfram.com/ElementaryFunctions/ArcTanh/06/01/03/01/
// approximation by taylor series in x at 0 up to order 2
double result = x;
if (fabs(x) >= SQUARE_ROOT_EPSILON) {
double x3 = x * x * x;
result += x3 / 3;
}
return result;
}
}
#endif
double
js::math_atanh_impl(MathCache* cache, double x)
{
return cache->lookup(atanh, x, MathCache::Atanh);
}
double
js::math_atanh_uncached(double x)
{
return atanh(x);
}
bool
js::math_atanh(JSContext* cx, unsigned argc, Value* vp)
{
return math_function<math_atanh_impl>(cx, argc, vp);
}
/* Consistency wrapper for platform deviations in hypot() */
double
js::ecmaHypot(double x, double y)
{
#ifdef XP_WIN
/*
* Workaround MS hypot bug, where hypot(Infinity, NaN or Math.MIN_VALUE)
* is NaN, not Infinity.
*/
if (mozilla::IsInfinite(x) || mozilla::IsInfinite(y)) {
return mozilla::PositiveInfinity<double>();
}
#endif
return hypot(x, y);
}
static inline
void
hypot_step(double& scale, double& sumsq, double x)
{
double xabs = mozilla::Abs(x);
if (scale < xabs) {
sumsq = 1 + sumsq * (scale / xabs) * (scale / xabs);
scale = xabs;
} else if (scale != 0) {
sumsq += (xabs / scale) * (xabs / scale);
}
}
double
js::hypot4(double x, double y, double z, double w)
{
/* Check for infinity or NaNs so that we can return immediatelly.
* Does not need to be WIN_XP specific as ecmaHypot
*/
if (mozilla::IsInfinite(x) || mozilla::IsInfinite(y) ||
mozilla::IsInfinite(z) || mozilla::IsInfinite(w))
return mozilla::PositiveInfinity<double>();
if (mozilla::IsNaN(x) || mozilla::IsNaN(y) || mozilla::IsNaN(z) ||
mozilla::IsNaN(w))
return GenericNaN();
double scale = 0;
double sumsq = 1;
hypot_step(scale, sumsq, x);
hypot_step(scale, sumsq, y);
hypot_step(scale, sumsq, z);
hypot_step(scale, sumsq, w);
return scale * sqrt(sumsq);
}
double
js::hypot3(double x, double y, double z)
{
return hypot4(x, y, z, 0.0);
}
bool
js::math_hypot(JSContext* cx, unsigned argc, Value* vp)
{
CallArgs args = CallArgsFromVp(argc, vp);
return math_hypot_handle(cx, args, args.rval());
}
bool
js::math_hypot_handle(JSContext* cx, HandleValueArray args, MutableHandleValue res)
{
// IonMonkey calls the system hypot function directly if two arguments are
// given. Do that here as well to get the same results.
if (args.length() == 2) {
double x, y;
if (!ToNumber(cx, args[0], &x))
return false;
if (!ToNumber(cx, args[1], &y))
return false;
double result = ecmaHypot(x, y);
res.setNumber(result);
return true;
}
bool isInfinite = false;
bool isNaN = false;
double scale = 0;
double sumsq = 1;
for (unsigned i = 0; i < args.length(); i++) {
double x;
if (!ToNumber(cx, args[i], &x))
return false;
isInfinite |= mozilla::IsInfinite(x);
isNaN |= mozilla::IsNaN(x);
if (isInfinite || isNaN)
continue;
hypot_step(scale, sumsq, x);
}
double result = isInfinite ? PositiveInfinity<double>() :
isNaN ? GenericNaN() :
scale * sqrt(sumsq);
res.setNumber(result);
return true;
}
double
js::math_trunc_impl(MathCache* cache, double x)
{
return cache->lookup(trunc, x, MathCache::Trunc);
}
double
js::math_trunc_uncached(double x)
{
return trunc(x);
}
bool
js::math_trunc(JSContext* cx, unsigned argc, Value* vp)
{
return math_function<math_trunc_impl>(cx, argc, vp);
}
static double sign(double x)
{
if (mozilla::IsNaN(x))
return GenericNaN();
return x == 0 ? x : x < 0 ? -1 : 1;
}
double
js::math_sign_impl(MathCache* cache, double x)
{
return cache->lookup(sign, x, MathCache::Sign);
}
double
js::math_sign_uncached(double x)
{
return sign(x);
}
bool
js::math_sign(JSContext* cx, unsigned argc, Value* vp)
{
return math_function<math_sign_impl>(cx, argc, vp);
}
#if !HAVE_CBRT
double cbrt(double x)
{
if (x > 0) {
return pow(x, 1.0 / 3.0);
} else if (x == 0) {
return x;
} else {
return -pow(-x, 1.0 / 3.0);
}
}
#endif
double
js::math_cbrt_impl(MathCache* cache, double x)
{
return cache->lookup(cbrt, x, MathCache::Cbrt);
}
double
js::math_cbrt_uncached(double x)
{
return cbrt(x);
}
bool
js::math_cbrt(JSContext* cx, unsigned argc, Value* vp)
{
return math_function<math_cbrt_impl>(cx, argc, vp);
}
#if JS_HAS_TOSOURCE
static bool
math_toSource(JSContext* cx, unsigned argc, Value* vp)
{
CallArgs args = CallArgsFromVp(argc, vp);
args.rval().setString(cx->names().Math);
return true;
}
#endif
static const JSFunctionSpec math_static_methods[] = {
#if JS_HAS_TOSOURCE
JS_FN(js_toSource_str, math_toSource, 0, 0),
#endif
JS_INLINABLE_FN("abs", math_abs, 1, 0, MathAbs),
JS_INLINABLE_FN("acos", math_acos, 1, 0, MathACos),
JS_INLINABLE_FN("asin", math_asin, 1, 0, MathASin),
JS_INLINABLE_FN("atan", math_atan, 1, 0, MathATan),
JS_INLINABLE_FN("atan2", math_atan2, 2, 0, MathATan2),
JS_INLINABLE_FN("ceil", math_ceil, 1, 0, MathCeil),
JS_INLINABLE_FN("clz32", math_clz32, 1, 0, MathClz32),
JS_INLINABLE_FN("cos", math_cos, 1, 0, MathCos),
JS_INLINABLE_FN("exp", math_exp, 1, 0, MathExp),
JS_INLINABLE_FN("floor", math_floor, 1, 0, MathFloor),
JS_INLINABLE_FN("imul", math_imul, 2, 0, MathImul),
JS_INLINABLE_FN("fround", math_fround, 1, 0, MathFRound),
JS_INLINABLE_FN("log", math_log, 1, 0, MathLog),
JS_INLINABLE_FN("max", math_max, 2, 0, MathMax),
JS_INLINABLE_FN("min", math_min, 2, 0, MathMin),
JS_INLINABLE_FN("pow", math_pow, 2, 0, MathPow),
JS_INLINABLE_FN("random", math_random, 0, 0, MathRandom),
JS_INLINABLE_FN("round", math_round, 1, 0, MathRound),
JS_INLINABLE_FN("sin", math_sin, 1, 0, MathSin),
JS_INLINABLE_FN("sqrt", math_sqrt, 1, 0, MathSqrt),
JS_INLINABLE_FN("tan", math_tan, 1, 0, MathTan),
JS_INLINABLE_FN("log10", math_log10, 1, 0, MathLog10),
JS_INLINABLE_FN("log2", math_log2, 1, 0, MathLog2),
JS_INLINABLE_FN("log1p", math_log1p, 1, 0, MathLog1P),
JS_INLINABLE_FN("expm1", math_expm1, 1, 0, MathExpM1),
JS_INLINABLE_FN("cosh", math_cosh, 1, 0, MathCosH),
JS_INLINABLE_FN("sinh", math_sinh, 1, 0, MathSinH),
JS_INLINABLE_FN("tanh", math_tanh, 1, 0, MathTanH),
JS_INLINABLE_FN("acosh", math_acosh, 1, 0, MathACosH),
JS_INLINABLE_FN("asinh", math_asinh, 1, 0, MathASinH),
JS_INLINABLE_FN("atanh", math_atanh, 1, 0, MathATanH),
JS_INLINABLE_FN("hypot", math_hypot, 2, 0, MathHypot),
JS_INLINABLE_FN("trunc", math_trunc, 1, 0, MathTrunc),
JS_INLINABLE_FN("sign", math_sign, 1, 0, MathSign),
JS_INLINABLE_FN("cbrt", math_cbrt, 1, 0, MathCbrt),
JS_FS_END
};
JSObject*
js::InitMathClass(JSContext* cx, HandleObject obj)
{
RootedObject proto(cx, obj->as<GlobalObject>().getOrCreateObjectPrototype(cx));
if (!proto)
return nullptr;
RootedObject Math(cx, NewObjectWithGivenProto(cx, &MathClass, proto, SingletonObject));
if (!Math)
return nullptr;
if (!JS_DefineProperty(cx, obj, js_Math_str, Math, JSPROP_RESOLVING,
JS_STUBGETTER, JS_STUBSETTER))
{
return nullptr;
}
if (!JS_DefineFunctions(cx, Math, math_static_methods))
return nullptr;
if (!JS_DefineConstDoubles(cx, Math, math_constants))
return nullptr;
obj->as<GlobalObject>().setConstructor(JSProto_Math, ObjectValue(*Math));
return Math;
}