Harmony: implement Math.cbrt, Math.expm1 and Math.log1p.
BUG=v8:2938 LOG=N R=jarin@chromium.org Review URL: https://codereview.chromium.org/163563003 git-svn-id: http://v8.googlecode.com/svn/branches/bleeding_edge@19486 ce2b1a6d-e550-0410-aec6-3dcde31c8c00
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yangguo@chromium.org
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84cf85598d
@ -174,6 +174,24 @@ function MathClz32(x) {
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}
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//ES6 draft 09-27-13, section 20.2.2.9.
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function MathCbrt(x) {
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return %Math_cbrt(TO_NUMBER_INLINE(x));
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}
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//ES6 draft 09-27-13, section 20.2.2.14.
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function MathExpm1(x) {
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return %Math_expm1(TO_NUMBER_INLINE(x));
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}
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//ES6 draft 09-27-13, section 20.2.2.20.
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function MathLog1p(x) {
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return %Math_log1p(TO_NUMBER_INLINE(x));
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}
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function ExtendMath() {
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%CheckIsBootstrapping();
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@ -191,7 +209,10 @@ function ExtendMath() {
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"log2", MathLog2,
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"hypot", MathHypot,
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"fround", MathFround,
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"clz32", MathClz32
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"clz32", MathClz32,
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"cbrt", MathCbrt,
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"log1p", MathLog1p,
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"expm1", MathExpm1
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));
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}
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119
src/runtime.cc
119
src/runtime.cc
@ -7647,33 +7647,110 @@ RUNTIME_FUNCTION(MaybeObject*, Runtime_StringCompare) {
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}
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RUNTIME_FUNCTION(MaybeObject*, Runtime_Math_acos) {
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SealHandleScope shs(isolate);
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ASSERT(args.length() == 1);
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isolate->counters()->math_acos()->Increment();
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#define RUNTIME_UNARY_MATH(NAME) \
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RUNTIME_FUNCTION(MaybeObject*, Runtime_Math_##NAME) { \
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SealHandleScope shs(isolate); \
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ASSERT(args.length() == 1); \
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isolate->counters()->math_##NAME()->Increment(); \
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CONVERT_DOUBLE_ARG_CHECKED(x, 0); \
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return isolate->heap()->AllocateHeapNumber(std::NAME(x)); \
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}
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CONVERT_DOUBLE_ARG_CHECKED(x, 0);
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return isolate->heap()->AllocateHeapNumber(std::acos(x));
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RUNTIME_UNARY_MATH(acos)
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RUNTIME_UNARY_MATH(asin)
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RUNTIME_UNARY_MATH(atan)
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RUNTIME_UNARY_MATH(log)
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#undef RUNTIME_UNARY_MATH
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// Cube root approximation, refer to: http://metamerist.com/cbrt/cbrt.htm
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// Using initial approximation adapted from Kahan's cbrt and 4 iterations
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// of Newton's method.
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inline double CubeRootNewtonIteration(double approx, double x) {
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return (1.0 / 3.0) * (x / (approx * approx) + 2 * approx);
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}
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RUNTIME_FUNCTION(MaybeObject*, Runtime_Math_asin) {
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SealHandleScope shs(isolate);
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ASSERT(args.length() == 1);
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isolate->counters()->math_asin()->Increment();
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inline double CubeRoot(double x) {
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static const uint64_t magic = V8_2PART_UINT64_C(0x2A9F7893, 00000000);
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uint64_t xhigh = double_to_uint64(x);
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double approx = uint64_to_double(xhigh / 3 + magic);
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CONVERT_DOUBLE_ARG_CHECKED(x, 0);
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return isolate->heap()->AllocateHeapNumber(std::asin(x));
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approx = CubeRootNewtonIteration(approx, x);
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approx = CubeRootNewtonIteration(approx, x);
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approx = CubeRootNewtonIteration(approx, x);
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return CubeRootNewtonIteration(approx, x);
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}
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RUNTIME_FUNCTION(MaybeObject*, Runtime_Math_atan) {
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RUNTIME_FUNCTION(MaybeObject*, Runtime_Math_cbrt) {
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SealHandleScope shs(isolate);
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ASSERT(args.length() == 1);
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isolate->counters()->math_atan()->Increment();
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CONVERT_DOUBLE_ARG_CHECKED(x, 0);
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return isolate->heap()->AllocateHeapNumber(std::atan(x));
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if (x == 0 || std::isinf(x)) return args[0];
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double result = (x > 0) ? CubeRoot(x) : -CubeRoot(-x);
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return isolate->heap()->AllocateHeapNumber(result);
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}
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RUNTIME_FUNCTION(MaybeObject*, Runtime_Math_log1p) {
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SealHandleScope shs(isolate);
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ASSERT(args.length() == 1);
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CONVERT_DOUBLE_ARG_CHECKED(x, 0);
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double x_abs = std::fabs(x);
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// Use Taylor series to approximate. With y = x + 1;
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// log(y) at 1 == log(1) + log'(1)(y-1)/1! + log''(1)(y-1)^2/2! + ...
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// == 0 + x - x^2/2 + x^3/3 ...
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// The closer x is to 0, the fewer terms are required.
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static const double threshold_2 = 1.0 / 0x00800000;
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static const double threshold_3 = 1.0 / 0x00008000;
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static const double threshold_7 = 1.0 / 0x00000080;
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double result;
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if (x_abs < threshold_2) {
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result = x * (1.0/1.0 - x * 1.0/2.0);
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} else if (x_abs < threshold_3) {
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result = x * (1.0/1.0 - x * (1.0/2.0 - x * (1.0/3.0)));
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} else if (x_abs < threshold_7) {
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result = x * (1.0/1.0 - x * (1.0/2.0 - x * (
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1.0/3.0 - x * (1.0/4.0 - x * (
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1.0/5.0 - x * (1.0/6.0 - x * (
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1.0/7.0)))))));
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} else { // Use regular log if not close enough to 0.
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result = std::log(1.0 + x);
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}
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return isolate->heap()->AllocateHeapNumber(result);
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}
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RUNTIME_FUNCTION(MaybeObject*, Runtime_Math_expm1) {
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SealHandleScope shs(isolate);
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ASSERT(args.length() == 1);
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CONVERT_DOUBLE_ARG_CHECKED(x, 0);
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double x_abs = std::fabs(x);
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// Use Taylor series to approximate.
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// exp(x) - 1 at 0 == -1 + exp(0) + exp'(0)*x/1! + exp''(0)*x^2/2! + ...
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// == x/1! + x^2/2! + x^3/3! + ...
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// The closer x is to 0, the fewer terms are required.
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static const double threshold_2 = 1.0 / 0x00400000;
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static const double threshold_3 = 1.0 / 0x00004000;
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static const double threshold_6 = 1.0 / 0x00000040;
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double result;
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if (x_abs < threshold_2) {
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result = x * (1.0/1.0 + x * (1.0/2.0));
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} else if (x_abs < threshold_3) {
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result = x * (1.0/1.0 + x * (1.0/2.0 + x * (1.0/6.0)));
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} else if (x_abs < threshold_6) {
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result = x * (1.0/1.0 + x * (1.0/2.0 + x * (
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1.0/6.0 + x * (1.0/24.0 + x * (
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1.0/120.0 + x * (1.0/720.0))))));
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} else { // Use regular exp if not close enough to 0.
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result = std::exp(x) - 1.0;
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}
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return isolate->heap()->AllocateHeapNumber(result);
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}
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@ -7724,16 +7801,6 @@ RUNTIME_FUNCTION(MaybeObject*, Runtime_Math_floor) {
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}
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RUNTIME_FUNCTION(MaybeObject*, Runtime_Math_log) {
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SealHandleScope shs(isolate);
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ASSERT(args.length() == 1);
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isolate->counters()->math_log()->Increment();
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CONVERT_DOUBLE_ARG_CHECKED(x, 0);
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return isolate->heap()->AllocateHeapNumber(std::log(x));
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}
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// Slow version of Math.pow. We check for fast paths for special cases.
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// Used if SSE2/VFP3 is not available.
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RUNTIME_FUNCTION(MaybeObject*, Runtime_Math_pow) {
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@ -177,14 +177,17 @@ namespace internal {
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F(Math_acos, 1, 1) \
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F(Math_asin, 1, 1) \
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F(Math_atan, 1, 1) \
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F(Math_atan2, 2, 1) \
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F(Math_log, 1, 1) \
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F(Math_cbrt, 1, 1) \
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F(Math_log1p, 1, 1) \
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F(Math_expm1, 1, 1) \
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F(Math_sqrt, 1, 1) \
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F(Math_exp, 1, 1) \
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F(Math_floor, 1, 1) \
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F(Math_log, 1, 1) \
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F(Math_pow, 2, 1) \
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F(Math_pow_cfunction, 2, 1) \
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F(Math_atan2, 2, 1) \
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F(RoundNumber, 1, 1) \
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F(Math_sqrt, 1, 1) \
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F(Math_fround, 1, 1) \
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\
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/* Regular expressions */ \
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27
test/mjsunit/harmony/math-cbrt.js
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27
test/mjsunit/harmony/math-cbrt.js
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@ -0,0 +1,27 @@
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// Copyright 2014 the V8 project authors. All rights reserved.
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// Use of this source code is governed by a BSD-style license that can be
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// found in the LICENSE file.
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// Flags: --harmony-maths
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assertTrue(isNaN(Math.cbrt(NaN)));
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assertTrue(isNaN(Math.cbrt(function() {})));
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assertTrue(isNaN(Math.cbrt({ toString: function() { return NaN; } })));
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assertTrue(isNaN(Math.cbrt({ valueOf: function() { return "abc"; } })));
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assertEquals("Infinity", String(1/Math.cbrt(0)));
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assertEquals("-Infinity", String(1/Math.cbrt(-0)));
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assertEquals("Infinity", String(Math.cbrt(Infinity)));
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assertEquals("-Infinity", String(Math.cbrt(-Infinity)));
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for (var i = 1E-100; i < 1E100; i *= Math.PI) {
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assertEqualsDelta(i, Math.cbrt(i*i*i), i * 1E-15);
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}
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for (var i = -1E-100; i > -1E100; i *= Math.E) {
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assertEqualsDelta(i, Math.cbrt(i*i*i), -i * 1E-15);
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}
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// Let's be exact at least for small integers.
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for (var i = 2; i < 10000; i++) {
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assertEquals(i, Math.cbrt(i*i*i));
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}
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38
test/mjsunit/harmony/math-expm1.js
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38
test/mjsunit/harmony/math-expm1.js
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@ -0,0 +1,38 @@
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// Copyright 2014 the V8 project authors. All rights reserved.
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// Use of this source code is governed by a BSD-style license that can be
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// found in the LICENSE file.
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// Flags: --harmony-maths --no-fast-math
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assertTrue(isNaN(Math.expm1(NaN)));
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assertTrue(isNaN(Math.expm1(function() {})));
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assertTrue(isNaN(Math.expm1({ toString: function() { return NaN; } })));
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assertTrue(isNaN(Math.expm1({ valueOf: function() { return "abc"; } })));
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assertEquals("Infinity", String(1/Math.expm1(0)));
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assertEquals("-Infinity", String(1/Math.expm1(-0)));
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assertEquals("Infinity", String(Math.expm1(Infinity)));
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assertEquals(-1, Math.expm1(-Infinity));
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for (var x = 0.1; x < 700; x += 0.1) {
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var expected = Math.exp(x) - 1;
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assertEqualsDelta(expected, Math.expm1(x), expected * 1E-14);
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expected = Math.exp(-x) - 1;
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assertEqualsDelta(expected, Math.expm1(-x), -expected * 1E-14);
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}
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// Values close to 0:
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// Use six terms of Taylor expansion at 0 for exp(x) as test expectation:
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// exp(x) - 1 == exp(0) + exp(0) * x + x * x / 2 + ... - 1
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// == x + x * x / 2 + x * x * x / 6 + ...
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function expm1(x) {
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return x * (1 + x * (1/2 + x * (
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1/6 + x * (1/24 + x * (
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1/120 + x * (1/720 + x * (
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1/5040 + x * (1/40320 + x*(
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1/362880 + x * (1/3628800))))))))));
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}
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for (var x = 1E-1; x > 1E-300; x *= 0.8) {
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var expected = expm1(x);
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assertEqualsDelta(expected, Math.expm1(x), expected * 1E-14);
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}
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41
test/mjsunit/harmony/math-log1p.js
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41
test/mjsunit/harmony/math-log1p.js
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@ -0,0 +1,41 @@
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// Copyright 2014 the V8 project authors. All rights reserved.
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// Use of this source code is governed by a BSD-style license that can be
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// found in the LICENSE file.
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// Flags: --harmony-maths
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assertTrue(isNaN(Math.log1p(NaN)));
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assertTrue(isNaN(Math.log1p(function() {})));
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assertTrue(isNaN(Math.log1p({ toString: function() { return NaN; } })));
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assertTrue(isNaN(Math.log1p({ valueOf: function() { return "abc"; } })));
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assertEquals("Infinity", String(1/Math.log1p(0)));
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assertEquals("-Infinity", String(1/Math.log1p(-0)));
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assertEquals("Infinity", String(Math.log1p(Infinity)));
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assertEquals("-Infinity", String(Math.log1p(-1)));
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assertTrue(isNaN(Math.log1p(-2)));
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assertTrue(isNaN(Math.log1p(-Infinity)));
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for (var x = 1E300; x > 1E-1; x *= 0.8) {
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var expected = Math.log(x + 1);
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assertEqualsDelta(expected, Math.log1p(x), expected * 1E-14);
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}
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// Values close to 0:
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// Use Taylor expansion at 1 for log(x) as test expectation:
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// log1p(x) == log(x + 1) == 0 + x / 1 - x^2 / 2 + x^3 / 3 - ...
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function log1p(x) {
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var terms = [];
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var prod = x;
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for (var i = 1; i <= 20; i++) {
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terms.push(prod / i);
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prod *= -x;
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}
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var sum = 0;
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while (terms.length > 0) sum += terms.pop();
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return sum;
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}
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for (var x = 1E-1; x > 1E-300; x *= 0.8) {
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var expected = log1p(x);
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assertEqualsDelta(expected, Math.log1p(x), expected * 1E-14);
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}
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