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Unified Diff: src/math.js

Issue 411263004: Implement trigonometric functions using a fdlibm port. (Closed) Base URL: https://v8.googlecode.com/svn/branches/bleeding_edge
Patch Set: rebase Created 6 years, 4 months ago
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Index: src/math.js
diff --git a/src/math.js b/src/math.js
index 9dc4b37d0ce2115ed9e9b5078f204fd060f926b9..436a41f5c44400609fe7cc446f318ca36ca6aacd 100644
--- a/src/math.js
+++ b/src/math.js
@@ -56,12 +56,6 @@ function MathCeil(x) {
return -MathFloor(-x);
}
-// ECMA 262 - 15.8.2.7
-function MathCos(x) {
- x = MathAbs(x); // Convert to number and get rid of -0.
- return TrigonometricInterpolation(x, 1);
-}
-
// ECMA 262 - 15.8.2.8
function MathExp(x) {
return %MathExpRT(TO_NUMBER_INLINE(x));
@@ -164,97 +158,16 @@ function MathRound(x) {
return %RoundNumber(TO_NUMBER_INLINE(x));
}
-// ECMA 262 - 15.8.2.16
-function MathSin(x) {
- x = x * 1; // Convert to number and deal with -0.
- if (%_IsMinusZero(x)) return x;
- return TrigonometricInterpolation(x, 0);
-}
-
// ECMA 262 - 15.8.2.17
function MathSqrt(x) {
return %_MathSqrtRT(TO_NUMBER_INLINE(x));
}
-// ECMA 262 - 15.8.2.18
-function MathTan(x) {
- return MathSin(x) / MathCos(x);
-}
-
// Non-standard extension.
function MathImul(x, y) {
return %NumberImul(TO_NUMBER_INLINE(x), TO_NUMBER_INLINE(y));
}
-
-var kInversePiHalf = 0.636619772367581343; // 2 / pi
-var kInversePiHalfS26 = 9.48637384723993156e-9; // 2 / pi / (2^26)
-var kS26 = 1 << 26;
-var kTwoStepThreshold = 1 << 27;
-// pi / 2 rounded up
-var kPiHalf = 1.570796326794896780; // 0x192d4454fb21f93f
-// We use two parts for pi/2 to emulate a higher precision.
-// pi_half_1 only has 26 significant bits for mantissa.
-// Note that pi_half > pi_half_1 + pi_half_2
-var kPiHalf1 = 1.570796325802803040; // 0x00000054fb21f93f
-var kPiHalf2 = 9.920935796805404252e-10; // 0x3326a611460b113e
-
-var kSamples; // Initialized to a number during genesis.
-var kIndexConvert; // Initialized to kSamples / (pi/2) during genesis.
-var kSinTable; // Initialized to a Float64Array during genesis.
-var kCosXIntervalTable; // Initialized to a Float64Array during genesis.
-
-// This implements sine using the following algorithm.
-// 1) Multiplication takes care of to-number conversion.
-// 2) Reduce x to the first quadrant [0, pi/2].
-// Conveniently enough, in case of +/-Infinity, we get NaN.
-// Note that we try to use only 26 instead of 52 significant bits for
-// mantissa to avoid rounding errors when multiplying. For very large
-// input we therefore have additional steps.
-// 3) Replace x by (pi/2-x) if x was in the 2nd or 4th quadrant.
-// 4) Do a table lookup for the closest samples to the left and right of x.
-// 5) Find the derivatives at those sampling points by table lookup:
-// dsin(x)/dx = cos(x) = sin(pi/2-x) for x in [0, pi/2].
-// 6) Use cubic spline interpolation to approximate sin(x).
-// 7) Negate the result if x was in the 3rd or 4th quadrant.
-// 8) Get rid of -0 by adding 0.
-function TrigonometricInterpolation(x, phase) {
- if (x < 0 || x > kPiHalf) {
- var multiple;
- while (x < -kTwoStepThreshold || x > kTwoStepThreshold) {
- // Let's assume this loop does not terminate.
- // All numbers x in each loop forms a set S.
- // (1) abs(x) > 2^27 for all x in S.
- // (2) abs(multiple) != 0 since (2^27 * inverse_pi_half_s26) > 1
- // (3) multiple is rounded down in 2^26 steps, so the rounding error is
- // at most max(ulp, 2^26).
- // (4) so for x > 2^27, we subtract at most (1+pi/4)x and at least
- // (1-pi/4)x
- // (5) The subtraction results in x' so that abs(x') <= abs(x)*pi/4.
- // Note that this difference cannot be simply rounded off.
- // Set S cannot exist since (5) violates (1). Loop must terminate.
- multiple = MathFloor(x * kInversePiHalfS26) * kS26;
- x = x - multiple * kPiHalf1 - multiple * kPiHalf2;
- }
- multiple = MathFloor(x * kInversePiHalf);
- x = x - multiple * kPiHalf1 - multiple * kPiHalf2;
- phase += multiple;
- }
- var double_index = x * kIndexConvert;
- if (phase & 1) double_index = kSamples - double_index;
- var index = double_index | 0;
- var t1 = double_index - index;
- var t2 = 1 - t1;
- var y1 = kSinTable[index];
- var y2 = kSinTable[index + 1];
- var dy = y2 - y1;
- return (t2 * y1 + t1 * y2 +
- t1 * t2 * ((kCosXIntervalTable[index] - dy) * t2 +
- (dy - kCosXIntervalTable[index + 1]) * t1))
- * (1 - (phase & 2)) + 0;
-}
-
-
// ES6 draft 09-27-13, section 20.2.2.28.
function MathSign(x) {
x = TO_NUMBER_INLINE(x);
@@ -264,7 +177,6 @@ function MathSign(x) {
return NAN;
}
-
// ES6 draft 09-27-13, section 20.2.2.34.
function MathTrunc(x) {
x = TO_NUMBER_INLINE(x);
@@ -274,7 +186,6 @@ function MathTrunc(x) {
return NAN;
}
-
// ES6 draft 09-27-13, section 20.2.2.30.
function MathSinh(x) {
if (!IS_NUMBER(x)) x = NonNumberToNumber(x);
@@ -283,7 +194,6 @@ function MathSinh(x) {
return (MathExp(x) - MathExp(-x)) / 2;
}
-
// ES6 draft 09-27-13, section 20.2.2.12.
function MathCosh(x) {
if (!IS_NUMBER(x)) x = NonNumberToNumber(x);
@@ -291,7 +201,6 @@ function MathCosh(x) {
return (MathExp(x) + MathExp(-x)) / 2;
}
-
// ES6 draft 09-27-13, section 20.2.2.33.
function MathTanh(x) {
if (!IS_NUMBER(x)) x = NonNumberToNumber(x);
@@ -304,7 +213,6 @@ function MathTanh(x) {
return (exp1 - exp2) / (exp1 + exp2);
}
-
// ES6 draft 09-27-13, section 20.2.2.5.
function MathAsinh(x) {
if (!IS_NUMBER(x)) x = NonNumberToNumber(x);
@@ -315,7 +223,6 @@ function MathAsinh(x) {
return -MathLog(-x + MathSqrt(x * x + 1));
}
-
// ES6 draft 09-27-13, section 20.2.2.3.
function MathAcosh(x) {
if (!IS_NUMBER(x)) x = NonNumberToNumber(x);
@@ -325,7 +232,6 @@ function MathAcosh(x) {
return MathLog(x + MathSqrt(x + 1) * MathSqrt(x - 1));
}
-
// ES6 draft 09-27-13, section 20.2.2.7.
function MathAtanh(x) {
if (!IS_NUMBER(x)) x = NonNumberToNumber(x);
@@ -336,7 +242,6 @@ function MathAtanh(x) {
return 0.5 * MathLog((1 + x) / (1 - x));
}
-
// ES6 draft 09-27-13, section 20.2.2.21.
function MathLog10(x) {
return MathLog(x) * 0.434294481903251828; // log10(x) = log(x)/log(10).
@@ -348,7 +253,6 @@ function MathLog2(x) {
return MathLog(x) * 1.442695040888963407; // log2(x) = log(x)/log(2).
}
-
// ES6 draft 09-27-13, section 20.2.2.17.
function MathHypot(x, y) { // Function length is 2.
// We may want to introduce fast paths for two arguments and when
@@ -381,13 +285,12 @@ function MathHypot(x, y) { // Function length is 2.
return MathSqrt(sum) * max;
}
-
// ES6 draft 09-27-13, section 20.2.2.16.
function MathFroundJS(x) {
return %MathFround(TO_NUMBER_INLINE(x));
}
-
+// ES6 draft 07-18-14, section 20.2.2.11
function MathClz32(x) {
x = ToUint32(TO_NUMBER_INLINE(x));
if (x == 0) return 32;
@@ -401,7 +304,6 @@ function MathClz32(x) {
return result;
}
-
// ES6 draft 09-27-13, section 20.2.2.9.
// Cube root approximation, refer to: http://metamerist.com/cbrt/cbrt.htm
// Using initial approximation adapted from Kahan's cbrt and 4 iterations
@@ -425,8 +327,6 @@ function CubeRoot(x) {
return NEWTON_ITERATION_CBRT(x, approx);
}
-
-
// ES6 draft 09-27-13, section 20.2.2.14.
// Use Taylor series to approximate.
// exp(x) - 1 at 0 == -1 + exp(0) + exp'(0)*x/1! + exp''(0)*x^2/2! + ...
@@ -447,7 +347,6 @@ function MathExpm1(x) {
}
}
-
// ES6 draft 09-27-13, section 20.2.2.20.
// Use Taylor series to approximate. With y = x + 1;
// log(y) at 1 == log(1) + log'(1)(y-1)/1! + log''(1)(y-1)^2/2! + ...
@@ -502,14 +401,14 @@ function SetUpMath() {
"asin", MathAsinJS,
"atan", MathAtanJS,
"ceil", MathCeil,
- "cos", MathCos,
+ "cos", MathCos, // implemented by third_party/fdlibm
"exp", MathExp,
"floor", MathFloor,
"log", MathLog,
"round", MathRound,
- "sin", MathSin,
+ "sin", MathSin, // implemented by third_party/fdlibm
"sqrt", MathSqrt,
- "tan", MathTan,
+ "tan", MathTan, // implemented by third_party/fdlibm
"atan2", MathAtan2JS,
"pow", MathPow,
"max", MathMax,
@@ -537,8 +436,6 @@ function SetUpMath() {
%SetInlineBuiltinFlag(MathRandom);
%SetInlineBuiltinFlag(MathSin);
%SetInlineBuiltinFlag(MathCos);
- %SetInlineBuiltinFlag(MathTan);
- %SetInlineBuiltinFlag(TrigonometricInterpolation);
}
SetUpMath();
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