src/math.js - Issue 411263004: Implement trigonometric functions using a fdlibm port.

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) {