| // Copyright 2012 the V8 project authors. All rights reserved. |
| // Use of this source code is governed by a BSD-style license that can be |
| // found in the LICENSE file. |
| |
| "use strict"; |
| |
| // This file relies on the fact that the following declarations have been made |
| // in runtime.js: |
| // var $Object = global.Object; |
| |
| // Keep reference to original values of some global properties. This |
| // has the added benefit that the code in this file is isolated from |
| // changes to these properties. |
| var $floor = MathFloor; |
| var $abs = MathAbs; |
| |
| // Instance class name can only be set on functions. That is the only |
| // purpose for MathConstructor. |
| function MathConstructor() {} |
| var $Math = new MathConstructor(); |
| |
| // ------------------------------------------------------------------- |
| |
| // ECMA 262 - 15.8.2.1 |
| function MathAbs(x) { |
| if (%_IsSmi(x)) return x >= 0 ? x : -x; |
| x = TO_NUMBER_INLINE(x); |
| if (x === 0) return 0; // To handle -0. |
| return x > 0 ? x : -x; |
| } |
| |
| // ECMA 262 - 15.8.2.2 |
| function MathAcosJS(x) { |
| return %MathAcos(TO_NUMBER_INLINE(x)); |
| } |
| |
| // ECMA 262 - 15.8.2.3 |
| function MathAsinJS(x) { |
| return %MathAsin(TO_NUMBER_INLINE(x)); |
| } |
| |
| // ECMA 262 - 15.8.2.4 |
| function MathAtanJS(x) { |
| return %MathAtan(TO_NUMBER_INLINE(x)); |
| } |
| |
| // ECMA 262 - 15.8.2.5 |
| // The naming of y and x matches the spec, as does the order in which |
| // ToNumber (valueOf) is called. |
| function MathAtan2JS(y, x) { |
| return %MathAtan2(TO_NUMBER_INLINE(y), TO_NUMBER_INLINE(x)); |
| } |
| |
| // ECMA 262 - 15.8.2.6 |
| 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)); |
| } |
| |
| // ECMA 262 - 15.8.2.9 |
| function MathFloor(x) { |
| x = TO_NUMBER_INLINE(x); |
| // It's more common to call this with a positive number that's out |
| // of range than negative numbers; check the upper bound first. |
| if (x < 0x80000000 && x > 0) { |
| // Numbers in the range [0, 2^31) can be floored by converting |
| // them to an unsigned 32-bit value using the shift operator. |
| // We avoid doing so for -0, because the result of Math.floor(-0) |
| // has to be -0, which wouldn't be the case with the shift. |
| return TO_UINT32(x); |
| } else { |
| return %MathFloorRT(x); |
| } |
| } |
| |
| // ECMA 262 - 15.8.2.10 |
| function MathLog(x) { |
| return %_MathLogRT(TO_NUMBER_INLINE(x)); |
| } |
| |
| // ECMA 262 - 15.8.2.11 |
| function MathMax(arg1, arg2) { // length == 2 |
| var length = %_ArgumentsLength(); |
| if (length == 2) { |
| arg1 = TO_NUMBER_INLINE(arg1); |
| arg2 = TO_NUMBER_INLINE(arg2); |
| if (arg2 > arg1) return arg2; |
| if (arg1 > arg2) return arg1; |
| if (arg1 == arg2) { |
| // Make sure -0 is considered less than +0. |
| return (arg1 === 0 && %_IsMinusZero(arg1)) ? arg2 : arg1; |
| } |
| // All comparisons failed, one of the arguments must be NaN. |
| return NAN; |
| } |
| var r = -INFINITY; |
| for (var i = 0; i < length; i++) { |
| var n = %_Arguments(i); |
| if (!IS_NUMBER(n)) n = NonNumberToNumber(n); |
| // Make sure +0 is considered greater than -0. |
| if (NUMBER_IS_NAN(n) || n > r || (r === 0 && n === 0 && %_IsMinusZero(r))) { |
| r = n; |
| } |
| } |
| return r; |
| } |
| |
| // ECMA 262 - 15.8.2.12 |
| function MathMin(arg1, arg2) { // length == 2 |
| var length = %_ArgumentsLength(); |
| if (length == 2) { |
| arg1 = TO_NUMBER_INLINE(arg1); |
| arg2 = TO_NUMBER_INLINE(arg2); |
| if (arg2 > arg1) return arg1; |
| if (arg1 > arg2) return arg2; |
| if (arg1 == arg2) { |
| // Make sure -0 is considered less than +0. |
| return (arg1 === 0 && %_IsMinusZero(arg1)) ? arg1 : arg2; |
| } |
| // All comparisons failed, one of the arguments must be NaN. |
| return NAN; |
| } |
| var r = INFINITY; |
| for (var i = 0; i < length; i++) { |
| var n = %_Arguments(i); |
| if (!IS_NUMBER(n)) n = NonNumberToNumber(n); |
| // Make sure -0 is considered less than +0. |
| if (NUMBER_IS_NAN(n) || n < r || (r === 0 && n === 0 && %_IsMinusZero(n))) { |
| r = n; |
| } |
| } |
| return r; |
| } |
| |
| // ECMA 262 - 15.8.2.13 |
| function MathPow(x, y) { |
| return %_MathPow(TO_NUMBER_INLINE(x), TO_NUMBER_INLINE(y)); |
| } |
| |
| // ECMA 262 - 15.8.2.14 |
| var rngstate; // Initialized to a Uint32Array during genesis. |
| function MathRandom() { |
| var r0 = (MathImul(18273, rngstate[0] & 0xFFFF) + (rngstate[0] >>> 16)) | 0; |
| rngstate[0] = r0; |
| var r1 = (MathImul(36969, rngstate[1] & 0xFFFF) + (rngstate[1] >>> 16)) | 0; |
| rngstate[1] = r1; |
| var x = ((r0 << 16) + (r1 & 0xFFFF)) | 0; |
| // Division by 0x100000000 through multiplication by reciprocal. |
| return (x < 0 ? (x + 0x100000000) : x) * 2.3283064365386962890625e-10; |
| } |
| |
| // ECMA 262 - 15.8.2.15 |
| 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; |
| } |
| |
| // ------------------------------------------------------------------- |
| |
| function SetUpMath() { |
| %CheckIsBootstrapping(); |
| |
| %SetPrototype($Math, $Object.prototype); |
| %SetProperty(global, "Math", $Math, DONT_ENUM); |
| %FunctionSetInstanceClassName(MathConstructor, 'Math'); |
| |
| // Set up math constants. |
| InstallConstants($Math, $Array( |
| // ECMA-262, section 15.8.1.1. |
| "E", 2.7182818284590452354, |
| // ECMA-262, section 15.8.1.2. |
| "LN10", 2.302585092994046, |
| // ECMA-262, section 15.8.1.3. |
| "LN2", 0.6931471805599453, |
| // ECMA-262, section 15.8.1.4. |
| "LOG2E", 1.4426950408889634, |
| "LOG10E", 0.4342944819032518, |
| "PI", 3.1415926535897932, |
| "SQRT1_2", 0.7071067811865476, |
| "SQRT2", 1.4142135623730951 |
| )); |
| |
| // Set up non-enumerable functions of the Math object and |
| // set their names. |
| InstallFunctions($Math, DONT_ENUM, $Array( |
| "random", MathRandom, |
| "abs", MathAbs, |
| "acos", MathAcosJS, |
| "asin", MathAsinJS, |
| "atan", MathAtanJS, |
| "ceil", MathCeil, |
| "cos", MathCos, |
| "exp", MathExp, |
| "floor", MathFloor, |
| "log", MathLog, |
| "round", MathRound, |
| "sin", MathSin, |
| "sqrt", MathSqrt, |
| "tan", MathTan, |
| "atan2", MathAtan2JS, |
| "pow", MathPow, |
| "max", MathMax, |
| "min", MathMin, |
| "imul", MathImul |
| )); |
| |
| %SetInlineBuiltinFlag(MathCeil); |
| %SetInlineBuiltinFlag(MathRandom); |
| %SetInlineBuiltinFlag(MathSin); |
| %SetInlineBuiltinFlag(MathCos); |
| %SetInlineBuiltinFlag(MathTan); |
| %SetInlineBuiltinFlag(TrigonometricInterpolation); |
| } |
| |
| SetUpMath(); |