| // 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. |
| |
| (function(global, utils) { |
| "use strict"; |
| |
| %CheckIsBootstrapping(); |
| |
| // ------------------------------------------------------------------- |
| // Imports |
| |
| define kRandomBatchSize = 64; |
| // The first two slots are reserved to persist PRNG state. |
| define kRandomNumberStart = 2; |
| |
| var GlobalFloat64Array = global.Float64Array; |
| var GlobalMath = global.Math; |
| var GlobalObject = global.Object; |
| var InternalArray = utils.InternalArray; |
| var NaN = %GetRootNaN(); |
| var nextRandomIndex = kRandomBatchSize; |
| var randomNumbers = UNDEFINED; |
| var toStringTagSymbol = utils.ImportNow("to_string_tag_symbol"); |
| |
| //------------------------------------------------------------------- |
| |
| // ECMA 262 - 15.8.2.1 |
| function MathAbs(x) { |
| x = +x; |
| return (x > 0) ? x : 0 - x; |
| } |
| |
| // ECMA 262 - 15.8.2.2 |
| function MathAcosJS(x) { |
| return %_MathAcos(+x); |
| } |
| |
| // ECMA 262 - 15.8.2.3 |
| function MathAsinJS(x) { |
| return %_MathAsin(+x); |
| } |
| |
| // ECMA 262 - 15.8.2.4 |
| function MathAtanJS(x) { |
| return %_MathAtan(+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) { |
| y = +y; |
| x = +x; |
| return %_MathAtan2(y, x); |
| } |
| |
| // ECMA 262 - 15.8.2.6 |
| function MathCeil(x) { |
| return -%_MathFloor(-x); |
| } |
| |
| // ECMA 262 - 15.8.2.8 |
| function MathExp(x) { |
| return %MathExpRT(TO_NUMBER(x)); |
| } |
| |
| // ECMA 262 - 15.8.2.9 |
| function MathFloorJS(x) { |
| return %_MathFloor(+x); |
| } |
| |
| // ECMA 262 - 15.8.2.10 |
| function MathLog(x) { |
| return %_MathLogRT(TO_NUMBER(x)); |
| } |
| |
| // ECMA 262 - 15.8.2.11 |
| function MathMax(arg1, arg2) { // length == 2 |
| var length = %_ArgumentsLength(); |
| if (length == 2) { |
| arg1 = TO_NUMBER(arg1); |
| arg2 = TO_NUMBER(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); |
| n = TO_NUMBER(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(arg1); |
| arg2 = TO_NUMBER(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); |
| n = TO_NUMBER(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 MathPowJS(x, y) { |
| return %_MathPow(TO_NUMBER(x), TO_NUMBER(y)); |
| } |
| |
| // ECMA 262 - 15.8.2.14 |
| function MathRandom() { |
| if (nextRandomIndex >= kRandomBatchSize) { |
| randomNumbers = %GenerateRandomNumbers(randomNumbers); |
| nextRandomIndex = kRandomNumberStart; |
| } |
| return randomNumbers[nextRandomIndex++]; |
| } |
| |
| function MathRandomRaw() { |
| if (nextRandomIndex >= kRandomBatchSize) { |
| randomNumbers = %GenerateRandomNumbers(randomNumbers); |
| nextRandomIndex = kRandomNumberStart; |
| } |
| return %_DoubleLo(randomNumbers[nextRandomIndex++]) & 0x3FFFFFFF; |
| } |
| |
| // ECMA 262 - 15.8.2.15 |
| function MathRound(x) { |
| return %RoundNumber(TO_NUMBER(x)); |
| } |
| |
| // ECMA 262 - 15.8.2.17 |
| function MathSqrtJS(x) { |
| return %_MathSqrt(+x); |
| } |
| |
| // Non-standard extension. |
| function MathImul(x, y) { |
| return %NumberImul(TO_NUMBER(x), TO_NUMBER(y)); |
| } |
| |
| // ES6 draft 09-27-13, section 20.2.2.28. |
| function MathSign(x) { |
| x = +x; |
| if (x > 0) return 1; |
| if (x < 0) return -1; |
| // -0, 0 or NaN. |
| return x; |
| } |
| |
| // ES6 draft 09-27-13, section 20.2.2.34. |
| function MathTrunc(x) { |
| x = +x; |
| if (x > 0) return %_MathFloor(x); |
| if (x < 0) return -%_MathFloor(-x); |
| // -0, 0 or NaN. |
| return x; |
| } |
| |
| // ES6 draft 09-27-13, section 20.2.2.5. |
| function MathAsinh(x) { |
| x = TO_NUMBER(x); |
| // Idempotent for NaN, +/-0 and +/-Infinity. |
| if (x === 0 || !NUMBER_IS_FINITE(x)) return x; |
| if (x > 0) return MathLog(x + %_MathSqrt(x * x + 1)); |
| // This is to prevent numerical errors caused by large negative x. |
| return -MathLog(-x + %_MathSqrt(x * x + 1)); |
| } |
| |
| // ES6 draft 09-27-13, section 20.2.2.3. |
| function MathAcosh(x) { |
| x = TO_NUMBER(x); |
| if (x < 1) return NaN; |
| // Idempotent for NaN and +Infinity. |
| if (!NUMBER_IS_FINITE(x)) return x; |
| return MathLog(x + %_MathSqrt(x + 1) * %_MathSqrt(x - 1)); |
| } |
| |
| // ES6 draft 09-27-13, section 20.2.2.7. |
| function MathAtanh(x) { |
| x = TO_NUMBER(x); |
| // Idempotent for +/-0. |
| if (x === 0) return x; |
| // Returns NaN for NaN and +/- Infinity. |
| if (!NUMBER_IS_FINITE(x)) return NaN; |
| return 0.5 * MathLog((1 + x) / (1 - x)); |
| } |
| |
| // 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 |
| // normalization to avoid overflow is not necessary. For now, we |
| // simply assume the general case. |
| var length = %_ArgumentsLength(); |
| var args = new InternalArray(length); |
| var max = 0; |
| for (var i = 0; i < length; i++) { |
| var n = %_Arguments(i); |
| n = TO_NUMBER(n); |
| if (n === INFINITY || n === -INFINITY) return INFINITY; |
| n = MathAbs(n); |
| if (n > max) max = n; |
| args[i] = n; |
| } |
| |
| // Kahan summation to avoid rounding errors. |
| // Normalize the numbers to the largest one to avoid overflow. |
| if (max === 0) max = 1; |
| var sum = 0; |
| var compensation = 0; |
| for (var i = 0; i < length; i++) { |
| var n = args[i] / max; |
| var summand = n * n - compensation; |
| var preliminary = sum + summand; |
| compensation = (preliminary - sum) - summand; |
| sum = preliminary; |
| } |
| return %_MathSqrt(sum) * max; |
| } |
| |
| // ES6 draft 09-27-13, section 20.2.2.16. |
| function MathFroundJS(x) { |
| return %MathFround(TO_NUMBER(x)); |
| } |
| |
| // ES6 draft 07-18-14, section 20.2.2.11 |
| function MathClz32JS(x) { |
| return %_MathClz32(x >>> 0); |
| } |
| |
| // 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 |
| // of Newton's method. |
| function MathCbrt(x) { |
| x = TO_NUMBER(x); |
| if (x == 0 || !NUMBER_IS_FINITE(x)) return x; |
| return x >= 0 ? CubeRoot(x) : -CubeRoot(-x); |
| } |
| |
| macro NEWTON_ITERATION_CBRT(x, approx) |
| (1.0 / 3.0) * (x / (approx * approx) + 2 * approx); |
| endmacro |
| |
| function CubeRoot(x) { |
| var approx_hi = MathFloorJS(%_DoubleHi(x) / 3) + 0x2A9F7893; |
| var approx = %_ConstructDouble(approx_hi | 0, 0); |
| approx = NEWTON_ITERATION_CBRT(x, approx); |
| approx = NEWTON_ITERATION_CBRT(x, approx); |
| approx = NEWTON_ITERATION_CBRT(x, approx); |
| return NEWTON_ITERATION_CBRT(x, approx); |
| } |
| |
| // ------------------------------------------------------------------- |
| |
| %AddNamedProperty(GlobalMath, toStringTagSymbol, "Math", READ_ONLY | DONT_ENUM); |
| |
| // Set up math constants. |
| utils.InstallConstants(GlobalMath, [ |
| // 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. |
| utils.InstallFunctions(GlobalMath, DONT_ENUM, [ |
| "random", MathRandom, |
| "abs", MathAbs, |
| "acos", MathAcosJS, |
| "asin", MathAsinJS, |
| "atan", MathAtanJS, |
| "ceil", MathCeil, |
| "exp", MathExp, |
| "floor", MathFloorJS, |
| "log", MathLog, |
| "round", MathRound, |
| "sqrt", MathSqrtJS, |
| "atan2", MathAtan2JS, |
| "pow", MathPowJS, |
| "max", MathMax, |
| "min", MathMin, |
| "imul", MathImul, |
| "sign", MathSign, |
| "trunc", MathTrunc, |
| "asinh", MathAsinh, |
| "acosh", MathAcosh, |
| "atanh", MathAtanh, |
| "hypot", MathHypot, |
| "fround", MathFroundJS, |
| "clz32", MathClz32JS, |
| "cbrt", MathCbrt |
| ]); |
| |
| %SetForceInlineFlag(MathAbs); |
| %SetForceInlineFlag(MathAcosJS); |
| %SetForceInlineFlag(MathAsinJS); |
| %SetForceInlineFlag(MathAtanJS); |
| %SetForceInlineFlag(MathAtan2JS); |
| %SetForceInlineFlag(MathCeil); |
| %SetForceInlineFlag(MathClz32JS); |
| %SetForceInlineFlag(MathFloorJS); |
| %SetForceInlineFlag(MathRandom); |
| %SetForceInlineFlag(MathSign); |
| %SetForceInlineFlag(MathSqrtJS); |
| %SetForceInlineFlag(MathTrunc); |
| |
| // ------------------------------------------------------------------- |
| // Exports |
| |
| utils.Export(function(to) { |
| to.MathAbs = MathAbs; |
| to.MathExp = MathExp; |
| to.MathFloor = MathFloorJS; |
| to.IntRandom = MathRandomRaw; |
| to.MathMax = MathMax; |
| to.MathMin = MathMin; |
| }); |
| |
| }) |
