// Copyright 2012 the V8 project authors. All rights reserved. // Redistribution and use in source and binary forms, with or without // modification, are permitted provided that the following conditions are // met: // // * Redistributions of source code must retain the above copyright // notice, this list of conditions and the following disclaimer. // * Redistributions in binary form must reproduce the above // copyright notice, this list of conditions and the following // disclaimer in the documentation and/or other materials provided // with the distribution. // * Neither the name of Google Inc. nor the names of its // contributors may be used to endorse or promote products derived // from this software without specific prior written permission. // // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. // 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 MathAcos(x) { return %Math_acos(TO_NUMBER_INLINE(x)); } // ECMA 262 - 15.8.2.3 function MathAsin(x) { return %Math_asin(TO_NUMBER_INLINE(x)); } // ECMA 262 - 15.8.2.4 function MathAtan(x) { return %Math_atan(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 MathAtan2(y, x) { return %Math_atan2(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 %Math_exp(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 %Math_floor(x); } } // ECMA 262 - 15.8.2.10 function MathLog(x) { return %_MathLog(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 %_MathSqrt(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", MathAcos, "asin", MathAsin, "atan", MathAtan, "ceil", MathCeil, "cos", MathCos, "exp", MathExp, "floor", MathFloor, "log", MathLog, "round", MathRound, "sin", MathSin, "sqrt", MathSqrt, "tan", MathTan, "atan2", MathAtan2, "pow", MathPow, "max", MathMax, "min", MathMin, "imul", MathImul )); %SetInlineBuiltinFlag(MathCeil); %SetInlineBuiltinFlag(MathRandom); %SetInlineBuiltinFlag(MathSin); %SetInlineBuiltinFlag(MathCos); %SetInlineBuiltinFlag(MathTan); %SetInlineBuiltinFlag(TrigonometricInterpolation); } SetUpMath();