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 // Copyright 2013 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'; // ES6 draft 09-27-13, section 20.2.2.28. function MathSign(x) { x = TO_NUMBER_INLINE(x); if (x > 0) return 1; if (x < 0) return -1; if (x === 0) return x; return NAN; } // ES6 draft 09-27-13, section 20.2.2.34. function MathTrunc(x) { x = TO_NUMBER_INLINE(x); if (x > 0) return MathFloor(x); if (x < 0) return MathCeil(x); if (x === 0) return x; return NAN; } // ES6 draft 09-27-13, section 20.2.2.30. function MathSinh(x) { if (!IS_NUMBER(x)) x = NonNumberToNumber(x); // Idempotent for NaN, +/-0 and +/-Infinity. if (x === 0 || !NUMBER_IS_FINITE(x)) return 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); if (!NUMBER_IS_FINITE(x)) return MathAbs(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); // Idempotent for +/-0. if (x === 0) return x; // Returns +/-1 for +/-Infinity. if (!NUMBER_IS_FINITE(x)) return MathSign(x); var exp1 = MathExp(x); var exp2 = MathExp(-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); // 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) { if (!IS_NUMBER(x)) x = NonNumberToNumber(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) { if (!IS_NUMBER(x)) x = NonNumberToNumber(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 20.2.2.21. function MathLog10(x) { return MathLog(x) * 0.434294481903251828; // log10(x) = log(x)/log(10). } // ES6 draft 09-27-13, section 20.2.2.22. 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 // 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); if (!IS_NUMBER(n)) n = NonNumberToNumber(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_INLINE(x)); } function MathClz32(x) { x = ToUint32(TO_NUMBER_INLINE(x)); if (x == 0) return 32; var result = 0; // Binary search. if ((x & 0xFFFF0000) === 0) { x <<= 16; result += 16; }; if ((x & 0xFF000000) === 0) { x <<= 8; result += 8; }; if ((x & 0xF0000000) === 0) { x <<= 4; result += 4; }; if ((x & 0xC0000000) === 0) { x <<= 2; result += 2; }; if ((x & 0x80000000) === 0) { x <<= 1; result += 1; }; 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 // of Newton's method. function MathCbrt(x) { if (!IS_NUMBER(x)) x = NonNumberToNumber(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 = MathFloor(%_DoubleHi(x) / 3) + 0x2A9F7893; var approx = %_ConstructDouble(approx_hi, 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); } // 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! + ... // == x/1! + x^2/2! + x^3/3! + ... // The closer x is to 0, the fewer terms are required. function MathExpm1(x) { if (!IS_NUMBER(x)) x = NonNumberToNumber(x); var xabs = MathAbs(x); if (xabs < 2E-7) { return x * (1 + x * (1/2)); } else if (xabs < 6E-5) { return x * (1 + x * (1/2 + x * (1/6))); } else if (xabs < 2E-2) { return x * (1 + x * (1/2 + x * (1/6 + x * (1/24 + x * (1/120 + x * (1/720)))))); } else { // Use regular exp if not close enough to 0. return MathExp(x) - 1; } } // 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! + ... // == 0 + x - x^2/2 + x^3/3 ... // The closer x is to 0, the fewer terms are required. function MathLog1p(x) { if (!IS_NUMBER(x)) x = NonNumberToNumber(x); var xabs = MathAbs(x); if (xabs < 1E-7) { return x * (1 - x * (1/2)); } else if (xabs < 3E-5) { return x * (1 - x * (1/2 - x * (1/3))); } else if (xabs < 7E-3) { return x * (1 - x * (1/2 - x * (1/3 - x * (1/4 - x * (1/5 - x * (1/6 - x * (1/7))))))); } else { // Use regular log if not close enough to 0. return MathLog(1 + x); } } function ExtendMath() { %CheckIsBootstrapping(); // Set up the non-enumerable functions on the Math object. InstallFunctions(\$Math, DONT_ENUM, \$Array( "sign", MathSign, "trunc", MathTrunc, "sinh", MathSinh, "cosh", MathCosh, "tanh", MathTanh, "asinh", MathAsinh, "acosh", MathAcosh, "atanh", MathAtanh, "log10", MathLog10, "log2", MathLog2, "hypot", MathHypot, "fround", MathFroundJS, "clz32", MathClz32, "cbrt", MathCbrt, "log1p", MathLog1p, "expm1", MathExpm1 )); } ExtendMath();