Ship ES6 Math functions.

src/harmony-math.js

-// 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();