src/math.js

// 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 - 15.8.2.8
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 - 15.8.2.17
function MathSqrt(x) {
  return %_MathSqrtRT(TO_NUMBER_INLINE(x));
}

// Non-standard extension.
function MathImul(x, y) {
  return %NumberImul(TO_NUMBER_INLINE(x), TO_NUMBER_INLINE(y));
}

// 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));
}

// ES6 draft 07-18-14, section 20.2.2.11
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 SetUpMath() {
  %CheckIsBootstrapping();

  %InternalSetPrototype($Math, $Object.prototype);
  %AddNamedProperty(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,       // implemented by third_party/fdlibm
    "exp", MathExp,
    "floor", MathFloor,
    "log", MathLog,
    "round", MathRound,
    "sin", MathSin,       // implemented by third_party/fdlibm
    "sqrt", MathSqrt,
    "tan", MathTan,       // implemented by third_party/fdlibm
    "atan2", MathAtan2JS,
    "pow", MathPow,
    "max", MathMax,
    "min", MathMin,
    "imul", MathImul,
    "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
  ));

  %SetInlineBuiltinFlag(MathCeil);
  %SetInlineBuiltinFlag(MathRandom);
  %SetInlineBuiltinFlag(MathSin);
  %SetInlineBuiltinFlag(MathCos);
}

SetUpMath();