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      1 // Copyright 2012 the V8 project authors. All rights reserved.
      2 // Use of this source code is governed by a BSD-style license that can be
      3 // found in the LICENSE file.
      4 
      5 (function(global, utils) {
      6 "use strict";
      7 
      8 %CheckIsBootstrapping();
      9 
     10 // -------------------------------------------------------------------
     11 // Imports
     12 
     13 // The first two slots are reserved to persist PRNG state.
     14 define kRandomNumberStart = 2;
     15 
     16 var GlobalFloat64Array = global.Float64Array;
     17 var GlobalMath = global.Math;
     18 var GlobalObject = global.Object;
     19 var NaN = %GetRootNaN();
     20 var nextRandomIndex = 0;
     21 var randomNumbers = UNDEFINED;
     22 var toStringTagSymbol = utils.ImportNow("to_string_tag_symbol");
     23 
     24 //-------------------------------------------------------------------
     25 
     26 // ECMA 262 - 15.8.2.1
     27 function MathAbs(x) {
     28   x = +x;
     29   return (x > 0) ? x : 0 - x;
     30 }
     31 
     32 // ECMA 262 - 15.8.2.13
     33 function MathPowJS(x, y) {
     34   return %_MathPow(TO_NUMBER(x), TO_NUMBER(y));
     35 }
     36 
     37 // ECMA 262 - 15.8.2.14
     38 function MathRandom() {
     39   // While creating a startup snapshot, %GenerateRandomNumbers returns a
     40   // normal array containing a single random number, and has to be called for
     41   // every new random number.
     42   // Otherwise, it returns a pre-populated typed array of random numbers. The
     43   // first two elements are reserved for the PRNG state.
     44   if (nextRandomIndex <= kRandomNumberStart) {
     45     randomNumbers = %GenerateRandomNumbers(randomNumbers);
     46     if (%_IsTypedArray(randomNumbers)) {
     47       nextRandomIndex = %_TypedArrayGetLength(randomNumbers);
     48     } else {
     49       nextRandomIndex = randomNumbers.length;
     50     }
     51   }
     52   return randomNumbers[--nextRandomIndex];
     53 }
     54 
     55 function MathRandomRaw() {
     56   if (nextRandomIndex <= kRandomNumberStart) {
     57     randomNumbers = %GenerateRandomNumbers(randomNumbers);
     58     nextRandomIndex = %_TypedArrayGetLength(randomNumbers);
     59   }
     60   return %_DoubleLo(randomNumbers[--nextRandomIndex]) & 0x3FFFFFFF;
     61 }
     62 
     63 // ES6 draft 09-27-13, section 20.2.2.28.
     64 function MathSign(x) {
     65   x = +x;
     66   if (x > 0) return 1;
     67   if (x < 0) return -1;
     68   // -0, 0 or NaN.
     69   return x;
     70 }
     71 
     72 // ES6 draft 09-27-13, section 20.2.2.5.
     73 function MathAsinh(x) {
     74   x = TO_NUMBER(x);
     75   // Idempotent for NaN, +/-0 and +/-Infinity.
     76   if (x === 0 || !NUMBER_IS_FINITE(x)) return x;
     77   if (x > 0) return %math_log(x + %math_sqrt(x * x + 1));
     78   // This is to prevent numerical errors caused by large negative x.
     79   return -%math_log(-x + %math_sqrt(x * x + 1));
     80 }
     81 
     82 // ES6 draft 09-27-13, section 20.2.2.3.
     83 function MathAcosh(x) {
     84   x = TO_NUMBER(x);
     85   if (x < 1) return NaN;
     86   // Idempotent for NaN and +Infinity.
     87   if (!NUMBER_IS_FINITE(x)) return x;
     88   return %math_log(x + %math_sqrt(x + 1) * %math_sqrt(x - 1));
     89 }
     90 
     91 // ES6 draft 09-27-13, section 20.2.2.17.
     92 function MathHypot(x, y) {  // Function length is 2.
     93   // We may want to introduce fast paths for two arguments and when
     94   // normalization to avoid overflow is not necessary.  For now, we
     95   // simply assume the general case.
     96   var length = arguments.length;
     97   var max = 0;
     98   for (var i = 0; i < length; i++) {
     99     var n = MathAbs(arguments[i]);
    100     if (n > max) max = n;
    101     arguments[i] = n;
    102   }
    103   if (max === INFINITY) return INFINITY;
    104 
    105   // Kahan summation to avoid rounding errors.
    106   // Normalize the numbers to the largest one to avoid overflow.
    107   if (max === 0) max = 1;
    108   var sum = 0;
    109   var compensation = 0;
    110   for (var i = 0; i < length; i++) {
    111     var n = arguments[i] / max;
    112     var summand = n * n - compensation;
    113     var preliminary = sum + summand;
    114     compensation = (preliminary - sum) - summand;
    115     sum = preliminary;
    116   }
    117   return %math_sqrt(sum) * max;
    118 }
    119 
    120 // -------------------------------------------------------------------
    121 
    122 %InstallToContext([
    123   "math_pow", MathPowJS,
    124 ]);
    125 
    126 %AddNamedProperty(GlobalMath, toStringTagSymbol, "Math", READ_ONLY | DONT_ENUM);
    127 
    128 // Set up math constants.
    129 utils.InstallConstants(GlobalMath, [
    130   "PI", 3.1415926535897932,
    131   "SQRT1_2", 0.7071067811865476,
    132   "SQRT2", 1.4142135623730951
    133 ]);
    134 
    135 // Set up non-enumerable functions of the Math object and
    136 // set their names.
    137 utils.InstallFunctions(GlobalMath, DONT_ENUM, [
    138   "random", MathRandom,
    139   "abs", MathAbs,
    140   "pow", MathPowJS,
    141   "sign", MathSign,
    142   "asinh", MathAsinh,
    143   "acosh", MathAcosh,
    144   "hypot", MathHypot,
    145 ]);
    146 
    147 %SetForceInlineFlag(MathRandom);
    148 %SetForceInlineFlag(MathSign);
    149 
    150 // -------------------------------------------------------------------
    151 // Exports
    152 
    153 utils.Export(function(to) {
    154   to.MathAbs = MathAbs;
    155   to.IntRandom = MathRandomRaw;
    156 });
    157 
    158 })
    159