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579ff5f
Math.acosh, Math.asinh, Math.atanh, Math.cosh, Math.sinh, Math.tanh
Yaffle May 11, 2015
6ab5226
FINE
Yaffle May 11, 2015
e3c67ec
Update es6-shim.js
Yaffle May 28, 2015
046ede0
Update README.md
Yaffle May 29, 2015
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89 changes: 48 additions & 41 deletions es6-shim.js
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Original file line number Diff line number Diff line change
Expand Up @@ -1310,29 +1310,29 @@
var MathShims = {
acosh: function acosh(value) {
var x = Number(value);
if (Number.isNaN(x) || value < 1) { return NaN; }
if (x === 1) { return 0; }
if (x === Infinity) { return x; }
return Math.log(x / Math.E + Math.sqrt(x + 1) * Math.sqrt(x - 1) / Math.E) + 1;
if (Math.abs(x) > Math.sqrt(2 / Number.EPSILON)) {
return Math.log(x) + Math.LN2;
}
return Math.log1p(x - 1 + Math.sqrt(x - 1) * Math.sqrt(x + 1));
},

asinh: function asinh(value) {
var x = Number(value);
if (x === 0 || !globalIsFinite(x)) {
if (x === 0) {
return x;
}
return x < 0 ? -Math.asinh(-x) : Math.log(x + Math.sqrt(x * x + 1));
if (x < 0) {
return -Math.asinh(-x);
}
if (Math.abs(x) > Math.sqrt(2 / Number.EPSILON)) {
return Math.log(x) + Math.LN2;
}
return Math.log1p(x + Math.expm1(Math.log1p(x * x) / 2));
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I was just about to post an issue recommending the use of a range-reduction method similar to that used for Math.acosh in the current shim:

if (x < 0) { return -Math.asinh(-x); }
var sqx = x * x;
if (sqx <= inverseEpsilon - 1) { return Math.log(x + Math.sqrt(sqx + 1)); }
if (sqx <= Number.MAX_VALUE - 1) {
  var sqrtEpsilon = Math.sqrt(Number.EPSILON);
  return Math.log(x * sqrtEpsilon + Math.sqrt(square(x * sqrtEpsilon) + Number.EPSILON)) - Math.log(sqrtEpsilon);
}
var sqrtMax = Math.sqrt(Number.MAX_VALUE);
return Math.log(x / sqrtMax + Math.sqrt(square(x / sqrtMax) + 1 / Number.MAX_VALUE)) + Math.log(Number.MAX_VALUE) / 2;

However, this solution looks less hackish (also, I'm not sure whether the function call to square() would be worth it if the argument contains an operator, compared to running the inner operations twice).

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@lewisje ,
Hi! Why is it better? Could you provide more details? Is Math.log(x) + Math.log(2) not accurate for "big" x ? I cannot find any x, for which your impl. produce too much different values.
Your implementation is not accurate for small values (Math.pow(2, -1021)),

What I do not like in my is : if (x * x + 1 === x * x) {. Possibly, I should use x > Math.sqrt(2 / Number.EPSILON) here.

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Sorry, by "this" I meant the line I was commenting on; that is, your idea is better than mine and I hope it is merged in.

},

atanh: function atanh(value) {
var x = Number(value);
if (Number.isNaN(x) || x < -1 || x > 1) {
return NaN;
}
if (x === -1) { return -Infinity; }
if (x === 1) { return Infinity; }
if (x === 0) { return x; }
return 0.5 * Math.log((1 + x) / (1 - x));
return (Math.log1p(x) - Math.log1p(-x)) / 2;
},

cbrt: function cbrt(value) {
Expand Down Expand Up @@ -1362,12 +1362,10 @@

cosh: function cosh(value) {
var x = Number(value);
if (x === 0) { return 1; } // +0 or -0
if (Number.isNaN(x)) { return NaN; }
if (!globalIsFinite(x)) { return Infinity; }
if (x < 0) { x = -x; }
if (x > 21) { return Math.exp(x) / 2; }
return (Math.exp(x) + Math.exp(-x)) / 2;
if (x === 0) {
return 1;
}
return (Math.exp(x - 1) + Math.exp(-x - 1)) * (Math.E / 2);
},

expm1: function expm1(value) {
Expand Down Expand Up @@ -1447,24 +1445,20 @@

sinh: function sinh(value) {
var x = Number(value);
if (!globalIsFinite(x) || x === 0) { return x; }

if (Math.abs(x) < 1) {
return (Math.expm1(x) - Math.expm1(-x)) / 2;
}
return (Math.exp(x - 1) - Math.exp(-x - 1)) * Math.E / 2;
return (Math.exp(x - 1) - Math.exp(-x - 1)) * (Math.E / 2);
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brackets are important here - Math.sinh(710)

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I'm fine with adding these parentheses (brackets are [ ]), but mathematically it shouldn't make a difference.

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mathematically - not, but from floating point perspective - should, because of overflows

Math.pow(2, 1023) * Math.E / 2 === Infinity
Math.pow(2, 1023) * (Math.E / 2) === 1.2216591454104522e+308

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ah ha, good point :-)

},

tanh: function tanh(value) {
var x = Number(value);
if (Number.isNaN(x) || x === 0) { return x; }
if (x === Infinity) { return 1; }
if (x === -Infinity) { return -1; }
var a = Math.expm1(x);
var b = Math.expm1(-x);
if (a === Infinity) { return 1; }
if (b === Infinity) { return -1; }
return (a - b) / (Math.exp(x) + Math.exp(-x));
var a = Math.expm1(2 * x);
var b = Math.expm1(2 * x) + 2;
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Why am I calculating Math.expm1(2 * x) twice?

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ha, good question

if (a === Infinity && b === Infinity) {
return 1;
}
return a / b;
},

trunc: function trunc(value) {
Expand Down Expand Up @@ -1505,21 +1499,34 @@
}
};
defineProperties(Math, MathShims);
// IE 11 TP has an imprecise log1p: reports Math.log1p(-1e-17) as 0
defineProperty(Math, 'log1p', MathShims.log1p, Math.log1p(-1e-17) !== -1e-17);

var BINARY_64_EPSILON = Math.pow(2, -52);
// https://code.google.com/p/v8/issues/detail?id=3468
var MATH_EXP_ERROR = Math.abs(1 - Math.exp(704.6589) / 1.0702171200481775e+306) / BINARY_64_EPSILON;
var isAlmostEqual = function (a, b) {
return Math.abs(1 - a / b) / BINARY_64_EPSILON < MATH_EXP_ERROR + 8;
};

// Chrome 40-43
defineProperty(Math, 'acosh', MathShims.acosh, !isAlmostEqual(Math.acosh(1.0000000000000009), 4.214684851089403e-8));
// IE 11 TP has an imprecise asinh: reports Math.asinh(-1e7) as not exactly equal to -Math.asinh(1e7)
defineProperty(Math, 'asinh', MathShims.asinh, Math.asinh(-1e7) !== -Math.asinh(1e7));
// Chrome 40 has an imprecise Math.tanh with very small numbers
defineProperty(Math, 'tanh', MathShims.tanh, Math.tanh(-2e-17) !== -2e-17);
// Chrome 40 loses Math.acosh precision with high numbers
defineProperty(Math, 'acosh', MathShims.acosh, Math.acosh(Number.MAX_VALUE) === Infinity);
// Chrome 40-43
defineProperty(Math, 'asinh', MathShims.asinh, !isAlmostEqual(Math.asinh(1.7976931348623157e+308), 710.475860073944));
// Chrome 40-43
defineProperty(Math, 'atanh', MathShims.atanh, !isAlmostEqual(Math.atanh(Math.pow(2, -1021)), Math.pow(2, -1021)));
// Firefox 38 on Windows
defineProperty(Math, 'cbrt', MathShims.cbrt, Math.abs(1 - Math.cbrt(1e-300) / 1e-100) / Number.EPSILON > 8);
// node 0.11 has an imprecise Math.sinh with very small numbers
defineProperty(Math, 'sinh', MathShims.sinh, Math.sinh(-2e-17) !== -2e-17);
defineProperty(Math, 'cbrt', MathShims.cbrt, !isAlmostEqual(Math.cbrt(1e-300), 1e-100));
// node 0.12
defineProperty(Math, 'cosh', MathShims.cosh, !isAlmostEqual(Math.cosh(710), 1.1169973830808555e+308));
// FF 35 on Linux reports 22025.465794806725 for Math.expm1(10)
var expm1OfTen = Math.expm1(10);
defineProperty(Math, 'expm1', MathShims.expm1, expm1OfTen > 22025.465794806719 || expm1OfTen < 22025.4657948067165168);
defineProperty(Math, 'expm1', MathShims.expm1, !isAlmostEqual(Math.expm1(10), 22025.465794806718));
// IE 11 TP has an imprecise log1p: reports Math.log1p(-1e-17) as 0
defineProperty(Math, 'log1p', MathShims.log1p, !isAlmostEqual(Math.log1p(-1e-17), -1e-17));
// node 0.11 has an imprecise Math.sinh with very small numbers
defineProperty(Math, 'sinh', MathShims.sinh, !isAlmostEqual(Math.sinh(-2e-17), -2e-17));
// Chrome 40 on Windows has an imprecise Math.tanh with very small numbers
defineProperty(Math, 'tanh', MathShims.tanh, !isAlmostEqual(Math.tanh(-2e-17), -2e-17));

var origMathRound = Math.round;
// breaks in e.g. Safari 8, Internet Explorer 11, Opera 12
Expand Down
63 changes: 41 additions & 22 deletions test/math.js
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Original file line number Diff line number Diff line change
@@ -1,11 +1,17 @@
/*global describe, it, expect, require */

var Assertion = expect().constructor;
Assertion.prototype.almostEqual = function (obj, precision) {

var EPSILON = Math.pow(2, -52);
var MIN_VALUE = Math.pow(2, -1022);
var MAX_VALUE = Math.pow(2, 1023) * (2 - EPSILON);

var MATH_EXP_ERROR = Math.abs(1 - Math.exp(704.6589) / 1.0702171200481775e+306) / EPSILON;
Assertion.prototype.almostEqual = function (expected) {
'use strict';

var allowedDiff = precision || 1e-11;
return this.within(obj - allowedDiff, obj + allowedDiff);
var C = (expected < 0 ? -1 : (expected > 0 ? 1 : expected)) * (MATH_EXP_ERROR + 8) * EPSILON;
return this.within(expected * (1 - C), expected * (1 + C));
};
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this is not ideal, I do not know how to access private "this.__flags.object" and I did not test it well.

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I think this.flags('object') might work better

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@ljharb , I fixed by using this.within


describe('Math', function () {
Expand All @@ -27,7 +33,6 @@ describe('Math', function () {
};
var valueOfIsNaN = { valueOf: function () { return NaN; } };
var valueOfIsInfinity = { valueOf: function () { return Infinity; } };
var EPSILON = Number.EPSILON || 2.2204460492503130808472633361816e-16;

(typeof process !== 'undefined' && process.env.NO_ES6_SHIM ? it.skip : it)('is on the exported object', function () {
var exported = require('../');
Expand All @@ -50,15 +55,16 @@ describe('Math', function () {
it('should be correct', function () {
expect(numberIsNaN(Math.acosh(NaN))).to.equal(true);
expect(numberIsNaN(Math.acosh(0))).to.equal(true);
expect(numberIsNaN(Math.acosh(0.9999999))).to.equal(true);
expect(numberIsNaN(Math.acosh(1 - EPSILON / 2))).to.equal(true);
expect(numberIsNaN(Math.acosh(-1e300))).to.equal(true);
expect(Math.acosh(1e+99)).to.almostEqual(228.64907138697046);
expect(isPositiveZero(Math.acosh(1))).to.equal(true);
expect(Math.acosh(Infinity)).to.equal(Infinity);
expect(Math.acosh(1234)).to.almostEqual(7.811163220849231);
expect(Math.acosh(8.88)).to.almostEqual(2.8737631531629235);
expect(Math.acosh(1e160)).to.almostEqual(369.10676205960726);
expect(Math.acosh(Number.MAX_VALUE)).to.almostEqual(710.4758600739439);
expect(Math.acosh(MAX_VALUE)).to.almostEqual(710.4758600739439);
expect(Math.acosh(1 + EPSILON)).to.almostEqual(2.1073424255447017e-8);
});
});

Expand Down Expand Up @@ -95,6 +101,10 @@ describe('Math', function () {
expect(Math.asinh(1e150)).to.almostEqual(346.0809111296668);
expect(Math.asinh(1e7)).to.almostEqual(16.811242831518268);
expect(Math.asinh(-1e7)).to.almostEqual(-16.811242831518268);
expect(Math.asinh(MAX_VALUE)).to.almostEqual(710.4758600739439);
expect(Math.asinh(-MAX_VALUE)).to.almostEqual(-710.4758600739439);
expect(Math.asinh(MIN_VALUE * 2)).to.almostEqual(MIN_VALUE * 2);
expect(Math.asinh(-MIN_VALUE * 2)).to.almostEqual(-MIN_VALUE * 2);
});
});

Expand All @@ -113,14 +123,18 @@ describe('Math', function () {

it('should be correct', function () {
expect(numberIsNaN(Math.atanh(NaN))).to.equal(true);
expect(numberIsNaN(Math.atanh(-1.00000001))).to.equal(true);
expect(numberIsNaN(Math.atanh(1.00000001))).to.equal(true);
expect(numberIsNaN(Math.atanh(-1e300))).to.equal(true);
expect(numberIsNaN(Math.atanh(1e300))).to.equal(true);
expect(numberIsNaN(Math.atanh(-1 - EPSILON))).to.equal(true);
expect(numberIsNaN(Math.atanh(1 + EPSILON))).to.equal(true);
expect(numberIsNaN(Math.atanh(-MAX_VALUE))).to.equal(true);
expect(numberIsNaN(Math.atanh(MAX_VALUE))).to.equal(true);
expect(Math.atanh(-1)).to.equal(-Infinity);
expect(Math.atanh(1)).to.equal(Infinity);
expect(isPositiveZero(Math.atanh(+0))).to.equal(true);
expect(isNegativeZero(Math.atanh(-0))).to.equal(true);
expect(Math.atanh(-1 + EPSILON / 2)).to.almostEqual(-18.714973875118524);
expect(Math.atanh(1 - EPSILON / 2)).to.almostEqual(18.714973875118524);
expect(Math.atanh(MIN_VALUE * 2)).to.almostEqual(MIN_VALUE * 2);
expect(Math.atanh(-MIN_VALUE * 2)).to.almostEqual(-MIN_VALUE * 2);
expect(Math.atanh(0.5)).to.almostEqual(0.5493061443340549);
expect(Math.atanh(-0.5)).to.almostEqual(-0.5493061443340549);
expect(Math.atanh(-0.5)).to.almostEqual(-0.5493061443340549);
Expand Down Expand Up @@ -151,10 +165,10 @@ describe('Math', function () {
expect(Math.cbrt(8)).to.almostEqual(2);
expect(Math.cbrt(-1000)).to.almostEqual(-10);
expect(Math.cbrt(1000)).to.almostEqual(10);
expect(Math.cbrt(-1e-300)).to.almostEqual(-1e-100);
expect(Math.cbrt(1e-300)).to.almostEqual(1e-100);
expect(Math.cbrt(-1e+300)).to.almostEqual(-1e+100);
expect(Math.cbrt(1e+300)).to.almostEqual(1e+100);
expect(Math.cbrt(-MIN_VALUE)).to.almostEqual(-2.8126442852362615e-103);
expect(Math.cbrt(MIN_VALUE)).to.almostEqual(2.8126442852362615e-103);
expect(Math.cbrt(-MAX_VALUE)).to.almostEqual(-5.643803094122361e+102);
expect(Math.cbrt(MAX_VALUE)).to.almostEqual(5.643803094122361e+102);
});
});

Expand Down Expand Up @@ -260,13 +274,13 @@ describe('Math', function () {
});

it('should be correct', function () {
// Overridden precision values here are for Chrome, as of v25.0.1364.172
// Broadened slightly for Firefox 31
expect(Math.cosh(12)).to.almostEqual(81377.39571257407, 9e-11);
expect(Math.cosh(22)).to.almostEqual(1792456423.065795780980053377, 1e-5);
expect(Math.cosh(12)).to.almostEqual(81377.39571257407);
expect(Math.cosh(22)).to.almostEqual(1792456423.065795780980053377);
expect(Math.cosh(-10)).to.almostEqual(11013.23292010332313972137);
expect(Math.cosh(-23)).to.almostEqual(4872401723.1244513000, 1e-5);
expect(Math.cosh(-2e-17)).to.equal(1);
expect(Math.cosh(-23)).to.almostEqual(4872401723.1244513000);
expect(Math.cosh(-2e-17)).to.almostEqual(1);
expect(Math.cosh(710)).to.almostEqual(1.1169973830808555e+308);
expect(Math.cosh(-710)).to.almostEqual(1.1169973830808555e+308);
});
});

Expand Down Expand Up @@ -551,7 +565,11 @@ describe('Math', function () {
expect(Math.sinh(-Infinity)).to.equal(-Infinity);
expect(Math.sinh(-5)).to.almostEqual(-74.20321057778875);
expect(Math.sinh(2)).to.almostEqual(3.6268604078470186);
expect(Math.sinh(-2e-17)).to.equal(-2e-17);
expect(Math.sinh(-2e-17)).to.almostEqual(-2e-17);
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In which browsers is Math.sinh(-2e-17) not precisely equal to -2e-17?

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@ljharb in a browser of 2150 year, which have Number.EPSILON < 2e-17 * 2e-17 / 3

expect(Math.sinh(MIN_VALUE * 2)).to.almostEqual(MIN_VALUE * 2);
expect(Math.sinh(-MIN_VALUE * 2)).to.almostEqual(-MIN_VALUE * 2);
expect(Math.sinh(710)).to.almostEqual(1.1169973830808555e+308);
expect(Math.sinh(-710)).to.almostEqual(-1.1169973830808555e+308);
});
});

Expand Down Expand Up @@ -582,7 +600,8 @@ describe('Math', function () {
expect(Math.tanh(-Infinity)).to.equal(-1);
expect(Math.tanh(90)).to.almostEqual(1);
expect(Math.tanh(10)).to.almostEqual(0.9999999958776927);
expect(Math.tanh(-2e-17)).to.equal(-2e-17);
expect(Math.tanh(MIN_VALUE * 2)).to.almostEqual(MIN_VALUE * 2);
expect(Math.tanh(-MIN_VALUE * 2)).to.almostEqual(-MIN_VALUE * 2);
});
});

Expand Down