Math.fround()

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The Math.fround() function returns the nearest 32-bit single precision float representation of a Number.

Syntax

var singleFloat = Math.fround(doubleFloat);

Parameters

doubleFloat
A Number. If the parameter is of a different type, it will get converted to a number or to NaN if it cannot be converted.

Return value

The nearest 32-bit single precision float representation of the given number.

Description

JavaScript uses 64-bit double floating-point numbers internally, which offer a very high precision. However, sometimes you may be working with 32-bit floating-point numbers, for example if you are reading values from a Float32Array. This can create confusion: Checking a 64-bit float and a 32-bit float for equality may fail even though the numbers are seemingly identical.

To solve this, Math.fround() can be used to cast the 64-bit float to a 32-bit float. Internally, JavaScript continues to treat the number as a 64-bit float, it just performs a "round to even" on the 23rd bit of the mantissa, and sets all following mantissa bits to 0. If the number is outside the range of a 32-bit float, Infinity or -Infinity is returned.

Because fround() is a static method of Math, you always use it as Math.fround(), rather than as a method of a Math object you created (Math is not a constructor).

Examples

Using Math.fround()

The number 1.5 can be precisely represented in the binary numeral system, and is identical in 32-bit and 64-bit:

Math.fround(1.5); // 1.5
Math.fround(1.5) === 1.5; // true

However, the number 1.337 cannot be precisely represented in the binary numeral system, so it differs in 32-bit and 64-bit:

Math.fround(1.337); // 1.3370000123977661
Math.fround(1.337) === 1.337; // false

$2^150$ is too big for a 32-bit float, so Infinity is returned:

2 ** 150; // 1.42724769270596e+45
Math.fround(2 ** 150); // Infinity

If the parameter cannot be converted to a number, or it is not-a-number (NaN), Math.fround() will return NaN:

Math.fround('abc'); // NaN
Math.fround(NaN); // NaN

Polyfill

This can be emulated with the following function, if Float32Array are supported:

Math.fround = Math.fround || (function (array) {
return function(x) {
return array = x, array;
};
})(new Float32Array(1));

Supporting older browsers is slower, but also possible:

if (!Math.fround) Math.fround = function(arg) {
arg = Number(arg);
// Return early for ±0 and NaN.
if (!arg) return arg;
var sign = arg < 0 ? -1 : 1;
if (sign < 0) arg = -arg;
// Compute the exponent (8 bits, signed).
var exp = Math.floor(Math.log(arg) / Math.LN2);
var powexp = Math.pow(2, Math.max(-126, Math.min(exp, 127)));
// Handle subnormals: leading digit is zero if exponent bits are all zero.
var leading = exp < -127 ? 0 : 1;
// Compute 23 bits of mantissa, inverted to round toward zero.
var mantissa = Math.round((leading - arg / powexp) * 0x800000);
if (mantissa <= -0x800000) return sign * Infinity;
return sign * powexp * (leading - mantissa / 0x800000);
};

Faster Alternative Polyfill (Work In Progress)

The below polyfill is much faster and uses double-precision rounding errors to emulate the rounding errors caused by floating point narrowing. Although the polyfill higher on the page is good for comprehension, all of the complex Math function that it uses make it terrible slow. Although this polyfill is much faster, it is off by a bit in about 1 out of 2048 of the tests due to the tendency to round upwards like Math.ceil instead of like Math.round in the division of the subnormal-handling section of the code. Because single precision floating points have 23 bits of precision, the mean error deviation from the correct value is roughly 2**-28 or 0.0000000058%. This deviation from the correct value should be insignifigant in most circumstances, however please edit this polyfill if you have some tweaks to increase correctness without bloating the code size too much. NaN is not optimized for because it is most likely (almost certain) that you will not be calling Math.fround with NaN exclusively in a tight loop. Moreover, an additional check just for NaN instead of letting NaN naturally arise would induce a performance penalty for this function in older browsers when not called with NaN. Thus, the code below handles NaN correctly, but inefficiently for good reason.

const Math_round = Math.round;
if (!Math.fround) Math.fround = function(x) {
if (x > 3.402823669209385e+38) return Infinity; // maximum float is 2**128
if (x < -3.402823669209385e+38) return -Infinity; // minimum is -2**128
if (-1.1754943508222875e-38 < x && x < 1.1754943508222875e-38) {
if (-1.401298464324817e-45 < x && x < 1.401298464324817e-45) return 0;
// else, it is a subnormal
var mul = Math_round(x/1.4012984643e-45)*1e-323;
return mul * 1.418129833677085e+278;
}

var hi = x * 9007199254740992; // 9007199254740992 is 2**53 which is the maximum of double precision
var exp = (x + hi) - hi; // adding this number chops off all lower bits, rounding the number.
exp /= 16777216; // 8388608 = 2**23 * 2, so preserve 23 bits in x because there are 23 bits in a float
//            The "* 2" compensates for the addition shifting up the bits unwantedly
return Math_round(x / exp) * exp;
}

Below is code used to test for deviations from the correct value. The code below is meant for testing the merit of the function, not for polyfilling older browsers (as evidenced by the fact that the native Math.fround function is used).

requestIdleCallback(function(){"use strict";
const Math_fround = Math.fround;
const Math_round = Math.round;
function my_fround(x) {
if (x > 3.402823669209385e+38) return Infinity; // maximum float is 2**128
if (x < -3.402823669209385e+38) return -Infinity; // minimum is -2**128
if (-1.1754943508222875e-38 < x && x < 1.1754943508222875e-38) {
if (-1.401298464324817e-45 < x && x < 1.401298464324817e-45) return 0;
// else, it is a subnormal
var mul = Math_round(x/1.4012984643e-45)*1e-323;
return mul * 1.418129833677085e+278;
}

var hi = x * 9007199254740992; // 9007199254740992 is 2**53 which is the maximum of double precision
var exp = (x + hi) - hi; // adding this number chops off all lower bits, rounding the number.
exp /= 16777216; // 8388608 = 2**23 * 2, so preserve 23 bits in x because there are 23 bits in a float
//            The "* 2" compensates for the addition shifting up the bits unwantedly
return Math_round(x / exp) * exp;
}

const doublesArray = new Float64Array(8192);
const int32s = new Uint32Array(doublesArray.buffer);

const crypto = window.crypto;

var hasWarned = false, warnings=0;
for (var i=0; i<4; i=i+1|0) {
crypto.getRandomValues(int32s);
for (var k=0; k<8192; k=k+1|0) {
const myValue = my_fround(doublesArray[k]);
const froundVal = Math_fround(doublesArray[k]);
// quicker version of Object.is because of no function call overhead:
if (myValue === myValue ? myValue !== froundVal : froundVal === froundVal) {
if (!hasWarned) console.error(doublesArray[k]); // only show the first incorrect number
hasWarned = true;
warnings = warnings + 1|0;
}
}
}
console[warnings > 0 ? "warn" : "log"]( "Total number of mishandled floats: " + warnings );
});

Specifications

Specification Status Comment
ECMAScript 2015 (6th Edition, ECMA-262)
The definition of 'Math.fround' in that specification.
Standard Initial definition.
ECMAScript Latest Draft (ECMA-262)
The definition of 'Math.fround' in that specification.
Draft

Browser compatibility

Update compatibility data on GitHub
Desktop Mobile Server Chrome Edge Firefox Internet Explorer Opera Safari Android webview Chrome for Android Firefox for Android Opera for Android Chrome Full support 38 Edge Full support 12 Firefox Full support 26 IE No support No Opera Full support 25 Safari Full support 8 WebView Android Full support Yes Chrome Android Full support Yes Firefox Android Full support 26 Opera Android Full support Yes Safari iOS Full support 8 Samsung Internet Android Full support Yes nodejs Full support 0.12

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