Math.fround()

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

Syntax

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[0] = x, array[0];
  };
})(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);
};

Specifications

Browser compatibility

See also

• A polyfill of Math.fround is available in core-js
• Math.round()