How do works Math.fround() function.

The Math.fround() function returns the nearest float representation of a number.

But when it is passed the float number Math.fround(1.5) it returns the same(1.5) value. But when it is passed the float number Math.fround(1.55) it returns a different value 1.5499999523162841. why and How?

• I am confused about how Math.fround() works.
• How is it different from the Math.round() function?
• Also let me know why it's not supported in Internet Explorer.

How do works Math.fround() function.

The Math.fround() function returns the nearest float representation of a number.

But when it is passed the float number Math.fround(1.5) it returns the same(1.5) value. But when it is passed the float number Math.fround(1.55) it returns a different value 1.5499999523162841. why and How?

• I am confused about how Math.fround() works.
• How is it different from the Math.round() function?
• Also let me know why it's not supported in Internet Explorer.

• javascript
• angularjs
• angular
• typescript
• math

Share Improve this question Follow edited Aug 24, 2017 at 17:53 JakeBoggs 27444 silver badges1717 bronze badges asked Jun 29, 2017 at 6:34 Ramesh RajendranRamesh Rajendran 38.7k4949 gold badges159159 silver badges240240 bronze badges 7

• you can start your understanding with JavaScript’s Number type in details – Max Koretskyi Commented Jun 29, 2017 at 6:36
• 6 Did you read about single-precision? en.m.wikipedia/wiki/Single-precision_floating-point_format – Gerardo Furtado Commented Jun 29, 2017 at 6:37
• I couldn't see that page :( – Ramesh Rajendran Commented Jun 29, 2017 at 6:37
• 1 write the number in binary and you will understand. 1.5 is 2^0 + 2^-1 but 1.55 can not be represented as sum of powers of 2 so it is like iracional number for binary representation ... that is why you got so many diigtis ... – Spektre Commented Jun 29, 2017 at 6:38
• 1 @RobG it's funny, but their polyfill doesn't work on pliant browsers since they don't construct Float32Array with new.. – Patrick Roberts Commented Jun 29, 2017 at 6:47

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2 Answers 2

Sorted by: Reset to default 9

To understand how this function works you actually have to know the following topics:

• JavaScript’s Number type in details
• The simple math behind decimal-binary conversion algorithms
• How to round binary numbers
• The mechanics behind exponent bias in floating point

The ECMA script specifies the following algorithm for the conversion:

When Math.fround is called with argument x, the following steps are taken:

• If x is NaN, return NaN.
• If x is one of +0, -0, +∞, -∞, return x.
• Let x32 be the result of converting x to a value in IEEE 754-2008 binary32 format using roundTiesToEven.
• Let x64 be the result of converting x32 to a value in IEEE 754-2008 binary64 format.
• Return the ECMAScript Number value corresponding to x64.

So, let's do that for 1.5 and 1.55.

Math.fround(1.5)

1) Represent in 64bit float

0 01111111111 1000000000000000000000000000000000000000000000000000

2) Represent in the scientific notation

1.1000000000000000000000000000000000000000000000000000 x 2^0

3) Round to 23 bit mantissa

1.10000000000000000000000

4) Convert to decimal:

1.5

Math.fround(1.55)

1) Represent in 64bit float

0 01111111111 1000110011001100110011001100110011001100110011001101

2) Represent in the scientific notation

1.1000110011001100110011001100110011001100110011001101 x 2^0

3) Round to 23 bit mantissa

1.10001100110011001100110

4) Convert to decimal:

1.5499999523162841

I got these below things which is I got from some of the documents. Kindly share your answers if you have more details.

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I have found something about Math.fround ( x ) from ECMAScript® 2015 Language Specification

When Math.fround() is called with argument x the following steps are taken:

• If x is NaN, return NaN.
• If x is one of +0, −0, +∞, −∞, return x.
• Let x32 be the result of converting x to a value in IEEE 754-2008 binary32 format using roundTiesToEven.
• Let x64 be the result of converting x32 to a value in IEEE 754-2008 binary64 format.
• Return the ECMAScript Number value corresponding to x64.

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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];
  };
})(Float32Array(1));

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** Kindly share more answers for learning more details