floorlog2: Exact arithmetic of binary logarithm with floor

When we handle exponent of a number (e.g. to extract IEEE 754 binary exponent value of a number x), we should handle floor(log2(x)) precisely.

This library defines floorLog2 function which calculates exact value of floor(log2(x)) for number x. Note that precision of Math.pow and Math.log2 as defined in ECMA-262 is implementation-defined and Math.floor is not effective if a result of Math.log2 is already rounded up.

In fact, simple so_called_floorlog2 function fails on many JavaScript environments. Try following example:

function so_called_floorlog2(x)
{
    return Math.floor(Math.log2(x));
}

// 52 is expected but 53 is returned on many environments
console.log(so_called_floorlog2(2**53-1));

That's exactly why this library is here.

This library also defines pow2I which calculates exact value of 2**x for integer x.

How to use it? (CommonJS)

Simple!

const floorlog2 = require('floorlog2');

let floorlog2_of_pi = floorlog2.floorLog2(Math.PI);
// floorlog2_of_pi === 1
// (because 2**1 < Math.PI < 2**2)

let pow2_of_16 = floorlog2.pow2I(16);  // argument must be an integer
// pow2_of_16 === 65536

How to use it? (ES Modules)

It's also simple!

import { floorLog2, pow2I } from 'floorlog2';

let floorlog2_of_pi = floorLog2(Math.PI);
// floorlog2_of_pi === 1
// (because 2**1 < Math.PI < 2**2)

let pow2_of_16 = pow2I(16);  // argument must be an integer
// pow2_of_16 === 65536