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# JavaScript - Math.log2() method example

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The Math.log2() method returns the logarithm with base 2 of a number.

// ONLINE-RUNNER:browser;

// Logarithm with base 2:
//                      x            y
console.log( Math.log2( 1    ) ); // 0
console.log( Math.log2( 2    ) ); // 1
console.log( Math.log2( 4    ) ); // 2
console.log( Math.log2( 8    ) ); // 3
console.log( Math.log2( 1024 ) ); // 10

console.log( Math.log2( -1        ) ); //  NaN
console.log( Math.log2(  0        ) ); // -Infinity
console.log( Math.log2( +Infinity ) ); // +Infinity

The Math.log2() method is presented on the following chart:

## 1. Documentation

 Syntax Math.log2(x) Parameters x - integer or float number value in range 0 to +Infinity (primitive value). Result number value calcualted as log_2(x) mathematical function (primitive value). If x is nagative it returns NaN. If x is equal to 0 it returns -Infinity. If x is equal to +Infinity it returns -Infinity. Description log2 is a static method that takes one parameter and returns an approximation of the log_2(x) mathematical function (logarithm with base 2). log2 is called binary logarithm. Note: this method has been introduced in ES 2015.

## 2. Custom method implemenetation example

// ONLINE-RUNNER:browser;

if (Math.log2 == null) {
Math.log2 = function(x) {
/*
1. Using logarithm definition:
b^y = x <=> log_b(x) = y
Where: b - base

2. We can create system of equations:
y = log_b(x)
x = b^y

3. Which can be expressed as:
x = b^log_b(x)

4. We can transform equation:
log_2(x) = log_2(e^log_e(x)) = log_2(e) * log_e(x) = log_e(x) * log_2(e)

5. It can be written in JavaScript:
log_2(e) <=> Math.LOG2E
log_e(x) * log_2(e) <=> Math.log(x) * Math.LOG2E
*/
return Math.log(x) * Math.LOG2E;
};
}

// Usage example:
//                      x              y
console.log( Math.log2( 1    ) ); //  0
console.log( Math.log2( 2    ) ); //  1
console.log( Math.log2( 4    ) ); // ~2
console.log( Math.log2( 8    ) ); //  3
console.log( Math.log2( 1024 ) ); // 10

console.log( Math.log2( -1        ) ); //  NaN
console.log( Math.log2(  0        ) ); // -Infinity
console.log( Math.log2( +Infinity ) ); // +Infinity

## 3. Canvas plot example

// ONLINE-RUNNER:browser;

<!doctype html>
<html>
<style> #canvas { border: 1px solid black; } </style>
<body>
<canvas id="canvas" width="400" height="400"></canvas>
<script>

var canvas = document.querySelector('#canvas');
var context = canvas.getContext('2d');

// logarithm chart range
var x1 =  0;
var x2 = 10;
var y1 = -5;
var y2 =  4;

var dx = 0.005;

var xRange = x2 - x1;
var yRange = y2 - y1;

function calculateLogarithm(base, x) {
var a = Math.log(x);
var b = Math.log(base);

return a / b;
}

function calculatePoint(base, x) {
var y = calculateLogarithm(base, x);

// chart will be reversed horizontaly because of reversed canvas pixels

var nx = (x - x1) / xRange;       // normalized x
var ny = 1.0 - (y - y1) / yRange; // normalized y

var point = {
x: nx * canvas.width,
y: ny * canvas.height
};

return point;
}

function drawChart(base, color, thickness) {
var point = calculatePoint(base, x1);

context.beginPath();
context.lineWidth = thickness;
context.strokeStyle = color;
context.moveTo(point.x, point.y);

for (var x = x1 + dx; x < x2; x += dx) {
point = calculatePoint(base, x);
context.lineTo(point.x, point.y);
}

point = calculatePoint(base, x2);
context.lineTo(point.x, point.y);
context.stroke();
}

console.log('log_2(x)  <- red');
console.log('log_e(x)  <- green');
console.log('log_10(x) <- blue');

//           base     color   thickness
drawChart(      2, '#ff001b',       2   ); // red
drawChart( Math.E, '#159600',       0.8 ); // green
drawChart(     10, '#0000ff',       0.8 ); // blue

console.log('x range: <' + x1 + '; ' + x2 + '>');
console.log('y range: <' + y1 + '; ' + y2 + '>');

</script>
</body>
</html>

## References

1. Binary logarithm - Wikipedia

## Alternative titles

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