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JavaScript - Math.log2() method example

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Root-ssh

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

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// 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
​

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

Math.log2(x) function visualization - JavaScript Math Object.

1. Documentation

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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

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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

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3. Canvas plot example

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<!doctype html>
<html>
<head>
  <style> #canvas { border: 1px solid black; } </style>
</head>
<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>