GLSL Learning

GLSL built-in function

log2()

Returns the base-2 logarithm of x: how many times you double 1.0 to reach x. The inverse of exp2.

Syntax

float log2(float x)
vec2 log2(vec2 x)
vec3 log2(vec3 x)

Parameters

x
A value greater than 0.

Return value

The base-2 logarithm of x.

Live example

Edit the code and the preview updates as you type.

How it works

log2(x) counts doublings: log2(1.0) is 0, log2(2.0) is 1, log2(8.0) is 3, and log2(0.5) is -1.

In the example every ring covers one doubling of distance from the center: 0.125 to 0.25, 0.25 to 0.5, 0.5 to 1.0. The rings therefore get wider as they go out, but each one looks like a scaled copy of the next, which creates a seamless, endless zoom.

Typical uses

  • Levels of detail: log2(size) picks which mip level or octave to use.
  • Fractal zooms: rings or tiles that repeat at every doubling.
  • Counting octaves: log2(maxFrequency / baseFrequency).

Common mistakes

  • Zero or negative input, which is undefined. Add a tiny offset.
  • Expecting an integer. log2(3.0) is about 1.585; wrap in floor if you need the level number.

Related functions

exp2()
Returns 2 raised to the power x. Doubling and halving per step, as in noise octaves and exposure stops.
log()
Returns the natural logarithm of x, the inverse of exp. It turns multiplication into addition, which makes infinite zooms possible.
fract()
Returns the fractional part of x, computed as x - floor(x), always in the range 0.0 to 1.0.