### Fast binary log approximations

Type : C code
References : Posted by musicdsp.org[AT]mindcontrol.org
Notes :
This code uses IEEE 32-bit floating point representation knowledge to quickly compute approximations to the log2 of a value. Both functions return under-estimates of the actual value, although the second flavour is less of an under-estimate than the first (and might be sufficient for using in, say, a dBV/FS level meter).

Running the test program, here's the output:

0.1: -4 -3.400000
1: 0 0.000000
2: 1 1.000000
5: 2 2.250000
100: 6 6.562500
Code :
// Fast logarithm (2-based) approximation
// by Jon Watte

#include <assert.h>

int floorOfLn2( float f ) {
assert( f > 0. );
assert( sizeof(f) == sizeof(int) );
assert( sizeof(f) == 4 );
return (((*(int *)&f)&0x7f800000)>>23)-0x7f;
}

float approxLn2( float f ) {
assert( f > 0. );
assert( sizeof(f) == sizeof(int) );
assert( sizeof(f) == 4 );
int i = (*(int *)&f);
return (((i&0x7f800000)>>23)-0x7f)+(i&0x007fffff)/(float)0x800000;
}

// Here's a test program:

#include <stdio.h>

// insert code from above here

int
main()
{
printf( "0.1: %d  %f\n", floorOfLn2( 0.1 ), approxLn2( 0.1 ) );
printf( "1:   %d  %f\n", floorOfLn2( 1. ), approxLn2( 1. ) );
printf( "2:   %d  %f\n", floorOfLn2( 2. ), approxLn2( 2. ) );
printf( "5:   %d  %f\n", floorOfLn2( 5. ), approxLn2( 5. ) );
printf( "100: %d  %f\n", floorOfLn2( 100. ), approxLn2( 100. ) );
return 0;
}