Fast approximation of logarithms.

fastlog.cpp

/* testing a log function */

// g++ -std=c++11 -pedantic -Wall -Werror -Wextra -W fastlog.cpp -o fastlog

#include <cmath>
#include <iomanip>
#include <limits>
#include <iostream>

const float TESTNUM = 2048.f;

/******************************************************************************
 *      LOGARITHMS
******************************************************************************/
/*
 * FORWARD DECLARATIONS
 */
template < typename type >
inline type fastLog2( type n );

template <>
inline float fastLog2< float >( float n );

template < typename type = float >
inline type fastLog( type n );

template < typename type = float >
inline type fastLogBase( type base, type n );

/*
 * FAST LOG (BASE-2) TEMPLATE
 */
template < typename type >
inline type fastLog2( type n ) {
    float val = (float)n;
    int* const exp = reinterpret_cast< int* >( &val );
    int x = *exp;
    
    const int log2 = ( (x >> 23) & 255 ) - 128;
    
    x &= ~(255 << 23);
    x += 127 << 23;
    
    *exp = x;
    val = ((-1.f/3.f) * val+2.f) * val - 2.f / 3.f;
    return (type)val + log2;
}

/*
 * FAST LOG (BASE-2) FLOAT SPECIALIZATION
 */
template <>
inline float fastLog2< float >( float n ) {
    int* const exp = reinterpret_cast< int* >( &n );
    int x = *exp;
    
    const int log2 = ( (x >> 23) & 255 ) - 128;
    
    x &= ~(255 << 23);
    x += 127 << 23;
    
    *exp = x;
    n = ((-1.f/3.f) * n+2.f) * n - 2.f / 3.f;
    return n + log2;
}

/*
 * FAST NATURAL LOG
 */
template < typename type >
inline type fastLog( type n ) {
    return fastLog2( n ) * 0.693147181f; // ln( 2 )
}

/*
 * FAST LOG (BASE-B)
 */
template < typename type >
inline type fastLogBase( type base, type n ) {
    return fastLog2( n ) / fastLog2( base );
}

/******************************************************************************
 *      MAIN()
******************************************************************************/
int main() {
    std::cout
        << std::setprecision( std::numeric_limits<float>::digits )
        << "The log2 of 2048 is: "  << fastLog2( TESTNUM )   << '\n'
        << "The log10 of 2048 is: " << fastLogBase( 10.f, TESTNUM )  << " versus: " << log10( TESTNUM ) << '\n'
        << "The log of 2048 is: "   << fastLog( TESTNUM )    << " versus: " << log( TESTNUM ) << '\n';
    
    return 0;
}