Original: http://www.flipcode.com/archives/Fast_log_Function.shtml - a code snippet to replace the slow log() function... It just performs an approximation, but the maximum error is below 0.007.

 

 

float fast_log2(float val) {     int * const  exp_ptr = reinterpret_cast<int *>(&val);     int          &x = *exp_ptr;     //const int  log_2 = ((x >> 23) & 255) - 128;     const int    log_2 = (x >> 23) - 128;    // (1) : "& 255" is not necessary as log of -0 (val < 0) is illegal anyway        x &= ~(255 << 23);     x += 127 << 23;     //*exp_ptr = x;       val = ((-1.0f/3) * val + 2) * val - 2.0f/3;   // (2)     return (val + log_2); }

 

1) The line "const int  log_2 = ((x >> 23) & 255) - 128" is commented out and replaced with a simplified one, because we do not need the bit mask given the requirement that val > 0.

2) The line marked with (2) computes 1 + log₂(m), m ranging from 1 to 2. The proposed formula is a 3rd degree polynomial keeping first derivate continuity. Higher degree could be used for more accuracy. For faster results, one can remove this line, if accuracy is not the matter (it gives some linear interpolation between powers of 2). 

 

 

* http://forums.appleinsider.com/archive/index.php/t-15207.html - Taylor series for calculating log function.

* http://roland.pri.ee/wiki/fast_math_functions - Fast implementations for various math functions

* http://roland.pri.ee/wiki/logarithm_of_a_sum - Method for calculating precise logarithm of a sum