
Fast log() Function
Submitted by 
Here is a code snippet to replace the slow log() function...
It just performs an approximation, but the maximum error is below
0.007. Speed gain is about x5, and probably could be increased by
tweaking the assembly code.
The function is based on floating point coding. It's easy to get
floor (log2(N)) by isolating exponent part. We can refine the
approximation by using the mantissa. This function returns log2(N) :
inline 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;
x &= ~(255 << 23);
x += 127 << 23;
*exp_ptr = x;
val = ((1.0f/3) * val + 2) * val  2.0f/3; // (1)
return (val + log_2);
} 
The line (1) 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).
Now we got log2(N), we have to multiply it by ln(2) to get the
natural log :
inline float fast_log (const float &val)
{
return (fast_log2 (val) * 0.69314718f);
} 
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The zip file viewer built into the Developer Toolbox made use
of the zlib library, as well as the zlibdll source additions.
