fast approximate float function fmath

fast exp(x) and log(x) of float x
What's this?
fmath.hpp provides a fast approximate exp(x)/log(x) of float x. The function is is 2~10 times faster than std::ofVC10/gcc on Core2Duo.

fmath.hpp is available on 32-bit/64-bit Visual Studio 2008/2010 and 32-bit/64-bit gcc 4.1 or later.

Copy fmath.hpp into your favorite directory. If you install Xbyak and define FMATH_USE_XBYAK before including fmath.hpp, then fmath::exp() and fmath::exp_ps() (uses SSE4.1 if available) will be 10~20% faster.
Remark: Xbyak requires -fno-operator-names for gcc.
How to use
The following functions are available.
name description
float fmath::exp(float x) exp
double fmath::expd(double x) exp for double [New]
void fmath::expd_v(double *px, int n) exp for array of double [New]
float fmath::log(float x) log
__m128 fmath::exp_ps(__m128 x) SIMD version of exp
__m128 fmath::log_ps(__m128 x) SIMD version of log

You can also use fmath::log2(x) (=log(x) / log(2)) and fmath::exp2(x) (=pow(2, x)).
fmath::PowGenerator is a class to generate a function to compute pow(x, y) of x >= 0 for a given fixed y > 0.
// example
fmath::PowGenerator f(1.234);
f.get(x) returns pow(x, 1.234);
Benchmark of exp and log
Measure the time of the following code:
    float sum = 0;
    for (float x = 0; x <= 2; x += 1e-6f) {
        sum += fmath::exp(x);
Core2duo 2.6GHz unit:cpu clock
VC10@32-bit Xp VC10@64-bit Xp gcc 4.4.3@64-bit Linux
std::expf 150.1 33.0 591.5
fmath::exp 20.3 14.1 14.6
std::expf x 4 585.5 133.3 2608.5
fmath::exp_ps 54.3 46.7 73.9
std::logf 77.0 31.8 91.7
fmath::log 21.1 13.3 13.9
std::logf x 4 286.1 136.1 356.3
fmath::log_ps 51.2 40.1 55.8

compile option:

The exp of gcc seems very slow.

See fastexp.cpp for the benchmark of fmath::expd.

Benchmark of pow(x, 1.234)
Core2duo 1.8GHz unit:cpu clock
VC10@32-bit Xp gcc 4.3.2@32-bit cygwin
std::pow(x, 1.234) 182.806 228.132
fmath::PowGenerator(1.234) 9.996 11.636
The BSD 3-Clause License
2010/Aug/27 add fmath::expd, fmath::expd_v for double precision
2010/Feb/16 add fmath::exp_ps, log_ps and optimize functions
2010/Jan/10 add fmath::PowGenerator
2009/Dec/28 add fmath::log()
2009/Dec/09 support cygwin
2009/Dec/08 first version
1st:2009/12/08, last update:2016/08/29

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