fast approximate function of exponential function exp and log

How to use

include fmath.hpp and use fmath::log, fmath::exp, fmath::expd.

fmath::PowGenerator is a class to generate a function to compute pow(x, y) of x >= 0 for a given fixed y > 0.

eg. fmath::PowGenerator f(1.234); f.get(x) returns pow(x, 1.234);

Prototype of function

• float fmath::exp(float);
• float fmath::log(float);
• double fmath::logd(double);
• __m128 fmath::exp_ps(__m128);
• __m128 fmath::log_ps(__m128);
• void fmath::expv_d(double *p, size_t n); // for double p[n];

for AVX-512

fmath.h provides the following functions:

void fmath_expf_avx512(float *dst, const float *src, size_t n);
void fmath_logf_avx512(float *dst, const float *src, size_t n);

void fmath::expf_v(float *dst, const float *src, size_t n);
void fmath::logf_v(float *dst, const float *src, size_t n);

Experimental

If you install xbyak and define FMATH_USE_XBYAK before including fmath.hpp, then fmath::exp() and fmath::exp_ps() will be about 10~20 % faster. Xbyak version uses SSE4.1 if available.

AVX version of fmath::exp is experimental

Remark

gcc puts warnings such as "dereferencing type-punned pointer will break strict-aliasing rules." It is no problem. Please change #if 1 in fmath.hpp:423 if you worry about it. But it causes a little slower.

-ffast-math option of gcc may generate bad code for fmath::expd.

License

• modified new BSD License
• http://opensource.org/licenses/BSD-3-Clause

History

• 2022/May/30 log for AVX-512 got 1.5 times faster
• 2020/Jul/10 add expf_v and logf_v for AVX-512
• 2012/Oct/30 fix fmath::expd for small value
• 2011/Aug/26 add fmath::expd_v
• 2011/Mar/25 exp supports AVX
• 2011/Mar/25 exp, exp_ps support avx
• 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

Author

MITSUNARI Shigeo(herumi@nifty.com) http://herumi.in.coocan.jp/

Benchmark

compiler

• Visual Studio 2010RC
• icc 11.1
• gcc 4.3.2 on cygwin
• gcc 4.4.1 on 64bit Linux

option

• cl(icl):

/Ox /Ob2 /GS- /Zi /D_SECURE_SCL=0 /MD /Oy /arch:SSE2 /fp:fast /DNOMINMAX

• gcc:

-O3 -fomit-frame-pointer -DNDEBUG -fno-operator-names -msse2 -mfpmath=sse -march=native

see fastexp.cpp