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fast approximate function of float exp(float) and float log(float)
-----------------------------------------------------------------------------
<How to use>
Include fmath.hpp and use fmath::log() and fmath::exp().
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>
-----------------------------------------------------------------------------
float fmath::exp(float);
float fmath::log(float);
__m128 fmath::exp_ps(__m128);
__m128 fmath::log_ps(__m128);
-----------------------------------------------------------------------------
<Experimental>
If you install xbyak(https://github.com/herumi/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
<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 -ffast-math -march=core2
unit ; <clocks without dummy loop> / <clocks with loop>
Core i7-2600 3.4GHz
Windows7 SP1 ubuntu 10.10
VC10(32bit) VC10(64bit) gcc4.5(64bit)
std::exp 91.8/101.0 14.1/ 23.5 639.8/650.8
fmath::exp 7.6/ 16.9 1.3/ 10.7 3.1/ 14.1
std::expx4 340.5/351.6 86.9/ 95.5 2608.2/2617.2
fmath::expx4 61.0/ 72.1 42.6/ 51.3 46.5/ 55.5
fmath::exp_ps 22.9/ 34.1 19.9/ 28.6 58.8/ 67.9
std log 57.2/ 66.3 15.9/ 24.1 41.4/ 49.6
fmath log 9.5/ 18.6 4.4/ 12.6 4.8/ 13.0
std logx4 230.8/241.9 94.7/103.5 204.5/213.5
fmath logx4 34.1/ 45.2 28.6/ 37.4 27.8/ 36.8
fmath log_ps 21.1/ 32.2 15.3/ 24.1 56.9/ 65.9
Xeon X5650 2.67GHz
ubuntu 10.04
gcc4.4.3-4(64bit)
std::exp 559.9/568.7
fmath::exp 5.1/ 13.8
std::expx4 2257.1/2266.0
fmath::expx4 44.5/ 53.3
fmath::exp_ps 59.8/ 68.7
std log 45.4/ 54.1
fmath log 4.2/ 12.9
std logx4 212.1/220.8
fmath logx4 27.2/ 35.9
fmath log_ps 58.0/ 66.7
Core i7 2.8GHz
VC2010 icc11.1
Xp(32bit) Xp(64bit) Xp(32bit) Xp(64bit)
std::exp 88.2/ 97.2 14.6/ 22.4 19.1/ 28.8 13.7/ 21.7
fmath::exp 10.2/ 19.2 3.6/ 11.4 8.2/ 17.9 3.5/ 11.5
std::exp x 4 342.0/357.5 94.8/102.8 79.1/ 91.9 94.3/102.6
fmath::exp_ps 25.7/ 41.2 25.2/ 33.3 31.8/ 44.6 25.6/ 34.0
icl::exp_ps 34.8/ 47.6 31.6/ 39.9
std::log 57.9/ 67.1 18.8/ 27.0 41.4/ 51.8 19.6/ 28.2
fmath::log 8.5/ 17.7 3.4/ 11.6 13.3/ 23.7 1.2/ 9.8
std::log x 4 241.2/255.8 114.2/122.5 113.0/127.0 102.0/110.6
fmath::log_ps 23.9/ 38.4 20.5/ 28.8 26.2/ 40.2 23.9/ 32.5
icl::log_ps 34.2/ 48.2 34.8/ 43.4
Core2Duo 2.6GHz
VC2010 icc11.1 gcc 4.4.3 gcc 4.3.2 on cygwin
Xp(32bit) Xp(64bit) Xp(32bit) Xp(64bit) Linux(64bit) Xp(32bit)
std::exp 139.9/150.1 24.5/ 33.0 27.4/ 38.4 18.0/ 27.1 586.0/591.5 157.8/167.9
fmath::exp 10.1/ 20.3 5.6/ 14.1 10.1/ 21.1 5.8/ 14.9 9.1/ 14.6 10.8/ 20.9
std::exp x 4 572.9/585.5 122.5/133.3 107.7/124.2 100.7/111.4 2583.6/2608.5 658.7/694.6
fmath::exp_ps 41.7/ 54.3 35.9/ 46.7 48.4/ 64.9 38.8/ 49.4 49.0/ 73.9 52.8/ 88.7
icl::exp_ps 45.1/ 61.6 47.8/ 58.5
std::log 66.3/ 77.0 22.8/ 31.8 42.8/ 53.9 18.8/ 27.8 82.8/ 91.7 114.7/124.8
fmath::log 10.3/ 21.1 4.2/ 13.3 12.3/ 23.4 2.6/ 11.7 5.0/ 13.9 13.1/ 23.2
std::log x 4 273.3/286.1 125.2/136.1 123.4/139.1 104.7/115.1 329.2/356.3 473.2/509.2
fmath::log_ps 38.4/ 51.2 29.3/ 40.1 36.3/ 52.0 31.8/ 42.3 28.8/ 55.8 50.5/ 86.4
icl::log_ps 58.7/ 74.4 56.3/ 66.7
Quad-Core AMD Opteron 2376
gcc 4.4.1 gcc.4.41
Linux(32bit) Linux(64bit)
std::exp 112.9/128.9 528.7/542.2
fmath::exp 23.7/ 39.6 17.1/ 30.7
std::exp x 4 540.7/562.4 2127.3/2159.7
fmath::exp_ps 108.6/130.3 71.3/103.7
std::log 182.4/198.7 110.7/124.0
fmath::log 23.0/ 39.3 11.6/ 24.9
std::log x 4 827.1/848.6 464.8/497.2
fmath::log_ps 102.0/123.5 76.5/108.9
-----------------------------------------------------------------------------
<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.
-----------------------------------------------------------------------------
<License>
modified new BSD License
http://www.opensource.org/licenses/bsd-license.php
-----------------------------------------------------------------------------
<History>
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>
http://herumi.in.coocan.jp/
MITSUNARI Shigeo(herumi@nifty.com)
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