SSE2 implementations of sin, cos, exp, log, tan, cot, atan, atan2 The sin, cos, exp and log functions were written by Julien Pommier (see unmodified sse_mathfun.h). The tan, cot, atan, atan2 are written by Tolga Mizrak.
sse_mathfun_extension.h serves as an extension to sse_mathfun.h, implementing tan, cot, atan and atan2. It is written as an extension to sse_mathfun.h instead of modifying it, just because I didn't want to maintain a modified version of the original library. This way switching to a newer version of the original library won't be a hassle.
License: zlib (same as sse_mathfun.h)
Here are the benchmarks on my machine:
Results on a 3.30 GHz AMD FX-6100 Six-Core, compiled with Visual C++ Enterprise 2015 Update 3 (x64)
command line: cl.exe /W4 /DUSE_SSE2 /EHsc- /MD /GS- /Gy /fp:fast /Ox /Oy- /GL /Oi /O2 sse_mathfun_test.c
checking sines on [0*Pi, 1*Pi]
max deviation from sinf(x): 5.96046e-08 at 0.193304238313*Pi, max deviation from cephes_sin(x): 0
max deviation from cosf(x): 5.96046e-08 at 0.303994872157*Pi, max deviation from cephes_cos(x): 0
deviation of sin(x)^2+cos(x)^2-1: 1.78814e-07 (ref deviation is 1.19209e-07)
->> precision OK for the sin_ps / cos_ps / sincos_ps <<-
checking sines on [-1000*Pi, 1000*Pi]
max deviation from sinf(x): 5.96046e-08 at 338.694424873*Pi, max deviation from cephes_sin(x): 0
max deviation from cosf(x): 5.96046e-08 at 338.694424873*Pi, max deviation from cephes_cos(x): 0
deviation of sin(x)^2+cos(x)^2-1: 1.78814e-07 (ref deviation is 1.19209e-07)
->> precision OK for the sin_ps / cos_ps / sincos_ps <<-
checking exp/log [-60, 60]
max (relative) deviation from expf(x): 1.18944e-07 at -56.8358421326, max deviation from cephes_expf(x): 0
max (absolute) deviation from logf(x): 1.19209e-07 at -1.67546617985, max deviation from cephes_logf(x): 0
deviation of x - log(exp(x)): 1.19209e-07 (ref deviation is 5.96046e-08)
->> precision OK for the exp_ps / log_ps <<-
checking tan on [-0.25*Pi, 0.25*Pi]
max deviation from tanf(x): 1.19209e-07 at 0.250000006957*Pi, max deviation from cephes_tan(x): 5.96046e-08
->> precision OK for the tan_ps <<-
checking tan on [-0.49*Pi, 0.49*Pi]
max deviation from tanf(x): 3.8147e-06 at -0.490000009841*Pi, max deviation from cephes_tan(x): 9.53674e-07
->> precision OK for the tan_ps <<-
checking cot on [0.2*Pi, 0.7*Pi]
max deviation from cotf(x): 1.19209e-07 at 0.204303119606*Pi, max deviation from cephes_cot(x): 1.19209e-07
->> precision OK for the cot_ps <<-
checking cot on [0.01*Pi, 0.99*Pi]
max deviation from cotf(x): 3.8147e-06 at 0.987876517942*Pi, max deviation from cephes_cot(x): 9.53674e-07
->> precision OK for the cot_ps <<-
checking atan on [-10*Pi, 10*Pi]
max deviation from atanf(x): 1.19209e-07 at -9.39207109497*Pi, max deviation from cephes_atan(x): 1.19209e-07
->> precision OK for the atan_ps <<-
checking atan on [-10000*Pi, 10000*Pi]
max deviation from atanf(x): 1.19209e-07 at -7350.3826719*Pi, max deviation from cephes_atan(x): 1.19209e-07
->> precision OK for the atan_ps <<-
checking atan2 on [-1*Pi, 1*Pi]
max deviation from atan2f(x): 2.38419e-07 at (0.797784384786*Pi, -0.913876806545*Pi), max deviation from cephes_atan2(x): 2.38419e-07
->> precision OK for the atan2_ps <<-
checking atan2 on [-10000*Pi, 10000*Pi]
max deviation from atan2f(x): 2.38419e-07 at ( 658.284195009*Pi, -2685.93394561*Pi), max deviation from cephes_atan2(x): 2.38419e-07
->> precision OK for the atan2_ps <<-
exp([ -1000, -100, 100, 1000]) = [ 0, 0, 2.4061436e+38, 2.4061436e+38]
exp([ -nan(ind), inf, -inf, nan]) = [2.4061436e+38, 2.4061436e+38, 0, 2.4061436e+38]
log([ 0, -10, 1e+30, 1.0005271e-42]) = [ -nan, -nan, 69.077553, -87.336548]
log([ -nan(ind), inf, -inf, nan]) = [ -87.336548, 88.722839, -nan, -87.336548]
sin([ -nan(ind), inf, -inf, nan]) = [ -nan(ind), -nan(ind), nan, nan]
cos([ -nan(ind), inf, -inf, nan]) = [ nan, -nan(ind), -nan(ind), nan]
sin([ -1e+30, -100000, 1e+30, 100000]) = [ inf, -0.035749275, -inf, 0.035749275]
cos([ -1e+30, -100000, 1e+30, 100000]) = [ -nan(ind), -0.9993608, -nan(ind), -0.9993608]
benching sinf .. -> 16.3 millions of vector evaluations/second -> 40 cycles/value on a 2600MHz computer
benching cosf .. -> 15.8 millions of vector evaluations/second -> 41 cycles/value on a 2600MHz computer
benching expf .. -> 18.8 millions of vector evaluations/second -> 35 cycles/value on a 2600MHz computer
benching logf .. -> 17.8 millions of vector evaluations/second -> 36 cycles/value on a 2600MHz computer
benching tanf .. -> 13.8 millions of vector evaluations/second -> 47 cycles/value on a 2600MHz computer
benching cotf .. -> 12.2 millions of vector evaluations/second -> 53 cycles/value on a 2600MHz computer
benching atanf .. -> 10.4 millions of vector evaluations/second -> 62 cycles/value on a 2600MHz computer
benching atan2f .. -> 5.3 millions of vector evaluations/second -> 121 cycles/value on a 2600MHz computer
benching atan2_ref .. -> 11.7 millions of vector evaluations/second -> 56 cycles/value on a 2600MHz computer
benching sqrtf .. -> 69.5 millions of vector evaluations/second -> 9 cycles/value on a 2600MHz computer
benching rsqrtf .. -> 70.2 millions of vector evaluations/second -> 9 cycles/value on a 2600MHz computer
benching cephes_sinf .. -> 15.2 millions of vector evaluations/second -> 43 cycles/value on a 2600MHz computer
benching cephes_cosf .. -> 16.6 millions of vector evaluations/second -> 39 cycles/value on a 2600MHz computer
benching cephes_expf .. -> 2.9 millions of vector evaluations/second -> 220 cycles/value on a 2600MHz computer
benching cephes_logf .. -> 3.4 millions of vector evaluations/second -> 186 cycles/value on a 2600MHz computer
benching sin_ps .. -> 30.6 millions of vector evaluations/second -> 21 cycles/value on a 2600MHz computer
benching cos_ps .. -> 31.1 millions of vector evaluations/second -> 21 cycles/value on a 2600MHz computer
benching sincos_ps .. -> 30.9 millions of vector evaluations/second -> 21 cycles/value on a 2600MHz computer
benching exp_ps .. -> 27.3 millions of vector evaluations/second -> 24 cycles/value on a 2600MHz computer
benching log_ps .. -> 23.5 millions of vector evaluations/second -> 28 cycles/value on a 2600MHz computer
benching tan_ps .. -> 22.2 millions of vector evaluations/second -> 29 cycles/value on a 2600MHz computer
benching cot_ps .. -> 22.0 millions of vector evaluations/second -> 29 cycles/value on a 2600MHz computer
benching atan_ps .. -> 31.1 millions of vector evaluations/second -> 21 cycles/value on a 2600MHz computer
benching atan2_ps .. -> 24.1 millions of vector evaluations/second -> 27 cycles/value on a 2600MHz computer
benching sqrt_ps .. -> 63.9 millions of vector evaluations/second -> 10 cycles/value on a 2600MHz computer
benching rsqrt_ps .. -> 64.1 millions of vector evaluations/second -> 10 cycles/value on a 2600MHz computer
As you can see the sinf, cosf, expf, logf, tanf, atanf, atan2f and sqrtf implementations of the Visual C++ c library are pretty well optimized themselves, but using the simd versions still gives you at least a boost of 2x, with atan_ps and atan2_ps having the biggest gains.