Here is an attempt to benchmark common mathematical functions to get a feeling for their relative performance.
Using clock_gettime(CLOCK_REALTIME, ..) to measure elapsed time. On
x86_64: Using the Time Stamp
Counter to count
CPU cycles. On AARch64 (Only tested on Rpi4), reading cntvct_el0,
cntfrq_el0 and the CPU frequency to estimate the number of
cycles/operation.
Please note that:
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For some operators/functions the speed changes with the values of the inputs. Change the code to match whatever range that is of interest for you.
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There might be more clever ways to time the commands.
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When the arrays are larger than the L3-cache size, speed is capped.
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The operators are called within a double loop. That overhead is not compensated for.
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Surprises:
cbrtmuch slower thansqrt.nearbyintmuch faster thanround. -
Adjust the compiler flags as you like.
Tested on Ubuntu 22.04, no special dependencies besides a compiler. To
spin up the cpu a command like stress could be used.
make
stress -t 1 -c 1; ./opsAMD Ryzen 7 3700X 8-Core Processor
operator time (s) rel. time op/s cyc/op
──────────────────────────────────────────────────────────
isnan 0.000164 1.000000 6.115e+09 0.059
nearbyint 0.000164 1.000874 6.110e+09 0.059
mult 0.000231 1.414469 4.323e+09 0.084
'max' 0.000232 1.421691 4.301e+09 0.084
minus 0.000235 1.435927 4.259e+09 0.083
plus 0.000244 1.492197 4.098e+09 0.083
copysign 0.000252 1.538910 3.974e+09 0.083
isnormal 0.000257 1.570396 3.894e+09 0.093
ceil 0.000269 1.642675 3.723e+09 0.097
floor 0.000271 1.659064 3.686e+09 0.097
div 0.000299 1.829177 3.343e+09 0.107
isinf 0.000710 4.338680 1.409e+09 0.255
sqrt 0.002010 12.291136 4.975e+08 0.746
round 0.002827 17.287882 3.537e+08 1.019
powf 0.003088 18.883179 3.238e+08 1.098
log 0.003894 23.814617 2.568e+08 1.395
exp 0.004944 30.235636 2.022e+08 1.778
atan 0.006559 40.108058 1.525e+08 2.377
pow 0.006588 40.288622 1.518e+08 2.366
log10 0.007011 42.869970 1.426e+08 2.525
sinh 0.007096 43.394510 1.409e+08 2.550
asin 0.007125 43.568286 1.404e+08 2.570
cbrt 0.011627 71.102163 8.600e+07 4.191
sin 0.034938 213.647684 2.862e+07 12.548
tan 0.039110 239.159822 2.557e+07 14.135
j0 0.089347 546.355930 1.119e+07 32.118
j1 0.091927 562.132543 1.088e+07 32.967
Intel(R) Core(TM) i7-6700K CPU @ 4.00GHz
operator time (s) rel. time op/s cyc/op
──────────────────────────────────────────────────────────
isnan 0.000275 1.000000 3.631e+09 0.111
nearbyint 0.000288 1.044634 3.475e+09 0.115
mult 0.000383 1.391573 2.609e+09 0.154
'max' 0.000386 1.402827 2.588e+09 0.155
minus 0.000387 1.403742 2.586e+09 0.154
plus 0.000396 1.437180 2.526e+09 0.162
ceil 0.000411 1.490724 2.435e+09 0.163
copysign 0.000432 1.566824 2.317e+09 0.173
isnormal 0.000462 1.676548 2.166e+09 0.183
div 0.000475 1.725989 2.103e+09 0.191
floor 0.000484 1.757510 2.066e+09 0.194
isinf 0.000508 1.846082 1.967e+09 0.196
sqrt 0.001425 5.174460 7.016e+08 0.571
round 0.002613 9.486650 3.827e+08 1.047
powf 0.003108 11.282463 3.218e+08 1.257
atan 0.003809 13.829610 2.625e+08 1.526
log 0.004814 17.479168 2.077e+08 1.916
exp 0.006186 22.458165 1.617e+08 2.475
asin 0.007825 28.409675 1.278e+08 3.191
sinh 0.007898 28.674003 1.266e+08 3.150
pow 0.008177 29.688547 1.223e+08 3.245
log10 0.008186 29.718808 1.222e+08 3.276
cbrt 0.014416 52.337495 6.937e+07 5.812
sin 0.042037 152.618081 2.379e+07 16.946
tan 0.046076 167.283007 2.170e+07 18.511
j0 0.109985 399.311192 9.092e+06 44.171
j1 0.114187 414.564443 8.758e+06 45.819
Raspberry PI4
operator time (s) rel. time op/s cyc/op
──────────────────────────────────────────────────────────
floor 0.002287 1.000000 4.373e+08 0.373
isnan 0.002324 1.016272 4.303e+08 0.379
ceil 0.002350 1.027875 4.255e+08 0.374
nearbyint 0.002400 1.049685 4.166e+08 0.383
isinf 0.002812 1.229950 3.556e+08 0.438
sqrtf 0.003265 1.427753 3.063e+08 0.521
round 0.004408 1.927640 2.269e+08 0.705
isnormal 0.004857 2.123958 2.059e+08 0.773
minus 0.005145 2.250004 1.944e+08 0.823
mult 0.005194 2.271539 1.925e+08 0.803
plus 0.005717 2.500276 1.749e+08 0.973
'max' 0.006498 2.841738 1.539e+08 1.145
copysign 0.009042 3.954276 1.106e+08 1.488
div 0.009433 4.125196 1.060e+08 1.566
exp 0.011626 5.084324 8.602e+07 1.857
sinf 0.014047 6.143250 7.119e+07 1.965
powf 0.014161 6.193201 7.061e+07 2.331
log 0.016647 7.280262 6.007e+07 2.631
pow 0.016711 7.308372 5.984e+07 2.647
sqrt 0.017015 7.441374 5.877e+07 2.743
atan 0.022098 9.664031 4.525e+07 3.565
log10 0.027966 12.230368 3.576e+07 4.535
sinh 0.028756 12.575869 3.478e+07 4.639
asin 0.034940 15.280118 2.862e+07 5.449
cbrt 0.059032 25.816230 1.694e+07 9.537
sin 0.168528 73.702043 5.934e+06 26.999
tan 0.185013 80.911684 5.405e+06 29.960
j0 0.394902 172.702376 2.532e+06 63.921
j1 0.411871 180.123053 2.428e+06 66.693
- Lincoln Atkinson's code/results (C++).
- Akseli Palén's code (JS) and his comparison between these tests.
- Jim Cownie's Fun with Timers and cpuid for timings on AArch64.