Simple ARM NEON optimized sin, cos, log and exp

This is the sequel of the single precision SSE optimized sin, cos, log and exp that I wrote some time ago. Adapted to the NEON fpu of my pandaboard. Precision and range are exactly the same than the SSE version, so I won't repeat them.

The code

The functions below are licensed under the zlib license, so you can do basically what you want with them.

Performance

Results on a pandaboard with a 1GHz dual-core ARM Cortex A9 (OMAP4), using gcc 4.6.1

command line: gcc -O3 -mfloat-abi=softfp -mfpu=neon -march=armv7-a -mtune=cortex-a9 -Wall -W neon_mathfun_test.c -lm 

exp([        -1000,          -100,           100,          1000]) = [            0,             0, 2.4061436e+38, 2.4061436e+38]
exp([         -nan,           inf,          -inf,           nan]) = [          nan, 2.4061436e+38,             0,           nan]
log([            0,           -10,         1e+30, 1.0005271e-42]) = [         -nan,          -nan,     69.077553,          -nan]
log([         -nan,           inf,          -inf,           nan]) = [    89.128304,     88.722839,          -nan,     89.128304]
sin([         -nan,           inf,          -inf,           nan]) = [          nan,           nan,          -nan,           nan]
cos([         -nan,           inf,          -inf,           nan]) = [          nan,           nan,           nan,           nan]
sin([       -1e+30,       -100000,         1e+30,        100000]) = [          inf,  -0.035749275,          -inf,   0.035749275]
cos([       -1e+30,       -100000,         1e+30,        100000]) = [          nan,    -0.9993608,           nan,    -0.9993608]
benching                 sinf .. ->    2.0 millions of vector evaluations/second -> 121 cycles/value on a 1000MHz computer
benching                 cosf .. ->    1.8 millions of vector evaluations/second -> 132 cycles/value on a 1000MHz computer
benching                 expf .. ->    1.1 millions of vector evaluations/second -> 221 cycles/value on a 1000MHz computer
benching                 logf .. ->    1.7 millions of vector evaluations/second -> 141 cycles/value on a 1000MHz computer
benching          cephes_sinf .. ->    2.4 millions of vector evaluations/second -> 103 cycles/value on a 1000MHz computer
benching          cephes_cosf .. ->    2.0 millions of vector evaluations/second -> 123 cycles/value on a 1000MHz computer
benching          cephes_expf .. ->    1.6 millions of vector evaluations/second -> 153 cycles/value on a 1000MHz computer
benching          cephes_logf .. ->    1.5 millions of vector evaluations/second -> 156 cycles/value on a 1000MHz computer
benching               sin_ps .. ->    5.8 millions of vector evaluations/second ->  43 cycles/value on a 1000MHz computer
benching               cos_ps .. ->    5.9 millions of vector evaluations/second ->  42 cycles/value on a 1000MHz computer
benching            sincos_ps .. ->    6.0 millions of vector evaluations/second ->  41 cycles/value on a 1000MHz computer
benching               exp_ps .. ->    5.6 millions of vector evaluations/second ->  44 cycles/value on a 1000MHz computer
benching               log_ps .. ->    5.3 millions of vector evaluations/second ->  47 cycles/value on a 1000MHz computer

So performance is not stellar. I recommend to use gcc 4.6.1 or newer as it generates much better code than previous (gcc 4.5) versions -- almost 20% faster here. I believe rewriting these functions in assembly would improve the performance by 30%, and should not be very hard as the ARM and NEON asm is quite nice and easy to write -- maybe I'll do it. Computing two SIMD vectors at once would also help to improve a lot the performance as there are enough registers on NEON, and it would reduce the dependancies between neon instructions.

Note also that I have no idea of the performance on a Cortex A8 -- it may be extremely bad, I don't know.

Comparison with an Intel Atom

For comparison purposes, here is the performance of the SSE version on a single core Intel Atom N270 running at 1.66GHz

command line: cl.exe /arch:SSE /O2 /TP /MD sse_mathfun_test.c (this is msvc 2010)

benching                 sinf .. ->    1.3 millions of vector evaluations/second -> 303 cycles/value on a 1600MHz computer
benching                 cosf .. ->    1.3 millions of vector evaluations/second -> 305 cycles/value on a 1600MHz computer
benching         sincos (x87) .. ->    1.2 millions of vector evaluations/second -> 314 cycles/value on a 1600MHz computer
benching                 expf .. ->    1.6 millions of vector evaluations/second -> 244 cycles/value on a 1600MHz computer
benching                 logf .. ->    1.4 millions of vector evaluations/second -> 276 cycles/value on a 1600MHz computer
benching          cephes_sinf .. ->    1.4 millions of vector evaluations/second -> 280 cycles/value on a 1600MHz computer
benching          cephes_cosf .. ->    1.5 millions of vector evaluations/second -> 265 cycles/value on a 1600MHz computer
benching          cephes_expf .. ->    0.7 millions of vector evaluations/second -> 548 cycles/value on a 1600MHz computer
benching          cephes_logf .. ->    0.8 millions of vector evaluations/second -> 489 cycles/value on a 1600MHz computer
benching               sin_ps .. ->    9.2 millions of vector evaluations/second ->  43 cycles/value on a 1600MHz computer
benching               cos_ps .. ->    9.5 millions of vector evaluations/second ->  42 cycles/value on a 1600MHz computer
benching            sincos_ps .. ->    8.8 millions of vector evaluations/second ->  45 cycles/value on a 1600MHz computer
benching               exp_ps .. ->    9.8 millions of vector evaluations/second ->  41 cycles/value on a 1600MHz computer
benching               log_ps .. ->    8.6 millions of vector evaluations/second ->  46 cycles/value on a 1600MHz computer
The number of cycles is quite similar -- but the atom has a higher clock..
Last modified: 2011/05/29