AK: Make atan() more precise and faster on non-x86#26691
Merged
nico merged 2 commits intoSerenityOS:masterfrom Apr 2, 2026
Merged
AK: Make atan() more precise and faster on non-x86#26691nico merged 2 commits intoSerenityOS:masterfrom
nico merged 2 commits intoSerenityOS:masterfrom
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On my system, with macOS system libm (including the existing
sin(), cos() perf tests):
% Build/lagom/bin/TestAKMath
...
Running benchmark 'bench_trig_cos'.
Completed benchmark 'bench_trig_cos' in 66ms
Running benchmark 'bench_trig_cosf'.
Completed benchmark 'bench_trig_cosf' in 58ms
Running benchmark 'bench_trig_sin'.
Completed benchmark 'bench_trig_sin' in 54ms
Running benchmark 'bench_trig_sinf'.
Completed benchmark 'bench_trig_sinf' in 58ms
Running benchmark 'bench_trig_tan'.
Completed benchmark 'bench_trig_tan' in 75ms
Running benchmark 'bench_trig_tanf'.
Completed benchmark 'bench_trig_tanf' in 82ms
Running benchmark 'bench_trig_acos'.
Completed benchmark 'bench_trig_acos' in 11ms
Running benchmark 'bench_trig_acosf'.
Completed benchmark 'bench_trig_acosf' in 10ms
Running benchmark 'bench_trig_asin'.
Completed benchmark 'bench_trig_asin' in 11ms
Running benchmark 'bench_trig_asinf'.
Completed benchmark 'bench_trig_asinf' in 11ms
Running benchmark 'bench_trig_atan'.
Completed benchmark 'bench_trig_atan' in 60ms
Running benchmark 'bench_trig_atanf'.
Completed benchmark 'bench_trig_atanf' in 63ms
With serenity libm (SerenityOS#26662):
% Build/lagom/bin/TestAKMath
...
Completed benchmark 'bench_trig_cos' in 87ms
Running benchmark 'bench_trig_cosf'.
Completed benchmark 'bench_trig_cosf' in 65ms
Running benchmark 'bench_trig_sin'.
Completed benchmark 'bench_trig_sin' in 75ms
Running benchmark 'bench_trig_sinf'.
Completed benchmark 'bench_trig_sinf' in 67ms
Running benchmark 'bench_trig_tan'.
Completed benchmark 'bench_trig_tan' in 184ms
Running benchmark 'bench_trig_tanf'.
Completed benchmark 'bench_trig_tanf' in 163ms
Running benchmark 'bench_trig_acos'.
Completed benchmark 'bench_trig_acos' in 10ms
Running benchmark 'bench_trig_acosf'.
Completed benchmark 'bench_trig_acosf' in 10ms
Running benchmark 'bench_trig_asin'.
Completed benchmark 'bench_trig_asin' in 10ms
Running benchmark 'bench_trig_asinf'.
Completed benchmark 'bench_trig_asinf' in 10ms
Running benchmark 'bench_trig_atan'.
Completed benchmark 'bench_trig_atan' in 176ms
Running benchmark 'bench_trig_atanf'.
Completed benchmark 'bench_trig_atanf' in 184ms
Instead of calling asin(), approximate atan() directly. Takes the biggest error of atan() over 0..2*pi (which is an arbitrary interval, given that atan()'s domain is all reals) from 7.15256e-07 to 1.19209e-07. That's enough to make TestPDF pass when run inside serenity (part of SerenityOS#25934). It also takes bench_trig_atan* from: Running benchmark 'bench_trig_atan'. Completed benchmark 'bench_trig_atan' in 181ms Running benchmark 'bench_trig_atanf'. Completed benchmark 'bench_trig_atanf' in 188ms to Running benchmark 'bench_trig_atan'. Completed benchmark 'bench_trig_atan' in 123ms Running benchmark 'bench_trig_atanf'. Completed benchmark 'bench_trig_atanf' in 72ms See the PR adding this commit for details on the program that computed the precision. (I first tried making asin() more precise, but even with a more precise asin(), atan()'s error never went below 7.15256e-07 when it was implemented in terms of asin(). Possibly because larger values all map to arguments close to 1.0 for asin().)
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Here's the atan precision test program, similar to the programs over in #26674: |
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| if (value < 0) | ||
| return -atan(-value); | ||
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| if (value > 1) | ||
| return Pi<T> / 2 - atan(1 / value); |
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You recently removed recursion from sin()/cos() to make it faster. Does recursion not cause any issues here?
(Or do you want to do this in a follow-up?)
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It's probably faster to not refuse here either, yes. But I leave that for the future 🙂
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Instead of calling asin(), approximate atan() directly.
Takes the biggest error of atan() over 0..2*pi (which is
an arbitrary interval, given that atan()'s domain is all
reals) from 7.15256e-07 to 1.19209e-07. That's enough to
make TestPDF pass when run inside serenity (part of #25934).
It also takes bench_trig_atan* from:
to
See the PR adding this commit for details on the program that
computed the precision.
(I first tried making asin() more precise, but even with a more
precise asin(), atan()'s error never went below 7.15256e-07 when
it was implemented in terms of asin(). Possibly because larger
values all map to arguments close to 1.0 for asin().)