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Added erf(x) Float64 and Float32 Julia implementations#491

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oscardssmith merged 26 commits intoJuliaMath:masterfrom
AhmedYKadah:erf(x)-implementation
Nov 15, 2025
Merged

Added erf(x) Float64 and Float32 Julia implementations#491
oscardssmith merged 26 commits intoJuliaMath:masterfrom
AhmedYKadah:erf(x)-implementation

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@AhmedYKadah AhmedYKadah commented Mar 31, 2025

Faster than current wrapper function call (including Float32 function call).
Uses algorithm based on https://github.com/ARM-software/optimized-routines/blob/master/math/erf.c

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codecov bot commented Mar 31, 2025 •
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Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 94.16%. Comparing base (46a2874) to head (f7470ba).
⚠️ Report is 27 commits behind head on master.

Additional details and impacted files 
@@            Coverage Diff             @@
##           master     #491      +/-   ##
==========================================
+ Coverage   94.02%   94.16%   +0.13%     
==========================================
  Files          14       14              
  Lines        2897     2965      +68     
==========================================
+ Hits         2724     2792      +68     
  Misses        173      173
Flag Coverage Δ
unittests 94.16% <100.00%> (+0.13%) ⬆️

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AhmedYKadah commented Mar 31, 2025

Old:
Float 64
@benchmark SpecialFunctions.erf(data) setup=(data=6*rand(Float64)-3) samples=1000000

BenchmarkTools.Trial: 217729 samples with 1000 evaluations per sample.
Range (min … max): 6.300 ns … 283.700 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 29.500 ns ┊ GC (median): 0.00%
Time (mean ± σ): 21.993 ns ± 13.209 ns ┊ GC (mean ± σ): 0.00% ± 0.00%

Float32
@benchmark SpecialFunctions.erf(data) setup=(data=6*rand(Float32)-3) samples=1000000

BenchmarkTools.Trial: 312732 samples with 1000 evaluations per sample.
Range (min … max): 4.300 ns … 125.100 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 19.900 ns ┊ GC (median): 0.00%
Time (mean ± σ): 15.035 ns ± 7.951 ns ┊ GC (mean ± σ): 0.00% ± 0.00%

New:
Float64
@benchmark erf(data) setup=(data=6*rand(Float64)-3) samples=1000000

BenchmarkTools.Trial: 507504 samples with 1000 evaluations per sample.
Range (min … max): 5.400 ns … 4.890 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 8.700 ns ┊ GC (median): 0.00%
Time (mean ± σ): 8.775 ns ± 9.855 ns ┊ GC (mean ± σ): 0.00% ± 0.00%

Float32
@benchmark Float32(erf(data)) setup=(data=6*rand(Float64)-3) samples=1000000

BenchmarkTools.Trial: 526797 samples with 1000 evaluations per sample.
Range (min … max): 5.400 ns … 195.500 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 8.800 ns ┊ GC (median): 0.00%
Time (mean ± σ): 8.521 ns ± 2.236 ns ┊ GC (mean ± σ): 0.00% ± 0.00%

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AhmedYKadah commented Mar 31, 2025

Float32 implementation available, but not faster than Float64 version due to a exp() call.
Float64 version still faster than old Float32.

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AhmedYKadah commented Apr 5, 2025

need to clean up polynomial evaluations.
code also could use more organization

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AhmedYKadah commented Aug 2, 2025

Remaining: erfc Float64 and Float32 implementations, and the erf Float32 implementation

@AhmedYKadah AhmedYKadah changed the title Added erf(x) Float64 Julia implementation Added erf(x) Float64 and Float32 Julia implementations Sep 14, 2025
oscardssmith
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@AhmedYKadah
cleaned up float32 polynomials, added accuracy of float32, removed un…
693f788 
…necessary whitespace, and removed explicit copysigns
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src/erf.jl

end

_erf(x::Float16)=Float16(_erf(Float32(x)))
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if you wanted to do a Float16 impl, it should be easier than the others. Specifically, the domain is only to 2, and the accuracy required is much reduced.

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100% could wait for a followup PR.

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I'm thinking that too to be honest.
this and the poli regen.

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oscardssmith commented Sep 15, 2025

Given that this is faster and accurate, seems good to merge to me!

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mschauer commented Sep 16, 2025

Are there any tests for edge cases/ULP in the c version we do not do ourselves?

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The implementation does not handle NaN32 and NaN16 correctly:

julia> erf(NaN32)
1.0f0

julia> erf(NaN16)
Float16(1.0)

AhmedYKadah and others added 3 commits September 17, 2025 11:13
@AhmedYKadah @devmotion
Removed unneccessary indent
bba5f9b 
Co-authored-by: David Müller-Widmann <devmotion@users.noreply.github.com>
@AhmedYKadah @devmotion
Fixed wrong NaN type
c2a37a1 
Co-authored-by: David Müller-Widmann <devmotion@users.noreply.github.com>
@AhmedYKadah
added test for NaN for erf
1d45644
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AhmedYKadah commented Sep 19, 2025

There aren't any tests for erfc. Is that expected?

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AhmedYKadah commented Sep 19, 2025

Any other changes needed?

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oscardssmith commented Sep 19, 2025

we should probably should test erfc.

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oscardssmith commented Nov 14, 2025

Other than missing tests for Inf, looks good to me. @devmotion any further sugestions?

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devmotion commented Nov 14, 2025

What do the benchmark shows with the latest iteration of this PR? In #491 (comment) performance with Float32 seemed to regress.

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AhmedYKadah commented Nov 14, 2025

Yes, you're correct. The old implementation was not efficient so I redid it.

Old

Float64
@benchmark erf(data) setup=(data=6*rand(Float64)-3) samples=1000000

BenchmarkTools.Trial: 217081 samples with 1000 evaluations per sample.
Range (min … max): 6.400 ns … 973.200 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 30.100 ns ┊ GC (median): 0.00%
Time (mean ± σ): 22.028 ns ± 13.612 ns ┊ GC (mean ± σ): 0.00% ± 0.00%

Float32
@benchmark erf(data) setup=(data=6*rand(Float32)-3) samples=1000000

BenchmarkTools.Trial: 308269 samples with 1000 evaluations per sample.
Range (min … max): 4.300 ns … 160.400 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 19.900 ns ┊ GC (median): 0.00%
Time (mean ± σ): 15.207 ns ± 8.609 ns ┊ GC (mean ± σ): 0.00% ± 0.00%

New

Float64
@benchmark erf(data) setup=(data=6*rand(Float64)-3) samples=1000000

BenchmarkTools.Trial: 604748 samples with 1000 evaluations per sample.
Range (min … max): 4.700 ns … 164.400 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 7.400 ns ┊ GC (median): 0.00%
Time (mean ± σ): 7.302 ns ± 3.017 ns ┊ GC (mean ± σ): 0.00% ± 0.00%

Float32
@benchmark erf(data) setup=(data=6*rand(Float32)-3) samples=1000000

BenchmarkTools.Trial: 641285 samples with 1000 evaluations per sample.
Range (min … max): 4.200 ns … 204.800 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 6.900 ns ┊ GC (median): 0.00%
Time (mean ± σ): 6.840 ns ± 2.961 ns ┊ GC (mean ± σ): 0.00% ± 0.00%

devmotion
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If you update the version number, we could tag a new release immediately after merging the PR.

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AhmedYKadah commented Nov 15, 2025

Anything left for me to do?

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oscardssmith commented Nov 15, 2025

yeah, can you bump the patch number (in Project.toml) so that when we merge the PR, we can tag a new version?

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@AhmedYKadah @devmotion
Release 2.7.0
f7470ba 
Co-authored-by: David Müller-Widmann <devmotion@users.noreply.github.com>
@oscardssmith oscardssmith merged commit a358e65 into JuliaMath:master Nov 15, 2025
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oscardssmith commented Nov 15, 2025

Thanks @AhmedYKadah for the Pr and @devmotion for the additional review!

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AhmedYKadah commented Nov 15, 2025

It's been a pleasure 😄

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@AhmedYKadah @oscardssmith @mschauer @devmotion