Use GPUToolbox's Float64-free overrides of Base math

[maleadt]

Several Base methods compute single-precision results in double precision, which Metal doesn't support, so they failed to compile. This stacks GPUToolbox.Overlays.float64_overrides (JuliaGPU/GPUToolbox.jl#21, GPUToolbox 3.1) underneath Metal's method table, which replaces them with Float64-free implementations:

• div, fld, cld and friends of Float32 values on Julia 1.12 and 1.13 (fixes div(::Float32, ::Float32) uses Float64 on Julia ≥ 1.12 #972);
• sind, cosd and friends (fixes sind/cosd/tand on Float32 use Float64 #973);
• inv and division of ComplexF32 (fixes Inversion of ComplexF32 numbers uses Float64 numbers and fails to compile #871);
• sincospi, and thus cispi and complex sinpi/cospi;
• comparisons between Float32/Float16 values and 32-bit integers;
• ^(::Float32, ::Integer) and hypot.

Metal's own overrides of complex division, integer powers and hypot are removed in favor of GPUToolbox's, which changes some results:

• complex division uses a port of Base's robust ComplexF64 algorithm (Baudin & Smith): within about 1.5 eps (normwise) over the whole range, no longer loses a normal-sized component when intermediate ratios underflow, and gives zeros the same signs as Base (e.g. (1+0im)/(-1-0im) is now -1+0im, so log of it has imaginary part +π like on the CPU);
• Base's own _cpow is used for complex powers again, instead of exp(p * log(z)), which is more accurate for integer exponents and matches the CPU;
• hypot uses Base's generic implementation, within 1 ulp.

Tests: a new testset covering the fixed functions, plus complex inv///atan/powers. The math tests pass locally on Julia 1.10 through 1.13 (M1, macOS 27), and a comparison against CPU Base on the GPU matched div in all rounding modes where the quotient is exact. Complex sinpi on Julia 1.13 additionally needs JuliaGPU/GPUCompiler.jl#936, so it's left out of the tests until that is released.

[github-actions]

Metal Benchmarks

Details

Benchmark suite	Current: 80327a2	Previous: 5210727	Ratio
array/accumulate/Float32/1d	391250 ns	390042 ns	1.00
array/accumulate/Float32/dims=1	363500 ns	367625 ns	0.99
array/accumulate/Float32/dims=1L	8768791 ns	8770083 ns	1.00
array/accumulate/Float32/dims=2	429875 ns	430042 ns	1.00
array/accumulate/Float32/dims=2L	2516041 ns	2030542 ns	1.24
array/accumulate/Int64/1d	806125 ns	813375 ns	0.99
array/accumulate/Int64/dims=1	904083 ns	901958 ns	1.00
array/accumulate/Int64/dims=1L	9451083 ns	9454916 ns	1.00
array/accumulate/Int64/dims=2	1210458 ns	1203041 ns	1.01
array/accumulate/Int64/dims=2L	6432583 ns	6431458 ns	1.00
array/broadcast	236541 ns	242542 ns	0.98
array/construct	2292 ns	2291 ns	1.00
array/permutedims/2d	436042 ns	384834 ns	1.13
array/permutedims/3d	999583 ns	999750 ns	1.00
array/permutedims/4d	1105791 ns	1083792 ns	1.02
array/private/copy	225834 ns	227459 ns	0.99
array/private/copyto!/cpu_to_gpu	214292 ns	213417 ns	1.00
array/private/copyto!/gpu_to_cpu	210791 ns	218875 ns	0.96
array/private/copyto!/gpu_to_gpu	221875 ns	220791 ns	1.00
array/private/iteration/findall/bool	1031708 ns	1034708 ns	1.00
array/private/iteration/findall/int	1208250 ns	1196167 ns	1.01
array/private/iteration/findfirst/bool	1143500 ns	1154250 ns	0.99
array/private/iteration/findfirst/int	1157292 ns	1153333 ns	1.00
array/private/iteration/findmin/1d	1206125 ns	1207917 ns	1.00
array/private/iteration/findmin/2d	1026250 ns	1038167 ns	0.99
array/private/iteration/logical	1630416 ns	1622125 ns	1.01
array/private/iteration/scalar	1378750 ns	1382000 ns	1.00
array/random/rand/Float32	418750 ns	421125 ns	0.99
array/random/rand/Int64	497333 ns	495250 ns	1.00
array/random/rand!/Float32	400250 ns	385667 ns	1.04
array/random/rand!/Int64	428625 ns	428750 ns	1.00
array/random/randn/Float32	389458 ns	388750 ns	1.00
array/random/randn!/Float32	375416 ns	373417 ns	1.01
array/reductions/mapreduce/Float32/1d	452333 ns	452125 ns	1.00
array/reductions/mapreduce/Float32/dims=1	354500 ns	355000 ns	1.00
array/reductions/mapreduce/Float32/dims=1L	609750 ns	618750 ns	0.99
array/reductions/mapreduce/Float32/dims=2	358000 ns	357709 ns	1.00
array/reductions/mapreduce/Float32/dims=2L	1239167 ns	1239666 ns	1.00
array/reductions/mapreduce/Int64/1d	640250 ns	636833 ns	1.01
array/reductions/mapreduce/Int64/dims=1	637291 ns	635709 ns	1.00
array/reductions/mapreduce/Int64/dims=1L	1013541 ns	1011542 ns	1.00
array/reductions/mapreduce/Int64/dims=2	790708 ns	792958 ns	1.00
array/reductions/mapreduce/Int64/dims=2L	2202875 ns	2208542 ns	1.00
array/reductions/reduce/Float32/1d	454792 ns	439791 ns	1.03
array/reductions/reduce/Float32/dims=1	358750 ns	358625 ns	1.00
array/reductions/reduce/Float32/dims=1L	619333 ns	613167 ns	1.01
array/reductions/reduce/Float32/dims=2	252500 ns	246125 ns	1.03
array/reductions/reduce/Float32/dims=2L	483583 ns	463833 ns	1.04
array/reductions/reduce/Int64/1d	635875 ns	634834 ns	1.00
array/reductions/reduce/Int64/dims=1	639750 ns	643459 ns	0.99
array/reductions/reduce/Int64/dims=1L	1006041 ns	1007708 ns	1.00
array/reductions/reduce/Int64/dims=2	254292 ns	253084 ns	1.00
array/reductions/reduce/Int64/dims=2L	671459 ns	667000 ns	1.01
array/shared/copy	128542 ns	128500 ns	1.00
array/shared/copyto!/cpu_to_gpu	37709 ns	37041 ns	1.02
array/shared/copyto!/gpu_to_cpu	37750 ns	37000 ns	1.02
array/shared/copyto!/gpu_to_gpu	38000 ns	37292 ns	1.02
array/shared/iteration/findall/bool	1030375 ns	1047000 ns	0.98
array/shared/iteration/findall/int	1206916 ns	1210750 ns	1.00
array/shared/iteration/findfirst/bool	973417 ns	968167 ns	1.01
array/shared/iteration/findfirst/int	979167 ns	981625 ns	1.00
array/shared/iteration/findmin/1d	1059708 ns	1066459 ns	0.99
array/shared/iteration/findmin/2d	1033666 ns	1027417 ns	1.01
array/shared/iteration/logical	1497334 ns	1500959 ns	1.00
array/shared/iteration/scalar	3921.875 ns	3729.25 ns	1.05
array/sorting/1d	2110708 ns	2066458 ns	1.02
array/sorting/2d	8345709 ns	8333292 ns	1.00
integration/byval/reference	1127458 ns	1120708 ns	1.01
integration/byval/slices=1	1123167 ns	1124667 ns	1.00
integration/byval/slices=2	2030375 ns	2032125 ns	1.00
integration/byval/slices=3	6621250 ns	6635000 ns	1.00
integration/metaldevrt	391625 ns	313542 ns	1.25
kernel/indexing	212375 ns	208417 ns	1.02
kernel/indexing_checked	396708 ns	393375 ns	1.01
kernel/launch	1829.1 ns	1762.5 ns	1.04
kernel/rand	406709 ns	401792 ns	1.01
latency/import	1786069250 ns	1780944041 ns	1.00
latency/precompile	32498069583 ns	26127754584 ns	1.24
latency/ttfp	2267194792 ns	2275447584 ns	1.00
metal/synchronization/context	556.5935828877006 ns	578.7292817679559 ns	0.96
metal/synchronization/stream	357.4766355140187 ns	347.47906976744184 ns	1.03

This comment was automatically generated by workflow using github-action-benchmark.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 86.53%. Comparing base (5210727) to head (80327a2).

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #975      +/-   ##
==========================================
- Coverage   86.80%   86.53%   -0.28%     
==========================================
  Files          77       77              
  Lines        5481     5482       +1     
==========================================
- Hits         4758     4744      -14     
- Misses        723      738      +15     

☔ View full report in Codecov by Harness.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.