Add FFT support via AbstractFFTs interface

[KaanKesginLW]

Adds FFT support for MtlArray via the AbstractFFTs.jl interface.

HEAVILY based on CUDA.jl's AbstractFFTs.jl interface implementation using MPSGraph functionality.

using Metal

x = MtlArray(randn(ComplexF32, 2048, 2048))
y = fft(x)  # Just works!

Performance

Benchmarked on Apple M2 Max with 30-core GPU against FFTW.jl on CPU:

Size	CPU (FFTW)	GPU (Metal)
512×512	4.1ms	5.3ms
1024×1024	19.7ms	8.5ms
2048×2048	119.7ms	10.5ms
4096×4096	460.6ms	15.8ms

Example Usage

using Metal

# Complex FFT
x = MtlArray(randn(ComplexF32, 1024, 1024))
y = fft(x)
z = ifft(y)  # z ≈ x

# Real FFT  
r = MtlArray(randn(Float32, 1024, 1024))
c = rfft(r)           # Real → Complex
r2 = irfft(c, 1024)   # Complex → Real, r2 ≈ r

# FFT along specific dimensions
y = fft(x, 1)         # First dimension only
y = fft(x, (1, 2))    # Batched transform

# Plan reuse
x = MtlArray(randn(ComplexF32, 1024, 1024))
another_x = MtlArray(randn(ComplexF32, 1024, 1024))
p = plan_fft(x)
y1 = p * x
y2 = p * another_x    # Same plan, different data

Close #270

[codecov]

Codecov Report

❌ Patch coverage is 80.59701% with 26 lines in your changes missing coverage. Please review.
✅ Project coverage is 82.21%. Comparing base (1d2f000) to head (25108fd).

Files with missing lines	Patch %	Lines
src/fft.jl	78.15%	26 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #713      +/-   ##
==========================================
+ Coverage   82.01%   82.21%   +0.20%     
==========================================
  Files          62       64       +2     
  Lines        2874     3008     +134     
==========================================
+ Hits         2357     2473     +116     
- Misses        517      535      +18     

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[github-actions]

Metal Benchmarks

Details

Benchmark suite	Current: 25108fd	Previous: 1d2f000	Ratio
latency/precompile	25538749208 ns	25549419083 ns	1.00
latency/ttfp	2355936292 ns	2346831687.5 ns	1.00
latency/import	1432847167 ns	1427666042 ns	1.00
integration/metaldevrt	875875 ns	877750 ns	1.00
integration/byval/slices=1	1565750 ns	1568625 ns	1.00
integration/byval/slices=3	8760125 ns	8402792 ns	1.04
integration/byval/reference	1561916 ns	1559958 ns	1.00
integration/byval/slices=2	2656437.5 ns	2629875 ns	1.01
kernel/indexing	652167 ns	627417 ns	1.04
kernel/indexing_checked	636729.5 ns	608750 ns	1.05
kernel/launch	12542 ns	12667 ns	0.99
kernel/rand	569458 ns	576167 ns	0.99
array/construct	6750 ns	6500 ns	1.04
array/broadcast	602750 ns	606708 ns	0.99
array/random/randn/Float32	1020979 ns	1011104 ns	1.01
array/random/randn!/Float32	742021 ns	753875 ns	0.98
array/random/rand!/Int64	550708 ns	548708 ns	1.00
array/random/rand!/Float32	592333 ns	586208.5 ns	1.01
array/random/rand/Int64	792687.5 ns	789709 ns	1.00
array/random/rand/Float32	585584 ns	645000 ns	0.91
array/accumulate/Int64/1d	1263333.5 ns	1260667 ns	1.00
array/accumulate/Int64/dims=1	1922583 ns	1859104.5 ns	1.03
array/accumulate/Int64/dims=2	2164958.5 ns	2179083 ns	0.99
array/accumulate/Int64/dims=1L	11703708 ns	11673271 ns	1.00
array/accumulate/Int64/dims=2L	9821083 ns	9628146 ns	1.02
array/accumulate/Float32/1d	1116833.5 ns	1121395.5 ns	1.00
array/accumulate/Float32/dims=1	1565667 ns	1571667 ns	1.00
array/accumulate/Float32/dims=2	1894187.5 ns	1889459 ns	1.00
array/accumulate/Float32/dims=1L	9867125 ns	9834209 ns	1.00
array/accumulate/Float32/dims=2L	7226562.5 ns	7249666.5 ns	1.00
array/reductions/reduce/Int64/1d	1353750 ns	1386875 ns	0.98
array/reductions/reduce/Int64/dims=1	1100666 ns	1117250 ns	0.99
array/reductions/reduce/Int64/dims=2	1145042 ns	1152958 ns	0.99
array/reductions/reduce/Int64/dims=1L	2028292 ns	2013209 ns	1.01
array/reductions/reduce/Int64/dims=2L	4254000 ns	4244083 ns	1.00
array/reductions/reduce/Float32/1d	1050125 ns	988750 ns	1.06
array/reductions/reduce/Float32/dims=1	834959 ns	843520.5 ns	0.99
array/reductions/reduce/Float32/dims=2	864958 ns	857917 ns	1.01
array/reductions/reduce/Float32/dims=1L	1333187 ns	1326625 ns	1.00
array/reductions/reduce/Float32/dims=2L	1831000 ns	1810667 ns	1.01
array/reductions/mapreduce/Int64/1d	1349250 ns	1356437.5 ns	0.99
array/reductions/mapreduce/Int64/dims=1	1107667 ns	1102166.5 ns	1.00
array/reductions/mapreduce/Int64/dims=2	1161667 ns	1149750 ns	1.01
array/reductions/mapreduce/Int64/dims=1L	2038875 ns	1988375 ns	1.03
array/reductions/mapreduce/Int64/dims=2L	3628729 ns	3626916 ns	1.00
array/reductions/mapreduce/Float32/1d	1034583.5 ns	1055917 ns	0.98
array/reductions/mapreduce/Float32/dims=1	847834 ns	847396 ns	1.00
array/reductions/mapreduce/Float32/dims=2	861584 ns	860979.5 ns	1.00
array/reductions/mapreduce/Float32/dims=1L	1339437.5 ns	1333042 ns	1.00
array/reductions/mapreduce/Float32/dims=2L	1821333 ns	1898125 ns	0.96
array/private/copyto!/gpu_to_gpu	641875 ns	633020.5 ns	1.01
array/private/copyto!/cpu_to_gpu	754854 ns	804354.5 ns	0.94
array/private/copyto!/gpu_to_cpu	807000 ns	816000 ns	0.99
array/private/iteration/findall/int	1582458 ns	1581312.5 ns	1.00
array/private/iteration/findall/bool	1413958 ns	1404916.5 ns	1.01
array/private/iteration/findfirst/int	2120875 ns	2075167 ns	1.02
array/private/iteration/findfirst/bool	2063250 ns	2048750 ns	1.01
array/private/iteration/scalar	3877812.5 ns	4526479 ns	0.86
array/private/iteration/logical	2691500 ns	2693625 ns	1.00
array/private/iteration/findmin/1d	2277458 ns	2518041 ns	0.90
array/private/iteration/findmin/2d	1814146 ns	1820229.5 ns	1.00
array/private/copy	581042 ns	568854 ns	1.02
array/shared/copyto!/gpu_to_gpu	84750 ns	84291 ns	1.01
array/shared/copyto!/cpu_to_gpu	84500 ns	82875 ns	1.02
array/shared/copyto!/gpu_to_cpu	83417 ns	83000 ns	1.01
array/shared/iteration/findall/int	1581291.5 ns	1585854.5 ns	1.00
array/shared/iteration/findall/bool	1431312 ns	1421875 ns	1.01
array/shared/iteration/findfirst/int	1657209 ns	1654709 ns	1.00
array/shared/iteration/findfirst/bool	1650937.5 ns	1643542 ns	1.00
array/shared/iteration/scalar	213334 ns	210375 ns	1.01
array/shared/iteration/logical	2285583.5 ns	2297959 ns	0.99
array/shared/iteration/findmin/1d	2127208 ns	2134229 ns	1.00
array/shared/iteration/findmin/2d	1801646 ns	1806042 ns	1.00
array/shared/copy	233667 ns	241812 ns	0.97
array/permutedims/4d	2392916.5 ns	2395583 ns	1.00
array/permutedims/2d	1168167 ns	1158833 ns	1.01
array/permutedims/3d	1686916.5 ns	1686541 ns	1.00
metal/synchronization/stream	19666 ns	19583 ns	1.00
metal/synchronization/context	20291.5 ns	20291 ns	1.00

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