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thread-safety fixes #31

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44c6925
use thread-safety macros from FFTW.jl
stevengj Apr 11, 2025
797b091
clean up test output
stevengj Apr 11, 2025
1d6f9fb
fix empty-matrix creation for Julia 1.6
stevengj Apr 11, 2025
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30 changes: 16 additions & 14 deletions src/Hadamard.jl
View file
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Original file line number Diff line number Diff line change
Expand Up @@ -17,8 +17,8 @@ module Hadamard
export fwht, ifwht, fwht_natural, ifwht_natural, fwht_natural!, ifwht_natural!, fwht_dyadic, ifwht_dyadic, hadamard, walsh

using FFTW, LinearAlgebra
import FFTW: set_timelimit, dims_howmany, unsafe_execute!, cFFTWPlan, r2rFFTWPlan, PlanPtr, fftwNumber, ESTIMATE, NO_TIMELIMIT, R2HC
import AbstractFFTs: normalization, complexfloat
using FFTW: unsafe_set_timelimit, @exclusive, dims_howmany, unsafe_execute!, cFFTWPlan, r2rFFTWPlan, PlanPtr, fftwNumber, ESTIMATE, NO_TIMELIMIT, R2HC
using AbstractFFTs: normalization, complexfloat

# A power-of-two dimension to be transformed is interpreted as a
# 2x2x2x....x2x2 multidimensional DFT. This function transforms
Expand Down Expand Up @@ -62,34 +62,36 @@ const libfftwf = isdefined(FFTW, :libfftwf) ? FFTW.libfftwf : FFTW.libfftw3f

for (Tr,Tc,fftw,lib) in ((:Float64,:ComplexF64,"fftw",libfftw),
(:Float32,:ComplexF32,"fftwf",libfftwf))
@eval function Plan_Hadamard(X::StridedArray{$Tc,N}, Y::StridedArray{$Tc,N},
@eval @exclusive function Plan_Hadamard(X::StridedArray{$Tc,N}, Y::StridedArray{$Tc,N},
region, flags::Unsigned, timelimit::Real,
bitreverse::Bool) where {N}
set_timelimit($Tr, timelimit)
dims, howmany = dims_howmany(X, Y, [size(X)...], region)
unsafe_set_timelimit($Tr, timelimit)
R = isa(region, Tuple) ? region : copy(region)
dims, howmany = dims_howmany(X, Y, size(X), R)
dims = hadamardize(dims, bitreverse)
plan = ccall(($(string(fftw,"_plan_guru64_dft")),$lib[]),
PlanPtr,
(Int32, Ptr{Int}, Int32, Ptr{Int},
Ptr{$Tc}, Ptr{$Tc}, Int32, UInt32),
size(dims,2), dims, size(howmany,2), howmany,
X, Y, FFTW.FORWARD, flags)
set_timelimit($Tr, NO_TIMELIMIT)
unsafe_set_timelimit($Tr, NO_TIMELIMIT)
if plan == C_NULL
if $(FFTW.fftw_provider == "mkl")
error("MKL is not supported — reconfigure FFTW.jl to use FFTW")
else
error("FFTW could not create plan") # shouldn't normally happen
end
end
return cFFTWPlan{$Tc,FFTW.FORWARD,X===Y,N}(plan, flags, region, X, Y)
return cFFTWPlan{$Tc,FFTW.FORWARD,X===Y,N}(plan, flags, R, X, Y)
end

@eval function Plan_Hadamard(X::StridedArray{$Tr,N}, Y::StridedArray{$Tr,N},
@eval @exclusive function Plan_Hadamard(X::StridedArray{$Tr,N}, Y::StridedArray{$Tr,N},
region, flags::Unsigned, timelimit::Real,
bitreverse::Bool) where {N}
set_timelimit($Tr, timelimit)
dims, howmany = dims_howmany(X, Y, [size(X)...], region)
unsafe_set_timelimit($Tr, timelimit)
R = isa(region, Tuple) ? region : copy(region)
dims, howmany = dims_howmany(X, Y, size(X), R)
dims = hadamardize(dims, bitreverse)
kind = Array{Int32}(undef, size(dims,2))
kind .= R2HC
Expand All @@ -99,15 +101,15 @@ for (Tr,Tc,fftw,lib) in ((:Float64,:ComplexF64,"fftw",libfftw),
Ptr{$Tr}, Ptr{$Tr}, Ptr{Int32}, UInt32),
size(dims,2), dims, size(howmany,2), howmany,
X, Y, kind, flags)
set_timelimit($Tr, NO_TIMELIMIT)
unsafe_set_timelimit($Tr, NO_TIMELIMIT)
if plan == C_NULL
if $(FFTW.fftw_provider == "mkl")
error("MKL is not supported — reconfigure FFTW.jl to use FFTW")
else
error("FFTW could not create plan") # shouldn't normally happen
end
end
return r2rFFTWPlan{$Tr,Vector{Int32},X===Y,N}(plan, flags, region, X, Y, kind)
return r2rFFTWPlan{$Tr,Vector{Int32},X===Y,N}(plan, flags, R, X, Y, kind)
end
end

Expand Down Expand Up @@ -371,7 +373,7 @@ end
"""
walsh(n)

Return a Walsh matrix of order `n`, which must be a power of two, in sequency ordering.
Return a Walsh matrix of order `n`, which must be a power of two, in sequency ordering.
This is related to the Hadamard matrix [`hadamard(n)`](@ref) by a bit-reversal permutation
followed by a Gray-code permutation of the rows.

Expand All @@ -390,7 +392,7 @@ function walsh(n::Int)
j = b ⊻ (b >> 1) # binary sequency index
j + 1 # 1-based index
end
for i in 0:n-1 ]
for i in 0:n-1 ]

return hadamard(n)[j, :]
end
Expand Down
238 changes: 121 additions & 117 deletions test/runtests.jl
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Open in desktop
Original file line number Diff line number Diff line change
@@ -1,133 +1,138 @@
using Hadamard, Test, LinearAlgebra

H8 = [ 1 1 1 1 1 1 1 1
1 1 1 1 -1 -1 -1 -1
1 1 -1 -1 -1 -1 1 1
1 1 -1 -1 1 1 -1 -1
1 -1 -1 1 1 -1 -1 1
1 -1 -1 1 -1 1 1 -1
1 -1 1 -1 -1 1 -1 1
1 -1 1 -1 1 -1 1 -1 ]

H8n = [ 1 1 1 1 1 1 1 1
1 -1 1 -1 1 -1 1 -1
1 1 -1 -1 1 1 -1 -1
1 -1 -1 1 1 -1 -1 1
1 1 1 1 -1 -1 -1 -1
1 -1 1 -1 -1 1 -1 1
1 1 -1 -1 -1 -1 1 1
1 -1 -1 1 -1 1 1 -1 ]

H8d = [ 1 1 1 1 1 1 1 1
1 1 1 1 -1 -1 -1 -1
1 1 -1 -1 1 1 -1 -1
1 1 -1 -1 -1 -1 1 1
1 -1 1 -1 1 -1 1 -1
1 -1 1 -1 -1 1 -1 1
1 -1 -1 1 1 -1 -1 1
1 -1 -1 1 -1 1 1 -1 ]


I8 = Matrix{Float64}(I,8,8)
iI8 = Matrix{Int8}(I,8,8)

@test ifwht(I8,1) == H8
@test ifwht(I8,2)' == H8
@test ifwht_natural(I8,1) == H8n
@test ifwht_natural(I8,2)' == H8n
@test ifwht_dyadic(I8,1) == H8d
@test ifwht_dyadic(I8,2)' == H8d

@test ifwht(iI8,1) == H8
@test ifwht(iI8,2)' == H8
@test ifwht_natural(iI8,1) == H8n
@test ifwht_natural(iI8,2)' == H8n
@test ifwht_dyadic(iI8,1) == H8d
@test ifwht_dyadic(iI8,2)' == H8d

H32 = [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1
1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1
1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 -1 -1 -1 -1
1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1
1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1
1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1
1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1
1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1
1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1
1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1
1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 1 1 -1 -1
1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1
1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1
1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1
1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1
1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1
1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1
1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1
1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1
1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1
1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1
1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1
1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1
1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1
1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1
1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1
1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1
1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1
1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 ]

I32 = Matrix{Float64}(I,32,32)
iI32 = Matrix{Int8}(I,32,32)

@test ifwht(I32,1) == H32
@test ifwht(I32,2)' == H32

@test ifwht(iI32,1) == H32
@test ifwht(iI32,2)' == H32

X = reshape(sin.([1:1024*32;]), 1024,32);
norminf(A) = maximum(abs, A)

# non-lazy transpose for 0.7:
transp(x::AbstractMatrix) = permutedims(x, (2,1))

for f in (:fwht, :fwht_natural, :fwht_dyadic)
fi = Symbol(string("i", f))
@eval begin
@test norminf(X - $fi($f(X))) < 1e-14
@test norminf(X - $fi($f(X,1),1)) < 1e-14
@test norminf(X - $fi($f(X,2),2)) < 1e-14
@test norminf($f($f(X,1),2) - $f(X)) < 1e-14
@test norminf(transp($f(transp(X),1)) - $f(X,2)) < 1e-14
# test input data
X = reshape(sin.([1:1024*32;]), 1024,32)

@testset "fast Walsh–Hadamard transforms" begin
H8 = [ 1 1 1 1 1 1 1 1
1 1 1 1 -1 -1 -1 -1
1 1 -1 -1 -1 -1 1 1
1 1 -1 -1 1 1 -1 -1
1 -1 -1 1 1 -1 -1 1
1 -1 -1 1 -1 1 1 -1
1 -1 1 -1 -1 1 -1 1
1 -1 1 -1 1 -1 1 -1 ]

H8n = [ 1 1 1 1 1 1 1 1
1 -1 1 -1 1 -1 1 -1
1 1 -1 -1 1 1 -1 -1
1 -1 -1 1 1 -1 -1 1
1 1 1 1 -1 -1 -1 -1
1 -1 1 -1 -1 1 -1 1
1 1 -1 -1 -1 -1 1 1
1 -1 -1 1 -1 1 1 -1 ]

H8d = [ 1 1 1 1 1 1 1 1
1 1 1 1 -1 -1 -1 -1
1 1 -1 -1 1 1 -1 -1
1 1 -1 -1 -1 -1 1 1
1 -1 1 -1 1 -1 1 -1
1 -1 1 -1 -1 1 -1 1
1 -1 -1 1 1 -1 -1 1
1 -1 -1 1 -1 1 1 -1 ]


I8 = Matrix{Float64}(I,8,8)
iI8 = Matrix{Int8}(I,8,8)

@test ifwht(I8,1) == H8
@test ifwht(I8,2)' == H8
@test ifwht_natural(I8,1) == H8n
@test ifwht_natural(I8,2)' == H8n
@test ifwht_dyadic(I8,1) == H8d
@test ifwht_dyadic(I8,2)' == H8d

@test ifwht(iI8,1) == H8
@test ifwht(iI8,2)' == H8
@test ifwht_natural(iI8,1) == H8n
@test ifwht_natural(iI8,2)' == H8n
@test ifwht_dyadic(iI8,1) == H8d
@test ifwht_dyadic(iI8,2)' == H8d

H32 = [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1
1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1
1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 1 1 1 1 -1 -1 -1 -1
1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1
1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1
1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1
1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1
1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1
1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1
1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1
1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 1 1 -1 -1
1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1
1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1
1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1
1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1
1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1
1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1
1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1
1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 -1
1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1
1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1
1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1
1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1
1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1
1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1
1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1
1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1
1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1
1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 ]

I32 = Matrix{Float64}(I,32,32)
iI32 = Matrix{Int8}(I,32,32)

@test ifwht(I32,1) == H32
@test ifwht(I32,2)' == H32

@test ifwht(iI32,1) == H32
@test ifwht(iI32,2)' == H32

for f in (:fwht, :fwht_natural, :fwht_dyadic)
fi = Symbol(string("i", f))
@eval begin
@test norminf(X - $fi($f(X))) < 1e-14
@test norminf(X - $fi($f(X,1),1)) < 1e-14
@test norminf(X - $fi($f(X,2),2)) < 1e-14
@test norminf($f($f(X,1),2) - $f(X)) < 1e-14
@test norminf(transp($f(transp(X),1)) - $f(X,2)) < 1e-14
end
end
end

@test hadamard(8) == H8n
@test ifwht_natural(I32, 1) == hadamard(32)
@test ifwht_natural(Matrix{Float64}(I,2,2), 1) == hadamard(2)
@test hadamard(8) == H8n
@test ifwht_natural(I32, 1) == hadamard(32)
@test ifwht_natural(Matrix{Float64}(I,2,2), 1) == hadamard(2)

let X = copy(I32)
@test ifwht_natural!(X, 1) == X == hadamard(32)
@test fwht_natural!(X, 1) == X == I32
let X = copy(I32)
@test ifwht_natural!(X, 1) == X == hadamard(32)
@test fwht_natural!(X, 1) == X == I32
end
end

print("Checking unitarity of hadamard(n): ")
sizes = Int[]
for i = 4:4:1200
H = try
Matrix{Int}(hadamard(i))
catch
Int[]
end
if !isempty(H)
print(i, ", ")
@test norminf(H'*H - size(H,1)*I) == 0
push!(sizes, i)
@testset "hadamard(n)" begin
sizes = Int[]
for i = 4:4:1200
H = try
Matrix{Int}(hadamard(i))
catch
Matrix{Int}(undef,0,0)
end
if !isempty(H)
# print(i, ", ")
@test norminf(H'*H - size(H,1)*I) == 0
push!(sizes, i)
end
end
@test sizes == [4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 196, 200, 204, 208, 212, 216, 220, 224, 228, 232, 236, 240, 244, 248, 252, 256, 264, 272, 280, 288, 296, 304, 312, 320, 328, 336, 344, 352, 360, 368, 376, 384, 392, 400, 408, 416, 424, 428, 432, 440, 448, 456, 464, 472, 480, 488, 496, 504, 512, 528, 544, 560, 576, 592, 608, 624, 640, 656, 672, 688, 704, 720, 736, 752, 768, 784, 800, 816, 832, 848, 856, 864, 880, 896, 912, 928, 944, 960, 976, 992, 1008, 1024, 1040, 1056, 1088, 1104, 1120, 1152, 1184, 1200]
end
@test sizes == [4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 196, 200, 204, 208, 212, 216, 220, 224, 228, 232, 236, 240, 244, 248, 252, 256, 264, 272, 280, 288, 296, 304, 312, 320, 328, 336, 344, 352, 360, 368, 376, 384, 392, 400, 408, 416, 424, 428, 432, 440, 448, 456, 464, 472, 480, 488, 496, 504, 512, 528, 544, 560, 576, 592, 608, 624, 640, 656, 672, 688, 704, 720, 736, 752, 768, 784, 800, 816, 832, 848, 856, 864, 880, 896, 912, 928, 944, 960, 976, 992, 1008, 1024, 1040, 1056, 1088, 1104, 1120, 1152, 1184, 1200]

@testset "walsh(n)" begin
@test walsh(8) == [1 1 1 1 1 1 1 1; 1 1 1 1 -1 -1 -1 -1; 1 1 -1 -1 -1 -1 1 1; 1 1 -1 -1 1 1 -1 -1; 1 -1 -1 1 1 -1 -1 1; 1 -1 -1 1 -1 1 1 -1; 1 -1 1 -1 -1 1 -1 1; 1 -1 1 -1 1 -1 1 -1]
Expand All @@ -137,4 +142,3 @@ end
end
end

println(".\nSuccess!")
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