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asm_fft_amd64.go
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asm_fft_amd64.go
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//go:build amd64 && !purego
package poly
import (
"golang.org/x/sys/cpu"
)
func fftInPlaceAVX2(coeffs []float64, tw []complex128)
// fftInPlace is a top-level function for FFT.
// All internal FFT implementations calls this function for performance.
func fftInPlace(coeffs []float64, tw []complex128) {
if cpu.X86.HasAVX2 && cpu.X86.HasFMA {
fftInPlaceAVX2(coeffs, tw)
return
}
N := len(coeffs)
w := 0
// First Loop
Wr := real(tw[w])
Wi := imag(tw[w])
w++
for j := 0; j < N/2; j += 8 {
Ur0 := coeffs[j+0]
Ur1 := coeffs[j+1]
Ur2 := coeffs[j+2]
Ur3 := coeffs[j+3]
Ui0 := coeffs[j+4]
Ui1 := coeffs[j+5]
Ui2 := coeffs[j+6]
Ui3 := coeffs[j+7]
Vr0 := coeffs[j+N/2+0]
Vr1 := coeffs[j+N/2+1]
Vr2 := coeffs[j+N/2+2]
Vr3 := coeffs[j+N/2+3]
Vi0 := coeffs[j+N/2+4]
Vi1 := coeffs[j+N/2+5]
Vi2 := coeffs[j+N/2+6]
Vi3 := coeffs[j+N/2+7]
Vr0W := Vr0*Wr - Vi0*Wi
Vr1W := Vr1*Wr - Vi1*Wi
Vr2W := Vr2*Wr - Vi2*Wi
Vr3W := Vr3*Wr - Vi3*Wi
Vi0W := Vr0*Wi + Vi0*Wr
Vi1W := Vr1*Wi + Vi1*Wr
Vi2W := Vr2*Wi + Vi2*Wr
Vi3W := Vr3*Wi + Vi3*Wr
coeffs[j+0] = Ur0 + Vr0W
coeffs[j+1] = Ur1 + Vr1W
coeffs[j+2] = Ur2 + Vr2W
coeffs[j+3] = Ur3 + Vr3W
coeffs[j+4] = Ui0 + Vi0W
coeffs[j+5] = Ui1 + Vi1W
coeffs[j+6] = Ui2 + Vi2W
coeffs[j+7] = Ui3 + Vi3W
coeffs[j+N/2+0] = Ur0 - Vr0W
coeffs[j+N/2+1] = Ur1 - Vr1W
coeffs[j+N/2+2] = Ur2 - Vr2W
coeffs[j+N/2+3] = Ur3 - Vr3W
coeffs[j+N/2+4] = Ui0 - Vi0W
coeffs[j+N/2+5] = Ui1 - Vi1W
coeffs[j+N/2+6] = Ui2 - Vi2W
coeffs[j+N/2+7] = Ui3 - Vi3W
}
// Main Loop
t := N / 2
for m := 2; m < N/8; m <<= 1 {
t >>= 1
for i := 0; i < m; i++ {
j1 := i * t << 1
j2 := j1 + t
Wr := real(tw[w])
Wi := imag(tw[w])
w++
for j := j1; j < j2; j += 8 {
Ur0 := coeffs[j+0]
Ur1 := coeffs[j+1]
Ur2 := coeffs[j+2]
Ur3 := coeffs[j+3]
Ui0 := coeffs[j+4]
Ui1 := coeffs[j+5]
Ui2 := coeffs[j+6]
Ui3 := coeffs[j+7]
Vr0 := coeffs[j+t+0]
Vr1 := coeffs[j+t+1]
Vr2 := coeffs[j+t+2]
Vr3 := coeffs[j+t+3]
Vi0 := coeffs[j+t+4]
Vi1 := coeffs[j+t+5]
Vi2 := coeffs[j+t+6]
Vi3 := coeffs[j+t+7]
Vr0W := Vr0*Wr - Vi0*Wi
Vr1W := Vr1*Wr - Vi1*Wi
Vr2W := Vr2*Wr - Vi2*Wi
Vr3W := Vr3*Wr - Vi3*Wi
Vi0W := Vr0*Wi + Vi0*Wr
Vi1W := Vr1*Wi + Vi1*Wr
Vi2W := Vr2*Wi + Vi2*Wr
Vi3W := Vr3*Wi + Vi3*Wr
coeffs[j+0] = Ur0 + Vr0W
coeffs[j+1] = Ur1 + Vr1W
coeffs[j+2] = Ur2 + Vr2W
coeffs[j+3] = Ur3 + Vr3W
coeffs[j+4] = Ui0 + Vi0W
coeffs[j+5] = Ui1 + Vi1W
coeffs[j+6] = Ui2 + Vi2W
coeffs[j+7] = Ui3 + Vi3W
coeffs[j+t+0] = Ur0 - Vr0W
coeffs[j+t+1] = Ur1 - Vr1W
coeffs[j+t+2] = Ur2 - Vr2W
coeffs[j+t+3] = Ur3 - Vr3W
coeffs[j+t+4] = Ui0 - Vi0W
coeffs[j+t+5] = Ui1 - Vi1W
coeffs[j+t+6] = Ui2 - Vi2W
coeffs[j+t+7] = Ui3 - Vi3W
}
}
}
// Stride 2
for j := 0; j < N; j += 8 {
Wr := real(tw[w])
Wi := imag(tw[w])
w++
Ur0 := coeffs[j+0]
Ur1 := coeffs[j+1]
Vr0 := coeffs[j+2]
Vr1 := coeffs[j+3]
Ui0 := coeffs[j+4]
Ui1 := coeffs[j+5]
Vi0 := coeffs[j+6]
Vi1 := coeffs[j+7]
Vr0W := Vr0*Wr - Vi0*Wi
Vr1W := Vr1*Wr - Vi1*Wi
Vi0W := Vr0*Wi + Vi0*Wr
Vi1W := Vr1*Wi + Vi1*Wr
coeffs[j+0] = Ur0 + Vr0W
coeffs[j+1] = Ur1 + Vr1W
coeffs[j+2] = Ur0 - Vr0W
coeffs[j+3] = Ur1 - Vr1W
coeffs[j+4] = Ui0 + Vi0W
coeffs[j+5] = Ui1 + Vi1W
coeffs[j+6] = Ui0 - Vi0W
coeffs[j+7] = Ui1 - Vi1W
}
// Stride 1
for j := 0; j < N; j += 8 {
Wr0 := real(tw[w])
Wi0 := imag(tw[w])
Wr1 := real(tw[w+1])
Wi1 := imag(tw[w+1])
w += 2
Ur0 := coeffs[j+0]
Vr0 := coeffs[j+1]
Ur1 := coeffs[j+2]
Vr1 := coeffs[j+3]
Ui0 := coeffs[j+4]
Vi0 := coeffs[j+5]
Ui1 := coeffs[j+6]
Vi1 := coeffs[j+7]
Vr0W := Vr0*Wr0 - Vi0*Wi0
Vi0W := Vr0*Wi0 + Vi0*Wr0
Vr1W := Vr1*Wr1 - Vi1*Wi1
Vi1W := Vr1*Wi1 + Vi1*Wr1
coeffs[j+0] = Ur0 + Vr0W
coeffs[j+1] = Ur0 - Vr0W
coeffs[j+2] = Ur1 + Vr1W
coeffs[j+3] = Ur1 - Vr1W
coeffs[j+4] = Ui0 + Vi0W
coeffs[j+5] = Ui0 - Vi0W
coeffs[j+6] = Ui1 + Vi1W
coeffs[j+7] = Ui1 - Vi1W
}
}
func invFFTInPlaceAVX2(coeffs []float64, twInv []complex128, NInv float64)
// invfftInPlace is a top-level function for inverse FFT.
// All internal inverse FFT implementations calls this function for performance.
func invFFTInPlace(coeffs []float64, twInv []complex128) {
if cpu.X86.HasAVX2 && cpu.X86.HasFMA {
invFFTInPlaceAVX2(coeffs, twInv, 2/float64(len(coeffs)))
return
}
N := len(coeffs)
w := 0
// Stride 1
for j := 0; j < N; j += 8 {
Wr0 := real(twInv[w])
Wi0 := imag(twInv[w])
Wr1 := real(twInv[w+1])
Wi1 := imag(twInv[w+1])
w += 2
Ur0 := coeffs[j+0]
Vr0 := coeffs[j+1]
Ur1 := coeffs[j+2]
Vr1 := coeffs[j+3]
Ui0 := coeffs[j+4]
Vi0 := coeffs[j+5]
Ui1 := coeffs[j+6]
Vi1 := coeffs[j+7]
coeffs[j+0] = Ur0 + Vr0
coeffs[j+2] = Ur1 + Vr1
coeffs[j+4] = Ui0 + Vi0
coeffs[j+6] = Ui1 + Vi1
UVr0 := Ur0 - Vr0
UVi0 := Ui0 - Vi0
UVr1 := Ur1 - Vr1
UVi1 := Ui1 - Vi1
UVr0W := UVr0*Wr0 - UVi0*Wi0
UVi0W := UVr0*Wi0 + UVi0*Wr0
UVr1W := UVr1*Wr1 - UVi1*Wi1
UVi1W := UVr1*Wi1 + UVi1*Wr1
coeffs[j+1] = UVr0W
coeffs[j+3] = UVr1W
coeffs[j+5] = UVi0W
coeffs[j+7] = UVi1W
}
// Stride 2
for j := 0; j < N; j += 8 {
Wr := real(twInv[w])
Wi := imag(twInv[w])
w++
Ur0 := coeffs[j+0]
Ur1 := coeffs[j+1]
Vr0 := coeffs[j+2]
Vr1 := coeffs[j+3]
Ui0 := coeffs[j+4]
Ui1 := coeffs[j+5]
Vi0 := coeffs[j+6]
Vi1 := coeffs[j+7]
coeffs[j+0] = Ur0 + Vr0
coeffs[j+1] = Ur1 + Vr1
coeffs[j+4] = Ui0 + Vi0
coeffs[j+5] = Ui1 + Vi1
UVr0 := Ur0 - Vr0
UVr1 := Ur1 - Vr1
UVi0 := Ui0 - Vi0
UVi1 := Ui1 - Vi1
UVr0W := UVr0*Wr - UVi0*Wi
UVr1W := UVr1*Wr - UVi1*Wi
UVi0W := UVr0*Wi + UVi0*Wr
UVi1W := UVr1*Wi + UVi1*Wr
coeffs[j+2] = UVr0W
coeffs[j+3] = UVr1W
coeffs[j+6] = UVi0W
coeffs[j+7] = UVi1W
}
// Main Loop
t := 8
for m := N / 8; m > 2; m >>= 1 {
j1 := 0
h := m >> 1
for i := 0; i < h; i++ {
j2 := j1 + t
Wr := real(twInv[w])
Wi := imag(twInv[w])
w++
for j := j1; j < j2; j += 8 {
Ur0 := coeffs[j+0]
Ur1 := coeffs[j+1]
Ur2 := coeffs[j+2]
Ur3 := coeffs[j+3]
Ui0 := coeffs[j+4]
Ui1 := coeffs[j+5]
Ui2 := coeffs[j+6]
Ui3 := coeffs[j+7]
Vr0 := coeffs[j+t+0]
Vr1 := coeffs[j+t+1]
Vr2 := coeffs[j+t+2]
Vr3 := coeffs[j+t+3]
Vi0 := coeffs[j+t+4]
Vi1 := coeffs[j+t+5]
Vi2 := coeffs[j+t+6]
Vi3 := coeffs[j+t+7]
coeffs[j+0] = Ur0 + Vr0
coeffs[j+1] = Ur1 + Vr1
coeffs[j+2] = Ur2 + Vr2
coeffs[j+3] = Ur3 + Vr3
coeffs[j+4] = Ui0 + Vi0
coeffs[j+5] = Ui1 + Vi1
coeffs[j+6] = Ui2 + Vi2
coeffs[j+7] = Ui3 + Vi3
UVr0 := Ur0 - Vr0
UVr1 := Ur1 - Vr1
UVr2 := Ur2 - Vr2
UVr3 := Ur3 - Vr3
UVi0 := Ui0 - Vi0
UVi1 := Ui1 - Vi1
UVi2 := Ui2 - Vi2
UVi3 := Ui3 - Vi3
UVr0W := UVr0*Wr - UVi0*Wi
UVr1W := UVr1*Wr - UVi1*Wi
UVr2W := UVr2*Wr - UVi2*Wi
UVr3W := UVr3*Wr - UVi3*Wi
UVi0W := UVr0*Wi + UVi0*Wr
UVi1W := UVr1*Wi + UVi1*Wr
UVi2W := UVr2*Wi + UVi2*Wr
UVi3W := UVr3*Wi + UVi3*Wr
coeffs[j+t+0] = UVr0W
coeffs[j+t+1] = UVr1W
coeffs[j+t+2] = UVr2W
coeffs[j+t+3] = UVr3W
coeffs[j+t+4] = UVi0W
coeffs[j+t+5] = UVi1W
coeffs[j+t+6] = UVi2W
coeffs[j+t+7] = UVi3W
}
j1 += t << 1
}
t <<= 1
}
// Last Loop
NInv := 2 / float64(N)
Wr := real(twInv[w])
Wi := imag(twInv[w])
for j := 0; j < N/2; j += 8 {
Ur0 := coeffs[j+0]
Ur1 := coeffs[j+1]
Ur2 := coeffs[j+2]
Ur3 := coeffs[j+3]
Ui0 := coeffs[j+4]
Ui1 := coeffs[j+5]
Ui2 := coeffs[j+6]
Ui3 := coeffs[j+7]
Vr0 := coeffs[j+N/2+0]
Vr1 := coeffs[j+N/2+1]
Vr2 := coeffs[j+N/2+2]
Vr3 := coeffs[j+N/2+3]
Vi0 := coeffs[j+N/2+4]
Vi1 := coeffs[j+N/2+5]
Vi2 := coeffs[j+N/2+6]
Vi3 := coeffs[j+N/2+7]
coeffs[j+0] = (Ur0 + Vr0) * NInv
coeffs[j+1] = (Ur1 + Vr1) * NInv
coeffs[j+2] = (Ur2 + Vr2) * NInv
coeffs[j+3] = (Ur3 + Vr3) * NInv
coeffs[j+4] = (Ui0 + Vi0) * NInv
coeffs[j+5] = (Ui1 + Vi1) * NInv
coeffs[j+6] = (Ui2 + Vi2) * NInv
coeffs[j+7] = (Ui3 + Vi3) * NInv
UVr0 := Ur0 - Vr0
UVr1 := Ur1 - Vr1
UVr2 := Ur2 - Vr2
UVr3 := Ur3 - Vr3
UVi0 := Ui0 - Vi0
UVi1 := Ui1 - Vi1
UVi2 := Ui2 - Vi2
UVi3 := Ui3 - Vi3
UVr0W := UVr0*Wr - UVi0*Wi
UVr1W := UVr1*Wr - UVi1*Wi
UVr2W := UVr2*Wr - UVi2*Wi
UVr3W := UVr3*Wr - UVi3*Wi
UVi0W := UVr0*Wi + UVi0*Wr
UVi1W := UVr1*Wi + UVi1*Wr
UVi2W := UVr2*Wi + UVi2*Wr
UVi3W := UVr3*Wi + UVi3*Wr
coeffs[j+N/2+0] = UVr0W
coeffs[j+N/2+1] = UVr1W
coeffs[j+N/2+2] = UVr2W
coeffs[j+N/2+3] = UVr3W
coeffs[j+N/2+4] = UVi0W
coeffs[j+N/2+5] = UVi1W
coeffs[j+N/2+6] = UVi2W
coeffs[j+N/2+7] = UVi3W
}
}