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fft.nim
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fft.nim
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import math, complex, timeit, sugar, arraymancer, sequtils
type
ComplexType = Complex[float] | Complex[float32]
# proc bitReverseCopy[T: ComplexType](x: var Tensor[T]) =
# let n = x.shape[1]
# var
# k: int
# j: int = 0
# for i in 0 ..< n - 1:
# if i < j:
# swap(x[0, i], x[0, j])
# k = n shr 1
# while j >= k:
# j -= k
# k = k shr 1
# j += k
proc bitReverseCopy[T: ComplexType](x: var seq[T]) =
let n = x.len
var
k: int
j: int = 0
for i in 0 ..< n - 1:
if i < j:
swap(x[i], x[j])
k = n shr 1
while j >= k:
j -= k
k = k shr 1
j += k
# proc fftAid[T: ComplexType](x: Tensor[T], flag: float = -1.0): Tensor[T] {.noinit.} =
# let
# n = x.shape[1]
# n1 = nextPowerOfTwo(n)
# n2 = int(log2(n.float32))
# result = newTensor[T](1, n1)
# for i in 0 ..< n:
# result[0, i] = x[0, i]
# bitReverseCopy[T](result)
# for s in 1 .. n2:
# let
# m = 2 ^ s
# # flag * 2 * Pi
# wm = exp(complex(0.0, flag * 2.0 * Pi / float(m)))
# for k in countup(0, n1 - 1, m):
# var w = complex(1.0)
# let m2 = m shr 1
# for j in 0 ..< m2:
# let
# t = w * result[0, k + j + m2]
# u = result[0, k + j]
# result[0, k + j] = u + t
# result[0, k + j + m2] = u - t
# w = w * wm
proc fftAid[T: ComplexType](x: seq[T], flag: float = -1.0): Tensor[T] {.noinit.} =
let
n = x.len
n1 = nextPowerOfTwo(n)
n2 = int(log2(n.float32))
paddingLength = n1 - n
var temp = x
for i in 1 .. padding_length:
temp.add(complex(0.0))
bitReverseCopy[T](temp)
for s in 1 .. n2:
let
m = 2 ^ s
# flag * 2 * Pi
wm = exp(complex(0.0, flag * 2.0 * Pi / float(m)))
for k in countup(0, n1 - 1, m):
var w = complex(1.0)
let m2 = m shr 1
for j in 0 ..< m2:
let
t = w * temp[k + j + m2]
u = temp[k + j]
temp[k + j] = u + t
temp[k + j + m2] = u - t
w = w * wm
temp.toTensor.reshape(1, temp.len)
# proc fft*[T: ComplexType](x: Tensor[T]): Tensor[Complex[float]] {.noinit.}=
# result = x.fftAid(-1)
proc fft*[T: ComplexType](x: seq[T] | Tensor[T]): Tensor[Complex[float]] {.noinit.}=
var temp: seq[T]
when x is seq:
temp = x
elif x is Tensor:
temp = x.toRawSeq
result = temp.fftAid(-1)
proc fft*[T: SomeFloat](x: seq[T] | Tensor[T]): Tensor[Complex[float]] {.noinit.}=
result = fft(x.map(t=>t.complex))
proc ifft*[T: ComplexType](x: seq[T] | Tensor[T]): Tensor[Complex[float]] {.noinit.}=
var temp: seq[T]
when x is seq:
temp = x
elif x is Tensor:
temp = x.toRawSeq
# when T is SomeFloat:
# temp = temp.map(x=>complex(x))
result = temp.fftAid(1).map(item => item / temp.len.float)
proc ifft*[T: SomeFloat](x: seq[T] | Tensor[T]): Tensor[Complex[float]] {.noinit.}=
result = ifft(x.map(t=>t.complex))
proc rfft*[T: SomeFloat](input: Tensor[T]): Tensor[Complex[float]] {.noinit.} =
assert input.rank == 2
var
n = input.shape[1]
half = n shr 1
A = newTensor[Complex[T]](half)
B = newTensor[Complex[T]](half)
# IA = newTensor[Complex[T]](half)
# IB = newTensor[Complex[T]](half)
X = newTensor[Complex[T]](1, half)
result = newTensor[Complex[T]](1, n)
for k in 0 ..< half:
let
coeff = 2.0 * float(k) * PI / float(n)
cosPart = 0.5 * cos(coeff)
sinPart = 0.5 * sin(coeff)
A[k] = complex(0.5 - sinPart, -cosPart)
B[k] = complex(0.5 + sinPart, cosPart)
# IA[k] = conjugate(A[k])
# IB[k] = conjugate(B[k])
for i in 0 ..< half:
X[0, i] = complex(input[0, 2 * i], input[0, 2 * i + 1])
var temp = newTensor[Complex[T]](1, half + 1)
# TODO not 2 ^ n
temp[0, 0 ..< half] = X.fft
temp[0, half] = temp[0, 0]
result[0, 0] = temp[0, 0] * A[0] + conjugate(temp[0, half]) * B[0]
for j in 1 ..< half:
result[0, j] = temp[0, j] * A[j] + conjugate(temp[0, half - j]) * B[j]
result[0, n-j] = conjugate(result[0, j])
result[0, half] = complex(temp[0, 0].re - temp[0, 0].im, 0.0)
proc dct*[T: SomeFloat](input: Tensor[T]): Tensor[float] {.noinit.} =
assert input.rank == 2
let
rows = input.shape[0]
cols = input.shape[1]
## assert rows == 1
n = input.size
half = (n - 1) div 2
var v = newTensor[T](rows, cols)
v[0, 0 .. half] = input[0, _.._|2]
if (n - 1) mod 2 == 1:
v[0, half+1 .. _] = input[0, ^1..0|-2]
else:
v[0, half+1 .. _] = input[0, ^2..0|-2]
var res = v.rfft
for i in 0 ..< res.size:
res[0, i] *= complex(2.0) * exp(complex(0.0, -Pi * float(i) / (2.0 * float(n))))
return res.map(x=>x.re)
proc naiveDct*[T: SomeFloat](input: Tensor[T]): Tensor[float] {.noinit.}=
assert input.rank == 2
let
_ = input.shape[0]
cols = input.shape[1]
factor = Pi / float(cols)
result = newTensor[float](1, cols)
for i in 0 ..< cols:
var s: T
for j in 0 ..< cols:
s += input[0, j] * cos((T(j) + 0.5) * T(i) * factor)
result[0, i] = 2 * s
when isMainModule:
import timeit
# var a = @[1.0, 1.0, 1.0, 1.0, 0.0, 0.0].map(x=>complex(x))
# var b = @[1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0].map(x=>complex(x))
# var c = @[1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0].toTensor.reshape(1, 9)
var c = randomTensor[float](1, 256, 3.0)
timeOnce("dct"):
echo dct(c)
timeOnce("naive dct"):
echo naiveDct(c)
# timeOnce:
# discard
# var c = randomTensor[float](1, 1024, 3.0)
# var c = randomTensor[float](1, 4096, max=2.0)
# echo ifft(fft(a))
# echo ifft(fft(b))
# let c = randomTensor[float](1, 4096, max=2.0)
# var s1 = monit("fft")
# var s2 = monit("rfft")
# s1.start()
# echo fft(c)[0, 2]
# s1.finish()
# s2.start()
# echo rfft(c)[0, 2]
# s2.finish()
# echo ifft(rfft(c))
# echo timeGo(fft(@[1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0]))
# echo timeGo(fft1(@[1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0]))
# echo timeGo(fft(aaa))
# echo timeGo(fft1(aaa))
# var res = fft1(@[1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0])
# for i in ifft(res):
# echo formatFloat(abs(i), ffDecimal, 10)