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September Morn Update

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Ingy döt Net 2019-09-12 10:33:56 -07:00
commit aac6731f2c
6856 changed files with 141518 additions and 21303 deletions
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24
Task/Fast-Fourier-transform/Nim/fast-fourier-transform.nim
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@ -1,26 +1,28 @@
import math, complex, strutils
proc toComplex(x: float): TComplex = result.re = x
proc toComplex(x: TComplex): TComplex = x
# Works with floats and complex numbers as input
proc fft[T](x: openarray[T]): seq[TComplex] =
proc fft[T: float | Complex[float]](x: openarray[T]): seq[Complex[float]] =
let n = x.len
result = newSeq[TComplex]()
if n <= 1:
for v in x: result.add toComplex(v)
if n == 0: return
result.newSeq(n)
if n == 1:
result[0] = (when T is float: complex(x[0]) else: x[0])
return
var evens, odds = newSeq[T]()
for i, v in x:
if i mod 2 == 0: evens.add v
else: odds.add v
var (even, odd) = (fft(evens), fft(odds))
for k in 0 .. < n div 2:
result.add(even[k] + exp((0.0, -2*pi*float(k)/float(n))) * odd[k])
let halfn = n div 2
for k in 0 .. < n div 2:
result.add(even[k] - exp((0.0, -2*pi*float(k)/float(n))) * odd[k])
for k in 0 .. < halfn:
let a = exp(complex(0.0, -2 * Pi* float(k) / float(n))) * odd[k]
result[k] = even[k] + a
result[k + halfn] = even[k] - a
for i in fft(@[1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0]):
echo formatFloat(abs(i), ffDecimal, 3)