def fft(clk, s0, s1, valid, num_stages):
for stage in reversed(list(range(num_stages))):
m = 2**stage
#generate constants
twiddles = [i/(2*m) for i in range(m)]
twiddles = [exp(-2.0j*pi*i) for i in twiddles]
twiddle_type = Complex(SFixed(s0.i.subtype.bits+2, s0.i.subtype.bits))
#butterfly
s0, s1 = s0+s1, s0-s1
s0 = delay(clk, s0, 1)
s1 = delay(clk, s1, 1)
valid = delay(clk, valid, 1)
#rotate
if stage:
count, _ = counter(clk, 0, m//2-1, 1, valid)
s1 = s1 * twiddle_type.rom(count, *twiddles)
s0 = delay(clk, s0, 1)
s1 = delay(clk, s1, 1)
valid = delay(clk, valid, 1)
#reorder
s0, s1, valid = reorder(clk, s0, s1, valid, stage)
return bit_reverse_order(clk, s0, s1, valid, 2**(num_stages-1))
