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moved fixed-point trigonometry to a separate file

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This commit is contained in:
Theodor Chikin
2025-10-08 19:07:22 +03:00
parent fffe096312
commit 9c30fc4405
5 changed files with 249 additions and 171 deletions
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127
FFT.py
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@ -13,12 +13,12 @@ def FFT_backup(inp):
def FFT_real(inp): def FFT_real(inp):
mode = 2 mode = 3
if (mode == 0): if (mode == 0):
inp = np.array(inp) inp = np.array(inp)
out = FFT_np(inp) out = FFT_np(inp)
out = [np.abs(val) for val in out] out = [np.abs(val) for val in out]
if (mode == 1): if (mode == 1): # simple with recursion
out = FFT_arr([[val, 0] for val in inp]) out = FFT_arr([[val, 0] for val in inp])
#out = [val for val in np.abs(out)] #out = [val for val in np.abs(out)]
@ -26,7 +26,7 @@ def FFT_real(inp):
print("output:", out) print("output:", out)
out = [sqrt(val[0]**2 + val[1]**2) for val in out] out = [sqrt(val[0]**2 + val[1]**2) for val in out]
# out = [2 for val in out] # out = [2 for val in out]
if (mode == 2): if (mode == 2): #no internal buffs
tmp = [] tmp = []
for re in inp: for re in inp:
@ -43,10 +43,32 @@ def FFT_real(inp):
#out = [val for val in np.abs(out)] #out = [val for val in np.abs(out)]
print("FFT_calculated!") print("FFT_calculated!")
print("output:", out) #print("output:", out)
out = [sqrt(val[0]**2 + val[1]**2) for val in out] out = [sqrt(val[0]**2 + val[1]**2) for val in out]
print(out) if (mode == 3): #fixed-point
tmp = []
for re in inp:
tmp.append(re)
tmp.append(0)
out = FFT_arr_FP(tmp)
tmp = out.copy()
out = []
for i in range(len(tmp)//2):
out.append([tmp[2*i], tmp[2*i+1]])
#out = [val for val in np.abs(out)]
print("FFT_calculated!")
#print("output:", out)
out = [sqrt(val[0]**2 + val[1]**2) for val in out]
#print(out)
return out return out
@ -97,8 +119,6 @@ def FFT_arr(x):
import math
def FFT_arr_inplace(buf): def FFT_arr_inplace(buf):
""" """
In-place radix-2 DIT FFT для списка buf длины N=2^m, где каждый элемент — [re, im]. In-place radix-2 DIT FFT для списка buf длины N=2^m, где каждый элемент — [re, im].
@ -159,6 +179,64 @@ def FFT_arr_inplace(buf):
FP_acc = 1e3
def FFT_arr_FP(buf):
"""
In-place radix-2 DIT FFT для списка buf длины N=2^m, где каждый элемент — [re, im].
Без массивов twiddle: твиддл на уровне обновляется рекуррентно.
"""
buf = [int(val*FP_acc) for val in buf]
N = len(buf)//2
# --- bit-reverse перестановка (чтобы бабочки шли последовательно) ---
j = 0
for i in range(1, N):
bit = N >> 1
while j & bit:
j ^= bit
bit >>= 1
j |= bit
if i < j:
buf[i*2], buf[i*2+1], buf[j*2], buf[j*2+1] = buf[j*2], buf[j*2+1], buf[i*2], buf[i*2+1]
# --- уровни бабочек ---
m = 2
while m <= N:
half = m // 2
# шаг угла Δ = 2π/m, базовый твиддл w_m = e^{-jΔ} => (cw, sw)
c_delta_FP = cos(2.0 * pi / m) * FP_acc
s_delta_FP = -sin(2.0 * pi / m) * FP_acc
for start in range(0, N, m):
# w = e^{-j*0*Δ} = 1 + j0
wr, wi = 1.0 * FP_acc, 0.0 * FP_acc
for k in range(half):
u_re, u_im = buf[(start + k)*2], buf[(start + k)*2 +1]
v_re, v_im = buf[(start + k + half)*2], buf[(start + k + half)*2 +1]
# t = w * v
print("wr, v_re, wi, v_im:", wr, v_re, wi, v_im)
t_re = (wr * v_re - wi * v_im) / FP_acc
t_im = (wr * v_im + wi * v_re) / FP_acc
# верх/низ
buf[(start + k)*2 +0] = u_re + t_re
buf[(start + k)*2 +1] = u_im + t_im
buf[(start + k + half)*2 + 0] = u_re - t_re
buf[(start + k + half)*2 + 1] = u_im - t_im
# w *= w_m (поворот на Δ с помощью рекуррентной формулы)
# (wr + j wi) * (cΔ + j sΔ)
wr, wi = (wr * c_delta_FP - wi * s_delta_FP)/ FP_acc, (wr * s_delta_FP + wi * c_delta_FP)/ FP_acc
m <<= 1
buf = [val/ FP_acc for val in buf]
return buf
@ -169,41 +247,6 @@ def FFT_arr_inplace(buf):
def FFT_arr_for_C(x):
print("x:", x)
N = len(x)
print("len(x):", N)
if N == 1:
print("As len(x) == 1, return it`s value")
return x
X_even = FFT_arr_for_C(x[::2])
X_odd = FFT_arr_for_C(x[1::2])
print("X_even:",X_even)
tw = []
for k in range(len(X_odd)):
a = cos(2*pi * k/N) #real
b = -sin(2*pi * k/N) #imag
c = X_odd[k][0] # real
d = X_odd[k][1] # imag
print("a,b,c,d:", a,b,c,d)
tw.append([a*c - b*d, b*c + a*d]) #(a + ib)(c + id) = (ac - bd) + i(bc + ad)
res = [0 for i in range(len(X_even)*2)]
for i in range(len(X_even)):
res[i] = [X_even[i][0] + tw[i][0], X_even[i][1] + tw[i][1]]
res[i+len(X_even)] = [X_even[i][0] - tw[i][0], X_even[i][1] - tw[i][1]]
return res

149
FP_trigonometry.py Executable file
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@ -0,0 +1,149 @@
#!/usr/bin/python3
from math import sin, cos, pi, sqrt
import plotly.graph_objs as go
from plotly.subplots import make_subplots
FP_acc = 2<<16
pi_FP = 1* FP_acc
def abs_FP(re, im):
return int(sqrt(re*re + im*im))
def sqrt_FP(val):
#print(val)
return int(sqrt(val))
def abs_FP(re, im):
# return sqrt(re*re + im*im)
return int(sqrt(re*re + im*im)/FP_acc)
trigon_debug = 0
def sin_FP(phi_fp):
if (trigon_debug):
print("sin_FP========")
print("phi:", phi_fp)
if phi_fp < 0:
if (trigon_debug):
print("phi < 0. recursive inversion...")
return -1 *sin_FP(-1*phi_fp)
while phi_fp >= 2*pi_FP:
if (trigon_debug):
print("phi is bigger than 2Pi. Decreasing...")
phi_fp -= 2*pi_FP
if (trigon_debug):
print("phi:", phi_fp)
if phi_fp >= pi_FP:
if (trigon_debug):
print("phi > pi_FP. recursive inversion...")
print(phi_fp, pi_FP)
return -1*sin_FP(phi_fp - pi_FP)
if phi_fp == pi_FP/2:
return 1*FP_acc
if phi_fp == 0:
return 0
if phi_fp > pi_FP/2:
if (trigon_debug):
print("phi > pi_FP/2. recursive inversion...")
return sin_FP(pi_FP - phi_fp)
#now phi should be inside [0, Pi/2). checking...
if phi_fp < 0:
raise ValueError('error in sin_FP. after all checks phi < 0')
if phi_fp >= pi_FP/2:
raise ValueError('error in sin_FP. after all checks phi > pi_FP/2')
#now phi is inside [0, Pi/2). So, cos(phi) > 1 always
if (trigon_debug):
print("phi:", phi_fp)
return sin_FP_constrained(phi_fp)
sin_05_debug = 0
def sin_FP_constrained(phi_fp):
phi_trh = pi_FP/16
if (trigon_debug):
print("sin_FP_constrained===========")
print("phi:", phi_fp)
print("check is phi inside [0, Pi/2)")
if phi_fp < 0:
raise ValueError('error in sin_FP. after all checks phi < 0')
if phi_fp >= pi_FP/2:
raise ValueError('error in sin_FP. after all checks phi > pi_FP/2')
if (trigon_debug):
print("Ok")
if (phi_fp > phi_trh):
if (sin_05_debug):
print("phi_fp:", phi_fp," >",phi_trh,"... recusion")
print("phi_fp/2:", phi_fp/2)
sin_phi_05 = sin_FP_constrained(phi_fp/2)
sin_phi = int((2*sin_phi_05 * sqrt_FP(FP_acc**2 - sin_phi_05*sin_phi_05))/FP_acc)
if (sin_05_debug):
print("sin_phi_05:", sin_phi_05)
print("sin_phi:",sin_phi)
return sin_phi
else:
res = int((phi_fp * 3.141592653589793238462643383279502884197169399375105820974944 * FP_acc)/FP_acc - ((phi_fp * 3.141592653589793238462643383279502884197169399375105820974944 * FP_acc)/FP_acc)**3/(6*FP_acc**2))
# res = int((phi_fp * 1.0 * FP_acc)/FP_acc - ((phi_fp * 1.0 * FP_acc)/FP_acc)**3/(6*FP_acc**2))
if (trigon_debug):
print("calculating sin(x) as x:",phi_fp, res)
return res
# return sin(pi*(phi_fp/FP_acc)/(pi_FP/FP_acc))
def cos_FP(phi_fp):
return sin_FP(phi_fp - pi_FP/2)
def sin_tester():
N = 4000
angs = [(i - N/2)/1000 for i in range(N)]
res_f = []
res_FP = []
res_cos_FP = []
for phi in angs:
res_f.append(sin(phi*pi))
# print(phi, phi*FP_acc*pi_FP/FP_acc)
val_fp = sin_FP(phi*FP_acc*pi_FP/FP_acc)
val_cos_fp = cos_FP(phi*FP_acc*pi_FP/FP_acc)
print("angle, sin, cos:",phi, val_fp, val_cos_fp)
res_FP.append(val_fp)
res_cos_FP.append(val_cos_fp)
chart = make_subplots(rows=2, cols=1)
chart.add_trace(go.Scatter(x = angs, y=res_f, name="sin_float", mode="markers+lines"), row=1, col=1)
chart.add_trace(go.Scatter(x = angs, y=[val/FP_acc for val in res_FP], name="sin_FP", mode="markers+lines"), row=1, col=1)
chart.add_trace(go.Scatter(x = angs, y=[val/FP_acc for val in res_cos_FP], name="cos_FP", mode="markers+lines"), row=1, col=1)
chart.add_trace(go.Scatter(x = angs, y=[a - b/FP_acc for a,b in zip(res_f, res_FP)], name="error", mode="markers+lines"), row=2, col=1)
chart.update_xaxes(matches="x1", row=2, col=1)
chart.show()
if __name__ == "__main__":
sin_tester()

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__pycache__/FFT.cpython-312.pyc
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__pycache__/FP_trigonometry.cpython-312.pyc Normal file
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122
naive_DFT.py
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@ -4,8 +4,8 @@ import plotly.graph_objs as go
from plotly.subplots import make_subplots from plotly.subplots import make_subplots
from FFT import FFT_real from FFT import FFT_real
from FP_trigonometry import *
FP_acc = 1e3
INP_L = 1024 INP_L = 1024
@ -13,19 +13,14 @@ INP_L = 1024
F_nyquist = INP_L//2 F_nyquist = INP_L//2
pi_FP = 1* FP_acc
def abs_f(re, im): def abs_f(re, im):
return sqrt(re*re + im*im) return sqrt(re*re + im*im)
def abs_FP(re, im):
return int(sqrt(re*re + im*im))
def sqrt_FP(val):
#print(val)
return int(sqrt(val))
def DFT_naive(inp, out): def DFT_naive(inp, out):
for f in range(len(out)): for f in range(len(out)):
@ -41,97 +36,6 @@ def DFT_naive(inp, out):
out[f] = val_abs out[f] = val_abs
def abs_FP(re, im):
# return sqrt(re*re + im*im)
return int(sqrt(re*re + im*im)/FP_acc)
trigon_debug = 0
def sin_FP(phi_fp):
if (trigon_debug):
print("sin_FP========")
print("phi:", phi_fp)
if phi_fp < 0:
if (trigon_debug):
print("phi < 0. recursive inversion...")
return -1 *sin_FP(-1*phi_fp)
while phi_fp >= 2*pi_FP:
if (trigon_debug):
print("phi is bigger than 2Pi. Decreasing...")
phi_fp -= 2*pi_FP
if (trigon_debug):
print("phi:", phi_fp)
if phi_fp >= pi_FP:
if (trigon_debug):
print("phi > pi_FP. recursive inversion...")
print(phi_fp, pi_FP)
return -1*sin_FP(phi_fp - pi_FP)
if phi_fp == pi_FP/2:
return 1*FP_acc
if phi_fp == 0:
return 0
if phi_fp > pi_FP/2:
if (trigon_debug):
print("phi > pi_FP/2. recursive inversion...")
return sin_FP(pi_FP - phi_fp)
#now phi should be inside [0, Pi/2). checking...
if phi_fp < 0:
raise ValueError('error in sin_FP. after all checks phi < 0')
if phi_fp >= pi_FP/2:
raise ValueError('error in sin_FP. after all checks phi > pi_FP/2')
#now phi is inside [0, Pi/2). So, cos(phi) > 1 always
if (trigon_debug):
print("phi:", phi_fp)
return sin_FP_constrained(phi_fp)
sin_05_debug = 0
def sin_FP_constrained(phi_fp):
phi_trh = pi_FP/16
if (trigon_debug):
print("sin_FP_constrained===========")
print("phi:", phi_fp)
print("check is phi inside [0, Pi/2)")
if phi_fp < 0:
raise ValueError('error in sin_FP. after all checks phi < 0')
if phi_fp >= pi_FP/2:
raise ValueError('error in sin_FP. after all checks phi > pi_FP/2')
if (trigon_debug):
print("Ok")
if (phi_fp > phi_trh):
if (sin_05_debug):
print("phi_fp:", phi_fp," >",phi_trh,"... recusion")
print("phi_fp/2:", phi_fp/2)
sin_phi_05 = sin_FP_constrained(phi_fp/2)
sin_phi = (2*sin_phi_05 * sqrt_FP(FP_acc**2 - sin_phi_05*sin_phi_05))/FP_acc
if (sin_05_debug):
print("sin_phi_05:", sin_phi_05)
print("sin_phi:",sin_phi)
return sin_phi
else:
res = int((phi_fp * 3.141592653589793238462643383279502884197169399375105820974944 * FP_acc)/FP_acc - ((phi_fp * 3.141592653589793238462643383279502884197169399375105820974944 * FP_acc)/FP_acc)**3/(6*FP_acc**2))
# res = int((phi_fp * 1.0 * FP_acc)/FP_acc - ((phi_fp * 1.0 * FP_acc)/FP_acc)**3/(6*FP_acc**2))
if (trigon_debug):
print("calculating sin(x) as x:",phi_fp, res)
return res
# return sin(pi*(phi_fp/FP_acc)/(pi_FP/FP_acc))
def cos_FP(phi_fp):
return sin_FP(phi_fp - pi_FP/2)
def DFT_naive_FP(inp_float, out): def DFT_naive_FP(inp_float, out):
@ -180,6 +84,7 @@ def FFT_tester():
chart.add_trace(go.Scatter(x=[i for i in range(len(out_DFT))], y=out_DFT, name="out_DFT", mode="markers+lines"), row=2, col=1) chart.add_trace(go.Scatter(x=[i for i in range(len(out_DFT))], y=out_DFT, name="out_DFT", mode="markers+lines"), row=2, col=1)
chart.add_trace(go.Scatter(x=[i for i in range(len(out_FFT))], y=out_FFT, name="out_FFT", mode="markers+lines"), row=2, col=1) chart.add_trace(go.Scatter(x=[i for i in range(len(out_FFT))], y=out_FFT, name="out_FFT", mode="markers+lines"), row=2, col=1)
chart.add_trace(go.Scatter(x=[i for i in range(len(Fourier_error))], y=Fourier_error, name="error", mode="markers+lines"), row=3, col=1) chart.add_trace(go.Scatter(x=[i for i in range(len(Fourier_error))], y=Fourier_error, name="error", mode="markers+lines"), row=3, col=1)
chart.update_xaxes(matches="x2", row=3, col=1)
chart.show() chart.show()
@ -201,31 +106,12 @@ def DFT_tester():
chart.add_trace(go.Scatter(x=[i for i in range(len(out_float))], y=out_float, name="out_float", mode="markers+lines"), row=2, col=1) chart.add_trace(go.Scatter(x=[i for i in range(len(out_float))], y=out_float, name="out_float", mode="markers+lines"), row=2, col=1)
chart.add_trace(go.Scatter(x=[i for i in range(len(out_FP))], y=[val/FP_acc for val in out_FP], name="out_FP", mode="markers+lines"), row=2, col=1) chart.add_trace(go.Scatter(x=[i for i in range(len(out_FP))], y=[val/FP_acc for val in out_FP], name="out_FP", mode="markers+lines"), row=2, col=1)
chart.add_trace(go.Scatter(x=[i for i in range(len(out_FP))], y=FP_error, name="FP_error", mode="markers+lines"), row=3, col=1) chart.add_trace(go.Scatter(x=[i for i in range(len(out_FP))], y=FP_error, name="FP_error", mode="markers+lines"), row=3, col=1)
chart.update_xaxes(matches="x2", row=3, col=1)
chart.show() chart.show()
def sin_tester():
N = 4000
angs = [(i - N/2)/1000 for i in range(N)]
res_f = []
res_FP = []
res_cos_FP = []
for phi in angs:
res_f.append(sin(phi*pi))
# print(phi, phi*FP_acc*pi_FP/FP_acc)
val_fp = sin_FP(phi*FP_acc*pi_FP/FP_acc)
val_cos_fp = cos_FP(phi*FP_acc*pi_FP/FP_acc)
print("angle, sin, cos:",phi, val_fp, val_cos_fp)
res_FP.append(val_fp)
res_cos_FP.append(val_cos_fp)
chart = go.Figure()
chart.add_trace(go.Scatter(x = angs, y=res_f, name="sin_float", mode="markers+lines"))
chart.add_trace(go.Scatter(x = angs, y=[val/FP_acc for val in res_FP], name="sin_FP", mode="markers+lines"))
chart.add_trace(go.Scatter(x = angs, y=[val/FP_acc for val in res_cos_FP], name="cos_FP", mode="markers+lines"))
chart.show()