ChTheo/FFT_and_FP_math
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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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126
naive_DFT.py
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@ -4,8 +4,8 @@ import plotly.graph_objs as go
from plotly.subplots import make_subplots
from FFT import FFT_real
from FP_trigonometry import *
FP_acc = 1e3
INP_L = 1024
@ -13,19 +13,14 @@ INP_L = 1024
F_nyquist = INP_L//2
pi_FP = 1* FP_acc
def abs_f(re, 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):
for f in range(len(out)):
@ -41,97 +36,6 @@ def DFT_naive(inp, out):
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):
@ -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_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.update_xaxes(matches="x2", row=3, col=1)
chart.show()
@ -201,32 +106,13 @@ 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_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.update_xaxes(matches="x2", row=3, col=1)
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()