moved fixed-point trigonometry to a separate file
This commit is contained in:
127
FFT.py
127
FFT.py
@ -13,12 +13,12 @@ def FFT_backup(inp):
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def FFT_real(inp):
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mode = 2
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mode = 3
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if (mode == 0):
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inp = np.array(inp)
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out = FFT_np(inp)
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out = [np.abs(val) for val in out]
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if (mode == 1):
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if (mode == 1): # simple with recursion
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out = FFT_arr([[val, 0] for val in inp])
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#out = [val for val in np.abs(out)]
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@ -26,7 +26,7 @@ def FFT_real(inp):
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print("output:", out)
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out = [sqrt(val[0]**2 + val[1]**2) for val in out]
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# out = [2 for val in out]
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if (mode == 2):
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if (mode == 2): #no internal buffs
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tmp = []
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for re in inp:
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@ -43,10 +43,32 @@ def FFT_real(inp):
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#out = [val for val in np.abs(out)]
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print("FFT_calculated!")
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print("output:", out)
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#print("output:", out)
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out = [sqrt(val[0]**2 + val[1]**2) for val in out]
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print(out)
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if (mode == 3): #fixed-point
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tmp = []
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for re in inp:
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tmp.append(re)
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tmp.append(0)
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out = FFT_arr_FP(tmp)
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tmp = out.copy()
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out = []
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for i in range(len(tmp)//2):
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out.append([tmp[2*i], tmp[2*i+1]])
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#out = [val for val in np.abs(out)]
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print("FFT_calculated!")
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#print("output:", out)
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out = [sqrt(val[0]**2 + val[1]**2) for val in out]
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#print(out)
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return out
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@ -97,8 +119,6 @@ def FFT_arr(x):
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import math
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def FFT_arr_inplace(buf):
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"""
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In-place radix-2 DIT FFT для списка buf длины N=2^m, где каждый элемент — [re, im].
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@ -159,6 +179,64 @@ def FFT_arr_inplace(buf):
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FP_acc = 1e3
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def FFT_arr_FP(buf):
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"""
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In-place radix-2 DIT FFT для списка buf длины N=2^m, где каждый элемент — [re, im].
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Без массивов twiddle: твиддл на уровне обновляется рекуррентно.
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"""
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buf = [int(val*FP_acc) for val in buf]
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N = len(buf)//2
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# --- bit-reverse перестановка (чтобы бабочки шли последовательно) ---
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j = 0
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for i in range(1, N):
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bit = N >> 1
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while j & bit:
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j ^= bit
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bit >>= 1
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j |= bit
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if i < j:
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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]
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# --- уровни бабочек ---
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m = 2
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while m <= N:
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half = m // 2
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# шаг угла Δ = 2π/m, базовый твиддл w_m = e^{-jΔ} => (cw, sw)
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c_delta_FP = cos(2.0 * pi / m) * FP_acc
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s_delta_FP = -sin(2.0 * pi / m) * FP_acc
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for start in range(0, N, m):
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# w = e^{-j*0*Δ} = 1 + j0
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wr, wi = 1.0 * FP_acc, 0.0 * FP_acc
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for k in range(half):
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u_re, u_im = buf[(start + k)*2], buf[(start + k)*2 +1]
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v_re, v_im = buf[(start + k + half)*2], buf[(start + k + half)*2 +1]
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# t = w * v
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print("wr, v_re, wi, v_im:", wr, v_re, wi, v_im)
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t_re = (wr * v_re - wi * v_im) / FP_acc
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t_im = (wr * v_im + wi * v_re) / FP_acc
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# верх/низ
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buf[(start + k)*2 +0] = u_re + t_re
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buf[(start + k)*2 +1] = u_im + t_im
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buf[(start + k + half)*2 + 0] = u_re - t_re
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buf[(start + k + half)*2 + 1] = u_im - t_im
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# w *= w_m (поворот на Δ с помощью рекуррентной формулы)
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# (wr + j wi) * (cΔ + j sΔ)
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wr, wi = (wr * c_delta_FP - wi * s_delta_FP)/ FP_acc, (wr * s_delta_FP + wi * c_delta_FP)/ FP_acc
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m <<= 1
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buf = [val/ FP_acc for val in buf]
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return buf
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@ -169,41 +247,6 @@ def FFT_arr_inplace(buf):
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def FFT_arr_for_C(x):
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print("x:", x)
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N = len(x)
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print("len(x):", N)
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if N == 1:
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print("As len(x) == 1, return it`s value")
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return x
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X_even = FFT_arr_for_C(x[::2])
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X_odd = FFT_arr_for_C(x[1::2])
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print("X_even:",X_even)
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tw = []
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for k in range(len(X_odd)):
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a = cos(2*pi * k/N) #real
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b = -sin(2*pi * k/N) #imag
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c = X_odd[k][0] # real
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d = X_odd[k][1] # imag
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print("a,b,c,d:", a,b,c,d)
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tw.append([a*c - b*d, b*c + a*d]) #(a + ib)(c + id) = (ac - bd) + i(bc + ad)
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res = [0 for i in range(len(X_even)*2)]
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for i in range(len(X_even)):
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res[i] = [X_even[i][0] + tw[i][0], X_even[i][1] + tw[i][1]]
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res[i+len(X_even)] = [X_even[i][0] - tw[i][0], X_even[i][1] - tw[i][1]]
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return res
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149
FP_trigonometry.py
Executable file
149
FP_trigonometry.py
Executable file
@ -0,0 +1,149 @@
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#!/usr/bin/python3
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from math import sin, cos, pi, sqrt
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import plotly.graph_objs as go
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from plotly.subplots import make_subplots
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FP_acc = 2<<16
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pi_FP = 1* FP_acc
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def abs_FP(re, im):
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return int(sqrt(re*re + im*im))
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def sqrt_FP(val):
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#print(val)
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return int(sqrt(val))
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def abs_FP(re, im):
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# return sqrt(re*re + im*im)
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return int(sqrt(re*re + im*im)/FP_acc)
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trigon_debug = 0
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def sin_FP(phi_fp):
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if (trigon_debug):
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print("sin_FP========")
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print("phi:", phi_fp)
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if phi_fp < 0:
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if (trigon_debug):
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print("phi < 0. recursive inversion...")
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return -1 *sin_FP(-1*phi_fp)
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while phi_fp >= 2*pi_FP:
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if (trigon_debug):
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print("phi is bigger than 2Pi. Decreasing...")
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phi_fp -= 2*pi_FP
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if (trigon_debug):
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print("phi:", phi_fp)
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if phi_fp >= pi_FP:
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if (trigon_debug):
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print("phi > pi_FP. recursive inversion...")
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print(phi_fp, pi_FP)
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return -1*sin_FP(phi_fp - pi_FP)
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if phi_fp == pi_FP/2:
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return 1*FP_acc
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if phi_fp == 0:
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return 0
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if phi_fp > pi_FP/2:
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if (trigon_debug):
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print("phi > pi_FP/2. recursive inversion...")
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return sin_FP(pi_FP - phi_fp)
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#now phi should be inside [0, Pi/2). checking...
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if phi_fp < 0:
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raise ValueError('error in sin_FP. after all checks phi < 0')
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if phi_fp >= pi_FP/2:
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raise ValueError('error in sin_FP. after all checks phi > pi_FP/2')
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#now phi is inside [0, Pi/2). So, cos(phi) > 1 always
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if (trigon_debug):
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print("phi:", phi_fp)
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return sin_FP_constrained(phi_fp)
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sin_05_debug = 0
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def sin_FP_constrained(phi_fp):
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phi_trh = pi_FP/16
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if (trigon_debug):
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print("sin_FP_constrained===========")
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print("phi:", phi_fp)
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print("check is phi inside [0, Pi/2)")
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if phi_fp < 0:
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raise ValueError('error in sin_FP. after all checks phi < 0')
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if phi_fp >= pi_FP/2:
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raise ValueError('error in sin_FP. after all checks phi > pi_FP/2')
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if (trigon_debug):
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print("Ok")
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if (phi_fp > phi_trh):
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if (sin_05_debug):
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print("phi_fp:", phi_fp," >",phi_trh,"... recusion")
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print("phi_fp/2:", phi_fp/2)
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sin_phi_05 = sin_FP_constrained(phi_fp/2)
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sin_phi = int((2*sin_phi_05 * sqrt_FP(FP_acc**2 - sin_phi_05*sin_phi_05))/FP_acc)
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if (sin_05_debug):
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print("sin_phi_05:", sin_phi_05)
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print("sin_phi:",sin_phi)
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return sin_phi
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else:
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res = int((phi_fp * 3.141592653589793238462643383279502884197169399375105820974944 * FP_acc)/FP_acc - ((phi_fp * 3.141592653589793238462643383279502884197169399375105820974944 * FP_acc)/FP_acc)**3/(6*FP_acc**2))
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# res = int((phi_fp * 1.0 * FP_acc)/FP_acc - ((phi_fp * 1.0 * FP_acc)/FP_acc)**3/(6*FP_acc**2))
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if (trigon_debug):
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print("calculating sin(x) as x:",phi_fp, res)
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return res
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# return sin(pi*(phi_fp/FP_acc)/(pi_FP/FP_acc))
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def cos_FP(phi_fp):
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return sin_FP(phi_fp - pi_FP/2)
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def sin_tester():
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N = 4000
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angs = [(i - N/2)/1000 for i in range(N)]
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res_f = []
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res_FP = []
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res_cos_FP = []
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for phi in angs:
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res_f.append(sin(phi*pi))
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# print(phi, phi*FP_acc*pi_FP/FP_acc)
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val_fp = sin_FP(phi*FP_acc*pi_FP/FP_acc)
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val_cos_fp = cos_FP(phi*FP_acc*pi_FP/FP_acc)
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print("angle, sin, cos:",phi, val_fp, val_cos_fp)
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res_FP.append(val_fp)
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res_cos_FP.append(val_cos_fp)
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chart = make_subplots(rows=2, cols=1)
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chart.add_trace(go.Scatter(x = angs, y=res_f, name="sin_float", mode="markers+lines"), row=1, col=1)
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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)
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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)
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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)
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chart.update_xaxes(matches="x1", row=2, col=1)
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chart.show()
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if __name__ == "__main__":
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sin_tester()
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Binary file not shown.
BIN
__pycache__/FP_trigonometry.cpython-312.pyc
Normal file
BIN
__pycache__/FP_trigonometry.cpython-312.pyc
Normal file
Binary file not shown.
122
naive_DFT.py
122
naive_DFT.py
@ -4,8 +4,8 @@ import plotly.graph_objs as go
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from plotly.subplots import make_subplots
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from FFT import FFT_real
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from FP_trigonometry import *
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FP_acc = 1e3
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INP_L = 1024
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@ -13,19 +13,14 @@ INP_L = 1024
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F_nyquist = INP_L//2
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pi_FP = 1* FP_acc
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def abs_f(re, im):
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return sqrt(re*re + im*im)
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def abs_FP(re, im):
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return int(sqrt(re*re + im*im))
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def sqrt_FP(val):
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#print(val)
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return int(sqrt(val))
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def DFT_naive(inp, out):
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for f in range(len(out)):
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@ -41,97 +36,6 @@ def DFT_naive(inp, out):
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out[f] = val_abs
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def abs_FP(re, im):
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# return sqrt(re*re + im*im)
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return int(sqrt(re*re + im*im)/FP_acc)
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trigon_debug = 0
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def sin_FP(phi_fp):
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if (trigon_debug):
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print("sin_FP========")
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print("phi:", phi_fp)
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if phi_fp < 0:
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if (trigon_debug):
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print("phi < 0. recursive inversion...")
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return -1 *sin_FP(-1*phi_fp)
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while phi_fp >= 2*pi_FP:
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if (trigon_debug):
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print("phi is bigger than 2Pi. Decreasing...")
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phi_fp -= 2*pi_FP
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if (trigon_debug):
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print("phi:", phi_fp)
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if phi_fp >= pi_FP:
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if (trigon_debug):
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print("phi > pi_FP. recursive inversion...")
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print(phi_fp, pi_FP)
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return -1*sin_FP(phi_fp - pi_FP)
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if phi_fp == pi_FP/2:
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return 1*FP_acc
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if phi_fp == 0:
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return 0
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if phi_fp > pi_FP/2:
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if (trigon_debug):
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print("phi > pi_FP/2. recursive inversion...")
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return sin_FP(pi_FP - phi_fp)
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#now phi should be inside [0, Pi/2). checking...
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if phi_fp < 0:
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raise ValueError('error in sin_FP. after all checks phi < 0')
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if phi_fp >= pi_FP/2:
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raise ValueError('error in sin_FP. after all checks phi > pi_FP/2')
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#now phi is inside [0, Pi/2). So, cos(phi) > 1 always
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if (trigon_debug):
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print("phi:", phi_fp)
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return sin_FP_constrained(phi_fp)
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sin_05_debug = 0
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def sin_FP_constrained(phi_fp):
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phi_trh = pi_FP/16
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if (trigon_debug):
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print("sin_FP_constrained===========")
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print("phi:", phi_fp)
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print("check is phi inside [0, Pi/2)")
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if phi_fp < 0:
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raise ValueError('error in sin_FP. after all checks phi < 0')
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if phi_fp >= pi_FP/2:
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raise ValueError('error in sin_FP. after all checks phi > pi_FP/2')
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if (trigon_debug):
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print("Ok")
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if (phi_fp > phi_trh):
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if (sin_05_debug):
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print("phi_fp:", phi_fp," >",phi_trh,"... recusion")
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print("phi_fp/2:", phi_fp/2)
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sin_phi_05 = sin_FP_constrained(phi_fp/2)
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sin_phi = (2*sin_phi_05 * sqrt_FP(FP_acc**2 - sin_phi_05*sin_phi_05))/FP_acc
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if (sin_05_debug):
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print("sin_phi_05:", sin_phi_05)
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print("sin_phi:",sin_phi)
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return sin_phi
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else:
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res = int((phi_fp * 3.141592653589793238462643383279502884197169399375105820974944 * FP_acc)/FP_acc - ((phi_fp * 3.141592653589793238462643383279502884197169399375105820974944 * FP_acc)/FP_acc)**3/(6*FP_acc**2))
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# res = int((phi_fp * 1.0 * FP_acc)/FP_acc - ((phi_fp * 1.0 * FP_acc)/FP_acc)**3/(6*FP_acc**2))
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if (trigon_debug):
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print("calculating sin(x) as x:",phi_fp, res)
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return res
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# return sin(pi*(phi_fp/FP_acc)/(pi_FP/FP_acc))
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def cos_FP(phi_fp):
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return sin_FP(phi_fp - pi_FP/2)
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||||
|
||||
|
||||
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()
|
||||
|
||||
|
||||
@ -201,31 +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_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()
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
Reference in New Issue
Block a user