added phase calculation (dummy, always return 0) in imagery2abs. Added FFT_Re, FFT_Im dumping to the output file. Possible issue: phase of simple sin is -1.

C/FFT_FP_realisation.c

@@ -0,0 +1,88 @@
+#include "FFT_FP_realisation.h"
+
+#include <math.h>
+#include <stdio.h>
+
+static int64_t twiddle_re[TWIDDLE_L] = {0,};
+static int64_t twiddle_im[TWIDDLE_L] = {0,};
+
+void fft_fp_prepare(void){
+	for (uint32_t k = 0; k < TWIDDLE_L; ++k){
+		double angle = 2.0 * PI * k / DATA_L;
+		twiddle_re[k] = lround(cos(angle) * FP_acc);
+		twiddle_im[k] = lround(-sin(angle) * FP_acc);
+		printf("k, angle, tw_re, tw_im: %u %g %lld %lld\n", k, angle, (long long)twiddle_re[k], (long long)twiddle_im[k]);
+	}
+}
+
+void FFT_fp(int64_t* inp, uint32_t inp_L, int64_t* buf){
+
+	    // buf имеет длину inp_L * 2 (Re, Im, Re, Im, ...)
+	    // inp содержит inp_L значений uint32_t
+
+	    uint32_t i, j, bit;
+//	    uint32_t N = inp_L / 2;  // длина комплексного массива (inp содержит только Re-часть)
+	    uint32_t N = inp_L;  // длина комплексного массива (inp содержит только Re-часть)
+
+	    // --- копирование входных данных в буфер ---
+	    for (i = 0; i < inp_L; i++) {
+	        buf[i * 2]     = inp[i];
+	        buf[i * 2 + 1] = 0;
+	    }
+
+	    // --- bit-reversal перестановка ---
+	    j = 0;
+	    for (i = 1; i < N; i++) {
+	        bit = N >> 1;
+	        while (j & bit) {
+	            j ^= bit;
+	            bit >>= 1;
+	        }
+	        j |= bit;
+	        if (i < j) {
+	            int64_t tmp_re = buf[i * 2];
+	            int64_t tmp_im = buf[i * 2 + 1];
+	            buf[i * 2]     = buf[j * 2];
+	            buf[i * 2 + 1] = buf[j * 2 + 1];
+	            buf[j * 2]     = tmp_re;
+	            buf[j * 2 + 1] = tmp_im;
+	        }
+	    }
+
+	    // --- уровни бабочек ---
+	    uint32_t m = 2;
+	    while (m <= N) {
+	        uint32_t half = m >> 1;
+	        uint32_t stride = N / m;
+
+	        for (uint32_t start = 0; start < N; start += m) {
+            for (uint32_t k = 0; k < half; k++) {
+                uint32_t tw_idx = k * stride;
+                int64_t wr = twiddle_re[tw_idx];
+                int64_t wi = twiddle_im[tw_idx];
+                int64_t u_re = buf[(start + k) * 2];
+                int64_t u_im = buf[(start + k) * 2 + 1];
+                int64_t v_re = buf[(start + k + half) * 2];
+                int64_t v_im = buf[(start + k + half) * 2 + 1];
+
+	                // t = w * v  (в фиксированной точке)
+	                int64_t t_re = (wr * v_re - wi * v_im) / FP_acc;
+	                int64_t t_im = (wr * v_im + wi * v_re) / FP_acc;
+
+	                // верх/низ
+	                buf[(start + k) * 2]              = u_re + t_re;
+	                buf[(start + k) * 2 + 1]          = u_im + t_im;
+	                buf[(start + k + half) * 2]       = u_re - t_re;
+	                buf[(start + k + half) * 2 + 1]   = u_im - t_im;
+
+            }
+        }
+        m <<= 1;
+    }
+	    for (uint32_t ii = 0; ii < inp_L; ++ii){
+	    	buf[ii*2] /= inp_L;
+	    	buf[ii*2+1] /= inp_L;
+	    	printf("re,im: %lld, %lld\n", (long long)buf[ii*2], (long long)buf[ii*2 +1]);
+	    }
+
+}

C/FFT_FP_realisation.h

@@ -0,0 +1,25 @@
+#ifndef FFT_FP_REALISATION_H
+#define FFT_FP_REALISATION_H
+
+#include <stdint.h>
+
+#ifndef DATA_L
+#define DATA_L (1 << 16)
+#endif
+
+#ifndef FP_acc
+#define FP_acc 1000
+#endif
+
+#ifndef TWIDDLE_L
+#define TWIDDLE_L (DATA_L / 2)
+#endif
+
+#ifndef PI
+#define PI 3.141592653589793238462643383279502884197169399375105820974944
+#endif
+
+void fft_fp_prepare(void);
+void FFT_fp(int64_t* inp, uint32_t inp_L, int64_t* buf);
+
+#endif

C/FFT_realistaion.h

@@ -0,0 +1,24 @@
+#include <string.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <stdint.h>
+#include <math.h>
+
+#define DATA_L (1<<17)
+#define FP_acc (1 << 10)
+#define TWIDDLE_L (DATA_L / 2)
+
+#define PI 3.141592653589793238462643383279502884197169399375105820974944
+
+int64_t twiddle_re[TWIDDLE_L] = {0,};
+int64_t twiddle_im[TWIDDLE_L] = {0,};
+
+void FFT_fp(int64_t* inp, uint32_t inp_L, int64_t* buf){
+
+}
+
+void twiddle_fill(int64_t* tw_re, int64_t* tw_im, uint32_t N){
+
+}
+
+

C/FFT_test.c

@@ -0,0 +1 @@
+ 

C/FP_math.c

@@ -0,0 +1,62 @@
+#include <string.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <stdint.h>
+#include <math.h>
+
+#define DATA_L (1<<16)
+#define FP_acc 1000
+
+#include "FFT_FP_realisation.h"
+
+
+void imagery2abs(int64_t* inp, uint32_t inp_L, int64_t *out_abs, int64_t *out_phase){
+	printf("+++++++++++++++++++++\n");
+	printf("calculating abs^2\n");
+	for (uint32_t i = 0; i < inp_L; ++i){
+		int64_t re = inp[i*2];
+		int64_t im = inp[i*2 +1];
+		int64_t val = (re * re + im * im) / FP_acc;
+		int64_t phase = 0;
+		printf("%lld, %ldd\n", (long long)val, (long long) phase);
+		out_abs[i] = val;
+		out_phase[i] = phase;
+
+	}
+}
+void data_generator(int64_t* X, int64_t* Y, uint32_t N){
+	for (int i = 0; i < N; ++i){
+		X[i] = (int64_t)i;
+		Y[i] = lround(sin(((double)i)*2.0* PI/(N/10))*FP_acc);
+		Y[i] += lround(cos(((double)i)*2.0* PI/(N/20))*FP_acc);
+		Y[i] += 1*FP_acc;
+	}
+}
+
+void main(){
+	char* logfilename = "tmp";
+	int64_t data_X[DATA_L] = {0,};
+	int64_t data_Y[DATA_L] = {0,};
+	int64_t data_res_FFT_imag[DATA_L*2] = {0,};
+	int64_t data_res_FFT_abs[DATA_L] = {0,};
+	int64_t data_res_FFT_phase[DATA_L] = {0,};
+
+
+	fft_fp_prepare();
+
+	data_generator(data_X, data_Y, DATA_L);
+
+
+	FFT_fp(data_Y, DATA_L, data_res_FFT_imag);
+
+
+	imagery2abs(data_res_FFT_imag, DATA_L, data_res_FFT_abs, data_res_FFT_phase);
+
+	FILE *logfile_ptr;
+    logfile_ptr = fopen(logfilename, "w");
+    fprintf(logfile_ptr, "X, Y, FFT_val, FFT_phase, FFT_Re, FFT_Im\n");
+	for (uint32_t i = 0; i < DATA_L; ++i){
+		fprintf(logfile_ptr, "%lld, %lg, %lg, %lg, %lg, %lg\n", (long long)data_X[i], ((double)data_Y[i])/(double)FP_acc , (double)data_res_FFT_abs[i]/(double)FP_acc, (double)data_res_FFT_phase[i]/(double)FP_acc,  (double)data_res_FFT_imag[2*i]/(double)FP_acc,  (double)data_res_FFT_imag[2*i +1]/(double)FP_acc     );
+	}
+	fclose(logfile_ptr);
+}

C/FP_math.c_backup

@@ -0,0 +1,152 @@
+#include <string.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <stdint.h>
+#include <math.h>
+
+#define DATA_L 1024
+#define FP_acc 1000
+
+#define PI 3.141592653589793238462643383279502884197169399375105820974944
+
+
+
+int cos_delta_FP_arr[DATA_L] = {0,};
+int sin_delta_FP_arr[DATA_L] = {0,};
+
+void FFT_fp(uint32_t* inp, uint32_t inp_L, uint32_t* buf){
+
+	    // buf имеет длину inp_L * 2 (Re, Im, Re, Im, ...)
+	    // inp содержит inp_L значений uint32_t
+
+	    uint32_t i, j, bit;
+//	    uint32_t N = inp_L / 2;  // длина комплексного массива (inp содержит только Re-часть)
+	    uint32_t N = inp_L;  // длина комплексного массива (inp содержит только Re-часть)
+
+	    // --- копирование входных данных в буфер ---
+	    for (i = 0; i < inp_L; i++) {
+	        buf[i * 2]     = (int)inp[i];  // Re
+	        buf[i * 2 + 1] = 0;            // Im = 0
+	    }
+
+	    // --- bit-reversal перестановка ---
+	    j = 0;
+	    for (i = 1; i < N; i++) {
+	        bit = N >> 1;
+	        while (j & bit) {
+	            j ^= bit;
+	            bit >>= 1;
+	        }
+	        j |= bit;
+	        if (i < j) {
+	            int tmp_re = buf[i * 2];
+	            int tmp_im = buf[i * 2 + 1];
+	            buf[i * 2]     = buf[j * 2];
+	            buf[i * 2 + 1] = buf[j * 2 + 1];
+	            buf[j * 2]     = tmp_re;
+	            buf[j * 2 + 1] = tmp_im;
+	        }
+	    }
+
+	    // --- уровни бабочек ---
+	    uint32_t m = 2;
+	    while (m <= N) {
+	        uint32_t half = m >> 1;
+
+	        int c_delta_FP = cos_delta_FP_arr[m - 2];
+	        int s_delta_FP = sin_delta_FP_arr[m - 2];
+
+	        for (uint32_t start = 0; start < N; start += m) {
+	            int wr = FP_acc;
+	            int wi = 0;
+
+	            for (uint32_t k = 0; k < half; k++) {
+	                int u_re = buf[(start + k) * 2];
+	                int u_im = buf[(start + k) * 2 + 1];
+	                int v_re = buf[(start + k + half) * 2];
+	                int v_im = buf[(start + k + half) * 2 + 1];
+
+	                // t = w * v  (в фиксированной точке)
+	                int64_t t_re = ((int64_t)wr * v_re - (int64_t)wi * v_im) / FP_acc;
+	                int64_t t_im = ((int64_t)wr * v_im + (int64_t)wi * v_re) / FP_acc;
+
+	                // верх/низ
+	                buf[(start + k) * 2]              = u_re + (int)t_re;
+	                buf[(start + k) * 2 + 1]          = u_im + (int)t_im;
+	                buf[(start + k + half) * 2]       = u_re - (int)t_re;
+	                buf[(start + k + half) * 2 + 1]   = u_im - (int)t_im;
+
+	                // w *= w_m (обновление twiddle)
+	                int64_t wr_new = ((int64_t)wr * c_delta_FP - (int64_t)wi * s_delta_FP) / FP_acc;
+	                int64_t wi_new = ((int64_t)wr * s_delta_FP + (int64_t)wi * c_delta_FP) / FP_acc;
+	                wr = (int)wr_new;
+	                wi = (int)wi_new;
+	            }
+	        }
+	        m <<= 1;
+	    }
+	    for (uint32_t i = 0; i < inp_L; ++i){
+	    	//buf[i*2] /= inp_L;
+	    	//buf[i*2+1] /= inp_L;
+	    	printf("re,im: %d, %d\n", buf[i*2], buf[i*2 +1]);
+	    }
+
+}
+
+void imagery2abs(uint32_t* inp, uint32_t inp_L, uint32_t *out){
+	printf("+++++++++++++++++++++\n");
+	printf("calculating abs^2\n");
+	for (uint32_t i = 0; i < inp_L; ++i){
+		int val = (inp[i*2]*inp[i*2] + inp[i*2 +1]*inp[i*2 +1])/FP_acc;
+		printf("%d\n", val);
+		out[i] = val;
+	}
+}
+
+
+
+void sin_cos_filler(int* sin_arr, int* cos_arr, uint32_t L){
+	//[int(-sin(2.0 * pi / m) * FP_acc) for m in range(2,inp_L//2 + 2)]
+	for (uint32_t i = 0; i < L; ++i){
+		int m = i + 2;
+		double angle = 2.0* PI/m;
+		sin_arr[i] = lround(-sin(angle) * FP_acc);
+		cos_arr[i] = lround(cos(angle) * FP_acc);
+		printf("i, angle, sin, cos: %d %g %d %d\n", i, angle, sin_arr[i], cos_arr[i]);
+	}
+}
+
+void data_generator(uint32_t* X, uint32_t* Y, uint32_t N){
+	for (int i = 0; i < N; ++i){
+		X[i] = (int) i;
+		Y[i] = lround(sin(((double)i)*2.0* PI/(N/10))*FP_acc);
+//		Y[I] += 10*FP_acc;
+	}
+}
+
+void main(){
+	char* logfilename = "tmp";
+	uint32_t data_X[DATA_L] = {0,};
+	uint32_t data_Y[DATA_L] = {0,};
+	uint32_t data_res_FFT_imag[DATA_L*2] = {0,};
+	uint32_t data_res_FFT_abs[DATA_L] = {0,};
+
+	sin_cos_filler(sin_delta_FP_arr, cos_delta_FP_arr, DATA_L);
+
+	data_generator(data_X, data_Y, DATA_L);
+
+
+	FFT_fp(data_Y, DATA_L, data_res_FFT_imag);
+
+
+	imagery2abs(data_res_FFT_imag, DATA_L, data_res_FFT_abs);
+
+	FILE *logfile_ptr;
+    logfile_ptr = fopen(logfilename, "w");
+    fprintf(logfile_ptr, "X, Y, FFT\n");
+	for (uint32_t i = 0; i < DATA_L; ++i){
+		fprintf(logfile_ptr, "%d, %d, %d \n", data_X[i], data_Y[i],data_res_FFT_abs[i]);
+	}
+	fclose(logfile_ptr);
+}
+

C/Makefile

@@ -0,0 +1,14 @@
+SRCS := FP_math.c FFT_FP_realisation.c
+OBJS := $(SRCS:.c=.o)
+TARGET := FP_math
+
+all: $(TARGET)
+
+$(TARGET): $(OBJS)
+	gcc $(OBJS) -o $@ -lm
+
+%.o: %.c
+	gcc -c $< -o $@
+
+clean:
+	-rm -f $(TARGET) $(OBJS)

C/plotter.py

@@ -0,0 +1,57 @@
+#!/usr/bin/pypy3
+import plotly.graph_objs as go
+from decimal import *
+from sys import argv
+import csv
+
+
+def main():
+  chart = go.Figure()
+  chart.add_trace(go.Scatter(x=[1,2,3], y=[1,2,3]))
+  chart.show()
+
+
+if __name__ == "__main__":
+  if len(argv) == 1:
+    main()
+  else:
+    f = open(argv[1], "rt")
+    #csv_reader = csv.reader(f)
+    data = {}
+#    for line in csv_reader:
+    headers = f.readline()
+    headers = headers.split(",")
+    headers[-1] = headers[-1][:-1]
+    for i in range(len(headers)):
+      headers[i] = headers[i].strip()
+    for header in headers:
+      data[header] = []
+    for line in f:
+      try:
+        line_data = line.split(",")
+        #line_data = line
+        #print(line_data)
+        for i in range(len(line_data)):
+          val = float(line_data[i])
+          if (i < len(headers)):
+            header = headers[i]
+            data[header].append(val)
+          else:
+            print("too much values!")
+            print("headers:", headers)
+            print("values:", line_data)
+      except ValueError:
+        pass
+    f.close()
+#    print(data)
+    chart = go.Figure()
+    keys = [k for k in data.keys()]
+#    print("data.keys:", keys)
+    X_name = keys[0]
+    print("data samples:",len(data[X_name]))
+    for key, val in data.items():
+      if key != X_name:
+#        chart.add_trace(go.Scatter(x=data[X_name], y=val, name=key, mode="markers+lines"))
+        chart.add_trace(go.Scatter(x=data[X_name], y=val, name=key, mode="lines"))
+    chart.show()
+

FFT.py

@@ -1,5 +1,5 @@
 import numpy as np
-
+from math import sin, cos, pi, sqrt
 
 
 
@@ -12,21 +12,315 @@ def FFT_backup(inp):
 
 
 def FFT_real(inp):
-  inp = np.array(inp)
-  out = FFT(inp)
-  out = [val for val in np.abs(out)]
-  print(out)
+  
+  mode = 3
+  if (mode == 0):
+    inp = np.array(inp)
+    out = FFT_np(inp)
+    out = [np.abs(val) for val in out]
+  if (mode == 1): # simple with recursion
+    
+    out = FFT_arr([[val, 0] for val  in inp])
+    #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]
+#    out = [2 for val in out]
+  if (mode == 2): #no internal buffs
+  
+    tmp = []
+    for re in inp:
+      tmp.append(re)
+      tmp.append(0)
+      
+    out = FFT_arr_inplace(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]
+    
+  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
 
 
 def FFT(inp):
+  return FFT_arr([[val, 0] for val  in inp])
+
+def FFT_np(inp):
+  print("inp:", inp)
   inp = np.array(inp)
   N = inp.shape[0]
   if N == 1:
     return inp
-  X_even = FFT(inp[::2])
-  X_odd  = FFT(inp[1::2])
+  X_even = FFT_np(inp[::2])
+  X_odd  = FFT_np(inp[1::2])
   k = np.arange(N // 2)
   tw = np.exp(-2j * np.pi * k / N) * X_odd
   return np.concatenate((X_even + tw, X_even - tw))
 
+def FFT_arr(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(x[::2])
+  X_odd = FFT_arr(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
+
+
+
+
+def FFT_arr_inplace(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.
+    """
+
+  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 = cos(2.0 * math.pi / m)
+    s_delta = -sin(2.0 * math.pi / m)
+
+    for start in range(0, N, m):
+      # w = e^{-j*0*Δ} = 1 + j0
+      wr, wi = 1.0, 0.0
+      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
+        t_im = wr * v_im + wi * v_re
+
+        # 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 - wi * s_delta, wr * s_delta + wi * c_delta
+
+    m <<= 1
+  return buf
+
+
+
+
+
+
+
+
+
+
+FP_acc = 2<<16
+
+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 ---
+  
+  c_delta_FP_arr = [cos(2.0 * pi / m) * FP_acc for m in range(2,N+2)]
+  s_delta_FP_arr = [-sin(2.0 * pi / m) * FP_acc for m in range(2,N+2)]
+  m = 2
+  while m <= N:
+    half = m // 2
+    # шаг угла Δ = 2π/m, базовый твиддл w_m = e^{-jΔ} => (cw, sw)
+    print("N, m:", N,m)
+    
+    c_delta_FP = c_delta_FP_arr[m -2]
+    s_delta_FP = s_delta_FP_arr[m -2]
+    #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
+
+#global arrays. calculated once at compile time. They store sin and cos values as fixed-point
+  c_delta_FP_arr = [int(cos(2.0 * pi / m) * FP_acc) for m in range(2,inp_L//2 + 2)]
+  s_delta_FP_arr = [int(-sin(2.0 * pi / m) * FP_acc) for m in range(2, inp_L//2 + 2)]
+
+def FFT_arr_FP_for_C(inp, inp_L, buf): #version for translation to C directly
+  """
+    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]
+  for i in range(inp_L):
+    buf[i*2] = inp[i] #take data from input as real and store it to the buf as Re, Im pairs.
+    buf[i*2 + 1] = 0
+
+  N = inp_L//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 ---
+  
+  c_delta_FP_arr = [cos(2.0 * pi / m) * FP_acc for m in range(2,N+2)]
+  s_delta_FP_arr = [-sin(2.0 * pi / m) * FP_acc for m in range(2,N+2)]
+  m = 2
+  while m <= N:
+    half = m // 2
+    # шаг угла Δ = 2π/m, базовый твиддл w_m = e^{-jΔ} => (cw, sw)
+    #print("N, m:", N,m)
+    
+    c_delta_FP = c_delta_FP_arr[m -2]
+    s_delta_FP = s_delta_FP_arr[m -2]
+    #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
+    
+
+
+
+
+
+
+
+
+
+
+

FP_trigonometry.py

@@ -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()
+  
+  
+  
+  
+  
+  
+  
+  
+  

naive_DFT.py

@@ -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)):
@@ -37,101 +32,10 @@ def DFT_naive(inp, out):
       val_im += inp[n] * cos(phi) /INP_L
       
     val_abs = abs_f(val_re, val_im)
-    print("F, val_abs:",f, val_abs)
+    #print("F, val_abs:",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):
@@ -148,7 +52,7 @@ def DFT_naive_FP(inp_float, out):
       val_im += inp[n] * phi_cos /INP_L
       
     val_abs = abs_FP(val_re, val_im)
-    print("F, val_abs:",f, val_abs)
+    #print("F, val_abs:",f, val_abs)
     out[f] = val_abs
   
 
@@ -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()
-