diff --git a/FFT.py b/FFT.py
index 59c7884..c2cef32 100644
--- a/FFT.py
+++ b/FFT.py
@@ -13,12 +13,12 @@ def FFT_backup(inp):
 
 def FFT_real(inp):
   
-  mode = 2
+  mode = 3
   if (mode == 0):
     inp = np.array(inp)
     out = FFT_np(inp)
     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 = [val for val in np.abs(out)]
@@ -26,7 +26,7 @@ def FFT_real(inp):
     print("output:", out)
     out = [sqrt(val[0]**2 + val[1]**2) for val in out]
 #    out = [2 for val in out]
-  if (mode == 2):
+  if (mode == 2): #no internal buffs
   
     tmp = []
     for re in inp:
@@ -43,10 +43,32 @@ def FFT_real(inp):
     
     #out = [val for val in np.abs(out)]
     print("FFT_calculated!")
-    print("output:", out)
+    #print("output:", 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
 
 
@@ -97,8 +119,6 @@ def FFT_arr(x):
 
 
 
-import math
-
 def FFT_arr_inplace(buf):
   """
     In-place radix-2 DIT FFT для списка buf длины N=2^m, где каждый элемент — [re, im].
@@ -159,51 +179,74 @@ def FFT_arr_inplace(buf):
 
 
 
+FP_acc = 1e3
 
-
-
-
-
-
-
-
-
-
-
-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
+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
     
-    
-    
-    
-    
-    
-    
\ No newline at end of file
+  buf = [val/ FP_acc for val in buf] 
+  return buf
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/FP_trigonometry.py b/FP_trigonometry.py
new file mode 100755
index 0000000..9476a9d
--- /dev/null
+++ b/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()
+  
+  
+  
+  
+  
+  
+  
+  
+  
\ No newline at end of file
diff --git a/__pycache__/FFT.cpython-312.pyc b/__pycache__/FFT.cpython-312.pyc
index 396ab2e..4a1791b 100644
Binary files a/__pycache__/FFT.cpython-312.pyc and b/__pycache__/FFT.cpython-312.pyc differ
diff --git a/__pycache__/FP_trigonometry.cpython-312.pyc b/__pycache__/FP_trigonometry.cpython-312.pyc
new file mode 100644
index 0000000..7474dc9
Binary files /dev/null and b/__pycache__/FP_trigonometry.cpython-312.pyc differ
diff --git a/naive_DFT.py b/naive_DFT.py
index 6b3b917..a7b119f 100755
--- a/naive_DFT.py
+++ b/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)):
@@ -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()
-  
-  
+