created and debugged precise fixed-pint sin and cos

naive_DFT.py

@@ -3,7 +3,7 @@ from math import sin, cos, pi, sqrt
 import plotly.graph_objs as go
 from plotly.subplots import make_subplots
 
-FP_acc = 1e2
+FP_acc = 1e3
 
 INP_L = 1000
 
@@ -20,6 +20,10 @@ def abs_f(re, 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)):
@@ -39,9 +43,90 @@ def abs_FP(re, im):
 #  return sqrt(re*re + im*im)
   return int(sqrt(re*re + im*im))
 
+trigon_debug = 0
 
 def sin_FP(phi_fp):
-  return sin(pi*(phi_fp/FP_acc)/(pi_FP/FP_acc))
+  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 = 1
+
+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)
@@ -54,8 +139,11 @@ def DFT_naive_FP(inp_float, out):
     val_im = 0
     for n in range(len(inp)):
       phi = 2*pi_FP*f*n/INP_L
-      val_re += inp[n] * sin_FP(phi) /INP_L
-      val_im += inp[n] * cos_FP(phi) /INP_L
+      phi_sin = sin_FP(phi)
+      phi_cos = cos_FP(phi)
+      print(phi, phi_sin, phi_cos)
+      val_re += inp[n] * phi_sin /INP_L
+      val_im += inp[n] * phi_cos /INP_L
       
     val_abs = abs_FP(val_re, val_im)
     print("F, val_abs:",f, val_abs)
@@ -82,16 +170,23 @@ def main():
 
 
 def sin_tester():
-  N = 400
-  angs = [(N/2 - i)/100 for i in range(N)]
+  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))
-    res_FP.append(sin_FP(phi*FP_acc*pi_FP))
+#    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=res_f, name="sin_FP", 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()