gistfile1.txt

import math

sintable = [int(math.sin(x*math.pi/512)*32768+32768) for x in range(256)]

def fp_sin(a):
  """Fixed point sine. Input range is [0-2^16), output range likewise."""
  a = a & 0xffff
  quadrant = a >> 14
  index = (a >> 6) & 0xff
  if quadrant == 1 or quadrant == 3:
    index = 255 - index
  value = sintable[index]
  if quadrant == 2 or quadrant == 3:
    value = 65535 - value
  return value

# >>> sum(abs(math.sin(x*math.pi/5000) - table_sin(x*math.pi/5000, fp_sin)) for x in range(10000))
# 19.536966968379307

def fp_sin_lin(a):
  """Fixed point sine. Input range is [0-2^16), output range likewise."""
  a = a & 0xffff
  quadrant = a >> 14
  index = (a >> 6) & 0xff
  remainder = a & 0x3f
  if quadrant == 1 or quadrant == 3:
    index = 255 - index
  value = sintable[index]
  if index < 255:
    value += ((sintable[index + 1] - value) * remainder) >> 6
  if quadrant == 2 or quadrant == 3:
    value = 65535 - value
  return value

# >>> sum(abs(math.sin(x*math.pi/5000) - table_sin(x*math.pi/5000, fp_sin_lin)) for x in range(10000))
# 9.992061405676871

def fp_sin_cos(a):
  """Fixed point sine. Input range is [0-2^16), output range likewise."""
  a = a & 0xffff
  quadrant = a >> 14
  index = (a >> 6) & 0xff
  remainder = a & 0x3f
  if quadrant == 1 or quadrant == 3:
    index = 255 - index
  value = sintable[index]
  value += (sintable[255 - index] * remainder) >> 16
  if quadrant == 2 or quadrant == 3:
    value = 65535 - value
  return value

# >>> sum(abs(math.sin(x*math.pi/5000) - table_sin(x*math.pi/5000, fp_sin_cos)) for x in range(10000))
# 14.54198779195309

def table_sin(a, fun):
  """Implements sine using fp_sin, without interpolation"""
  idx = int(a / math.pi * 32768)
  return fun(idx) / 32768.0 - 1