# approximate sin and cos using continued fraction expansion
# and module decimal to set higher precision
# convergence cutoff = 5 gives module math precision
# tested with Python27  by  vegaseat

import decimal as dc
# for comparison
import math
try:
    from sympy.mpmath import *
    # set precision
    mp.dps = 60
    print(type(sin(0.5)))
    print(sin(0.5))
    print(cos(0.5))
    print('-'*62)
except:
    print("Install module SymPy from http://code.google.com/p/sympy")

def cont_fraction(r, cutoff=5):
    """
    continued fraction expansion
    higher convergence cutoff gives higher precision
    but of course makes the approximation slower
    """
    t = dc.Decimal(4)*cutoff + 2
    for k in range(cutoff, 0, -1):
        t = 4*k - 2 + dc.Decimal(r)/t
    return t

def get_sin(x, cutoff=5):
    """returns an approximation of math.sin(x)"""
    r = dc.Decimal(-x)*dc.Decimal(x)
    s = cont_fraction(r, cutoff)
    return 2*dc.Decimal(x)*s/(s*s - r)

def get_cos(x, cutoff=5):
    """returns an approximation of math.cos(x)"""
    r = dc.Decimal(-x)*dc.Decimal(x)
    s = cont_fraction(r, cutoff)
    return (s*s + r)/(s*s - r)

# set decimal precision
dc.getcontext().prec = 60

# x is angle in radians
x = 0.5

print(type(get_sin(x)))
print(get_sin(x, 20))
print(math.sin(x))
# and some cosine approximations different cutoff values
print('-'*62)
print(get_cos(x, 15))
print(get_cos(x, 20))
print(get_cos(x, 25))
print(math.cos(x))

'''
<class 'sympy.mpmath.ctx_mp_python.mpf'>
0.479425538604203000273287935215571388081803367940600675188617
0.877582561890372716116281582603829651991645197109744052997611
--------------------------------------------------------------
<class 'decimal.Decimal'>
0.479425538604203000273287935215571388081803367940600675188618
0.479425538604
--------------------------------------------------------------
0.877582561890372716116281582603829651991645197109744053008284
0.877582561890372716116281582603829651991645197109744052997610
0.877582561890372716116281582603829651991645197109744052997610
0.87758256189
'''