gistfile1.py

#!/usr/bin/python
# -*- coding: utf-8 -*-

'''
    e^x, e^-x, cos x をテイラー展開を用いて計算する。
'''

import math


factorial = lambda x: x * factorial(x - 1) if x > 1 else 1
sign = lambda i: 1 if i >= 0 else -1


def mycos(x, limit=200):
    '''
        テイラー展開を用いて x(ラジアン)から cos を求める
        cos x = Σ (-1)^0 / (2n)! * x^2n
    '''
    def monomial(x, limit):
        value = 1
        for n in xrange(1, limit, 2):
            yield value
            value = -value * x * x / (n * (n + 1))
    x = x % (2 * math.pi)
    return sum(monomial(x, limit))


def myexp(x, limit=200):
    '''
        テイラー展開を用いて e^x を求める
        e^x = Σ (x^n / n!)
        e^-x = 1.0 / e^x
    '''
    def monomial(x, limit):
        value = 1.0
        for n in xrange(1, limit):
            yield value
            value = value * x / n
    return sum(monomial(abs(x), limit)) ** sign(x)


def main():
    for x in xrange(-40, 41, 10):
        print '%5.1f%14.6g%14.6g' % (x, myexp(x), math.exp(x))

    for x in xrange(0, 91):
        xrad = math.radians(x)
        c1, c2 = mycos(xrad), math.cos(xrad)
        diff = c1 - c2
        print '%d: %f, %f : [%2.5e]' % (x, c1, c2, diff)


if __name__ == '__main__':
    main()