Python中的浮点精度

Question

I have written this function in python:

import math

def radical(a, b, k): 
    return (1-((a**2-b**2)/a**2)*(math.sin(math.pi*(2*k-1)/180))**2)**.5

def f(a, b): 
 sigma = 0 
 for k in range(1,180/4):
    sigma = sigma + radical(a, b, k)
 return 8*a*math.sin(math.pi/180)*sigma

print f(25.,35.)

When I calculate this function in Wolphramapha and Maple I will get 189.797 but with python I will get 184.91089913 What is the problem in my program?

Answer 1

You are off by one. The range method excludes the end point. Try adding one:

for k in range(1,180/4 + 1):

Result: 189.797208409

Answer 2

Well, first of all, python assumes integer division, so there is some serious round off in this code. I believe there is an import in division for this. Also, Here is some information on python's floating point arithmetic issues/problems:

http://docs.python.org/2/tutorial/floatingpoint.html