power series expansion for sine function

Question

import math


def sine_func(x):
    power = 0
    sine = x
    add = (-1)**(power)*(x**(2*power+1))/(math.factorial((2*power+1)))
    while math.fabs(add) > 1.0e-8:
        sine += add        
        power += 1
        add == (-1)**(power)*(x**2*power+1)/(math.factorial((2*power+1)))

return sine

print(sine_func(1))

Program is just running forever, any thoughts on where I made my error?

... and perhaps that last "`==`" should be something else? ... and sine() vs sine_func()? Sounds like this isn't actually your code.. — Andrew Jaffe, Jan 28 '14 at 14:46
oops, thanks, i changed some variable names to make for easier readability on the forums, but still produces the same problem though — Brian, Jan 28 '14 at 14:46
Why would I remove the "==", i want to set add equal to that — Brian, Jan 28 '14 at 14:47
I couldn't make the code run OOTB ... and add seems to always be one. — hochl, Jan 28 '14 at 14:47
I made some changes for easier readability because i had to have long ass names for class, i think i fixed all the naming errors though — Brian, Jan 28 '14 at 14:48
Actually, repeatedly calculating the power and factorial is not a good idea, it would be better to remember the actual value of them and simply adjust them for each iteration. This will save tons of calculation time. Additionally [see this answer](http://stackoverflow.com/a/345117/589206). — hochl, Jan 28 '14 at 15:19
Thanks, I'll take a look at that. We have to use power series approximation though — Brian, Jan 28 '14 at 15:25
Just compared my version to yours and it performs 25% faster, so the speedup is modest. Still a speedup :) [both versions use a Taylor series]. — hochl, Jan 28 '14 at 15:48

score 3 · Answer 1 · answered Jan 28 '14 at 14:46

This line:

add_ == (-1)**(power_int)*(x**2*power_int+1))/(math.factorial((2*power_int+1)))

Neither refers to the previous variable ("add" != "add_") nor assigns any value - == is comparison in Python, not assignment. Try:

add = (-1)**(power_int)*(x**2*power_int+1))/(math.factorial((2*power_int+1)))

score 0 · Accepted Answer · answered Jan 28 '14 at 14:57

Your code is running fine for me (Python 3.3.3), after fixing the brackets and the initialization as sine=0.

import math

def sine_func(x):
    power = 0
    sine = 0
    add = (-1)**(power)*(x**(2*power+1))/(math.factorial((2*power+1)))
    while math.fabs(add) > 1.0e-8:
        sine += add        
        power += 1
        add = (-1)**(power)*(x**(2*power+1))/(math.factorial((2*power+1)))
return sine

power series expansion for sine function

2 Answers2