(Term0 + Term1 - Term2 + Term3) How can I do the alternating plus minus?

potsky · 08-22-2009, 07:08 AM

I am working on a problem involving Taylor's Series of cosine x and sine x. (cosx = 1 - (x^2/2!) + (x^4/4!) - ...)
My only problem is how I can do the alternating plus minus on each term. This is the code I currently have in which I can't still figure out if it is right or wrong.

double cosine(double x)
{
int n, ctr;
double cos;

cos = 0;
n = 2*NUMBER_OF_TERMS;
ctr = NUMBER_OF_TERMS;
while(ctr > 0)
{
ctr--;
cos = cos + (RaiseTo(x, n)/factorial(n));
cos *= -1;
n -= 2;
}
return cos;
}

*Note: We were only allowed to use stdio.h as the header file.

cyberfish · 08-22-2009, 09:04 AM

Code:

if (term % 2 == 0) {
x *= -1;
}

or, if you want to avoid a branch

Code:

double sign = 1;
while (...) {
     x *= sign;
     sign *= -1;
}

Not sure which one would be faster.

Elysia · 08-23-2009, 08:52 AM

x *= -1 is also the same as x = -x. The latter would probably be faster in terms of instructions, but a good compiler will probably optimize it.
However, be sure to read this: << !! Posting Code? Read this First !! >>

08-22-2009, 07:08 AM	#1
potsky Registered User Join Date: Aug 2009 Posts: 1	(Term0 + Term1 - Term2 + Term3) How can I do the alternating plus minus? I am working on a problem involving Taylor's Series of cosine x and sine x. (cosx = 1 - (x^2/2!) + (x^4/4!) - ...) My only problem is how I can do the alternating plus minus on each term. This is the code I currently have in which I can't still figure out if it is right or wrong. double cosine(double x) { int n, ctr; double cos; cos = 0; n = 2NUMBER_OF_TERMS; ctr = NUMBER_OF_TERMS; while(ctr > 0) { ctr--; cos = cos + (RaiseTo(x, n)/factorial(n)); cos = -1; n -= 2; } return cos; } *Note: We were only allowed to use stdio.h as the header file.
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08-22-2009, 09:04 AM	#2
cyberfish Registered User Join Date: Dec 2006 Location: Canada Posts: 2,003	Code: if (term % 2 == 0) { x = -1; } or, if you want to avoid a branch Code: double sign = 1; while (...) { x = sign; sign *= -1; } Not sure which one would be faster.
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