sin, cos, tan and rounding error

Question

I\'m doing some trigonometry calculations in C/C++ and am running into problems with rounding errors. For example, on my Linux system:

#include 

        

Answer 1

I rather think that will be system-dependent. I don't think the Standard has anything to say on how accurate the transcendental functions will be. Unfortunately, I don't remember seeing any discussion of function precision, so you'll probably have to figure it out yourself.

Answer 2

The answer is only 0 for sin(pi) - did you include all the digits of Pi ?

-Has anyone else noticed a distinct lack of, irony/sense of humour around here?

Answer 3

I get the exact same result on my system - I'd say it is close enough

I would solve the problem by changing the format string to "%f\n" :)

However, this gives you a "better" result, or at least on my system it does give -3.661369e-245

#include <stdio.h>
#include <math.h>

int main(int argc, char *argv[]) {
    printf("%e\n", (long double)sin(M_PI));
    return 0;
}

Answer 4

Sine of π is 0.0.
Sine of M_PI is about 1.224647e-16.

M_PI is not π.

program gives ... 1.224647e-16 when the correct answer is of course 0.

Code gave a correct answer to 7 places.

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The following does not print the sine of π. It prints the sine of a number close to π. See below pic.

π                            // 3.1415926535897932384626433832795...
printf("%.21\n", M_PI);      // 3.141592653589793115998
printf("%.21f\n", sin(M_PI));// 0.000000000000000122465

Note: With the math function sine(x), the slope of the curve is -1.0 at x = π. The difference of π and M_PI is about the sin(M_PI) - as expected.

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am running into problems with rounding errors

The rounding problem occurs when using M_PI to present π. M_PI is the double closest to π, yet since π is irrational and all finite double are rational, they must differ - even by a small amount. So not a direct rounding issue with sin(), cos(), tan(). sin(M_PI) simple exposed the issue started with using an inexact π.

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This problem, with different non-zero results of sin(M_PI), occurs if code used a different FP type like float, long double or double with something other than 53 binary bits of precision. This is not a precision issue so much as a irrational/rational one.

Answer 5

Maybe too low accuracy of implementation

M_PI = 3.14159265358979323846 (20 digits)

http://fresh2refresh.com/c/c-function/c-math-h-library-functions/

Answer 6

There are two sources of error. The sin() function and the approximated value of M_PI. Even if the sin() function were 'perfect', it would not return zero unless the value of M_PI were also perfect - which it is not.