NAME

__cospi — cosine-pi function

SYNOPSIS

#include <math.h>

float
__cospif(float x);

double
__cospi(double x);

DESCRIPTION

The __cospi() function returns the cosine of pi times x (measured in radians). This can be computed more accurately than cos(M_PI * x), because it can implicitly use as many bits of pi as are necessary to deliver a well-rounded result, instead of the 53-bits to which M_PI is limited. For large x it may also be more efficient, as the argument reduction involved is significantly simpler.

This function may be especially useful for working with degrees; whereas cos(M_PI * x / 180.0) cannot produce exact results for angles that naively "should" be exact, like 90 degrees, __cospi(x / 180.0) can be computed exactly.

SPECIAL VALUES

__cospi(-x) is the same as __cospi(x) for any finite x.
__cospi(n) returns +1 for any even integer n.
__cospi(n) returns -1 for any odd integer n.
__cospi(n + 0.5) returns +0 for any integer n.
__cospi(±infinity) raises the invalid floating-point exception and returns NaN.

VECTOR OPERATIONS

If you need to apply the __cospi() function to SIMD vectors or arrays, using the following functions provided by the Accelerate.framework may be useful:

#include <Accelerate/Accelerate.h>

vFloat vcospif(vFloat x);
void vvcospif(float *y, const float *x, const int *n);
void vvcospi(double *y, const double *x, const int *n);

SEE ALSO

__sinpi(3), __tanpi(3), __sincospi(3), math(3)