__cospi(3) [osx man page]

__COSPI(3)						   BSD Library Functions Manual 						__COSPI(3)

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

SEE ALSO

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

BSD
								 December 15, 2012							       BSD

__SINPI(3)						   BSD Library Functions Manual 						__SINPI(3)

NAME

     __sinpi -- sine-pi function

SYNOPSIS

     #include <math.h>

     float
     __sinpif(float x);

     double
     __sinpi(double x);

DESCRIPTION

     The __sinpi() function returns the sine of pi times x (measured in radians).  This can be computed more accurately than sin(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 sin(M_PI * x / 180.0) cannot produce exact results for angles that
     naively "should" be exact, like 180 degrees, __sinpi(x / 180.0) can be computed exactly.

SPECIAL VALUES

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

VECTOR OPERATIONS

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

     #include <Accelerate/Accelerate.h>

     vFloat vsinpif(vFloat x);
     void vvsinpif(float *y, float *x, const int n);
     void vvsinpi(double *y, double *x, const int n);

SEE ALSO

     __cospi(3), __tanpi(3), __sincospi(3), math(3)

BSD
								 December 15, 2012							       BSD