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__TANPI(3)               BSD Library Functions Manual               __TANPI(3)

NAME
     __tanpi -- tangent-pi function

SYNOPSIS
     #include <math.h>

     float
     __tanpif(float x);

     double
     __tanpi(double x);

DESCRIPTION
     The __tanpi() function returns the tangent of pi times x (measured in radians).  This can be computed
     more accurately than tan(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 tan(M_PI * x / 18_._) cannot
     produce exact results for angles that naively "should" be exact, like 90 degrees, __tanpi(x / 18_._)
     can be computed exactly.

SPECIAL VALUES
     __tanpi(-x) is the same as - __tanpi(x) for any finite x.
     __tanpi(+-_) returns +-0.
     __tanpi(n) returns +0 for any positive even integer n.
     __tanpi(n) returns -0 for any positive odd integer n.
     __tanpi(n + _.5) returns +infinity for any even integer n.
     __tanpi(n + _.5) returns -infinity for any odd integer n.
     __tanpi(+-infinity) raises the invalid floating-point exception and returns NaN.

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

     #include <Accelerate/Accelerate.h>

     vFloat vtanpif(vFloat x);
     void vvtanpif(float *y, float *x, const int n);
     void vvtanpi(double *y, double *x, const int n);

SEE ALSO
     __cospi(3), __sinpi(3), __sincospi(3), math(3)

BSD                            December 15, 2012                           BSD