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/* tanf.c
*
* Circular tangent
*
*
*
* SYNOPSIS:
*
* float x, y, tanf();
*
* y = tanf( x );
*
*
*
* DESCRIPTION:
*
* Returns the circular tangent of the radian argument x.
*
* Range reduction is modulo pi/4. A polynomial approximation
* is employed in the basic interval [0, pi/4].
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE +-4096 100000 3.3e-7 4.5e-8
*
* ERROR MESSAGES:
*
* message condition value returned
* tanf total loss x > 2^24 0.0
*
*/
/* cotf.c
*
* Circular cotangent
*
*
*
* SYNOPSIS:
*
* float x, y, cotf();
*
* y = cotf( x );
*
*
*
* DESCRIPTION:
*
* Returns the circular cotangent of the radian argument x.
* A common routine computes either the tangent or cotangent.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE +-4096 100000 3.0e-7 4.5e-8
*
*
* ERROR MESSAGES:
*
* message condition value returned
* cot total loss x > 2^24 0.0
* cot singularity x = 0 MAXNUMF
*
*/
/*
Cephes Math Library Release 2.2: June, 1992
Copyright 1984, 1987, 1989 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
/* Single precision circular tangent
* test interval: [-pi/4, +pi/4]
* trials: 10000
* peak relative error: 8.7e-8
* rms relative error: 2.8e-8
*/
#include <math.h>
extern float MAXNUMF;
static float DP1 = 0.78515625;
static float DP2 = 2.4187564849853515625e-4;
static float DP3 = 3.77489497744594108e-8;
float FOPI = 1.27323954473516; /* 4/pi */
static float lossth = 8192.;
/*static float T24M1 = 16777215.;*/
static float tancotf( float xx, int cotflg )
{
float x, y, z, zz;
long j;
int sign;
/* make argument positive but save the sign */
if( xx < 0.0 )
{
x = -xx;
sign = -1;
}
else
{
x = xx;
sign = 1;
}
if( x > lossth )
{
if( cotflg )
mtherr( "cotf", TLOSS );
else
mtherr( "tanf", TLOSS );
return(0.0);
}
/* compute x mod PIO4 */
j = FOPI * x; /* integer part of x/(PI/4) */
y = j;
/* map zeros and singularities to origin */
if( j & 1 )
{
j += 1;
y += 1.0;
}
z = ((x - y * DP1) - y * DP2) - y * DP3;
zz = z * z;
if( x > 1.0e-4 )
{
/* 1.7e-8 relative error in [-pi/4, +pi/4] */
y =
((((( 9.38540185543E-3 * zz
+ 3.11992232697E-3) * zz
+ 2.44301354525E-2) * zz
+ 5.34112807005E-2) * zz
+ 1.33387994085E-1) * zz
+ 3.33331568548E-1) * zz * z
+ z;
}
else
{
y = z;
}
if( j & 2 )
{
if( cotflg )
y = -y;
else
y = -1.0/y;
}
else
{
if( cotflg )
y = 1.0/y;
}
if( sign < 0 )
y = -y;
return( y );
}
float tanf( float x )
{
return( tancotf(x,0) );
}
float cotf( float x )
{
if( x == 0.0 )
{
mtherr( "cotf", SING );
return( MAXNUMF );
}
return( tancotf(x,1) );
}
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