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raze-gles/source/common/thirdparty/math/tan.c

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- migrated to GZDoom's utility code.
2020-04-11 21:50:43 +00:00
/* tan.c
*
* Circular tangent
*
*
*
* SYNOPSIS:
*
* double x, y, tan();
*
* y = tan( x );
*
*
*
* DESCRIPTION:
*
* Returns the circular tangent of the radian argument x.
*
* Range reduction is modulo pi/4. A rational function
* x + x**3 P(x**2)/Q(x**2)
* is employed in the basic interval [0, pi/4].
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC +-1.07e9 44000 4.1e-17 1.0e-17
* IEEE +-1.07e9 30000 2.9e-16 8.1e-17
*
* ERROR MESSAGES:
*
* message condition value returned
* tan total loss x > 1.073741824e9 0.0
*
*/
/* cot.c
*
* Circular cotangent
*
*
*
* SYNOPSIS:
*
* double x, y, cot();
*
* y = cot( x );
*
*
*
* DESCRIPTION:
*
* Returns the circular cotangent of the radian argument x.
*
* Range reduction is modulo pi/4. A rational function
* x + x**3 P(x**2)/Q(x**2)
* is employed in the basic interval [0, pi/4].
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE +-1.07e9 30000 2.9e-16 8.2e-17
*
*
* ERROR MESSAGES:
*
* message condition value returned
* cot total loss x > 1.073741824e9 0.0
* cot singularity x = 0 INFINITY
*
*/
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1995, 2000 by Stephen L. Moshier
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
1. Redistributions of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
3. Neither the name of the <ORGANIZATION> nor the names of its
contributors may be used to endorse or promote products derived from
this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE.
*/
#include "mconf.h"
#ifdef UNK
static double P[] = {
-1.30936939181383777646E4,
1.15351664838587416140E6,
-1.79565251976484877988E7
};
static double Q[] = {
/* 1.00000000000000000000E0,*/
1.36812963470692954678E4,
-1.32089234440210967447E6,
2.50083801823357915839E7,
-5.38695755929454629881E7
};
static double DP1 = 7.853981554508209228515625E-1;
static double DP2 = 7.94662735614792836714E-9;
static double DP3 = 3.06161699786838294307E-17;
static double lossth = 1.073741824e9;
#endif
#ifdef DEC
static unsigned short P[] = {
0143514,0113306,0111171,0174674,
0045214,0147545,0027744,0167346,
0146210,0177526,0114514,0105660
};
static unsigned short Q[] = {
/*0040200,0000000,0000000,0000000,*/
0043525,0142457,0072633,0025617,
0145241,0036742,0140525,0162256,
0046276,0146176,0013526,0143573,
0146515,0077401,0162762,0150607
};
/* 7.853981629014015197753906250000E-1 */
static unsigned short P1[] = {0040111,0007732,0120000,0000000,};
/* 4.960467869796758577649598009884E-10 */
static unsigned short P2[] = {0030410,0055060,0100000,0000000,};
/* 2.860594363054915898381331279295E-18 */
static unsigned short P3[] = {0021523,0011431,0105056,0001560,};
#define DP1 *(double *)P1
#define DP2 *(double *)P2
#define DP3 *(double *)P3
static double lossth = 1.073741824e9;
#endif
#ifdef IBMPC
static unsigned short P[] = {
0x3f38,0xd24f,0x92d8,0xc0c9,
0x9ddd,0xa5fc,0x99ec,0x4131,
0x9176,0xd329,0x1fea,0xc171
};
static unsigned short Q[] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0x6572,0xeeb3,0xb8a5,0x40ca,
0xbc96,0x582a,0x27bc,0xc134,
0xd8ef,0xc2ea,0xd98f,0x4177,
0x5a31,0x3cbe,0xafe0,0xc189
};
/*
7.85398125648498535156E-1,
3.77489470793079817668E-8,
2.69515142907905952645E-15,
*/
static unsigned short P1[] = {0x0000,0x4000,0x21fb,0x3fe9};
static unsigned short P2[] = {0x0000,0x0000,0x442d,0x3e64};
static unsigned short P3[] = {0x5170,0x98cc,0x4698,0x3ce8};
#define DP1 *(double *)P1
#define DP2 *(double *)P2
#define DP3 *(double *)P3
static double lossth = 1.073741824e9;
#endif
#ifdef MIEEE
static unsigned short P[] = {
0xc0c9,0x92d8,0xd24f,0x3f38,
0x4131,0x99ec,0xa5fc,0x9ddd,
0xc171,0x1fea,0xd329,0x9176
};
static unsigned short Q[] = {
0x40ca,0xb8a5,0xeeb3,0x6572,
0xc134,0x27bc,0x582a,0xbc96,
0x4177,0xd98f,0xc2ea,0xd8ef,
0xc189,0xafe0,0x3cbe,0x5a31
};
static unsigned short P1[] = {
0x3fe9,0x21fb,0x4000,0x0000
};
static unsigned short P2[] = {
0x3e64,0x442d,0x0000,0x0000
};
static unsigned short P3[] = {
0x3ce8,0x4698,0x98cc,0x5170,
};
#define DP1 *(double *)P1
#define DP2 *(double *)P2
#define DP3 *(double *)P3
static double lossth = 1.073741824e9;
#endif
#ifdef ANSIPROT
extern double polevl ( double, void *, int );
extern double p1evl ( double, void *, int );
extern double floor ( double );
extern double ldexp ( double, int );
extern int isnan ( double );
extern int isfinite ( double );
static double tancot(double, int);
#else
double polevl(), p1evl(), floor(), ldexp();
static double tancot();
int isnan(), isfinite();
#endif
extern double PIO4;
extern double INFINITY;
extern double NAN;
double c_tan(x)
double x;
{
#ifdef MINUSZERO
if( x == 0.0 )
return(x);
#endif
#ifdef NANS
if( isnan(x) )
return(x);
if( !isfinite(x) )
{
mtherr( "tan", DOMAIN );
return(NAN);
}
#endif
return( tancot(x,0) );
}
double c_cot(x)
double x;
{
if( x == 0.0 )
{
mtherr( "cot", SING );
return( INFINITY );
}
return( tancot(x,1) );
}
static double tancot( xx, cotflg )
double xx;
int cotflg;
{
double x, y, z, zz;
int j, sign;
/* make argument positive but save the sign */
if( xx < 0 )
{
x = -xx;
sign = -1;
}
else
{
x = xx;
sign = 1;
}
if( x > lossth )
{
if( cotflg )
mtherr( "cot", TLOSS );
else
mtherr( "tan", TLOSS );
return(0.0);
}
/* compute x mod PIO4 */
y = floor( x/PIO4 );
/* strip high bits of integer part */
z = ldexp( y, -3 );
z = floor(z); /* integer part of y/8 */
z = y - ldexp( z, 3 ); /* y - 16 * (y/16) */
/* integer and fractional part modulo one octant */
j = (int)z;
/* 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( zz > 1.0e-14 )
y = z + z * (zz * polevl( zz, P, 2 )/p1evl(zz, Q, 4));
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 );
}
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