mirror of
https://github.com/ZDoom/raze-gles.git
synced 2024-11-18 10:11:50 +00:00
328 lines
7.1 KiB
C
328 lines
7.1 KiB
C
/* 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 );
|
||
}
|