mirror of
https://github.com/ZDoom/gzdoom-gles.git
synced 2024-12-16 07:10:53 +00:00
387 lines
7.9 KiB
C
387 lines
7.9 KiB
C
/* sin.c
|
||
*
|
||
* Circular sine
|
||
*
|
||
*
|
||
*
|
||
* SYNOPSIS:
|
||
*
|
||
* double x, y, sin();
|
||
*
|
||
* y = sin( x );
|
||
*
|
||
*
|
||
*
|
||
* DESCRIPTION:
|
||
*
|
||
* Range reduction is into intervals of pi/4. The reduction
|
||
* error is nearly eliminated by contriving an extended precision
|
||
* modular arithmetic.
|
||
*
|
||
* Two polynomial approximating functions are employed.
|
||
* Between 0 and pi/4 the sine is approximated by
|
||
* x + x**3 P(x**2).
|
||
* Between pi/4 and pi/2 the cosine is represented as
|
||
* 1 - x**2 Q(x**2).
|
||
*
|
||
*
|
||
* ACCURACY:
|
||
*
|
||
* Relative error:
|
||
* arithmetic domain # trials peak rms
|
||
* DEC 0, 10 150000 3.0e-17 7.8e-18
|
||
* IEEE -1.07e9,+1.07e9 130000 2.1e-16 5.4e-17
|
||
*
|
||
* ERROR MESSAGES:
|
||
*
|
||
* message condition value returned
|
||
* sin total loss x > 1.073741824e9 0.0
|
||
*
|
||
* Partial loss of accuracy begins to occur at x = 2**30
|
||
* = 1.074e9. The loss is not gradual, but jumps suddenly to
|
||
* about 1 part in 10e7. Results may be meaningless for
|
||
* x > 2**49 = 5.6e14. The routine as implemented flags a
|
||
* TLOSS error for x > 2**30 and returns 0.0.
|
||
*/
|
||
/* cos.c
|
||
*
|
||
* Circular cosine
|
||
*
|
||
*
|
||
*
|
||
* SYNOPSIS:
|
||
*
|
||
* double x, y, cos();
|
||
*
|
||
* y = cos( x );
|
||
*
|
||
*
|
||
*
|
||
* DESCRIPTION:
|
||
*
|
||
* Range reduction is into intervals of pi/4. The reduction
|
||
* error is nearly eliminated by contriving an extended precision
|
||
* modular arithmetic.
|
||
*
|
||
* Two polynomial approximating functions are employed.
|
||
* Between 0 and pi/4 the cosine is approximated by
|
||
* 1 - x**2 Q(x**2).
|
||
* Between pi/4 and pi/2 the sine is represented as
|
||
* x + x**3 P(x**2).
|
||
*
|
||
*
|
||
* ACCURACY:
|
||
*
|
||
* Relative error:
|
||
* arithmetic domain # trials peak rms
|
||
* IEEE -1.07e9,+1.07e9 130000 2.1e-16 5.4e-17
|
||
* DEC 0,+1.07e9 17000 3.0e-17 7.2e-18
|
||
*/
|
||
|
||
/* sin.c */
|
||
|
||
/*
|
||
Cephes Math Library Release 2.8: June, 2000
|
||
Copyright 1985, 1995, 2000 by Stephen L. Moshier
|
||
*/
|
||
|
||
#include "mconf.h"
|
||
|
||
#ifdef UNK
|
||
static double sincof[] = {
|
||
1.58962301576546568060E-10,
|
||
-2.50507477628578072866E-8,
|
||
2.75573136213857245213E-6,
|
||
-1.98412698295895385996E-4,
|
||
8.33333333332211858878E-3,
|
||
-1.66666666666666307295E-1,
|
||
};
|
||
static double coscof[6] = {
|
||
-1.13585365213876817300E-11,
|
||
2.08757008419747316778E-9,
|
||
-2.75573141792967388112E-7,
|
||
2.48015872888517045348E-5,
|
||
-1.38888888888730564116E-3,
|
||
4.16666666666665929218E-2,
|
||
};
|
||
static double DP1 = 7.85398125648498535156E-1;
|
||
static double DP2 = 3.77489470793079817668E-8;
|
||
static double DP3 = 2.69515142907905952645E-15;
|
||
/* static double lossth = 1.073741824e9; */
|
||
#endif
|
||
|
||
#ifdef DEC
|
||
static unsigned short sincof[] = {
|
||
0030056,0143750,0177214,0163153,
|
||
0131727,0027455,0044510,0175352,
|
||
0033470,0167432,0131752,0042414,
|
||
0135120,0006400,0146776,0174027,
|
||
0036410,0104210,0104207,0137202,
|
||
0137452,0125252,0125252,0125103,
|
||
};
|
||
static unsigned short coscof[24] = {
|
||
0127107,0151115,0002060,0152325,
|
||
0031017,0072353,0155161,0174053,
|
||
0132623,0171173,0172542,0057056,
|
||
0034320,0006400,0147102,0023652,
|
||
0135666,0005540,0133012,0076213,
|
||
0037052,0125252,0125252,0125126,
|
||
};
|
||
/* 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
|
||
#endif
|
||
|
||
#ifdef IBMPC
|
||
static unsigned short sincof[] = {
|
||
0x9ccd,0x1fd1,0xd8fd,0x3de5,
|
||
0x1f5d,0xa929,0xe5e5,0xbe5a,
|
||
0x48a1,0x567d,0x1de3,0x3ec7,
|
||
0xdf03,0x19bf,0x01a0,0xbf2a,
|
||
0xf7d0,0x1110,0x1111,0x3f81,
|
||
0x5548,0x5555,0x5555,0xbfc5,
|
||
};
|
||
static unsigned short coscof[24] = {
|
||
0x1a9b,0xa086,0xfa49,0xbda8,
|
||
0x3f05,0x7b4e,0xee9d,0x3e21,
|
||
0x4bc6,0x7eac,0x7e4f,0xbe92,
|
||
0x44f5,0x19c8,0x01a0,0x3efa,
|
||
0x4f91,0x16c1,0xc16c,0xbf56,
|
||
0x554b,0x5555,0x5555,0x3fa5,
|
||
};
|
||
/*
|
||
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
|
||
#endif
|
||
|
||
#ifdef MIEEE
|
||
static unsigned short sincof[] = {
|
||
0x3de5,0xd8fd,0x1fd1,0x9ccd,
|
||
0xbe5a,0xe5e5,0xa929,0x1f5d,
|
||
0x3ec7,0x1de3,0x567d,0x48a1,
|
||
0xbf2a,0x01a0,0x19bf,0xdf03,
|
||
0x3f81,0x1111,0x1110,0xf7d0,
|
||
0xbfc5,0x5555,0x5555,0x5548,
|
||
};
|
||
static unsigned short coscof[24] = {
|
||
0xbda8,0xfa49,0xa086,0x1a9b,
|
||
0x3e21,0xee9d,0x7b4e,0x3f05,
|
||
0xbe92,0x7e4f,0x7eac,0x4bc6,
|
||
0x3efa,0x01a0,0x19c8,0x44f5,
|
||
0xbf56,0xc16c,0x16c1,0x4f91,
|
||
0x3fa5,0x5555,0x5555,0x554b,
|
||
};
|
||
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
|
||
#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 );
|
||
#else
|
||
double polevl(), floor(), ldexp();
|
||
int isnan(), isfinite();
|
||
#endif
|
||
extern double PIO4;
|
||
static double lossth = 1.073741824e9;
|
||
#ifdef NANS
|
||
extern double NAN;
|
||
#endif
|
||
#ifdef INFINITIES
|
||
extern double INFINITY;
|
||
#endif
|
||
|
||
|
||
double c_sin(x)
|
||
double x;
|
||
{
|
||
double y, z, zz;
|
||
int j, sign;
|
||
|
||
#ifdef MINUSZERO
|
||
if( x == 0.0 )
|
||
return(x);
|
||
#endif
|
||
#ifdef NANS
|
||
if( isnan(x) )
|
||
return(x);
|
||
if( !isfinite(x) )
|
||
{
|
||
mtherr( "sin", DOMAIN );
|
||
return(NAN);
|
||
}
|
||
#endif
|
||
/* make argument positive but save the sign */
|
||
sign = 1;
|
||
if( x < 0 )
|
||
{
|
||
x = -x;
|
||
sign = -1;
|
||
}
|
||
|
||
if( x > lossth )
|
||
{
|
||
mtherr( "sin", TLOSS );
|
||
return(0.0);
|
||
}
|
||
|
||
y = floor( x/PIO4 ); /* integer part of x/PIO4 */
|
||
|
||
/* strip high bits of integer part to prevent integer overflow */
|
||
z = ldexp( y, -4 );
|
||
z = floor(z); /* integer part of y/8 */
|
||
z = y - ldexp( z, 4 ); /* y - 16 * (y/16) */
|
||
|
||
j = (int)z; /* convert to integer for tests on the phase angle */
|
||
/* map zeros to origin */
|
||
if( j & 1 )
|
||
{
|
||
j += 1;
|
||
y += 1.0;
|
||
}
|
||
j = j & 07; /* octant modulo 360 degrees */
|
||
/* reflect in x axis */
|
||
if( j > 3)
|
||
{
|
||
sign = -sign;
|
||
j -= 4;
|
||
}
|
||
|
||
/* Extended precision modular arithmetic */
|
||
z = ((x - y * DP1) - y * DP2) - y * DP3;
|
||
|
||
zz = z * z;
|
||
|
||
if( (j==1) || (j==2) )
|
||
{
|
||
y = 1.0 - ldexp(zz,-1) + zz * zz * polevl( zz, coscof, 5 );
|
||
}
|
||
else
|
||
{
|
||
/* y = z + z * (zz * polevl( zz, sincof, 5 ));*/
|
||
y = z + z * z * z * polevl( zz, sincof, 5 );
|
||
}
|
||
|
||
if(sign < 0)
|
||
y = -y;
|
||
|
||
return(y);
|
||
}
|
||
|
||
|
||
|
||
|
||
|
||
double c_cos(x)
|
||
double x;
|
||
{
|
||
double y, z, zz;
|
||
int i;
|
||
int j, sign;
|
||
|
||
#ifdef NANS
|
||
if( isnan(x) )
|
||
return(x);
|
||
if( !isfinite(x) )
|
||
{
|
||
mtherr( "cos", DOMAIN );
|
||
return(NAN);
|
||
}
|
||
#endif
|
||
|
||
/* make argument positive */
|
||
sign = 1;
|
||
if( x < 0 )
|
||
x = -x;
|
||
|
||
if( x > lossth )
|
||
{
|
||
mtherr( "cos", TLOSS );
|
||
return(0.0);
|
||
}
|
||
|
||
y = floor( x/PIO4 );
|
||
z = ldexp( y, -4 );
|
||
z = floor(z); /* integer part of y/8 */
|
||
z = y - ldexp( z, 4 ); /* y - 16 * (y/16) */
|
||
|
||
/* integer and fractional part modulo one octant */
|
||
i = (int)z;
|
||
if( i & 1 ) /* map zeros to origin */
|
||
{
|
||
i += 1;
|
||
y += 1.0;
|
||
}
|
||
j = i & 07;
|
||
if( j > 3)
|
||
{
|
||
j -=4;
|
||
sign = -sign;
|
||
}
|
||
|
||
if( j > 1 )
|
||
sign = -sign;
|
||
|
||
/* Extended precision modular arithmetic */
|
||
z = ((x - y * DP1) - y * DP2) - y * DP3;
|
||
|
||
zz = z * z;
|
||
|
||
if( (j==1) || (j==2) )
|
||
{
|
||
/* y = z + z * (zz * polevl( zz, sincof, 5 ));*/
|
||
y = z + z * z * z * polevl( zz, sincof, 5 );
|
||
}
|
||
else
|
||
{
|
||
y = 1.0 - ldexp(zz,-1) + zz * zz * polevl( zz, coscof, 5 );
|
||
}
|
||
|
||
if(sign < 0)
|
||
y = -y;
|
||
|
||
return(y);
|
||
}
|
||
|
||
|
||
|
||
|
||
|
||
/* Degrees, minutes, seconds to radians: */
|
||
|
||
/* 1 arc second, in radians = 4.8481368110953599358991410e-5 */
|
||
#ifdef DEC
|
||
static unsigned short P648[] = {034513,054170,0176773,0116043,};
|
||
#define P64800 *(double *)P648
|
||
#else
|
||
static double P64800 = 4.8481368110953599358991410e-5;
|
||
#endif
|
||
|
||
double radian(d,m,s)
|
||
double d,m,s;
|
||
{
|
||
|
||
return( ((d*60.0 + m)*60.0 + s)*P64800 );
|
||
}
|