/* sinl.c
*
* Circular sine, long double precision
*
*
*
* SYNOPSIS:
*
* long double x, y, sinl();
*
* y = sinl( 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 the Cody
* and Waite polynomial form
* x + x**3 P(x**2) .
* Between pi/4 and pi/2 the cosine is represented as
* 1 - .5 x**2 + x**4 Q(x**2) .
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE +-5.5e11 200,000 1.2e-19 2.9e-20
*
* ERROR MESSAGES:
*
* message condition value returned
* sin total loss x > 2**39 0.0
*
* Loss of precision occurs for x > 2**39 = 5.49755813888e11.
* The routine as implemented flags a TLOSS error for
* x > 2**39 and returns 0.0.
*/
/* cosl.c
*
* Circular cosine, long double precision
*
*
*
* SYNOPSIS:
*
* long double x, y, cosl();
*
* y = cosl( 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 - .5 x**2 + x**4 Q(x**2) .
* Between pi/4 and pi/2 the sine is represented by the Cody
* and Waite polynomial form
* x + x**3 P(x**2) .
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE +-5.5e11 50000 1.2e-19 2.9e-20
*/
/* sin.c */
/*
Cephes Math Library Release 2.7: May, 1998
Copyright 1985, 1990, 1998 by Stephen L. Moshier
*/
#include <math.h>
#ifdef UNK
static long double sincof[7] = {
-7.5785404094842805756289E-13L,
1.6058363167320443249231E-10L,
-2.5052104881870868784055E-8L,
2.7557319214064922217861E-6L,
-1.9841269841254799668344E-4L,
8.3333333333333225058715E-3L,
-1.6666666666666666640255E-1L,
};
static long double coscof[7] = {
4.7377507964246204691685E-14L,
-1.1470284843425359765671E-11L,
2.0876754287081521758361E-9L,
-2.7557319214999787979814E-7L,
2.4801587301570552304991E-5L,
-1.3888888888888872993737E-3L,
4.1666666666666666609054E-2L,
};
static long double DP1 = 7.853981554508209228515625E-1L;
static long double DP2 = 7.946627356147928367136046290398E-9L;
static long double DP3 = 3.061616997868382943065164830688E-17L;
#endif
#ifdef IBMPC
static short sincof[] = {
0x4e27,0xe1d6,0x2389,0xd551,0xbfd6, XPD
0x64d7,0xe706,0x4623,0xb090,0x3fde, XPD
0x01b1,0xbf34,0x2946,0xd732,0xbfe5, XPD
0xc8f7,0x9845,0x1d29,0xb8ef,0x3fec, XPD
0x6514,0x0c53,0x00d0,0xd00d,0xbff2, XPD
0x569a,0x8888,0x8888,0x8888,0x3ff8, XPD
0xaa97,0xaaaa,0xaaaa,0xaaaa,0xbffc, XPD
};
static short coscof[] = {
0x7436,0x6f99,0x8c3a,0xd55e,0x3fd2, XPD
0x2f37,0x58f4,0x920f,0xc9c9,0xbfda, XPD
0x5350,0x659e,0xc648,0x8f76,0x3fe2, XPD
0x4d2b,0xf5c6,0x7dba,0x93f2,0xbfe9, XPD
0x53ed,0x0c66,0x00d0,0xd00d,0x3fef, XPD
0x7b67,0x0b60,0x60b6,0xb60b,0xbff5, XPD
0xaa9a,0xaaaa,0xaaaa,0xaaaa,0x3ffa, XPD
};
static short P1[] = {0x0000,0x0000,0xda80,0xc90f,0x3ffe, XPD};
static short P2[] = {0x0000,0x0000,0xa300,0x8885,0x3fe4, XPD};
static short P3[] = {0x3707,0xa2e0,0x3198,0x8d31,0x3fc8, XPD};
#define DP1 *(long double *)P1
#define DP2 *(long double *)P2
#define DP3 *(long double *)P3
#endif
#ifdef MIEEE
static long sincof[] = {
0xbfd60000,0xd5512389,0xe1d64e27,
0x3fde0000,0xb0904623,0xe70664d7,
0xbfe50000,0xd7322946,0xbf3401b1,
0x3fec0000,0xb8ef1d29,0x9845c8f7,
0xbff20000,0xd00d00d0,0x0c536514,
0x3ff80000,0x88888888,0x8888569a,
0xbffc0000,0xaaaaaaaa,0xaaaaaa97,
};
static long coscof[] = {
0x3fd20000,0xd55e8c3a,0x6f997436,
0xbfda0000,0xc9c9920f,0x58f42f37,
0x3fe20000,0x8f76c648,0x659e5350,
0xbfe90000,0x93f27dba,0xf5c64d2b,
0x3fef0000,0xd00d00d0,0x0c6653ed,
0xbff50000,0xb60b60b6,0x0b607b67,
0x3ffa0000,0xaaaaaaaa,0xaaaaaa9a,
};
static long P1[] = {0x3ffe0000,0xc90fda80,0x00000000};
static long P2[] = {0x3fe40000,0x8885a300,0x00000000};
static long P3[] = {0x3fc80000,0x8d313198,0xa2e03707};
#define DP1 *(long double *)P1
#define DP2 *(long double *)P2
#define DP3 *(long double *)P3
#endif
static long double lossth = 5.49755813888e11L; /* 2^39 */
extern long double PIO4L;
#ifdef ANSIPROT
extern long double polevll ( long double, void *, int );
extern long double floorl ( long double );
extern long double ldexpl ( long double, int );
extern int isnanl ( long double );
extern int isfinitel ( long double );
#else
long double polevll(), floorl(), ldexpl(), isnanl(), isfinitel();
#endif
#ifdef INFINITIES
extern long double INFINITYL;
#endif
#ifdef NANS
extern long double NANL;
#endif
long double sinl(x)
long double x;
{
long double y, z, zz;
int j, sign;
#ifdef NANS
if( isnanl(x) )
return(x);
#endif
#ifdef MINUSZERO
if( x == 0.0L )
return(x);
#endif
#ifdef NANS
if( !isfinitel(x) )
{
mtherr( "sinl", DOMAIN );
#ifdef NANS
return(NANL);
#else
return(0.0L);
#endif
}
#endif
/* make argument positive but save the sign */
sign = 1;
if( x < 0 )
{
x = -x;
sign = -1;
}
if( x > lossth )
{
mtherr( "sinl", TLOSS );
return(0.0L);
}
y = floorl( x/PIO4L ); /* integer part of x/PIO4 */
/* strip high bits of integer part to prevent integer overflow */
z = ldexpl( y, -4 );
z = floorl(z); /* integer part of y/8 */
z = y - ldexpl( z, 4 ); /* y - 16 * (y/16) */
j = z; /* convert to integer for tests on the phase angle */
/* map zeros to origin */
if( j & 1 )
{
j += 1;
y += 1.0L;
}
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 = 1.0L - ldexpl(zz,-1) + zz * zz * polevll( zz, coscof, 6 );
}
else
{
y = z + z * (zz * polevll( zz, sincof, 6 ));
}
if(sign < 0)
y = -y;
return(y);
}
long double cosl(x)
long double x;
{
long double y, z, zz;
long i;
int j, sign;
#ifdef NANS
if( isnanl(x) )
return(x);
#endif
#ifdef INFINITIES
if( !isfinitel(x) )
{
mtherr( "cosl", DOMAIN );
#ifdef NANS
return(NANL);
#else
return(0.0L);
#endif
}
#endif
/* make argument positive */
sign = 1;
if( x < 0 )
x = -x;
if( x > lossth )
{
mtherr( "cosl", TLOSS );
return(0.0L);
}
y = floorl( x/PIO4L );
z = ldexpl( y, -4 );
z = floorl(z); /* integer part of y/8 */
z = y - ldexpl( z, 4 ); /* y - 16 * (y/16) */
/* integer and fractional part modulo one octant */
i = z;
if( i & 1 ) /* map zeros to origin */
{
i += 1;
y += 1.0L;
}
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 * polevll( zz, sincof, 6 ));
}
else
{
y = 1.0L - ldexpl(zz,-1) + zz * zz * polevll( zz, coscof, 6 );
}
if(sign < 0)
y = -y;
return(y);
}