/*							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, 1998Copyright 1985, 1990, 1998 by Stephen L. Moshier*/#include <math.h>#ifdef UNKstatic 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 IBMPCstatic short sincof[] = {0x4e27,0xe1d6,0x2389,0xd551,0xbfd6, XPD0x64d7,0xe706,0x4623,0xb090,0x3fde, XPD0x01b1,0xbf34,0x2946,0xd732,0xbfe5, XPD0xc8f7,0x9845,0x1d29,0xb8ef,0x3fec, XPD0x6514,0x0c53,0x00d0,0xd00d,0xbff2, XPD0x569a,0x8888,0x8888,0x8888,0x3ff8, XPD0xaa97,0xaaaa,0xaaaa,0xaaaa,0xbffc, XPD};static short coscof[] = {0x7436,0x6f99,0x8c3a,0xd55e,0x3fd2, XPD0x2f37,0x58f4,0x920f,0xc9c9,0xbfda, XPD0x5350,0x659e,0xc648,0x8f76,0x3fe2, XPD0x4d2b,0xf5c6,0x7dba,0x93f2,0xbfe9, XPD0x53ed,0x0c66,0x00d0,0xd00d,0x3fef, XPD0x7b67,0x0b60,0x60b6,0xb60b,0xbff5, XPD0xaa9a,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 MIEEEstatic 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#endifstatic long double lossth = 5.49755813888e11L; /* 2^39 */extern long double PIO4L;#ifdef ANSIPROTextern 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 );#elselong double polevll(), floorl(), ldexpl(), isnanl(), isfinitel();#endif#ifdef INFINITIESextern long double INFINITYL;#endif#ifdef NANSextern long double NANL;#endiflong double sinl(x)long double x;{long double y, z, zz;int j, sign;#ifdef NANSif( isnanl(x) )	return(x);#endif#ifdef MINUSZEROif( x == 0.0L )	return(x);#endif#ifdef NANSif( !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 NANSif( isnanl(x) )	return(x);#endif#ifdef INFINITIESif( !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);}