newlib-cygwin/newlib/libm/ld128/k_sinl.c

/* From: @(#)k_sin.c 1.3 95/01/18 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");

/*
 * ld128 version of k_sin.c.  See ../src/k_sin.c for most comments.
 */
#include <math.h>
#include "../ld/math_private.h"

static const double
half =  0.5;

/*
 * Domain [-0.7854, 0.7854], range ~[-1.53e-37, 1.659e-37]
 * |sin(x)/x - s(x)| < 2**-122.1
 *
 * See ../ld80/k_cosl.c for more details about the polynomial.
 */
static const long double
S1 = -0.16666666666666666666666666666666666606732416116558L,
S2 =  0.0083333333333333333333333333333331135404851288270047L,
S3 = -0.00019841269841269841269841269839935785325638310428717L,
S4 =  0.27557319223985890652557316053039946268333231205686e-5L,
S5 = -0.25052108385441718775048214826384312253862930064745e-7L,
S6 =  0.16059043836821614596571832194524392581082444805729e-9L,
S7 = -0.76471637318198151807063387954939213287488216303768e-12L,
S8 =  0.28114572543451292625024967174638477283187397621303e-14L;

static const double
S9  = -0.82206352458348947812512122163446202498005154296863e-17,
S10 =  0.19572940011906109418080609928334380560135358385256e-19,
S11 = -0.38680813379701966970673724299207480965452616911420e-22,
S12 =  0.64038150078671872796678569586315881020659912139412e-25;

long double
__kernel_sinl(long double x, long double y, int iy)
{
	long double z,r,v;

	z	=  x*x;
	v	=  z*x;
	r	=  S2+z*(S3+z*(S4+z*(S5+z*(S6+z*(S7+z*(S8+
	    z*(S9+z*(S10+z*(S11+z*S12)))))))));
	if(iy==0) return x+v*(S1+z*r);
	else      return x-((z*(half*y-v*r)-y)-v*S1);
}