/* @(#)k_sin.c 1.3 95/01/18 */

/*

 * ====================================================

 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.

 *

 * 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.

 * ====================================================

 */

/* __kernel_sin( x, y, iy)

 * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854

 * Input x is assumed to be bounded by ~pi/4 in magnitude.

 * Input y is the tail of x.

 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). 

 *

 * Algorithm

 *	1. Since sin(-x) = -sin(x), we need only to consider positive x. 

 *	2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.

 *	3. sin(x) is approximated by a polynomial of degree 13 on

 *	   [0,pi/4]

 *		  	         3            13

 *	   	sin(x) ~ x + S1*x + ... + S6*x

 *	   where

 *	

 * 	|sin(x)         2     4     6     8     10     12  |     -58

 * 	|----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2

 * 	|  x 					           | 

 * 

 *	4. sin(x+y) = sin(x) + sin'(x')*y

 *		    ~ sin(x) + (1-x*x/2)*y

 *	   For better accuracy, let 

 *		     3      2      2      2      2

 *		r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))

 *	   then                   3    2

 *		sin(x) = x + (S1*x + (x *(r-y/2)+y))

 */

#include "fdlibm.h"

#ifdef __STDC__

static const double 

#else

static double 

#endif

half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */

S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */

S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */

S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */

S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */

S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */

S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */

#ifdef __STDC__

	double __kernel_sin(double x, double y, int iy)

#else

	double __kernel_sin(x, y, iy)

	double x,y; int iy;		/* iy=0 if y is zero */

#endif

{

	double z,r,v;

	int ix;

	ix = __HI(x)&0x7fffffff;	/* high word of x */

	if(ix<0x3e400000)			/* |x| < 2**-27 */

	   {if((int)x==0) return x;}		/* generate inexact */

	z	=  x*x;

	v	=  z*x;

	r	=  S2+z*(S3+z*(S4+z*(S5+z*S6)));

	if(iy==0) return x+v*(S1+z*r);

	else      return x-((z*(half*y-v*r)-y)-v*S1);

}