/* @(#)k_sin.c 5.1 93/09/24 */

/*

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

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

 *

 * Developed at SunPro, a Sun Microsystems, Inc. business.

 * Permission to use, copy, modify, and distribute this

 * software is freely granted, provided that this notice

 * is preserved.

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

 */

#if defined(LIBM_SCCS) && !defined(lint)

static const char rcsid[] =

    "$NetBSD: k_sin.c,v 1.8 1995/05/10 20:46:31 jtc Exp $";

#endif

/* __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 "math.h"

#include "math_private.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 attribute_hidden

__kernel_sin(double x, double y, int iy)

#else

double attribute_hidden

__kernel_sin(x, y, iy)

     double x, y;

     int iy;                    /* iy=0 if y is zero */

#endif

{

    double z, r, v;

    int32_t ix;

    GET_HIGH_WORD(ix, x);

    ix &= 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);

}