k_sin.c

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/* @(#)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_libm.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);
}