s_sin.c

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/* @(#)s_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: s_sin.c,v 1.7 1995/05/10 20:48:15 jtc Exp $";
#endif

/* sin(x)
 * Return sine function of x.
 *
 * kernel function:
 *  __kernel_sin    ... sine function on [-pi/4,pi/4]
 *  __kernel_cos    ... cose function on [-pi/4,pi/4]
 *  __ieee754_rem_pio2  ... argument reduction routine
 *
 * Method.
 *      Let S,C and T denote the sin, cos and tan respectively on
 *  [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
 *  in [-pi/4 , +pi/4], and let n = k mod 4.
 *  We have
 *
 *          n        sin(x)      cos(x)        tan(x)
 *     ----------------------------------------------------------
 *      0        S     C     T
 *      1        C    -S    -1/T
 *      2       -S    -C     T
 *      3       -C     S    -1/T
 *     ----------------------------------------------------------
 *
 * Special cases:
 *      Let trig be any of sin, cos, or tan.
 *      trig(+-INF)  is NaN, with signals;
 *      trig(NaN)    is that NaN;
 *
 * Accuracy:
 *  TRIG(x) returns trig(x) nearly rounded
 */

#include "math_libm.h"
#include "math_private.h"

libm_hidden_proto(sin)
#ifdef __STDC__
     double sin(double x)
#else
     double sin(x)
     double x;
#endif
{
    double y[2], z = 0.0;
    int32_t n, ix;

    /* High word of x. */
    GET_HIGH_WORD(ix, x);

    /* |x| ~< pi/4 */
    ix &= 0x7fffffff;
    if (ix <= 0x3fe921fb)
        return __kernel_sin(x, z, 0);

    /* sin(Inf or NaN) is NaN */
    else if (ix >= 0x7ff00000)
        return x - x;

    /* argument reduction needed */
    else {
        n = __ieee754_rem_pio2(x, y);
        switch (n & 3) {
        case 0:
            return __kernel_sin(y[0], y[1], 1);
        case 1:
            return __kernel_cos(y[0], y[1]);
        case 2:
            return -__kernel_sin(y[0], y[1], 1);
        default:
            return -__kernel_cos(y[0], y[1]);
        }
    }
}

libm_hidden_def(sin)