sin.c

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/*
 * (c) copyright 1988 by the Vrije Universiteit, Amsterdam, The Netherlands.
 * See the copyright notice in the ACK home directory, in the file "Copyright".
 *
 * Author: Ceriel J.H. Jacobs
 */
/* $Header: /opt/proj/minix/cvsroot/src/lib/math/sin.c,v 1.1.1.1 2005/04/21 14:56:26 beng Exp $ */

#include        <math.h>
#include        <float.h>
#include        <errno.h>
#include        "localmath.h"

static double
sinus(double x, int cos_flag)
{
        /*      Algorithm and coefficients from:
                        "Software manual for the elementary functions"
                        by W.J. Cody and W. Waite, Prentice-Hall, 1980
        */

        static double r[] = {
                -0.16666666666666665052e+0,
                 0.83333333333331650314e-2,
                -0.19841269841201840457e-3,
                 0.27557319210152756119e-5,
                -0.25052106798274584544e-7,
                 0.16058936490371589114e-9,
                -0.76429178068910467734e-12,
                 0.27204790957888846175e-14
        };

        double  y;
        int     neg = 1;

        if (__IsNan(x)) {
                errno = EDOM;
                return x;
        }
        if (x < 0) {
                x = -x;
                neg = -1;
        }
        if (cos_flag) {
                neg = 1;
                y = M_PI_2 + x;
        }
        else    y = x;

        /* ??? avoid loss of significance, if y is too large, error ??? */

        y = y * M_1_PI + 0.5;

        if (y >= DBL_MAX/M_PI) return 0.0;

        /*      Use extended precision to calculate reduced argument.
                Here we used 12 bits of the mantissa for a1.
                Also split x in integer part x1 and fraction part x2.
        */
#define A1 3.1416015625
#define A2 -8.908910206761537356617e-6
        {
                double x1, x2;

                modf(y, &y);
                if (modf(0.5*y, &x1)) neg = -neg;
                if (cos_flag) y -= 0.5;
                x2 = modf(x, &x1);
                x = x1 - y * A1;
                x += x2;
                x -= y * A2;
#undef A1
#undef A2
        }
 
        if (x < 0) {
                neg = -neg;
                x = -x;
        }

        /* ??? avoid underflow ??? */

        y = x * x;
        x += x * y * POLYNOM7(y, r);
        return neg==-1 ? -x : x;
}

double
sin(double x)
{
        return sinus(x, 0);
}

double
cos(double x)
{
        if (x < 0) x = -x;
        return sinus(x, 1);
}

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