Subversion Repositories or1k

/* @(#)k_tan.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 char rcsid[] = "$NetBSD: k_tan.c,v 1.8 1995/05/10 20:46:37 jtc Exp $";

#endif

/* __kernel_tan( x, y, k )

 * kernel tan 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 k indicates whether tan (if k=1) or

 * -1/tan (if k= -1) is returned.

 *

 * Algorithm

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

 *      2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0.

 *      3. tan(x) is approximated by a odd polynomial of degree 27 on

 *         [0,0.67434]

 *                               3             27

 *              tan(x) ~ x + T1*x + ... + T13*x

 *         where

 *

 *              |tan(x)         2     4            26   |     -59.2

 *              |----- - (1+T1*x +T2*x +.... +T13*x    )| <= 2

 *              |  x                                    |

 *

 *         Note: tan(x+y) = tan(x) + tan'(x)*y

 *                        ~ tan(x) + (1+x*x)*y

 *         Therefore, for better accuracy in computing tan(x+y), let

 *                   3      2      2       2       2

 *              r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))

 *         then

 *                                  3    2

 *              tan(x+y) = x + (T1*x + (x *(r+y)+y))

 *

 *      4. For x in [0.67434,pi/4],  let y = pi/4 - x, then

 *              tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))

 *                     = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))

 */

#include "math.h"

#include "math_private.h"

#ifdef __STDC__

static const double

#else

static double

#endif

one   =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */

pio4  =  7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */

pio4lo=  3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */

T[] =  {

  3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */

  1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */

  5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */

  2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */

  8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */

  3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */

  1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */

  5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */

  2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */

  7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */

  7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */

 -1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */

  2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */

};

#ifdef __STDC__

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

#else

        double __kernel_tan(x, y, iy)

        double x,y; int iy;

#endif

{

        double z,r,v,w,s;

        int32_t ix,hx;

        GET_HIGH_WORD(hx,x);

        ix = hx&0x7fffffff;     /* high word of |x| */

        if(ix<0x3e300000)                       /* x < 2**-28 */

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

                u_int32_t low;

                GET_LOW_WORD(low,x);

                if(((ix|low)|(iy+1))==0) return one/fabs(x);

                else return (iy==1)? x: -one/x;

            }

            }

        if(ix>=0x3FE59428) {                    /* |x|>=0.6744 */

            if(hx<0) {x = -x; y = -y;}

            z = pio4-x;

            w = pio4lo-y;

            x = z+w; y = 0.0;

        }

        z       =  x*x;

        w       =  z*z;

    /* Break x^5*(T[1]+x^2*T[2]+...) into

     *    x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +

     *    x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))

     */

        r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));

        v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));

        s = z*x;

        r = y + z*(s*(r+v)+y);

        r += T[0]*s;

        w = x+r;

        if(ix>=0x3FE59428) {

            v = (double)iy;

            return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r)));

        }

        if(iy==1) return w;

        else {          /* if allow error up to 2 ulp,

                           simply return -1.0/(x+r) here */

     /*  compute -1.0/(x+r) accurately */

            double a,t;

            z  = w;

            SET_LOW_WORD(z,0);

            v  = r-(z - x);     /* z+v = r+x */

            t = a  = -1.0/w;    /* a = -1.0/w */

            SET_LOW_WORD(t,0);

            s  = 1.0+t*z;

            return t+a*(s+t*v);

        }

}