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/* @(#)s_atan.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.

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

 *

 */

/*

FUNCTION

        <<atan>>, <<atanf>>---arc tangent

INDEX

   atan

INDEX

   atanf

ANSI_SYNOPSIS

        #include <math.h>

        double atan(double <[x]>);

        float atanf(float <[x]>);

TRAD_SYNOPSIS

        #include <math.h>

        double atan(<[x]>);

        double <[x]>;

        float atanf(<[x]>);

        float <[x]>;

DESCRIPTION

<<atan>> computes the inverse tangent (arc tangent) of the input value.

<<atanf>> is identical to <<atan>>, save that it operates on <<floats>>.

RETURNS

@ifnottex

<<atan>> returns a value in radians, in the range of -pi/2 to pi/2.

@end ifnottex

@tex

<<atan>> returns a value in radians, in the range of $-\pi/2$ to $\pi/2$.

@end tex

PORTABILITY

<<atan>> is ANSI C.  <<atanf>> is an extension.

*/

/* atan(x)

 * Method

 *   1. Reduce x to positive by atan(x) = -atan(-x).

 *   2. According to the integer k=4t+0.25 chopped, t=x, the argument

 *      is further reduced to one of the following intervals and the

 *      arctangent of t is evaluated by the corresponding formula:

 *

 *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)

 *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )

 *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )

 *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )

 *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )

 *

 * Constants:

 * The hexadecimal values are the intended ones for the following

 * constants. The decimal values may be used, provided that the

 * compiler will convert from decimal to binary accurately enough

 * to produce the hexadecimal values shown.

 */

#include "fdlibm.h"

#ifndef _DOUBLE_IS_32BITS

#ifdef __STDC__

static const double atanhi[] = {

#else

static double atanhi[] = {

#endif

  4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */

  7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */

  9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */

  1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */

};

#ifdef __STDC__

static const double atanlo[] = {

#else

static double atanlo[] = {

#endif

  2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */

  3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */

  1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */

  6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */

};

#ifdef __STDC__

static const double aT[] = {

#else

static double aT[] = {

#endif

  3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */

 -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */

  1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */

 -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */

  9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */

 -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */

  6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */

 -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */

  4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */

 -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */

  1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */

};

#ifdef __STDC__

        static const double

#else

        static double

#endif

one   = 1.0,

huge   = 1.0e300;

#ifdef __STDC__

        double atan(double x)

#else

        double atan(x)

        double x;

#endif

{

        double w,s1,s2,z;

        __int32_t ix,hx,id;

        GET_HIGH_WORD(hx,x);

        ix = hx&0x7fffffff;

        if(ix>=0x44100000) {    /* if |x| >= 2^66 */

            __uint32_t low;

            GET_LOW_WORD(low,x);

            if(ix>0x7ff00000||

                (ix==0x7ff00000&&(low!=0)))

                return x+x;             /* NaN */

            if(hx>0) return  atanhi[3]+atanlo[3];

            else     return -atanhi[3]-atanlo[3];

        } if (ix < 0x3fdc0000) {        /* |x| < 0.4375 */

            if (ix < 0x3e200000) {      /* |x| < 2^-29 */

                if(huge+x>one) return x;        /* raise inexact */

            }

            id = -1;

        } else {

        x = fabs(x);

        if (ix < 0x3ff30000) {          /* |x| < 1.1875 */

            if (ix < 0x3fe60000) {      /* 7/16 <=|x|<11/16 */

                id = 0; x = (2.0*x-one)/(2.0+x);

            } else {                    /* 11/16<=|x|< 19/16 */

                id = 1; x  = (x-one)/(x+one);

            }

        } else {

            if (ix < 0x40038000) {      /* |x| < 2.4375 */

                id = 2; x  = (x-1.5)/(one+1.5*x);

            } else {                    /* 2.4375 <= |x| < 2^66 */

                id = 3; x  = -1.0/x;

            }

        }}

    /* end of argument reduction */

        z = x*x;

        w = z*z;

    /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */

        s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));

        s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));

        if (id<0) return x - x*(s1+s2);

        else {

            z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);

            return (hx<0)? -z:z;

        }

}

#endif /* _DOUBLE_IS_32BITS */