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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.
`````` * ====================================================
`````` */
``````
``````//#include <sys/cdefs.h>
``````//__FBSDID("\$FreeBSD\$");
``````
``````/* 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 <float.h>
``````
``````#include "math_private.h"
``````
``````static const double atanhi[] = {
``````  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 */
``````};
``````
``````static const double atanlo[] = {
``````  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 */
``````};
``````
``````static const double aT[] = {
``````  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 */
``````};
``````
``````	static const double
``````one   = 1.0,
``````huge   = 1.0e300;
``````
``````double
``````atan(double x)
``````{
``````	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 */
``````	    u_int32_t low;
``````	    GET_LOW_WORD(low,x);
``````	    if(ix>0x7ff00000||
``````		(ix==0x7ff00000&&(low!=0)))
``````		return x+x;		/* NaN */
``````	    if(hx>0) return  atanhi[3]+*(volatile double *)&atanlo[3];
``````	    else     return -atanhi[3]-*(volatile double *)&atanlo[3];
``````	} if (ix < 0x3fdc0000) {	/* |x| < 0.4375 */
``````	    if (ix < 0x3e400000) {	/* |x| < 2^-27 */
``````		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;
``````	}
``````}
``````