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s_atan.c
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00001 /* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
00002  *
00003  * ***** BEGIN LICENSE BLOCK *****
00004  * Version: MPL 1.1/GPL 2.0/LGPL 2.1
00005  *
00006  * The contents of this file are subject to the Mozilla Public License Version
00007  * 1.1 (the "License"); you may not use this file except in compliance with
00008  * the License. You may obtain a copy of the License at
00009  * http://www.mozilla.org/MPL/
00010  *
00011  * Software distributed under the License is distributed on an "AS IS" basis,
00012  * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
00013  * for the specific language governing rights and limitations under the
00014  * License.
00015  *
00016  * The Original Code is Mozilla Communicator client code, released
00017  * March 31, 1998.
00018  *
00019  * The Initial Developer of the Original Code is
00020  * Sun Microsystems, Inc.
00021  * Portions created by the Initial Developer are Copyright (C) 1998
00022  * the Initial Developer. All Rights Reserved.
00023  *
00024  * Contributor(s):
00025  *
00026  * Alternatively, the contents of this file may be used under the terms of
00027  * either of the GNU General Public License Version 2 or later (the "GPL"),
00028  * or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
00029  * in which case the provisions of the GPL or the LGPL are applicable instead
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00037  *
00038  * ***** END LICENSE BLOCK ***** */
00039 
00040 /* @(#)s_atan.c 1.3 95/01/18 */
00041 /*
00042  * ====================================================
00043  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
00044  *
00045  * Developed at SunSoft, a Sun Microsystems, Inc. business.
00046  * Permission to use, copy, modify, and distribute this
00047  * software is freely granted, provided that this notice 
00048  * is preserved.
00049  * ====================================================
00050  *
00051  */
00052 
00053 /* atan(x)
00054  * Method
00055  *   1. Reduce x to positive by atan(x) = -atan(-x).
00056  *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
00057  *      is further reduced to one of the following intervals and the
00058  *      arctangent of t is evaluated by the corresponding formula:
00059  *
00060  *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
00061  *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
00062  *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
00063  *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
00064  *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
00065  *
00066  * Constants:
00067  * The hexadecimal values are the intended ones for the following 
00068  * constants. The decimal values may be used, provided that the 
00069  * compiler will convert from decimal to binary accurately enough 
00070  * to produce the hexadecimal values shown.
00071  */
00072 
00073 #include "fdlibm.h"
00074 
00075 #ifdef __STDC__
00076 static const double atanhi[] = {
00077 #else
00078 static double atanhi[] = {
00079 #endif
00080   4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
00081   7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
00082   9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
00083   1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
00084 };
00085 
00086 #ifdef __STDC__
00087 static const double atanlo[] = {
00088 #else
00089 static double atanlo[] = {
00090 #endif
00091   2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
00092   3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
00093   1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
00094   6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
00095 };
00096 
00097 #ifdef __STDC__
00098 static const double aT[] = {
00099 #else
00100 static double aT[] = {
00101 #endif
00102   3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
00103  -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
00104   1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
00105  -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
00106   9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
00107  -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
00108   6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
00109  -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
00110   4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
00111  -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
00112   1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
00113 };
00114 
00115 #ifdef __STDC__
00116        static const double 
00117 #else
00118        static double 
00119 #endif
00120 one   = 1.0,
00121 really_big   = 1.0e300;
00122 
00123 #ifdef __STDC__
00124        double fd_atan(double x)
00125 #else
00126        double fd_atan(x)
00127        double x;
00128 #endif
00129 {
00130         fd_twoints u;
00131        double w,s1,s2,z;
00132        int ix,hx,id;
00133 
00134         u.d = x;
00135        hx = __HI(u);
00136        ix = hx&0x7fffffff;
00137        if(ix>=0x44100000) { /* if |x| >= 2^66 */
00138             u.d = x;
00139            if(ix>0x7ff00000||
00140               (ix==0x7ff00000&&(__LO(u)!=0)))
00141               return x+x;          /* NaN */
00142            if(hx>0) return  atanhi[3]+atanlo[3];
00143            else     return -atanhi[3]-atanlo[3];
00144        } if (ix < 0x3fdc0000) {    /* |x| < 0.4375 */
00145            if (ix < 0x3e200000) {  /* |x| < 2^-29 */
00146               if(really_big+x>one) return x;     /* raise inexact */
00147            }
00148            id = -1;
00149        } else {
00150        x = fd_fabs(x);
00151        if (ix < 0x3ff30000) {             /* |x| < 1.1875 */
00152            if (ix < 0x3fe60000) {  /* 7/16 <=|x|<11/16 */
00153               id = 0; x = (2.0*x-one)/(2.0+x); 
00154            } else {                /* 11/16<=|x|< 19/16 */
00155               id = 1; x  = (x-one)/(x+one); 
00156            }
00157        } else {
00158            if (ix < 0x40038000) {  /* |x| < 2.4375 */
00159               id = 2; x  = (x-1.5)/(one+1.5*x);
00160            } else {                /* 2.4375 <= |x| < 2^66 */
00161               id = 3; x  = -1.0/x;
00162            }
00163        }}
00164     /* end of argument reduction */
00165        z = x*x;
00166        w = z*z;
00167     /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
00168        s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
00169        s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
00170        if (id<0) return x - x*(s1+s2);
00171        else {
00172            z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
00173            return (hx<0)? -z:z;
00174        }
00175 }