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/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*- |
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* |
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* ***** BEGIN LICENSE BLOCK ***** |
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* Version: MPL 1.1/GPL 2.0/LGPL 2.1 |
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* |
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* The contents of this file are subject to the Mozilla Public License Version |
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* 1.1 (the "License"); you may not use this file except in compliance with |
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* the License. You may obtain a copy of the License at |
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* http://www.mozilla.org/MPL/ |
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* |
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* Software distributed under the License is distributed on an "AS IS" basis, |
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* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License |
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* for the specific language governing rights and limitations under the |
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* License. |
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* |
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* The Original Code is Mozilla Communicator client code, released |
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* March 31, 1998. |
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* |
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* The Initial Developer of the Original Code is |
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* Sun Microsystems, Inc. |
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* Portions created by the Initial Developer are Copyright (C) 1998 |
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* the Initial Developer. All Rights Reserved. |
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* |
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* Contributor(s): |
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* |
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* Alternatively, the contents of this file may be used under the terms of |
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* either of the GNU General Public License Version 2 or later (the "GPL"), |
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* or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"), |
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* in which case the provisions of the GPL or the LGPL are applicable instead |
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* of those above. If you wish to allow use of your version of this file only |
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* under the terms of either the GPL or the LGPL, and not to allow others to |
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* use your version of this file under the terms of the MPL, indicate your |
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* decision by deleting the provisions above and replace them with the notice |
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* and other provisions required by the GPL or the LGPL. If you do not delete |
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* the provisions above, a recipient may use your version of this file under |
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* the terms of any one of the MPL, the GPL or the LGPL. |
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* |
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* ***** END LICENSE BLOCK ***** */ |
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|
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/* @(#)s_atan.c 1.3 95/01/18 */ |
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/* |
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* ==================================================== |
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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* |
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* Developed at SunSoft, a Sun Microsystems, Inc. business. |
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* Permission to use, copy, modify, and distribute this |
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* software is freely granted, provided that this notice |
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* is preserved. |
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* ==================================================== |
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* |
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*/ |
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|
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/* atan(x) |
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* Method |
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* 1. Reduce x to positive by atan(x) = -atan(-x). |
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* 2. According to the integer k=4t+0.25 chopped, t=x, the argument |
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* is further reduced to one of the following intervals and the |
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* arctangent of t is evaluated by the corresponding formula: |
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* |
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* [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) |
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* [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) ) |
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* [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) ) |
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* [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) ) |
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* [39/16,INF] atan(x) = atan(INF) + atan( -1/t ) |
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* |
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* Constants: |
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* The hexadecimal values are the intended ones for the following |
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* constants. The decimal values may be used, provided that the |
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* compiler will convert from decimal to binary accurately enough |
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* to produce the hexadecimal values shown. |
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*/ |
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|
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#include "fdlibm.h" |
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|
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#ifdef __STDC__ |
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static const double atanhi[] = { |
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#else |
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static double atanhi[] = { |
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#endif |
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4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ |
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7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */ |
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9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */ |
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1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */ |
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}; |
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|
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#ifdef __STDC__ |
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static const double atanlo[] = { |
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#else |
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static double atanlo[] = { |
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#endif |
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2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */ |
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3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */ |
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1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */ |
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6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */ |
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}; |
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|
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#ifdef __STDC__ |
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static const double aT[] = { |
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#else |
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static double aT[] = { |
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#endif |
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3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */ |
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-1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */ |
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1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */ |
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-1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */ |
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9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */ |
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-7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */ |
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6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */ |
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-5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */ |
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4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */ |
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-3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */ |
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1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */ |
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}; |
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|
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#ifdef __STDC__ |
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static const double |
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#else |
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static double |
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#endif |
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one = 1.0, |
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really_big = 1.0e300; |
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|
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#ifdef __STDC__ |
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double fd_atan(double x) |
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#else |
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double fd_atan(x) |
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double x; |
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#endif |
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{ |
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fd_twoints u; |
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double w,s1,s2,z; |
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int ix,hx,id; |
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|
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u.d = x; |
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hx = __HI(u); |
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ix = hx&0x7fffffff; |
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if(ix>=0x44100000) { /* if |x| >= 2^66 */ |
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u.d = x; |
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if(ix>0x7ff00000|| |
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(ix==0x7ff00000&&(__LO(u)!=0))) |
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return x+x; /* NaN */ |
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if(hx>0) return atanhi[3]+atanlo[3]; |
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else return -atanhi[3]-atanlo[3]; |
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} if (ix < 0x3fdc0000) { /* |x| < 0.4375 */ |
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if (ix < 0x3e200000) { /* |x| < 2^-29 */ |
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if(really_big+x>one) return x; /* raise inexact */ |
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} |
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id = -1; |
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} else { |
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x = fd_fabs(x); |
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if (ix < 0x3ff30000) { /* |x| < 1.1875 */ |
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if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */ |
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id = 0; x = (2.0*x-one)/(2.0+x); |
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} else { /* 11/16<=|x|< 19/16 */ |
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id = 1; x = (x-one)/(x+one); |
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} |
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} else { |
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if (ix < 0x40038000) { /* |x| < 2.4375 */ |
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id = 2; x = (x-1.5)/(one+1.5*x); |
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} else { /* 2.4375 <= |x| < 2^66 */ |
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id = 3; x = -1.0/x; |
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} |
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}} |
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/* end of argument reduction */ |
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z = x*x; |
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w = z*z; |
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/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ |
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s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); |
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s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); |
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if (id<0) return x - x*(s1+s2); |
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else { |
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z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); |
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return (hx<0)? -z:z; |
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} |
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} |
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