| /* |
| * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. |
| * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
| * |
| * This code is free software; you can redistribute it and/or modify it |
| * under the terms of the GNU General Public License version 2 only, as |
| * published by the Free Software Foundation. Oracle designates this |
| * particular file as subject to the "Classpath" exception as provided |
| * by Oracle in the LICENSE file that accompanied this code. |
| * |
| * This code is distributed in the hope that it will be useful, but WITHOUT |
| * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
| * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
| * version 2 for more details (a copy is included in the LICENSE file that |
| * accompanied this code). |
| * |
| * You should have received a copy of the GNU General Public License version |
| * 2 along with this work; if not, write to the Free Software Foundation, |
| * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. |
| * |
| * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
| * or visit www.oracle.com if you need additional information or have any |
| * questions. |
| */ |
| |
| /* 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" |
| |
| #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; |
| int ix,hx,id; |
| |
| hx = __HI(x); |
| ix = hx&0x7fffffff; |
| if(ix>=0x44100000) { /* if |x| >= 2^66 */ |
| if(ix>0x7ff00000|| |
| (ix==0x7ff00000&&(__LO(x)!=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; |
| } |
| } |