Ziele Untersuchung
mit Columbo Integrität von
Datenbanken Interaktion und
Portierbarkeit Ergonomie der
Schnittstellen

Angebot Produkte Projekt Beratung

Mittel Analytik Modellierung Sprachen Algebra Logik Hardware Denken Kreativität

Zusammenhänge Gesellschaft Wirtschaft Branche Firma


products/sources/formale Sprachen/Java/Openjdk/src/java.base/share/native/libfdlibm/ (Sun/Oracle ^©) Datei vom 13.11.2022 mit Größe 5 kB

Quelle s_atan.c Sprache: C

/*
* 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;
        }
}

quality100%

¤ Dauer der Verarbeitung: 0.12 Sekunden (vorverarbeitet) ¤

Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.