Java atan atan(double a)

Description

Returns the arc tangent of an angle, in the range of -pi/2 through pi/2.

License

Open Source License

Parameter

Parameter	Description
a	the value whose arc tangent is to be returned.

Return

the arc tangent of the argument.

Declaration

public static double atan(double a) 

Method Source Code

//package com.java2s;
/*/*from   w ww .j a va 2  s.c  o m*/
 * Copyright 2007-2008 Sun Microsystems, Inc. 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.
 * 
 * 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 Sun Microsystems, Inc., 16 Network Circle, Menlo
 * Park, CA 94025 or visit www.sun.com if you need additional
 * information or have any questions.
 */

public class Main {
    private static final long no_sign_mask = 0x7FFFFFFFFFFFFFFFL;
    private static final long exp_mask = 0x7FF0000000000000L;
    private static final 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 */
    };
    private static final 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 */
    };
    private static final 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 */
    };

    /**
     * Returns the arc tangent of an angle, in the range of -<i>pi</i>/2 through <i>pi</i>/2. 
     * Special cases:
     * <ul>
     *  <li>If the argument is NaN, then the result is NaN.
     *  <li>If the argument is zero, then the result is a zero with the same sign as the argument.
     * </ul>
     *
     * @param a the value whose arc tangent is to be returned.
     * @return the arc tangent of the argument.
     */
    public static double atan(double a) {
        double w, s1, s2, z;
        int id;
        long hx = Double.doubleToLongBits(a);
        long ix = hx & no_sign_mask;

        /* |a| >= 2^66 */
        if (ix >= 0x4410000000000000L) {
            /* NaN */
            if (ix > exp_mask) {
                return (a + a);
            }
            if (hx > 0)
                return (atanhi[3] + atanlo[3]);
            else
                return (-atanhi[3] - atanlo[3]);
        }

        /* |a| < 0.4375 */
        if (ix < 0x3fdc000000000000L) {
            /* |a| < 2^-29 */
            if (ix < 0x3e20000000000000L) {
                return (a);
            }
            id = -1;
        } else {
            a = Math.abs(a);
            /* |a| < 1.1875 */
            if (ix < 0x3ff3000000000000L) {
                /* 7/16 <= |a| < 11/16 */
                if (ix < 0x3fe6000000000000L) {
                    id = 0;
                    a = (2.0 * a - 1.0) / (2.0 + a);
                }
                /* 11/16 <= |a| < 19/16 */
                else {
                    id = 1;
                    a = (a - 1.0) / (a + 1.0);
                }
            } else {
                /* |x| < 2.4375 */
                if (ix < 0x4003800000000000L) {
                    id = 2;
                    a = (a - 1.5) / (1.0 + 1.5 * a);
                } else {
                    id = 3;
                    a = -1.0 / a;
                }
            }
        }

        /* end of argument reduction */
        z = a * a;
        w = z * z;

        /* break sum from i=0 to 10 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 (a - a * (s1 + s2));
        else {
            z = atanhi[id] - ((a * (s1 + s2) - atanlo[id]) - a);
            if (hx < 0)
                return (-z);
            else
                return (z);
        }
    }
}

Related

1. atan(double a)
2. atan(double arg)
3. atan(double x)
4. atan(float tan_value)