/*
 * CDDL HEADER START
 *
 * The contents of this file are subject to the terms of the
 * Common Development and Distribution License (the "License").
 * You may not use this file except in compliance with the License.
 *
 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
 * or http://www.opensolaris.org/os/licensing.
 * See the License for the specific language governing permissions
 * and limitations under the License.
 *
 * When distributing Covered Code, include this CDDL HEADER in each
 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
 * If applicable, add the following below this CDDL HEADER, with the
 * fields enclosed by brackets "[]" replaced with your own identifying
 * information: Portions Copyright [yyyy] [name of copyright owner]
 *
 * CDDL HEADER END
 */

/*
 * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
 */
/*
 * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
 * Use is subject to license terms.
 */

/*
 * atan2l(y,x)
 *
 * Method :
 *      1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
 *      2. Reduce x to positive by (if x and y are unexceptional):
 *              ARG (x+iy) = arctan(y/x)           ... if x > 0,
 *              ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
 *
 * Special cases:
 *
 *      ATAN2((anything), NaN ) is NaN;
 *      ATAN2(NAN , (anything) ) is NaN;
 *      ATAN2(+-0, +(anything but NaN)) is +-0  ;
 *      ATAN2(+-0, -(anything but NaN)) is +-PI ;
 *      ATAN2(+-(anything but 0 and NaN), 0) is +-PI/2;
 *      ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
 *      ATAN2(+-(anything but INF and NaN), -INF) is +-PI;
 *      ATAN2(+-INF,+INF ) is +-PI/4 ;
 *      ATAN2(+-INF,-INF ) is +-3PI/4;
 *      ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-PI/2;
 *
 * 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.
 */

#pragma weak __atan2l = atan2l

#include "libm.h"
#include "longdouble.h"

static const long double
        zero    =  0.0L,
        tiny    =  1.0e-40L,
        one     =  1.0L,
        half    =  0.5L,
        PI3o4   =  2.356194490192344928846982537459627163148L,
        PIo4    =  0.785398163397448309615660845819875721049L,
        PIo2    =  1.570796326794896619231321691639751442099L,
        PI      =  3.141592653589793238462643383279502884197L,
        PI_lo   =  8.671810130123781024797044026043351968762e-35L;

long double
atan2l(long double y, long double x)
{
        long double t, z;
        int k, m, signy, signx;

        if (x != x || y != y)
                return (x + y); /* return NaN if x or y is NAN */
        signy = signbitl(y);
        signx = signbitl(x);
        if (x == one)
                return (atanl(y));
        /* Ensure sign indicators are boolean */
        m = (signy != 0) + (signx != 0) + (signx != 0);

        /* when y = 0 */
        if (y == zero)
                switch (m) {
                case 0:
                        return (y);     /* atan(+0,+anything) */
                case 1:
                        return (y);     /* atan(-0,+anything) */
                case 2:
                        return (PI + tiny);     /* atan(+0,-anything) */
                case 3:
                        return (-PI - tiny);    /* atan(-0,-anything) */
                }

        /* when x = 0 */
        if (x == zero)
                return (signy != 0 ? -PIo2 - tiny : PIo2 + tiny);

        /* when x is INF */
        if (!finitel(x)) {
                if (!finitel(y)) {
                        switch (m) {
                        case 0:
                                return (PIo4 + tiny);   /* atan(+INF,+INF) */
                        case 1:
                                return (-PIo4 - tiny);  /* atan(-INF,+INF) */
                        case 2:
                                return (PI3o4 + tiny);  /* atan(+INF,-INF) */
                        case 3:
                                return (-PI3o4 - tiny); /* atan(-INF,-INF) */
                        }
                } else {
                        switch (m) {
                        case 0:
                                return (zero);  /* atan(+...,+INF) */
                        case 1:
                                return (-zero); /* atan(-...,+INF) */
                        case 2:
                                return (PI + tiny);     /* atan(+...,-INF) */
                        case 3:
                                return (-PI - tiny);    /* atan(-...,-INF) */
                        }
                }
        }
        /* when y is INF */
        if (!finitel(y))
                return (signy != 0 ? -PIo2 - tiny : PIo2 + tiny);

        /* compute y/x */
        x = fabsl(x);
        y = fabsl(y);
        t = PI_lo;
        k = (ilogbl(y) - ilogbl(x));

        if (k > 120)
                z = PIo2 + half * t;
        else if (m > 1 && k < -120)
                z = zero;
        else
                z = atanl(y / x);

        switch (m) {
        case 0:
                return (z);     /* atan(+,+) */
        case 1:
                return (-z);    /* atan(-,+) */
        case 2:
                return (PI - (z - t));  /* atan(+,-) */
        case 3:
                return ((z - t) - PI);  /* atan(-,-) */
        }
        /* NOTREACHED */
        return (0.0L);
}