/*
 * 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 2005 Sun Microsystems, Inc.  All rights reserved.
 * Use is subject to license terms.
 */

#pragma weak __cabs = cabs

#include <math.h>
#include "complex_wrapper.h"

/*
 * If C were the only standard we cared about, cabs could just call
 * hypot.  Unfortunately, various other standards say that hypot must
 * call matherr and/or set errno to ERANGE when the result overflows.
 * Since cabs should do neither of these things, we have to either
 * make hypot a wrapper on another internal function or duplicate
 * the hypot implementation here.  I've chosen to do the latter.
 */

static const double
        zero = 0.0,
        onep1u = 1.00000000000000022204e+00,    /* 0x3ff00000 1 = 1+2**-52 */
        twom53 = 1.11022302462515654042e-16,    /* 0x3ca00000 0 = 2**-53 */
        twom768 = 6.441148769597133308e-232,    /* 2^-768 */
        two768  = 1.552518092300708935e+231;    /* 2^768 */

double
cabs(dcomplex z)
{
        double          x, y, xh, yh, w, ax, ay;
        int             i, j, nx, ny, ix, iy, iscale = 0;
        unsigned        lx, ly;

        x = D_RE(z);
        y = D_IM(z);

        ix = ((int *)&x)[HIWORD] & ~0x80000000;
        lx = ((int *)&x)[LOWORD];
        iy = ((int *)&y)[HIWORD] & ~0x80000000;
        ly = ((int *)&y)[LOWORD];

        /* force ax = |x| ~>~ ay = |y| */
        if (iy > ix) {
                ax = fabs(y);
                ay = fabs(x);
                i = ix;
                ix = iy;
                iy = i;
                i = lx;
                lx = ly;
                ly = i;
        } else {
                ax = fabs(x);
                ay = fabs(y);
        }
        nx = ix >> 20;
        ny = iy >> 20;
        j  = nx - ny;

        if (nx >= 0x5f3) {
                /* x >= 2^500 (x*x or y*y may overflow) */
                if (nx == 0x7ff) {
                        /* inf or NaN, signal of sNaN */
                        if (((ix - 0x7ff00000) | lx) == 0)
                                return ((ax == ay)? ay : ax);
                        else if (((iy - 0x7ff00000) | ly) == 0)
                                return ((ay == ax)? ax : ay);
                        else
                                return (ax * ay);
                } else if (j > 32) {
                        /* x >> y */
                        if (j <= 53)
                                ay *= twom53;
                        ax += ay;
                        return (ax);
                }
                ax *= twom768;
                ay *= twom768;
                iscale = 2;
                ix -= 768 << 20;
                iy -= 768 << 20;
        } else if (ny < 0x23d) {
                /* y < 2^-450 (x*x or y*y may underflow) */
                if ((ix | lx) == 0)
                        return (ay);
                if ((iy | ly) == 0)
                        return (ax);
                if (j > 53)             /* x >> y */
                        return (ax + ay);
                iscale = 1;
                ax *= two768;
                ay *= two768;
                if (nx == 0) {
                        if (ax == zero) /* guard subnormal flush to zero */
                                return (ax);
                        ix = ((int *)&ax)[HIWORD];
                } else {
                        ix += 768 << 20;
                }
                if (ny == 0) {
                        if (ay == zero) /* guard subnormal flush to zero */
                                return (ax * twom768);
                        iy = ((int *)&ay)[HIWORD];
                } else {
                        iy += 768 << 20;
                }
                j = (ix >> 20) - (iy >> 20);
                if (j > 32) {
                        /* x >> y */
                        if (j <= 53)
                                ay *= twom53;
                        return ((ax + ay) * twom768);
                }
        } else if (j > 32) {
                /* x >> y */
                if (j <= 53)
                        ay *= twom53;
                return (ax + ay);
        }

        /*
         * Medium range ax and ay with max{|ax/ay|,|ay/ax|} bounded by 2^32.
         * First check rounding mode by comparing onep1u*onep1u with onep1u
         * + twom53.  Make sure the computation is done at run-time.
         */
        if (((lx | ly) << 5) == 0) {
                ay = ay * ay;
                ax += ay / (ax + sqrt(ax * ax + ay));
        } else if (onep1u * onep1u != onep1u + twom53) {
                /* round-to-zero, positive, negative mode */
                /* magic formula with less than an ulp error */
                w = sqrt(ax * ax + ay * ay);
                ax += ay / ((ax + w) / ay);
        } else {
                /* round-to-nearest mode */
                w = ax - ay;
                if (w > ay) {
                        ((int *)&xh)[HIWORD] = ix;
                        ((int *)&xh)[LOWORD] = 0;
                        ay = ay * ay + (ax - xh) * (ax + xh);
                        ax = sqrt(xh * xh + ay);
                } else {
                        ax = ax + ax;
                        ((int *)&xh)[HIWORD] = ix + 0x00100000;
                        ((int *)&xh)[LOWORD] = 0;
                        ((int *)&yh)[HIWORD] = iy;
                        ((int *)&yh)[LOWORD] = 0;
                        ay = w * w + ((ax - xh) * yh + (ay - yh) * ax);
                        ax = sqrt(xh * yh + ay);
                }
        }
        if (iscale > 0) {
                if (iscale == 1)
                        ax *= twom768;
                else
                        ax *= two768;   /* must generate side effect here */
        }
        return (ax);
}