common/complex/cabs.c

	cabs.c revision 25c28e83beb90e7c80452a7c818c5e6f73a07dc8
/*
 * 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 "libm_synonyms.h"
#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);
}