sparc/fp/_Q_cplx_div.c

/*
 * CDDL HEADER START
 *
 * The contents of this file are subject to the terms of the
 * Common Development and Distribution License, Version 1.0 only
 * (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 2003 Sun Microsystems, Inc.  All rights reserved.
 * Use is subject to license terms.
 */

#pragma ident   "%Z%%M% %I% %E% SMI"

/*
 * On SPARC V8, _Q_cplx_div(v, z, w) sets *v = *z / *w with infin-
 * ities handling according to C99.
 *
 * On SPARC V9, _Q_cplx_div(z, w) returns *z / *w with infinities
 * handled according to C99.
 *
 * If z and w are both finite and w is nonzero, _Q_cplx_div delivers
 * the complex quotient q according to the usual formula: let a =
 * Re(z), b = Im(z), c = Re(w), and d = Im(w); then q = x + I * y
 * where x = (a * c + b * d) / r and y = (b * c - a * d) / r with
 * r = c * c + d * d.  This implementation scales to avoid premature
 * underflow or overflow.
 *
 * If z is neither NaN nor zero and w is zero, or if z is infinite
 * and w is finite and nonzero, _Q_cplx_div delivers an infinite
 * result.  If z is finite and w is infinite, _Q_cplx_div delivers
 * a zero result.
 *
 * If z and w are both zero or both infinite, or if either z or w is
 * a complex NaN, _Q_cplx_div delivers NaN + I * NaN.  C99 doesn't
 * specify these cases.
 *
 * This implementation can raise spurious underflow, overflow, in-
 * valid operation, inexact, and division-by-zero exceptions.  C99
 * allows this.
 */

#if !defined(sparc) && !defined(__sparc)
#error This code is for SPARC only
#endif

static union {
    int     i[4];
    long double q;
} inf = {
    0x7fff0000, 0, 0, 0
};

/*
 * Return +1 if x is +Inf, -1 if x is -Inf, and 0 otherwise
 */
static int
testinfl(long double x)
{
    union {
        int     i[4];
        long double q;
    } xx;

    xx.q = x;
    return (((((xx.i[0] << 1) - 0xfffe0000) | xx.i[1] | xx.i[2] | xx.i[3])
        == 0)? (1 | (xx.i[0] >> 31)) : 0);
}

#ifdef __sparcv9
long double _Complex
_Q_cplx_div(const long double _Complex *z, const long double _Complex *w)
{
    long double _Complex    v;
#else
void
_Q_cplx_div(long double _Complex *v, const long double _Complex *z,
    const long double _Complex *w)
{
#endif
    union {
        int     i[4];
        long double q;
    } aa, bb, cc, dd, ss;
    long double a, b, c, d, r;
    int     ha, hb, hc, hd, hz, hw, hs, i, j;

    /*
     * The following is equivalent to
     *
     *  a = creall(*z); b = cimagl(*z);
     *  c = creall(*w); d = cimagl(*w);
     */
    a = ((long double *)z)[0];
    b = ((long double *)z)[1];
    c = ((long double *)w)[0];
    d = ((long double *)w)[1];

    /* extract high-order words to estimate |z| and |w| */
    aa.q = a;
    bb.q = b;
    ha = aa.i[0] & ~0x80000000;
    hb = bb.i[0] & ~0x80000000;
    hz = (ha > hb)? ha : hb;

    cc.q = c;
    dd.q = d;
    hc = cc.i[0] & ~0x80000000;
    hd = dd.i[0] & ~0x80000000;
    hw = (hc > hd)? hc : hd;

    /* check for special cases */
    if (hw >= 0x7fff0000) { /* w is inf or nan */
        r = 0.0l;
        i = testinfl(c);
        j = testinfl(d);
        if (i | j) { /* w is infinite */
            /*
             * "factor out" infinity, being careful to preserve
             * signs of finite values
             */
            c = i? i : ((cc.i[0] < 0)? -0.0l : 0.0l);
            d = j? j : ((dd.i[0] < 0)? -0.0l : 0.0l);
            if (hz >= 0x7ffe0000) {
                /* scale to avoid overflow below */
                c *= 0.5l;
                d *= 0.5l;
            }
        }
        goto done;
    }

    if (hw == 0 && (cc.i[1] | cc.i[2] | cc.i[3] |
        dd.i[1] | dd.i[2] | dd.i[3]) == 0) {
        /* w is zero; multiply z by 1/Re(w) - I * Im(w) */
        r = 1.0l;
        c = 1.0l / c;
        i = testinfl(a);
        j = testinfl(b);
        if (i | j) { /* z is infinite */
            a = i;
            b = j;
        }
        goto done;
    }

    if (hz >= 0x7fff0000) { /* z is inf or nan */
        r = 1.0l;
        i = testinfl(a);
        j = testinfl(b);
        if (i | j) { /* z is infinite */
            a = i;
            b = j;
            r = inf.q;
        }
        goto done;
    }

    /*
     * Scale c and d to compute 1/|w|^2 and the real and imaginary
     * parts of the quotient.
     */
    hs = (((hw >> 2) - hw) + 0x6ffd7fff) & 0xffff0000;
    if (hz < 0x00ea0000) { /* |z| < 2^-16149 */
        if (((hw - 0x3e380000) | (0x40e90000 - hw)) >= 0)
            hs = (((0x40e90000 - hw) >> 1) & 0xffff0000)
                + 0x3fff0000;
    }
    ss.i[0] = hs;
    ss.i[1] = ss.i[2] = ss.i[3] = 0;

    c *= ss.q;
    d *= ss.q;
    r = 1.0l / (c * c + d * d);

    c *= ss.q;
    d *= ss.q;

done:
#ifdef __sparcv9
    ((long double *)&v)[0] = (a * c + b * d) * r;
    ((long double *)&v)[1] = (b * c - a * d) * r;
    return (v);
#else
    ((long double *)v)[0] = (a * c + b * d) * r;
    ((long double *)v)[1] = (b * c - a * d) * r;
#endif
}