i386/fp/_X_cplx_div_ix.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 2004 Sun Microsystems, Inc.  All rights reserved.
 * Use is subject to license terms.
 */

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

/*
 * _X_cplx_div_ix(b, w) returns (I * b) / w with infinities handled
 * according to C99.
 *
 * If b and w are both finite and w is nonzero, _X_cplx_div_ix de-
 * livers the complex quotient q according to the usual formula: let
 * c = Re(w), and d = Im(w); then q = x + I * y where x = (b * d) / r
 * and y = (b * c) / r with r = c * c + d * d.  This implementation
 * scales to avoid premature underflow or overflow.
 *
 * If b is neither NaN nor zero and w is zero, or if b is infinite
 * and w is finite and nonzero, _X_cplx_div_ix delivers an infinite
 * result.  If b is finite and w is infinite, _X_cplx_div_ix delivers
 * a zero result.
 *
 * If b and w are both zero or both infinite, or if either b or w is
 * NaN, _X_cplx_div_ix 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(i386) && !defined(__i386) && !defined(__amd64)
#error This code is for x86 only
#endif

/*
 * scl[i].e = 2^(4080*(4-i)) for i = 0, ..., 9
 */
static const union {
    unsigned int    i[3];
    long double e;
} scl[9] = {
    { 0, 0x80000000, 0x7fbf },
    { 0, 0x80000000, 0x6fcf },
    { 0, 0x80000000, 0x5fdf },
    { 0, 0x80000000, 0x4fef },
    { 0, 0x80000000, 0x3fff },
    { 0, 0x80000000, 0x300f },
    { 0, 0x80000000, 0x201f },
    { 0, 0x80000000, 0x102f },
    { 0, 0x80000000, 0x003f }
};

/*
 * Return +1 if x is +Inf, -1 if x is -Inf, and 0 otherwise
 */
static int
testinfl(long double x)
{
    union {
        int     i[3];
        long double e;
    } xx;

    xx.e = x;
    if ((xx.i[2] & 0x7fff) != 0x7fff || ((xx.i[1] << 1) | xx.i[0]) != 0)
        return (0);
    return (1 | ((xx.i[2] << 16) >> 31));
}

long double _Complex
_X_cplx_div_ix(long double b, long double _Complex w)
{
    long double _Complex    v;
    union {
        int     i[3];
        long double e;
    } bb, cc, dd;
    long double c, d, sc, sd, r;
    int     eb, ec, ed, ew, i, j;

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

    /* extract exponents to estimate |z| and |w| */
    bb.e = b;
    eb = bb.i[2] & 0x7fff;

    cc.e = c;
    dd.e = d;
    ec = cc.i[2] & 0x7fff;
    ed = dd.i[2] & 0x7fff;
    ew = (ec > ed)? ec : ed;

    /* check for special cases */
    if (ew >= 0x7fff) { /* w is inf or nan */
        i = testinfl(c);
        j = testinfl(d);
        if (i | j) { /* w is infinite */
            c = ((cc.i[2] << 16) < 0)? -0.0f : 0.0f;
            d = ((dd.i[2] << 16) < 0)? -0.0f : 0.0f;
        } else /* w is nan */
            b += c + d;
        ((long double *)&v)[0] = b * d;
        ((long double *)&v)[1] = b * c;
        return (v);
    }

    if (ew == 0 && (cc.i[1] | cc.i[0] | dd.i[1] | dd.i[0]) == 0) {
        /* w is zero; multiply b by 1/Re(w) - I * Im(w) */
        c = 1.0f / c;
        j = testinfl(b);
        if (j) { /* b is infinite */
            b = j;
        }
        ((long double *)&v)[0] = (b == 0.0f)? b * c : b * d;
        ((long double *)&v)[1] = b * c;
        return (v);
    }

    if (eb >= 0x7fff) { /* a is inf or nan */
        ((long double *)&v)[0] = b * d;
        ((long double *)&v)[1] = b * c;
        return (v);
    }

    /*
     * Compute the real and imaginary parts of the quotient,
     * scaling to avoid overflow or underflow.
     */
    ew = (ew - 0x3800) >> 12;
    sc = c * scl[ew + 4].e;
    sd = d * scl[ew + 4].e;
    r = sc * sc + sd * sd;

    eb = (eb - 0x3800) >> 12;
    b = (b * scl[eb + 4].e) / r;
    eb -= (ew + ew);

    ec = (ec - 0x3800) >> 12;
    c = (c * scl[ec + 4].e) * b;
    ec += eb;

    ed = (ed - 0x3800) >> 12;
    d = (d * scl[ed + 4].e) * b;
    ed += eb;

    /* compensate for scaling */
    sc = scl[3].e; /* 2^4080 */
    if (ec < 0) {
        ec = -ec;
        sc = scl[5].e; /* 2^-4080 */
    }
    while (ec--)
        c *= sc;

    sd = scl[3].e;
    if (ed < 0) {
        ed = -ed;
        sd = scl[5].e;
    }
    while (ed--)
        d *= sd;

    ((long double *)&v)[0] = d;
    ((long double *)&v)[1] = c;
    return (v);
}