common/m9x/fmal.c

	fmal.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 2006 Sun Microsystems, Inc.  All rights reserved.
 * Use is subject to license terms.
 */

#if defined(ELFOBJ)
#pragma weak fmal = __fmal
#endif

#include "libm.h"
#include "fma.h"
#include "fenv_inlines.h"

#if defined(__sparc)

static const union {
    unsigned i[2];
    double d;
} C[] = {
    { 0x3fe00000u, 0 },
    { 0x40000000u, 0 },
    { 0x3ef00000u, 0 },
    { 0x3e700000u, 0 },
    { 0x41300000u, 0 },
    { 0x3e300000u, 0 },
    { 0x3b300000u, 0 },
    { 0x38300000u, 0 },
    { 0x42300000u, 0 },
    { 0x3df00000u, 0 },
    { 0x7fe00000u, 0 },
    { 0x00100000u, 0 },
    { 0x00100001u, 0 },
    { 0, 0 },
    { 0x7ff00000u, 0 },
    { 0x7ff00001u, 0 }
};

#define half    C[0].d
#define two C[1].d
#define twom16  C[2].d
#define twom24  C[3].d
#define two20   C[4].d
#define twom28  C[5].d
#define twom76  C[6].d
#define twom124 C[7].d
#define two36   C[8].d
#define twom32  C[9].d
#define huge    C[10].d
#define tiny    C[11].d
#define tiny2   C[12].d
#define zero    C[13].d
#define inf C[14].d
#define snan    C[15].d

static const unsigned int fsr_rm = 0xc0000000u;

/*
 * fmal for SPARC: 128-bit quad precision, big-endian
 */
long double
__fmal(long double x, long double y, long double z) {
    union {
        unsigned int i[4];
        long double q;
    } xx, yy, zz;
    union {
        unsigned int i[2];
        double d;
    } u;
    double dx[5], dy[5], dxy[9], c, s;
    unsigned int xy0, xy1, xy2, xy3, xy4, xy5, xy6, xy7;
    unsigned int z0, z1, z2, z3, z4, z5, z6, z7;
    unsigned int rm, sticky;
    unsigned int fsr;
    int hx, hy, hz, ex, ey, ez, exy, sxy, sz, e, ibit;
    int cx, cy, cz;
    volatile double dummy;

    /* extract the high order words of the arguments */
    xx.q = x;
    yy.q = y;
    zz.q = z;
    hx = xx.i[0] & ~0x80000000;
    hy = yy.i[0] & ~0x80000000;
    hz = zz.i[0] & ~0x80000000;

    /*
     * distinguish zero, finite nonzero, infinite, and quiet nan
     * arguments; raise invalid and return for signaling nans
     */
    if (hx >= 0x7fff0000) {
        if ((hx & 0xffff) | xx.i[1] | xx.i[2] | xx.i[3]) {
            if (!(hx & 0x8000)) {
                /* signaling nan, raise invalid */
                dummy = snan;
                dummy += snan;
                xx.i[0] |= 0x8000;
                return (xx.q);
            }
            cx = 3; /* quiet nan */
        } else
            cx = 2; /* inf */
    } else if (hx == 0) {
        cx = (xx.i[1] | xx.i[2] | xx.i[3]) ? 1 : 0;
                /* subnormal or zero */
    } else
        cx = 1;     /* finite nonzero */

    if (hy >= 0x7fff0000) {
        if ((hy & 0xffff) | yy.i[1] | yy.i[2] | yy.i[3]) {
            if (!(hy & 0x8000)) {
                dummy = snan;
                dummy += snan;
                yy.i[0] |= 0x8000;
                return (yy.q);
            }
            cy = 3;
        } else
            cy = 2;
    } else if (hy == 0) {
        cy = (yy.i[1] | yy.i[2] | yy.i[3]) ? 1 : 0;
    } else
        cy = 1;

    if (hz >= 0x7fff0000) {
        if ((hz & 0xffff) | zz.i[1] | zz.i[2] | zz.i[3]) {
            if (!(hz & 0x8000)) {
                dummy = snan;
                dummy += snan;
                zz.i[0] |= 0x8000;
                return (zz.q);
            }
            cz = 3;
        } else
            cz = 2;
    } else if (hz == 0) {
        cz = (zz.i[1] | zz.i[2] | zz.i[3]) ? 1 : 0;
    } else
        cz = 1;

    /* get the fsr and clear current exceptions */
    __fenv_getfsr32(&fsr);
    fsr &= ~FSR_CEXC;

    /* handle all other zero, inf, and nan cases */
    if (cx != 1 || cy != 1 || cz != 1) {
        /* if x or y is a quiet nan, return it */
        if (cx == 3) {
            __fenv_setfsr32(&fsr);
            return (x);
        }
        if (cy == 3) {
            __fenv_setfsr32(&fsr);
            return (y);
        }

        /* if x*y is 0*inf, raise invalid and return the default nan */
        if ((cx == 0 && cy == 2) || (cx == 2 && cy == 0)) {
            dummy = zero;
            dummy *= inf;
            zz.i[0] = 0x7fffffff;
            zz.i[1] = zz.i[2] = zz.i[3] = 0xffffffff;
            return (zz.q);
        }

        /* if z is a quiet nan, return it */
        if (cz == 3) {
            __fenv_setfsr32(&fsr);
            return (z);
        }

        /*
         * now none of x, y, or z is nan; handle cases where x or y
         * is inf
         */
        if (cx == 2 || cy == 2) {
            /*
             * if z is also inf, either we have inf-inf or
             * the result is the same as z depending on signs
             */
            if (cz == 2) {
                if ((int) ((xx.i[0] ^ yy.i[0]) ^ zz.i[0]) < 0) {
                    dummy = inf;
                    dummy -= inf;
                    zz.i[0] = 0x7fffffff;
                    zz.i[1] = zz.i[2] = zz.i[3] =
                        0xffffffff;
                    return (zz.q);
                }
                __fenv_setfsr32(&fsr);
                return (z);
            }

            /* otherwise the result is inf with appropriate sign */
            zz.i[0] = ((xx.i[0] ^ yy.i[0]) & 0x80000000) |
                0x7fff0000;
            zz.i[1] = zz.i[2] = zz.i[3] = 0;
            __fenv_setfsr32(&fsr);
            return (zz.q);
        }

        /* if z is inf, return it */
        if (cz == 2) {
            __fenv_setfsr32(&fsr);
            return (z);
        }

        /*
         * now x, y, and z are all finite; handle cases where x or y
         * is zero
         */
        if (cx == 0 || cy == 0) {
            /* either we have 0-0 or the result is the same as z */
            if (cz == 0 && (int) ((xx.i[0] ^ yy.i[0]) ^ zz.i[0]) <
                0) {
                zz.i[0] = (fsr >> 30) == FSR_RM ? 0x80000000 :
                    0;
                __fenv_setfsr32(&fsr);
                return (zz.q);
            }
            __fenv_setfsr32(&fsr);
            return (z);
        }

        /* if we get here, x and y are nonzero finite, z must be zero */
        return (x * y);
    }

    /*
     * now x, y, and z are all finite and nonzero; set round-to-
     * negative-infinity mode
     */
    __fenv_setfsr32(&fsr_rm);

    /*
     * get the signs and exponents and normalize the significands
     * of x and y
     */
    sxy = (xx.i[0] ^ yy.i[0]) & 0x80000000;
    ex = hx >> 16;
    hx &= 0xffff;
    if (!ex) {
        if (hx | (xx.i[1] & 0xfffe0000)) {
            ex = 1;
        } else if (xx.i[1] | (xx.i[2] & 0xfffe0000)) {
            hx = xx.i[1];
            xx.i[1] = xx.i[2];
            xx.i[2] = xx.i[3];
            xx.i[3] = 0;
            ex = -31;
        } else if (xx.i[2] | (xx.i[3] & 0xfffe0000)) {
            hx = xx.i[2];
            xx.i[1] = xx.i[3];
            xx.i[2] = xx.i[3] = 0;
            ex = -63;
        } else {
            hx = xx.i[3];
            xx.i[1] = xx.i[2] = xx.i[3] = 0;
            ex = -95;
        }
        while ((hx & 0x10000) == 0) {
            hx = (hx << 1) | (xx.i[1] >> 31);
            xx.i[1] = (xx.i[1] << 1) | (xx.i[2] >> 31);
            xx.i[2] = (xx.i[2] << 1) | (xx.i[3] >> 31);
            xx.i[3] <<= 1;
            ex--;
        }
    } else
        hx |= 0x10000;
    ey = hy >> 16;
    hy &= 0xffff;
    if (!ey) {
        if (hy | (yy.i[1] & 0xfffe0000)) {
            ey = 1;
        } else if (yy.i[1] | (yy.i[2] & 0xfffe0000)) {
            hy = yy.i[1];
            yy.i[1] = yy.i[2];
            yy.i[2] = yy.i[3];
            yy.i[3] = 0;
            ey = -31;
        } else if (yy.i[2] | (yy.i[3] & 0xfffe0000)) {
            hy = yy.i[2];
            yy.i[1] = yy.i[3];
            yy.i[2] = yy.i[3] = 0;
            ey = -63;
        } else {
            hy = yy.i[3];
            yy.i[1] = yy.i[2] = yy.i[3] = 0;
            ey = -95;
        }
        while ((hy & 0x10000) == 0) {
            hy = (hy << 1) | (yy.i[1] >> 31);
            yy.i[1] = (yy.i[1] << 1) | (yy.i[2] >> 31);
            yy.i[2] = (yy.i[2] << 1) | (yy.i[3] >> 31);
            yy.i[3] <<= 1;
            ey--;
        }
    } else
        hy |= 0x10000;
    exy = ex + ey - 0x3fff;

    /* convert the significands of x and y to doubles */
    c = twom16;
    dx[0] = (double) ((int) hx) * c;
    dy[0] = (double) ((int) hy) * c;

    c *= twom24;
    dx[1] = (double) ((int) (xx.i[1] >> 8)) * c;
    dy[1] = (double) ((int) (yy.i[1] >> 8)) * c;

    c *= twom24;
    dx[2] = (double) ((int) (((xx.i[1] << 16) | (xx.i[2] >> 16)) &
        0xffffff)) * c;
    dy[2] = (double) ((int) (((yy.i[1] << 16) | (yy.i[2] >> 16)) &
        0xffffff)) * c;

    c *= twom24;
    dx[3] = (double) ((int) (((xx.i[2] << 8) | (xx.i[3] >> 24)) &
        0xffffff)) * c;
    dy[3] = (double) ((int) (((yy.i[2] << 8) | (yy.i[3] >> 24)) &
        0xffffff)) * c;

    c *= twom24;
    dx[4] = (double) ((int) (xx.i[3] & 0xffffff)) * c;
    dy[4] = (double) ((int) (yy.i[3] & 0xffffff)) * c;

    /* form the "digits" of the product */
    dxy[0] = dx[0] * dy[0];
    dxy[1] = dx[0] * dy[1] + dx[1] * dy[0];
    dxy[2] = dx[0] * dy[2] + dx[1] * dy[1] + dx[2] * dy[0];
    dxy[3] = dx[0] * dy[3] + dx[1] * dy[2] + dx[2] * dy[1] +
        dx[3] * dy[0];
    dxy[4] = dx[0] * dy[4] + dx[1] * dy[3] + dx[2] * dy[2] +
        dx[3] * dy[1] + dx[4] * dy[0];
    dxy[5] = dx[1] * dy[4] + dx[2] * dy[3] + dx[3] * dy[2] +
        dx[4] * dy[1];
    dxy[6] = dx[2] * dy[4] + dx[3] * dy[3] + dx[4] * dy[2];
    dxy[7] = dx[3] * dy[4] + dx[4] * dy[3];
    dxy[8] = dx[4] * dy[4];

    /* split odd-numbered terms and combine into even-numbered terms */
    c = (dxy[1] + two20) - two20;
    dxy[0] += c;
    dxy[1] -= c;
    c = (dxy[3] + twom28) - twom28;
    dxy[2] += c + dxy[1];
    dxy[3] -= c;
    c = (dxy[5] + twom76) - twom76;
    dxy[4] += c + dxy[3];
    dxy[5] -= c;
    c = (dxy[7] + twom124) - twom124;
    dxy[6] += c + dxy[5];
    dxy[8] += (dxy[7] - c);

    /* propagate carries, adjusting the exponent if need be */
    dxy[7] = dxy[6] + dxy[8];
    dxy[5] = dxy[4] + dxy[7];
    dxy[3] = dxy[2] + dxy[5];
    dxy[1] = dxy[0] + dxy[3];
    if (dxy[1] >= two) {
        dxy[0] *= half;
        dxy[1] *= half;
        dxy[2] *= half;
        dxy[3] *= half;
        dxy[4] *= half;
        dxy[5] *= half;
        dxy[6] *= half;
        dxy[7] *= half;
        dxy[8] *= half;
        exy++;
    }

    /* extract the significand of x*y */
    s = two36;
    u.d = c = dxy[1] + s;
    xy0 = u.i[1];
    c -= s;
    dxy[1] -= c;
    dxy[0] -= c;

    s *= twom32;
    u.d = c = dxy[1] + s;
    xy1 = u.i[1];
    c -= s;
    dxy[2] += (dxy[0] - c);
    dxy[3] = dxy[2] + dxy[5];

    s *= twom32;
    u.d = c = dxy[3] + s;
    xy2 = u.i[1];
    c -= s;
    dxy[4] += (dxy[2] - c);
    dxy[5] = dxy[4] + dxy[7];

    s *= twom32;
    u.d = c = dxy[5] + s;
    xy3 = u.i[1];
    c -= s;
    dxy[4] -= c;
    dxy[5] = dxy[4] + dxy[7];

    s *= twom32;
    u.d = c = dxy[5] + s;
    xy4 = u.i[1];
    c -= s;
    dxy[6] += (dxy[4] - c);
    dxy[7] = dxy[6] + dxy[8];

    s *= twom32;
    u.d = c = dxy[7] + s;
    xy5 = u.i[1];
    c -= s;
    dxy[8] += (dxy[6] - c);

    s *= twom32;
    u.d = c = dxy[8] + s;
    xy6 = u.i[1];
    c -= s;
    dxy[8] -= c;

    s *= twom32;
    u.d = c = dxy[8] + s;
    xy7 = u.i[1];

    /* extract the sign, exponent, and significand of z */
    sz = zz.i[0] & 0x80000000;
    ez = hz >> 16;
    z0 = hz & 0xffff;
    if (!ez) {
        if (z0 | (zz.i[1] & 0xfffe0000)) {
            z1 = zz.i[1];
            z2 = zz.i[2];
            z3 = zz.i[3];
            ez = 1;
        } else if (zz.i[1] | (zz.i[2] & 0xfffe0000)) {
            z0 = zz.i[1];
            z1 = zz.i[2];
            z2 = zz.i[3];
            z3 = 0;
            ez = -31;
        } else if (zz.i[2] | (zz.i[3] & 0xfffe0000)) {
            z0 = zz.i[2];
            z1 = zz.i[3];
            z2 = z3 = 0;
            ez = -63;
        } else {
            z0 = zz.i[3];
            z1 = z2 = z3 = 0;
            ez = -95;
        }
        while ((z0 & 0x10000) == 0) {
            z0 = (z0 << 1) | (z1 >> 31);
            z1 = (z1 << 1) | (z2 >> 31);
            z2 = (z2 << 1) | (z3 >> 31);
            z3 <<= 1;
            ez--;
        }
    } else {
        z0 |= 0x10000;
        z1 = zz.i[1];
        z2 = zz.i[2];
        z3 = zz.i[3];
    }
    z4 = z5 = z6 = z7 = 0;

    /*
     * now x*y is represented by sxy, exy, and xy[0-7], and z is
     * represented likewise; swap if need be so |xy| <= |z|
     */
    if (exy > ez || (exy == ez && (xy0 > z0 || (xy0 == z0 && (xy1 > z1 ||
        (xy1 == z1 && (xy2 > z2 || (xy2 == z2 && (xy3 > z3 ||
        (xy3 == z3 && (xy4 | xy5 | xy6 | xy7) != 0)))))))))) {
        e = sxy; sxy = sz; sz = e;
        e = exy; exy = ez; ez = e;
        e = xy0; xy0 = z0; z0 = e;
        e = xy1; xy1 = z1; z1 = e;
        e = xy2; xy2 = z2; z2 = e;
        e = xy3; xy3 = z3; z3 = e;
        z4 = xy4; xy4 = 0;
        z5 = xy5; xy5 = 0;
        z6 = xy6; xy6 = 0;
        z7 = xy7; xy7 = 0;
    }

    /* shift the significand of xy keeping a sticky bit */
    e = ez - exy;
    if (e > 236) {
        xy0 = xy1 = xy2 = xy3 = xy4 = xy5 = xy6 = 0;
        xy7 = 1;
    } else if (e >= 224) {
        sticky = xy7 | xy6 | xy5 | xy4 | xy3 | xy2 | xy1 |
            ((xy0 << 1) << (255 - e));
        xy7 = xy0 >> (e - 224);
        if (sticky)
            xy7 |= 1;
        xy0 = xy1 = xy2 = xy3 = xy4 = xy5 = xy6 = 0;
    } else if (e >= 192) {
        sticky = xy7 | xy6 | xy5 | xy4 | xy3 | xy2 |
            ((xy1 << 1) << (223 - e));
        xy7 = (xy1 >> (e - 192)) | ((xy0 << 1) << (223 - e));
        if (sticky)
            xy7 |= 1;
        xy6 = xy0 >> (e - 192);
        xy0 = xy1 = xy2 = xy3 = xy4 = xy5 = 0;
    } else if (e >= 160) {
        sticky = xy7 | xy6 | xy5 | xy4 | xy3 |
            ((xy2 << 1) << (191 - e));
        xy7 = (xy2 >> (e - 160)) | ((xy1 << 1) << (191 - e));
        if (sticky)
            xy7 |= 1;
        xy6 = (xy1 >> (e - 160)) | ((xy0 << 1) << (191 - e));
        xy5 = xy0 >> (e - 160);
        xy0 = xy1 = xy2 = xy3 = xy4 = 0;
    } else if (e >= 128) {
        sticky = xy7 | xy6 | xy5 | xy4 | ((xy3 << 1) << (159 - e));
        xy7 = (xy3 >> (e - 128)) | ((xy2 << 1) << (159 - e));
        if (sticky)
            xy7 |= 1;
        xy6 = (xy2 >> (e - 128)) | ((xy1 << 1) << (159 - e));
        xy5 = (xy1 >> (e - 128)) | ((xy0 << 1) << (159 - e));
        xy4 = xy0 >> (e - 128);
        xy0 = xy1 = xy2 = xy3 = 0;
    } else if (e >= 96) {
        sticky = xy7 | xy6 | xy5 | ((xy4 << 1) << (127 - e));
        xy7 = (xy4 >> (e - 96)) | ((xy3 << 1) << (127 - e));
        if (sticky)
            xy7 |= 1;
        xy6 = (xy3 >> (e - 96)) | ((xy2 << 1) << (127 - e));
        xy5 = (xy2 >> (e - 96)) | ((xy1 << 1) << (127 - e));
        xy4 = (xy1 >> (e - 96)) | ((xy0 << 1) << (127 - e));
        xy3 = xy0 >> (e - 96);
        xy0 = xy1 = xy2 = 0;
    } else if (e >= 64) {
        sticky = xy7 | xy6 | ((xy5 << 1) << (95 - e));
        xy7 = (xy5 >> (e - 64)) | ((xy4 << 1) << (95 - e));
        if (sticky)
            xy7 |= 1;
        xy6 = (xy4 >> (e - 64)) | ((xy3 << 1) << (95 - e));
        xy5 = (xy3 >> (e - 64)) | ((xy2 << 1) << (95 - e));
        xy4 = (xy2 >> (e - 64)) | ((xy1 << 1) << (95 - e));
        xy3 = (xy1 >> (e - 64)) | ((xy0 << 1) << (95 - e));
        xy2 = xy0 >> (e - 64);
        xy0 = xy1 = 0;
    } else if (e >= 32) {
        sticky = xy7 | ((xy6 << 1) << (63 - e));
        xy7 = (xy6 >> (e - 32)) | ((xy5 << 1) << (63 - e));
        if (sticky)
            xy7 |= 1;
        xy6 = (xy5 >> (e - 32)) | ((xy4 << 1) << (63 - e));
        xy5 = (xy4 >> (e - 32)) | ((xy3 << 1) << (63 - e));
        xy4 = (xy3 >> (e - 32)) | ((xy2 << 1) << (63 - e));
        xy3 = (xy2 >> (e - 32)) | ((xy1 << 1) << (63 - e));
        xy2 = (xy1 >> (e - 32)) | ((xy0 << 1) << (63 - e));
        xy1 = xy0 >> (e - 32);
        xy0 = 0;
    } else if (e) {
        sticky = (xy7 << 1) << (31 - e);
        xy7 = (xy7 >> e) | ((xy6 << 1) << (31 - e));
        if (sticky)
            xy7 |= 1;
        xy6 = (xy6 >> e) | ((xy5 << 1) << (31 - e));
        xy5 = (xy5 >> e) | ((xy4 << 1) << (31 - e));
        xy4 = (xy4 >> e) | ((xy3 << 1) << (31 - e));
        xy3 = (xy3 >> e) | ((xy2 << 1) << (31 - e));
        xy2 = (xy2 >> e) | ((xy1 << 1) << (31 - e));
        xy1 = (xy1 >> e) | ((xy0 << 1) << (31 - e));
        xy0 >>= e;
    }

    /* if this is a magnitude subtract, negate the significand of xy */
    if (sxy ^ sz) {
        xy0 = ~xy0;
        xy1 = ~xy1;
        xy2 = ~xy2;
        xy3 = ~xy3;
        xy4 = ~xy4;
        xy5 = ~xy5;
        xy6 = ~xy6;
        xy7 = -xy7;
        if (xy7 == 0)
            if (++xy6 == 0)
                if (++xy5 == 0)
                    if (++xy4 == 0)
                        if (++xy3 == 0)
                            if (++xy2 == 0)
                                if (++xy1 == 0)
                                    xy0++;
    }

    /* add, propagating carries */
    z7 += xy7;
    e = (z7 < xy7);
    z6 += xy6;
    if (e) {
        z6++;
        e = (z6 <= xy6);
    } else
        e = (z6 < xy6);
    z5 += xy5;
    if (e) {
        z5++;
        e = (z5 <= xy5);
    } else
        e = (z5 < xy5);
    z4 += xy4;
    if (e) {
        z4++;
        e = (z4 <= xy4);
    } else
        e = (z4 < xy4);
    z3 += xy3;
    if (e) {
        z3++;
        e = (z3 <= xy3);
    } else
        e = (z3 < xy3);
    z2 += xy2;
    if (e) {
        z2++;
        e = (z2 <= xy2);
    } else
        e = (z2 < xy2);
    z1 += xy1;
    if (e) {
        z1++;
        e = (z1 <= xy1);
    } else
        e = (z1 < xy1);
    z0 += xy0;
    if (e)
        z0++;

    /* postnormalize and collect rounding information into z4 */
    if (ez < 1) {
        /* result is tiny; shift right until exponent is within range */
        e = 1 - ez;
        if (e > 116) {
            z4 = 1; /* result can't be exactly zero */
            z0 = z1 = z2 = z3 = 0;
        } else if (e >= 96) {
            sticky = z7 | z6 | z5 | z4 | z3 | z2 |
                ((z1 << 1) << (127 - e));
            z4 = (z1 >> (e - 96)) | ((z0 << 1) << (127 - e));
            if (sticky)
                z4 |= 1;
            z3 = z0 >> (e - 96);
            z0 = z1 = z2 = 0;
        } else if (e >= 64) {
            sticky = z7 | z6 | z5 | z4 | z3 |
                ((z2 << 1) << (95 - e));
            z4 = (z2 >> (e - 64)) | ((z1 << 1) << (95 - e));
            if (sticky)
                z4 |= 1;
            z3 = (z1 >> (e - 64)) | ((z0 << 1) << (95 - e));
            z2 = z0 >> (e - 64);
            z0 = z1 = 0;
        } else if (e >= 32) {
            sticky = z7 | z6 | z5 | z4 | ((z3 << 1) << (63 - e));
            z4 = (z3 >> (e - 32)) | ((z2 << 1) << (63 - e));
            if (sticky)
                z4 |= 1;
            z3 = (z2 >> (e - 32)) | ((z1 << 1) << (63 - e));
            z2 = (z1 >> (e - 32)) | ((z0 << 1) << (63 - e));
            z1 = z0 >> (e - 32);
            z0 = 0;
        } else {
            sticky = z7 | z6 | z5 | (z4 << 1) << (31 - e);
            z4 = (z4 >> e) | ((z3 << 1) << (31 - e));
            if (sticky)
                z4 |= 1;
            z3 = (z3 >> e) | ((z2 << 1) << (31 - e));
            z2 = (z2 >> e) | ((z1 << 1) << (31 - e));
            z1 = (z1 >> e) | ((z0 << 1) << (31 - e));
            z0 >>= e;
        }
        ez = 1;
    } else if (z0 >= 0x20000) {
        /* carry out; shift right by one */
        sticky = (z4 & 1) | z5 | z6 | z7;
        z4 = (z4 >> 1) | (z3 << 31);
        if (sticky)
            z4 |= 1;
        z3 = (z3 >> 1) | (z2 << 31);
        z2 = (z2 >> 1) | (z1 << 31);
        z1 = (z1 >> 1) | (z0 << 31);
        z0 >>= 1;
        ez++;
    } else {
        if (z0 < 0x10000 && (z0 | z1 | z2 | z3 | z4 | z5 | z6 | z7)
            != 0) {
            /*
             * borrow/cancellation; shift left as much as
             * exponent allows
             */
            while (!(z0 | (z1 & 0xfffe0000)) && ez >= 33) {
                z0 = z1;
                z1 = z2;
                z2 = z3;
                z3 = z4;
                z4 = z5;
                z5 = z6;
                z6 = z7;
                z7 = 0;
                ez -= 32;
            }
            while (z0 < 0x10000 && ez > 1) {
                z0 = (z0 << 1) | (z1 >> 31);
                z1 = (z1 << 1) | (z2 >> 31);
                z2 = (z2 << 1) | (z3 >> 31);
                z3 = (z3 << 1) | (z4 >> 31);
                z4 = (z4 << 1) | (z5 >> 31);
                z5 = (z5 << 1) | (z6 >> 31);
                z6 = (z6 << 1) | (z7 >> 31);
                z7 <<= 1;
                ez--;
            }
        }
        if (z5 | z6 | z7)
            z4 |= 1;
    }

    /* get the rounding mode */
    rm = fsr >> 30;

    /* strip off the integer bit, if there is one */
    ibit = z0 & 0x10000;
    if (ibit)
        z0 -= 0x10000;
    else {
        ez = 0;
        if (!(z0 | z1 | z2 | z3 | z4)) { /* exact zero */
            zz.i[0] = rm == FSR_RM ? 0x80000000 : 0;
            zz.i[1] = zz.i[2] = zz.i[3] = 0;
            __fenv_setfsr32(&fsr);
            return (zz.q);
        }
    }

    /*
     * flip the sense of directed roundings if the result is negative;
     * the logic below applies to a positive result
     */
    if (sz)
        rm ^= rm >> 1;

    /* round and raise exceptions */
    if (z4) {
        fsr |= FSR_NXC;

        /* decide whether to round the fraction up */
        if (rm == FSR_RP || (rm == FSR_RN && (z4 > 0x80000000u ||
            (z4 == 0x80000000u && (z3 & 1))))) {
            /* round up and renormalize if necessary */
            if (++z3 == 0)
                if (++z2 == 0)
                    if (++z1 == 0)
                        if (++z0 == 0x10000) {
                            z0 = 0;
                            ez++;
                        }
        }
    }

    /* check for under/overflow */
    if (ez >= 0x7fff) {
        if (rm == FSR_RN || rm == FSR_RP) {
            zz.i[0] = sz | 0x7fff0000;
            zz.i[1] = zz.i[2] = zz.i[3] = 0;
        } else {
            zz.i[0] = sz | 0x7ffeffff;
            zz.i[1] = zz.i[2] = zz.i[3] = 0xffffffff;
        }
        fsr |= FSR_OFC | FSR_NXC;
    } else {
        zz.i[0] = sz | (ez << 16) | z0;
        zz.i[1] = z1;
        zz.i[2] = z2;
        zz.i[3] = z3;

        /*
         * !ibit => exact result was tiny before rounding,
         * z4 nonzero => result delivered is inexact
         */
        if (!ibit) {
            if (z4)
                fsr |= FSR_UFC | FSR_NXC;
            else if (fsr & FSR_UFM)
                fsr |= FSR_UFC;
        }
    }

    /* restore the fsr and emulate exceptions as needed */
    if ((fsr & FSR_CEXC) & (fsr >> 23)) {
        __fenv_setfsr32(&fsr);
        if (fsr & FSR_OFC) {
            dummy = huge;
            dummy *= huge;
        } else if (fsr & FSR_UFC) {
            dummy = tiny;
            if (fsr & FSR_NXC)
                dummy *= tiny;
            else
                dummy -= tiny2;
        } else {
            dummy = huge;
            dummy += tiny;
        }
    } else {
        fsr |= (fsr & 0x1f) << 5;
        __fenv_setfsr32(&fsr);
    }
    return (zz.q);
}

#elif defined(__x86)

static const union {
    unsigned i[2];
    double d;
} C[] = {
    { 0, 0x3fe00000u },
    { 0, 0x40000000u },
    { 0, 0x3df00000u },
    { 0, 0x3bf00000u },
    { 0, 0x41f00000u },
    { 0, 0x43e00000u },
    { 0, 0x7fe00000u },
    { 0, 0x00100000u },
    { 0, 0x00100001u }
};

#define half    C[0].d
#define two C[1].d
#define twom32  C[2].d
#define twom64  C[3].d
#define two32   C[4].d
#define two63   C[5].d
#define huge    C[6].d
#define tiny    C[7].d
#define tiny2   C[8].d

#if defined(__amd64)
#define NI  4
#else
#define NI  3
#endif

/*
 * fmal for x86: 80-bit extended double precision, little-endian
 */
long double
__fmal(long double x, long double y, long double z) {
    union {
        unsigned i[NI];
        long double e;
    } xx, yy, zz;
    long double xhi, yhi, xlo, ylo, t;
    unsigned xy0, xy1, xy2, xy3, xy4, z0, z1, z2, z3, z4;
    unsigned oldcwsw, cwsw, rm, sticky, carry;
    int ex, ey, ez, exy, sxy, sz, e, tinyafter;
    volatile double dummy;

    /* extract the exponents of the arguments */
    xx.e = x;
    yy.e = y;
    zz.e = z;
    ex = xx.i[2] & 0x7fff;
    ey = yy.i[2] & 0x7fff;
    ez = zz.i[2] & 0x7fff;

    /* dispense with inf, nan, and zero cases */
    if (ex == 0x7fff || ey == 0x7fff || (ex | xx.i[1] | xx.i[0]) == 0 ||
        (ey | yy.i[1] | yy.i[0]) == 0)  /* x or y is inf, nan, or 0 */
        return (x * y + z);

    if (ez == 0x7fff)           /* z is inf or nan */
        return (x + z); /* avoid spurious under/overflow in x * y */

    if ((ez | zz.i[1] | zz.i[0]) == 0)  /* z is zero */
        /*
         * x * y isn't zero but could underflow to zero,
         * so don't add z, lest we perturb the sign
         */
        return (x * y);

    /*
     * now x, y, and z are all finite and nonzero; extract signs and
     * normalize the significands (this will raise the denormal operand
     * exception if need be)
     */
    sxy = (xx.i[2] ^ yy.i[2]) & 0x8000;
    sz = zz.i[2] & 0x8000;
    if (!ex) {
        xx.e = x * two63;
        ex = (xx.i[2] & 0x7fff) - 63;
    }
    if (!ey) {
        yy.e = y * two63;
        ey = (yy.i[2] & 0x7fff) - 63;
    }
    if (!ez) {
        zz.e = z * two63;
        ez = (zz.i[2] & 0x7fff) - 63;
    }

    /*
     * save the control and status words, mask all exceptions, and
     * set rounding to 64-bit precision and toward-zero
     */
    __fenv_getcwsw(&oldcwsw);
    cwsw = (oldcwsw & 0xf0c0ffff) | 0x0f3f0000;
    __fenv_setcwsw(&cwsw);

    /* multiply x*y to 128 bits */
    exy = ex + ey - 0x3fff;
    xx.i[2] = 0x3fff;
    yy.i[2] = 0x3fff;
    x = xx.e;
    y = yy.e;
    xhi = ((x + twom32) + two32) - two32;
    yhi = ((y + twom32) + two32) - two32;
    xlo = x - xhi;
    ylo = y - yhi;
    x *= y;
    y = ((xhi * yhi - x) + xhi * ylo + xlo * yhi) + xlo * ylo;
    if (x >= two) {
        x *= half;
        y *= half;
        exy++;
    }

    /* extract the significands */
    xx.e = x;
    xy0 = xx.i[1];
    xy1 = xx.i[0];
    yy.e = t = y + twom32;
    xy2 = yy.i[0];
    yy.e = (y - (t - twom32)) + twom64;
    xy3 = yy.i[0];
    xy4 = 0;
    z0 = zz.i[1];
    z1 = zz.i[0];
    z2 = z3 = z4 = 0;

    /*
     * now x*y is represented by sxy, exy, and xy[0-4], and z is
     * represented likewise; swap if need be so |xy| <= |z|
     */
    if (exy > ez || (exy == ez && (xy0 > z0 || (xy0 == z0 &&
        (xy1 > z1 || (xy1 == z1 && (xy2 | xy3) != 0)))))) {
        e = sxy; sxy = sz; sz = e;
        e = exy; exy = ez; ez = e;
        e = xy0; xy0 = z0; z0 = e;
        e = xy1; xy1 = z1; z1 = e;
        z2 = xy2; xy2 = 0;
        z3 = xy3; xy3 = 0;
    }

    /* shift the significand of xy keeping a sticky bit */
    e = ez - exy;
    if (e > 130) {
        xy0 = xy1 = xy2 = xy3 = 0;
        xy4 = 1;
    } else if (e >= 128) {
        sticky = xy3 | xy2 | xy1 | ((xy0 << 1) << (159 - e));
        xy4 = xy0 >> (e - 128);
        if (sticky)
            xy4 |= 1;
        xy0 = xy1 = xy2 = xy3 = 0;
    } else if (e >= 96) {
        sticky = xy3 | xy2 | ((xy1 << 1) << (127 - e));
        xy4 = (xy1 >> (e - 96)) | ((xy0 << 1) << (127 - e));
        if (sticky)
            xy4 |= 1;
        xy3 = xy0 >> (e - 96);
        xy0 = xy1 = xy2 = 0;
    } else if (e >= 64) {
        sticky = xy3 | ((xy2 << 1) << (95 - e));
        xy4 = (xy2 >> (e - 64)) | ((xy1 << 1) << (95 - e));
        if (sticky)
            xy4 |= 1;
        xy3 = (xy1 >> (e - 64)) | ((xy0 << 1) << (95 - e));
        xy2 = xy0 >> (e - 64);
        xy0 = xy1 = 0;
    } else if (e >= 32) {
        sticky = (xy3 << 1) << (63 - e);
        xy4 = (xy3 >> (e - 32)) | ((xy2 << 1) << (63 - e));
        if (sticky)
            xy4 |= 1;
        xy3 = (xy2 >> (e - 32)) | ((xy1 << 1) << (63 - e));
        xy2 = (xy1 >> (e - 32)) | ((xy0 << 1) << (63 - e));
        xy1 = xy0 >> (e - 32);
        xy0 = 0;
    } else if (e) {
        xy4 = (xy3 << 1) << (31 - e);
        xy3 = (xy3 >> e) | ((xy2 << 1) << (31 - e));
        xy2 = (xy2 >> e) | ((xy1 << 1) << (31 - e));
        xy1 = (xy1 >> e) | ((xy0 << 1) << (31 - e));
        xy0 >>= e;
    }

    /* if this is a magnitude subtract, negate the significand of xy */
    if (sxy ^ sz) {
        xy0 = ~xy0;
        xy1 = ~xy1;
        xy2 = ~xy2;
        xy3 = ~xy3;
        xy4 = -xy4;
        if (xy4 == 0)
            if (++xy3 == 0)
                if (++xy2 == 0)
                    if (++xy1 == 0)
                        xy0++;
    }

    /* add, propagating carries */
    z4 += xy4;
    carry = (z4 < xy4);
    z3 += xy3;
    if (carry) {
        z3++;
        carry = (z3 <= xy3);
    } else
        carry = (z3 < xy3);
    z2 += xy2;
    if (carry) {
        z2++;
        carry = (z2 <= xy2);
    } else
        carry = (z2 < xy2);
    z1 += xy1;
    if (carry) {
        z1++;
        carry = (z1 <= xy1);
    } else
        carry = (z1 < xy1);
    z0 += xy0;
    if (carry) {
        z0++;
        carry = (z0 <= xy0);
    } else
        carry = (z0 < xy0);

    /* for a magnitude subtract, ignore the last carry out */
    if (sxy ^ sz)
        carry = 0;

    /* postnormalize and collect rounding information into z2 */
    if (ez < 1) {
        /* result is tiny; shift right until exponent is within range */
        e = 1 - ez;
        if (e > 67) {
            z2 = 1; /* result can't be exactly zero */
            z0 = z1 = 0;
        } else if (e >= 64) {
            sticky = z4 | z3 | z2 | z1 | ((z0 << 1) << (95 - e));
            z2 = (z0 >> (e - 64)) | ((carry << 1) << (95 - e));
            if (sticky)
                z2 |= 1;
            z1 = carry >> (e - 64);
            z0 = 0;
        } else if (e >= 32) {
            sticky = z4 | z3 | z2 | ((z1 << 1) << (63 - e));
            z2 = (z1 >> (e - 32)) | ((z0 << 1) << (63 - e));
            if (sticky)
                z2 |= 1;
            z1 = (z0 >> (e - 32)) | ((carry << 1) << (63 - e));
            z0 = carry >> (e - 32);
        } else {
            sticky = z4 | z3 | (z2 << 1) << (31 - e);
            z2 = (z2 >> e) | ((z1 << 1) << (31 - e));
            if (sticky)
                z2 |= 1;
            z1 = (z1 >> e) | ((z0 << 1) << (31 - e));
            z0 = (z0 >> e) | ((carry << 1) << (31 - e));
        }
        ez = 1;
    } else if (carry) {
        /* carry out; shift right by one */
        sticky = (z2 & 1) | z3 | z4;
        z2 = (z2 >> 1) | (z1 << 31);
        if (sticky)
            z2 |= 1;
        z1 = (z1 >> 1) | (z0 << 31);
        z0 = (z0 >> 1) | 0x80000000;
        ez++;
    } else {
        if (z0 < 0x80000000u && (z0 | z1 | z2 | z3 | z4) != 0) {
            /*
             * borrow/cancellation; shift left as much as
             * exponent allows
             */
            while (!z0 && ez >= 33) {
                z0 = z1;
                z1 = z2;
                z2 = z3;
                z3 = z4;
                z4 = 0;
                ez -= 32;
            }
            while (z0 < 0x80000000u && ez > 1) {
                z0 = (z0 << 1) | (z1 >> 31);
                z1 = (z1 << 1) | (z2 >> 31);
                z2 = (z2 << 1) | (z3 >> 31);
                z3 = (z3 << 1) | (z4 >> 31);
                z4 <<= 1;
                ez--;
            }
        }
        if (z3 | z4)
            z2 |= 1;
    }

    /* get the rounding mode */
    rm = oldcwsw & 0x0c000000;

    /* adjust exponent if result is subnormal */
    tinyafter = 0;
    if (!(z0 & 0x80000000)) {
        ez = 0;
        tinyafter = 1;
        if (!(z0 | z1 | z2)) { /* exact zero */
            zz.i[2] = rm == FCW_RM ? 0x8000 : 0;
            zz.i[1] = zz.i[0] = 0;
            __fenv_setcwsw(&oldcwsw);
            return (zz.e);
        }
    }

    /*
     * flip the sense of directed roundings if the result is negative;
     * the logic below applies to a positive result
     */
    if (sz && (rm == FCW_RM || rm == FCW_RP))
        rm = (FCW_RM + FCW_RP) - rm;

    /* round */
    if (z2) {
        if (rm == FCW_RP || (rm == FCW_RN && (z2 > 0x80000000u ||
            (z2 == 0x80000000u && (z1 & 1))))) {
            /* round up and renormalize if necessary */
            if (++z1 == 0) {
                if (++z0 == 0) {
                    z0 = 0x80000000;
                    ez++;
                } else if (z0 == 0x80000000) {
                    /* rounded up to smallest normal */
                    ez = 1;
                    if ((rm == FCW_RP && z2 >
                        0x80000000u) || (rm == FCW_RN &&
                        z2 >= 0xc0000000u))
                        /*
                         * would have rounded up to
                         * smallest normal even with
                         * unbounded range
                         */
                        tinyafter = 0;
                }
            }
        }
    }

    /* restore the control and status words, check for over/underflow */
    __fenv_setcwsw(&oldcwsw);
    if (ez >= 0x7fff) {
        if (rm == FCW_RN || rm == FCW_RP) {
            zz.i[2] = sz | 0x7fff;
            zz.i[1] = 0x80000000;
            zz.i[0] = 0;
        } else {
            zz.i[2] = sz | 0x7ffe;
            zz.i[1] = 0xffffffff;
            zz.i[0] = 0xffffffff;
        }
        dummy = huge;
        dummy *= huge;
    } else {
        zz.i[2] = sz | ez;
        zz.i[1] = z0;
        zz.i[0] = z1;

        /*
         * tinyafter => result rounded w/ unbounded range would be tiny,
         * z2 nonzero => result delivered is inexact
         */
        if (tinyafter) {
            dummy = tiny;
            if (z2)
                dummy *= tiny;
            else
                dummy -= tiny2;
        } else if (z2) {
            dummy = huge;
            dummy += tiny;
        }
    }

    return (zz.e);
}

#else
#error Unknown architecture
#endif