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/*-

 * Copyright (c) 1992, 1993

 *      The Regents of the University of California.  All rights reserved.

 *

 * This software was developed by the Computer Systems Engineering group

 * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and

 * contributed to Berkeley.

 *

 * Redistribution and use in source and binary forms, with or without

 * modification, are permitted provided that the following conditions

 * are met:

 * 1. Redistributions of source code must retain the above copyright

 *    notice, this list of conditions and the following disclaimer.

 * 2. Redistributions in binary form must reproduce the above copyright

 *    notice, this list of conditions and the following disclaimer in the

 *    documentation and/or other materials provided with the distribution.

 * 3. All advertising materials mentioning features or use of this software

 *    must display the following acknowledgement:

 *      This product includes software developed by the University of

 *      California, Berkeley and its contributors.

 * 4. Neither the name of the University nor the names of its contributors

 *    may be used to endorse or promote products derived from this software

 *    without specific prior written permission.

 *

 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND

 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE

 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE

 * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE

 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL

 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS

 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)

 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT

 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY

 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF

 * SUCH DAMAGE.

 */

#if defined(LIBC_SCCS) && !defined(lint)

static char sccsid[] = "@(#)muldi3.c    8.1 (Berkeley) 6/4/93";

#endif /* LIBC_SCCS and not lint */

#include "quad.h"

/*

 * Multiply two quads.

 *

 * Our algorithm is based on the following.  Split incoming quad values

 * u and v (where u,v >= 0) into

 *

 *      u = 2^n u1  *  u0       (n = number of bits in `u_long', usu. 32)

 *

 * and

 *

 *      v = 2^n v1  *  v0

 *

 * Then

 *

 *      uv = 2^2n u1 v1  +  2^n u1 v0  +  2^n v1 u0  +  u0 v0

 *         = 2^2n u1 v1  +     2^n (u1 v0 + v1 u0)   +  u0 v0

 *

 * Now add 2^n u1 v1 to the first term and subtract it from the middle,

 * and add 2^n u0 v0 to the last term and subtract it from the middle.

 * This gives:

 *

 *      uv = (2^2n + 2^n) (u1 v1)  +

 *               (2^n)    (u1 v0 - u1 v1 + u0 v1 - u0 v0)  +

 *             (2^n + 1)  (u0 v0)

 *

 * Factoring the middle a bit gives us:

 *

 *      uv = (2^2n + 2^n) (u1 v1)  +                    [u1v1 = high]

 *               (2^n)    (u1 - u0) (v0 - v1)  +        [(u1-u0)... = mid]

 *             (2^n + 1)  (u0 v0)                       [u0v0 = low]

 *

 * The terms (u1 v1), (u1 - u0) (v0 - v1), and (u0 v0) can all be done

 * in just half the precision of the original.  (Note that either or both

 * of (u1 - u0) or (v0 - v1) may be negative.)

 *

 * This algorithm is from Knuth vol. 2 (2nd ed), section 4.3.3, p. 278.

 *

 * Since C does not give us a `long * long = quad' operator, we split

 * our input quads into two longs, then split the two longs into two

 * shorts.  We can then calculate `short * short = long' in native

 * arithmetic.

 *

 * Our product should, strictly speaking, be a `long quad', with 128

 * bits, but we are going to discard the upper 64.  In other words,

 * we are not interested in uv, but rather in (uv mod 2^2n).  This

 * makes some of the terms above vanish, and we get:

 *

 *      (2^n)(high) + (2^n)(mid) + (2^n + 1)(low)

 *

 * or

 *

 *      (2^n)(high + mid + low) + low

 *

 * Furthermore, `high' and `mid' can be computed mod 2^n, as any factor

 * of 2^n in either one will also vanish.  Only `low' need be computed

 * mod 2^2n, and only because of the final term above.

 */

static quad_t __lmulq(u_long, u_long);

quad_t

__muldi3(a, b)

        quad_t a, b;

{

        union uu u, v, low, prod;

        register u_long high, mid, udiff, vdiff;

        register int negall, negmid;

#define u1      u.ul[H]

#define u0      u.ul[L]

#define v1      v.ul[H]

#define v0      v.ul[L]

        /*

         * Get u and v such that u, v >= 0.  When this is finished,

         * u1, u0, v1, and v0 will be directly accessible through the

         * longword fields.

         */

        if (a >= 0)

                u.q = a, negall = 0;

        else

                u.q = -a, negall = 1;

        if (b >= 0)

                v.q = b;

        else

                v.q = -b, negall ^= 1;

        if (u1 == 0 && v1 == 0) {

                /*

                 * An (I hope) important optimization occurs when u1 and v1

                 * are both 0.  This should be common since most numbers

                 * are small.  Here the product is just u0*v0.

                 */

                prod.q = __lmulq(u0, v0);

        } else {

                /*

                 * Compute the three intermediate products, remembering

                 * whether the middle term is negative.  We can discard

                 * any upper bits in high and mid, so we can use native

                 * u_long * u_long => u_long arithmetic.

                 */

                low.q = __lmulq(u0, v0);

                if (u1 >= u0)

                        negmid = 0, udiff = u1 - u0;

                else

                        negmid = 1, udiff = u0 - u1;

                if (v0 >= v1)

                        vdiff = v0 - v1;

                else

                        vdiff = v1 - v0, negmid ^= 1;

                mid = udiff * vdiff;

                high = u1 * v1;

                /*

                 * Assemble the final product.

                 */

                prod.ul[H] = high + (negmid ? -mid : mid) + low.ul[L] +

                    low.ul[H];

                prod.ul[L] = low.ul[L];

        }

        return (negall ? -prod.q : prod.q);

#undef u1

#undef u0

#undef v1

#undef v0

}

/*

 * Multiply two 2N-bit longs to produce a 4N-bit quad, where N is half

 * the number of bits in a long (whatever that is---the code below

 * does not care as long as quad.h does its part of the bargain---but

 * typically N==16).

 *

 * We use the same algorithm from Knuth, but this time the modulo refinement

 * does not apply.  On the other hand, since N is half the size of a long,

 * we can get away with native multiplication---none of our input terms

 * exceeds (ULONG_MAX >> 1).

 *

 * Note that, for u_long l, the quad-precision result

 *

 *      l << N

 *

 * splits into high and low longs as HHALF(l) and LHUP(l) respectively.

 */

static quad_t

__lmulq(u_long u, u_long v)

{

        u_long u1, u0, v1, v0, udiff, vdiff, high, mid, low;

        u_long prodh, prodl, was;

        union uu prod;

        int neg;

        u1 = HHALF(u);

        u0 = LHALF(u);

        v1 = HHALF(v);

        v0 = LHALF(v);

        low = u0 * v0;

        /* This is the same small-number optimization as before. */

        if (u1 == 0 && v1 == 0)

                return (low);

        if (u1 >= u0)

                udiff = u1 - u0, neg = 0;

        else

                udiff = u0 - u1, neg = 1;

        if (v0 >= v1)

                vdiff = v0 - v1;

        else

                vdiff = v1 - v0, neg ^= 1;

        mid = udiff * vdiff;

        high = u1 * v1;

        /* prod = (high << 2N) + (high << N); */

        prodh = high + HHALF(high);

        prodl = LHUP(high);

        /* if (neg) prod -= mid << N; else prod += mid << N; */

        if (neg) {

                was = prodl;

                prodl -= LHUP(mid);

                prodh -= HHALF(mid) + (prodl > was);

        } else {

                was = prodl;

                prodl += LHUP(mid);

                prodh += HHALF(mid) + (prodl < was);

        }

        /* prod += low << N */

        was = prodl;

        prodl += LHUP(low);

        prodh += HHALF(low) + (prodl < was);

        /* ... + low; */

        if ((prodl += low) < low)

                prodh++;

        /* return 4N-bit product */

        prod.ul[H] = prodh;

        prod.ul[L] = prodl;

        return (prod.q);

}