muldi3.c

Version: - FREEBSD - FREEBSD-13-STABLE - FREEBSD-13-0 - FREEBSD-12-STABLE - FREEBSD-12-0 - FREEBSD-11-STABLE - FREEBSD-11-0 - FREEBSD-10-STABLE - FREEBSD-10-0 - FREEBSD-9-STABLE - FREEBSD-9-0 - FREEBSD-8-STABLE - FREEBSD-8-0 - FREEBSD-7-STABLE - FREEBSD-7-0 - FREEBSD-6-STABLE - FREEBSD-6-0 - FREEBSD-5-STABLE - FREEBSD-5-0 - FREEBSD-4-STABLE - FREEBSD-3-STABLE - FREEBSD22 - l41 - OPENBSD - linux-2.6 - MK84 - PLAN9 - xnu-8792
SearchContext: - none - 3 - 10

    1 /*-
    2  * Copyright (c) 1992, 1993
    3  *      The Regents of the University of California.  All rights reserved.
    4  *
    5  * This software was developed by the Computer Systems Engineering group
    6  * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and
    7  * contributed to Berkeley.
    8  *
    9  * Redistribution and use in source and binary forms, with or without
   10  * modification, are permitted provided that the following conditions
   11  * are met:
   12  * 1. Redistributions of source code must retain the above copyright
   13  *    notice, this list of conditions and the following disclaimer.
   14  * 2. Redistributions in binary form must reproduce the above copyright
   15  *    notice, this list of conditions and the following disclaimer in the
   16  *    documentation and/or other materials provided with the distribution.
   17  * 3. All advertising materials mentioning features or use of this software
   18  *    must display the following acknowledgement:
   19  *      This product includes software developed by the University of
   20  *      California, Berkeley and its contributors.
   21  * 4. Neither the name of the University nor the names of its contributors
   22  *    may be used to endorse or promote products derived from this software
   23  *    without specific prior written permission.
   24  *
   25  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
   26  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
   27  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
   28  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
   29  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
   30  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
   31  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
   32  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
   33  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
   34  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
   35  * SUCH DAMAGE.
   36  *
   37  * $FreeBSD: src/sys/libkern/muldi3.c,v 1.3.8.1 1999/09/05 08:16:06 peter Exp $
   38  */
   39 
   40 #include "quad.h"
   41 
   42 /*
   43  * Multiply two quads.
   44  *
   45  * Our algorithm is based on the following.  Split incoming quad values
   46  * u and v (where u,v >= 0) into
   47  *
   48  *      u = 2^n u1  *  u0       (n = number of bits in `u_long', usu. 32)
   49  *
   50  * and
   51  *
   52  *      v = 2^n v1  *  v0
   53  *
   54  * Then
   55  *
   56  *      uv = 2^2n u1 v1  +  2^n u1 v0  +  2^n v1 u0  +  u0 v0
   57  *         = 2^2n u1 v1  +     2^n (u1 v0 + v1 u0)   +  u0 v0
   58  *
   59  * Now add 2^n u1 v1 to the first term and subtract it from the middle,
   60  * and add 2^n u0 v0 to the last term and subtract it from the middle.
   61  * This gives:
   62  *
   63  *      uv = (2^2n + 2^n) (u1 v1)  +
   64  *               (2^n)    (u1 v0 - u1 v1 + u0 v1 - u0 v0)  +
   65  *             (2^n + 1)  (u0 v0)
   66  *
   67  * Factoring the middle a bit gives us:
   68  *
   69  *      uv = (2^2n + 2^n) (u1 v1)  +                    [u1v1 = high]
   70  *               (2^n)    (u1 - u0) (v0 - v1)  +        [(u1-u0)... = mid]
   71  *             (2^n + 1)  (u0 v0)                       [u0v0 = low]
   72  *
   73  * The terms (u1 v1), (u1 - u0) (v0 - v1), and (u0 v0) can all be done
   74  * in just half the precision of the original.  (Note that either or both
   75  * of (u1 - u0) or (v0 - v1) may be negative.)
   76  *
   77  * This algorithm is from Knuth vol. 2 (2nd ed), section 4.3.3, p. 278.
   78  *
   79  * Since C does not give us a `long * long = quad' operator, we split
   80  * our input quads into two longs, then split the two longs into two
   81  * shorts.  We can then calculate `short * short = long' in native
   82  * arithmetic.
   83  *
   84  * Our product should, strictly speaking, be a `long quad', with 128
   85  * bits, but we are going to discard the upper 64.  In other words,
   86  * we are not interested in uv, but rather in (uv mod 2^2n).  This
   87  * makes some of the terms above vanish, and we get:
   88  *
   89  *      (2^n)(high) + (2^n)(mid) + (2^n + 1)(low)
   90  *
   91  * or
   92  *
   93  *      (2^n)(high + mid + low) + low
   94  *
   95  * Furthermore, `high' and `mid' can be computed mod 2^n, as any factor
   96  * of 2^n in either one will also vanish.  Only `low' need be computed
   97  * mod 2^2n, and only because of the final term above.
   98  */
   99 static quad_t __lmulq(u_long, u_long);
  100 
  101 quad_t
  102 __muldi3(a, b)
  103         quad_t a, b;
  104 {
  105         union uu u, v, low, prod;
  106         register u_long high, mid, udiff, vdiff;
  107         register int negall, negmid;
  108 #define u1      u.ul[H]
  109 #define u0      u.ul[L]
  110 #define v1      v.ul[H]
  111 #define v0      v.ul[L]
  112 
  113         /*
  114          * Get u and v such that u, v >= 0.  When this is finished,
  115          * u1, u0, v1, and v0 will be directly accessible through the
  116          * longword fields.
  117          */
  118         if (a >= 0)
  119                 u.q = a, negall = 0;
  120         else
  121                 u.q = -a, negall = 1;
  122         if (b >= 0)
  123                 v.q = b;
  124         else
  125                 v.q = -b, negall ^= 1;
  126 
  127         if (u1 == 0 && v1 == 0) {
  128                 /*
  129                  * An (I hope) important optimization occurs when u1 and v1
  130                  * are both 0.  This should be common since most numbers
  131                  * are small.  Here the product is just u0*v0.
  132                  */
  133                 prod.q = __lmulq(u0, v0);
  134         } else {
  135                 /*
  136                  * Compute the three intermediate products, remembering
  137                  * whether the middle term is negative.  We can discard
  138                  * any upper bits in high and mid, so we can use native
  139                  * u_long * u_long => u_long arithmetic.
  140                  */
  141                 low.q = __lmulq(u0, v0);
  142 
  143                 if (u1 >= u0)
  144                         negmid = 0, udiff = u1 - u0;
  145                 else
  146                         negmid = 1, udiff = u0 - u1;
  147                 if (v0 >= v1)
  148                         vdiff = v0 - v1;
  149                 else
  150                         vdiff = v1 - v0, negmid ^= 1;
  151                 mid = udiff * vdiff;
  152 
  153                 high = u1 * v1;
  154 
  155                 /*
  156                  * Assemble the final product.
  157                  */
  158                 prod.ul[H] = high + (negmid ? -mid : mid) + low.ul[L] +
  159                     low.ul[H];
  160                 prod.ul[L] = low.ul[L];
  161         }
  162         return (negall ? -prod.q : prod.q);
  163 #undef u1
  164 #undef u0
  165 #undef v1
  166 #undef v0
  167 }
  168 
  169 /*
  170  * Multiply two 2N-bit longs to produce a 4N-bit quad, where N is half
  171  * the number of bits in a long (whatever that is---the code below
  172  * does not care as long as quad.h does its part of the bargain---but
  173  * typically N==16).
  174  *
  175  * We use the same algorithm from Knuth, but this time the modulo refinement
  176  * does not apply.  On the other hand, since N is half the size of a long,
  177  * we can get away with native multiplication---none of our input terms
  178  * exceeds (ULONG_MAX >> 1).
  179  *
  180  * Note that, for u_long l, the quad-precision result
  181  *
  182  *      l << N
  183  *
  184  * splits into high and low longs as HHALF(l) and LHUP(l) respectively.
  185  */
  186 static quad_t
  187 __lmulq(u_long u, u_long v)
  188 {
  189         u_long u1, u0, v1, v0, udiff, vdiff, high, mid, low;
  190         u_long prodh, prodl, was;
  191         union uu prod;
  192         int neg;
  193 
  194         u1 = HHALF(u);
  195         u0 = LHALF(u);
  196         v1 = HHALF(v);
  197         v0 = LHALF(v);
  198 
  199         low = u0 * v0;
  200 
  201         /* This is the same small-number optimization as before. */
  202         if (u1 == 0 && v1 == 0)
  203                 return (low);
  204 
  205         if (u1 >= u0)
  206                 udiff = u1 - u0, neg = 0;
  207         else
  208                 udiff = u0 - u1, neg = 1;
  209         if (v0 >= v1)
  210                 vdiff = v0 - v1;
  211         else
  212                 vdiff = v1 - v0, neg ^= 1;
  213         mid = udiff * vdiff;
  214 
  215         high = u1 * v1;
  216 
  217         /* prod = (high << 2N) + (high << N); */
  218         prodh = high + HHALF(high);
  219         prodl = LHUP(high);
  220 
  221         /* if (neg) prod -= mid << N; else prod += mid << N; */
  222         if (neg) {
  223                 was = prodl;
  224                 prodl -= LHUP(mid);
  225                 prodh -= HHALF(mid) + (prodl > was);
  226         } else {
  227                 was = prodl;
  228                 prodl += LHUP(mid);
  229                 prodh += HHALF(mid) + (prodl < was);
  230         }
  231 
  232         /* prod += low << N */
  233         was = prodl;
  234         prodl += LHUP(low);
  235         prodh += HHALF(low) + (prodl < was);
  236         /* ... + low; */
  237         if ((prodl += low) < low)
  238                 prodh++;
  239 
  240         /* return 4N-bit product */
  241         prod.ul[H] = prodh;
  242         prod.ul[L] = prodl;
  243         return (prod.q);
  244 }

Cache object: dfa369054293ba9f561559ae3a0fb1a3

[ source navigation ] [ diff markup ] [ identifier search ] [ freetext search ] [ file search ] [ list types ] [ track identifier ]

This page is part of the FreeBSD/Linux Linux Kernel Cross-Reference, and was automatically generated using a modified version of the LXR engine.

FreeBSD/Linux Kernel Cross Reference sys/libkern/muldi3.c

FreeBSD/Linux Kernel Cross Reference
sys/libkern/muldi3.c