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 /*      $NetBSD: muldi3.c,v 1.8 2003/08/07 16:32:09 agc Exp $   */
    2 
    3 /*-
    4  * SPDX-License-Identifier: BSD-3-Clause
    5  *
    6  * Copyright (c) 1992, 1993
    7  *      The Regents of the University of California.  All rights reserved.
    8  *
    9  * This software was developed by the Computer Systems Engineering group
   10  * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and
   11  * contributed to Berkeley.
   12  *
   13  * Redistribution and use in source and binary forms, with or without
   14  * modification, are permitted provided that the following conditions
   15  * are met:
   16  * 1. Redistributions of source code must retain the above copyright
   17  *    notice, this list of conditions and the following disclaimer.
   18  * 2. Redistributions in binary form must reproduce the above copyright
   19  *    notice, this list of conditions and the following disclaimer in the
   20  *    documentation and/or other materials provided with the distribution.
   21  * 3. 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 
   38 #include <sys/cdefs.h>
   39 #if defined(LIBC_SCCS) && !defined(lint)
   40 #if 0
   41 static char sccsid[] = "@(#)muldi3.c    8.1 (Berkeley) 6/4/93";
   42 #else
   43 __FBSDID("$FreeBSD$");
   44 #endif
   45 #endif /* LIBC_SCCS and not lint */
   46 
   47 #include <libkern/quad.h>
   48 
   49 /*
   50  * Multiply two quads.
   51  *
   52  * Our algorithm is based on the following.  Split incoming quad values
   53  * u and v (where u,v >= 0) into
   54  *
   55  *      u = 2^n u1  *  u0       (n = number of bits in `u_int', usu. 32)
   56  *
   57  * and 
   58  *
   59  *      v = 2^n v1  *  v0
   60  *
   61  * Then
   62  *
   63  *      uv = 2^2n u1 v1  +  2^n u1 v0  +  2^n v1 u0  +  u0 v0
   64  *         = 2^2n u1 v1  +     2^n (u1 v0 + v1 u0)   +  u0 v0
   65  *
   66  * Now add 2^n u1 v1 to the first term and subtract it from the middle,
   67  * and add 2^n u0 v0 to the last term and subtract it from the middle.
   68  * This gives:
   69  *
   70  *      uv = (2^2n + 2^n) (u1 v1)  +
   71  *               (2^n)    (u1 v0 - u1 v1 + u0 v1 - u0 v0)  +
   72  *             (2^n + 1)  (u0 v0)
   73  *
   74  * Factoring the middle a bit gives us:
   75  *
   76  *      uv = (2^2n + 2^n) (u1 v1)  +                    [u1v1 = high]
   77  *               (2^n)    (u1 - u0) (v0 - v1)  +        [(u1-u0)... = mid]
   78  *             (2^n + 1)  (u0 v0)                       [u0v0 = low]
   79  *
   80  * The terms (u1 v1), (u1 - u0) (v0 - v1), and (u0 v0) can all be done
   81  * in just half the precision of the original.  (Note that either or both
   82  * of (u1 - u0) or (v0 - v1) may be negative.)
   83  *
   84  * This algorithm is from Knuth vol. 2 (2nd ed), section 4.3.3, p. 278.
   85  *
   86  * Since C does not give us a `int * int = quad' operator, we split
   87  * our input quads into two ints, then split the two ints into two
   88  * shorts.  We can then calculate `short * short = int' in native
   89  * arithmetic.
   90  *
   91  * Our product should, strictly speaking, be a `long quad', with 128
   92  * bits, but we are going to discard the upper 64.  In other words,
   93  * we are not interested in uv, but rather in (uv mod 2^2n).  This
   94  * makes some of the terms above vanish, and we get:
   95  *
   96  *      (2^n)(high) + (2^n)(mid) + (2^n + 1)(low)
   97  *
   98  * or
   99  *
  100  *      (2^n)(high + mid + low) + low
  101  *
  102  * Furthermore, `high' and `mid' can be computed mod 2^n, as any factor
  103  * of 2^n in either one will also vanish.  Only `low' need be computed
  104  * mod 2^2n, and only because of the final term above.
  105  */
  106 static quad_t __lmulq(u_int, u_int);
  107 
  108 quad_t __muldi3(quad_t, quad_t);
  109 quad_t
  110 __muldi3(quad_t a, quad_t b)
  111 {
  112         union uu u, v, low, prod;
  113         u_int high, mid, udiff, vdiff;
  114         int negall, negmid;
  115 #define u1      u.ul[H]
  116 #define u0      u.ul[L]
  117 #define v1      v.ul[H]
  118 #define v0      v.ul[L]
  119 
  120         /*
  121          * Get u and v such that u, v >= 0.  When this is finished,
  122          * u1, u0, v1, and v0 will be directly accessible through the
  123          * int fields.
  124          */
  125         if (a >= 0)
  126                 u.q = a, negall = 0;
  127         else
  128                 u.q = -a, negall = 1;
  129         if (b >= 0)
  130                 v.q = b;
  131         else
  132                 v.q = -b, negall ^= 1;
  133 
  134         if (u1 == 0 && v1 == 0) {
  135                 /*
  136                  * An (I hope) important optimization occurs when u1 and v1
  137                  * are both 0.  This should be common since most numbers
  138                  * are small.  Here the product is just u0*v0.
  139                  */
  140                 prod.q = __lmulq(u0, v0);
  141         } else {
  142                 /*
  143                  * Compute the three intermediate products, remembering
  144                  * whether the middle term is negative.  We can discard
  145                  * any upper bits in high and mid, so we can use native
  146                  * u_int * u_int => u_int arithmetic.
  147                  */
  148                 low.q = __lmulq(u0, v0);
  149 
  150                 if (u1 >= u0)
  151                         negmid = 0, udiff = u1 - u0;
  152                 else
  153                         negmid = 1, udiff = u0 - u1;
  154                 if (v0 >= v1)
  155                         vdiff = v0 - v1;
  156                 else
  157                         vdiff = v1 - v0, negmid ^= 1;
  158                 mid = udiff * vdiff;
  159 
  160                 high = u1 * v1;
  161 
  162                 /*
  163                  * Assemble the final product.
  164                  */
  165                 prod.ul[H] = high + (negmid ? -mid : mid) + low.ul[L] +
  166                     low.ul[H];
  167                 prod.ul[L] = low.ul[L];
  168         }
  169         return (negall ? -prod.q : prod.q);
  170 #undef u1
  171 #undef u0
  172 #undef v1
  173 #undef v0
  174 }
  175 
  176 /*
  177  * Multiply two 2N-bit ints to produce a 4N-bit quad, where N is half
  178  * the number of bits in an int (whatever that is---the code below
  179  * does not care as long as quad.h does its part of the bargain---but
  180  * typically N==16).
  181  *
  182  * We use the same algorithm from Knuth, but this time the modulo refinement
  183  * does not apply.  On the other hand, since N is half the size of an int,
  184  * we can get away with native multiplication---none of our input terms
  185  * exceeds (UINT_MAX >> 1).
  186  *
  187  * Note that, for u_int l, the quad-precision result
  188  *
  189  *      l << N
  190  *
  191  * splits into high and low ints as HHALF(l) and LHUP(l) respectively.
  192  */
  193 static quad_t
  194 __lmulq(u_int u, u_int v)
  195 {
  196         u_int u1, u0, v1, v0, udiff, vdiff, high, mid, low;
  197         u_int prodh, prodl, was;
  198         union uu prod;
  199         int neg;
  200 
  201         u1 = HHALF(u);
  202         u0 = LHALF(u);
  203         v1 = HHALF(v);
  204         v0 = LHALF(v);
  205 
  206         low = u0 * v0;
  207 
  208         /* This is the same small-number optimization as before. */
  209         if (u1 == 0 && v1 == 0)
  210                 return (low);
  211 
  212         if (u1 >= u0)
  213                 udiff = u1 - u0, neg = 0;
  214         else
  215                 udiff = u0 - u1, neg = 1;
  216         if (v0 >= v1)
  217                 vdiff = v0 - v1;
  218         else
  219                 vdiff = v1 - v0, neg ^= 1;
  220         mid = udiff * vdiff;
  221 
  222         high = u1 * v1;
  223 
  224         /* prod = (high << 2N) + (high << N); */
  225         prodh = high + HHALF(high);
  226         prodl = LHUP(high);
  227 
  228         /* if (neg) prod -= mid << N; else prod += mid << N; */
  229         if (neg) {
  230                 was = prodl;
  231                 prodl -= LHUP(mid);
  232                 prodh -= HHALF(mid) + (prodl > was);
  233         } else {
  234                 was = prodl;
  235                 prodl += LHUP(mid);
  236                 prodh += HHALF(mid) + (prodl < was);
  237         }
  238 
  239         /* prod += low << N */
  240         was = prodl;
  241         prodl += LHUP(low);
  242         prodh += HHALF(low) + (prodl < was);
  243         /* ... + low; */
  244         if ((prodl += low) < low)
  245                 prodh++;
  246 
  247         /* return 4N-bit product */
  248         prod.ul[H] = prodh;
  249         prod.ul[L] = prodl;
  250         return (prod.q);
  251 }

Cache object: 78ba5807f7da332619ce628104be44f7

[ 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/arm/muldi3.c

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