gas/flonum-mult.c

   1 /* flonum_mult.c - multiply two flonums
   2    Copyright (C) 1987, 1990, 1991, 1992 Free Software Foundation, Inc.
   3
   4    This file is part of Gas, the GNU Assembler.
   5
   6    The GNU assembler is distributed in the hope that it will be
   7    useful, but WITHOUT ANY WARRANTY.  No author or distributor
   8    accepts responsibility to anyone for the consequences of using it
   9    or for whether it serves any particular purpose or works at all,
  10    unless he says so in writing.  Refer to the GNU Assembler General
  11    Public License for full details.
  12
  13    Everyone is granted permission to copy, modify and redistribute
  14    the GNU Assembler, but only under the conditions described in the
  15    GNU Assembler General Public License.  A copy of this license is
  16    supposed to have been given to you along with the GNU Assembler
  17    so you can know your rights and responsibilities.  It should be
  18    in a file named COPYING.  Among other things, the copyright
  19    notice and this notice must be preserved on all copies.  */
  20
  21 #include <ansidecl.h>
  22 #include "flonum.h"
  23
  24 /*      plan for a . b => p(roduct)
  25
  26
  27         +-------+-------+-/   /-+-------+-------+
  28         | a     | a     |  ...  | a     | a     |
  29         |  A    |  A-1  |       |  1    |  0    |
  30         +-------+-------+-/   /-+-------+-------+
  31
  32
  33         +-------+-------+-/   /-+-------+-------+
  34         | b     | b     |  ...  | b     | b     |
  35         |  B    |  B-1  |       |  1    |  0    |
  36         +-------+-------+-/   /-+-------+-------+
  37
  38
  39         +-------+-------+-/   /-+-------+-/   /-+-------+-------+
  40         | p     | p     |  ...  | p     |  ...  | p     | p     |
  41         |  A+B+1|  A+B  |       |  N    |       |  1    |  0    |
  42         +-------+-------+-/   /-+-------+-/   /-+-------+-------+
  43
  44         /^\
  45         (carry) a .b       ...      |      ...   a .b    a .b
  46         A  B                |             0  1    0  0
  47         |
  48         ...         |      ...   a .b
  49         |                 1  0
  50         |
  51         |          ...
  52         |
  53         |
  54         |
  55         |                 ___
  56         |                 \
  57         +-----  P  =   >  a .b
  58         N         /__  i  j
  59
  60         N = 0 ... A+B
  61
  62         for all i,j where i+j=N
  63         [i,j integers > 0]
  64
  65         a[], b[], p[] may not intersect.
  66         Zero length factors signify 0 significant bits: treat as 0.0.
  67         0.0 factors do the right thing.
  68         Zero length product OK.
  69
  70         I chose the ForTran accent "foo[bar]" instead of the C accent "*garply"
  71         because I felt the ForTran way was more intuitive. The C way would
  72         probably yield better code on most C compilers. Dean Elsner.
  73         (C style also gives deeper insight [to me] ... oh well ...)
  74         */
  75 \f
  76 void
  77 flonum_multip (a, b, product)
  78      const FLONUM_TYPE *a;
  79      const FLONUM_TYPE *b;
  80      FLONUM_TYPE *product;
  81 {
  82   int size_of_a;                /* 0 origin */
  83   int size_of_b;                /* 0 origin */
  84   int size_of_product;          /* 0 origin */
  85   int size_of_sum;              /* 0 origin */
  86   int extra_product_positions;  /* 1 origin */
  87   unsigned long work;
  88   unsigned long carry;
  89   long exponent;
  90   LITTLENUM_TYPE *q;
  91   long significant;             /* TRUE when we emit a non-0 littlenum  */
  92   /* ForTran accent follows. */
  93   int P;                        /* Scan product low-order -> high. */
  94   int N;                        /* As in sum above.  */
  95   int A;                        /* Which [] of a? */
  96   int B;                        /* Which [] of b? */
  97
  98   if ((a->sign != '-' && a->sign != '+') || (b->sign != '-' && b->sign != '+'))
  99     {
 100       /* ...
 101                    Got to fail somehow.  Any suggestions? */
 102       product->sign = 0;
 103       return;
 104     }
 105   product->sign = (a->sign == b->sign) ? '+' : '-';
 106   size_of_a = a->leader - a->low;
 107   size_of_b = b->leader - b->low;
 108   exponent = a->exponent + b->exponent;
 109   size_of_product = product->high - product->low;
 110   size_of_sum = size_of_a + size_of_b;
 111   extra_product_positions = size_of_product - size_of_sum;
 112   if (extra_product_positions < 0)
 113     {
 114       P = extra_product_positions;      /* P < 0 */
 115       exponent -= extra_product_positions;      /* Increases exponent. */
 116     }
 117   else
 118     {
 119       P = 0;
 120     }
 121   carry = 0;
 122   significant = 0;
 123   for (N = 0; N <= size_of_sum; N++)
 124     {
 125       work = carry;
 126       carry = 0;
 127       for (A = 0; A <= N; A++)
 128         {
 129           B = N - A;
 130           if (A <= size_of_a && B <= size_of_b && B >= 0)
 131             {
 132 #ifdef TRACE
 133               printf ("a:low[%d.]=%04x b:low[%d.]=%04x work_before=%08x\n", A, a->low[A], B, b->low[B], work);
 134 #endif
 135               /* Watch out for sign extension!  Without the casts, on
 136                  the DEC Alpha, the multiplication result is *signed*
 137                  int, which gets sign-extended to convert to the
 138                  unsigned long!  */
 139               work += (unsigned long) a->low[A] * (unsigned long) b->low[B];
 140               carry += work >> LITTLENUM_NUMBER_OF_BITS;
 141               work &= LITTLENUM_MASK;
 142 #ifdef TRACE
 143               printf ("work=%08x carry=%04x\n", work, carry);
 144 #endif
 145             }
 146         }
 147       significant |= work;
 148       if (significant || P < 0)
 149         {
 150           if (P >= 0)
 151             {
 152               product->low[P] = work;
 153 #ifdef TRACE
 154               printf ("P=%d. work[p]:=%04x\n", P, work);
 155 #endif
 156             }
 157           P++;
 158         }
 159       else
 160         {
 161           extra_product_positions++;
 162           exponent++;
 163         }
 164     }
 165   /*
 166    * [P]-> position # size_of_sum + 1.
 167    * This is where 'carry' should go.
 168    */
 169 #ifdef TRACE
 170   printf ("final carry =%04x\n", carry);
 171 #endif
 172   if (carry)
 173     {
 174       if (extra_product_positions > 0)
 175         {
 176           product->low[P] = carry;
 177         }
 178       else
 179         {
 180           /* No room at high order for carry littlenum. */
 181           /* Shift right 1 to make room for most significant littlenum. */
 182           exponent++;
 183           P--;
 184           for (q = product->low + P; q >= product->low; q--)
 185             {
 186               work = *q;
 187               *q = carry;
 188               carry = work;
 189             }
 190         }
 191     }
 192   else
 193     {
 194       P--;
 195     }
 196   product->leader = product->low + P;
 197   product->exponent = exponent;
 198 }
 199
 200 /* end of flonum_mult.c */