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 "flonum.h"
  22
  23 /*      plan for a . b => p(roduct)
  24
  25
  26         +-------+-------+-/   /-+-------+-------+
  27         | a     | a     |  ...  | a     | a     |
  28         |  A    |  A-1  |       |  1    |  0    |
  29         +-------+-------+-/   /-+-------+-------+
  30
  31
  32         +-------+-------+-/   /-+-------+-------+
  33         | b     | b     |  ...  | b     | b     |
  34         |  B    |  B-1  |       |  1    |  0    |
  35         +-------+-------+-/   /-+-------+-------+
  36
  37
  38         +-------+-------+-/   /-+-------+-/   /-+-------+-------+
  39         | p     | p     |  ...  | p     |  ...  | p     | p     |
  40         |  A+B+1|  A+B  |       |  N    |       |  1    |  0    |
  41         +-------+-------+-/   /-+-------+-/   /-+-------+-------+
  42
  43         /^\
  44         (carry) a .b       ...      |      ...   a .b    a .b
  45         A  B                |             0  1    0  0
  46         |
  47         ...         |      ...   a .b
  48         |                 1  0
  49         |
  50         |          ...
  51         |
  52         |
  53         |
  54         |                 ___
  55         |                 \
  56         +-----  P  =   >  a .b
  57         N         /__  i  j
  58
  59         N = 0 ... A+B
  60
  61         for all i,j where i+j=N
  62         [i,j integers > 0]
  63
  64         a[], b[], p[] may not intersect.
  65         Zero length factors signify 0 significant bits: treat as 0.0.
  66         0.0 factors do the right thing.
  67         Zero length product OK.
  68
  69         I chose the ForTran accent "foo[bar]" instead of the C accent "*garply"
  70         because I felt the ForTran way was more intuitive. The C way would
  71         probably yield better code on most C compilers. Dean Elsner.
  72         (C style also gives deeper insight [to me] ... oh well ...)
  73         */
  74 \f
  75 void
  76 flonum_multip (a, b, product)
  77      const FLONUM_TYPE *a;
  78      const FLONUM_TYPE *b;
  79      FLONUM_TYPE *product;
  80 {
  81   int size_of_a;                /* 0 origin */
  82   int size_of_b;                /* 0 origin */
  83   int size_of_product;          /* 0 origin */
  84   int size_of_sum;              /* 0 origin */
  85   int extra_product_positions;  /* 1 origin */
  86   unsigned long work;
  87   unsigned long carry;
  88   long exponent;
  89   LITTLENUM_TYPE *q;
  90   long significant;             /* TRUE when we emit a non-0 littlenum  */
  91   /* ForTran accent follows. */
  92   int P;                        /* Scan product low-order -> high. */
  93   int N;                        /* As in sum above.  */
  94   int A;                        /* Which [] of a? */
  95   int B;                        /* Which [] of b? */
  96
  97   if ((a->sign != '-' && a->sign != '+') || (b->sign != '-' && b->sign != '+'))
  98     {
  99       /* ...
 100                    Got to fail somehow.  Any suggestions? */
 101       product->sign = 0;
 102       return;
 103     }
 104   product->sign = (a->sign == b->sign) ? '+' : '-';
 105   size_of_a = a->leader - a->low;
 106   size_of_b = b->leader - b->low;
 107   exponent = a->exponent + b->exponent;
 108   size_of_product = product->high - product->low;
 109   size_of_sum = size_of_a + size_of_b;
 110   extra_product_positions = size_of_product - size_of_sum;
 111   if (extra_product_positions < 0)
 112     {
 113       P = extra_product_positions;      /* P < 0 */
 114       exponent -= extra_product_positions;      /* Increases exponent. */
 115     }
 116   else
 117     {
 118       P = 0;
 119     }
 120   carry = 0;
 121   significant = 0;
 122   for (N = 0;
 123        N <= size_of_sum;
 124        N++)
 125     {
 126       work = carry;
 127       carry = 0;
 128       for (A = 0;
 129            A <= N;
 130            A++)
 131         {
 132           B = N - A;
 133           if (A <= size_of_a && B <= size_of_b && B >= 0)
 134             {
 135 #ifdef TRACE
 136               printf ("a:low[%d.]=%04x b:low[%d.]=%04x work_before=%08x\n", A, a->low[A], B, b->low[B], work);
 137 #endif
 138               work += a->low[A] * b->low[B];
 139               carry += work >> LITTLENUM_NUMBER_OF_BITS;
 140               work &= LITTLENUM_MASK;
 141 #ifdef TRACE
 142               printf ("work=%08x carry=%04x\n", work, carry);
 143 #endif
 144             }
 145         }
 146       significant |= work;
 147       if (significant || P < 0)
 148         {
 149           if (P >= 0)
 150             {
 151               product->low[P] = work;
 152 #ifdef TRACE
 153               printf ("P=%d. work[p]:=%04x\n", P, work);
 154 #endif
 155             }
 156           P++;
 157         }
 158       else
 159         {
 160           extra_product_positions++;
 161           exponent++;
 162         }
 163     }
 164   /*
 165          * [P]-> position # size_of_sum + 1.
 166          * This is where 'carry' should go.
 167          */
 168 #ifdef TRACE
 169   printf ("final carry =%04x\n", carry);
 170 #endif
 171   if (carry)
 172     {
 173       if (extra_product_positions > 0)
 174         {
 175           product->low[P] = carry;
 176         }
 177       else
 178         {
 179           /* No room at high order for carry littlenum. */
 180           /* Shift right 1 to make room for most significant littlenum. */
 181           exponent++;
 182           P--;
 183           for (q = product->low + P;
 184                q >= product->low;
 185                q--)
 186             {
 187               work = *q;
 188               *q = carry;
 189               carry = work;
 190             }
 191         }
 192     }
 193   else
 194     {
 195       P--;
 196     }
 197   product->leader = product->low + P;
 198   product->exponent = exponent;
 199 }
 200
 201 /* end of flonum_mult.c */