gas/flonum-mult.c

   1 /* flonum_mult.c - multiply two flonums
   2    Copyright 1987, 1990, 1991, 1992, 1995, 2000
   3    Free Software Foundation, Inc.
   4
   5    This file is part of Gas, the GNU Assembler.
   6
   7    The GNU assembler is distributed in the hope that it will be
   8    useful, but WITHOUT ANY WARRANTY.  No author or distributor
   9    accepts responsibility to anyone for the consequences of using it
  10    or for whether it serves any particular purpose or works at all,
  11    unless he says so in writing.  Refer to the GNU Assembler General
  12    Public License for full details.
  13
  14    Everyone is granted permission to copy, modify and redistribute
  15    the GNU Assembler, but only under the conditions described in the
  16    GNU Assembler General Public License.  A copy of this license is
  17    supposed to have been given to you along with the GNU Assembler
  18    so you can know your rights and responsibilities.  It should be
  19    in a file named COPYING.  Among other things, the copyright
  20    notice and this notice must be preserved on all copies.  */
  21
  22 #include <ansidecl.h>
  23 #include "flonum.h"
  24
  25 /*      plan for a . b => p(roduct)
  26
  27         +-------+-------+-/   /-+-------+-------+
  28         | a     | a     |  ...  | a     | a     |
  29         |  A    |  A-1  |       |  1    |  0    |
  30         +-------+-------+-/   /-+-------+-------+
  31
  32         +-------+-------+-/   /-+-------+-------+
  33         | b     | b     |  ...  | b     | b     |
  34         |  B    |  B-1  |       |  1    |  0    |
  35         +-------+-------+-/   /-+-------+-------+
  36
  37         +-------+-------+-/   /-+-------+-/   /-+-------+-------+
  38         | p     | p     |  ...  | p     |  ...  | p     | p     |
  39         |  A+B+1|  A+B  |       |  N    |       |  1    |  0    |
  40         +-------+-------+-/   /-+-------+-/   /-+-------+-------+
  41
  42         /^\
  43         (carry) a .b       ...      |      ...   a .b    a .b
  44         A  B                |             0  1    0  0
  45         |
  46         ...         |      ...   a .b
  47         |                 1  0
  48         |
  49         |          ...
  50         |
  51         |
  52         |
  53         |                 ___
  54         |                 \
  55         +-----  P  =   >  a .b
  56         N         /__  i  j
  57
  58         N = 0 ... A+B
  59
  60         for all i,j where i+j=N
  61         [i,j integers > 0]
  62
  63         a[], b[], p[] may not intersect.
  64         Zero length factors signify 0 significant bits: treat as 0.0.
  65         0.0 factors do the right thing.
  66         Zero length product OK.
  67
  68         I chose the ForTran accent "foo[bar]" instead of the C accent "*garply"
  69         because I felt the ForTran way was more intuitive. The C way would
  70         probably yield better code on most C compilers. Dean Elsner.
  71         (C style also gives deeper insight [to me] ... oh well ...)  */
  72 \f
  73 void
  74 flonum_multip (a, b, product)
  75      const FLONUM_TYPE *a;
  76      const FLONUM_TYPE *b;
  77      FLONUM_TYPE *product;
  78 {
  79   int size_of_a;                /* 0 origin  */
  80   int size_of_b;                /* 0 origin  */
  81   int size_of_product;          /* 0 origin  */
  82   int size_of_sum;              /* 0 origin  */
  83   int extra_product_positions;  /* 1 origin  */
  84   unsigned long work;
  85   unsigned long carry;
  86   long exponent;
  87   LITTLENUM_TYPE *q;
  88   long significant;             /* TRUE when we emit a non-0 littlenum  */
  89   /* ForTran accent follows.  */
  90   int P;                        /* Scan product low-order -> high.  */
  91   int N;                        /* As in sum above.  */
  92   int A;                        /* Which [] of a?  */
  93   int B;                        /* Which [] of b?  */
  94
  95   if ((a->sign != '-' && a->sign != '+')
  96       || (b->sign != '-' && b->sign != '+'))
  97     {
  98       /* Got to fail somehow.  Any suggestions?  */
  99       product->sign = 0;
 100       return;
 101     }
 102   product->sign = (a->sign == b->sign) ? '+' : '-';
 103   size_of_a = a->leader - a->low;
 104   size_of_b = b->leader - b->low;
 105   exponent = a->exponent + b->exponent;
 106   size_of_product = product->high - product->low;
 107   size_of_sum = size_of_a + size_of_b;
 108   extra_product_positions = size_of_product - size_of_sum;
 109   if (extra_product_positions < 0)
 110     {
 111       P = extra_product_positions;      /* P < 0  */
 112       exponent -= extra_product_positions;      /* Increases exponent.  */
 113     }
 114   else
 115     {
 116       P = 0;
 117     }
 118   carry = 0;
 119   significant = 0;
 120   for (N = 0; N <= size_of_sum; N++)
 121     {
 122       work = carry;
 123       carry = 0;
 124       for (A = 0; A <= N; A++)
 125         {
 126           B = N - A;
 127           if (A <= size_of_a && B <= size_of_b && B >= 0)
 128             {
 129 #ifdef TRACE
 130               printf ("a:low[%d.]=%04x b:low[%d.]=%04x work_before=%08x\n",
 131                       A, a->low[A], B, b->low[B], work);
 132 #endif
 133               /* Watch out for sign extension!  Without the casts, on
 134                  the DEC Alpha, the multiplication result is *signed*
 135                  int, which gets sign-extended to convert to the
 136                  unsigned long!  */
 137               work += (unsigned long) a->low[A] * (unsigned long) b->low[B];
 138               carry += work >> LITTLENUM_NUMBER_OF_BITS;
 139               work &= LITTLENUM_MASK;
 140 #ifdef TRACE
 141               printf ("work=%08x carry=%04x\n", work, carry);
 142 #endif
 143             }
 144         }
 145       significant |= work;
 146       if (significant || P < 0)
 147         {
 148           if (P >= 0)
 149             {
 150               product->low[P] = work;
 151 #ifdef TRACE
 152               printf ("P=%d. work[p]:=%04x\n", P, work);
 153 #endif
 154             }
 155           P++;
 156         }
 157       else
 158         {
 159           extra_product_positions++;
 160           exponent++;
 161         }
 162     }
 163   /* [P]-> position # size_of_sum + 1.
 164      This is where 'carry' should go.  */
 165 #ifdef TRACE
 166   printf ("final carry =%04x\n", carry);
 167 #endif
 168   if (carry)
 169     {
 170       if (extra_product_positions > 0)
 171         product->low[P] = carry;
 172       else
 173         {
 174           /* No room at high order for carry littlenum.  */
 175           /* Shift right 1 to make room for most significant littlenum.  */
 176           exponent++;
 177           P--;
 178           for (q = product->low + P; q >= product->low; q--)
 179             {
 180               work = *q;
 181               *q = carry;
 182               carry = work;
 183             }
 184         }
 185     }
 186   else
 187     P--;
 188   product->leader = product->low + P;
 189   product->exponent = exponent;
 190 }