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         | a     | a     |  ...  | a     | a     |
  28         |  A    |  A-1  |       |  1    |  0    |
  29         +-------+-------+-/   /-+-------+-------+
  30
  31         +-------+-------+-/   /-+-------+-------+
  32         | b     | b     |  ...  | b     | b     |
  33         |  B    |  B-1  |       |  1    |  0    |
  34         +-------+-------+-/   /-+-------+-------+
  35
  36         +-------+-------+-/   /-+-------+-/   /-+-------+-------+
  37         | p     | p     |  ...  | p     |  ...  | p     | p     |
  38         |  A+B+1|  A+B  |       |  N    |       |  1    |  0    |
  39         +-------+-------+-/   /-+-------+-/   /-+-------+-------+
  40
  41         /^\
  42         (carry) a .b       ...      |      ...   a .b    a .b
  43         A  B                |             0  1    0  0
  44         |
  45         ...         |      ...   a .b
  46         |                 1  0
  47         |
  48         |          ...
  49         |
  50         |
  51         |
  52         |                 ___
  53         |                 \
  54         +-----  P  =   >  a .b
  55         N         /__  i  j
  56
  57         N = 0 ... A+B
  58
  59         for all i,j where i+j=N
  60         [i,j integers > 0]
  61
  62         a[], b[], p[] may not intersect.
  63         Zero length factors signify 0 significant bits: treat as 0.0.
  64         0.0 factors do the right thing.
  65         Zero length product OK.
  66
  67         I chose the ForTran accent "foo[bar]" instead of the C accent "*garply"
  68         because I felt the ForTran way was more intuitive. The C way would
  69         probably yield better code on most C compilers. Dean Elsner.
  70         (C style also gives deeper insight [to me] ... oh well ...)  */
  71 \f
  72 void
  73 flonum_multip (a, b, product)
  74      const FLONUM_TYPE *a;
  75      const FLONUM_TYPE *b;
  76      FLONUM_TYPE *product;
  77 {
  78   int size_of_a;                /* 0 origin  */
  79   int size_of_b;                /* 0 origin  */
  80   int size_of_product;          /* 0 origin  */
  81   int size_of_sum;              /* 0 origin  */
  82   int extra_product_positions;  /* 1 origin  */
  83   unsigned long work;
  84   unsigned long carry;
  85   long exponent;
  86   LITTLENUM_TYPE *q;
  87   long significant;             /* TRUE when we emit a non-0 littlenum  */
  88   /* ForTran accent follows.  */
  89   int P;                        /* Scan product low-order -> high.  */
  90   int N;                        /* As in sum above.  */
  91   int A;                        /* Which [] of a?  */
  92   int B;                        /* Which [] of b?  */
  93
  94   if ((a->sign != '-' && a->sign != '+')
  95       || (b->sign != '-' && b->sign != '+'))
  96     {
  97       /* Got to fail somehow.  Any suggestions?  */
  98       product->sign = 0;
  99       return;
 100     }
 101   product->sign = (a->sign == b->sign) ? '+' : '-';
 102   size_of_a = a->leader - a->low;
 103   size_of_b = b->leader - b->low;
 104   exponent = a->exponent + b->exponent;
 105   size_of_product = product->high - product->low;
 106   size_of_sum = size_of_a + size_of_b;
 107   extra_product_positions = size_of_product - size_of_sum;
 108   if (extra_product_positions < 0)
 109     {
 110       P = extra_product_positions;      /* P < 0  */
 111       exponent -= extra_product_positions;      /* Increases exponent.  */
 112     }
 113   else
 114     {
 115       P = 0;
 116     }
 117   carry = 0;
 118   significant = 0;
 119   for (N = 0; N <= size_of_sum; N++)
 120     {
 121       work = carry;
 122       carry = 0;
 123       for (A = 0; A <= N; A++)
 124         {
 125           B = N - A;
 126           if (A <= size_of_a && B <= size_of_b && B >= 0)
 127             {
 128 #ifdef TRACE
 129               printf ("a:low[%d.]=%04x b:low[%d.]=%04x work_before=%08x\n",
 130                       A, a->low[A], B, b->low[B], work);
 131 #endif
 132               /* Watch out for sign extension!  Without the casts, on
 133                  the DEC Alpha, the multiplication result is *signed*
 134                  int, which gets sign-extended to convert to the
 135                  unsigned long!  */
 136               work += (unsigned long) a->low[A] * (unsigned long) b->low[B];
 137               carry += work >> LITTLENUM_NUMBER_OF_BITS;
 138               work &= LITTLENUM_MASK;
 139 #ifdef TRACE
 140               printf ("work=%08x carry=%04x\n", work, carry);
 141 #endif
 142             }
 143         }
 144       significant |= work;
 145       if (significant || P < 0)
 146         {
 147           if (P >= 0)
 148             {
 149               product->low[P] = work;
 150 #ifdef TRACE
 151               printf ("P=%d. work[p]:=%04x\n", P, work);
 152 #endif
 153             }
 154           P++;
 155         }
 156       else
 157         {
 158           extra_product_positions++;
 159           exponent++;
 160         }
 161     }
 162   /* [P]-> position # size_of_sum + 1.
 163      This is where 'carry' should go. */
 164 #ifdef TRACE
 165   printf ("final carry =%04x\n", carry);
 166 #endif
 167   if (carry)
 168     {
 169       if (extra_product_positions > 0)
 170         product->low[P] = carry;
 171       else
 172         {
 173           /* No room at high order for carry littlenum.  */
 174           /* Shift right 1 to make room for most significant littlenum.  */
 175           exponent++;
 176           P--;
 177           for (q = product->low + P; q >= product->low; q--)
 178             {
 179               work = *q;
 180               *q = carry;
 181               carry = work;
 182             }
 183         }
 184     }
 185   else
 186     P--;
 187   product->leader = product->low + P;
 188   product->exponent = exponent;
 189 }