gas/flonum-mult.c

   1 /* flonum_mult.c - multiply two flonums
   2    Copyright 1987, 1990, 1991, 1992, 1995, 2000, 2002
   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 (const FLONUM_TYPE *a, const FLONUM_TYPE *b,
  75                FLONUM_TYPE *product)
  76 {
  77   int size_of_a;                /* 0 origin  */
  78   int size_of_b;                /* 0 origin  */
  79   int size_of_product;          /* 0 origin  */
  80   int size_of_sum;              /* 0 origin  */
  81   int extra_product_positions;  /* 1 origin  */
  82   unsigned long work;
  83   unsigned long carry;
  84   long exponent;
  85   LITTLENUM_TYPE *q;
  86   long significant;             /* TRUE when we emit a non-0 littlenum  */
  87   /* ForTran accent follows.  */
  88   int P;                        /* Scan product low-order -> high.  */
  89   int N;                        /* As in sum above.  */
  90   int A;                        /* Which [] of a?  */
  91   int B;                        /* Which [] of b?  */
  92
  93   if ((a->sign != '-' && a->sign != '+')
  94       || (b->sign != '-' && b->sign != '+'))
  95     {
  96       /* Got to fail somehow.  Any suggestions?  */
  97       product->sign = 0;
  98       return;
  99     }
 100   product->sign = (a->sign == b->sign) ? '+' : '-';
 101   size_of_a = a->leader - a->low;
 102   size_of_b = b->leader - b->low;
 103   exponent = a->exponent + b->exponent;
 104   size_of_product = product->high - product->low;
 105   size_of_sum = size_of_a + size_of_b;
 106   extra_product_positions = size_of_product - size_of_sum;
 107   if (extra_product_positions < 0)
 108     {
 109       P = extra_product_positions;      /* P < 0  */
 110       exponent -= extra_product_positions;      /* Increases exponent.  */
 111     }
 112   else
 113     {
 114       P = 0;
 115     }
 116   carry = 0;
 117   significant = 0;
 118   for (N = 0; N <= size_of_sum; N++)
 119     {
 120       work = carry;
 121       carry = 0;
 122       for (A = 0; A <= N; A++)
 123         {
 124           B = N - A;
 125           if (A <= size_of_a && B <= size_of_b && B >= 0)
 126             {
 127 #ifdef TRACE
 128               printf ("a:low[%d.]=%04x b:low[%d.]=%04x work_before=%08x\n",
 129                       A, a->low[A], B, b->low[B], work);
 130 #endif
 131               /* Watch out for sign extension!  Without the casts, on
 132                  the DEC Alpha, the multiplication result is *signed*
 133                  int, which gets sign-extended to convert to the
 134                  unsigned long!  */
 135               work += (unsigned long) a->low[A] * (unsigned long) b->low[B];
 136               carry += work >> LITTLENUM_NUMBER_OF_BITS;
 137               work &= LITTLENUM_MASK;
 138 #ifdef TRACE
 139               printf ("work=%08x carry=%04x\n", work, carry);
 140 #endif
 141             }
 142         }
 143       significant |= work;
 144       if (significant || P < 0)
 145         {
 146           if (P >= 0)
 147             {
 148               product->low[P] = work;
 149 #ifdef TRACE
 150               printf ("P=%d. work[p]:=%04x\n", P, work);
 151 #endif
 152             }
 153           P++;
 154         }
 155       else
 156         {
 157           extra_product_positions++;
 158           exponent++;
 159         }
 160     }
 161   /* [P]-> position # size_of_sum + 1.
 162      This is where 'carry' should go.  */
 163 #ifdef TRACE
 164   printf ("final carry =%04x\n", carry);
 165 #endif
 166   if (carry)
 167     {
 168       if (extra_product_positions > 0)
 169         product->low[P] = carry;
 170       else
 171         {
 172           /* No room at high order for carry littlenum.  */
 173           /* Shift right 1 to make room for most significant littlenum.  */
 174           exponent++;
 175           P--;
 176           for (q = product->low + P; q >= product->low; q--)
 177             {
 178               work = *q;
 179               *q = carry;
 180               carry = work;
 181             }
 182         }
 183     }
 184   else
 185     P--;
 186   product->leader = product->low + P;
 187   product->exponent = exponent;
 188 }