gas/flonum-mult.c

   1 /* flonum_mult.c - multiply two flonums
   2    Copyright 1987, 1990, 1991, 1992, 1995, 2000, 2002, 2003, 2007
   3    Free Software Foundation, Inc.
   4
   5    This file is part of GAS, the GNU Assembler.
   6
   7    GAS is free software; you can redistribute it and/or modify
   8    it under the terms of the GNU General Public License as published by
   9    the Free Software Foundation; either version 3, or (at your option)
  10    any later version.
  11
  12    GAS is distributed in the hope that it will be useful, but WITHOUT
  13    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  14    or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public
  15    License for more details.
  16
  17    You should have received a copy of the GNU General Public License
  18    along with GAS; see the file COPYING.  If not, write to the Free
  19    Software Foundation, 51 Franklin Street - Fifth Floor, Boston, MA
  20    02110-1301, USA.  */
  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 }