gas/flonum-mult.c

   1 /* flonum_mult.c - multiply two flonums
   2    Copyright (C) 1987-2024 Free Software Foundation, Inc.
   3
   4    This file is part of GAS, the GNU Assembler.
   5
   6    GAS is free software; you can redistribute it and/or modify
   7    it under the terms of the GNU General Public License as published by
   8    the Free Software Foundation; either version 3, or (at your option)
   9    any later version.
  10
  11    GAS is distributed in the hope that it will be useful, but WITHOUT
  12    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  13    or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public
  14    License for more details.
  15
  16    You should have received a copy of the GNU General Public License
  17    along with GAS; see the file COPYING.  If not, write to the Free
  18    Software Foundation, 51 Franklin Street - Fifth Floor, Boston, MA
  19    02110-1301, USA.  */
  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 (const FLONUM_TYPE *a, const FLONUM_TYPE *b,
  74                FLONUM_TYPE *product)
  75 {
  76   int size_of_a;                /* 0 origin  */
  77   int size_of_b;                /* 0 origin  */
  78   int size_of_product;          /* 0 origin  */
  79   int size_of_sum;              /* 0 origin  */
  80   int extra_product_positions;  /* 1 origin  */
  81   unsigned long work;
  82   unsigned long carry;
  83   long exponent;
  84   LITTLENUM_TYPE *q;
  85   long significant;             /* TRUE when we emit a non-0 littlenum  */
  86   /* ForTran accent follows.  */
  87   int P;                        /* Scan product low-order -> high.  */
  88   int N;                        /* As in sum above.  */
  89   int A;                        /* Which [] of a?  */
  90   int B;                        /* Which [] of b?  */
  91
  92   if ((a->sign != '-' && a->sign != '+')
  93       || (b->sign != '-' && b->sign != '+'))
  94     {
  95       /* Got to fail somehow.  Any suggestions?  */
  96       product->sign = 0;
  97       return;
  98     }
  99   product->sign = (a->sign == b->sign) ? '+' : '-';
 100   size_of_a = a->leader - a->low;
 101   size_of_b = b->leader - b->low;
 102   exponent = a->exponent + b->exponent;
 103   size_of_product = product->high - product->low;
 104   size_of_sum = size_of_a + size_of_b;
 105   extra_product_positions = size_of_product - size_of_sum;
 106   if (extra_product_positions < 0)
 107     {
 108       P = extra_product_positions;      /* P < 0  */
 109       exponent -= extra_product_positions;      /* Increases exponent.  */
 110     }
 111   else
 112     {
 113       P = 0;
 114     }
 115   carry = 0;
 116   significant = 0;
 117   for (N = 0; N <= size_of_sum; N++)
 118     {
 119       work = carry;
 120       carry = 0;
 121       for (A = 0; A <= N; A++)
 122         {
 123           B = N - A;
 124           if (A <= size_of_a && B <= size_of_b && B >= 0)
 125             {
 126 #ifdef TRACE
 127               printf ("a:low[%d.]=%04x b:low[%d.]=%04x work_before=%08x\n",
 128                       A, a->low[A], B, b->low[B], work);
 129 #endif
 130               /* Watch out for sign extension!  Without the casts, on
 131                  the DEC Alpha, the multiplication result is *signed*
 132                  int, which gets sign-extended to convert to the
 133                  unsigned long!  */
 134               work += (unsigned long) a->low[A] * (unsigned long) b->low[B];
 135               carry += work >> LITTLENUM_NUMBER_OF_BITS;
 136               work &= LITTLENUM_MASK;
 137 #ifdef TRACE
 138               printf ("work=%08x carry=%04x\n", work, carry);
 139 #endif
 140             }
 141         }
 142       significant |= work;
 143       if (significant || P < 0)
 144         {
 145           if (P >= 0)
 146             {
 147               product->low[P] = work;
 148 #ifdef TRACE
 149               printf ("P=%d. work[p]:=%04x\n", P, work);
 150 #endif
 151             }
 152           P++;
 153         }
 154       else
 155         {
 156           extra_product_positions++;
 157           exponent++;
 158         }
 159     }
 160   /* [P]-> position # size_of_sum + 1.
 161      This is where 'carry' should go.  */
 162 #ifdef TRACE
 163   printf ("final carry =%04x\n", carry);
 164 #endif
 165   if (carry)
 166     {
 167       if (extra_product_positions > 0)
 168         product->low[P] = carry;
 169       else
 170         {
 171           /* No room at high order for carry littlenum.  */
 172           /* Shift right 1 to make room for most significant littlenum.  */
 173           exponent++;
 174           P--;
 175           for (q = product->low + P; q >= product->low; q--)
 176             {
 177               work = *q;
 178               *q = carry;
 179               carry = work;
 180             }
 181         }
 182     }
 183   else
 184     P--;
 185   product->leader = product->low + P;
 186   product->exponent = exponent;
 187 }