summaryrefslogtreecommitdiff
path: root/gas/flonum-mult.c
blob: e5f32fca2e4a25cc6728e3ea064b1afcdaf5f41f (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
/* flonum_mult.c - multiply two flonums
   Copyright 1987, 1990, 1991, 1992, 1995, 2000, 2002, 2003, 2007
   Free Software Foundation, Inc.

   This file is part of GAS, the GNU Assembler.

   GAS is free software; you can redistribute it and/or modify
   it under the terms of the GNU General Public License as published by
   the Free Software Foundation; either version 3, or (at your option)
   any later version.

   GAS is distributed in the hope that it will be useful, but WITHOUT
   ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
   or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public
   License for more details.

   You should have received a copy of the GNU General Public License
   along with GAS; see the file COPYING.  If not, write to the Free
   Software Foundation, 51 Franklin Street - Fifth Floor, Boston, MA
   02110-1301, USA.  */

#include "ansidecl.h"
#include "flonum.h"

/*	plan for a . b => p(roduct)

	+-------+-------+-/   /-+-------+-------+
	| a	| a	|  ...	| a	| a	|
	|  A	|  A-1	|	|  1	|  0	|
	+-------+-------+-/   /-+-------+-------+

	+-------+-------+-/   /-+-------+-------+
	| b	| b	|  ...	| b	| b	|
	|  B	|  B-1	|	|  1	|  0	|
	+-------+-------+-/   /-+-------+-------+

	+-------+-------+-/   /-+-------+-/   /-+-------+-------+
	| p	| p	|  ...	| p	|  ...	| p	| p	|
	|  A+B+1|  A+B	|	|  N	|	|  1	|  0	|
	+-------+-------+-/   /-+-------+-/   /-+-------+-------+

	/^\
	(carry) a .b	   ...	    |	   ...	 a .b	 a .b
	A  B 		    |		  0  1	  0  0
	|
	...	    |	   ...	 a .b
	|		  1  0
	|
	|	   ...
	|
	|
	|
	|		  ___
	|		  \
	+-----  P  =   >  a .b
	N	  /__  i  j

	N = 0 ... A+B

	for all i,j where i+j=N
	[i,j integers > 0]

	a[], b[], p[] may not intersect.
	Zero length factors signify 0 significant bits: treat as 0.0.
	0.0 factors do the right thing.
	Zero length product OK.

	I chose the ForTran accent "foo[bar]" instead of the C accent "*garply"
	because I felt the ForTran way was more intuitive. The C way would
	probably yield better code on most C compilers. Dean Elsner.
	(C style also gives deeper insight [to me] ... oh well ...)  */

void
flonum_multip (const FLONUM_TYPE *a, const FLONUM_TYPE *b,
	       FLONUM_TYPE *product)
{
  int size_of_a;		/* 0 origin  */
  int size_of_b;		/* 0 origin  */
  int size_of_product;		/* 0 origin  */
  int size_of_sum;		/* 0 origin  */
  int extra_product_positions;	/* 1 origin  */
  unsigned long work;
  unsigned long carry;
  long exponent;
  LITTLENUM_TYPE *q;
  long significant;		/* TRUE when we emit a non-0 littlenum  */
  /* ForTran accent follows.  */
  int P;			/* Scan product low-order -> high.  */
  int N;			/* As in sum above.  */
  int A;			/* Which [] of a?  */
  int B;			/* Which [] of b?  */

  if ((a->sign != '-' && a->sign != '+')
      || (b->sign != '-' && b->sign != '+'))
    {
      /* Got to fail somehow.  Any suggestions?  */
      product->sign = 0;
      return;
    }
  product->sign = (a->sign == b->sign) ? '+' : '-';
  size_of_a = a->leader - a->low;
  size_of_b = b->leader - b->low;
  exponent = a->exponent + b->exponent;
  size_of_product = product->high - product->low;
  size_of_sum = size_of_a + size_of_b;
  extra_product_positions = size_of_product - size_of_sum;
  if (extra_product_positions < 0)
    {
      P = extra_product_positions;	/* P < 0  */
      exponent -= extra_product_positions;	/* Increases exponent.  */
    }
  else
    {
      P = 0;
    }
  carry = 0;
  significant = 0;
  for (N = 0; N <= size_of_sum; N++)
    {
      work = carry;
      carry = 0;
      for (A = 0; A <= N; A++)
	{
	  B = N - A;
	  if (A <= size_of_a && B <= size_of_b && B >= 0)
	    {
#ifdef TRACE
	      printf ("a:low[%d.]=%04x b:low[%d.]=%04x work_before=%08x\n",
		      A, a->low[A], B, b->low[B], work);
#endif
	      /* Watch out for sign extension!  Without the casts, on
		 the DEC Alpha, the multiplication result is *signed*
		 int, which gets sign-extended to convert to the
		 unsigned long!  */
	      work += (unsigned long) a->low[A] * (unsigned long) b->low[B];
	      carry += work >> LITTLENUM_NUMBER_OF_BITS;
	      work &= LITTLENUM_MASK;
#ifdef TRACE
	      printf ("work=%08x carry=%04x\n", work, carry);
#endif
	    }
	}
      significant |= work;
      if (significant || P < 0)
	{
	  if (P >= 0)
	    {
	      product->low[P] = work;
#ifdef TRACE
	      printf ("P=%d. work[p]:=%04x\n", P, work);
#endif
	    }
	  P++;
	}
      else
	{
	  extra_product_positions++;
	  exponent++;
	}
    }
  /* [P]-> position # size_of_sum + 1.
     This is where 'carry' should go.  */
#ifdef TRACE
  printf ("final carry =%04x\n", carry);
#endif
  if (carry)
    {
      if (extra_product_positions > 0)
	product->low[P] = carry;
      else
	{
	  /* No room at high order for carry littlenum.  */
	  /* Shift right 1 to make room for most significant littlenum.  */
	  exponent++;
	  P--;
	  for (q = product->low + P; q >= product->low; q--)
	    {
	      work = *q;
	      *q = carry;
	      carry = work;
	    }
	}
    }
  else
    P--;
  product->leader = product->low + P;
  product->exponent = exponent;
}