flonum-mult.c revision 104834 
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
73void
74flonum_multip (a, b, product)
75     const FLONUM_TYPE *a;
76     const FLONUM_TYPE *b;
77     FLONUM_TYPE *product;
78{
79  int size_of_a;		/* 0 origin  */
80  int size_of_b;		/* 0 origin  */
81  int size_of_product;		/* 0 origin  */
82  int size_of_sum;		/* 0 origin  */
83  int extra_product_positions;	/* 1 origin  */
84  unsigned long work;
85  unsigned long carry;
86  long exponent;
87  LITTLENUM_TYPE *q;
88  long significant;		/* TRUE when we emit a non-0 littlenum  */
89  /* ForTran accent follows.  */
90  int P;			/* Scan product low-order -> high.  */
91  int N;			/* As in sum above.  */
92  int A;			/* Which [] of a?  */
93  int B;			/* Which [] of b?  */
94
95  if ((a->sign != '-' && a->sign != '+')
96      || (b->sign != '-' && b->sign != '+'))
97    {
98      /* Got to fail somehow.  Any suggestions?  */
99      product->sign = 0;
100      return;
101    }
102  product->sign = (a->sign == b->sign) ? '+' : '-';
103  size_of_a = a->leader - a->low;
104  size_of_b = b->leader - b->low;
105  exponent = a->exponent + b->exponent;
106  size_of_product = product->high - product->low;
107  size_of_sum = size_of_a + size_of_b;
108  extra_product_positions = size_of_product - size_of_sum;
109  if (extra_product_positions < 0)
110    {
111      P = extra_product_positions;	/* P < 0  */
112      exponent -= extra_product_positions;	/* Increases exponent.  */
113    }
114  else
115    {
116      P = 0;
117    }
118  carry = 0;
119  significant = 0;
120  for (N = 0; N <= size_of_sum; N++)
121    {
122      work = carry;
123      carry = 0;
124      for (A = 0; A <= N; A++)
125	{
126	  B = N - A;
127	  if (A <= size_of_a && B <= size_of_b && B >= 0)
128	    {
129#ifdef TRACE
130	      printf ("a:low[%d.]=%04x b:low[%d.]=%04x work_before=%08x\n",
131		      A, a->low[A], B, b->low[B], work);
132#endif
133	      /* Watch out for sign extension!  Without the casts, on
134		 the DEC Alpha, the multiplication result is *signed*
135		 int, which gets sign-extended to convert to the
136		 unsigned long!  */
137	      work += (unsigned long) a->low[A] * (unsigned long) b->low[B];
138	      carry += work >> LITTLENUM_NUMBER_OF_BITS;
139	      work &= LITTLENUM_MASK;
140#ifdef TRACE
141	      printf ("work=%08x carry=%04x\n", work, carry);
142#endif
143	    }
144	}
145      significant |= work;
146      if (significant || P < 0)
147	{
148	  if (P >= 0)
149	    {
150	      product->low[P] = work;
151#ifdef TRACE
152	      printf ("P=%d. work[p]:=%04x\n", P, work);
153#endif
154	    }
155	  P++;
156	}
157      else
158	{
159	  extra_product_positions++;
160	  exponent++;
161	}
162    }
163  /* [P]-> position # size_of_sum + 1.
164     This is where 'carry' should go.  */
165#ifdef TRACE
166  printf ("final carry =%04x\n", carry);
167#endif
168  if (carry)
169    {
170      if (extra_product_positions > 0)
171	product->low[P] = carry;
172      else
173	{
174	  /* No room at high order for carry littlenum.  */
175	  /* Shift right 1 to make room for most significant littlenum.  */
176	  exponent++;
177	  P--;
178	  for (q = product->low + P; q >= product->low; q--)
179	    {
180	      work = *q;
181	      *q = carry;
182	      carry = work;
183	    }
184	}
185    }
186  else
187    P--;
188  product->leader = product->low + P;
189  product->exponent = exponent;
190}
191