1 /* flonum_mult.c - multiply two flonums
2 Copyright (C) 1987-2023 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
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 }