1 /* flonum_mult.c - multiply two flonums 2 Copyright (C) 1987-2020 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 } 188