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