| 1 | /* flonum_mult.c - multiply two flonums |
| 2 | Copyright (C) 1987, 1990, 1991, 1992 Free Software Foundation, Inc. |
| 3 | |
| 4 | This file is part of Gas, the GNU Assembler. |
| 5 | |
| 6 | The GNU assembler is distributed in the hope that it will be |
| 7 | useful, but WITHOUT ANY WARRANTY. No author or distributor |
| 8 | accepts responsibility to anyone for the consequences of using it |
| 9 | or for whether it serves any particular purpose or works at all, |
| 10 | unless he says so in writing. Refer to the GNU Assembler General |
| 11 | Public License for full details. |
| 12 | |
| 13 | Everyone is granted permission to copy, modify and redistribute |
| 14 | the GNU Assembler, but only under the conditions described in the |
| 15 | GNU Assembler General Public License. A copy of this license is |
| 16 | supposed to have been given to you along with the GNU Assembler |
| 17 | so you can know your rights and responsibilities. It should be |
| 18 | in a file named COPYING. Among other things, the copyright |
| 19 | notice and this notice must be preserved on all copies. */ |
| 20 | |
| 21 | #include "flonum.h" |
| 22 | |
| 23 | /* plan for a . b => p(roduct) |
| 24 | |
| 25 | |
| 26 | +-------+-------+-/ /-+-------+-------+ |
| 27 | | a | a | ... | a | a | |
| 28 | | A | A-1 | | 1 | 0 | |
| 29 | +-------+-------+-/ /-+-------+-------+ |
| 30 | |
| 31 | |
| 32 | +-------+-------+-/ /-+-------+-------+ |
| 33 | | b | b | ... | b | b | |
| 34 | | B | B-1 | | 1 | 0 | |
| 35 | +-------+-------+-/ /-+-------+-------+ |
| 36 | |
| 37 | |
| 38 | +-------+-------+-/ /-+-------+-/ /-+-------+-------+ |
| 39 | | p | p | ... | p | ... | p | p | |
| 40 | | A+B+1| A+B | | N | | 1 | 0 | |
| 41 | +-------+-------+-/ /-+-------+-/ /-+-------+-------+ |
| 42 | |
| 43 | /^\ |
| 44 | (carry) a .b ... | ... a .b a .b |
| 45 | A B | 0 1 0 0 |
| 46 | | |
| 47 | ... | ... a .b |
| 48 | | 1 0 |
| 49 | | |
| 50 | | ... |
| 51 | | |
| 52 | | |
| 53 | | |
| 54 | | ___ |
| 55 | | \ |
| 56 | +----- P = > a .b |
| 57 | N /__ i j |
| 58 | |
| 59 | N = 0 ... A+B |
| 60 | |
| 61 | for all i,j where i+j=N |
| 62 | [i,j integers > 0] |
| 63 | |
| 64 | a[], b[], p[] may not intersect. |
| 65 | Zero length factors signify 0 significant bits: treat as 0.0. |
| 66 | 0.0 factors do the right thing. |
| 67 | Zero length product OK. |
| 68 | |
| 69 | I chose the ForTran accent "foo[bar]" instead of the C accent "*garply" |
| 70 | because I felt the ForTran way was more intuitive. The C way would |
| 71 | probably yield better code on most C compilers. Dean Elsner. |
| 72 | (C style also gives deeper insight [to me] ... oh well ...) |
| 73 | */ |
| 74 | \f |
| 75 | void |
| 76 | flonum_multip (a, b, product) |
| 77 | const FLONUM_TYPE *a; |
| 78 | const FLONUM_TYPE *b; |
| 79 | FLONUM_TYPE *product; |
| 80 | { |
| 81 | int size_of_a; /* 0 origin */ |
| 82 | int size_of_b; /* 0 origin */ |
| 83 | int size_of_product; /* 0 origin */ |
| 84 | int size_of_sum; /* 0 origin */ |
| 85 | int extra_product_positions; /* 1 origin */ |
| 86 | unsigned long work; |
| 87 | unsigned long carry; |
| 88 | long exponent; |
| 89 | LITTLENUM_TYPE *q; |
| 90 | long significant; /* TRUE when we emit a non-0 littlenum */ |
| 91 | /* ForTran accent follows. */ |
| 92 | int P; /* Scan product low-order -> high. */ |
| 93 | int N; /* As in sum above. */ |
| 94 | int A; /* Which [] of a? */ |
| 95 | int B; /* Which [] of b? */ |
| 96 | |
| 97 | if ((a->sign != '-' && a->sign != '+') || (b->sign != '-' && b->sign != '+')) |
| 98 | { |
| 99 | /* ... |
| 100 | Got to fail somehow. Any suggestions? */ |
| 101 | product->sign = 0; |
| 102 | return; |
| 103 | } |
| 104 | product->sign = (a->sign == b->sign) ? '+' : '-'; |
| 105 | size_of_a = a->leader - a->low; |
| 106 | size_of_b = b->leader - b->low; |
| 107 | exponent = a->exponent + b->exponent; |
| 108 | size_of_product = product->high - product->low; |
| 109 | size_of_sum = size_of_a + size_of_b; |
| 110 | extra_product_positions = size_of_product - size_of_sum; |
| 111 | if (extra_product_positions < 0) |
| 112 | { |
| 113 | P = extra_product_positions; /* P < 0 */ |
| 114 | exponent -= extra_product_positions; /* Increases exponent. */ |
| 115 | } |
| 116 | else |
| 117 | { |
| 118 | P = 0; |
| 119 | } |
| 120 | carry = 0; |
| 121 | significant = 0; |
| 122 | for (N = 0; |
| 123 | N <= size_of_sum; |
| 124 | N++) |
| 125 | { |
| 126 | work = carry; |
| 127 | carry = 0; |
| 128 | for (A = 0; |
| 129 | A <= N; |
| 130 | A++) |
| 131 | { |
| 132 | B = N - A; |
| 133 | if (A <= size_of_a && B <= size_of_b && B >= 0) |
| 134 | { |
| 135 | #ifdef TRACE |
| 136 | printf ("a:low[%d.]=%04x b:low[%d.]=%04x work_before=%08x\n", A, a->low[A], B, b->low[B], work); |
| 137 | #endif |
| 138 | work += a->low[A] * b->low[B]; |
| 139 | carry += work >> LITTLENUM_NUMBER_OF_BITS; |
| 140 | work &= LITTLENUM_MASK; |
| 141 | #ifdef TRACE |
| 142 | printf ("work=%08x carry=%04x\n", work, carry); |
| 143 | #endif |
| 144 | } |
| 145 | } |
| 146 | significant |= work; |
| 147 | if (significant || P < 0) |
| 148 | { |
| 149 | if (P >= 0) |
| 150 | { |
| 151 | product->low[P] = work; |
| 152 | #ifdef TRACE |
| 153 | printf ("P=%d. work[p]:=%04x\n", P, work); |
| 154 | #endif |
| 155 | } |
| 156 | P++; |
| 157 | } |
| 158 | else |
| 159 | { |
| 160 | extra_product_positions++; |
| 161 | exponent++; |
| 162 | } |
| 163 | } |
| 164 | /* |
| 165 | * [P]-> position # size_of_sum + 1. |
| 166 | * This is where 'carry' should go. |
| 167 | */ |
| 168 | #ifdef TRACE |
| 169 | printf ("final carry =%04x\n", carry); |
| 170 | #endif |
| 171 | if (carry) |
| 172 | { |
| 173 | if (extra_product_positions > 0) |
| 174 | { |
| 175 | product->low[P] = carry; |
| 176 | } |
| 177 | else |
| 178 | { |
| 179 | /* No room at high order for carry littlenum. */ |
| 180 | /* Shift right 1 to make room for most significant littlenum. */ |
| 181 | exponent++; |
| 182 | P--; |
| 183 | for (q = product->low + P; |
| 184 | q >= product->low; |
| 185 | q--) |
| 186 | { |
| 187 | work = *q; |
| 188 | *q = carry; |
| 189 | carry = work; |
| 190 | } |
| 191 | } |
| 192 | } |
| 193 | else |
| 194 | { |
| 195 | P--; |
| 196 | } |
| 197 | product->leader = product->low + P; |
| 198 | product->exponent = exponent; |
| 199 | } |
| 200 | |
| 201 | /* end of flonum_mult.c */ |