| 1 | /* |
| 2 | * 128-bit division and remainder for compilers not supporting __int128 |
| 3 | * |
| 4 | * Copyright (c) 2021 Frédéric Pétrot <frederic.petrot@univ-grenoble-alpes.fr> |
| 5 | * |
| 6 | * Permission is hereby granted, free of charge, to any person obtaining a copy |
| 7 | * of this software and associated documentation files (the "Software"), to deal |
| 8 | * in the Software without restriction, including without limitation the rights |
| 9 | * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell |
| 10 | * copies of the Software, and to permit persons to whom the Software is |
| 11 | * furnished to do so, subject to the following conditions: |
| 12 | * |
| 13 | * The above copyright notice and this permission notice shall be included in |
| 14 | * all copies or substantial portions of the Software. |
| 15 | * |
| 16 | * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
| 17 | * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
| 18 | * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL |
| 19 | * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
| 20 | * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
| 21 | * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN |
| 22 | * THE SOFTWARE. |
| 23 | */ |
| 24 | |
| 25 | #include "qemu/osdep.h" |
| 26 | #include "qemu/host-utils.h" |
| 27 | #include "qemu/int128.h" |
| 28 | |
| 29 | #ifndef CONFIG_INT128 |
| 30 | |
| 31 | /* |
| 32 | * Division and remainder algorithms for 128-bit due to Stefan Kanthak, |
| 33 | * https://skanthak.homepage.t-online.de/integer.html#udivmodti4 |
| 34 | * Preconditions: |
| 35 | * - function should never be called with v equals to 0, it has to |
| 36 | * be dealt with beforehand |
| 37 | * - quotien pointer must be valid |
| 38 | */ |
| 39 | static Int128 divrem128(Int128 u, Int128 v, Int128 *q) |
| 40 | { |
| 41 | Int128 qq; |
| 42 | uint64_t hi, lo, tmp; |
| 43 | int s = clz64(v.hi); |
| 44 | |
| 45 | if (s == 64) { |
| 46 | /* we have uu÷0v => let's use divu128 */ |
| 47 | hi = u.hi; |
| 48 | lo = u.lo; |
| 49 | tmp = divu128(&lo, &hi, v.lo); |
| 50 | *q = int128_make128(lo, hi); |
| 51 | return int128_make128(tmp, 0); |
| 52 | } else { |
| 53 | hi = int128_gethi(int128_lshift(v, s)); |
| 54 | |
| 55 | if (hi > u.hi) { |
| 56 | lo = u.lo; |
| 57 | tmp = u.hi; |
| 58 | divu128(&lo, &tmp, hi); |
| 59 | lo = int128_gethi(int128_lshift(int128_make128(lo, 0), s)); |
| 60 | } else { /* prevent overflow */ |
| 61 | lo = u.lo; |
| 62 | tmp = u.hi - hi; |
| 63 | divu128(&lo, &tmp, hi); |
| 64 | lo = int128_gethi(int128_lshift(int128_make128(lo, 1), s)); |
| 65 | } |
| 66 | |
| 67 | qq = int128_make64(lo); |
| 68 | |
| 69 | tmp = lo * v.hi; |
| 70 | mulu64(&lo, &hi, lo, v.lo); |
| 71 | hi += tmp; |
| 72 | |
| 73 | if (hi < tmp /* quotient * divisor >= 2**128 > dividend */ |
| 74 | || hi > u.hi /* quotient * divisor > dividend */ |
| 75 | || (hi == u.hi && lo > u.lo)) { |
| 76 | qq.lo -= 1; |
| 77 | mulu64(&lo, &hi, qq.lo, v.lo); |
| 78 | hi += qq.lo * v.hi; |
| 79 | } |
| 80 | |
| 81 | *q = qq; |
| 82 | u.hi -= hi + (u.lo < lo); |
| 83 | u.lo -= lo; |
| 84 | return u; |
| 85 | } |
| 86 | } |
| 87 | |
| 88 | Int128 int128_divu(Int128 a, Int128 b) |
| 89 | { |
| 90 | Int128 q; |
| 91 | divrem128(a, b, &q); |
| 92 | return q; |
| 93 | } |
| 94 | |
| 95 | Int128 int128_remu(Int128 a, Int128 b) |
| 96 | { |
| 97 | Int128 q; |
| 98 | return divrem128(a, b, &q); |
| 99 | } |
| 100 | |
| 101 | Int128 int128_divs(Int128 a, Int128 b) |
| 102 | { |
| 103 | Int128 q; |
| 104 | bool sgna = !int128_nonneg(a); |
| 105 | bool sgnb = !int128_nonneg(b); |
| 106 | |
| 107 | if (sgna) { |
| 108 | a = int128_neg(a); |
| 109 | } |
| 110 | |
| 111 | if (sgnb) { |
| 112 | b = int128_neg(b); |
| 113 | } |
| 114 | |
| 115 | divrem128(a, b, &q); |
| 116 | |
| 117 | if (sgna != sgnb) { |
| 118 | q = int128_neg(q); |
| 119 | } |
| 120 | |
| 121 | return q; |
| 122 | } |
| 123 | |
| 124 | Int128 int128_rems(Int128 a, Int128 b) |
| 125 | { |
| 126 | Int128 q, r; |
| 127 | bool sgna = !int128_nonneg(a); |
| 128 | bool sgnb = !int128_nonneg(b); |
| 129 | |
| 130 | if (sgna) { |
| 131 | a = int128_neg(a); |
| 132 | } |
| 133 | |
| 134 | if (sgnb) { |
| 135 | b = int128_neg(b); |
| 136 | } |
| 137 | |
| 138 | r = divrem128(a, b, &q); |
| 139 | |
| 140 | if (sgna) { |
| 141 | r = int128_neg(r); |
| 142 | } |
| 143 | |
| 144 | return r; |
| 145 | } |
| 146 | |
| 147 | #elif defined(CONFIG_TCG_INTERPRETER) |
| 148 | |
| 149 | Int128 int128_divu(Int128 a_s, Int128 b_s) |
| 150 | { |
| 151 | Int128Alias r, a, b; |
| 152 | |
| 153 | a.s = a_s; |
| 154 | b.s = b_s; |
| 155 | r.u = a.u / b.u; |
| 156 | return r.s; |
| 157 | } |
| 158 | |
| 159 | Int128 int128_remu(Int128 a_s, Int128 b_s) |
| 160 | { |
| 161 | Int128Alias r, a, b; |
| 162 | |
| 163 | a.s = a_s; |
| 164 | b.s = b_s; |
| 165 | r.u = a.u % b.u; |
| 166 | return r.s; |
| 167 | } |
| 168 | |
| 169 | Int128 int128_divs(Int128 a_s, Int128 b_s) |
| 170 | { |
| 171 | Int128Alias r, a, b; |
| 172 | |
| 173 | a.s = a_s; |
| 174 | b.s = b_s; |
| 175 | r.i = a.i / b.i; |
| 176 | return r.s; |
| 177 | } |
| 178 | |
| 179 | Int128 int128_rems(Int128 a_s, Int128 b_s) |
| 180 | { |
| 181 | Int128Alias r, a, b; |
| 182 | |
| 183 | a.s = a_s; |
| 184 | b.s = b_s; |
| 185 | r.i = a.i % b.i; |
| 186 | return r.s; |
| 187 | } |
| 188 | |
| 189 | #endif |