147 lines
3.7 KiB
C
147 lines
3.7 KiB
C
/*
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* 128-bit division and remainder for compilers not supporting __int128
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*
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* Copyright (c) 2021 Frédéric Pétrot <frederic.petrot@univ-grenoble-alpes.fr>
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*
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* Permission is hereby granted, free of charge, to any person obtaining a copy
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* of this software and associated documentation files (the "Software"), to deal
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* in the Software without restriction, including without limitation the rights
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* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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* copies of the Software, and to permit persons to whom the Software is
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* furnished to do so, subject to the following conditions:
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*
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* The above copyright notice and this permission notice shall be included in
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* all copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
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* THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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* THE SOFTWARE.
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*/
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#include "qemu/osdep.h"
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#include "qemu/host-utils.h"
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#include "qemu/int128.h"
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#ifndef CONFIG_INT128
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/*
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* Division and remainder algorithms for 128-bit due to Stefan Kanthak,
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* https://skanthak.homepage.t-online.de/integer.html#udivmodti4
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* Preconditions:
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* - function should never be called with v equals to 0, it has to
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* be dealt with beforehand
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* - quotien pointer must be valid
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*/
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static Int128 divrem128(Int128 u, Int128 v, Int128 *q)
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{
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Int128 qq;
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uint64_t hi, lo, tmp;
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int s = clz64(v.hi);
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if (s == 64) {
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/* we have uu÷0v => let's use divu128 */
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hi = u.hi;
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lo = u.lo;
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tmp = divu128(&lo, &hi, v.lo);
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*q = int128_make128(lo, hi);
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return int128_make128(tmp, 0);
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} else {
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hi = int128_gethi(int128_lshift(v, s));
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if (hi > u.hi) {
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lo = u.lo;
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tmp = u.hi;
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divu128(&lo, &tmp, hi);
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lo = int128_gethi(int128_lshift(int128_make128(lo, 0), s));
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} else { /* prevent overflow */
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lo = u.lo;
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tmp = u.hi - hi;
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divu128(&lo, &tmp, hi);
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lo = int128_gethi(int128_lshift(int128_make128(lo, 1), s));
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}
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qq = int128_make64(lo);
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tmp = lo * v.hi;
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mulu64(&lo, &hi, lo, v.lo);
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hi += tmp;
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if (hi < tmp /* quotient * divisor >= 2**128 > dividend */
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|| hi > u.hi /* quotient * divisor > dividend */
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|| (hi == u.hi && lo > u.lo)) {
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qq.lo -= 1;
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mulu64(&lo, &hi, qq.lo, v.lo);
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hi += qq.lo * v.hi;
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}
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*q = qq;
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u.hi -= hi + (u.lo < lo);
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u.lo -= lo;
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return u;
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}
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}
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Int128 int128_divu(Int128 a, Int128 b)
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{
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Int128 q;
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divrem128(a, b, &q);
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return q;
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}
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Int128 int128_remu(Int128 a, Int128 b)
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{
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Int128 q;
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return divrem128(a, b, &q);
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}
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Int128 int128_divs(Int128 a, Int128 b)
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{
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Int128 q;
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bool sgna = !int128_nonneg(a);
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bool sgnb = !int128_nonneg(b);
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if (sgna) {
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a = int128_neg(a);
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}
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if (sgnb) {
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b = int128_neg(b);
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}
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divrem128(a, b, &q);
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if (sgna != sgnb) {
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q = int128_neg(q);
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}
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return q;
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}
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Int128 int128_rems(Int128 a, Int128 b)
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{
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Int128 q, r;
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bool sgna = !int128_nonneg(a);
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bool sgnb = !int128_nonneg(b);
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if (sgna) {
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a = int128_neg(a);
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}
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if (sgnb) {
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b = int128_neg(b);
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}
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r = divrem128(a, b, &q);
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if (sgna) {
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r = int128_neg(r);
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}
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return r;
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}
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#endif
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