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