/*
* Utility compute operations used by translated code.
*
* Copyright (c) 2003 Fabrice Bellard
* Copyright (c) 2007 Aurelien Jarno
*
* 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"
#ifndef CONFIG_INT128
/* Long integer helpers */
static inline void mul64(uint64_t *plow, uint64_t *phigh,
uint64_t a, uint64_t b)
{
typedef union {
uint64_t ll;
struct {
#if HOST_BIG_ENDIAN
uint32_t high, low;
#else
uint32_t low, high;
#endif
} l;
} LL;
LL rl, rm, rn, rh, a0, b0;
uint64_t c;
a0.ll = a;
b0.ll = b;
rl.ll = (uint64_t)a0.l.low * b0.l.low;
rm.ll = (uint64_t)a0.l.low * b0.l.high;
rn.ll = (uint64_t)a0.l.high * b0.l.low;
rh.ll = (uint64_t)a0.l.high * b0.l.high;
c = (uint64_t)rl.l.high + rm.l.low + rn.l.low;
rl.l.high = c;
c >>= 32;
c = c + rm.l.high + rn.l.high + rh.l.low;
rh.l.low = c;
rh.l.high += (uint32_t)(c >> 32);
*plow = rl.ll;
*phigh = rh.ll;
}
/* Unsigned 64x64 -> 128 multiplication */
void mulu64 (uint64_t *plow, uint64_t *phigh, uint64_t a, uint64_t b)
{
mul64(plow, phigh, a, b);
}
/* Signed 64x64 -> 128 multiplication */
void muls64 (uint64_t *plow, uint64_t *phigh, int64_t a, int64_t b)
{
uint64_t rh;
mul64(plow, &rh, a, b);
/* Adjust for signs. */
if (b < 0) {
rh -= a;
}
if (a < 0) {
rh -= b;
}
*phigh = rh;
}
/*
* Unsigned 128-by-64 division.
* Returns the remainder.
* Returns quotient via plow and phigh.
* Also returns the remainder via the function return value.
*/
uint64_t divu128(uint64_t *plow, uint64_t *phigh, uint64_t divisor)
{
uint64_t dhi = *phigh;
uint64_t dlo = *plow;
uint64_t rem, dhighest;
int sh;
if (divisor == 0 || dhi == 0) {
*plow = dlo / divisor;
*phigh = 0;
return dlo % divisor;
} else {
sh = clz64(divisor);
if (dhi < divisor) {
if (sh != 0) {
/* normalize the divisor, shifting the dividend accordingly */
divisor <<= sh;
dhi = (dhi << sh) | (dlo >> (64 - sh));
dlo <<= sh;
}
*phigh = 0;
*plow = udiv_qrnnd(&rem, dhi, dlo, divisor);
} else {
if (sh != 0) {
/* normalize the divisor, shifting the dividend accordingly */
divisor <<= sh;
dhighest = dhi >> (64 - sh);
dhi = (dhi << sh) | (dlo >> (64 - sh));
dlo <<= sh;
*phigh = udiv_qrnnd(&dhi, dhighest, dhi, divisor);
} else {
/**
* dhi >= divisor
* Since the MSB of divisor is set (sh == 0),
* (dhi - divisor) < divisor
*
* Thus, the high part of the quotient is 1, and we can
* calculate the low part with a single call to udiv_qrnnd
* after subtracting divisor from dhi
*/
dhi -= divisor;
*phigh = 1;
}
*plow = udiv_qrnnd(&rem, dhi, dlo, divisor);
}
/*
* since the dividend/divisor might have been normalized,
* the remainder might also have to be shifted back
*/
return rem >> sh;
}
}
/*
* Signed 128-by-64 division.
* Returns quotient via plow and phigh.
* Also returns the remainder via the function return value.
*/
int64_t divs128(uint64_t *plow, int64_t *phigh, int64_t divisor)
{
bool neg_quotient = false, neg_remainder = false;
uint64_t unsig_hi = *phigh, unsig_lo = *plow;
uint64_t rem;
if (*phigh < 0) {
neg_quotient = !neg_quotient;
neg_remainder = !neg_remainder;
if (unsig_lo == 0) {
unsig_hi = -unsig_hi;
} else {
unsig_hi = ~unsig_hi;
unsig_lo = -unsig_lo;
}
}
if (divisor < 0) {
neg_quotient = !neg_quotient;
divisor = -divisor;
}
rem = divu128(&unsig_lo, &unsig_hi, (uint64_t)divisor);
if (neg_quotient) {
if (unsig_lo == 0) {
*phigh = -unsig_hi;
*plow = 0;
} else {
*phigh = ~unsig_hi;
*plow = -unsig_lo;
}
} else {
*phigh = unsig_hi;
*plow = unsig_lo;
}
if (neg_remainder) {
return -rem;
} else {
return rem;
}
}
#endif
/**
* urshift - 128-bit Unsigned Right Shift.
* @plow: in/out - lower 64-bit integer.
* @phigh: in/out - higher 64-bit integer.
* @shift: in - bytes to shift, between 0 and 127.
*
* Result is zero-extended and stored in plow/phigh, which are
* input/output variables. Shift values outside the range will
* be mod to 128. In other words, the caller is responsible to
* verify/assert both the shift range and plow/phigh pointers.
*/
void urshift(uint64_t *plow, uint64_t *phigh, int32_t shift)
{
shift &= 127;
if (shift == 0) {
return;
}
uint64_t h = *phigh >> (shift & 63);
if (shift >= 64) {
*plow = h;
*phigh = 0;
} else {
*plow = (*plow >> (shift & 63)) | (*phigh << (64 - (shift & 63)));
*phigh = h;
}
}
/**
* ulshift - 128-bit Unsigned Left Shift.
* @plow: in/out - lower 64-bit integer.
* @phigh: in/out - higher 64-bit integer.
* @shift: in - bytes to shift, between 0 and 127.
* @overflow: out - true if any 1-bit is shifted out.
*
* Result is zero-extended and stored in plow/phigh, which are
* input/output variables. Shift values outside the range will
* be mod to 128. In other words, the caller is responsible to
* verify/assert both the shift range and plow/phigh pointers.
*/
void ulshift(uint64_t *plow, uint64_t *phigh, int32_t shift, bool *overflow)
{
uint64_t low = *plow;
uint64_t high = *phigh;
shift &= 127;
if (shift == 0) {
return;
}
/* check if any bit will be shifted out */
urshift(&low, &high, 128 - shift);
if (low | high) {
*overflow = true;
}
if (shift >= 64) {
*phigh = *plow << (shift & 63);
*plow = 0;
} else {
*phigh = (*plow >> (64 - (shift & 63))) | (*phigh << (shift & 63));
*plow = *plow << shift;
}
}
/*
* Unsigned 256-by-128 division.
* Returns the remainder via r.
* Returns lower 128 bit of quotient.
* Needs a normalized divisor (most significant bit set to 1).
*
* Adapted from include/qemu/host-utils.h udiv_qrnnd,
* from the GNU Multi Precision Library - longlong.h __udiv_qrnnd
* (https://gmplib.org/repo/gmp/file/tip/longlong.h)
*
* Licensed under the GPLv2/LGPLv3
*/
static Int128 udiv256_qrnnd(Int128 *r, Int128 n1, Int128 n0, Int128 d)
{
Int128 d0, d1, q0, q1, r1, r0, m;
uint64_t mp0, mp1;
d0 = int128_make64(int128_getlo(d));
d1 = int128_make64(int128_gethi(d));
r1 = int128_remu(n1, d1);
q1 = int128_divu(n1, d1);
mp0 = int128_getlo(q1);
mp1 = int128_gethi(q1);
mulu128(&mp0, &mp1, int128_getlo(d0));
m = int128_make128(mp0, mp1);
r1 = int128_make128(int128_gethi(n0), int128_getlo(r1));
if (int128_ult(r1, m)) {
q1 = int128_sub(q1, int128_one());
r1 = int128_add(r1, d);
if (int128_uge(r1, d)) {
if (int128_ult(r1, m)) {
q1 = int128_sub(q1, int128_one());
r1 = int128_add(r1, d);
}
}
}
r1 = int128_sub(r1, m);
r0 = int128_remu(r1, d1);
q0 = int128_divu(r1, d1);
mp0 = int128_getlo(q0);
mp1 = int128_gethi(q0);
mulu128(&mp0, &mp1, int128_getlo(d0));
m = int128_make128(mp0, mp1);
r0 = int128_make128(int128_getlo(n0), int128_getlo(r0));
if (int128_ult(r0, m)) {
q0 = int128_sub(q0, int128_one());
r0 = int128_add(r0, d);
if (int128_uge(r0, d)) {
if (int128_ult(r0, m)) {
q0 = int128_sub(q0, int128_one());
r0 = int128_add(r0, d);
}
}
}
r0 = int128_sub(r0, m);
*r = r0;
return int128_or(int128_lshift(q1, 64), q0);
}
/*
* Unsigned 256-by-128 division.
* Returns the remainder.
* Returns quotient via plow and phigh.
* Also returns the remainder via the function return value.
*/
Int128 divu256(Int128 *plow, Int128 *phigh, Int128 divisor)
{
Int128 dhi = *phigh;
Int128 dlo = *plow;
Int128 rem, dhighest;
int sh;
if (!int128_nz(divisor) || !int128_nz(dhi)) {
*plow = int128_divu(dlo, divisor);
*phigh = int128_zero();
return int128_remu(dlo, divisor);
} else {
sh = clz128(divisor);
if (int128_ult(dhi, divisor)) {
if (sh != 0) {
/* normalize the divisor, shifting the dividend accordingly */
divisor = int128_lshift(divisor, sh);
dhi = int128_or(int128_lshift(dhi, sh),
int128_urshift(dlo, (128 - sh)));
dlo = int128_lshift(dlo, sh);
}
*phigh = int128_zero();
*plow = udiv256_qrnnd(&rem, dhi, dlo, divisor);
} else {
if (sh != 0) {
/* normalize the divisor, shifting the dividend accordingly */
divisor = int128_lshift(divisor, sh);
dhighest = int128_rshift(dhi, (128 - sh));
dhi = int128_or(int128_lshift(dhi, sh),
int128_urshift(dlo, (128 - sh)));
dlo = int128_lshift(dlo, sh);
*phigh = udiv256_qrnnd(&dhi, dhighest, dhi, divisor);
} else {
/*
* dhi >= divisor
* Since the MSB of divisor is set (sh == 0),
* (dhi - divisor) < divisor
*
* Thus, the high part of the quotient is 1, and we can
* calculate the low part with a single call to udiv_qrnnd
* after subtracting divisor from dhi
*/
dhi = int128_sub(dhi, divisor);
*phigh = int128_one();
}
*plow = udiv256_qrnnd(&rem, dhi, dlo, divisor);
}
/*
* since the dividend/divisor might have been normalized,
* the remainder might also have to be shifted back
*/
rem = int128_urshift(rem, sh);
return rem;
}
}
/*
* Signed 256-by-128 division.
* Returns quotient via plow and phigh.
* Also returns the remainder via the function return value.
*/
Int128 divs256(Int128 *plow, Int128 *phigh, Int128 divisor)
{
bool neg_quotient = false, neg_remainder = false;
Int128 unsig_hi = *phigh, unsig_lo = *plow;
Int128 rem;
if (!int128_nonneg(*phigh)) {
neg_quotient = !neg_quotient;
neg_remainder = !neg_remainder;
if (!int128_nz(unsig_lo)) {
unsig_hi = int128_neg(unsig_hi);
} else {
unsig_hi = int128_not(unsig_hi);
unsig_lo = int128_neg(unsig_lo);
}
}
if (!int128_nonneg(divisor)) {
neg_quotient = !neg_quotient;
divisor = int128_neg(divisor);
}
rem = divu256(&unsig_lo, &unsig_hi, divisor);
if (neg_quotient) {
if (!int128_nz(unsig_lo)) {
*phigh = int128_neg(unsig_hi);
*plow = int128_zero();
} else {
*phigh = int128_not(unsig_hi);
*plow = int128_neg(unsig_lo);
}
} else {
*phigh = unsig_hi;
*plow = unsig_lo;
}
if (neg_remainder) {
return int128_neg(rem);
} else {
return rem;
}
}
