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