mirror of
https://github.com/Z3Prover/z3
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490 lines
15 KiB
C++
490 lines
15 KiB
C++
/*++
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Copyright (c) 2024 Microsoft Corporation
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Module Name:
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sls_valuation.cpp
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Abstract:
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A Stochastic Local Search (SLS) engine
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Uses invertibility conditions,
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interval annotations
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don't care annotations
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Author:
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Nikolaj Bjorner (nbjorner) 2024-02-07
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--*/
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#include "ast/sls/sls_valuation.h"
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namespace bv {
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void bvect::set_bw(unsigned bw) {
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this->bw = bw;
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nw = (bw + sizeof(digit_t) * 8 - 1) / (8 * sizeof(digit_t));
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mask = (1 << (bw % (8 * sizeof(digit_t)))) - 1;
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if (mask == 0)
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mask = ~(digit_t)0;
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reserve(nw + 1);
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}
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bool operator==(bvect const& a, bvect const& b) {
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SASSERT(a.nw > 0);
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return 0 == mpn_manager().compare(a.data(), a.nw, b.data(), a.nw);
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}
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bool operator<(bvect const& a, bvect const& b) {
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SASSERT(a.nw > 0);
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return mpn_manager().compare(a.data(), a.nw, b.data(), a.nw) < 0;
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}
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bool operator>(bvect const& a, bvect const& b) {
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SASSERT(a.nw > 0);
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return mpn_manager().compare(a.data(), a.nw, b.data(), a.nw) > 0;
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}
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bool operator<=(bvect const& a, bvect const& b) {
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SASSERT(a.nw > 0);
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return mpn_manager().compare(a.data(), a.nw, b.data(), a.nw) <= 0;
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}
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bool operator>=(bvect const& a, bvect const& b) {
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SASSERT(a.nw > 0);
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return mpn_manager().compare(a.data(), a.nw, b.data(), a.nw) >= 0;
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}
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sls_valuation::sls_valuation(unsigned bw) {
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set_bw(bw);
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lo.set_bw(bw);
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hi.set_bw(bw);
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m_bits.set_bw(bw);
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fixed.set_bw(bw);
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// have lo, hi bits, fixed point to memory allocated within this of size num_bytes each allocated
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for (unsigned i = 0; i < nw; ++i)
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lo[i] = 0, hi[i] = 0, m_bits[i] = 0, fixed[i] = 0;
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fixed[nw - 1] = ~mask;
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}
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void sls_valuation::set_bw(unsigned b) {
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bw = b;
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nw = (bw + sizeof(digit_t) * 8 - 1) / (8 * sizeof(digit_t));
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mask = (1 << (bw % (8 * sizeof(digit_t)))) - 1;
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if (mask == 0)
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mask = ~(digit_t)0;
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}
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bool sls_valuation::in_range(bvect const& bits) const {
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mpn_manager m;
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auto c = m.compare(lo.data(), nw, hi.data(), nw);
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SASSERT(!has_overflow(bits));
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// full range
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if (c == 0)
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return true;
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// lo < hi: then lo <= bits & bits < hi
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if (c < 0)
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return
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m.compare(lo.data(), nw, bits.data(), nw) <= 0 &&
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m.compare(bits.data(), nw, hi.data(), nw) < 0;
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// hi < lo: bits < hi or lo <= bits
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return
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m.compare(lo.data(), nw, bits.data(), nw) <= 0 ||
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m.compare(bits.data(), nw, hi.data(), nw) < 0;
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}
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//
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// largest dst <= src and dst is feasible
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// set dst := src & (~fixed | bits)
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//
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// increment dst if dst < src by setting bits below msb(src & ~dst) to 1
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//
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// if dst < lo < hi:
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// return false
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// if lo < hi <= dst:
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// set dst := hi - 1
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// if hi <= dst < lo
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// set dst := hi - 1
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//
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bool sls_valuation::get_at_most(bvect const& src, bvect& dst) const {
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SASSERT(!has_overflow(src));
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for (unsigned i = 0; i < nw; ++i)
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dst[i] = src[i] & (~fixed[i] | m_bits[i]);
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//
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// If dst < src, then find the most significant
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// bit where src[idx] = 1, dst[idx] = 0
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// set dst[j] = bits_j | ~fixed_j for j < idx
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//
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for (unsigned i = nw; i-- > 0; ) {
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if (0 != (~dst[i] & src[i])) {
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auto idx = log2(~dst[i] & src[i]);
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auto mask = (1 << idx) - 1;
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dst[i] = (~fixed[i] & mask) | dst[i];
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for (unsigned j = i; j-- > 0; )
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dst[j] = (~fixed[j] | m_bits[j]);
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break;
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}
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}
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SASSERT(!has_overflow(dst));
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return round_down(dst);
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}
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//
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// smallest dst >= src and dst is feasible with respect to this.
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// set dst := (src & ~fixed) | (fixed & bits)
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//
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// decrement dst if dst > src by setting bits below msb to 0 unless fixed
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//
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// if lo < hi <= dst
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// return false
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// if dst < lo < hi:
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// set dst := lo
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// if hi <= dst < lo
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// set dst := lo
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//
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bool sls_valuation::get_at_least(bvect const& src, bvect& dst) const {
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SASSERT(!has_overflow(src));
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for (unsigned i = 0; i < nw; ++i)
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dst[i] = (~fixed[i] & src[i]) | (fixed[i] & m_bits[i]);
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//
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// If dst > src, then find the most significant
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// bit where src[idx] = 0, dst[idx] = 1
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// set dst[j] = dst[j] & fixed_j for j < idx
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//
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for (unsigned i = nw; i-- > 0; ) {
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if (0 != (dst[i] & ~src[i])) {
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auto idx = log2(dst[i] & ~src[i]);
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auto mask = (1 << idx);
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dst[i] = dst[i] & (fixed[i] | mask);
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for (unsigned j = i; j-- > 0; )
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dst[j] = dst[j] & fixed[j];
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break;
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}
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}
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SASSERT(!has_overflow(dst));
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return round_up(dst);
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}
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bool sls_valuation::round_up(bvect& dst) const {
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if (lo < hi) {
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if (hi <= dst)
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return false;
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if (lo > dst)
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set(dst, lo);
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}
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else if (hi <= dst && lo > dst)
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set(dst, lo);
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SASSERT(!has_overflow(dst));
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return true;
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}
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bool sls_valuation::round_down(bvect& dst) const {
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if (lo < hi) {
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if (lo > dst)
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return false;
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if (hi <= dst) {
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set(dst, hi);
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sub1(dst);
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}
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}
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else if (hi <= dst && lo > dst) {
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set(dst, hi);
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sub1(dst);
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}
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SASSERT(well_formed());
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return true;
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}
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bool sls_valuation::set_repair(bool try_down, bvect& dst) {
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for (unsigned i = 0; i < nw; ++i)
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dst[i] = (~fixed[i] & dst[i]) | (fixed[i] & m_bits[i]);
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bool ok = try_down ? round_down(dst) : round_up(dst);
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if (!ok)
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VERIFY(try_down ? round_up(dst) : round_down(dst));
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DEBUG_CODE(SASSERT(0 == (mask & (fixed[nw-1] & (m_bits[nw-1] ^ dst[nw-1])))); for (unsigned i = 0; i + 1 < nw; ++i) SASSERT(0 == (fixed[i] & (m_bits[i] ^ dst[i]))););
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if (m_bits == dst)
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return false;
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set(m_bits, dst);
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SASSERT(well_formed());
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return true;
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}
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void sls_valuation::min_feasible(bvect& out) const {
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if (lo < hi) {
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for (unsigned i = 0; i < nw; ++i)
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out[i] = lo[i];
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}
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else {
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for (unsigned i = 0; i < nw; ++i)
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out[i] = fixed[i] & m_bits[i];
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}
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SASSERT(!has_overflow(out));
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}
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void sls_valuation::max_feasible(bvect& out) const {
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if (lo < hi) {
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for (unsigned i = 0; i < nw; ++i)
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out[i] = hi[i];
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sub1(out);
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}
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else {
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for (unsigned i = 0; i < nw; ++i)
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out[i] = ~fixed[i] | m_bits[i];
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}
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SASSERT(!has_overflow(out));
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}
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unsigned sls_valuation::msb(bvect const& src) const {
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SASSERT(!has_overflow(src));
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for (unsigned i = nw; i-- > 0; )
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if (src[i] != 0)
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return i * 8 * sizeof(digit_t) + log2(src[i]);
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return bw;
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}
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void sls_valuation::set_value(bvect& bits, rational const& n) {
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for (unsigned i = 0; i < bw; ++i)
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bits.set(i, n.get_bit(i));
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clear_overflow_bits(bits);
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}
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rational sls_valuation::get_value(bvect const& bits) const {
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rational p(1), r(0);
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for (unsigned i = 0; i < nw; ++i) {
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r += p * rational(bits[i]);
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p *= rational::power_of_two(8 * sizeof(digit_t));
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}
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return r;
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}
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void sls_valuation::get(bvect& dst) const {
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for (unsigned i = 0; i < nw; ++i)
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dst[i] = m_bits[i];
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}
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//
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// new_bits != bits => ~fixed
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// 0 = (new_bits ^ bits) & fixed
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// also check that new_bits are in range
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//
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bool sls_valuation::can_set(bvect const& new_bits) const {
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SASSERT(!has_overflow(new_bits));
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for (unsigned i = 0; i < nw; ++i)
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if (0 != ((new_bits[i] ^ m_bits[i]) & fixed[i]))
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return false;
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return in_range(new_bits);
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}
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unsigned sls_valuation::to_nat(unsigned max_n) {
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bvect const& d = m_bits;
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SASSERT(!has_overflow(d));
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SASSERT(max_n < UINT_MAX / 2);
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unsigned p = 1;
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unsigned value = 0;
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for (unsigned i = 0; i < bw; ++i) {
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if (p >= max_n) {
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for (unsigned j = i; j < bw; ++j)
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if (d.get(j))
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return max_n;
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return value;
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}
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if (d.get(i))
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value += p;
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p <<= 1;
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}
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return value;
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}
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void sls_valuation::shift_right(bvect& out, unsigned shift) const {
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SASSERT(shift < bw);
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for (unsigned i = 0; i < bw; ++i)
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out.set(i, i + shift < bw ? m_bits.get(i + shift) : false);
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SASSERT(well_formed());
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}
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void sls_valuation::add_range(rational l, rational h) {
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l = mod(l, rational::power_of_two(bw));
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h = mod(h, rational::power_of_two(bw));
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if (h == l)
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return;
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SASSERT(is_zero(fixed)); // ranges can only be added before fixed bits are set.
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if (lo == hi) {
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set_value(lo, l);
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set_value(hi, h);
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}
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else {
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auto old_lo = get_value(lo);
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auto old_hi = get_value(hi);
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if (old_lo < old_hi) {
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if (old_lo < l && l < old_hi)
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set_value(lo, l),
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old_lo = l;
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if (old_hi < h && h < old_hi)
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set_value(hi, h);
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}
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else {
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SASSERT(old_hi < old_lo);
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if (old_lo < l || l < old_hi)
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set_value(lo, l),
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old_lo = l;
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if (old_lo < h && h < old_hi)
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set_value(hi, h);
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else if (old_hi < old_lo && (h < old_hi || old_lo < h))
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set_value(hi, h);
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}
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}
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SASSERT(!has_overflow(lo));
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SASSERT(!has_overflow(hi));
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if (!in_range(m_bits))
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set(m_bits, lo);
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SASSERT(well_formed());
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}
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//
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// tighten lo/hi based on fixed bits.
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// lo[bit_i] != fixedbit[bit_i]
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// let bit_i be most significant bit position of disagreement.
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// if fixedbit = 1, lo = 0, increment lo
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// if fixedbit = 0, lo = 1, lo := fixed & bits
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// (hi-1)[bit_i] != fixedbit[bit_i]
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// if fixedbit = 0, hi-1 = 1, set hi-1 := 0, maximize below bit_i
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// if fixedbit = 1, hi-1 = 0, hi := fixed & bits
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// tighten fixed bits based on lo/hi
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// lo + 1 = hi -> set bits = lo
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// lo < hi, set most significant bits based on hi
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//
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void sls_valuation::init_fixed() {
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if (lo == hi)
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return;
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for (unsigned i = bw; i-- > 0; ) {
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if (!fixed.get(i))
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continue;
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if (m_bits.get(i) == lo.get(i))
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continue;
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if (m_bits.get(i)) {
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lo.set(i, true);
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for (unsigned j = i; j-- > 0; )
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lo.set(j, fixed.get(j) && m_bits.get(j));
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}
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else {
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for (unsigned j = bw; j-- > 0; )
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lo.set(j, fixed.get(j) && m_bits.get(j));
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}
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break;
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}
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bvect hi1(nw + 1);
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bvect one(nw + 1);
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one[0] = 1;
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digit_t c;
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mpn_manager().sub(hi.data(), nw, one.data(), nw, hi1.data(), &c);
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clear_overflow_bits(hi1);
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for (unsigned i = bw; i-- > 0; ) {
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if (!fixed.get(i))
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continue;
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if (m_bits.get(i) == hi1.get(i))
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continue;
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if (hi1.get(i)) {
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hi1.set(i, false);
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for (unsigned j = i; j-- > 0; )
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hi1.set(j, !fixed.get(j) || m_bits.get(j));
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}
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else {
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for (unsigned j = bw; j-- > 0; )
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hi1.set(j, fixed.get(j) && m_bits.get(j));
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}
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mpn_manager().add(hi1.data(), nw, one.data(), nw, hi.data(), nw + 1, &c);
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clear_overflow_bits(hi);
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break;
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}
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// set fixed bits based on bounds
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auto set_fixed_bit = [&](unsigned i, bool b) {
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if (!fixed.get(i)) {
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fixed.set(i, true);
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m_bits.set(i, b);
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}
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};
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// set most significant bits
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if (lo < hi) {
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unsigned i = bw;
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for (; i-- > 0 && !hi.get(i); )
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set_fixed_bit(i, false);
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if (is_power_of2(hi))
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set_fixed_bit(i, false);
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}
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// lo + 1 = hi: then bits = lo
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mpn_manager().add(lo.data(), nw, one.data(), nw, hi1.data(), nw + 1, &c);
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clear_overflow_bits(hi1);
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if (hi == hi1) {
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for (unsigned i = 0; i < bw; ++i)
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set_fixed_bit(i, lo.get(i));
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}
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SASSERT(well_formed());
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}
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void sls_valuation::set_sub(bvect& out, bvect const& a, bvect const& b) const {
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digit_t c;
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mpn_manager().sub(a.data(), nw, b.data(), nw, out.data(), &c);
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clear_overflow_bits(out);
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out.set_bw(bw);
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}
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bool sls_valuation::set_add(bvect& out, bvect const& a, bvect const& b) const {
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digit_t c;
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mpn_manager().add(a.data(), nw, b.data(), nw, out.data(), nw + 1, &c);
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bool ovfl = out[nw] != 0 || has_overflow(out);
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clear_overflow_bits(out);
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out.set_bw(bw);
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return ovfl;
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}
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bool sls_valuation::set_mul(bvect& out, bvect const& a, bvect const& b, bool check_overflow) const {
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mpn_manager().mul(a.data(), nw, b.data(), nw, out.data());
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bool ovfl = false;
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if (check_overflow) {
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ovfl = has_overflow(out);
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for (unsigned i = nw; i < 2 * nw; ++i)
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ovfl |= out[i] != 0;
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}
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clear_overflow_bits(out);
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out.set_bw(bw);
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return ovfl;
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}
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bool sls_valuation::is_power_of2(bvect const& src) const {
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unsigned c = 0;
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for (unsigned i = 0; i < nw; ++i)
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c += get_num_1bits(src[i]);
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return c == 1;
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}
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std::ostream& sls_valuation::print_bits(std::ostream& out, bvect const& v) const {
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bool nz = false;
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for (unsigned i = nw; i-- > 0;) {
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auto w = v[i];
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if (i + 1 == nw)
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w &= mask;
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if (nz)
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out << std::setw(8) << std::setfill('0') << w;
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else if (w != 0)
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out << w, nz = true;
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}
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if (!nz)
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out << "0";
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return out;
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|
}
|
|
|
|
|
|
}
|