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64 lines
2.1 KiB
C++
64 lines
2.1 KiB
C++
/*++
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Copyright (c) 2026 Microsoft Corporation
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Module Name:
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bv_divrem_bounds.h
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Abstract:
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Simplifier that adds range/bound lemmas for bit-vector division and
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remainder terms with a non-constant divisor.
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Bit-blasting a division circuit with a symbolic divisor hides the algebraic
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fact that the remainder magnitude is bounded by the divisor magnitude. For a
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divisor b that is not a numeral the following facts hold and are added as
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(implied) lemmas so that a downstream bit-blasting + SAT solver can reason
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about the magnitudes without unfolding the division circuit:
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b != 0 => bvult (bvurem a b) b (unsigned remainder)
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b != 0 => bvult |bvsrem a b| |b| (signed remainder)
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b != 0 => bvult |bvsmod a b| |b| (signed modulo)
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b != 0 => bvule (bvudiv a b) a (unsigned quotient)
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b != 0 => bvule |bvsdiv a b| |a| (signed quotient)
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where |x| = ite(x <s 0, -x, x). These lemmas are logically implied by the
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semantics of the operators for a non-zero divisor, so the transformation
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preserves satisfiability and all models. The unsigned comparison on the
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absolute values keeps the bounds sound at INT_MIN: -INT_MIN overflows to
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INT_MIN whose unsigned value is the maximum magnitude, so the bound only
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ever loosens, never becomes unsound.
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Author:
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Nikolaj Bjorner (nbjorner)
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--*/
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#pragma once
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#include "ast/bv_decl_plugin.h"
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#include "ast/simplifiers/dependent_expr_state.h"
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namespace bv {
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class divrem_bounds : public dependent_expr_simplifier {
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bv_util m_util;
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unsigned m_num_lemmas = 0;
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public:
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divrem_bounds(ast_manager& m, dependent_expr_state& fmls) :
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dependent_expr_simplifier(m, fmls), m_util(m) {}
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char const* name() const override { return "bv-divrem-bounds"; }
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void reduce() override;
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bool supports_proofs() const override { return true; }
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void collect_statistics(statistics& st) const override {
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st.update("bv-divrem-bounds", m_num_lemmas);
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}
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void reset_statistics() override { m_num_lemmas = 0; }
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};
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}
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