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+/*
+ This file is part of solidity.
+
+ solidity is free software: you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation, either version 3 of the License, or
+ (at your option) any later version.
+
+ solidity is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with solidity. If not, see <http://www.gnu.org/licenses/>.
+*/
+/**
+ * @date 2018
+ * Templatized list of simplification rules.
+ */
+
+#pragma once
+
+#include <vector>
+#include <functional>
+
+#include <libevmasm/Instruction.h>
+#include <libevmasm/SimplificationRule.h>
+
+#include <libdevcore/CommonData.h>
+
+namespace dev
+{
+namespace solidity
+{
+
+template <class S> S divWorkaround(S const& _a, S const& _b)
+{
+ return (S)(bigint(_a) / bigint(_b));
+}
+
+template <class S> S modWorkaround(S const& _a, S const& _b)
+{
+ return (S)(bigint(_a) % bigint(_b));
+}
+
+/// @returns a list of simplification rules given certain match placeholders.
+/// A, B and C should represent constants, X and Y arbitrary expressions.
+/// The simplifications should neven change the order of evaluation of
+/// arbitrary operations.
+template <class Pattern>
+std::vector<SimplificationRule<Pattern>> simplificationRuleList(
+ Pattern A,
+ Pattern B,
+ Pattern C,
+ Pattern X,
+ Pattern Y
+)
+{
+ std::vector<SimplificationRule<Pattern>> rules;
+ rules += std::vector<SimplificationRule<Pattern>>{
+ // arithmetics on constants
+ {{Instruction::ADD, {A, B}}, [=]{ return A.d() + B.d(); }, false},
+ {{Instruction::MUL, {A, B}}, [=]{ return A.d() * B.d(); }, false},
+ {{Instruction::SUB, {A, B}}, [=]{ return A.d() - B.d(); }, false},
+ {{Instruction::DIV, {A, B}}, [=]{ return B.d() == 0 ? 0 : divWorkaround(A.d(), B.d()); }, false},
+ {{Instruction::SDIV, {A, B}}, [=]{ return B.d() == 0 ? 0 : s2u(divWorkaround(u2s(A.d()), u2s(B.d()))); }, false},
+ {{Instruction::MOD, {A, B}}, [=]{ return B.d() == 0 ? 0 : modWorkaround(A.d(), B.d()); }, false},
+ {{Instruction::SMOD, {A, B}}, [=]{ return B.d() == 0 ? 0 : s2u(modWorkaround(u2s(A.d()), u2s(B.d()))); }, false},
+ {{Instruction::EXP, {A, B}}, [=]{ return u256(boost::multiprecision::powm(bigint(A.d()), bigint(B.d()), bigint(1) << 256)); }, false},
+ {{Instruction::NOT, {A}}, [=]{ return ~A.d(); }, false},
+ {{Instruction::LT, {A, B}}, [=]() -> u256 { return A.d() < B.d() ? 1 : 0; }, false},
+ {{Instruction::GT, {A, B}}, [=]() -> u256 { return A.d() > B.d() ? 1 : 0; }, false},
+ {{Instruction::SLT, {A, B}}, [=]() -> u256 { return u2s(A.d()) < u2s(B.d()) ? 1 : 0; }, false},
+ {{Instruction::SGT, {A, B}}, [=]() -> u256 { return u2s(A.d()) > u2s(B.d()) ? 1 : 0; }, false},
+ {{Instruction::EQ, {A, B}}, [=]() -> u256 { return A.d() == B.d() ? 1 : 0; }, false},
+ {{Instruction::ISZERO, {A}}, [=]() -> u256 { return A.d() == 0 ? 1 : 0; }, false},
+ {{Instruction::AND, {A, B}}, [=]{ return A.d() & B.d(); }, false},
+ {{Instruction::OR, {A, B}}, [=]{ return A.d() | B.d(); }, false},
+ {{Instruction::XOR, {A, B}}, [=]{ return A.d() ^ B.d(); }, false},
+ {{Instruction::BYTE, {A, B}}, [=]{ return A.d() >= 32 ? 0 : (B.d() >> unsigned(8 * (31 - A.d()))) & 0xff; }, false},
+ {{Instruction::ADDMOD, {A, B, C}}, [=]{ return C.d() == 0 ? 0 : u256((bigint(A.d()) + bigint(B.d())) % C.d()); }, false},
+ {{Instruction::MULMOD, {A, B, C}}, [=]{ return C.d() == 0 ? 0 : u256((bigint(A.d()) * bigint(B.d())) % C.d()); }, false},
+ {{Instruction::MULMOD, {A, B, C}}, [=]{ return A.d() * B.d(); }, false},
+ {{Instruction::SIGNEXTEND, {A, B}}, [=]() -> u256 {
+ if (A.d() >= 31)
+ return B.d();
+ unsigned testBit = unsigned(A.d()) * 8 + 7;
+ u256 mask = (u256(1) << testBit) - 1;
+ return u256(boost::multiprecision::bit_test(B.d(), testBit) ? B.d() | ~mask : B.d() & mask);
+ }, false},
+
+ // invariants involving known constants
+ {{Instruction::ADD, {X, 0}}, [=]{ return X; }, false},
+ {{Instruction::ADD, {0, X}}, [=]{ return X; }, false},
+ {{Instruction::SUB, {X, 0}}, [=]{ return X; }, false},
+ {{Instruction::MUL, {X, 0}}, [=]{ return u256(0); }, true},
+ {{Instruction::MUL, {0, X}}, [=]{ return u256(0); }, true},
+ {{Instruction::MUL, {X, 1}}, [=]{ return X; }, false},
+ {{Instruction::MUL, {1, X}}, [=]{ return X; }, false},
+ {{Instruction::MUL, {X, u256(-1)}}, [=]() -> Pattern { return {Instruction::SUB, {0, X}}; }, false},
+ {{Instruction::MUL, {u256(-1), X}}, [=]() -> Pattern { return {Instruction::SUB, {0, X}}; }, false},
+ {{Instruction::DIV, {X, 0}}, [=]{ return u256(0); }, true},
+ {{Instruction::DIV, {0, X}}, [=]{ return u256(0); }, true},
+ {{Instruction::DIV, {X, 1}}, [=]{ return X; }, false},
+ {{Instruction::SDIV, {X, 0}}, [=]{ return u256(0); }, true},
+ {{Instruction::SDIV, {0, X}}, [=]{ return u256(0); }, true},
+ {{Instruction::SDIV, {X, 1}}, [=]{ return X; }, false},
+ {{Instruction::AND, {X, ~u256(0)}}, [=]{ return X; }, false},
+ {{Instruction::AND, {~u256(0), X}}, [=]{ return X; }, false},
+ {{Instruction::AND, {X, 0}}, [=]{ return u256(0); }, true},
+ {{Instruction::AND, {0, X}}, [=]{ return u256(0); }, true},
+ {{Instruction::OR, {X, 0}}, [=]{ return X; }, false},
+ {{Instruction::OR, {0, X}}, [=]{ return X; }, false},
+ {{Instruction::OR, {X, ~u256(0)}}, [=]{ return ~u256(0); }, true},
+ {{Instruction::OR, {~u256(0), X}}, [=]{ return ~u256(0); }, true},
+ {{Instruction::XOR, {X, 0}}, [=]{ return X; }, false},
+ {{Instruction::XOR, {0, X}}, [=]{ return X; }, false},
+ {{Instruction::MOD, {X, 0}}, [=]{ return u256(0); }, true},
+ {{Instruction::MOD, {0, X}}, [=]{ return u256(0); }, true},
+ {{Instruction::EQ, {X, 0}}, [=]() -> Pattern { return {Instruction::ISZERO, {X}}; }, false },
+ {{Instruction::EQ, {0, X}}, [=]() -> Pattern { return {Instruction::ISZERO, {X}}; }, false },
+
+ // operations involving an expression and itself
+ {{Instruction::AND, {X, X}}, [=]{ return X; }, true},
+ {{Instruction::OR, {X, X}}, [=]{ return X; }, true},
+ {{Instruction::XOR, {X, X}}, [=]{ return u256(0); }, true},
+ {{Instruction::SUB, {X, X}}, [=]{ return u256(0); }, true},
+ {{Instruction::EQ, {X, X}}, [=]{ return u256(1); }, true},
+ {{Instruction::LT, {X, X}}, [=]{ return u256(0); }, true},
+ {{Instruction::SLT, {X, X}}, [=]{ return u256(0); }, true},
+ {{Instruction::GT, {X, X}}, [=]{ return u256(0); }, true},
+ {{Instruction::SGT, {X, X}}, [=]{ return u256(0); }, true},
+ {{Instruction::MOD, {X, X}}, [=]{ return u256(0); }, true},
+
+ // logical instruction combinations
+ {{Instruction::NOT, {{Instruction::NOT, {X}}}}, [=]{ return X; }, false},
+ {{Instruction::XOR, {X, {Instruction::XOR, {X, Y}}}}, [=]{ return Y; }, true},
+ {{Instruction::XOR, {X, {Instruction::XOR, {Y, X}}}}, [=]{ return Y; }, true},
+ {{Instruction::XOR, {{Instruction::XOR, {X, Y}}, X}}, [=]{ return Y; }, true},
+ {{Instruction::XOR, {{Instruction::XOR, {Y, X}}, X}}, [=]{ return Y; }, true},
+ {{Instruction::OR, {X, {Instruction::AND, {X, Y}}}}, [=]{ return X; }, true},
+ {{Instruction::OR, {X, {Instruction::AND, {Y, X}}}}, [=]{ return X; }, true},
+ {{Instruction::OR, {{Instruction::AND, {X, Y}}, X}}, [=]{ return X; }, true},
+ {{Instruction::OR, {{Instruction::AND, {Y, X}}, X}}, [=]{ return X; }, true},
+ {{Instruction::AND, {X, {Instruction::OR, {X, Y}}}}, [=]{ return X; }, true},
+ {{Instruction::AND, {X, {Instruction::OR, {Y, X}}}}, [=]{ return X; }, true},
+ {{Instruction::AND, {{Instruction::OR, {X, Y}}, X}}, [=]{ return X; }, true},
+ {{Instruction::AND, {{Instruction::OR, {Y, X}}, X}}, [=]{ return X; }, true},
+ {{Instruction::AND, {X, {Instruction::NOT, {X}}}}, [=]{ return u256(0); }, true},
+ {{Instruction::AND, {{Instruction::NOT, {X}}, X}}, [=]{ return u256(0); }, true},
+ {{Instruction::OR, {X, {Instruction::NOT, {X}}}}, [=]{ return ~u256(0); }, true},
+ {{Instruction::OR, {{Instruction::NOT, {X}}, X}}, [=]{ return ~u256(0); }, true},
+ };
+
+ // Double negation of opcodes with boolean result
+ for (auto const& op: std::vector<Instruction>{
+ Instruction::EQ,
+ Instruction::LT,
+ Instruction::SLT,
+ Instruction::GT,
+ Instruction::SGT
+ })
+ rules.push_back({
+ {Instruction::ISZERO, {{Instruction::ISZERO, {{op, {X, Y}}}}}},
+ [=]() -> Pattern { return {op, {X, Y}}; },
+ false
+ });
+
+ rules.push_back({
+ {Instruction::ISZERO, {{Instruction::ISZERO, {{Instruction::ISZERO, {X}}}}}},
+ [=]() -> Pattern { return {Instruction::ISZERO, {X}}; },
+ false
+ });
+
+ rules.push_back({
+ {Instruction::ISZERO, {{Instruction::XOR, {X, Y}}}},
+ [=]() -> Pattern { return { Instruction::EQ, {X, Y} }; },
+ false
+ });
+
+ // Associative operations
+ for (auto const& opFun: std::vector<std::pair<Instruction,std::function<u256(u256 const&,u256 const&)>>>{
+ {Instruction::ADD, std::plus<u256>()},
+ {Instruction::MUL, std::multiplies<u256>()},
+ {Instruction::AND, std::bit_and<u256>()},
+ {Instruction::OR, std::bit_or<u256>()},
+ {Instruction::XOR, std::bit_xor<u256>()}
+ })
+ {
+ auto op = opFun.first;
+ auto fun = opFun.second;
+ // Moving constants to the outside, order matters here - we first add rules
+ // for constants and then for non-constants.
+ // xa can be (X, A) or (A, X)
+ for (auto xa: {std::vector<Pattern>{X, A}, std::vector<Pattern>{A, X}})
+ {
+ rules += std::vector<SimplificationRule<Pattern>>{{
+ // (X+A)+B -> X+(A+B)
+ {op, {{op, xa}, B}},
+ [=]() -> Pattern { return {op, {X, fun(A.d(), B.d())}}; },
+ false
+ }, {
+ // (X+A)+Y -> (X+Y)+A
+ {op, {{op, xa}, Y}},
+ [=]() -> Pattern { return {op, {{op, {X, Y}}, A}}; },
+ false
+ }, {
+ // B+(X+A) -> X+(A+B)
+ {op, {B, {op, xa}}},
+ [=]() -> Pattern { return {op, {X, fun(A.d(), B.d())}}; },
+ false
+ }, {
+ // Y+(X+A) -> (Y+X)+A
+ {op, {Y, {op, xa}}},
+ [=]() -> Pattern { return {op, {{op, {Y, X}}, A}}; },
+ false
+ }};
+ }
+ }
+
+ // move constants across subtractions
+ rules += std::vector<SimplificationRule<Pattern>>{
+ {
+ // X - A -> X + (-A)
+ {Instruction::SUB, {X, A}},
+ [=]() -> Pattern { return {Instruction::ADD, {X, 0 - A.d()}}; },
+ false
+ }, {
+ // (X + A) - Y -> (X - Y) + A
+ {Instruction::SUB, {{Instruction::ADD, {X, A}}, Y}},
+ [=]() -> Pattern { return {Instruction::ADD, {{Instruction::SUB, {X, Y}}, A}}; },
+ false
+ }, {
+ // (A + X) - Y -> (X - Y) + A
+ {Instruction::SUB, {{Instruction::ADD, {A, X}}, Y}},
+ [=]() -> Pattern { return {Instruction::ADD, {{Instruction::SUB, {X, Y}}, A}}; },
+ false
+ }, {
+ // X - (Y + A) -> (X - Y) + (-A)
+ {Instruction::SUB, {X, {Instruction::ADD, {Y, A}}}},
+ [=]() -> Pattern { return {Instruction::ADD, {{Instruction::SUB, {X, Y}}, 0 - A.d()}}; },
+ false
+ }, {
+ // X - (A + Y) -> (X - Y) + (-A)
+ {Instruction::SUB, {X, {Instruction::ADD, {A, Y}}}},
+ [=]() -> Pattern { return {Instruction::ADD, {{Instruction::SUB, {X, Y}}, 0 - A.d()}}; },
+ false
+ }
+ };
+ return rules;
+}
+
+}
+}