/* 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 . */ /** * @date 2018 * Templatized list of simplification rules. */ #pragma once #include #include #include #include #include #include namespace dev { namespace eth { template S divWorkaround(S const& _a, S const& _b) { return (S)(bigint(_a) / bigint(_b)); } template S modWorkaround(S const& _a, S const& _b) { return (S)(bigint(_a) % bigint(_b)); } // This works around a bug fixed with Boost 1.64. // https://www.boost.org/doc/libs/1_68_0/libs/multiprecision/doc/html/boost_multiprecision/map/hist.html#boost_multiprecision.map.hist.multiprecision_2_3_1_boost_1_64 inline u256 shlWorkaround(u256 const& _x, unsigned _amount) { return u256((bigint(_x) << _amount) & u256(-1)); } // simplificationRuleList below was split up into parts to prevent // stack overflows in the JavaScript optimizer for emscripten builds // that affected certain browser versions. template std::vector> simplificationRuleListPart1( Pattern A, Pattern B, Pattern C, Pattern, Pattern ) { return std::vector> { // arithmetic 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 boost::multiprecision::bit_test(B.d(), testBit) ? B.d() | ~mask : B.d() & mask; }, false}, {{Instruction::SHL, {A, B}}, [=]{ if (A.d() > 255) return u256(0); return shlWorkaround(B.d(), unsigned(A.d())); }, false}, {{Instruction::SHR, {A, B}}, [=]{ if (A.d() > 255) return u256(0); return B.d() >> unsigned(A.d()); }, false} }; } template std::vector> simplificationRuleListPart2( Pattern, Pattern, Pattern, Pattern X, Pattern Y ) { return std::vector> { // 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 }, {{Instruction::SHL, {0, X}}, [=]{ return X; }, false}, {{Instruction::SHR, {0, X}}, [=]{ return X; }, false}, {{Instruction::SHL, {X, 0}}, [=]{ return u256(0); }, true}, {{Instruction::SHR, {X, 0}}, [=]{ return u256(0); }, true}, {{Instruction::GT, {X, 0}}, [=]() -> Pattern { return {Instruction::ISZERO, {{Instruction::ISZERO, {X}}}}; }, false}, {{Instruction::LT, {0, X}}, [=]() -> Pattern { return {Instruction::ISZERO, {{Instruction::ISZERO, {X}}}}; }, false}, {{Instruction::GT, {X, ~u256(0)}}, [=]{ return u256(0); }, true}, {{Instruction::LT, {~u256(0), X}}, [=]{ return u256(0); }, true}, {{Instruction::GT, {0, X}}, [=]{ return u256(0); }, true}, {{Instruction::LT, {X, 0}}, [=]{ return u256(0); }, true}, {{Instruction::AND, {{Instruction::BYTE, {X, Y}}, {u256(0xff)}}}, [=]() -> Pattern { return {Instruction::BYTE, {X, Y}}; }, false}, {{Instruction::BYTE, {31, X}}, [=]() -> Pattern { return {Instruction::AND, {X, u256(0xff)}}; }, false} }; } template std::vector> simplificationRuleListPart3( Pattern, Pattern, Pattern, Pattern X, Pattern ) { return std::vector> { // 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} }; } template std::vector> simplificationRuleListPart4( Pattern, Pattern, Pattern, Pattern X, Pattern Y ) { return std::vector> { // 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}, }; } template std::vector> simplificationRuleListPart5( Pattern A, Pattern, Pattern, Pattern X, Pattern ) { std::vector> rules; // Replace MOD X, with AND X, - 1 for (size_t i = 0; i < 256; ++i) { u256 value = u256(1) << i; rules.push_back({ {Instruction::MOD, {X, value}}, [=]() -> Pattern { return {Instruction::AND, {X, value - 1}}; }, false }); } // Replace SHL >=256, X with 0 rules.push_back({ {Instruction::SHL, {A, X}}, [=]() -> Pattern { return u256(0); }, true, [=]() { return A.d() >= 256; } }); // Replace SHR >=256, X with 0 rules.push_back({ {Instruction::SHR, {A, X}}, [=]() -> Pattern { return u256(0); }, true, [=]() { return A.d() >= 256; } }); for (auto const& op: std::vector{ Instruction::ADDRESS, Instruction::CALLER, Instruction::ORIGIN, Instruction::COINBASE, Instruction::CREATE, Instruction::CREATE2 }) { u256 const mask = (u256(1) << 160) - 1; rules.push_back({ {Instruction::AND, {{op, mask}}}, [=]() -> Pattern { return op; }, false }); rules.push_back({ {Instruction::AND, {{mask, op}}}, [=]() -> Pattern { return op; }, false }); } return rules; } template std::vector> simplificationRuleListPart6( Pattern, Pattern, Pattern, Pattern X, Pattern Y ) { std::vector> rules; // Double negation of opcodes with boolean result for (auto const& op: std::vector{ 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 }); return rules; } template std::vector> simplificationRuleListPart7( Pattern A, Pattern B, Pattern, Pattern X, Pattern Y ) { std::vector> rules; // Associative operations for (auto const& opFun: std::vector>>{ {Instruction::ADD, std::plus()}, {Instruction::MUL, std::multiplies()}, {Instruction::AND, std::bit_and()}, {Instruction::OR, std::bit_or()}, {Instruction::XOR, std::bit_xor()} }) { 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{X, A}, std::vector{A, X}}) { rules += std::vector>{{ // (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 }}; } } // Combine two SHL by constant rules.push_back({ // SHL(B, SHL(A, X)) -> SHL(min(A+B, 256), X) {Instruction::SHL, {{B}, {Instruction::SHL, {{A}, {X}}}}}, [=]() -> Pattern { bigint sum = bigint(A.d()) + B.d(); if (sum >= 256) return {Instruction::AND, {X, u256(0)}}; else return {Instruction::SHL, {u256(sum), X}}; }, false }); // Combine two SHR by constant rules.push_back({ // SHR(B, SHR(A, X)) -> SHR(min(A+B, 256), X) {Instruction::SHR, {{B}, {Instruction::SHR, {{A}, {X}}}}}, [=]() -> Pattern { bigint sum = bigint(A.d()) + B.d(); if (sum >= 256) return {Instruction::AND, {X, u256(0)}}; else return {Instruction::SHR, {u256(sum), X}}; }, false }); // Combine SHL-SHR by constant rules.push_back({ // SHR(B, SHL(A, X)) -> AND(SH[L/R]([B - A / A - B], X), Mask) {Instruction::SHR, {{B}, {Instruction::SHL, {{A}, {X}}}}}, [=]() -> Pattern { u256 mask = shlWorkaround(u256(-1), unsigned(A.d())) >> unsigned(B.d()); if (A.d() > B.d()) return {Instruction::AND, {{Instruction::SHL, {A.d() - B.d(), X}}, mask}}; else if (B.d() > A.d()) return {Instruction::AND, {{Instruction::SHR, {B.d() - A.d(), X}}, mask}}; else return {Instruction::AND, {X, mask}}; }, false, [=] { return A.d() < 256 && B.d() < 256; } }); // Combine SHR-SHL by constant rules.push_back({ // SHL(B, SHR(A, X)) -> AND(SH[L/R]([B - A / A - B], X), Mask) {Instruction::SHL, {{B}, {Instruction::SHR, {{A}, {X}}}}}, [=]() -> Pattern { u256 mask = shlWorkaround(u256(-1) >> unsigned(A.d()), unsigned(B.d())); if (A.d() > B.d()) return {Instruction::AND, {{Instruction::SHR, {A.d() - B.d(), X}}, mask}}; else if (B.d() > A.d()) return {Instruction::AND, {{Instruction::SHL, {B.d() - A.d(), X}}, mask}}; else return {Instruction::AND, {X, mask}}; }, false, [=] { return A.d() < 256 && B.d() < 256; } }); // Move AND with constant across SHL and SHR by constant for (auto shiftOp: {Instruction::SHL, Instruction::SHR}) { auto replacement = [=]() -> Pattern { u256 mask = shiftOp == Instruction::SHL ? shlWorkaround(A.d(), unsigned(B.d())) : A.d() >> unsigned(B.d()); return {Instruction::AND, {{shiftOp, {B.d(), X}}, std::move(mask)}}; }; rules.push_back({ // SH[L/R](B, AND(X, A)) -> AND(SH[L/R](B, X), [ A << B / A >> B ]) {shiftOp, {{B}, {Instruction::AND, {{X}, {A}}}}}, replacement, false, [=] { return B.d() < 256; } }); rules.push_back({ // SH[L/R](B, AND(A, X)) -> AND(SH[L/R](B, X), [ A << B / A >> B ]) {shiftOp, {{B}, {Instruction::AND, {{A}, {X}}}}}, replacement, false, [=] { return B.d() < 256; } }); } rules.push_back({ // MUL(X, SHL(Y, 1)) -> SHL(Y, X) {Instruction::MUL, {X, {Instruction::SHL, {Y, u256(1)}}}}, [=]() -> Pattern { return {Instruction::SHL, {Y, X}}; }, false }); rules.push_back({ // MUL(SHL(X, 1), Y) -> SHL(X, Y) {Instruction::MUL, {{Instruction::SHL, {X, u256(1)}}, Y}}, [=]() -> Pattern { return {Instruction::SHL, {X, Y}}; }, false }); rules.push_back({ // DIV(X, SHL(Y, 1)) -> SHR(Y, X) {Instruction::DIV, {X, {Instruction::SHL, {Y, u256(1)}}}}, [=]() -> Pattern { return {Instruction::SHR, {Y, X}}; }, false }); std::function feasibilityFunction = [=]() { if (B.d() > 256) return false; unsigned bAsUint = static_cast(B.d()); return (A.d() & (u256(-1) >> bAsUint)) == (u256(-1) >> bAsUint); }; rules.push_back({ // AND(A, SHR(B, X)) -> A & ((2^256-1) >> B) == ((2^256-1) >> B) {Instruction::AND, {A, {Instruction::SHR, {B, X}}}}, [=]() -> Pattern { return {Instruction::SHR, {B, X}}; }, false, feasibilityFunction }); rules.push_back({ // AND(SHR(B, X), A) -> ((2^256-1) >> B) & A == ((2^256-1) >> B) {Instruction::AND, {{Instruction::SHR, {B, X}}, A}}, [=]() -> Pattern { return {Instruction::SHR, {B, X}}; }, false, feasibilityFunction }); return rules; } template std::vector> simplificationRuleListPart8( Pattern A, Pattern, Pattern, Pattern X, Pattern Y ) { std::vector> rules; // move constants across subtractions rules += std::vector>{ { // 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; } /// @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 never change the order of evaluation of /// arbitrary operations. template std::vector> simplificationRuleList( Pattern A, Pattern B, Pattern C, Pattern X, Pattern Y ) { std::vector> rules; rules += simplificationRuleListPart1(A, B, C, X, Y); rules += simplificationRuleListPart2(A, B, C, X, Y); rules += simplificationRuleListPart3(A, B, C, X, Y); rules += simplificationRuleListPart4(A, B, C, X, Y); rules += simplificationRuleListPart5(A, B, C, X, Y); rules += simplificationRuleListPart6(A, B, C, X, Y); rules += simplificationRuleListPart7(A, B, C, X, Y); rules += simplificationRuleListPart8(A, B, C, X, Y); return rules; } } }