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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 <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 third element in the tuple is a boolean flag that indicates whether
/// any non-constant elements in the pattern are removed by applying it.
/// The simplifications should neven change the order of evaluation of
/// arbitrary operations, though.
template <class Pattern>
std::vector<std::tuple<Pattern, std::function<Pattern()>, bool>> simplificationRuleList(
Pattern A,
Pattern B,
Pattern C,
Pattern X,
Pattern Y
)
{
std::vector<std::tuple<Pattern, std::function<Pattern()>, bool>> rules;
rules += std::vector<std::tuple<Pattern, std::function<Pattern()>, bool>>{
// 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<std::tuple<Pattern, std::function<Pattern()>, bool>>{{
// (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<std::tuple<Pattern, std::function<Pattern()>, bool>>{
{
// 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;
}
}
}
|
