├── .gitignore ├── LICENSE ├── Makefile ├── README.md ├── sematrope.cc ├── sematrope.hh └── targets └── isPowerOfTwo.hh /.gitignore: -------------------------------------------------------------------------------- 1 | *~ 2 | sematrope 3 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. 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Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /Makefile: -------------------------------------------------------------------------------- 1 | CXX = g++ 2 | CXXFLAGS = -std=c++17 -g -Ofast -march=native -W -Wall 3 | INCLUDES = -I/usr/include/z3 -I. 4 | LIBS = -lz3 5 | PROG = sematrope 6 | 7 | all: $(PROG) 8 | 9 | $(PROG): $(PROG).cc 10 | $(CXX) $(CXXFLAGS) $(INCLUDES) $^ $(LIBS) -o $@ 11 | 12 | clean: 13 | rm -f *.o $(PROG) 14 | 15 | %.o: %.cc 16 | $(CXX) $(CXXFLAGS) -c -o $@ $< 17 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # sematrope 2 | Superoptimizer using the z3 SMT solver 3 | -------------------------------------------------------------------------------- /sematrope.cc: -------------------------------------------------------------------------------- 1 | /* sematrope - superoptimizer using the z3 SMT solver 2 | Copyright (C) 2018 Falk Hüffner 3 | 4 | This program is free software: you can redistribute it and/or modify 5 | it under the terms of the GNU General Public License as published by 6 | the Free Software Foundation, either version 3 of the License, or 7 | (at your option) any later version. 8 | 9 | This program is distributed in the hope that it will be useful, 10 | but WITHOUT ANY WARRANTY; without even the implied warranty of 11 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 12 | GNU General Public License for more details. 13 | 14 | You should have received a copy of the GNU General Public License 15 | along with this program. If not, see . */ 16 | 17 | #include "targets/isPowerOfTwo.hh" 18 | 19 | #include "sematrope.hh" 20 | 21 | #include 22 | #include 23 | #include 24 | 25 | #include 26 | 27 | #include 28 | 29 | std::vector& getTargets() { 30 | static std::vector targets; 31 | return targets; 32 | } 33 | 34 | void registerTarget(const Target& target) { 35 | getTargets().push_back(target); 36 | } 37 | 38 | z3::context context; 39 | int registerWidth; 40 | int shiftMask; 41 | 42 | // Return a constant with the same context and width as variable x. 43 | z3::expr bvConst(uint64_t x) { 44 | return context.bv_val(x, registerWidth); 45 | } 46 | 47 | z3::expr boolToBv(const z3::expr& b) { 48 | return z3::ite(b, bvConst(1), bvConst(0)); 49 | } 50 | 51 | struct Op { 52 | std::string name; 53 | std::function eval; 54 | }; 55 | 56 | using Opcode = int; 57 | 58 | std::vector ops = { 59 | {"not", [](const z3::expr& a, const z3::expr&){ return ~a; }}, 60 | {"neg", [](const z3::expr& a, const z3::expr&){ return -a; }}, 61 | {"add", [](const z3::expr& a, const z3::expr& b){ return a + b; }}, 62 | {"sub", [](const z3::expr& a, const z3::expr& b){ return a - b; }}, 63 | {"mul", [](const z3::expr& a, const z3::expr& b){ return a * b; }}, 64 | {"div", [](const z3::expr& a, const z3::expr& b){ return a * b; }}, 65 | {"and", [](const z3::expr& a, const z3::expr& b){ return a & b; }}, 66 | {"or", [](const z3::expr& a, const z3::expr& b){ return a | b; }}, 67 | {"xor", [](const z3::expr& a, const z3::expr& b){ return a ^ b; }}, 68 | {"shl", [](const z3::expr& a, const z3::expr& b){ return z3::shl(a, b & shiftMask); }}, 69 | {"shr", [](const z3::expr& a, const z3::expr& b){ return z3::lshr(a, b & shiftMask); }}, 70 | {"ashr", [](const z3::expr& a, const z3::expr& b){ return z3::ashr(a, b & shiftMask); }}, 71 | {"cmpeq", [](const z3::expr& a, const z3::expr& b){ return boolToBv(a == b); }}, 72 | {"cmpne", [](const z3::expr& a, const z3::expr& b){ return boolToBv(a != b); }}, 73 | {"cmplt", [](const z3::expr& a, const z3::expr& b){ return boolToBv(a < b); }}, 74 | {"cmpgt", [](const z3::expr& a, const z3::expr& b){ return boolToBv(a > b); }}, 75 | {"cmple", [](const z3::expr& a, const z3::expr& b){ return boolToBv(a <= b); }}, 76 | {"cmpge", [](const z3::expr& a, const z3::expr& b){ return boolToBv(a >= b); }}, 77 | {"cmpult", [](const z3::expr& a, const z3::expr& b){ return boolToBv(z3::ult(a, b)); }}, 78 | {"cmpugt", [](const z3::expr& a, const z3::expr& b){ return boolToBv(z3::ugt(a, b)); }}, 79 | {"cmpule", [](const z3::expr& a, const z3::expr& b){ return boolToBv(z3::ule(a, b)); }}, 80 | {"cmpuge", [](const z3::expr& a, const z3::expr& b){ return boolToBv(z3::uge(a, b)); }}, 81 | }; 82 | 83 | template 84 | std::string hex(T x) { 85 | std::stringstream stream; 86 | stream << std::hex << uint64_t(x); 87 | return stream.str(); 88 | } 89 | 90 | struct Insn { 91 | Opcode opcode; 92 | int r1, r2; 93 | bool isImm; 94 | uint64_t imm; 95 | 96 | std::string toString(int dest) const { 97 | std::string s = ops[opcode].name; 98 | s += " r" + std::to_string(r1) + ", "; 99 | if (isImm) 100 | s += "0x" + hex(imm); 101 | else 102 | s += "r" + std::to_string(r2); 103 | s += ", r" + std::to_string(dest); 104 | return s; 105 | } 106 | }; 107 | 108 | // The z3 variables that define an instruction. 109 | struct SymbolicInsn { 110 | SymbolicInsn(z3::context& c, const std::string& prefix) 111 | : opcode(c.int_const((prefix + "_op").c_str())), 112 | r1(c.int_const((prefix + "_r1").c_str())), 113 | r2(c.int_const((prefix + "_r2").c_str())), 114 | imm(c.bv_const((prefix + "_imm").c_str(), registerWidth)) {} 115 | z3::expr opcode; 116 | // r1 is the number of a register; r2 is the number of a register 117 | // or implies use of the immediate if the number is out of the 118 | // valid range. 119 | z3::expr r1, r2; 120 | z3::expr imm; 121 | // We use a SSA representation where the output register is always 122 | // implicitly a new register, thus it doesn't need to be specified 123 | // here. 124 | }; 125 | 126 | // Returns an expression representing the result of running the 127 | // program in insns on the input value x. 128 | z3::expr eval(const std::vector& input, const std::vector& insns) { 129 | std::vector regs; 130 | for (const auto& x : input) 131 | regs.push_back(x); 132 | for (std::size_t i = 0; i < insns.size(); ++i) { 133 | z3::expr in1 = regs[0]; 134 | for (int j = 1; j < static_cast(regs.size()); ++j) 135 | in1 = z3::ite(insns[i].r1 == j, regs[j], in1); 136 | z3::expr in2 = insns[i].imm; 137 | for (int j = 0; j < static_cast(regs.size()); ++j) 138 | in2 = z3::ite(insns[i].r2 == j, regs[j], in2); 139 | 140 | z3::expr result = ops[0].eval(in1, in2); 141 | for (int opcode = 1; opcode < static_cast(ops.size()); ++opcode) 142 | result = z3::ite(insns[i].opcode == opcode, ops[opcode].eval(in1, in2), result); 143 | regs.push_back(result); 144 | } 145 | return regs.back(); 146 | } 147 | 148 | std::pair< 149 | std::vector, 150 | std::vector 151 | > 152 | makeInsns(int numInsns, z3::context& c) { 153 | std::vector insns; 154 | std::vector constraints; 155 | for (int i = 0; i < numInsns; ++i) { 156 | insns.push_back(SymbolicInsn(c, std::string("op") + std::to_string(i))); 157 | constraints.push_back(z3::ult(insns.back().imm, bvConst(0xff))); 158 | } 159 | return {insns, constraints}; 160 | } 161 | 162 | int getIntDefault(z3::expr e, int d = 0) { 163 | return e.is_numeral() ? e.get_numeral_int() : d; 164 | } 165 | uint64_t getUint64Default(z3::expr e, uint64_t d = 0) { 166 | return e.is_numeral() ? e.get_numeral_uint64() : d; 167 | } 168 | 169 | std::vector reconstructProgram(const std::vector& insns, 170 | const z3::model& model, 171 | const int numInputRegisters) { 172 | std::vector result; 173 | for (int i = 0; i < static_cast(insns.size()); ++i) { 174 | Insn insn; 175 | int opcode = getIntDefault(model.eval(insns[i].opcode), 0); 176 | insn.opcode = (opcode < 0 || opcode >= static_cast(ops.size())) ? 0 : opcode; 177 | int r1 = getIntDefault(model.eval(insns[i].r1), 0); 178 | insn.r1 = (r1 < 0 || r1 >= numInputRegisters + i) ? 0 : r1; 179 | int r2 = getIntDefault(model.eval(insns[i].r2), 0); 180 | const bool outOfRange = r2 < 0 || r2 >= numInputRegisters + i; 181 | if (outOfRange) { 182 | insn.isImm = true; 183 | insn.r2 = 0; 184 | insn.imm = getUint64Default(model.eval(insns[i].imm), 0); 185 | } else { 186 | insn.isImm = false; 187 | insn.r2 = r2; 188 | insn.imm = 0; 189 | } 190 | result.push_back(insn); 191 | } 192 | return result; 193 | } 194 | 195 | int main() { 196 | const auto targetName = "isPowerOfTwoNonzero"; 197 | Target target; 198 | for (const auto& t : getTargets()) { 199 | if (t.name == targetName) { 200 | target = t; 201 | break; 202 | } 203 | } 204 | assert(!target.name.empty()); 205 | registerWidth = target.registerWidth; 206 | assert((registerWidth & (registerWidth - 1)) == 0); 207 | shiftMask = registerWidth - 1; 208 | 209 | std::cerr << "=== Finding optimal program for " << target.name << " ===\n"; 210 | try { 211 | std::vector> testCases; 212 | for (int numInsns = 1; ; ++numInsns) { 213 | std::cerr << "\n=== Trying with " << numInsns << " instructions ===\n\n"; 214 | while (true) { 215 | std::cerr << "Finding program with " << numInsns 216 | << " instructions that is correct for all " << testCases.size() << " test cases...\n"; 217 | auto solver = z3::solver(context); 218 | const auto [insns, constraints] = makeInsns(numInsns, context); 219 | for (const auto& constraint : constraints) 220 | solver.add(constraint); 221 | for (const auto t : testCases) { 222 | std::vector inputs; 223 | for (auto x : t) 224 | inputs.push_back(bvConst(x)); 225 | const uint64_t correctResult = target.target(inputs).simplify().get_numeral_uint64(); 226 | const auto programResult = eval(inputs, insns); 227 | solver.add(programResult == bvConst(correctResult)); 228 | } 229 | const auto result = solver.check(); 230 | if (result != z3::sat) { 231 | if (result != z3::unsat) 232 | throw z3::exception("unexpected check value"); 233 | std::cerr << "Not possible to find program that is correct for all " << testCases.size() << " test cases.\n"; 234 | break; 235 | } 236 | 237 | std::cerr << "Found program:\n"; 238 | const auto& model = solver.get_model(); 239 | std::vector inputs; 240 | for (int i = 0; i < target.arity; ++i) 241 | inputs.push_back(context.bv_const(("x" + std::to_string(i)).c_str(), target.registerWidth)); 242 | const auto solutionProgram = model.eval(eval(inputs, insns)); 243 | const auto program = reconstructProgram(insns, model, target.arity); 244 | for (std::size_t i = 0; i < program.size(); ++i) 245 | std::cerr << program[i].toString(i + target.arity) << std::endl; 246 | 247 | std::cerr << "\nFinding counterexample...\n"; 248 | auto cesolver = z3::solver(context); 249 | cesolver.add(target.isValidInput(inputs) && solutionProgram != target.target(inputs)); 250 | const auto ceResult = cesolver.check(); 251 | if (ceResult != z3::sat) { 252 | if (ceResult != z3::unsat) 253 | throw z3::exception("unexpected check value"); 254 | std::cerr << "No counterexample found. Correct program is:\n"; 255 | for (std::size_t i = 0; i < program.size(); ++i) 256 | std::cout << program[i].toString(i + target.arity) << std::endl; 257 | return 0; 258 | } 259 | const auto& cemodel = cesolver.get_model(); 260 | std::vector t; 261 | for (int i = 0; i < static_cast(inputs.size()); ++i) { 262 | const auto& v = cemodel.eval(inputs[i]); 263 | t.push_back(v.is_numeral() ? v.get_numeral_uint64() : 0); 264 | } 265 | std::vector z3t; 266 | for (auto x : t) 267 | z3t.push_back(bvConst(x)); 268 | 269 | std::cerr << "Found counterexample: [ "; 270 | for (auto x : t) 271 | std::cerr << x << ' '; 272 | std::cerr << "] evals to " << cemodel.eval(solutionProgram).get_numeral_uint64() 273 | << " but should be " << target.target(z3t).simplify().get_numeral_uint64() 274 | << std::endl; 275 | testCases.push_back(t); 276 | } 277 | } 278 | } catch (const z3::exception& e) { 279 | std::cerr << e.msg() << std::endl; 280 | return 1; 281 | } 282 | } 283 | -------------------------------------------------------------------------------- /sematrope.hh: -------------------------------------------------------------------------------- 1 | /* sematrope - superoptimizer using the z3 SMT solver 2 | Copyright (C) 2018 Falk Hüffner 3 | 4 | This program is free software: you can redistribute it and/or modify 5 | it under the terms of the GNU General Public License as published by 6 | the Free Software Foundation, either version 3 of the License, or 7 | (at your option) any later version. 8 | 9 | This program is distributed in the hope that it will be useful, 10 | but WITHOUT ANY WARRANTY; without even the implied warranty of 11 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 12 | GNU General Public License for more details. 13 | 14 | You should have received a copy of the GNU General Public License 15 | along with this program. If not, see . */ 16 | 17 | #ifndef SEMATROPE_SEMATROPE_HH 18 | #define SEMATROPE_SEMATROPE_HH 19 | 20 | #include 21 | #include 22 | 23 | #include 24 | 25 | struct Target { 26 | std::string name; 27 | int registerWidth = 0; 28 | int arity = 1; 29 | std::function&)> target; 30 | std::function&)> isValidInput; 31 | }; 32 | 33 | extern z3::context context; 34 | extern int registerWidth; 35 | extern int shiftMask; 36 | 37 | z3::expr bvConst(uint64_t x); 38 | void registerTarget(const Target& target); 39 | z3::expr boolToBv(const z3::expr& b); 40 | 41 | #endif // SEMATROPE_SEMATROPE_HH 42 | -------------------------------------------------------------------------------- /targets/isPowerOfTwo.hh: -------------------------------------------------------------------------------- 1 | /* sematrope - superoptimizer using the z3 SMT solver 2 | Copyright (C) 2019 Falk Hüffner 3 | 4 | This program is free software: you can redistribute it and/or modify 5 | it under the terms of the GNU General Public License as published by 6 | the Free Software Foundation, either version 3 of the License, or 7 | (at your option) any later version. 8 | 9 | This program is distributed in the hope that it will be useful, 10 | but WITHOUT ANY WARRANTY; without even the implied warranty of 11 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 12 | GNU General Public License for more details. 13 | 14 | You should have received a copy of the GNU General Public License 15 | along with this program. If not, see . */ 16 | 17 | #ifndef SEMATROPE_ISPOWEROFTWO_HH 18 | #define SEMATROPE_ISPOWEROFTWO_HH 19 | 20 | #include "sematrope.hh" 21 | 22 | // Test whether a nonzero number is a power of two. 23 | __attribute__((constructor)) void registerIsPowerOfTwoNonzero() { 24 | constexpr auto REGISTER_WIDTH = 8; 25 | 26 | Target target = { 27 | .name = "isPowerOfTwoNonzero", 28 | .registerWidth = REGISTER_WIDTH, 29 | .arity = 1, 30 | .target = [](const std::vector& xs) { 31 | assert(xs.size() == 1); 32 | const auto& x = xs[0]; 33 | auto r = context.bool_val(false); 34 | uint64_t p = 1; 35 | for (int i = 0; i < REGISTER_WIDTH; ++i) { 36 | r = r || (x == bvConst(p)); 37 | p <<= 1; 38 | } 39 | return boolToBv(r); 40 | }, 41 | .isValidInput = [](const std::vector& xs) { 42 | assert(xs.size() == 1); 43 | const auto& x = xs[0]; 44 | return x != 0; 45 | }, 46 | }; 47 | 48 | registerTarget(target); 49 | } 50 | 51 | #endif // SEMATROPE_ISPOWEROFTWO_HH 52 | --------------------------------------------------------------------------------