support recursive formulas (#191)

Author: ckrause

CHANGELOG.md

@@ -5,6 +5,7 @@ To install or update LODA, please follow the [installation instructions](https:/
 ### Enhancements
 
 * Support `mod`, `min` and `max` in formulas
+* Support recursive formulas for a small subset of IE programs
 * Use `floor` instead of `truncate` in PARI if possible
 * Add insecure fall-back option for `curl`
 

src/Makefile

@@ -8,7 +8,7 @@ ifdef LODA_PLATFORM
 CXXFLAGS += -DLODA_PLATFORM=$(LODA_PLATFORM)
 endif
 
-OBJS = api_client.o benchmark.o big_number.o blocks.o boinc.o commands.o config.o distribution.o evaluator.o evaluator_inc.o expression.o expression_util.o extender.o external/jute.o file.o finder.o formula.o generator.o generator_v1.o generator_v2.o generator_v3.o generator_v4.o generator_v5.o generator_v6.o generator_v7.o interpreter.o iterator.o log.o main.o matcher.o memory.o metrics.o miner.o minimizer.o mutator.o number.o oeis_list.o oeis_manager.o oeis_sequence.o optimizer.o pari.o parser.o process.o program.o program_util.o reducer.o semantics.o setup.o sequence.o stats.o test.o util.o web_client.o
+OBJS = api_client.o benchmark.o big_number.o blocks.o boinc.o commands.o config.o distribution.o evaluator.o evaluator_inc.o expression.o expression_util.o extender.o external/jute.o file.o finder.o formula.o formula_gen.o generator.o generator_v1.o generator_v2.o generator_v3.o generator_v4.o generator_v5.o generator_v6.o generator_v7.o interpreter.o iterator.o log.o main.o matcher.o memory.o metrics.o miner.o minimizer.o mutator.o number.o oeis_list.o oeis_manager.o oeis_sequence.o optimizer.o pari.o parser.o process.o program.o program_util.o reducer.o semantics.o setup.o sequence.o stats.o test.o util.o web_client.o
 
 loda: external/jute.h external/jute.cpp $(OBJS)
 	$(CXX) $(LDFLAGS) -o loda $(OBJS)

src/Makefile.windows.mk

@@ -10,7 +10,7 @@ CXXFLAGS = $(CXXFLAGS) /Z7
 CXXFLAGS = $(CXXFLAGS) /DLODA_PLATFORM=$(LODA_PLATFORM)
 !ENDIF
 
-SRCS = api_client.cpp benchmark.cpp big_number.cpp blocks.cpp boinc.cpp commands.cpp config.cpp distribution.cpp evaluator.cpp evaluator_inc.cpp expression.cpp expression_util.cpp extender.cpp external/jute.cpp file.cpp finder.cpp formula.cpp generator.cpp generator_v1.cpp generator_v2.cpp generator_v3.cpp generator_v4.cpp generator_v5.cpp generator_v6.cpp generator_v7.cpp interpreter.cpp iterator.cpp log.cpp main.cpp matcher.cpp memory.cpp metrics.cpp miner.cpp minimizer.cpp mutator.cpp number.cpp oeis_list.cpp oeis_manager.cpp oeis_sequence.cpp optimizer.cpp pari.cpp parser.cpp process.cpp program.cpp program_util.cpp reducer.cpp semantics.cpp sequence.cpp setup.cpp stats.cpp test.cpp util.cpp web_client.cpp
+SRCS = api_client.cpp benchmark.cpp big_number.cpp blocks.cpp boinc.cpp commands.cpp config.cpp distribution.cpp evaluator.cpp evaluator_inc.cpp expression.cpp expression_util.cpp extender.cpp external/jute.cpp file.cpp finder.cpp formula.cpp formula_gen.cpp generator.cpp generator_v1.cpp generator_v2.cpp generator_v3.cpp generator_v4.cpp generator_v5.cpp generator_v6.cpp generator_v7.cpp interpreter.cpp iterator.cpp log.cpp main.cpp matcher.cpp memory.cpp metrics.cpp miner.cpp minimizer.cpp mutator.cpp number.cpp oeis_list.cpp oeis_manager.cpp oeis_sequence.cpp optimizer.cpp pari.cpp parser.cpp process.cpp program.cpp program_util.cpp reducer.cpp semantics.cpp sequence.cpp setup.cpp stats.cpp test.cpp util.cpp web_client.cpp
 
 loda: external/jute.h external/jute.cpp $(SRCS)
 	cl /EHsc /Feloda.exe $(CXXFLAGS) $(SRCS)

src/commands.cpp

@@ -5,6 +5,8 @@
 #include "benchmark.hpp"
 #include "boinc.hpp"
 #include "evaluator.hpp"
+#include "evaluator_inc.hpp"
+#include "formula_gen.hpp"
 #include "iterator.hpp"
 #include "log.hpp"
 #include "miner.hpp"
@@ -192,17 +194,17 @@ void Commands::export_(const std::string& path) {
   Program program = parser.parse(getProgramPathAndSeqId(path).first);
   const auto& format = settings.export_format;
   if (format.empty() || format == "formula") {
-    auto formula = Formula::fromProgram(program, false);
+    auto formula = FormulaGenerator::generate(program, false);
     if (!formula.first) {
       throw std::runtime_error("program cannot be converted to formula");
     }
-    std::cout << Pari::generate(formula.second) << std::endl;
+    std::cout << formula.second.toString(false) << std::endl;
   } else if (format == "pari") {
-    auto formula = Formula::fromProgram(program, true);
+    auto formula = FormulaGenerator::generate(program, true);
     if (!formula.first) {
       throw std::runtime_error("program cannot be converted to pari");
     }
-    std::cout << Pari::generate(formula.second) << std::endl;
+    std::cout << formula.second.toString(true) << std::endl;
   } else if (format == "loda") {
     ProgramUtil::print(program, std::cout);
   } else {
@@ -299,7 +301,9 @@ void Commands::testPari() {
   initLog(false);
   Parser parser;
   Settings settings;
+  Interpreter interpreter(settings);
   Evaluator evaluator(settings);
+  IncrementalEvaluator inceval(interpreter);
   OeisManager manager(settings);
   manager.load();
   auto& stats = manager.getStats();
@@ -310,14 +314,18 @@ void Commands::testPari() {
     }
     auto seq = manager.getSequences().at(id);
     auto program = parser.parse(seq.getProgramPath());
-    auto formula = Formula::fromProgram(program, true);
+    auto formula = FormulaGenerator::generate(program, true);
     if (!formula.first) {
       continue;
     }
-    Log::get().info(seq.id_str() + ": " + formula.second.toString());
+    Log::get().info(seq.id_str() + ": " + formula.second.toString(true));
     Sequence expSeq;
-    evaluator.eval(program, expSeq, seq.existingNumTerms());
-    auto genSeq = Pari::eval(formula.second, 0, seq.existingNumTerms() - 1);
+    size_t numTerms = seq.existingNumTerms();
+    if (inceval.init(program)) {
+      numTerms = std::min<size_t>(numTerms, 10);
+    }
+    evaluator.eval(program, expSeq, numTerms);
+    auto genSeq = Pari::eval(formula.second, 0, numTerms - 1);
     if (genSeq != expSeq) {
       Log::get().info("Generated sequence: " + genSeq.to_string());
       Log::get().info("Expected sequence:  " + expSeq.to_string());

src/expression.cpp

@@ -77,6 +77,7 @@ bool Expression::operator==(const Expression& e) const {
     case Expression::Type::FRACTION:
     case Expression::Type::POWER:
     case Expression::Type::MODULUS:
+    case Expression::Type::IF:
       return equalChildren(e);
   }
   throw std::runtime_error("internal error");  // unreachable
@@ -106,12 +107,13 @@ bool Expression::operator<(const Expression& e) const {
     case Expression::Type::FRACTION:
     case Expression::Type::POWER:
     case Expression::Type::MODULUS:
+    case Expression::Type::IF:
       return lessChildren(e);
   }
   throw std::runtime_error("internal error");  // unreachable
 }
 
-bool Expression::contains(const Expression& e) {
+bool Expression::contains(const Expression& e) const {
   if (*this == e) {
     return true;
   }
@@ -123,6 +125,12 @@ bool Expression::contains(const Expression& e) {
   return false;
 }
 
+void Expression::assertNumChildren(size_t num) const {
+  if (children.size() != num) {
+    throw std::runtime_error("unexpected number of children: " + toString());
+  }
+}
+
 bool Expression::equalChildren(const Expression& e) const {
   if (children.size() != e.children.size()) {
     return false;
@@ -207,6 +215,7 @@ void Expression::print(std::ostream& out, size_t index, bool isRoot,
       break;
     case Expression::Type::NEGATION:
       out << "-";
+      assertNumChildren(1);
       children.front()->print(out, index, false, type);
       break;
     case Expression::Type::FUNCTION:
@@ -232,6 +241,12 @@ void Expression::print(std::ostream& out, size_t index, bool isRoot,
     case Expression::Type::MODULUS:
       printChildren(out, "%", isRoot, parentType);
       break;
+    case Expression::Type::IF:
+      assertNumChildren(3);
+      out << name << "if(n==";
+      printChildren(out, ",", isRoot, parentType);
+      out << ")";
+      break;
   }
   if (brackets) {
     out << ")";
@@ -253,6 +268,9 @@ bool Expression::needsBrackets(size_t index, bool isRoot,
       parentType == Expression::Type::FUNCTION) {
     return false;
   }
+  if (type == Expression::Type::IF || parentType == Expression::Type::IF) {
+    return false;
+  }
   if (type == Expression::Type::NEGATION &&
       (parentType == Expression::Type::SUM ||
        parentType == Expression::Type::DIFFERENCE) &&

src/expression_util.cpp

@@ -178,13 +178,6 @@ bool ExpressionUtil::normalize(Expression& e) {
     normalize(*c);
   }
   switch (e.type) {
-    case Expression::Type::CONSTANT:
-    case Expression::Type::PARAMETER:
-    case Expression::Type::FUNCTION:
-    case Expression::Type::NEGATION:
-    case Expression::Type::POWER:
-    case Expression::Type::MODULUS:
-      break;
     case Expression::Type::SUM:
       if (e.children.size() > 1) {  // at least two elements
         std::sort(e.children.rbegin(), e.children.rend(), compareExprPtr);
@@ -204,6 +197,8 @@ bool ExpressionUtil::normalize(Expression& e) {
         mergeAllChildren(e);
       }
       break;
+    default:
+      break;
   }
   if (pullUpChildren(e)) {
     normalize(e);
@@ -230,6 +225,7 @@ bool ExpressionUtil::canBeNegative(const Expression& e) {
     case Expression::Type::FRACTION:
     case Expression::Type::POWER:
     case Expression::Type::MODULUS:
+    case Expression::Type::IF:
       for (auto c : e.children) {
         if (canBeNegative(*c)) {
           return true;