Implement logarithms simplify

fintarin · Jul 31, 2023 · abbc6cf · abbc6cf
1 parent 514dcb8
commit abbc6cf
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Showing 7 changed files with 175 additions and 49 deletions.
diff --git a/include/fintamath/functions/logarithms/Log.hpp b/include/fintamath/functions/logarithms/Log.hpp
@@ -2,6 +2,9 @@
 
 #include "fintamath/functions/IFunction.hpp"
 #include "fintamath/numbers/INumber.hpp"
+#include "fintamath/numbers/Integer.hpp"
+#include "fintamath/numbers/Rational.hpp"
+#include "fintamath/numbers/Real.hpp"
 
 namespace fintamath {
 
@@ -19,6 +22,14 @@ class Log : public IFunctionCRTP<INumber, Log, INumber, INumber> {
 
 protected:
   std::unique_ptr<IMathObject> call(const ArgumentsRefVector &argsVect) const override;
+
+  static std::unique_ptr<IMathObject> multiLogSimpl(const INumber &lhs, const INumber &rhs);
+
+  static std::unique_ptr<IMathObject> logSimpl(const Integer &lhs, const Integer &rhs);
+
+  static std::unique_ptr<IMathObject> logSimpl(const Rational &lhs, const Rational &rhs);
+
+  static std::unique_ptr<IMathObject> logSimpl(const Real &lhs, const Real &rhs);
 };
 
 }
diff --git a/src/fintamath/expressions/binary/LogExpression.cpp b/src/fintamath/expressions/binary/LogExpression.cpp
@@ -50,7 +50,6 @@ ArgumentPtr LogExpression::preciseSimplify() const {
 
 LogExpression::SimplifyFunctionsVector LogExpression::getFunctionsForPreSimplify() const {
   static const LogExpression::SimplifyFunctionsVector simplifyFunctions = {
-      &LogExpression::numSimplify,   //
       &LogExpression::equalSimplify, //
       &LogExpression::powSimplify,   //
   };
@@ -59,34 +58,22 @@ LogExpression::SimplifyFunctionsVector LogExpression::getFunctionsForPreSimplify
 
 LogExpression::SimplifyFunctionsVector LogExpression::getFunctionsForPostSimplify() const {
   static const LogExpression::SimplifyFunctionsVector simplifyFunctions = {
+      &LogExpression::constSimplify, //
       &LogExpression::powSimplify,   //
-      &LogExpression::numSimplify,   //
       &LogExpression::equalSimplify, //
   };
   return simplifyFunctions;
 }
 
-ArgumentPtr LogExpression::numSimplify(const IFunction & /*func*/, const ArgumentPtr &lhs, const ArgumentPtr &rhs) {
-  if (*lhs == Integer(1)) {
-    throw UndefinedFunctionException(Log().toString(), {lhs->toString(), rhs->toString()});
+ArgumentPtr LogExpression::constSimplify(const IFunction & /*func*/, const ArgumentPtr &lhs, const ArgumentPtr &rhs) {
+  if (*rhs == Integer(1)) {
+    return Integer(0).clone();
   }
 
   if (*lhs == E()) {
     return callFunction(Ln(), {rhs});
   }
 
-  if (Log().doArgsMatch({*lhs, *rhs})) {
-    if (*lhs == Integer(2)) {
-      return callFunction(Lb(), {rhs});
-    }
-
-    if (*lhs == Integer(10)) {
-      return callFunction(Lg(), {rhs});
-    }
-
-    return callFunction(Log(), {lhs, rhs});
-  }
-
   return {};
 }
 

diff --git a/src/fintamath/expressions/binary/LogExpression.hpp b/src/fintamath/expressions/binary/LogExpression.hpp
@@ -24,7 +24,7 @@ class LogExpression : public IBinaryExpressionCRTP<LogExpression> {
   SimplifyFunctionsVector getFunctionsForPostSimplify() const override;
 
 private:
-  static ArgumentPtr numSimplify(const IFunction &func, const ArgumentPtr &lhs, const ArgumentPtr &rhs);
+  static ArgumentPtr constSimplify(const IFunction &func, const ArgumentPtr &lhs, const ArgumentPtr &rhs);
 
   static ArgumentPtr equalSimplify(const IFunction &func, const ArgumentPtr &lhs, const ArgumentPtr &rhs);
 

diff --git a/src/fintamath/functions/logarithms/Log.cpp b/src/fintamath/functions/logarithms/Log.cpp
@@ -1,11 +1,132 @@
 #include "fintamath/functions/logarithms/Log.hpp"
 
+#include "fintamath/exceptions/UndefinedException.hpp"
+#include "fintamath/functions/arithmetic/Neg.hpp"
+#include "fintamath/literals/constants/ComplexInf.hpp"
+#include "fintamath/literals/constants/Inf.hpp"
+#include "fintamath/literals/constants/NegInf.hpp"
+#include "fintamath/literals/constants/Undefined.hpp"
 #include "fintamath/numbers/RealFunctions.hpp"
 
 namespace fintamath {
 
 std::unique_ptr<IMathObject> Log::call(const ArgumentsRefVector &argsVect) const {
-  return log(convert<Real>(argsVect.front().get()), convert<Real>(argsVect.back().get())).toMinimalObject();
+  const auto &lhs = cast<INumber>(argsVect.front().get());
+  const auto &rhs = cast<INumber>(argsVect.back().get());
+
+  if (lhs == Integer(1)) {
+    if (rhs == Integer(1)) {
+      return Undefined().clone();
+    }
+
+    return ComplexInf().clone();
+  }
+
+  if (lhs < Integer(0) || rhs < Integer(0)) {
+    // TODO: cast to Complex, when it is implemented
+    throw UndefinedFunctionException(toString(), {lhs.toString(), rhs.toString()});
+  }
+
+  if (lhs == Integer(0)) {
+    if (rhs == Integer(0)) {
+      return Undefined().clone();
+    }
+
+    return Integer(0).clone();
+  }
+
+  if (rhs == Integer(0)) {
+    if (lhs > Integer(1)) {
+      return NegInf().clone();
+    }
+
+    return Inf().clone();
+  }
+
+  if (rhs == Integer(1)) {
+    return Integer(0).clone();
+  }
+
+  if (lhs == rhs) {
+    return Integer(1).clone();
+  }
+
+  if (lhs < Integer(1)) {
+    auto newLhs = Rational(1) / lhs;
+
+    if (rhs < Integer(1)) {
+      auto newRhs = Rational(1) / rhs;
+      return multiLogSimpl(*newLhs, *newRhs);
+    }
+
+    return Neg()(*multiLogSimpl(*newLhs, rhs));
+  }
+
+  if (rhs < Integer(1)) {
+    auto newRhs = Rational(1) / rhs;
+    return Neg()(*multiLogSimpl(lhs, *newRhs));
+  }
+
+  return multiLogSimpl(lhs, rhs);
+}
+
+std::unique_ptr<IMathObject> Log::multiLogSimpl(const INumber &lhs, const INumber &rhs) {
+  static const auto multiLog = [] {
+    static MultiMethod<std::unique_ptr<IMathObject>(const INumber &, const INumber &)> outMultiPow;
+
+    outMultiPow.add<Integer, Integer>([](const Integer &inLhs, const Integer &inRhs) {
+      return logSimpl(inLhs, inRhs);
+    });
+
+    outMultiPow.add<Rational, Rational>([](const Rational &inLhs, const Rational &inRhs) {
+      return logSimpl(inLhs, inRhs);
+    });
+
+    outMultiPow.add<Real, Real>([](const Real &inLhs, const Real &inRhs) {
+      return logSimpl(inLhs, inRhs);
+    });
+
+    return outMultiPow;
+  }();
+
+  if (auto rhsConv = cast<INumber>(convert(lhs, rhs))) {
+    return multiLog(lhs, *rhsConv);
+  }
+
+  auto lhsConv = cast<INumber>(convert(rhs, lhs));
+  return multiLog(*lhsConv, rhs);
+}
+
+std::unique_ptr<IMathObject> Log::logSimpl(const Integer &lhs, const Integer &rhs) {
+  return logSimpl(Rational(lhs), Rational(rhs));
+}
+
+std::unique_ptr<IMathObject> Log::logSimpl(const Rational &lhs, const Rational &rhs) {
+  const bool isResInverted = lhs > rhs;
+  const Rational divider = isResInverted ? rhs : lhs;
+  Rational remainder = isResInverted ? lhs : rhs;
+  Rational res = 0;
+
+  while (remainder > divider) {
+    res += 1;
+    remainder /= divider;
+  }
+
+  if (remainder == divider) {
+    res += 1;
+
+    if (isResInverted) {
+      return (Rational(1) / res).toMinimalObject();
+    }
+
+    return res.toMinimalObject();
+  }
+
+  return logSimpl(Real(lhs), Real(rhs));
+}
+
+std::unique_ptr<IMathObject> Log::logSimpl(const Real &lhs, const Real &rhs) {
+  return log(lhs, rhs).toMinimalObject();
 }
 
 }
diff --git a/tests/src/expressions/ExpressionFunctionsTests.cpp b/tests/src/expressions/ExpressionFunctionsTests.cpp
@@ -123,7 +123,7 @@ TEST(ExpressionFunctionsTests, expTest) {
 }
 
 TEST(ExpressionFunctionsTests, logTest) {
-  EXPECT_EQ(log(Expression("a+b"), Expression("1")).toString(), "log(a + b, 1)");
+  EXPECT_EQ(log(Expression("a+b"), Expression("1")).toString(), "0");
   EXPECT_EQ(log(Expression("2*a"), Expression("a+b")).toString(), "log(2 a, a + b)");
   EXPECT_EQ(log(Expression("a"), Expression("a^5")).toString(), "5");
 }
@@ -134,8 +134,8 @@ TEST(ExpressionFunctionsTests, lnTest) {
 }
 
 TEST(ExpressionFunctionsTests, lbTest) {
-  EXPECT_EQ(lb(Expression("1024*a")).toString(), "log(2, 1024 a)"); // TODO logarithms
-  EXPECT_EQ(lb(Expression("2+a")).toString(), "log(2, a + 2)");     // TODO logarithms
+  EXPECT_EQ(lb(Expression("1024*a")).toString(), "log(2, 1024 a)");
+  EXPECT_EQ(lb(Expression("2+a")).toString(), "log(2, a + 2)");
 }
 
 TEST(ExpressionFunctionsTests, lgTest) {

diff --git a/tests/src/expressions/ExpressionTests.cpp b/tests/src/expressions/ExpressionTests.cpp
@@ -142,22 +142,6 @@ TEST(ExpressionTests, stringConstructorTest) {
   EXPECT_EQ(Expression("exp100").toString(), "E^100");
   EXPECT_EQ(Expression("E^101").toString(), "E^101");
   EXPECT_EQ(Expression("E^(-101)").toString(), "1/(E^101)");
-  EXPECT_EQ(Expression("log(E,E)").toString(), "1");
-  EXPECT_EQ(Expression("log(Pi, Pi^10)").toString(), "10");
-  EXPECT_EQ(Expression("log(E,E^3)").toString(), "3");
-  EXPECT_EQ(Expression("log((Pi),(E)^((Pi)))").toString(), "Pi log(Pi, E)");
-  EXPECT_EQ(Expression("log(E^3, E)").toString(), "1/3");
-  EXPECT_EQ(Expression("log(E^Pi, E)").toString(), "1/Pi");
-  EXPECT_EQ(Expression("ln3").toString(), "ln(3)");
-  EXPECT_EQ(Expression("ln2").toString(), "ln(2)");
-  EXPECT_EQ(Expression("ln100").toString(), "ln(100)");
-  EXPECT_EQ(Expression("ln(E)").toString(), "1");
-  EXPECT_EQ(Expression("lg99").toString(), "log(10, 99)");
-  EXPECT_EQ(Expression("lg100").toString(), "2");
-  EXPECT_EQ(Expression("lb100").toString(), "log(2, 100)");
-  EXPECT_EQ(Expression("lb4").toString(), "2");
-  EXPECT_EQ(Expression("ln(ln(E))").toString(), "0");
-  EXPECT_EQ(Expression("ln(E)!").toString(), "1");
   EXPECT_EQ(Expression("sin10").toString(), "sin(10)");
   EXPECT_EQ(Expression("cos10").toString(), "cos(10)");
   EXPECT_EQ(Expression("tan10").toString(), "tan(10)");
@@ -188,7 +172,6 @@ TEST(ExpressionTests, stringConstructorTest) {
   EXPECT_EQ(Expression("sqrt((1-cos(2*(Pi/3)))/2)").toString(), "sqrt(-cos((2 Pi)/3)/2 + 1/2)");
   EXPECT_EQ(Expression("2*sqrt((1-cos(2*(Pi/3)))/2)*cos(Pi/3)").toString(), "2 sqrt(-cos((2 Pi)/3)/2 + 1/2) cos(Pi/3)");
   EXPECT_EQ(Expression("-sin(2)").toString(), "-sin(2)");
-  EXPECT_EQ(Expression("log(2, 256)").toString(), "8");
   EXPECT_EQ(Expression("2^(3/2)").toString(), "2 sqrt(2)");
   EXPECT_EQ(Expression("sqrt(sqrt5)").toString(), "root(5, 4)");
   EXPECT_EQ(Expression("sqrt4!").toString(), "2");
@@ -377,6 +360,33 @@ TEST(ExpressionTests, stringConstructorTest) {
   EXPECT_EQ(Expression("(x-1)/(x^(4/3) - x)").toString(), "(x - 1)/(x^(4/3) - x)");
   EXPECT_EQ(Expression("(x-1)/(2 x^(4/3) - x)").toString(), "(x - 1)/(2 x^(4/3) - x)");
 
+  EXPECT_EQ(Expression("log(2, 2)").toString(), "1");
+  EXPECT_EQ(Expression("log(2, 256)").toString(), "8");
+  EXPECT_EQ(Expression("log(3, 515377520732011331036461129765621272702107522001)").toString(), "100");
+  EXPECT_EQ(Expression("log(515377520732011331036461129765621272702107522001, 3)").toString(), "1/100");
+  EXPECT_EQ(Expression("log(2/3, 4/9)").toString(), "2");
+  EXPECT_EQ(Expression("log(9/4, 3/2)").toString(), "1/2");
+  EXPECT_EQ(Expression("log(4/9, 2/3)").toString(), "1/2");
+  EXPECT_EQ(Expression("log(4/11, 2/3)").toString(), "log(4/11, 2/3)");
+  EXPECT_EQ(Expression("ln1").toString(), "0");
+  EXPECT_EQ(Expression("ln3").toString(), "ln(3)");
+  EXPECT_EQ(Expression("ln2").toString(), "ln(2)");
+  EXPECT_EQ(Expression("ln100").toString(), "ln(100)");
+  EXPECT_EQ(Expression("ln(E)").toString(), "1");
+  EXPECT_EQ(Expression("lg99").toString(), "log(10, 99)");
+  EXPECT_EQ(Expression("lg100").toString(), "2");
+  EXPECT_EQ(Expression("lb100").toString(), "log(2, 100)");
+  EXPECT_EQ(Expression("lb4").toString(), "2");
+  EXPECT_EQ(Expression("ln(ln(E))").toString(), "0");
+  EXPECT_EQ(Expression("ln(E)!").toString(), "1");
+  EXPECT_EQ(Expression("log(0, 1)").toString(), "0");
+  EXPECT_EQ(Expression("log(E,E)").toString(), "1");
+  EXPECT_EQ(Expression("log(Pi, Pi^10)").toString(), "10");
+  EXPECT_EQ(Expression("log(E,E^3)").toString(), "3");
+  EXPECT_EQ(Expression("log((Pi),(E)^((Pi)))").toString(), "Pi log(Pi, E)");
+  EXPECT_EQ(Expression("log(E^3, E)").toString(), "1/3");
+  EXPECT_EQ(Expression("log(E^Pi, E)").toString(), "1/Pi");
+
   // TODO! implement this
   // EXPECT_EQ(Expression("sqrt(x^2)").toString(), "abs(x)");
   // EXPECT_EQ(Expression("(x^10)^(1/10))").toString(), "abs(x)");
@@ -722,6 +732,8 @@ TEST(ExpressionTests, stringConstructorTest) {
   EXPECT_EQ(Expression("x = -Inf").toString(), "False");
   EXPECT_EQ(Expression("Inf = Inf").toString(), "True");
   EXPECT_EQ(Expression("Inf = -Inf").toString(), "False");
+  EXPECT_EQ(Expression("log(1, 0)").toString(), "ComplexInf");
+  EXPECT_EQ(Expression("log(1, 0)").toString(), "ComplexInf");
 
   EXPECT_EQ(Expression("0*Inf").toString(), "Undefined");
   EXPECT_EQ(Expression("0*-Inf").toString(), "Undefined");
@@ -1051,21 +1063,14 @@ TEST(ExpressionTests, stringConstructorNegativeTest) {
   EXPECT_THROW(Expression("(-1)!!"), UndefinedException);
   EXPECT_THROW(Expression("(2/3)!!"), UndefinedException);
   EXPECT_THROW(Expression("sqrt(-1)"), UndefinedException);
-  EXPECT_THROW(Expression("ln(0)"), UndefinedException);
-  EXPECT_THROW(Expression("ln(-1)"), UndefinedException);
-  EXPECT_THROW(Expression("log(-1, 1)"), UndefinedException);
-  EXPECT_THROW(Expression("log(0, 1)"), UndefinedException);
-  EXPECT_THROW(Expression("log(1, 0)"), UndefinedException);
-  EXPECT_THROW(Expression("lb(-1)"), UndefinedException);
-  EXPECT_THROW(Expression("lg(-1)"), UndefinedException);
   EXPECT_THROW(Expression("sqrt(-1)"), UndefinedException);
   EXPECT_THROW(Expression("(-1)^(2/3)"), UndefinedException);
   EXPECT_THROW(Expression("ln(0)"), UndefinedException);
   EXPECT_THROW(Expression("ln(-1)"), UndefinedException);
   EXPECT_THROW(Expression("log(-1, 1)"), UndefinedException);
-  EXPECT_THROW(Expression("log(0, 1)"), UndefinedException);
-  EXPECT_THROW(Expression("log(1, 0)"), UndefinedException);
   EXPECT_THROW(Expression("lb(-1)"), UndefinedException);
+  EXPECT_THROW(Expression("lg(-1)"), UndefinedException);
+  EXPECT_THROW(Expression("log(-1, 1)"), UndefinedException);
   // TODO constants
   // EXPECT_THROW(Expression("E!"), UndefinedException);
   // EXPECT_THROW(Expression("tan(Pi/2)"), UndefinedException);

diff --git a/tests/src/functions/logarithms/LogTests.cpp b/tests/src/functions/logarithms/LogTests.cpp
@@ -30,8 +30,10 @@ TEST(LogTests, callTest) {
 
   EXPECT_EQ(f(Variable("a"), Variable("b"))->toString(), "log(a, b)");
 
+  EXPECT_EQ(f(Integer(1), Integer(10))->toString(), "ComplexInf");
+  // TODO!!! add tests
+
   EXPECT_THROW(f(Integer(-10), Integer(10)), UndefinedFunctionException);
-  EXPECT_THROW(f(Integer(1), Integer(10)), UndefinedFunctionException);
 
   EXPECT_THROW(f(), InvalidInputFunctionException);
   EXPECT_THROW(f(Integer(10)), InvalidInputFunctionException);