Simplify inverse trigonometric constants

fintarin · Aug 11, 2023 · 254f95e · 254f95e
1 parent 45aee7a
commit 254f95e
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diff --git a/src/fintamath/expressions/unary/InvTrigExpression.cpp b/src/fintamath/expressions/unary/InvTrigExpression.cpp
@@ -1,7 +1,25 @@
 #include "fintamath/expressions/unary/InvTrigExpression.hpp"
 
+#include "fintamath/functions/arithmetic/Mul.hpp"
+#include "fintamath/functions/arithmetic/Neg.hpp"
+#include "fintamath/functions/powers/Sqrt.hpp"
+#include "fintamath/functions/trigonometry/Acos.hpp"
+#include "fintamath/functions/trigonometry/Acot.hpp"
+#include "fintamath/functions/trigonometry/Asin.hpp"
+#include "fintamath/functions/trigonometry/Atan.hpp"
+#include "fintamath/literals/constants/ComplexInf.hpp"
+#include "fintamath/literals/constants/Pi.hpp"
+#include "fintamath/numbers/IntegerFunctions.hpp"
+#include "fintamath/numbers/Rational.hpp"
+
 namespace fintamath {
 
+using TrigonometryFunctionsTable = std::map<std::string, std::function<ArgumentPtr(const Rational &)>>;
+
+using TrigonometryTable = std::map<Rational, ArgumentPtr>;
+
+ArgumentPtr findValue(const TrigonometryTable &trigTable, const Rational &key);
+
 InvTrigExpression::InvTrigExpression(const IFunction &inFunc, const ArgumentPtr &inChild)
     : IUnaryExpressionCRTP(inFunc, inChild) {
 }
@@ -13,8 +31,121 @@ InvTrigExpression::SimplifyFunctionsVector InvTrigExpression::getFunctionsForPos
   return simplifyFunctions;
 }
 
-ArgumentPtr InvTrigExpression::constSimplify(const IFunction & /*func*/, const ArgumentPtr & /*rhs*/) {
-  // TODO! implement
+ArgumentPtr InvTrigExpression::constSimplify(const IFunction &func, const ArgumentPtr &rhs) {
+  if (const auto rat = cast<Rational>(rhs)) {
+    Rational sqr = pow(*rat, 2) * rat->sign();
+    return trigTableSimplify(func, sqr);
+  }
+
+  if (auto expr = cast<IExpression>(rhs)) {
+    // TODO! remove this check
+    int sign = 1;
+    if (is<Neg>(expr->getFunction())) {
+      expr = cast<IExpression>(expr->getChildren().front());
+      sign *= -1;
+
+      if (!expr) {
+        return {};
+      }
+    }
+
+    if (is<Sqrt>(expr->getOutputFunction())) {
+      if (const auto sqrtChildInt = cast<Integer>(expr->getChildren().front())) {
+        Rational sqr = (*sqrtChildInt) * sign;
+        return trigTableSimplify(func, sqr);
+      }
+    }
+
+    if (is<Mul>(expr->getOutputFunction())) {
+      const auto childRat = convert<Rational>(*expr->getChildren().front());
+      const auto childExpr = cast<IExpression>(expr->getChildren().back());
+
+      if (childRat && childExpr &&
+          is<Sqrt>(childExpr->getOutputFunction())) {
+
+        if (const auto sqrtChildInt = cast<Integer>(childExpr->getChildren().front())) {
+          sign *= childRat->sign();
+          Rational sqr = pow(*childRat, 2) * (*sqrtChildInt) * sign;
+          return trigTableSimplify(func, sqr);
+        }
+      }
+    }
+  }
+
+  return {};
+}
+
+ArgumentPtr InvTrigExpression::trigTableSimplify(const IFunction &func, const Rational &rhs) {
+  static const TrigonometryFunctionsTable trigTable = {
+      {Asin().toString(), &trigTableAsinSimplify},
+      {Acos().toString(), &trigTableAcosSimplify},
+      {Atan().toString(), &trigTableAtanSimplify},
+      {Acot().toString(), &trigTableAcotSimplify},
+  };
+  return trigTable.at(func.toString())(rhs);
+}
+
+ArgumentPtr InvTrigExpression::trigTableAsinSimplify(const Rational &rhs) {
+  static const TrigonometryTable trigTable = {
+      {Rational(-1), makeExpr(Mul(), Rational(-1, 2), Pi())},    // -1    | -π/2
+      {Rational(-3, 4), makeExpr(Mul(), Rational(-1, 3), Pi())}, // -√3/2 | -π/3
+      {Rational(-1, 2), makeExpr(Mul(), Rational(-1, 4), Pi())}, // -√2/2 | -π/4
+      {Rational(-1, 4), makeExpr(Mul(), Rational(-1, 6), Pi())}, // -1/2  | -π/6
+      {Rational(0), Integer(0).clone()},                         // 0     | 0
+      {Rational(1, 4), makeExpr(Mul(), Rational(1, 6), Pi())},   // 1/2   | π/6
+      {Rational(1, 2), makeExpr(Mul(), Rational(1, 4), Pi())},   // √2/2  | π/4
+      {Rational(3, 4), makeExpr(Mul(), Rational(1, 3), Pi())},   // √3/2  | π/3
+      {Rational(1), makeExpr(Mul(), Rational(-1, 2), Pi())},     // 1    | -π/2
+  };
+  return findValue(trigTable, rhs);
+}
+
+ArgumentPtr InvTrigExpression::trigTableAcosSimplify(const Rational &rhs) {
+  static const TrigonometryTable trigTable = {
+      {Rational(-1), Pi().clone()},                             // -1    | π
+      {Rational(-3, 4), makeExpr(Mul(), Rational(5, 6), Pi())}, // -√3/2 | 5π/6
+      {Rational(-1, 2), makeExpr(Mul(), Rational(3, 4), Pi())}, // -√2/2 | 3π/4
+      {Rational(-1, 4), makeExpr(Mul(), Rational(2, 3), Pi())}, // -1/2  | 2π/3
+      {Rational(0), makeExpr(Mul(), Rational(1, 2), Pi())},     // 0     | π/2
+      {Rational(1, 4), makeExpr(Mul(), Rational(1, 3), Pi())},  // 1/2   | π/3
+      {Rational(1, 2), makeExpr(Mul(), Rational(1, 4), Pi())},  // √2/2  | π/4
+      {Rational(3, 4), makeExpr(Mul(), Rational(1, 6), Pi())},  // √3/2  | π/6
+      {Rational(1), Integer(0).clone()},                        // 1     | 0
+  };
+  return findValue(trigTable, rhs);
+}
+
+ArgumentPtr InvTrigExpression::trigTableAtanSimplify(const Rational &rhs) {
+  static const TrigonometryTable trigTable = {
+      {Rational(-3), makeExpr(Mul(), Rational(-1, 3), Pi())},    // -√3   | -π/3
+      {Rational(-1), makeExpr(Mul(), Rational(-1, 4), Pi())},    // -1    | -π/4
+      {Rational(-1, 3), makeExpr(Mul(), Rational(-1, 6), Pi())}, // -√3/3 | -π/6
+      {Rational(0), Integer(0).clone()},                         // 0     | 0
+      {Rational(1, 3), makeExpr(Mul(), Rational(1, 6), Pi())},   // √3/3  | π/6
+      {Rational(1), makeExpr(Mul(), Rational(1, 4), Pi())},      // 1     | π/4
+      {Rational(3), makeExpr(Mul(), Rational(1, 3), Pi())},      // √3    | π/3
+  };
+  return findValue(trigTable, rhs);
+}
+
+ArgumentPtr InvTrigExpression::trigTableAcotSimplify(const Rational &rhs) {
+  static const TrigonometryTable trigTable = {
+      {Rational(-3), makeExpr(Mul(), Rational(-1, 6), Pi())},    // -√3   | -π/6
+      {Rational(-1), makeExpr(Mul(), Rational(-1, 4), Pi())},    // -1    | -π/4
+      {Rational(-1, 3), makeExpr(Mul(), Rational(-1, 3), Pi())}, // -√3/3 | -π/3
+      {Rational(0), makeExpr(Mul(), Rational(1, 2), Pi())},      // 0     | π/2
+      {Rational(1, 3), makeExpr(Mul(), Rational(1, 3), Pi())},   // √3/3  | π/3
+      {Rational(1), makeExpr(Mul(), Rational(1, 4), Pi())},      // 1     | π/4
+      {Rational(3), makeExpr(Mul(), Rational(1, 6), Pi())},      // √3    | π/6
+  };
+  return findValue(trigTable, rhs);
+}
+
+ArgumentPtr findValue(const TrigonometryTable &trigTable, const Rational &key) {
+  if (auto res = trigTable.find(key); res != trigTable.end()) {
+    return res->second;
+  }
+
   return {};
 }
 

diff --git a/src/fintamath/expressions/unary/InvTrigExpression.hpp b/src/fintamath/expressions/unary/InvTrigExpression.hpp
@@ -4,6 +4,8 @@
 
 namespace fintamath {
 
+class Rational;
+
 class InvTrigExpression : public IUnaryExpressionCRTP<InvTrigExpression, true> {
 public:
   explicit InvTrigExpression(const IFunction &inFunc, const ArgumentPtr &inChild);
@@ -17,6 +19,16 @@ class InvTrigExpression : public IUnaryExpressionCRTP<InvTrigExpression, true> {
 
 private:
   static ArgumentPtr constSimplify(const IFunction &func, const ArgumentPtr &rhs);
+
+  static ArgumentPtr trigTableSimplify(const IFunction &func, const Rational &rhs);
+
+  static ArgumentPtr trigTableAsinSimplify(const Rational &rhs);
+
+  static ArgumentPtr trigTableAcosSimplify(const Rational &rhs);
+
+  static ArgumentPtr trigTableAtanSimplify(const Rational &rhs);
+
+  static ArgumentPtr trigTableAcotSimplify(const Rational &rhs);
 };
 
 }
diff --git a/tests/src/expressions/ExpressionTests.cpp b/tests/src/expressions/ExpressionTests.cpp
@@ -843,6 +843,77 @@ TEST(ExpressionTests, stringConstructorTest) {
   EXPECT_EQ(Expression("tan(E Pi)").toString(), "tan(E Pi)");
   EXPECT_EQ(Expression("cot(E Pi)").toString(), "cot(E Pi)");
 
+  EXPECT_EQ(Expression("asin(-1)").toString(), "-Pi/2");
+  EXPECT_EQ(Expression("asin(-sqrt(3)/2)").toString(), "-Pi/3");
+  EXPECT_EQ(Expression("asin(-sqrt(2)/2)").toString(), "-Pi/4");
+  EXPECT_EQ(Expression("asin(-1/2)").toString(), "-Pi/6");
+  EXPECT_EQ(Expression("asin(0)").toString(), "0");
+  EXPECT_EQ(Expression("asin(1/2)").toString(), "Pi/6");
+  EXPECT_EQ(Expression("asin(sqrt(2)/2)").toString(), "Pi/4");
+  EXPECT_EQ(Expression("asin(sqrt(3)/2)").toString(), "Pi/3");
+  EXPECT_EQ(Expression("asin(1)").toString(), "Pi/2");
+
+  EXPECT_EQ(Expression("acos(-1)").toString(), "Pi");
+  EXPECT_EQ(Expression("acos(-sqrt(3)/2)").toString(), "(5 Pi)/6");
+  EXPECT_EQ(Expression("acos(-sqrt(2)/2)").toString(), "(3 Pi)/4");
+  EXPECT_EQ(Expression("acos(-1/2)").toString(), "(2 Pi)/3");
+  EXPECT_EQ(Expression("acos(0)").toString(), "Pi/2");
+  EXPECT_EQ(Expression("acos(1/2)").toString(), "Pi/3");
+  EXPECT_EQ(Expression("acos(sqrt(2)/2)").toString(), "Pi/4");
+  EXPECT_EQ(Expression("acos(sqrt(3)/2)").toString(), "Pi/6");
+  EXPECT_EQ(Expression("acos(1)").toString(), "0");
+
+  EXPECT_EQ(Expression("atan(-sqrt(3))").toString(), "-Pi/3");
+  EXPECT_EQ(Expression("atan(-1)").toString(), "-Pi/4");
+  EXPECT_EQ(Expression("atan(-sqrt(3)/3)").toString(), "-Pi/6");
+  EXPECT_EQ(Expression("atan(0)").toString(), "0");
+  EXPECT_EQ(Expression("atan(sqrt(3)/3)").toString(), "Pi/6");
+  EXPECT_EQ(Expression("atan(1)").toString(), "Pi/4");
+  EXPECT_EQ(Expression("atan(sqrt(3))").toString(), "Pi/3");
+
+  EXPECT_EQ(Expression("acot(-sqrt(3))").toString(), "-Pi/6");
+  EXPECT_EQ(Expression("acot(-1)").toString(), "-Pi/4");
+  EXPECT_EQ(Expression("acot(-sqrt(3)/3)").toString(), "-Pi/3");
+  EXPECT_EQ(Expression("acot(0)").toString(), "Pi/2");
+  EXPECT_EQ(Expression("acot(sqrt(3)/3)").toString(), "Pi/3");
+  EXPECT_EQ(Expression("acot(1)").toString(), "Pi/4");
+  EXPECT_EQ(Expression("acot(sqrt(3))").toString(), "Pi/6");
+
+  EXPECT_EQ(Expression("asin(sqrt(5)/10)").toString(), "asin(sqrt(5)/10)");
+  EXPECT_EQ(Expression("acos(sqrt(5)/10)").toString(), "acos(sqrt(5)/10)");
+  EXPECT_EQ(Expression("atan(sqrt(5)/10)").toString(), "atan(sqrt(5)/10)");
+  EXPECT_EQ(Expression("acot(sqrt(5)/10)").toString(), "acot(sqrt(5)/10)");
+
+  EXPECT_EQ(Expression("asin(x)").toString(), "asin(x)");
+  EXPECT_EQ(Expression("acos(x)").toString(), "acos(x)");
+  EXPECT_EQ(Expression("atan(x)").toString(), "atan(x)");
+  EXPECT_EQ(Expression("acot(x)").toString(), "acot(x)");
+
+  EXPECT_EQ(Expression("asin(sqrt(x))").toString(), "asin(sqrt(x))");
+  EXPECT_EQ(Expression("acos(sqrt(x))").toString(), "acos(sqrt(x))");
+  EXPECT_EQ(Expression("atan(sqrt(x))").toString(), "atan(sqrt(x))");
+  EXPECT_EQ(Expression("acot(sqrt(x))").toString(), "acot(sqrt(x))");
+
+  EXPECT_EQ(Expression("asin(sqrt(x)/2)").toString(), "asin(sqrt(x)/2)");
+  EXPECT_EQ(Expression("acos(sqrt(x)/2)").toString(), "acos(sqrt(x)/2)");
+  EXPECT_EQ(Expression("atan(sqrt(x)/2)").toString(), "atan(sqrt(x)/2)");
+  EXPECT_EQ(Expression("acot(sqrt(x)/2)").toString(), "acot(sqrt(x)/2)");
+
+  EXPECT_EQ(Expression("asin(-x)").toString(), "asin(-x)");
+  EXPECT_EQ(Expression("acos(-x)").toString(), "acos(-x)");
+  EXPECT_EQ(Expression("atan(-x)").toString(), "atan(-x)");
+  EXPECT_EQ(Expression("acot(-x)").toString(), "acot(-x)");
+
+  EXPECT_EQ(Expression("asin(-sqrt(x))").toString(), "asin(-sqrt(x))");
+  EXPECT_EQ(Expression("acos(-sqrt(x))").toString(), "acos(-sqrt(x))");
+  EXPECT_EQ(Expression("atan(-sqrt(x))").toString(), "atan(-sqrt(x))");
+  EXPECT_EQ(Expression("acot(-sqrt(x))").toString(), "acot(-sqrt(x))");
+
+  EXPECT_EQ(Expression("asin(-sqrt(x)/2)").toString(), "asin(-sqrt(x)/2)");
+  EXPECT_EQ(Expression("acos(-sqrt(x)/2)").toString(), "acos(-sqrt(x)/2)");
+  EXPECT_EQ(Expression("atan(-sqrt(x)/2)").toString(), "atan(-sqrt(x)/2)");
+  EXPECT_EQ(Expression("acot(-sqrt(x)/2)").toString(), "acot(-sqrt(x)/2)");
+
   // EXPECT_EQ(Expression("sin(x)^2 + cos(x)^2").toString(), "1"); // TODO: implement
   // EXPECT_EQ(Expression("tan(x)*cot(x)").toString(), "1"); // TODO: implement
   // EXPECT_EQ(Expression("tanh(x)*coth(x)").toString(), "1"); // TODO: implement