Add arcsin, arccos and arctan functions

CHANGELOG.md

@@ -1,6 +1,7 @@
 ### 1.1.0
 
 - Drop support for Dart SDK versions below 2.0.0
+- Add arcsin, arccos, arctan functions
 - Update examples and documentation
 - Switch to [pendantic](https://pub.dartlang.org/packages/pedantic) analysis
   options

lib/math_expressions.dart

@@ -1,7 +1,7 @@
 /*
  * math_expressions
  *
- * Copyright (c) 2013-2016  Frederik Leonhardt <frederik.leonhardt@gmail.com>,
+ * Copyright (c) 2013-2019  Frederik Leonhardt <frederik.leonhardt@gmail.com>,
  *                          Michael Frey <asakash117@gmail.com>
  *
  * Permission is hereby granted, free of charge, to any person obtaining a copy

lib/src/functions.dart

@@ -359,7 +359,7 @@ class Exponential extends DefaultFunction {
       return new Interval(math.exp(expEval.min), math.exp(expEval.max));
     }
 
-    throw new UnimplementedError('Can not evaluate exp on $type yet.');
+    throw new UnimplementedError('Can not evaluate $name on $type yet.');
   }
 }
 
@@ -412,7 +412,7 @@ class Log extends DefaultFunction {
       return asNaturalLogarithm().evaluate(type, context);
     }
 
-    throw new UnimplementedError('Can not evaluate log on $type yet.');
+    throw new UnimplementedError('Can not evaluate $name on $type yet.');
   }
 
   @override
@@ -475,7 +475,7 @@ class Ln extends Log {
       return new Interval(math.log(argEval.min), math.log(argEval.max));
     }
 
-    throw new UnimplementedError('Can not evaluate ln on $type yet.');
+    throw new UnimplementedError('Can not evaluate $name on $type yet.');
   }
 
   @override
@@ -612,7 +612,7 @@ class Sqrt extends Root {
       return new Interval(math.sqrt(argEval.min), math.sqrt(argEval.max));
     }
 
-    throw new UnimplementedError('Can not evaluate sqrt on $type yet.');
+    throw new UnimplementedError('Can not evaluate $name on $type yet.');
   }
 
   @override
@@ -667,7 +667,7 @@ class Sin extends DefaultFunction {
       // or just return [-1, 1] if half a period is in the given interval
     }
 
-    throw new UnimplementedError('Can not evaluate sin on $type yet.');
+    throw new UnimplementedError('Can not evaluate $name on $type yet.');
   }
 }
 
@@ -719,7 +719,7 @@ class Cos extends DefaultFunction {
       // or just return [-1, 1] if half a period is in the given interval
     }
 
-    throw new UnimplementedError('Can not evaluate cos on $type yet.');
+    throw new UnimplementedError('Can not evaluate $name on $type yet.');
   }
 }
 
@@ -766,7 +766,7 @@ class Tan extends DefaultFunction {
       //TODO apply function to all vector elements
     }
 
-    throw new UnimplementedError('Can not evaluate tan on $type yet.');
+    throw new UnimplementedError('Can not evaluate $name on $type yet.');
   }
 
   /**
@@ -777,6 +777,117 @@ class Tan extends DefaultFunction {
   Expression asSinCos() => new Sin(arg) / new Cos(arg);
 }
 
+/**
+ * The arcus sine function.
+ */
+class Asin extends DefaultFunction {
+  /**
+   * Creates a new arcus sine function with given argument expression.
+   */
+  Asin(Expression arg) : super._unary('arcsin', arg);
+
+  /// The argument of this arcus sine function.
+  Expression get arg => getParam(0);
+
+  @override
+  Expression derive(String toVar) =>
+      new Number(1) / new Sqrt(new Number(1) - (arg ^ new Number(2)));
+
+  /**
+   * Possible simplifications:
+   */
+  @override
+  Expression simplify() {
+    return new Asin(arg.simplify());
+  }
+
+  @override
+  dynamic evaluate(EvaluationType type, ContextModel context) {
+    final dynamic argEval = arg.evaluate(type, context);
+
+    if (type == EvaluationType.REAL) {
+      return math.asin(argEval);
+    }
+
+    // TODO VECTOR and INTERVAL evaluation
+    throw new UnimplementedError('Can not evaluate $name on $type yet.');
+  }
+}
+
+/**
+ * The arcus cosine function.
+ */
+class Acos extends DefaultFunction {
+  /**
+   * Creates a new arcus cosine function with given argument expression.
+   */
+  Acos(Expression arg) : super._unary('arccos', arg);
+
+  /// The argument of this arcus cosine function.
+  Expression get arg => getParam(0);
+
+  @override
+  Expression derive(String toVar) =>
+      -new Number(1) / new Sqrt(new Number(1) - (arg ^ new Number(2)));
+
+  /**
+   * Possible simplifications:
+   */
+  @override
+  Expression simplify() {
+    return new Acos(arg.simplify());
+  }
+
+  @override
+  dynamic evaluate(EvaluationType type, ContextModel context) {
+    final dynamic argEval = arg.evaluate(type, context);
+
+    if (type == EvaluationType.REAL) {
+      return math.acos(argEval);
+    }
+
+    // TODO VECTOR and INTERVAL evaluation
+    throw new UnimplementedError('Can not evaluate $name on $type yet.');
+  }
+}
+
+/**
+ * The arcus tangens function.
+ */
+class Atan extends DefaultFunction {
+  /**
+   * Creates a new arcus tangens function with given argument expression.
+   */
+  Atan(Expression arg) : super._unary('arctan', arg);
+
+  /// The argument of this arcus tangens function.
+  Expression get arg => getParam(0);
+
+  @override
+  Expression derive(String toVar) =>
+      new Number(1) / (new Number(1) + (arg ^ new Number(2)));
+
+  /**
+   * Possible simplifications:
+   */
+  @override
+  Expression simplify() {
+    return new Atan(arg.simplify());
+  }
+
+  @override
+  dynamic evaluate(EvaluationType type, ContextModel context) {
+    final dynamic argEval = arg.evaluate(type, context);
+
+    if (type == EvaluationType.REAL) {
+      return math.atan(argEval);
+    }
+
+    // TODO VECTOR and INTERVAL evaluation
+    throw new UnimplementedError('Can not evaluate $name on $type yet.');
+  }
+}
+
 /**
  * The absolute value function.
  */
@@ -812,7 +923,7 @@ class Abs extends DefaultFunction {
       //TODO apply function to all vector elements
     }
 
-    throw new UnimplementedError('Can not evaluate abs on $type yet.');
+    throw new UnimplementedError('Can not evaluate $name on $type yet.');
   }
 }
 
@@ -857,7 +968,7 @@ class Ceil extends DefaultFunction {
       //TODO apply function to all vector elements
     }
 
-    throw new UnimplementedError('Can not evaluate ceil on $type yet.');
+    throw new UnimplementedError('Can not evaluate $name on $type yet.');
   }
 }
 
@@ -902,7 +1013,7 @@ class Floor extends DefaultFunction {
       //TODO apply function to all vector elements
     }
 
-    throw new UnimplementedError('Can not evaluate floor on $type yet.');
+    throw new UnimplementedError('Can not evaluate $name on $type yet.');
   }
 }
 
@@ -935,6 +1046,6 @@ class Sgn extends DefaultFunction {
       if (argEval > 0) return 1.0;
     }
 
-    throw new UnimplementedError('Can not evaluate sgn on $type yet.');
+    throw new UnimplementedError('Can not evaluate $name on $type yet.');
   }
 }

lib/src/parser.dart

@@ -103,6 +103,15 @@ class Parser {
         case TokenType.TAN:
           currExpr = new Tan(exprStack.removeLast());
           break;
+        case TokenType.ASIN:
+          currExpr = new Asin(exprStack.removeLast());
+          break;
+        case TokenType.ACOS:
+          currExpr = new Acos(exprStack.removeLast());
+          break;
+        case TokenType.ATAN:
+          currExpr = new Atan(exprStack.removeLast());
+          break;
         case TokenType.ABS:
           currExpr = new Abs(exprStack.removeLast());
           break;
@@ -164,6 +173,9 @@ class Lexer {
     keywords['cos'] = TokenType.COS;
     keywords['sin'] = TokenType.SIN;
     keywords['tan'] = TokenType.TAN;
+    keywords['arccos'] = TokenType.ACOS;
+    keywords['arcsin'] = TokenType.ASIN;
+    keywords['arctan'] = TokenType.ATAN;
     keywords['abs'] = TokenType.ABS;
     keywords['ceil'] = TokenType.CEIL;
     keywords['floor'] = TokenType.FLOOR;
@@ -509,6 +521,12 @@ class TokenType {
       const TokenType._internal('SIN', 4, function: true);
   static const TokenType TAN =
       const TokenType._internal('TAN', 4, function: true);
+  static const TokenType ACOS =
+      const TokenType._internal('ACOS', 4, function: true);
+  static const TokenType ASIN =
+      const TokenType._internal('ASIN', 4, function: true);
+  static const TokenType ATAN =
+      const TokenType._internal('ATAN', 4, function: true);
   static const TokenType ABS =
       const TokenType._internal('ABS', 4, function: true);
   static const TokenType CEIL =