Precalculate common angles for trigonometric functions (#292)

* Close #269 - Precalculate common angles for trigonometric functions

* Fix ComplexNumber format

xFunc.Maths/Expressions/Abs.cs

@@ -63,7 +63,7 @@ public override object Execute(ExpressionParameters parameters)
             return result switch
             {
                 double number => Math.Abs(number),
-                Angle angle => Angle.Abs(angle),
+                Angle angle => AngleExtensions.Abs(angle),
                 Complex complex => Complex.Abs(complex),
                 Vector vector => vector.Abs(parameters),
                 _ => throw new ResultIsNotSupportedException(this, result),

xFunc.Maths/Expressions/Angles/Angle.cs

@@ -402,51 +402,38 @@ private static AngleUnit GetCommonUnit(AngleUnit left, AngleUnit right)
         };
 
         /// <summary>
-        /// Converts <see cref="Angle"/> to <see cref="AngleNumber"/>.
+        /// Normalizes the current angle between [0, 2pi).
         /// </summary>
-        /// <returns>The angle number.</returns>
-        public AngleNumber AsExpression()
-            => new AngleNumber(this);
+        /// <returns>The normalized angle.</returns>
+        public Angle Normalize()
+        {
+            const double degreeFullCircle = 360.0;
+            const double radianFullCircle = 2 * Math.PI;
+            const double gradianFullCircle = 400.0;
 
-        /// <summary>
-        /// Returns the absolute value of a specified angle.
-        /// </summary>
-        /// <param name="angle">The angle.</param>
-        /// <returns>The angle, <c>x</c>, that such that 0 ≤ <c>x</c> ≤ <c>MaxValue</c>.</returns>
-        public static Angle Abs(Angle angle)
-            => new Angle(Math.Abs(angle.Value), angle.Unit);
+            static double NormalizeInternal(double value, double circle)
+            {
+                value %= circle;
+                if (value < 0)
+                    value += circle;
 
-        /// <summary>
-        /// Returns the smallest integral value that is greater than or equal to the specified angle number.
-        /// </summary>
-        /// <param name="angle">The angle.</param>
-        /// <returns>The smallest integral value.</returns>
-        public static Angle Ceiling(Angle angle)
-            => new Angle(Math.Ceiling(angle.Value), angle.Unit);
+                return value;
+            }
 
-        /// <summary>
-        /// Returns the largest integral value less than or equal to the specified angle number.
-        /// </summary>
-        /// <param name="angle">The angle.</param>
-        /// <returns>The largest integral value.</returns>
-        public static Angle Floor(Angle angle)
-            => new Angle(Math.Floor(angle.Value), angle.Unit);
-
-        /// <summary>
-        /// Calculates the integral part of a specified angle number.
-        /// </summary>
-        /// <param name="angle">An angle to truncate.</param>
-        /// <returns>The integral part of angle number.</returns>
-        public static Angle Truncate(Angle angle)
-            => new Angle(Math.Truncate(angle.Value), angle.Unit);
+            return Unit switch
+            {
+                AngleUnit.Radian => Radian(NormalizeInternal(Value, radianFullCircle)),
+                AngleUnit.Gradian => Gradian(NormalizeInternal(Value, gradianFullCircle)),
+                _ => Degree(NormalizeInternal(Value, degreeFullCircle)),
+            };
+        }
 
         /// <summary>
-        /// Returns the fractional part of the angle number.
+        /// Converts <see cref="Angle"/> to <see cref="AngleNumber"/>.
         /// </summary>
-        /// <param name="angle">The angle number.</param>
-        /// <returns>The fractional part.</returns>
-        public static Angle Frac(Angle angle)
-            => new Angle(MathExtensions.Frac(angle.Value), angle.Unit);
+        /// <returns>The angle number.</returns>
+        public AngleNumber AsExpression()
+            => new AngleNumber(this);
 
         /// <summary>
         /// Gets a value.

xFunc.Maths/Expressions/Ceil.cs

@@ -60,7 +60,7 @@ public override object Execute(ExpressionParameters parameters)
             return result switch
             {
                 double number => Math.Ceiling(number),
-                Angle angle => Angle.Ceiling(angle),
+                Angle angle => AngleExtensions.Ceiling(angle),
                 _ => throw new ResultIsNotSupportedException(this, result),
             };
         }

xFunc.Maths/Expressions/Floor.cs

@@ -60,7 +60,7 @@ public override object Execute(ExpressionParameters parameters)
             return result switch
             {
                 double number => Math.Floor(number),
-                Angle angle => Angle.Floor(angle),
+                Angle angle => AngleExtensions.Floor(angle),
                 _ => throw new ResultIsNotSupportedException(this, result),
             };
         }

xFunc.Maths/Expressions/Frac.cs

@@ -58,7 +58,7 @@ public override object Execute(ExpressionParameters parameters)
             return result switch
             {
                 double number => MathExtensions.Frac(number),
-                Angle angle => Angle.Frac(angle),
+                Angle angle => AngleExtensions.Frac(angle),
                 _ => throw new ResultIsNotSupportedException(this, result),
             };
         }

xFunc.Maths/Expressions/Trigonometric/Cos.cs

@@ -13,7 +13,6 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-using System;
 using System.Collections.Generic;
 using System.Numerics;
 using xFunc.Maths.Analyzers;
@@ -53,8 +52,8 @@ internal Cos(IList<IExpression> arguments)
         /// A result of the calculation.
         /// </returns>
         /// <seealso cref="ExpressionParameters" />
-        protected override double ExecuteInternal(Angle angle) =>
-            Math.Cos(angle.Value);
+        protected override double ExecuteInternal(Angle angle)
+            => AngleExtensions.Cos(angle);
 
         /// <summary>
         /// Calculates the this mathematical expression (complex number).
@@ -63,8 +62,8 @@ internal Cos(IList<IExpression> arguments)
         /// <returns>
         /// A result of the calculation.
         /// </returns>
-        protected override Complex ExecuteComplex(Complex complex) =>
-            Complex.Cos(complex);
+        protected override Complex ExecuteComplex(Complex complex)
+            => Complex.Cos(complex);
 
         /// <summary>
         /// Analyzes the current expression.
@@ -94,7 +93,7 @@ private protected override TResult AnalyzeInternal<TResult>(IAnalyzer<TResult> a
         /// Clones this instance.
         /// </summary>
         /// <returns>The new instance of <see cref="IExpression"/> that is a clone of this instance.</returns>
-        public override IExpression Clone() =>
-            new Cos(Argument.Clone());
+        public override IExpression Clone()
+            => new Cos(Argument.Clone());
     }
 }

xFunc.Maths/Expressions/Trigonometric/Cot.cs

@@ -52,8 +52,8 @@ internal Cot(IList<IExpression> arguments)
         /// A result of the calculation.
         /// </returns>
         /// <seealso cref="ExpressionParameters" />
-        protected override double ExecuteInternal(Angle angle) =>
-            MathExtensions.Cot(angle.Value);
+        protected override double ExecuteInternal(Angle angle)
+            => AngleExtensions.Cot(angle);
 
         /// <summary>
         /// Calculates the this mathematical expression (complex number).
@@ -62,8 +62,8 @@ internal Cot(IList<IExpression> arguments)
         /// <returns>
         /// A result of the calculation.
         /// </returns>
-        protected override Complex ExecuteComplex(Complex complex) =>
-            ComplexExtensions.Cot(complex);
+        protected override Complex ExecuteComplex(Complex complex)
+            => ComplexExtensions.Cot(complex);
 
         /// <summary>
         /// Analyzes the current expression.
@@ -93,7 +93,7 @@ private protected override TResult AnalyzeInternal<TResult>(IAnalyzer<TResult> a
         /// Clones this instance.
         /// </summary>
         /// <returns>The new instance of <see cref="IExpression"/> that is a clone of this instance.</returns>
-        public override IExpression Clone() =>
-            new Cot(Argument.Clone());
+        public override IExpression Clone()
+            => new Cot(Argument.Clone());
     }
 }

xFunc.Maths/Expressions/Trigonometric/Csc.cs

@@ -52,8 +52,8 @@ internal Csc(IList<IExpression> arguments)
         /// A result of the calculation.
         /// </returns>
         /// <seealso cref="ExpressionParameters" />
-        protected override double ExecuteInternal(Angle angle) =>
-            MathExtensions.Csc(angle.Value);
+        protected override double ExecuteInternal(Angle angle)
+            => AngleExtensions.Csc(angle);
 
         /// <summary>
         /// Calculates the this mathematical expression (complex number).
@@ -62,8 +62,8 @@ internal Csc(IList<IExpression> arguments)
         /// <returns>
         /// A result of the calculation.
         /// </returns>
-        protected override Complex ExecuteComplex(Complex complex) =>
-            ComplexExtensions.Csc(complex);
+        protected override Complex ExecuteComplex(Complex complex)
+            => ComplexExtensions.Csc(complex);
 
         /// <summary>
         /// Analyzes the current expression.
@@ -93,7 +93,7 @@ private protected override TResult AnalyzeInternal<TResult>(IAnalyzer<TResult> a
         /// Clones this instance.
         /// </summary>
         /// <returns>The new instance of <see cref="IExpression"/> that is a clone of this instance.</returns>
-        public override IExpression Clone() =>
-            new Csc(Argument.Clone());
+        public override IExpression Clone()
+            => new Csc(Argument.Clone());
     }
 }

xFunc.Maths/Expressions/Trigonometric/Sec.cs

@@ -52,8 +52,8 @@ internal Sec(IList<IExpression> arguments)
         /// A result of the calculation.
         /// </returns>
         /// <seealso cref="ExpressionParameters" />
-        protected override double ExecuteInternal(Angle angle) =>
-            MathExtensions.Sec(angle.Value);
+        protected override double ExecuteInternal(Angle angle)
+            => AngleExtensions.Sec(angle);
 
         /// <summary>
         /// Calculates the this mathematical expression (complex number).
@@ -62,8 +62,8 @@ internal Sec(IList<IExpression> arguments)
         /// <returns>
         /// A result of the calculation.
         /// </returns>
-        protected override Complex ExecuteComplex(Complex complex) =>
-            ComplexExtensions.Sec(complex);
+        protected override Complex ExecuteComplex(Complex complex)
+            => ComplexExtensions.Sec(complex);
 
         /// <summary>
         /// Analyzes the current expression.
@@ -93,7 +93,7 @@ private protected override TResult AnalyzeInternal<TResult>(IAnalyzer<TResult> a
         /// Clones this instance.
         /// </summary>
         /// <returns>The new instance of <see cref="IExpression"/> that is a clone of this instance.</returns>
-        public override IExpression Clone() =>
-            new Sec(Argument.Clone());
+        public override IExpression Clone()
+            => new Sec(Argument.Clone());
     }
 }

xFunc.Maths/Expressions/Trigonometric/Sin.cs

@@ -13,7 +13,6 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-using System;
 using System.Collections.Generic;
 using System.Numerics;
 using xFunc.Maths.Analyzers;
@@ -53,8 +52,8 @@ internal Sin(IList<IExpression> arguments)
         /// A result of the calculation.
         /// </returns>
         /// <seealso cref="ExpressionParameters" />
-        protected override double ExecuteInternal(Angle angle) =>
-            Math.Sin(angle.Value);
+        protected override double ExecuteInternal(Angle angle)
+            => AngleExtensions.Sin(angle);
 
         /// <summary>
         /// Calculates the this mathematical expression (complex number).
@@ -63,8 +62,8 @@ internal Sin(IList<IExpression> arguments)
         /// <returns>
         /// A result of the calculation.
         /// </returns>
-        protected override Complex ExecuteComplex(Complex complex) =>
-            Complex.Sin(complex);
+        protected override Complex ExecuteComplex(Complex complex)
+            => Complex.Sin(complex);
 
         /// <summary>
         /// Analyzes the current expression.
@@ -94,7 +93,7 @@ private protected override TResult AnalyzeInternal<TResult>(IAnalyzer<TResult> a
         /// Clones this instance.
         /// </summary>
         /// <returns>The new instance of <see cref="IExpression"/> that is a clone of this instance.</returns>
-        public override IExpression Clone() =>
-            new Sin(Argument.Clone());
+        public override IExpression Clone()
+            => new Sin(Argument.Clone());
     }
 }

xFunc.Maths/Expressions/Trigonometric/Tan.cs

@@ -13,7 +13,6 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-using System;
 using System.Collections.Generic;
 using System.Numerics;
 using xFunc.Maths.Analyzers;
@@ -53,8 +52,8 @@ internal Tan(IList<IExpression> arguments)
         /// A result of the calculation.
         /// </returns>
         /// <seealso cref="ExpressionParameters" />
-        protected override double ExecuteInternal(Angle angle) =>
-            Math.Tan(angle.Value);
+        protected override double ExecuteInternal(Angle angle)
+            => AngleExtensions.Tan(angle);
 
         /// <summary>
         /// Calculates the this mathematical expression (complex number).
@@ -63,8 +62,8 @@ internal Tan(IList<IExpression> arguments)
         /// <returns>
         /// A result of the calculation.
         /// </returns>
-        protected override Complex ExecuteComplex(Complex complex) =>
-            Complex.Tan(complex);
+        protected override Complex ExecuteComplex(Complex complex)
+            => Complex.Tan(complex);
 
         /// <summary>
         /// Analyzes the current expression.
@@ -94,7 +93,7 @@ private protected override TResult AnalyzeInternal<TResult>(IAnalyzer<TResult> a
         /// Clones this instance.
         /// </summary>
         /// <returns>The new instance of <see cref="IExpression"/> that is a clone of this instance.</returns>
-        public override IExpression Clone() =>
-            new Tan(Argument.Clone());
+        public override IExpression Clone()
+            => new Tan(Argument.Clone());
     }
 }

xFunc.Maths/Expressions/Trunc.cs

@@ -59,7 +59,7 @@ public override object Execute(ExpressionParameters parameters)
             return result switch
             {
                 double number => Math.Truncate(number),
-                Angle angle => Angle.Truncate(angle),
+                Angle angle => AngleExtensions.Truncate(angle),
                 _ => throw new ResultIsNotSupportedException(this, result),
             };
         }