Recipe 1.3. Converting Radians to Degrees

Problem

When using the trigonometric functions of the Math class, all units are in radians; instead, you require a result in degrees.

Solution

To convert a value in radians to degrees, multiply it by 180/ p :

using System;

	public static double ConvertRadiansToDegrees(double radians)
	{
	    double degrees = (180 / Math.PI) * radians;
	    return (degrees);
	}

Discussion

All of the static trigonometric methods in the Math class use radians as their unit of measure for angles. It is very handy to have conversion routines to convert between radians and degrees; displaying degrees to a user is more informative than displaying radians.

The equation for converting radians to degrees is shown here:

degrees = (180 / Math.PI) * radians

The static field Math.PI contains the constant p .

Recipe 1.4. Using the Bitwise Complement Operator with Various Data Types

Problem

The bitwise complement operator (~) is overloaded to work directly with int, uint, long, ulong , and enumeration data types consisting of the underlying types int, uint, long , and ulong . However, you need to perform a bitwise complement operation on a different numeric data type.

Solution

To use the bitwise complement operator with any data type, you must cast the resultant value of the bitwise operation to the type you wish to work with. The following code demonstrates this technique with the byte data type:

byte y = 1;
	byte result = (byte)~y;

The value assigned to result is 254 .

Discussion

The following code shows incorrect use of the bitwise complement operator on the byte data type:

byte y = 1;
	Console.WriteLine("~y = " + ~y);

This code outputs the following surprising value:

-2

Clearly, the result from performing the bitwise complement of the byte variable is incorrect; it should be 254 . In fact, byte is an unsigned data type, so it cannot be equal to a negative number. If you rewrite the code as follows :

byte y = 1;
	byte result = ~y;

you get a compile-time error: "Cannot implicitly convert type 'int' to 'byte.'" This error message gives some insight into why this operation does not work as expected. To fix this problem, you must explicitly cast this value to a byte before you assign it to the result variable, as shown here:

byte y = 1;
	byte result = (byte)~y;

This cast is required because the bitwise operators are overloaded to operate on only six specific data types: int, uint, long, ulong, bool , and enumeration data types. When one of the bitwise operators is used on another data type, that data type is converted to the supported data type that matches it most closely. Therefore, a byte data type is converted to an int before the bitwise complement operator is evaluated:

0x01 // byte y = 1;
	0xFFFFFFFE // The value 01h is converted to an int and its
	           // bitwise complement is taken.
	           // This bit pattern equals -2 as an int.
	      0xFE // The resultant int value is cast to its original byte data type.

Notice that the int data type is a signed data type, unlike the byte data type. This is why you receive -2 for a result instead of the expected value 254 . This conversion of the byte data type to its nearest equivalent is called numeric promotion . Numeric promotion also comes into play when you use differing data types with binary operators, including the bitwise binary operators.

Numeric promotion is discussed in detail in the C# Language Specification document in section 7.2.6 (this document is available at http://msdn.microsoft.com/vcsharp/programming/language). Understanding how numeric promotion works is essential when using operators on differing data types and when using operators with a data type that is not overloaded to handle them. Knowing this can save you hours of debugging time.