Machine constants

The MachineConstants class contains constants related to the specific implementation of floating-point arithmetic in the .NET framework and the Common Language Runtime. The System.Single and Double floating-point types in the Common Language Specification (CLS) follow the IEEE-754 standard for single and double-precision floating-point numbers.

Any number representation is necessarily limited. This class provides constants that specify these limits for the CLS' floating-point types.

Many of these constants are also available in the System.Single and Double structures. Unfortunately, these definitions do not follow the standard conventions. For example, the name epsilon normally refers to the machine precision. It is equal to the smallest difference between numbers close to unity, roughly 10^-16. The Double.Epsilon field uses the smallest positive number (roughly 10^-308) instead. This makes Double.Epsilon completely useless for its intended purpose.

All machine constants are implemented as static fields of the MachineConstants class.

The following example prints the values of some of the machine constants to the console:

Console.WriteLine("Machine precision: {0:R}", MachineConstants.Epsilon);
Console.WriteLine("Largest value: {0:R}", MachineConstants.MaxDouble);
Console.WriteLine("Smallest normalized value: {0:R}", 
    MachineConstants.MinNormalizedDouble);
Console.WriteLine("Logarithm of largest value: {0:R}", MachineConstants.LogMaxDouble);

The following table summarizes the machine constants for the Double type:

Machine constants for the Double data type

Machine precision
Epsilon	Represents the machine precision for Double-precision floating point numbers.
SqrtEpsilon	Represents the square root of the machine precision Epsilon for Double-precision floating point numbers.
CubeRootEpsilon	Represents the cube root of the machine precision Epsilon for Double-precision floating point numbers.
MaxDouble	Represents the largest possible value of a Double-precision floating point number.
SqrtMaxDouble	Represents the square root of MaxDouble.
LogMaxDouble	Represents the natural logarithm of MaxDouble.
MinDouble	Represents the smallest Double-precision floating point number that is greater than zero.
SqrtMinDouble	Represents the square root of MinDouble.
LogMinDouble	Represents the natural logarithm of MinDouble.

A similar set of constants is available for the Single type.

Machine constants for the Double data type.

Machine precision
SingleEpsilon	Represents the machine precision for Single-precision floating point numbers.
SqrtSingleEpsilon	Represents the square root of the machine precision SingleEpsilon for Single-precision floating point numbers.
CubeRootSingleEpsilon	Represents the cube root of the machine precision SingleEpsilon for Single-precision floating point numbers.
MaxSingle	Represents the largest possible value of a Single-precision floating point number.
SqrtMaxSingle	Represents the square root of MaxSingle.
LogMaxSingle	Represents the natural logarithm of MaxSingle.
MinSingle	Represents the smallest Single-precision floating point number that is greater than zero.
SqrtMinSingle	Represents the square root of MinSingle.
LogMinSingle	Represents the natural logarithm of MinSingle.