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# 4.1.6 Floating point types

Visual Studio .NET 2003

C# supports two floating point types: `float` and `double`. The `float` and `double` types are represented using the 32-bit single-precision and 64-bit double-precision IEEE 754 formats, which provide the following sets of values:

• Positive zero and negative zero. In most situations, positive zero and negative zero behave identically as the simple value zero, but certain operations distinguish between the two (Section 7.7.2).
• Positive infinity and negative infinity. Infinities are produced by such operations as dividing a non-zero number by zero. For example, `1.0` `/` `0.0` yields positive infinity, and `–1.0` `/` `0.0` yields negative infinity.
• The Not-a-Number value, often abbreviated NaN. NaN's are produced by invalid floating-point operations, such as dividing zero by zero.
• The finite set of non-zero values of the form s × m × 2e, where s is 1 or −1, and m and e are determined by the particular floating-point type: For `float`, 0 < m < 224 and −149 &le; e &le; 104, and for `double`, 0 < m < 253 and −1075 &le; e &le; 970. Denormalized floating-point numbers are considered valid non-zero values.

The `float` type can represent values ranging from approximately 1.5 × 10−45 to 3.4 × 1038 with a precision of 7 digits.

The `double` type can represent values ranging from approximately 5.0 × 10−324 to 1.7 × 10308 with a precision of 15-16 digits.

If one of the operands of a binary operator is of a floating-point type, then the other operand must be of an integral type or a floating-point type, and the operation is evaluated as follows:

• If one of the operands is of an integral type, then that operand is converted to the floating-point type of the other operand.
• Then, if either of the operands is of type `double`, the other operand is converted to `double`, the operation is performed using at least `double` range and precision, and the type of the result is `double` (or `bool` for the relational operators).
• Otherwise, the operation is performed using at least `float` range and precision, and the type of the result is `float` (or `bool` for the relational operators).

The floating-point operators, including the assignment operators, never produce exceptions. Instead, in exceptional situations, floating-point operations produce zero, infinity, or NaN, as described below:

• If the result of a floating-point operation is too small for the destination format, the result of the operation becomes positive zero or negative zero.
• If the result of a floating-point operation is too large for the destination format, the result of the operation becomes positive infinity or negative infinity.
• If a floating-point operation is invalid, the result of the operation becomes NaN.
• If one or both operands of a floating-point operation is NaN, the result of the operation becomes NaN.

Floating-point operations may be performed with higher precision than the result type of the operation. For example, some hardware architectures support an "extended" or "long double" floating-point type with greater range and precision than the `double` type, and implicitly perform all floating-point operations using this higher precision type. Only at excessive cost in performance can such hardware architectures be made to perform floating-point operations with less precision, and rather than require an implementation to forfeit both performance and precision, C# allows a higher precision type to be used for all floating-point operations. Other than delivering more precise results, this rarely has any measurable effects. However, in expressions of the form `x` `*` `y` `/` `z`, where the multiplication produces a result that is outside the `double` range, but the subsequent division brings the temporary result back into the `double` range, the fact that the expression is evaluated in a higher range format may cause a finite result to be produced instead of an infinity.

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