ECMA-334: 11.1.6 Floating point types

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C# Language Specification

11. Types 11.1 Value types 11.1.1 System.ValueType type 11.1.2 Default constructors 11.1.3 Struct types 11.1.4 Simple types 11.1.5 Integral types 11.1.6 Floating point types 11.1.7 decimal type 11.1.8 bool type 11.1.9 Enumeration types

© 2006 ECMA International

11.1.6 Floating point types

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 IEC 60559 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 (§14.7.2).

• Positive infinity and negative infinity. Infinities are produced by such operations as dividing a non-zero number by zero. [Example: 1.0 / 0.0 yields positive infinity, and –1.0 / 0.0 yields negative infinity. end example]

• The Not-a-Number value, often abbreviated NaN. NaNs 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 × 2^e, 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 ≤ e ≤ 104, and for double, 0 < m < 253 and −1075 ≤ e ≤ 970. Denormalized floating-point numbers are considered valid non-zero values. C# neither requires nor forbids that a conforming implementation support denormalized floatingpoint numbers.

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.

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:

• The result of a floating-point operation is rounded to the nearest representable value in the destination format. This may cause a non-zero value to be rounded to zero.

• If the magnitude of 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 can be performed with higher precision than the result type of the operation. [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 can cause a finite result to be produced instead of an infinity. end example]