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 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 (§7.8.2).

· 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. 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.

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.