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A floating-point variable can represent a wider range of numbers than a fixed-point variable of the same bit width at the cost of precision. A signed 32-bit integer variable has a maximum value of 2 31 − 1 = 2,147,483,647, whereas an IEEE 754 32-bit base-2 floating-point variable has a maximum value of (2 − 2 −23 ) × 2 127 ≈ 3.4028235 ...
If a decimal string with at most 15 significant digits is converted to the IEEE 754 double-precision format, giving a normal number, and then converted back to a decimal string with the same number of digits, the final result should match the original string. If an IEEE 754 double-precision number is converted to a decimal string with at least ...
This is usually measured in bits, but sometimes in decimal digits. It is related to precision in mathematics, which describes the number of digits that are used to express a value. Some of the standardized precision formats are: Half-precision floating-point format; Single-precision floating-point format; Double-precision floating-point format
float and double, floating-point numbers with single and double precisions; boolean, a Boolean type with logical values true and false; returnAddress, a value referring to an executable memory address. This is not accessible from the Java programming language and is usually left out. [13] [14]
Since 2 10 = 1024, the complete range of the positive normal floating-point numbers in this format is from 2 −1022 ≈ 2 × 10 −308 to approximately 2 1024 ≈ 2 × 10 308. The number of normal floating-point numbers in a system (B, P, L, U) where B is the base of the system, P is the precision of the significand (in base B),
Go: the standard library package math/big implements arbitrary-precision integers (Int type), rational numbers (Rat type), and floating-point numbers (Float type) Guile: the built-in exact numbers are of arbitrary precision. Example: (expt 10 100) produces the expected (large) result. Exact numbers also include rationals, so (/ 3 4) produces 3/4.
C# standard library does not have classes to deal with arbitrary-precision floating point numbers (see software for arbitrary-precision arithmetic). C# can help mathematical applications with the checked and unchecked operators that allow the enabling or disabling of run-time checking for arithmetic overflow for a region of code.
The IEEE standard stores the sign, exponent, and significand in separate fields of a floating point word, each of which has a fixed width (number of bits). The two most commonly used levels of precision for floating-point numbers are single precision and double precision.