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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 ...
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.
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]
If a decimal string with at most 33 significant digits is converted to the IEEE 754 quadruple-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 quadruple-precision number is converted to a decimal string with at ...
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.