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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 ...
In the floating-point case, a variable exponent would represent the power of ten to which the mantissa of the number is multiplied. Languages that support a rational data type usually allow the construction of such a value from two integers, instead of a base-2 floating-point number, due to the loss of exactness the latter would cause.
For floating-point arithmetic, the mantissa was restricted to a hundred digits or fewer, and the exponent was restricted to two digits only. The largest memory supplied offered 60 000 digits, however Fortran compilers for the 1620 settled on fixed sizes such as 10, though it could be specified on a control card if the default was not satisfactory.
Double-precision floating-point format (sometimes called FP64 or float64) is a floating-point number format, usually occupying 64 bits in computer memory; it represents a wide range of numeric values by using a floating radix point. Double precision may be chosen when the range or precision of single precision would be insufficient.
Programming languages that support arbitrary precision computations, either built-in, or in the standard library of the language: Ada: the upcoming Ada 202x revision adds the Ada.Numerics.Big_Numbers.Big_Integers and Ada.Numerics.Big_Numbers.Big_Reals packages to the standard library, providing arbitrary precision integers and real numbers.
Variable length arithmetic represents numbers as a string of digits of a variable's length limited only by the memory available. Variable-length arithmetic operations are considerably slower than fixed-length format floating-point instructions.
Block floating point (BFP) is a method used to provide an arithmetic approaching floating point while using a fixed-point processor. BFP assigns a group of significands (the non-exponent part of the floating-point number) to a single exponent, rather than single significand being assigned its own exponent. BFP can be advantageous to limit space ...
In Python 2 (and most other programming languages), unless explicitly requested, x / y performed integer division, returning a float only if either input was a float. However, because Python is a dynamically-typed language, it was not always possible to tell which operation was being performed, which often led to subtle bugs, thus prompting the ...