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Example: (expt 10 100) produces the expected (large) result. Exact numbers also include rationals, so (/ 3 4) produces 3/4. Arbitrary precision floating point numbers are included in the standard library math/bigfloat module. Raku: Rakudo supports Int and FatRat data types that promote to arbitrary-precision integers and rationals.
In computer science, type conversion, [1] [2] type casting, [1] [3] type coercion, [3] and type juggling [4] [5] are different ways of changing an expression from one data type to another. An example would be the conversion of an integer value into a floating point value or its textual representation as a string, and vice versa.
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 ...
With the example in view, a number of details can be discussed. The most important is the choice of the representation of the big number. In this case, only integer values are required for digits, so an array of fixed-width integers is adequate. It is convenient to have successive elements of the array represent higher powers of the base.
The representation has a limited precision. For example, only 15 decimal digits can be represented with a 64-bit real. If a very small floating-point number is added to a large one, the result is just the large one. The small number was too small to even show up in 15 or 16 digits of resolution, and the computer effectively discards it.
A floating-point number is a rational number, because it can be represented as one integer divided by another; for example 1.45 × 10 3 is (145/100)×1000 or 145,000 /100. The base determines the fractions that can be represented; for instance, 1/5 cannot be represented exactly as a floating-point number using a binary base, but 1/5 can be ...
The standard type hierarchy of Python 3. In computer science and computer programming, a data type (or simply type) is a collection or grouping of data values, usually specified by a set of possible values, a set of allowed operations on these values, and/or a representation of these values as machine types. [1]
Integer addition, for example, can be performed as a single machine instruction, and some offer specific instructions to process sequences of characters with a single instruction. [7] But the choice of primitive data type may affect performance, for example it is faster using SIMD operations and data types to operate on an array of floats.