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ColdFusion: the built-in PrecisionEvaluate() function evaluates one or more string expressions, dynamically, from left to right, using BigDecimal precision arithmetic to calculate the values of arbitrary precision arithmetic expressions. D: standard library module std.bigint; Dart: the built-in int datatype implements arbitrary-precision ...
The computer may also offer facilities for splitting a product into a digit and carry without requiring the two operations of mod and div as in the example, and nearly all arithmetic units provide a carry flag which can be exploited in multiple-precision addition and subtraction. This sort of detail is the grist of machine-code programmers, and ...
In mathematics, the hyperoperation sequence [nb 1] is an infinite sequence of arithmetic operations (called hyperoperations in this context) [1] [11] [13] that starts with a unary operation (the successor function with n = 0). The sequence continues with the binary operations of addition (n = 1), multiplication (n = 2), and exponentiation (n = 3).
Pentation is the next hyperoperation (infinite sequence of arithmetic operations, based off the previous one each time) after tetration and before hexation. It is defined as iterated (repeated) tetration (assuming right-associativity). This is similar to as tetration is iterated right-associative exponentiation. [1]
The term tetration, introduced by Goodstein in his 1947 paper Transfinite Ordinals in Recursive Number Theory [2] (generalizing the recursive base-representation used in Goodstein's theorem to use higher operations), has gained dominance. It was also popularized in Rudy Rucker's Infinity and the Mind.
However, for most operations, such as arithmetic operations, the result (value) does not depend on the representation of the inputs. For the decimal formats, any representation is valid, and the set of these representations is called a cohort. When a result can have several representations, the standard specifies which member of the cohort is ...
The register width of a processor determines the range of values that can be represented in its registers. Though the vast majority of computers can perform multiple-precision arithmetic on operands in memory, allowing numbers to be arbitrarily long and overflow to be avoided, the register width limits the sizes of numbers that can be operated on (e.g., added or subtracted) using a single ...
The aforementioned lack of associativity of floating-point operations in general means that compilers cannot as effectively reorder arithmetic expressions as they could with integer and fixed-point arithmetic, presenting a roadblock in optimizations such as common subexpression elimination and auto-vectorization. [66]