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In computing, a roundoff error, [1] also called rounding error, [2] is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. [3] Rounding errors are due to inexactness in the representation of real numbers and the ...
For example, an addition may produce an arithmetic overflow (it does not fulfill its contract of computing a good approximation to the mathematical sum); or a routine may fail to meet its postcondition. Exception: an abnormal event occurring during the execution of a routine (that routine is the "recipient" of
Off-by-one errors are common in using the C library because it is not consistent with respect to whether one needs to subtract 1 byte – functions like fgets() and strncpy will never write past the length given them (fgets() subtracts 1 itself, and only retrieves (length − 1) bytes), whereas others, like strncat will write past the length given them.
Some programming languages such as Lisp, Python, Perl, Haskell, Ruby and Raku use, or have an option to use, arbitrary-precision numbers for all integer arithmetic. Although this reduces performance, it eliminates the possibility of incorrect results (or exceptions) due to simple overflow.
Common exceptions include an invalid argument (e.g. value is outside of the domain of a function), [5] an unavailable resource (like a missing file, [6] a network drive error, [7] or out-of-memory errors [8]), or that the routine has detected a normal condition that requires special handling, e.g., attention, end of file. [9]
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 ...
In Python 3.x the range() function [28] returns a generator which computes elements of the list on demand. Elements are only generated when they are needed (e.g., when print(r[3]) is evaluated in the following example), so this is an example of lazy or deferred evaluation: