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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]
One may also round half away from zero (or round half toward infinity), a tie-breaking rule that is commonly taught and used, namely: If the fractional part of x is exactly 0.5, then y = x + 0.5 if x is positive, and y = x − 0.5 if x is negative.
In languages with typed pointers like C, the increment operator steps the pointer to the next item of that type -- increasing the value of the pointer by the size of that type. When a pointer (of the right type) points to any item in an array, incrementing (or decrementing) makes the pointer point to the "next" (or "previous") item of that array.
For tie-breaking, Python 3 uses round to even: round(1.5) and round(2.5) both produce 2. [124] Versions before 3 used round-away-from-zero: round(0.5) is 1.0, round(-0.5) is −1.0. [125] Python allows Boolean expressions with multiple equality relations in a manner that is consistent with general use in mathematics.
PHP: The BC Math module provides arbitrary precision mathematics. PicoLisp: supports arbitrary precision integers. Pike: the built-in int type will silently change from machine-native integer to arbitrary precision as soon as the value exceeds the former's capacity. Prolog: ISO standard compatible Prolog systems can check the Prolog flag ...
is how one would use Fortran to create arrays from the even and odd entries of an array. Another common use of vectorized indices is a filtering operation. Consider a clipping operation of a sine wave where amplitudes larger than 0.5 are to be set to 0.5. Using S-Lang, this can be done by y = sin(x); y[where(abs(y)>0.5)] = 0.5;
Rather than storing values as a fixed number of bits related to the size of the processor register, these implementations typically use variable-length arrays of digits. Arbitrary precision is used in applications where the speed of arithmetic is not a limiting factor, or where precise results with very large numbers are required.
The main objective of interval arithmetic is to provide a simple way of calculating upper and lower bounds of a function's range in one or more variables. These endpoints are not necessarily the true supremum or infimum of a range since the precise calculation of those values can be difficult or impossible; the bounds only need to contain the function's range as a subset.