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In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x, denoted ⌈x⌉ or ceil(x). [1]
One method, more obscure than most, is to alternate direction when rounding a number with 0.5 fractional part. All others are rounded to the closest integer. Whenever the fractional part is 0.5, alternate rounding up or down: for the first occurrence of a 0.5 fractional part, round up, for the second occurrence, round down, and so on.
SmartXML big numbers can have up to 100,000,000 decimal digits and up to 100,000,000 whole digits. Standard ML: The optional built-in IntInf structure implements the INTEGER signature and supports arbitrary-precision integers. Tcl: As of version 8.5 (2007), integers are arbitrary-precision by default. (Behind the scenes, the language switches ...
The functions that operate on integers, such as abs, labs, div, and ldiv, are instead defined in the <stdlib.h> header (<cstdlib> header in C++). Any functions that operate on angles use radians as the unit of angle. [1] Not all of these functions are available in the C89 version of the standard. For those that are, the functions accept only ...
Saturation arithmetic for integers has also been implemented in software for a number of programming languages including C, C++, such as the GNU Compiler Collection, [2] LLVM IR, and Eiffel. Support for saturation arithmetic is included as part of the C++26 Standard Library. This helps programmers anticipate and understand the effects of ...
round up (toward +∞; negative results thus round toward zero) round down (toward −∞; negative results thus round away from zero) round toward zero (truncation; it is similar to the common behavior of float-to-integer conversions, which convert −3.9 to −3 and 3.9 to 3)
HP has never made another calculator specifically for programmers, [2] but has incorporated many of the HP-16C's functions in later scientific and graphing calculators, for example the HP-42S (1988) and its successors. Like many other vintage HP calculators, the HP-16C is now highly sought-after by collectors. [14]
This rounding rule is more accurate but more computationally expensive. Rounding so that the last stored digit is even when there is a tie ensures that it is not rounded up or down systematically. This is to try to avoid the possibility of an unwanted slow drift in long calculations due simply to a biased rounding.