Rounding Functions in Programming Languages
Most programming languages provide functions or special syntax to round fractional numbers in various ways. The earliest numeric languages, such as FORTRAN and C, would provide only one method, usually truncation (towards zero). This default method could be implied in certain contexts, such as when assigning a fractional number to an integer variable, or using a fractional number as an index of an array. Other kinds of rounding had to be programmed explicitly; for example, rounding a positive number to the nearest integer could be implemented by adding 0.5 and truncating.
In the last decades, however, the syntax and/or the standard libraries of most languages have commonly provided at least the four basic rounding functions (up, down, to nearest, and towards zero). The tie-breaking method may vary depending the language and version, and/or may be selectable by the programmer. Several languages follow the lead of the IEEE-754 floating-point standard, and define these functions as taking a double precision float argument and returning the result of the same type, which then may be converted to an integer if necessary. Since the IEEE double precision format has 52 fraction bits, this approach may avoid spurious overflows in languages have 32-bit integers. Some languages, such as PHP, provide functions that round a value to a specified number of decimal digits, e.g. from 4321.5678 to 4321.57 or 4300. In addition, many languages provide a printf or similar string formatting function, which allows one to convert a fractional number to a string, rounded to a user-specified number of decimal places (the precision). On the other hand, truncation (round to zero) is still the default rounding method used by many languages, especially for the division of two integer values.
On the opposite, CSS and SVG do not define any specific maximum precision for numbers and measurements, that are treated and exposed in their DOM and in their IDL interface as strings as if they had infinite precision, and do not discriminate between integers and floating point values; however, the implementations of these languages will typically convert these numbers into IEEE-754 double floating points before exposing the computed digits with a limited precision (notably within standard Javascript or ECMAScript interface bindings).
Read more about this topic: Rounding
Famous quotes containing the words rounding, functions, programming and/or languages:
“People forget that it is the eye that makes the horizon, and the rounding mind’s eye which makes this or that man a type or representative of humanity with the name of hero or saint.”
—Ralph Waldo Emerson (1803–1882)
“Let us stop being afraid. Of our own thoughts, our own minds. Of madness, our own or others’. Stop being afraid of the mind itself, its astonishing functions and fandangos, its complications and simplifications, the wonderful operation of its machinery—more wonderful because it is not machinery at all or predictable.”
—Kate Millett (b. 1934)
“If there is a price to pay for the privilege of spending the early years of child rearing in the driver’s seat, it is our reluctance, our inability, to tolerate being demoted to the backseat. Spurred by our success in programming our children during the preschool years, we may find it difficult to forgo in later states the level of control that once afforded us so much satisfaction.”
—Melinda M. Marshall (20th century)
“Wealth is so much the greatest good that Fortune has to bestow that in the Latin and English languages it has usurped her name.”
—William Lamb Melbourne, 2nd Viscount (1779–1848)