Bits and Pieces

Fraction(): approximate a number as a common fraction

The Fraction() function approximates a number as a common fraction. For example, Fraction( 0.625, 16 ) = 5/8. Here 0.625 is the number being approximated and 16 is the maximum allowed denominator of the result.

The function considers the maximum denominator only as a limit it cannot exceed, but uses the denominator that gives the most precise approximation. For example, Fraction( 3.1415926, 100 ) = 3 1/7, because 3 1/7 is the most precise approximation of 3.1415926 among all fractions with denominators less than 100; only 106 will give better precision.

Greatest Common Divisor

The function finds the greatest common divisor or greatest common factor for two numbers; for example, the greatest common divisor for 8 and 12 is 4. It's very simple and is widely available in fact, but I'll need it for some next posts, which are almost written now.

Rounding to a given number

These custom functions round a number “naturally”. For example, they can be used to round time to 15 minutes, or money to $.25, or just any number to a multiple of another number.

All the functions have the same syntax:

Round To( number, precision )

Round Down To( number, precision )

Round Up To( number, precision )

where number is the number to round and precision is the number to calculate the appropriate multiple of. For example, Round To( 13, 5 ) rounds 13 to the nearest multiple of 5, i.e. 15. The Round Up To() and Round Down To() round the number to higher or lower multiple of precision respectively.

Functions themselves are very simple:

Round To( number, precision )

Round( number / precision; 0 ) * precision

Round Down To( number, precision )

Floor( number / precision; 0 ) * precision

Round Up To( number, precision )

Ceiling( number / precision; 0 ) * precision

How to round time

Don't calculate the number of seconds: use the Time() function instead. For example, to round to an hour:

Round To( Time Field, Time( 1, 0, 0 ) )

to 15 minutes:

Round To( Time Field, Time( 0, 15, 0 ) )

You might also want to make a few constant custom functions: HOURS and MINUTES. These function must return Time( 1, 0, 0 ), Time( 0, 1, 0 ) respectively. (You could make a function for seconds, if you need them, but you'll need to select a name carefully, because Seconds is taken already.) With such functions your code will be more readable, like this:

Round To( Time Field, 2 * HOURS )

Round To( Time Field, 0.5 * HOURS )

Round To( Time Field, 15 * MINUTES )

Round To( Time Field, 1/2 * MINUTES )

There's yet another good use of this function: it can help to approximate a number to a common fraction. I'll write about this later.

Soundex and Miracode

Sometimes data are entered incorrectly because the person entering data mishears a word (most often a name); for example, enters Awbrey instead of Aubrey. This is especially true for English language, which has complex spelling rules. There are algorithms may help you to find all words that are pronounced closely to a sample. Given an English word, such an algorithm calculates a code that represents how the word sounds. Take a look at the following sample of an algorithm called Soundex:

Here A160 is the calculated code of Aubrey. You can see that similar names like Awbrey or Abra have the same code. Such algorithms are called phonetic or phonetic indexing algorithms; the word “index” reflects the fact that the algorithm takes a single word and calculates a phonetic code, which is same for all words that sound alike. (The latter is not always true because algorithms aren't perfect). The code can be used on its own for searching, sorting, grouping and so on. In FileMaker terms this means the calculated code can be stored and used for fast searching and making relationships:

Other algorithms that can make a fuzzy comparison work differently: they take two words and compare their similarity. This isn't as convenient as having an index of a word; every time you need to search for words similar to the given one you must check each record in a table. In FileMaker terms this means the calculation will be unstored and slow.

Most known of phonetic indexing algorithms are: the Soundex family, Daitch-Motokotoff Soundex, NYSIIS, Caverphone, and Metaphone; I wish I could be able to write a custom function for each. For now let's start from the simplest and the most famous Soundex and Miracode.