frac constellation library

This commit is contained in:
SheetJS 2024-04-24 04:40:31 -04:00
parent e273f11b46
commit 922b84e1e3

@ -0,0 +1,141 @@
title: Rational Approximation
hide_table_of_contents: true
<script src=""></script>
The SheetJS `frac` library computes rational approximations to floating point
numbers with bounded denominator. It is a core component in number formatting,
powering "Fraction with up to 1 digit" and related number formats.
The library is also available for standalone use on the SheetJS CDN[^1].
Source code and project documentation are hosted on the SheetJS git server at
## Live Demo
The formatted text is calculated from the specified number format and value.
Please [report an issue]( if a
particular format is not supported.
```jsx live
function SheetJSFrac() {
const [val, setVal] = React.useState(0.6994);
const [text, setText] = React.useState("");
const fmt = arr => `${(""+arr[1]).padStart(3)} / ${(""+arr[2]).padEnd(3)}`;
React.useEffect(() => {
if(typeof frac == "undefined") return setText("ERROR: Reload this page!");
let v = +val;
if(!isFinite(v)) return setText(`ERROR: ${val} is not a valid number!`);
try {
fmt(frac(val, 9)); setText("");
} catch(e) { setText("ERROR: " + (e && e.message || e)); }
}, [val]);
const g = { backgroundColor:"#C6EFCE", color:"#006100", whiteSpace:"pre-wrap" };
const b = { backgroundColor:"#FFC7CE", color:"#9C0006" };
return ( <table>
<tr><td><b>Number Value</b></td><td colspan="2">
<input type="text" value={val} onChange={e => setVal(}/>
<tr><td><b>Up to 1 Digit</b></td>
<td><code style={text?b:g}>{text||fmt(frac(val,9))}</code></td>
<td><code style={text?b:g}>{text||fmt(frac.cont(val,9))}</code></td>
<tr><td><b>Up to 2 Digits</b></td>
<td><code style={text?b:g}>{text||fmt(frac(val,99))}</code></td>
<td><code style={text?b:g}>{text||fmt(frac.cont(val,99))}</code></td>
<tr><td><b>Up to 3 Digits</b></td>
<td><code style={text?b:g}>{text||fmt(frac(val,999))}</code></td>
<td><code style={text?b:g}>{text||fmt(frac.cont(val,999))}</code></td>
</table> );
## API
In the browser, the library exports the `frac` global. In NodeJS, the library
default export is a function.
#### Algorithms
The "Mediant" algorithm (`frac` in the browser; the default export in NodeJS)
calculates the exact solution.
The "Continued Fractions" algorithm (`frac.cont` in the browser; the `cont`
field in the NodeJS export) calculates an approximate solution. Excel uses this
approach since the mediant algorithm has exponential worst-case performance.
:::caution LibreOffice bugs
There are known rounding bugs in LibreOffice[^2] which result in inaccurate
fraction calculations.
The LibreOffice developers believe these numerical errors are desirable:
> "We ignore the last two bits for many stuff to improve the user experience."
It is strongly recommended to use a different spreadsheet tool for accurate data
processing involving fractions and numeric data.
#### Functions
Both functions accept three arguments:
var fract_mediant = frac(value, denominator, mixed);
var frac_cont = frac.cont(value, denominator, mixed);
- `value`: original value
- `D`: maximum denominator (e.g. 99 = "Up to 2 digits")
- `mixed`: if `true`, return a mixed fraction.
The return value is an array with three integers:
var [ int, num, den ] = result;
- `int` (first element) represents the integer part of the estimate.
- `num` (second element) is the numerator of the fraction
- `den` (second element) is the positive denominator of the fraction
The estimate can be recovered from the array:
var estimate = int + num / den;
If `mixed` is `false`, then `int = 0` and `0` &leq; `|num|` &lt; `den` &leq; `D`
If `mixed` is `true`, then `0` &leq; `num` &lt; `den` &leq; `D`
:::info Negative Values
When `mixed` is true, `int` will be the floor of the result. For example, in
var result = frac( -0.125 , 9, true);
the result will be `[ -1, 7, 8 ]`. This is interpreted as
-0.125 ~ (-1) + (7/8)
[^1]: See for more details.
[^2]: See [issue #83511]( in the LibreOffice bug tracker.