> For the complete documentation index, see [llms.txt](https://php-fhir-tools.ardenexal.net/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://php-fhir-tools.ardenexal.net/fhirpath/functions/math.md).

# Math

Math functions operate on numeric values. Single-value functions (`abs()`, `ceiling()`, etc.) expect a single-item numeric input; aggregate functions (`sum()`, `min()`, `max()`, `avg()`) operate over the whole collection.

| Function             | Description                                               | Example                       |
| -------------------- | --------------------------------------------------------- | ----------------------------- |
| `sum()`              | Sum of all numeric items in the collection.               | `(1 \| 2 \| 3).sum()` → `6`   |
| `abs()`              | Absolute value.                                           | `(-5).abs()` → `5`            |
| `ceiling()`          | Smallest integer greater than or equal to the input.      | `(1.1).ceiling()` → `2`       |
| `floor()`            | Largest integer less than or equal to the input.          | `(1.9).floor()` → `1`         |
| `truncate()`         | Integer part, dropping any fraction.                      | `(1.9).truncate()` → `1`      |
| `round([precision])` | Rounds to the given number of decimal places (default 0). | `(3.14159).round(2)` → `3.14` |
| `exp()`              | e raised to the power of the input.                       | `(1).exp()` → `2.718...`      |
| `ln()`               | Natural logarithm.                                        | `(2.718281828).ln()` → `1.0`  |
| `log(base)`          | Logarithm to the given base.                              | `(100).log(10)` → `2`         |
| `power(exponent)`    | Raises the input to `exponent`.                           | `(2).power(3)` → `8`          |
| `sqrt()`             | Square root.                                              | `(9).sqrt()` → `3`            |
| `min()`              | Smallest item in the collection.                          | `(3 \| 1 \| 2).min()` → `1`   |
| `max()`              | Largest item in the collection.                           | `(3 \| 1 \| 2).max()` → `3`   |
| `avg()`              | Arithmetic mean of the collection.                        | `(2 \| 4 \| 6).avg()` → `4`   |

## Precision & boundaries

These three functions report or derive the precision of a value. They accept a decimal, integer, date, dateTime, or time, using FHIRPath positional precision numbers (e.g. `YYYY`=4, `YYYY-MM`=6, `YYYY-MM-DD`=8 for dates; digits after the decimal point for numbers). `lowBoundary()` and `highBoundary()` take an optional output-precision argument.

| Function                    | Description                                                                                                                                                          | Example                                |
| --------------------------- | -------------------------------------------------------------------------------------------------------------------------------------------------------------------- | -------------------------------------- |
| `precision()`               | Number of significant positions in the input. Trailing zeros on a decimal are preserved.                                                                             | `(1.58700).precision()` → `5`          |
| `lowBoundary([precision])`  | Lowest value in the natural range the input represents. For numbers, `value - 0.5×10^-precision`; for dates/times, fills unspecified components with their minimum.  | `(1.587).lowBoundary()` → `1.5865...`  |
| `highBoundary([precision])` | Highest value in the natural range the input represents. For numbers, `value + 0.5×10^-precision`; for dates/times, fills unspecified components with their maximum. | `(1.587).highBoundary()` → `1.5875...` |


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