Patrom:Order of magnitude/doc

This is a documentation subpage for Patrom:Order of magnitude.
It contains usage information, categories, interlanguage links and other content that is not part of the original patrom page.

Usage

This template calculates the (decimal) order of magnitude of numbers within the ranges 10³⁰⁰ to 10⁻³⁰⁰ and −10⁻³⁰⁰ to −10³⁰⁰.

The acceptable input and the output produced are optimised for use in other templates.

The hyphen (not a true minus sign) is used for negative numbers.
No separator is used for thousands.
The template gives 0 for 0. Although, strictly speaking, this is mathematically incorrect it has been designed this way so as to be more useful in other templates. An important example of this is that when used by (tl) 0 °C or 0 °F is considered to be on the same order of magnitude as ±1 °C or ±1 °F respectively.

Examples

{{Order of magnitude|123400}} → 5 [1]
{{Order of magnitude|12340}} → 4 [2]
{{Order of magnitude|1234}} → 3 [3]
{{Order of magnitude|123.4}} → 2 [4]
{{Order of magnitude|12.34}} → 1 [5]
{{Order of magnitude|1.234}} → 0 [6]
{{Order of magnitude|.1234}} → -1 [7]
{{Order of magnitude|.01234}} → -2 [8]
{{Order of magnitude|0}} → 0 [9]
{{Order of magnitude}} gives 0 [10]

Incorrect usage

The input must be an unformatted number, or the template will emit errors:

{{Order of magnitude|}} → Expression error: Unexpected = operator
{{Order of magnitude|123,400}} → Expression error: Unrecognised punctuation character ","
{{Order of magnitude|foo}} → Expression error: Unrecognised word "foo"

Technical points

This template calculates the order of magnitude of a number, using the natural logarithm of the absolute value of the number, divided by the log of 10. The amount is adjusted for truncation error in the digital format, and the floor number of the results is used. The magnitude of fractions, such as 0+1/1000 (-3), will also be calculated. The code uses four expansion-depth levels.