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CLDR-18848 Specify the algorithm for compact number formatting (#5097)
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‎docs/ldml/tr35-modifications.md‎

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@@ -79,8 +79,9 @@ There is also now a mechanism for finding the region code from short timezone id
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### Numbers
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* [Plural rules syntax](tr35-numbers.md#plural-rules-syntax) Added substantial clarifications and new examples.
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The order of execution is also clearly specified.
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* [Rule-Based Number Formatting]() Added a full specification.
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The rules have been converted to a “flat” format, which is easier for clients to handle (the old format will be retained for one more release).
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* [Compact Number Formats](tr35-numbers.md#compact-number-formats) Specified the mechanism for formatting compact numbers more precisely.
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* [Rule-Based Number Formatting]() The rules are also now represented by a new XML structure with a “flat” format,
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which is easier for clients to handle (the old format will be retained for one more release).
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### Units of Measurement
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* [Unit Syntax](tr35-general.md#unit-syntax) Simplified the EBNF `product_unit` and added an additional well-formedness constraint for mixed units.

‎docs/ldml/tr35-numbers.md‎

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@@ -372,50 +372,102 @@ A pattern `type` attribute is used for _compact number formats_, such as the fol
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```xml
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<decimalFormatLength type="long">
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<decimalFormat>
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<pattern type="1000" count="one">0 millier</pattern>
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<pattern type="1000" count="other">0 milliers</pattern>
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<pattern type="10000" count="one">00 mille</pattern>
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<pattern type="10000" count="other">00 mille</pattern>
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<pattern type="100000" count="one">000 mille</pattern>
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<pattern type="100000" count="other">000 mille</pattern>
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<pattern type="1000000" count="one">0 million</pattern>
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<pattern type="1000000" count="other">0 millions</pattern>
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…
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</decimalFormat>
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<decimalFormat>
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<pattern type="1000" count="one">0 thousand</pattern>
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<pattern type="1000" count="other">0 thousand</pattern>
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<pattern type="10000" count="one">00 thousand</pattern>
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<pattern type="10000" count="other">00 thousand</pattern>
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<pattern type="100000" count="one">000 thousand</pattern>
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<pattern type="100000" count="other">000 thousand</pattern>
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<pattern type="1000000" count="one">0 million</pattern>
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<pattern type="1000000" count="other">0 million</pattern>
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<pattern type="10000000" count="one">00 million</pattern>
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<pattern type="10000000" count="other">00 million</pattern>
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…
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</decimalFormat>
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</decimalFormatLength>
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<decimalFormatLength type="short">
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<decimalFormat>
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<pattern type="1000" count="one">0 K</pattern>
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<pattern type="1000" count="other">0 K</pattern>
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<pattern type="10000" count="one">00 K</pattern>
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<pattern type="10000" count="other">00 K</pattern>
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<pattern type="100000" count="one">000 K</pattern>
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<pattern type="100000" count="other">000 K</pattern>
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<pattern type="1000000" count="one">0 M</pattern>
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<pattern type="1000000" count="other">0 M</pattern>
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…
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</decimalFormat>
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<decimalFormat>
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<pattern type="1000" count="one">0K</pattern>
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<pattern type="1000" count="other">0K</pattern>
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<pattern type="10000" count="one">00K</pattern>
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<pattern type="10000" count="other">00K</pattern>
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<pattern type="100000" count="one">000K</pattern>
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<pattern type="100000" count="other">000K</pattern>
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<pattern type="1000000" count="one">0M</pattern>
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<pattern type="1000000" count="other">0M</pattern>
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<pattern type="10000000" count="one">00M</pattern>
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<pattern type="10000000" count="other">00M</pattern>
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…
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</decimalFormat>
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</decimalFormatLength>
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…
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<currencyFormatLength type="short">
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<currencyFormat type="standard">
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<pattern type="1000" count="one">0 K ¤</pattern>
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<pattern type="1000" count="other">0 K ¤</pattern>
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<pattern type="10000" count="one">00 K ¤</pattern>
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<pattern type="10000" count="other">00 K ¤</pattern>
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<pattern type="100000" count="one">000 K ¤</pattern>
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<pattern type="100000" count="other">000 K ¤</pattern>
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<pattern type="1000000" count="one">0 M ¤</pattern>
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<pattern type="1000000" count="other">0 M ¤</pattern>
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…
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<pattern type="1000" count="one">¤0K</pattern>
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<pattern type="1000" count="one" alt="alphaNextToNumber">¤ 0K</pattern>
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<pattern type="1000" count="other">¤0K</pattern>
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<pattern type="1000" count="other" alt="alphaNextToNumber">¤ 0K</pattern>
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<pattern type="10000" count="one">¤00K</pattern>
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<pattern type="10000" count="one" alt="alphaNextToNumber">¤ 00K</pattern>
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<pattern type="10000" count="other">¤00K</pattern>
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<pattern type="10000" count="other" alt="alphaNextToNumber">¤ 00K</pattern>
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<pattern type="100000" count="one">¤000K</pattern>
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<pattern type="100000" count="one" alt="alphaNextToNumber">¤ 000K</pattern>
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<pattern type="100000" count="other">¤000K</pattern>
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<pattern type="100000" count="other" alt="alphaNextToNumber">¤ 000K</pattern>
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<pattern type="1000000" count="one">¤0M</pattern>
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<pattern type="1000000" count="one" alt="alphaNextToNumber">¤ 0M</pattern>
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<pattern type="1000000" count="other">¤0M</pattern>
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<pattern type="1000000" count="other" alt="alphaNextToNumber">¤ 0M</pattern>
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<pattern type="10000000" count="one">¤00M</pattern>
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<pattern type="10000000" count="one" alt="alphaNextToNumber">¤ 00M</pattern>
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<pattern type="10000000" count="other">¤00M</pattern>
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<pattern type="10000000" count="other" alt="alphaNextToNumber">¤ 00M</pattern> …
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</currencyFormat>
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</currencyFormatLength>
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```
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Formats can be supplied for numbers (as above) or for currencies or other units. They can also be used with ranges of numbers, resulting in formatting strings like “$10K” or “$3–7M”.
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To format a number N, the greatest type less than or equal to N is used, with the appropriate plural category. N is divided by the type, after removing the number of zeros in the pattern, less 1. APIs supporting this format should provide control over the number of significant or fraction digits.
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To format a number N, use the following steps:
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Notes:
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- A _letter grapheme cluster_ is a grapheme cluster that starts with a letter and then 0 or more combining marks.
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For example, each of the following are are _letter grapheme clusters_: \<q>, \<q, _combining ring above_>, \<q, _combining ring above_, _acute accent_>.
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- All of the pattern elements with the same type must have the same number of zeros in the pattern element value.
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- The examples use N = 123456, the currency = CAD, and the currency symbol string = "$CA"
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1. Let P be the pattern element with greatest type less than or equal to N, and any count value.
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* P = `<pattern type="100000" count="**one**">¤000K</pattern>`
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2. Let V be the pattern element value.
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* V = "¤000K"
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3. If the element value of P is "0", then use the corresponding non-compact number formatting instead, and skip the rest of these steps — but adjust the precision as described below.
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* For example, instead of `currencyFormat` `<pattern type="10000" count="one">¤00K</pattern>`, use `<pattern>¤#,##0.00</pattern>`.
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4. If P is a currency format, look at the currency symbol string, and the position of the currency symbol ¤ in the pattern element value.
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If ¤ is immediately to the left of a 0 and the currency string ends with a _letter grapheme cluster_ (eg, "$CA"),
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or to the right and the currency starts with a letter (eg, "CA$"),
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then switch to the `alt=alphaNextToNumber` pattern, if there is one.
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* P = `<pattern type="100000" count="**one**" alt="alphaNextToNumber">¤ 000K</pattern>` // with the currency symbol "CA$"
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* V = "¤ 000K"
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5. Let Z be the number of 0 characters in V, minus 1.
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* Z = 2
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6. Let T be the numeric value of the `type` attribute value, after removing the final Z zeros.
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* "100000" removing "00" = "1000"
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* T = 1000
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7. Let N' be N / T
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* N = 123.456
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8. Determine the plural category of N, based on the numeric precision settings (the min/max number of significant or fraction digits), and switch the value of V if necessary.
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* In this case, the plural category of 123.456 in English with any precision is "other", so the
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* P = `<pattern type="100000" count="**other**" alt="alphaNextToNumber">¤ 000K</pattern>`
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* V = "¤ 000K"
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* For the short compact formats, it doesn't make a difference for English, but may for other locales!
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9. Let V' be the same as V, but replacing that sequence of zeros by "{0}".
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* V' = "¤ {0}K"
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10. Let F be N' formatted according to V' and the numeric precision settings.
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* F = "$CA 123K" // where the precision is min = max = 3 significant digits
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* F = "$CA 123.4K" // where the precision is min = max = 1 fraction digit
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The default pattern for any type that is not supplied is the special value “0”, as in the following. The value “0” must be used when a child locale overrides a parent locale to drop the compact pattern for that type and use the default pattern.
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Formatting 1200 in USD would result in “1.2 K $”, while 990 implicitly maps to the special value “0”, which maps to `<currencyFormat type="standard"><pattern>#,##0.00 ¤</pattern>`, and would result in simply “990 $”.
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The short format is designed for UI environments where space is at a premium, and should ideally result in a formatted string no more than about 6 em wide (with no fractional digits).
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The short non-currency format is designed for UI environments where space is at a premium, and should ideally result in a formatted string no more than about 6 em wide (with no fractional digits).
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The short currency format will include currency symbols, and should ideally be no more than 8 em in width.
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#### <a name="Currency_Formats" href="#Currency_Formats">Currency Formats</a>
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