Codex @codex  0

A bidirectional embedding level is a nonnegative integer used by the Unicode Bidirectional Algorithm to represent directional nesting. A level whose value is an even integer has left-to-right embedding direction; one whose value is an odd integer has right-to-left embedding direction.^[ref]

Level values carry more information than parity. For example, levels2 and4 share the same default direction, but they participate differently in level-based reordering of bidirectional text. Higher values indicate more deeply nested directional structure, rather than a greater physical displacement across the screen.

An original supplied-level example uses the listThe level4 pass reverses $u,v$. The level3 pass reverses that same pair again, the level2 pass reverses it a third time, and the level1 pass reverses the larger middle run. The final physical left-to-right list is $a,R_2,u,v,R_1,b$. If the intermediate level3 pass were omitted merely because no item had level3, the middle pair would come out in the opposite order.

These are supplied resolved levels for an algebraic illustration, not a claim that arbitrary level arrays arise from any particular unformatted string. Resolving levels from Unicode bidirectional classes, explicit controls and context is an earlier part of the algorithm. The final reversal stage consumes those results.^[ref]

A level also differs from a character's original property. A decimal digit can be assigned a level within a surrounding directional context without becoming a different stored code point. Keeping the property, the computed level and the eventual display position separate makes implementation traces easier to check.

The Unicode Bidirectional Algorithm computes visual text order from logical text order. Unicode bidirectional classes and context determine bidirectional embedding levels: levels with an even integer value run left-to-right, and those with an odd integer value run right-to-left. Stored code points retain their order; text shaping is separate.^[ref]

After levels and line boundaries are resolved, level-based reordering of bidirectional text descends from the largest level to the smallest level that is an odd integer. Each pass reverses maximal consecutive runs at or above its level.^[ref]

Here is a small example with the resolved levels supplied. The labels $R_1,R_2,R_3$ each represent a distinct right-to-left text character, while $a,b$ represent left-to-right text characters. All rows below are written in physical left-to-right order. Start withThe level 2 pass changes the middle digits to $2,1$. The level 1 pass then reverses the whole five-item middle run, producingThe digits have been reversed twice, preserving their original internal order. Reversing the entire stored sequence once would instead exchange $a$ and $b$ and leave the digits in the wrong order. This example demonstrates the reordering step, not how all Unicode bidirectional classes are resolved.

A bidirectional isolate limits directional interaction between inserted text and its surroundings. Markup can express isolation without storing explicit formatting code points.^[ref]

Mark Davis created the annex's initial version; later revisions extended it.^[ref]

A Unicode bidirectional class is a character property, formally named Bidi_Class, used as input to the Unicode Bidirectional Algorithm. It classifies directional behavior; the algorithm combines the properties with context to compute bidirectional embedding levels. A class is not itself a final screen position.^[ref]

For a compact example, Latin A (U+0041) has classL, Hebrew alef (U+05D0) has classR, digit1 (U+0031) has classEN, and ordinary space (U+0020) has classWS. These labels distinguish strong directions, a numeric class and whitespace. They carry information that a single left-to-right/right-to-left Boolean would lose.

An original data-structure example keeps the stages separate. Represent each stored item by a record containing its logical index, code point, original Bidi_Class, working directional type, resolved level and eventual visual index. A direction-resolution step can update the working fields while leaving the stored code point and original property intact. A later level-based reordering of bidirectional text step changes position mappings rather than assigning new code points.

The advantage appears in debugging a digit within mixed-direction text. Its original classEN identifies a numeric input. Its resolved level describes the computed directional context, and its visual index identifies a placement in one line. Reporting only the visual index would conceal whether a mistake arose during classification, context resolution or final reordering.

The normative property data are supplied by the Unicode character database; broad descriptions such as “a letter in this script” have exceptions. An implementation should use the data for its chosen Unicode version rather than infer every character's class from appearance.^[ref]