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canonical composition algorithm

Starting from the second character in the coded character sequence (of a Canonical Decomposition or Compatibility Decomposition) and proceeding sequentially to the final character, perform the following steps: R1 Seek back (left) in the coded character sequence from the character C to find the last Starter L preceding C in the character sequence.

R2 If there is such an L, and C is not blocked from L, and there exists a Primary Composite P which is canonically equivalent to the sequence , then replace L by P in the sequence and delete C from the sequence.

  • When the algorithm completes, all Non-blocked Pairs canonically equivalent to a Primary Composite will have been systematically replaced by those Primary Composites.
  • The replacement of the Starter L in R2 requires continuing to check the succeeding characters until the character at that position is no longer part of any Non-blocked Pair that can be replaced by a Primary Composite. For example, consider the following hypothetical coded character sequence: . None of the first three combining marks forms a Primary Composite with the letter z. However, the fourth combining mark in the sequence, acute, does form a Primary Composite with z, and it is not Blocked from the z. Therefore, R2 mandates the replacement of the sequence with , even though there are three other combining marks intervening in the sequence.
  • The character C in R1 is not necessarily a non-starter. It is necessary to check all characters in the sequence, because there are sequences where both L and C are Starters, yet there is a Primary Composite P which is canonically equivalent to that sequence. For example, Indic two-part vowels often have canonical decompositions into sequences of two spacing vowel signs, each of which has Canonical_Combining_Class=0 and which is thus a Starter by definition.
Nevertheless, such a decomposed sequence has an equivalent Primary Composite.

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