Compressing entropy tables with interpolative coding
A symbol sequence is entropy-encoded using a table of symbol occurrences, and an integer value f is used to encode the table of symbol occurrences. The integer value f is used to adaptively decode the table of symbol occurrences, including (i) decoding each entry of a cumulative table of symbol occurrences by successively subdividing decoding ranges of the cumulative table of symbol occurrences at their respective middle indexes and, for each decoding range: calculating, from decoded entries of the cumulative table of symbol occurrences, an entry at a first index+f mod(an entry at a last index−the entry at the first index+1) to decode an entry at the respective middle index of the decoding range, and calculating f div(the entry at the last index−the entry at the first index+1) to update f; (ii) calculating the table of symbol occurrences from the decoded entries of the cumulative table of symbol occurrences; and applying the decoded table of symbol occurrences to entropy-decode the received encoded symbol sequence.
1. A decoder comprising at least one processor and/or processing circuit configured to perform operations comprising:
access an integer value f that encodes a table of symbol occurrences;
use the integer value f to adaptively decode the table of symbol occurrences, including:
(i) decode each entry of a cumulative table of symbol occurrences by successively subdividing decoding ranges of the cumulative table of symbol occurrences at their respective middle indexes and, for each decoding range:
calculate, from decoded entries of the cumulative table of symbol occurrences, an entry at a first index+f mod(an entry at a last index−the entry at the first index+1) to decode an entry at the respective middle index of the decoding range, and calculate f div(the entry at the last index−the entry at the first index+1) to update f; and
(ii) calculate the table of symbol occurrences from the decoded entries of the cumulative table of symbol occurrences.
2. The decoder of claim 1 wherein the operations further include apply the calculated table of symbol occurrences to entropy-decode an encoded symbol sequence.
3. The decoder of claim 2 wherein the operations further comprise execute at least a portion of the entropy-decoded symbol sequence.
4. The decoder of claim 2 wherein the operations further comprise stream at least a portion of the entropy-decoded symbol sequence and/or information derived therefrom.
5. The decoder of claim 1 wherein the operations further comprise:
receiving a second integer value m,
using a zero value as a lower bound of the cumulative table of symbol occurrences, and
using the received second integer value m as an upper bound of the cumulative table of symbol occurrences.
6. The decoder of claim 5 wherein the operations further comprise obtaining the received second integer value m from a header metadata of the encoded symbol sequence.
7. The decoder of claim 1 wherein the operations further comprise:
receiving a second integer value m,
inserting a zero value as a first entry of the cumulative table of symbol occurrences, and
inserting the received second integer value m as a last entry of the cumulative table of symbol occurrences.
8. The decoder of claim 1 wherein the operations further comprise decode the entries of the cumulative table by traversing a tree of subdivided decoding ranges and calculate an arithmetic division at each node of the tree before child nodes of said each node.
9. The decoder of claim 8 wherein the operations further comprise decoding the entries of the cumulative table by traversing the tree of subdivided decoding ranges in a depth-first pre-order and calculating an arithmetic division at each node of the tree.
10. The decoder of claim 1 wherein the received integer value f is represented as a big number (bignum).
11. The decoder of claim 1 wherein the operations further comprise renormalizing to allow faster and more memory-efficient decoding.
12. The decoder of claim 1 wherein the encoded symbol sequence comprises an aggregation of different components comprising token, literal length, literals, offset, and match length, of sequences of an LZ4 block.
13. A non-transitory storage configured to store instructions that cause at least one processor and/or processing circuit to perform operations comprising:
access an integer value f that encodes a table of symbol occurrences;
use the integer value f to adaptively decode the table of symbol occurrences, including:
(i) decode each entry of a cumulative table of symbol occurrences by successively subdividing decoding ranges of the cumulative table of symbol occurrences at their respective middle indexes and, for each decoding range:
calculate, from decoded entries of the cumulative table of symbol occurrences, an entry at a first index+f mod(an entry at a last index−the entry at the first index+1) to decode an entry at the respective middle index of the decoding range, and
calculate f div(the entry at the last index−the entry at the first index+1) to update f; and
(ii) calculate the table of symbol occurrences from the decoded entries of the cumulative table of symbol occurrences.
14. The non-transitory storage of claim 13 wherein the operations further comprise apply the calculated table of symbol occurrences to entropy-decode an encoded symbol sequence.
15. The non-transitory storage of claim 14 wherein the operations further comprise use at least a portion of the entropy-decoded symbol sequence to stream data representing at least a portion of a graphical user interaction.
16. The non-transitory storage of claim 14 wherein the operations further comprise execute at least a portion of the entropy-decoded symbol sequence.
17. The non-transitory storage of claim 14 wherein the operations further comprise stream information based on at least a portion of the entropy-decoded symbol sequence.
18. The non-transitory storage of claim 14 wherein the encoded symbol sequence comprises an aggregation of different components comprising token, literal length, literals, offset, and match length, of sequences of an LZ4 block.
19. The non-transitory storage of claim 14 wherein applying comprises applying Asymmetric Numeral Systems (ANS) entropy decoding to decode the received encoded symbol sequence.
20. The non-transitory storage of claim 13 wherein the operations further comprise iterating the successively subdividing and the calculating for each decoding range.
21. The non-transitory storage of claim 13 wherein the operations further comprise recursing the successively subdividing and the calculating for each decoding range.
22. The non-transitory storage of claim 14 wherein the operations further comprise independently decoding segments of the encoded symbol sequence resulting from entropy-based binary segmentation of the symbol sequence and reconstructing the symbol sequence based on segment headers.
23. The non-transitory storage of claim 13 wherein the operations further comprise:
receiving a second integer value m,
using a zero value as a lower bound of the cumulative table of symbol occurrences, and
using the received second integer value m as an upper bound of the cumulative table of symbol occurrences.
24. The non-transitory storage of claim 23 wherein the operations further comprise obtaining the received second integer value m from a header metadata of the encoded symbol sequence.
25. The non-transitory storage of claim 13 wherein the operations further comprise:
receiving a second integer value m,
inserting a zero value as a first entry of the cumulative table of symbol occurrences, and
inserting the received second integer value m as a last entry of the cumulative table of symbol occurrences.
26. The non-transitory storage of claim 13 wherein the operations further comprise decode the entries of the cumulative table by traversing a tree of subdivided decoding ranges and calculating an arithmetic division at each node of the tree before child nodes of said each node.
27. The non-transitory storage of claim 26 wherein the operations further comprise decoding the entries of the cumulative table by traversing the tree of subdivided decoding ranges in a depth-first pre-order and calculating an arithmetic division at each node of the tree.
28. The non-transitory storage of claim 13 wherein the received integer value f is represented as a big number (bignum).
29. The non-transitory storage of claim 13 wherein the operations further comprise renormalizing to allow faster and more memory-efficient decoding.
30. The non-transitory storage of claim 13 wherein the operations further comprise using only integer arithmetic, shifts, logic operations, loads and stores to recover entries of the table of symbol occurrences from integer value f.