Tweak std/bzip2's "inverse of T" description
diff --git a/std/bzip2/README.md b/std/bzip2/README.md
index 5e0bcf0..e2627c7 100644
--- a/std/bzip2/README.md
+++ b/std/bzip2/README.md
@@ -241,13 +241,13 @@
(assigning 0, 1 and 2), all the 'b' elements (assigning 3), all the 'c'
elements (assinging 4) and all the 'r' elements (assigning 5).
- Index L T
- 0 c 4
- 1 a 0
- 2 r 5
- 3 a 1
- 4 a 2
- 5 b 3
+ Index L T
+ 0 c 4
+ 1 a 0
+ 2 r 5
+ 3 a 1
+ 4 a 2
+ 5 b 3
Starting with the *I* value given in the (g) bitslice, which was 1, calculate
*I*, *T[I]*, *T[T[I]]*, *T[T[T[I]]]*, etc to give [1, 0, 4, 2, 5, 3]. Indexing
@@ -258,23 +258,20 @@
## Alternative BWT Inversion
It's not in the BWT technical report, but instead of walking *I*, *T[I]*,
-*T[T[I]]*, etc, an alternative but equivalent algorithm starts with the *Index
-L T* table but then sorts the rows by *T*, modifying the *Index* and *T*
-columns (to produce *Index2* and *T2*) but leaving the *L* column unchanged.
-For example *Index == 4* matches *T == 2*, so *T2 == 2* matches *Index2 == 4*.
+*T[T[I]]*, etc, an alternative but equivalent algorithm works on *U*, the
+inverse of the *T* vector. For example *T[4] == 2* and so *U[2] == 4*.
- Index2 L T2
- 1 c 0
- 3 a 1
- 4 r 2
- 5 a 3
- 0 a 4
- 2 b 5
+ Index L T F U
+ 0 c 4 a 1
+ 1 a 0 a 3
+ 2 r 5 a 4
+ 3 a 1 b 5
+ 4 a 2 c 0
+ 5 b 3 r 2
-Our original *I* value was 1, and when *T2* is 1, *Index2* is 3. Call this
-value *I2*. Calculate *I2*, *Index2[I2]*, *Index2[Index2[I2]]*, etc to give [3,
-5, 2, 4, 0, 1]. Indexing *L* with these values gives "abraca", the uncompressed
-text (without being reversed).
+Calculate *U[I]*, *U[U[I]]*, *U[U[U[I]]]*, etc to give [3, 5, 2, 4, 0, 1].
+Indexing *L* with these values gives "abraca", the uncompressed text (without
+being reversed).
## Final Run Length Encoding
diff --git a/std/bzip2/decode_bzip2.wuffs b/std/bzip2/decode_bzip2.wuffs
index a334792..8da8d77 100644
--- a/std/bzip2/decode_bzip2.wuffs
+++ b/std/bzip2/decode_bzip2.wuffs
@@ -67,7 +67,7 @@
// bwt is the Burrows Wheeler Transform state. Per the README.md file, each
// entry is a row with the low 8 bits holding the L column and the high 20
- // bits holding the Index2 column. The middle 4 bits are unused.
+ // bits holding the U column. The middle 4 bits are unused.
//
// The read_code_lengths and build_huffman_tree methods also re-purpose
// this buffer to temporarily hold up to 258 symbols' code lengths.
@@ -727,8 +727,8 @@
i += 1
} endwhile
- // Second data pass, but per the README.md file, calculate the Index2
- // column instead of the T column calculated by SRC-RR-124.pdf.
+ // Second data pass, but per the README.md file, calculate the U column
+ // instead of the BWT technical report's T column.
i = 0
while i < this.block_size {
assert i < 900000 via "a < b: a < c; c <= b"(c: this.block_size)
