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Unified Diff: Modules/_decimal/libmpdec/literature/six-step.txt

Issue 7652: Merge C version of decimal into py3k.
Patch Set: Created 7 years, 3 months ago
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Modules/_decimal/libmpdec/literature/six-step.txt Sat Mar 10 18:12:20 2012 +0100
@@ -0,0 +1,63 @@
+
+
+(* Copyright (c) 2011 Stefan Krah. All rights reserved. *)
+
+
+The Six Step Transform:
+=======================
+
+In libmpdec, the six-step transform is the Matrix Fourier Transform (See
+matrix-transform.txt) in disguise. It is called six-step transform after
+a variant that appears in [1]. The algorithm requires that the input
+array can be viewed as an R*C matrix.
+
+
+Algorithm six-step (forward transform):
+---------------------------------------
+
+ 1a) Transpose the matrix.
+
+ 1b) Apply a length R FNT to each row.
+
+ 1c) Transpose the matrix.
+
+ 2) Multiply each matrix element (addressed by j*C+m) by r**(j*m).
+
+ 3) Apply a length C FNT to each row.
+
+ 4) Transpose the matrix.
+
+Note that steps 1a) - 1c) are exactly equivalent to step 1) of the Matrix
+Fourier Transform. For large R, it is faster to transpose twice and do
+a transform on the rows than to perform a column transpose directly.
+
+
+
+Algorithm six-step (inverse transform):
+---------------------------------------
+
+ 0) View the matrix as a C*R matrix.
+
+ 1) Transpose the matrix, producing an R*C matrix.
+
+ 2) Apply a length C FNT to each row.
+
+ 3) Multiply each matrix element (addressed by i*C+n) by r**(i*n).
+
+ 4a) Transpose the matrix.
+
+ 4b) Apply a length R FNT to each row.
+
+ 4c) Transpose the matrix.
+
+Again, steps 4a) - 4c) are equivalent to step 4) of the Matrix Fourier
+Transform.
+
+
+
+--
+
+ [1] David H. Bailey: FFTs in External or Hierarchical Memory
+ http://crd.lbl.gov/~dhbailey/dhbpapers/
+
+
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