1 files changed, 94 insertions, 0 deletions
diff --git a/phil-spc.scm b/phil-spc.scm
new file mode 100644
index 0000000..3372ce6
--- /dev/null
+++ b/phil-spc.scm
@@ -0,0 +1,94 @@
+; "phil-spc.scm": Peano-Hilbert space filling mapping
+; Copyright (c) 2003 Aubrey Jaffer
+;
+;Permission to copy this software, to modify it, to redistribute it,
+;to distribute modified versions, and to use it for any purpose is
+;granted, subject to the following restrictions and understandings.
+;
+;1.  Any copy made of this software must include this copyright notice
+;in full.
+;
+;2.  I have made no warranty or representation that the operation of
+;this software will be error-free, and I am under no obligation to
+;provide any services, by way of maintenance, update, or otherwise.
+;
+;3.  In conjunction with products arising from the use of this
+;material, there shall be no use of my name in any advertising,
+;promotional, or sales literature without prior written consent in
+;each case.
+
+(require 'logical)
+
+;;@code{(require 'hilbert-fill)}
+;;@ftindex hilbert-fill
+;;
+;;@noindent
+;;@cindex Peano
+;;@cindex Hilbert
+;;@cindex Space-Filling
+;;The @dfn{Peano-Hilbert Space-Filling Curve} is a one-to-one mapping
+;;between a unit line segment and an @var{n}-dimensional unit cube.
+;;
+;;@noindent
+;;The integer procedures map the non-negative integers to an
+;;arbitrarily large @var{n}-dimensional cube with its corner at the
+;;origin and all coordinates are non-negative.
+;;
+;;@noindent
+;;For any exact nonnegative integers @var{scalar} and @var{rank},
+;;
+;;@example
+;;(= @var{scalar} (hilbert-coordinates->integer
+;;           (integer->hilbert-coordinates @var{scalar} @var{rank})))
+;;                                       @result{} #t
+;;@end example
+
+;;@body
+;;Returns a list of @2 integer coordinates corresponding to exact
+;;non-negative integer @1.  The lists returned by @0 for @1 arguments
+;;0 and 1 will differ in the first element.
+(define (integer->hilbert-coordinates scalar rank)
+  (define ndones (logical:ones rank))
+  (define rank*nbits
+    (let ((rank^2 (* rank rank)))
+      (* (quotient (+ -1 rank^2 (integer-length scalar)) rank^2)
+	 rank^2)))
+  (let ((nthbits (quotient (logical:ones rank*nbits) ndones)))
+    (define igry (logxor (integer->gray-code scalar) (ash nthbits -1)))
+    (do ((bdxn (- rank rank*nbits) (+ rank bdxn))
+	 (chnk (logand (ash igry (- rank rank*nbits)) ndones)
+	       (logand (ash igry (+ rank bdxn)) ndones))
+	 (rotation 0 (modulo (+ (integer-length (logand (- chnk) chnk))
+				1 rotation)
+			     rank))
+	 (flipbit 0 (ash 1 rotation))
+	 (bignum 0 (+ (logxor flipbit (logical:rotate chnk rotation rank))
+		      (ash bignum rank))))
+	((positive? bdxn)
+	 (map gray-code->integer (bitwise:delaminate rank bignum))))))
+
+;;@body
+;;Returns an exact non-negative integer corresponding to @1, a list
+;;of non-negative integer coordinates.
+(define (hilbert-coordinates->integer coords)
+  (define rank (length coords))
+  (define bignum (apply bitwise:laminate (map integer->gray-code coords)))
+  (let ((rank*nbits
+	 (* (quotient (+ -1 rank (integer-length (apply max coords))) rank)
+	    rank rank))
+	(ndones (logical:ones rank)))
+    (define nthbits (quotient (logical:ones rank*nbits) ndones))
+    (define (loop bdxn rotation flipbit scalar)
+      (if (positive? bdxn)
+	  (gray-code->integer (logxor scalar (ash nthbits -1)))
+	  (let ((chnk (logical:rotate
+		       (logxor flipbit (logand ndones (ash bignum bdxn)))
+		       (- rotation)
+		       rank)))
+	    (loop (+ rank bdxn)
+		  (modulo (+ (integer-length (logand (- chnk) chnk))
+			     1 rotation)
+			  rank)
+		  (ash 1 rotation)
+		  (+ chnk (ash scalar rank))))))
+    (loop (- rank rank*nbits) 0 0 0)))