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+; "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)))