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authorBryan Newbold <bnewbold@robocracy.org>2017-02-20 00:05:36 -0800
committerBryan Newbold <bnewbold@robocracy.org>2017-02-20 00:05:36 -0800
commit5bea21e81ed516440e34e480f2c33ca41aa8c597 (patch)
tree653ace1b8fe0a9916d861d35ff8f611b46c80d37 /peanosfc.scm
parent237c6e380aebdcbc70bd1c9ecf7d3f6effca2752 (diff)
downloadslib-5bea21e81ed516440e34e480f2c33ca41aa8c597.tar.gz
slib-5bea21e81ed516440e34e480f2c33ca41aa8c597.zip
Import Upstream version 3a4upstream/3a4
Diffstat (limited to 'peanosfc.scm')
-rw-r--r--peanosfc.scm78
1 files changed, 37 insertions, 41 deletions
diff --git a/peanosfc.scm b/peanosfc.scm
index 5cac088..388be9f 100644
--- a/peanosfc.scm
+++ b/peanosfc.scm
@@ -1,5 +1,5 @@
; "peanospc.scm": Peano space filling mapping
-; Copyright (C) 2005 Aubrey Jaffer
+; Copyright (C) 2005, 2006 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
@@ -26,24 +26,23 @@
;;; Space filling curves and mathematical programming.
;;; Information and Control, 12:314-330, 1968.
-(define (natural->tet-array scalar rank)
- (do ((tets '() (cons (modulo scl 3) tets))
+(define (natural->trit-array scalar rank)
+ (do ((trits '() (cons (modulo scl 3) trits))
(scl scalar (quotient scl 3)))
((zero? scl)
- (let* ((len (length tets))
- (depth (quotient (+ len rank -1) rank)))
+ (let ((depth (quotient (+ (length trits) rank -1) rank)))
(define tra (make-array (A:fixZ8b 0) rank depth))
- (set! tets (reverse tets))
+ (set! trits (reverse trits))
(do ((idx (+ -1 depth) (+ -1 idx)))
((negative? idx))
(do ((rdx 0 (+ 1 rdx)))
((>= rdx rank))
- (cond ((null? tets))
- (else (array-set! tra (car tets) rdx idx)
- (set! tets (cdr tets))))))
+ (cond ((null? trits))
+ (else (array-set! tra (car trits) rdx idx)
+ (set! trits (cdr trits))))))
tra))))
-(define (tet-array->natural tra)
+(define (trit-array->natural tra)
(define rank (car (array-dimensions tra)))
(define depth (cadr (array-dimensions tra)))
(define val 0)
@@ -53,22 +52,20 @@
((negative? rdx))
(set! val (+ (array-ref tra rdx idx) (* 3 val))))))
-(define (tet-array->coordinates tra)
- (define rank (car (array-dimensions tra)))
+(define (trit-array->natural-coordinates tra)
(define depth (cadr (array-dimensions tra)))
- (do ((rdx (+ -1 rank) (+ -1 rdx))
+ (do ((rdx (+ -1 (car (array-dimensions tra))) (+ -1 rdx))
(lst '() (cons (do ((idx 0 (+ 1 idx))
(val 0 (+ (array-ref tra rdx idx) (* 3 val))))
((>= idx depth) val))
lst)))
((negative? rdx) lst)))
-(define (coordinates->tet-array coords)
+(define (natural-coordinates->trit-array coords)
(define depth (do ((scl (apply max coords) (quotient scl 3))
(dpt 0 (+ 1 dpt)))
((zero? scl) dpt)))
- (define rank (length coords))
- (let ((tra (make-array (A:fixN8b 0) rank depth)))
+ (let ((tra (make-array (A:fixN8b 0) (length coords) depth)))
(do ((rdx 0 (+ 1 rdx))
(cds coords (cdr cds)))
((null? cds))
@@ -82,63 +79,62 @@
(define parity 0)
(define rank (car (array-dimensions tra)))
(define depth (cadr (array-dimensions tra)))
+ (define rra (make-array (A:fixN8b 0) (car (array-dimensions tra))))
(do ((idx 0 (+ 1 idx)))
((>= idx depth))
(do ((rdx (+ -1 rank) (+ -1 rdx)))
((negative? rdx))
- (let ((v_ij (array-ref tra rdx idx))
- (tpar parity))
- (do ((idx (+ -1 idx) (+ -1 idx)))
- ((negative? idx))
- (set! tpar (+ (array-ref tra rdx idx) tpar)))
- (if (odd? tpar) (array-set! tra (- 2 v_ij) rdx idx))
- (set! parity (modulo (+ parity v_ij) 2))))))
+ (let ((v_ij (array-ref tra rdx idx)))
+ (if (odd? (+ parity (array-ref rra rdx)))
+ (array-set! tra (- 2 v_ij) rdx idx))
+ (set! parity (modulo (+ v_ij parity) 2))
+ (array-set! rra (modulo (+ v_ij (array-ref rra rdx)) 2) rdx)))))
;;@body
;;Returns a list of @2 nonnegative integer coordinates corresponding
;;to exact nonnegative integer @1. The lists returned by @0 for @1
;;arguments 0 and 1 will differ in the first element.
(define (natural->peano-coordinates scalar rank)
- (define tra (natural->tet-array scalar rank))
+ (define tra (natural->trit-array scalar rank))
(peano-flip! tra)
- (tet-array->coordinates tra))
+ (trit-array->natural-coordinates tra))
;;@body
;;Returns an exact nonnegative integer corresponding to @1, a list of
;;nonnegative integer coordinates.
(define (peano-coordinates->natural coords)
- (define tra (coordinates->tet-array coords))
+ (define tra (natural-coordinates->trit-array coords))
(peano-flip! tra)
- (tet-array->natural tra))
+ (trit-array->natural tra))
;;@body
;;Returns a list of @2 integer coordinates corresponding to exact
;;integer @1. The lists returned by @0 for @1 arguments 0 and 1 will
;;differ in the first element.
(define (integer->peano-coordinates scalar rank)
- (define three^rank (expt 3 rank))
- (do ((edx 1 (* edx three^rank))
- (m 0 (+ 1 m)))
+ (define nine^rank (expt 9 rank))
+ (do ((edx 1 (* edx nine^rank))
+ (cdx 1 (* cdx 9)))
((>= (quotient edx 2) (abs scalar))
- (let ((tra (natural->tet-array (+ scalar (quotient edx 2)) rank))
- (offset (quotient (expt 3 m) 2)))
+ (let ((tra (natural->trit-array (+ scalar (quotient edx 2)) rank))
+ (offset (quotient cdx 2)))
(peano-flip! tra)
- (map (lambda (k) (* (if (odd? m) -1 1) (- k offset)))
- (tet-array->coordinates tra))))))
+ (map (lambda (k) (- k offset))
+ (trit-array->natural-coordinates tra))))))
;;@body
;;Returns an exact integer corresponding to @1, a list of integer
;;coordinates.
(define (peano-coordinates->integer coords)
+ (define nine^rank (expt 9 (length coords)))
(define cobs (apply max (map abs coords)))
- (let loop ((xpo 1))
- (define offset (quotient (expt 3 xpo) 2))
+ (let loop ((edx 1) (cdx 1))
+ (define offset (quotient cdx 2))
(if (>= offset cobs)
- (let ((tra (coordinates->tet-array
+ (let ((tra (natural-coordinates->trit-array
(map (lambda (elt) (+ elt offset))
coords))))
(peano-flip! tra)
- ((if (odd? xpo) - +)
- (- (tet-array->natural tra)
- (quotient (expt 3 (* (length coords) xpo)) 2))))
- (loop (+ 1 xpo)))))
+ (- (trit-array->natural tra)
+ (quotient edx 2)))
+ (loop (* nine^rank edx) (* 9 cdx)))))