1 files changed, 126 insertions, 4 deletions
diff --git a/phil-spc.txi b/phil-spc.txi
index 1193c6c..ac1743c 100644
--- a/phil-spc.txi
+++ b/phil-spc.txi
@@ -2,12 +2,13 @@
 @ftindex hilbert-fill
 
 @noindent
-@cindex Peano
 @cindex Hilbert
 @cindex Space-Filling
-The @dfn{Peano-Hilbert Space-Filling Curve} is a one-to-one mapping
-@cindex Peano-Hilbert Space-Filling Curve
+The @dfn{Hilbert Space-Filling Curve} is a one-to-one mapping
+@cindex Hilbert Space-Filling Curve
 between a unit line segment and an @var{n}-dimensional unit cube.
+This implementation treats the nonnegative integers either as
+fractional bits of a given width or as nonnegative integers.
 
 @noindent
 The integer procedures map the non-negative integers to an
@@ -15,7 +16,8 @@ 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},
+For any exact nonnegative integer @var{scalar} and exact integer
+@var{rank} > 2,
 
 @example
 (= @var{scalar} (hilbert-coordinates->integer
@@ -23,16 +25,136 @@ For any exact nonnegative integers @var{scalar} and @var{rank},
                                        @result{} #t
 @end example
 
+When treating integers as @var{k} fractional bits,
+
+@example
+(= @var{scalar} (hilbert-coordinates->integer
+           (integer->hilbert-coordinates @var{scalar} @var{rank} @var{k})) @var{k})
+                                       @result{} #t
+@end example
+
 
 @defun integer->hilbert-coordinates scalar rank
 
 Returns a list of @var{rank} integer coordinates corresponding to exact
 non-negative integer @var{scalar}.  The lists returned by @code{integer->hilbert-coordinates} for @var{scalar} arguments
 0 and 1 will differ in the first element.
+
+
+@defunx integer->hilbert-coordinates scalar rank k
+
+@var{scalar} must be a nonnegative integer of no more than
+@code{@var{rank}*@var{k}} bits.
+
+@code{integer->hilbert-coordinates} Returns a list of @var{rank} @var{k}-bit nonnegative integer
+coordinates corresponding to exact non-negative integer @var{scalar}.  The
+curves generated by @code{integer->hilbert-coordinates} have the same alignment independent of
+@var{k}.
 @end defun
 
+
 @defun hilbert-coordinates->integer coords
 
+
+@defunx hilbert-coordinates->integer coords k
 Returns an exact non-negative integer corresponding to @var{coords}, a list
 of non-negative integer coordinates.
 @end defun
+
+@subsubsection Gray code
+
+@cindex Gray code
+@noindent
+A @dfn{Gray code} is an ordering of non-negative integers in which
+@cindex Gray code
+exactly one bit differs between each pair of successive elements.  There
+are multiple Gray codings.  An n-bit Gray code corresponds to a
+Hamiltonian cycle on an n-dimensional hypercube.
+
+@noindent
+Gray codes find use communicating incrementally changing values between
+asynchronous agents.  De-laminated Gray codes comprise the coordinates
+of Hilbert space-filling curves.
+
+
+@defun integer->gray-code k
+Converts @var{k} to a Gray code of the same @code{integer-length} as
+@var{k}.
+
+@defunx gray-code->integer k
+Converts the Gray code @var{k} to an integer of the same
+@code{integer-length} as @var{k}.
+
+For any non-negative integer @var{k},
+@example
+(eqv? k (gray-code->integer (integer->gray-code k)))
+@end example
+@end defun
+
+@defun = k1 k2
+@defunx gray-code<? k1 k2
+@defunx gray-code>? k1 k2
+@defunx gray-code<=? k1 k2
+@defunx gray-code>=? k1 k2
+These procedures return #t if their Gray code arguments are
+(respectively): equal, monotonically increasing, monotonically
+decreasing, monotonically nondecreasing, or monotonically nonincreasing.
+
+For any non-negative integers @var{k1} and @var{k2}, the Gray code
+predicate of @code{(integer->gray-code k1)} and
+@code{(integer->gray-code k2)} will return the same value as the
+corresponding predicate of @var{k1} and @var{k2}.
+@end defun
+
+@subsubsection Bitwise Lamination
+@cindex lamination
+
+
+@defun bitwise-laminate k1 @dots{}
+@defunx bitwise-delaminate count k
+
+Returns an integer composed of the bits of @var{k1} @dots{} interlaced
+in argument order.  Given @var{k1}, @dots{} @var{kn}, the n low-order
+bits of the returned value will be the lowest-order bit of each
+argument.
+
+
+@defunx bitwise-laminate count k
+Returns a list of @var{count} integers comprised of every @var{count}h
+bit of the integer @var{k}.
+
+@example
+(map (lambda (k) (number->string k 2))
+     (bitwise-delaminate 4 #x7654))
+    @result{} ("0" "1111" "1100" "1010")
+(number->string (bitwise-laminate 0 #b1111 #b1100 #b1010) 16)
+    @result{} "7654"
+@end example
+
+For any non-negative integers @var{k} and @var{count}:
+@example
+(eqv? k (bitwise-laminate (bitwise-delaminate count k)))
+@end example
+@end defun
+
+
+@defun delaminate-list count ks
+
+
+Returns a list of @var{count} integers comprised of the @var{j}th
+bit of the integers @var{ks} where @var{j} ranges from @var{count}-1
+to 0.
+
+@example
+(map (lambda (k) (number->string k 2))
+     (delaminate-list 4 '(7 6 5 4 0 0 0 0)))
+    @result{} ("0" "11110000" "11000000" "10100000")
+@end example
+
+@code{delaminate-list} is its own inverse:
+@example
+(delaminate-list 8 (delaminate-list 4 '(7 6 5 4 0 0 0 0)))
+    @result{} (7 6 5 4 0 0 0 0)
+@end example
+@end defun
+