I hope we agree that unit?(i) for an interval is true only of 0 is NOT
in the interval.
Patch attached.
Ralf
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From 8919f59f02c72dace49174ba917f0142d8a79f34 Mon Sep 17 00:00:00 2001
From: Ralf Hemmecke <r...@hemmecke.org>
Date: Thu, 19 Dec 2024 15:54:55 +0100
Subject: use rem instead of positiveRemainder
---
src/algebra/hashstate.spad | 3 ++-
src/algebra/xhash.spad | 21 +++++++--------------
2 files changed, 9 insertions(+), 15 deletions(-)
diff --git a/src/algebra/hashstate.spad b/src/algebra/hashstate.spad
index ca95aa31..bd04fdf8 100644
--- a/src/algebra/hashstate.spad
+++ b/src/algebra/hashstate.spad
@@ -58,7 +58,8 @@ HashState() : with
++ update!(hs, x) computes new values of HashState from hs
++ and x and might destructively operate on its first argument.
value : % -> SingleInteger
- ++ value(x) returns a SingleInteger value corresponding to x.
+ ++ value(x) returns a non-negative SingleInteger value
+ ++ corresponding to x.
== add
-- These two macros are necessary to distinguish between Rep and \%.
rep x ==> (x@%) pretend Rep
diff --git a/src/algebra/xhash.spad b/src/algebra/xhash.spad
index 6c101ea6..2c626285 100644
--- a/src/algebra/xhash.spad
+++ b/src/algebra/xhash.spad
@@ -1,16 +1,7 @@
)abbrev domain XHASHTBL XHashTable
)if LiterateDoc
\documentclass{article}
-\usepackage{url}
-\usepackage{color}
-\definecolor{bgcode}{rgb}{1,1,0.7}
-
-\usepackage{listings}
-\lstdefinelanguage{spad}{basicstyle=\footnotesize\ttfamily,%
- numbers=left,firstnumber=last,backgroundcolor=\color{bgcode}}
-\parindent0pt
-\parskip\medskipamount
-
+\usepackage{literatedoc}
\begin{document}
\title{A hash table implementation via double hashing}
\author{Ralf Hemmecke}
@@ -45,7 +36,7 @@ respectively. \texttt{VACANT} and \texttt{DELETED} should not be part
of the key space.
Let's assume that the type of the marker values is \texttt{Marker}.
-Naively, and type correctly, we would have to use as representation
+Naively, and type correctly, we would have to use a representation
like the following.
\begin{verbatim}
Union(Marker, Record(key: Key, entry: Entry))
@@ -111,6 +102,8 @@ XHashTable(Key: Hashable, Entry: Type):
++ the sense that from k1=k2 follows h(k1)=h(k2). If that is not
++ the case, k1 and k2 will internally be considered as being
++ different keys.
+ ++ For XHashTable to work correctly, the function h must only
+ ++ yield non-negative values.
== add
KE ==> Record(key: Key, entry: Entry)
UE ==> Union(Entry, "failed")
@@ -341,9 +334,9 @@ stored and thus the loops eventually terminate.
mk := getMKey(a, p)
n: Z := numOfBuckets a
- h1: Z := (h k)::Z
- p: Z := positiveRemainder(h1, n) -- position in array
- h2: Z := 1 + positiveRemainder(h1, n-2)
+ h1: Z := (h k)::Z -- h1>=0
+ p: Z := h1 rem n -- position in array (p>=0)
+ h2: Z := 1 + (h1 rem (n-2)) -- h2>=0
mk: MKey := getMKey(a, p)
deletedPosition?: Boolean := false
while not vacant? mk repeat
--
2.43.0
