NOTICE-binary

Apache Pinot (incubating)
Copyright 2018-2021 Apache Software Foundation

This product includes software developed at
The Apache Software Foundation (http://www.apache.org/).


Apache Commons Configuration
Copyright 2001-2013 The Apache Software Foundation

Apache Commons Codec
Copyright 2002-2011 The Apache Software Foundation

This product includes software developed by
The Apache Software Foundation (http://www.apache.org/).

--------------------------------------------------------------------------------
src/test/org/apache/commons/codec/language/DoubleMetaphoneTest.java contains 
test data from http://aspell.sourceforge.net/test/batch0.tab.

Copyright (C) 2002 Kevin Atkinson (kevina@gnu.org). Verbatim copying
and distribution of this entire article is permitted in any medium,
provided this notice is preserved.
--------------------------------------------------------------------------------

Apache Commons IO
Copyright 2002-2012 The Apache Software Foundation

Apache Commons Lang
Copyright 2001-2011 The Apache Software Foundation

Apache Commons Logging
Copyright 2003-2014 The Apache Software Foundation

Apache Commons Lang
Copyright 2001-2016 The Apache Software Foundation

This product includes software from the Spring Framework,
under the Apache License 2.0 (see: StringUtils.containsWhitespace())

Apache Commons Collections
Copyright 2001-2008 The Apache Software Foundation

Apache Log4j SLF4J Binding
Copyright 1999-2019 The Apache Software Foundation

Apache Log4j API
Copyright 1999-2019 The Apache Software Foundation

Apache Log4j 1.x Compatibility API
Copyright 1999-2019 The Apache Software Foundation

=============================================================================
= NOTICE file corresponding to section 4d of the Apache License Version 2.0 =
=============================================================================
This product includes software developed by
Joda.org (https://www.joda.org/).

# Jackson JSON processor

Jackson is a high-performance, Free/Open Source JSON processing library.
It was originally written by Tatu Saloranta (tatu.saloranta@iki.fi), and has
been in development since 2007.
It is currently developed by a community of developers, as well as supported
commercially by FasterXML.com.

## Licensing

Jackson core and extension components may be licensed under different licenses.
To find the details that apply to this artifact see the accompanying LICENSE file.
For more information, including possible other licensing options, contact
FasterXML.com (http://fasterxml.com).

## Credits

A list of contributors may be found from CREDITS file, which is included
in some artifacts (usually source distributions); but is always available
from the source code management (SCM) system project uses.

Apache Avro
Copyright 2009-2014 The Apache Software Foundation

This product currently only contains code developed by authors
of specific components, as identified by the source code files;
if such notes are missing files have been created by
Tatu Saloranta.

For additional credits (generally to people who reported problems)
see CREDITS file.

Apache Groovy
Copyright 2003-2020 The Apache Software Foundation

This product includes/uses ANTLR (http://www.antlr2.org/)
developed by Terence Parr 1989-2006

This product bundles icons from the famfamfam.com silk icons set
http://www.famfamfam.com/lab/icons/silk/
Licensed under the Creative Commons Attribution Licence v2.5
http://creativecommons.org/licenses/by/2.5/

Apache HttpClient Mime
Copyright 1999-2017 The Apache Software Foundation

Apache HttpClient
Copyright 1999-2019 The Apache Software Foundation

Apache HttpCore
Copyright 2005-2018 The Apache Software Foundation

Calcite Core
Copyright 2012-2019 The Apache Software Foundation

Apache Calcite Avatica
Copyright 2012-2018 The Apache Software Foundation

Calcite Linq4j
Copyright 2012-2019 The Apache Software Foundation

Calcite Babel
Copyright 2012-2019 The Apache Software Foundation

Apache Thrift
Copyright 2006-2017 The Apache Software Foundation.

Apache Jakarta HttpClient
Copyright 1999-2007 The Apache Software Foundation

Apache Commons Compress
Copyright 2002-2020 The Apache Software Foundation

This product includes software developed at
The Apache Software Foundation (https://www.apache.org/).

---

The files in the package org.apache.commons.compress.archivers.sevenz
were derived from the LZMA SDK, version 9.20 (C/ and CPP/7zip/),
which has been placed in the public domain:

"LZMA SDK is placed in the public domain." (http://www.7-zip.org/sdk.html)

The test file lbzip2_32767.bz2 has been copied from libbzip2's source
repository:

This program, "bzip2", the associated library "libbzip2", and all
documentation, are copyright (C) 1996-2019 Julian R Seward.  All
rights reserved.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:

1. Redistributions of source code must retain the above copyright
   notice, this list of conditions and the following disclaimer.

2. The origin of this software must not be misrepresented; you must 
   not claim that you wrote the original software.  If you use this 
   software in a product, an acknowledgment in the product 
   documentation would be appreciated but is not required.

3. Altered source versions must be plainly marked as such, and must
   not be misrepresented as being the original software.

4. The name of the author may not be used to endorse or promote 
   products derived from this software without specific prior written 
   permission.

THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS
OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

Julian Seward, jseward@acm.org

Apache Helix :: Core
Copyright 2020 The Apache Software Foundation

                            The Netty Project
                            =================

Please visit the Netty web site for more information:

  * http://netty.io/

Copyright 2011 The Netty Project

The Netty Project licenses this file to you under the Apache License,
version 2.0 (the "License"); you may not use this file except in compliance
with the License. You may obtain a copy of the License at:

http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
License for the specific language governing permissions and limitations
under the License.

Also, please refer to each LICENSE.<component>.txt file, which is located in
the 'license' directory of the distribution file, for the license terms of the
components that this product depends on.

-------------------------------------------------------------------------------
This product contains the extensions to Java Collections Framework which has
been derived from the works by JSR-166 EG, Doug Lea, and Jason T. Greene:

  * LICENSE:
    * license/LICENSE.jsr166y.txt (Public Domain)
  * HOMEPAGE:
    * http://gee.cs.oswego.edu/cgi-bin/viewcvs.cgi/jsr166/
    * http://viewvc.jboss.org/cgi-bin/viewvc.cgi/jbosscache/experimental/jsr166/

This product contains a modified version of Robert Harder's Public Domain
Base64 Encoder and Decoder, which can be obtained at:

  * LICENSE:
    * license/LICENSE.base64.txt (Public Domain)
  * HOMEPAGE:
    * http://iharder.sourceforge.net/current/java/base64/

This product contains a modified version of 'JZlib', a re-implementation of
zlib in pure Java, which can be obtained at:

  * LICENSE:
    * license/LICENSE.jzlib.txt (BSD Style License)
  * HOMEPAGE:
    * http://www.jcraft.com/jzlib/

This product contains a modified version of 'Webbit', a Java event based
WebSocket and HTTP server:

  * LICENSE:
    * license/LICENSE.webbit.txt (BSD License)
  * HOMEPAGE:
    * https://github.com/joewalnes/webbit

This product optionally depends on 'Protocol Buffers', Google's data
interchange format, which can be obtained at:

  * LICENSE:
    * license/LICENSE.protobuf.txt (New BSD License)
  * HOMEPAGE:
    * http://code.google.com/p/protobuf/

This product optionally depends on 'Bouncy Castle Crypto APIs' to generate
a temporary self-signed X.509 certificate when the JVM does not provide the
equivalent functionality.  It can be obtained at:

  * LICENSE:
    * license/LICENSE.bouncycastle.txt (MIT License)
  * HOMEPAGE:
    * http://www.bouncycastle.org/

This product optionally depends on 'SLF4J', a simple logging facade for Java,
which can be obtained at:

  * LICENSE:
    * license/LICENSE.slf4j.txt (MIT License)
  * HOMEPAGE:
    * http://www.slf4j.org/

This product optionally depends on 'Apache Commons Logging', a logging
framework, which can be obtained at:

  * LICENSE:
    * license/LICENSE.commons-logging.txt (Apache License 2.0)
  * HOMEPAGE:
    * http://commons.apache.org/logging/

This product optionally depends on 'Apache Log4J', a logging framework,
which can be obtained at:

  * LICENSE:
    * license/LICENSE.log4j.txt (Apache License 2.0)
  * HOMEPAGE:
    * http://logging.apache.org/log4j/

This product optionally depends on 'JBoss Logging', a logging framework,
which can be obtained at:

  * LICENSE:
    * license/LICENSE.jboss-logging.txt (GNU LGPL 2.1)
  * HOMEPAGE:
    * http://anonsvn.jboss.org/repos/common/common-logging-spi/

This product optionally depends on 'Apache Felix', an open source OSGi
framework implementation, which can be obtained at:

  * LICENSE:
    * license/LICENSE.felix.txt (Apache License 2.0)
  * HOMEPAGE:
    * http://felix.apache.org/

Apache ZooKeeper - Server
Copyright 2008-2020 The Apache Software Foundation

Apache ZooKeeper - Jute
Copyright 2008-2020 The Apache Software Foundation

Apache Yetus - Audience Annotations
Copyright 2015-2017 The Apache Software Foundation

Apache Commons Math
Copyright 2001-2010 The Apache Software Foundation

===============================================================================
The LinearConstraint, LinearObjectiveFunction, LinearOptimizer,
RelationShip, SimplexSolver and SimplexTableau classes in package
org.apache.commons.math.optimization.linear include software developed by
Benjamin McCann (http://www.benmccann.com) and distributed with
the following copyright: Copyright 2009 Google Inc.
===============================================================================

This product includes software developed by the
University of Chicago, as Operator of Argonne National
Laboratory.
The LevenbergMarquardtOptimizer class in package
org.apache.commons.math.optimization.general includes software
translated from the lmder, lmpar and qrsolv Fortran routines
from the Minpack package
Minpack Copyright Notice (1999) University of Chicago.  All rights reserved
===============================================================================

The GraggBulirschStoerIntegrator class in package
org.apache.commons.math.ode.nonstiff includes software translated
from the odex Fortran routine developed by E. Hairer and G. Wanner.
Original source copyright:
Copyright (c) 2004, Ernst Hairer
===============================================================================

The EigenDecompositionImpl class in package
org.apache.commons.math.linear includes software translated
from some LAPACK Fortran routines.  Original source copyright:
Copyright (c) 1992-2008 The University of Tennessee.  All rights reserved.
===============================================================================

The MersenneTwister class in package org.apache.commons.math.random
includes software translated from the 2002-01-26 version of
the Mersenne-Twister generator written in C by Makoto Matsumoto and Takuji
Nishimura. Original source copyright:
Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
All rights reserved
===============================================================================

The complete text of licenses and disclaimers associated with the the original
sources enumerated above at the time of code translation are in the LICENSE.txt
file.

datasketches-java
Copyright 2015-2020 The Apache Software Foundation

datasketches-memory
Copyright 2015-2019 The Apache Software Foundation

Apache Lucene
Copyright 2001-2019 The Apache Software Foundation

Includes software from other Apache Software Foundation projects,
including, but not limited to:
 - Apache Ant
 - Apache Jakarta Regexp
 - Apache Commons
 - Apache Xerces

ICU4J, (under analysis/icu) is licensed under an MIT styles license
and Copyright (c) 1995-2008 International Business Machines Corporation and others

Some data files (under analysis/icu/src/data) are derived from Unicode data such
as the Unicode Character Database. See http://unicode.org/copyright.html for more
details.

Brics Automaton (under core/src/java/org/apache/lucene/util/automaton) is
BSD-licensed, created by Anders Møller. See http://www.brics.dk/automaton/

The levenshtein automata tables (under core/src/java/org/apache/lucene/util/automaton) were
automatically generated with the moman/finenight FSA library, created by
Jean-Philippe Barrette-LaPierre. This library is available under an MIT license,
see http://sites.google.com/site/rrettesite/moman and
http://bitbucket.org/jpbarrette/moman/overview/

The class org.apache.lucene.util.WeakIdentityMap was derived from
the Apache CXF project and is Apache License 2.0.

The Google Code Prettify is Apache License 2.0.
See http://code.google.com/p/google-code-prettify/

JUnit (junit-4.10) is licensed under the Common Public License v. 1.0
See http://junit.sourceforge.net/cpl-v10.html

This product includes code (JaspellTernarySearchTrie) from Java Spelling Checkin
g Package (jaspell): http://jaspell.sourceforge.net/
License: The BSD License (http://www.opensource.org/licenses/bsd-license.php)

The snowball stemmers in
  analysis/common/src/java/net/sf/snowball
were developed by Martin Porter and Richard Boulton.
The snowball stopword lists in
  analysis/common/src/resources/org/apache/lucene/analysis/snowball
were developed by Martin Porter and Richard Boulton.
The full snowball package is available from
  http://snowball.tartarus.org/

The KStem stemmer in
  analysis/common/src/org/apache/lucene/analysis/en
was developed by Bob Krovetz and Sergio Guzman-Lara (CIIR-UMass Amherst)
under the BSD-license.

The Arabic,Persian,Romanian,Bulgarian, Hindi and Bengali analyzers (common) come with a default
stopword list that is BSD-licensed created by Jacques Savoy.  These files reside in:
analysis/common/src/resources/org/apache/lucene/analysis/ar/stopwords.txt,
analysis/common/src/resources/org/apache/lucene/analysis/fa/stopwords.txt,
analysis/common/src/resources/org/apache/lucene/analysis/ro/stopwords.txt,
analysis/common/src/resources/org/apache/lucene/analysis/bg/stopwords.txt,
analysis/common/src/resources/org/apache/lucene/analysis/hi/stopwords.txt,
analysis/common/src/resources/org/apache/lucene/analysis/bn/stopwords.txt
See http://members.unine.ch/jacques.savoy/clef/index.html.

The German,Spanish,Finnish,French,Hungarian,Italian,Portuguese,Russian and Swedish light stemmers
(common) are based on BSD-licensed reference implementations created by Jacques Savoy and
Ljiljana Dolamic. These files reside in:
analysis/common/src/java/org/apache/lucene/analysis/de/GermanLightStemmer.java
analysis/common/src/java/org/apache/lucene/analysis/de/GermanMinimalStemmer.java
analysis/common/src/java/org/apache/lucene/analysis/es/SpanishLightStemmer.java
analysis/common/src/java/org/apache/lucene/analysis/fi/FinnishLightStemmer.java
analysis/common/src/java/org/apache/lucene/analysis/fr/FrenchLightStemmer.java
analysis/common/src/java/org/apache/lucene/analysis/fr/FrenchMinimalStemmer.java
analysis/common/src/java/org/apache/lucene/analysis/hu/HungarianLightStemmer.java
analysis/common/src/java/org/apache/lucene/analysis/it/ItalianLightStemmer.java
analysis/common/src/java/org/apache/lucene/analysis/pt/PortugueseLightStemmer.java
analysis/common/src/java/org/apache/lucene/analysis/ru/RussianLightStemmer.java
analysis/common/src/java/org/apache/lucene/analysis/sv/SwedishLightStemmer.java

The Stempel analyzer (stempel) includes BSD-licensed software developed
by the Egothor project http://egothor.sf.net/, created by Leo Galambos, Martin Kvapil,
and Edmond Nolan.

The Polish analyzer (stempel) comes with a default
stopword list that is BSD-licensed created by the Carrot2 project. The file resides
in stempel/src/resources/org/apache/lucene/analysis/pl/stopwords.txt.
See http://project.carrot2.org/license.html.

The SmartChineseAnalyzer source code (smartcn) was
provided by Xiaoping Gao and copyright 2009 by www.imdict.net.

WordBreakTestUnicode_*.java (under modules/analysis/common/src/test/)
is derived from Unicode data such as the Unicode Character Database.
See http://unicode.org/copyright.html for more details.

The Morfologik analyzer (morfologik) includes BSD-licensed software
developed by Dawid Weiss and Marcin Miłkowski (http://morfologik.blogspot.com/).

Morfologik uses data from Polish ispell/myspell dictionary
(http://www.sjp.pl/slownik/en/) licenced on the terms of (inter alia)
LGPL and Creative Commons ShareAlike.

Morfologic includes data from BSD-licensed dictionary of Polish (SGJP)
(http://sgjp.pl/morfeusz/)

Servlet-api.jar and javax.servlet-*.jar are under the CDDL license, the original
source code for this can be found at http://www.eclipse.org/jetty/downloads.php

===========================================================================
Kuromoji Japanese Morphological Analyzer - Apache Lucene Integration
===========================================================================

This software includes a binary and/or source version of data from

  mecab-ipadic-2.7.0-20070801

which can be obtained from

  http://atilika.com/releases/mecab-ipadic/mecab-ipadic-2.7.0-20070801.tar.gz

or

  http://jaist.dl.sourceforge.net/project/mecab/mecab-ipadic/2.7.0-20070801/mecab-ipadic-2.7.0-20070801.tar.gz

===========================================================================
mecab-ipadic-2.7.0-20070801 Notice
===========================================================================

Nara Institute of Science and Technology (NAIST),
the copyright holders, disclaims all warranties with regard to this
software, including all implied warranties of merchantability and
fitness, in no event shall NAIST be liable for
any special, indirect or consequential damages or any damages
whatsoever resulting from loss of use, data or profits, whether in an
action of contract, negligence or other tortuous action, arising out
of or in connection with the use or performance of this software.

A large portion of the dictionary entries
originate from ICOT Free Software.  The following conditions for ICOT
Free Software applies to the current dictionary as well.

Each User may also freely distribute the Program, whether in its
original form or modified, to any third party or parties, PROVIDED
that the provisions of Section 3 ("NO WARRANTY") will ALWAYS appear
on, or be attached to, the Program, which is distributed substantially
in the same form as set out herein and that such intended
distribution, if actually made, will neither violate or otherwise
contravene any of the laws and regulations of the countries having
jurisdiction over the User or the intended distribution itself.

NO WARRANTY

The program was produced on an experimental basis in the course of the
research and development conducted during the project and is provided
to users as so produced on an experimental basis.  Accordingly, the
program is provided without any warranty whatsoever, whether express,
implied, statutory or otherwise.  The term "warranty" used herein
includes, but is not limited to, any warranty of the quality,
performance, merchantability and fitness for a particular purpose of
the program and the nonexistence of any infringement or violation of
any right of any third party.

Each user of the program will agree and understand, and be deemed to
have agreed and understood, that there is no warranty whatsoever for
the program and, accordingly, the entire risk arising from or
otherwise connected with the program is assumed by the user.

Therefore, neither ICOT, the copyright holder, or any other
organization that participated in or was otherwise related to the
development of the program and their respective officials, directors,
officers and other employees shall be held liable for any and all
damages, including, without limitation, general, special, incidental
and consequential damages, arising out of or otherwise in connection
with the use or inability to use the program or any product, material
or result produced or otherwise obtained by using the program,
regardless of whether they have been advised of, or otherwise had
knowledge of, the possibility of such damages at any time during the
project or thereafter.  Each user will be deemed to have agreed to the
foregoing by his or her commencement of use of the program.  The term
"use" as used herein includes, but is not limited to, the use,
modification, copying and distribution of the program and the
production of secondary products from the program.

In the case where the program, whether in its original form or
modified, was distributed or delivered to or received by a user from
any person, organization or entity other than ICOT, unless it makes or
grants independently of ICOT any specific warranty to the user in
writing, such person, organization or entity, will also be exempted
from and not be held liable to the user for any such damages as noted
above as far as the program is concerned.

===========================================================================
Nori Korean Morphological Analyzer - Apache Lucene Integration
===========================================================================

  mecab-ko-dic-2.0.3-20170922

  https://bitbucket.org/eunjeon/mecab-ko-dic/downloads/mecab-ko-dic-2.0.3-20170922.tar.gz

Apache Commons CLI
Copyright 2001-2009 The Apache Software Foundation

Jackson core and extension components may licensed under different licenses.
To find the details that apply to this artifact see the accompanying LICENSE file.
For more information, including possible other licensing options, contact
FasterXML.com (http://fasterxml.com).

ORC Core
Copyright 2013-2020 The Apache Software Foundation

ORC Shims
Copyright 2013-2020 The Apache Software Foundation

Hive Storage API
Copyright 2019 The Apache Software Foundation

Apache Parquet Avro
Copyright 2015 The Apache Software Foundation

Apache Parquet Column
Copyright 2015 The Apache Software Foundation

Apache Parquet Common
Copyright 2015 The Apache Software Foundation

Apache Parquet Encodings
Copyright 2015 The Apache Software Foundation

Apache Parquet Hadoop
Copyright 2015 The Apache Software Foundation

Apache Parquet Jackson
Copyright 2015 The Apache Software Foundation

Apache Parquet Format (Incubating)
Copyright 2015 The Apache Software Foundation

Apache Log4j Core
Copyright 1999-2012 Apache Software Foundation

ResolverUtil.java
Copyright 2005-2006 Tim Fennell

Apache Commons Math
Copyright 2001-2013 The Apache Software Foundation

===============================================================================

The inverse error function implementation in the Erf class is based on CUDA
code developed by Mike Giles, Oxford-Man Institute of Quantitative Finance,
and published in GPU Computing Gems, volume 2, 2010.
===============================================================================

The BracketFinder (package org.apache.commons.math3.optimization.univariate)
and PowellOptimizer (package org.apache.commons.math3.optimization.general)
classes are based on the Python code in module "optimize.py" (version 0.5)
developed by Travis E. Oliphant for the SciPy library (http://www.scipy.org/)
Copyright © 2003-2009 SciPy Developers.
===============================================================================

The LinearConstraint, LinearObjectiveFunction, LinearOptimizer,
RelationShip, SimplexSolver and SimplexTableau classes in package
org.apache.commons.math3.optimization.linear include software developed by
Benjamin McCann (http://www.benmccann.com) and distributed with
the following copyright: Copyright 2009 Google Inc.
===============================================================================

This product includes software developed by the
University of Chicago, as Operator of Argonne National
Laboratory.
The LevenbergMarquardtOptimizer class in package
org.apache.commons.math3.optimization.general includes software
translated from the lmder, lmpar and qrsolv Fortran routines
from the Minpack package
Minpack Copyright Notice (1999) University of Chicago.  All rights reserved
===============================================================================

The GraggBulirschStoerIntegrator class in package
org.apache.commons.math3.ode.nonstiff includes software translated
from the odex Fortran routine developed by E. Hairer and G. Wanner.
Original source copyright:
Copyright (c) 2004, Ernst Hairer
===============================================================================

The EigenDecompositionImpl class in package
org.apache.commons.math3.linear includes software translated
from some LAPACK Fortran routines.  Original source copyright:
Copyright (c) 1992-2008 The University of Tennessee.  All rights reserved.
===============================================================================

The MersenneTwister class in package org.apache.commons.math3.random
includes software translated from the 2002-01-26 version of
the Mersenne-Twister generator written in C by Makoto Matsumoto and Takuji
Nishimura. Original source copyright:
Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
All rights reserved
===============================================================================

The LocalizedFormatsTest class in the unit tests is an adapted version of
the OrekitMessagesTest class from the orekit library distributed under the
terms of the Apache 2 licence. Original source copyright:
Copyright 2010 CS Systèmes d'Information
===============================================================================

The HermiteInterpolator class and its corresponding test have been imported from
the orekit library distributed under the terms of the Apache 2 licence. Original
source copyright:
Copyright 2010-2012 CS Systèmes d'Information
===============================================================================

The creation of the package "o.a.c.m.analysis.integration.gauss" was inspired
by an original code donated by Sébastien Brisard.
===============================================================================