************************************************************
*                        Core Library
*
*            A C/C++ Library for Robust Computation
*
*                Department of Computer Science
*          Courant Institute of Mathematical Sciences
*                     New York University
*                      251 Mercer Street
*                      New York, NY 10012
*                            USA
*
*                    http://cs.nyu.edu/exact/
*        
*  Copyright (c) 1998-2004 by Exact Computation Project, NYU
*
*  $Id: README,v 1.46 2004/11/12 22:56:33 exact Exp $
*************************************************************

README FILE: TABLE OF CONTENTS

    1) ORIENTATION
    2) DIRECTORIES AND FILES
    3) DOWNLOAD AND INSTALLATION
    4) NEWS, PLANS AND BUGS
    5) ACKNOWLEDGEMENT AND HISTORY
    6) LICENSE INFORMATION

*************************************************************
1) ORIENTATION

   This is Core Library Version 1.7, released on Nov 12, 2004.

   The Core Library is a collection of C/C++ classes for exact
   computation with real algebraic numbers.
   It embodies our precision-driven approach and is 
   useful for robust numerical (especially geometric) algorithms.
   The library supports the Exact Geometric Computation (EGC) philosophy
   through its novel and easy-to-use notion of accuracy levels.
   We define four "Core Accuracy Levels":

     Level I:  Machine Accuracy
                    This is the IEEE 754 Standard.
     Level II: Arbitrary Accuracy
                    If a user specify "1000 bits" of accuracy,
                    this means no overflow/underflow occurs as long
                    as long as number sizes do not exceed 1000 bits. 
     Level III: Guaranteed Accuracy
                    The user can specify "10 bits" (relative or
                    absolute) and any computed number will have
                    at least 10 bits of accuracy.
     Level IV: Mixed Accuracy
                    The above three levels are intermixed.

   Level III is the most interesting level. It is the default level,
   Ideally, a single C++ program can be compiled to run at any chosen
   level.  Level IV is not fully defined at the present time.
   The current library focuses on Level III.  Most programs should
   be able to run both Levels I and III.   Such multi-level capability
   in a single program is useful for debugging and program development.

   A key design goal is to allow any standard C/C++ program to access
   critical CORE facilities with minimal changes to the program.  Most
   basic standalone C++ programs can be ``CORE-ized'' with little fuss.
   In the ideal case, one only has to insert the following statement

                #include "CORE/CORE.h"

   following all the standard include statements.  The default accuracy
   is Level III.  At this level, a variable with the machine type
   "double" or "long" is redefined as an instance of the class "Expr"
   (a C++ class).  All comparisons involving Expr are error-free,
   provided your expressions involve only the four arithmetic operations
   and square-roots.  Example:

                double x, y, a, b;
                x = 2; y = 3;
                a = sqrt(x) + sqrt(y);
                b = sqrt(x + y + 2*sqrt(x)*sqrt(y));
                if (a == b)  cout << "Equal   (CORRECT!)\n";
                    else     cout << "Not Equal (ERROR!)\n";

   When run in Level III, the expressions for a and b are always equal
   regardless of the values (x=2 and y=3) assigned to x and y.
   
   In the framework of EGC, error-free comparisons amount to
   computing the ''exact geometry'' in your programs.  Nonrobustness
   issues from round-off errors are thereby abolished.

   A tutorial in this "doc" subdirectory, plus the many
   sample programs in the "progs" subdirectory, should allow you
   to start writing CORE programs rather quickly.   In particular,
   you may use the examples in progs/generic as template
   to develop your own CORE programs.  For extra functionality, 
   we define domain specific "CORE eXtensions" (COREX for short). 
   These include a linear algebra COREX and a geometry
   COREX.  They are still rudimentary.
   
   The Core Library is relatively small.  The "base distribution"
   of Version 1.7, which includes source code and examples, is less
   than 800 KB.  The "full distribution" which includes the base distribution,
   documentation and gmp, is over 3.5MB.  The library has been tested
   on solaris, linux, cygwin and Windows.  It is
   also fully compatible with CGAL.

   NOTE ON TERMINOLOGY.
   "Core" is not an abbreviation; we chose this name to suggest its
   role as the "numerical core" for robust geometric computations.
   It is also to remind ourselves (the designers) that "cores" are
   usually small.  However, we use the capitalized sequence "CORE"
   as a shorthand for "Core Library" (e.g., a CORE program).

*************************************************************
2) DIRECTORIES AND FILES

   The Core Directory is denoted ${CORE_PATH} in these notes.
   The base distribution has the following files and subdirectories:

       README        This file
       ANNOUNCEMENT  Release announcement
       LICENSE.QPL   The Q Public License 
       FAQs          Frequently asked questions
       Makefile      Makefile for the whole library
       Make.config   Compilation flags for CORE programs

       ext/          CORE eXtensions (linear algebra, geometry, etc)
       inc/          The header files.
       lib/          The compiled library is found here.
       progs/        Sample programs that use Core Library.
       src/          Source code for the Core Library.
       tmp/          Temporary files (e.g., installation diagnostic messages)
       win32/        Windows related files (can be deleted for unix-base)
       gmp/          gmp installation directory (may be a link).  This
                         directory may be missing if you have your own gmp.

   The full distribution has these additional files and directories:

       doc/            Core Library Documentation  
       gmp-xxx.tar.gz  GNU's gmp distribution (version xxx)
       gmp-xxx/        GNU's gmp directory for unpacking and compiling
                       (can be deleted after installing gmp)

*************************************************************
3) DOWNLOAD AND INSTALLATION

   3.0) PREREQUISITE:
        You must have "make" (GNU's gmake is recommended), "tar" and "gzip".
        For compilers, "g++" is also recommended but not required.
        In turn, "g++" will need "m4" (the macro preprocessor).
        We DO NOT assume that you already have "gmp" (GNU's multiprecision
        number package).

        For Windows: you could replace g++ with Visual C++.
        However we highly recommend "Cygwin" from Red Hat.  This is a free
        and easy-to-install Unix-like environment that sits on top of all 
        versions of Windows.   It comes with g++, make, tar, gzip that are
        needed to install the Core Library.  The big bonus of Cygwin are 
        (I) There is no need for dual booting;
        (II) There is no need to partition your disc;
        (III) You can share files between Windows and Cygwin; 
        (IV) There is a convenient setup.exe utility that allows you to
                install / update / re-install / uninstall 
        any component in a large suite of Unix tools and utilities, directly 
        from the web.  You can download Cygwin at

                http://www.cygwin.com.  

   3.1) DOWNLOAD. First download the file core_vX.Y.Z_full.tgz 
        (for version X.Y.Z).  The current distribution is X.Y=1.7.0.  
        The website for download is

                http://cs.nyu.edu/exact/core.

        There are three distributions, a "base distribution", a "standard
	distribution" and a "full distribution".  The standard distribution
	includes the base distribution and documentation.  The full 
	distribution includes the standard distribution, plus gmp.  

        The main steps here describes on installation from a full distribution 
        in a unix-like environment: it is the simplest to install.
	But see 3.9) below for *variant* installations: these include
	installing only the base distribution, using dynamic libraries,
	Windows platform, re-installing the Core Library, building Debugging
	Versions of Core Library, etc.

        The overall installation time is 20-40 minutes on a typical
        machine.  If you already have gmp, the time is halved (on Pentium III
        800 MHz, 256 MB RAM, it takes 10 minutes).

   3.2) UNPACK. In your computer, go to the directory where you wish to
        install the Core Library.  If this location is the value of
        the environment variable CORE_INSTALL (in unix), you would do:

            % cd $(CORE_INSTALL)

        (% denotes the unix prompt in these instructions)
        Move the file core_vX.Y_full.tgz there.  Now unzip and untar the
        file by typing:

            % gzip -cd core_vX.Y_full.tgz | tar xvf -

        This creates a directory called core_vX.Y.  All the files and 
        directories mentioned in 2) above, including this README file,
        should now be in this directory.

        In the following, the variable CORE_PATH denotes the full path
        name of this newly created directory.  Hence, $(CORE_PATH) is really

                $(CORE_INSTALL)/core_vX.Y
   
   3.3) There are three stages of installation:
                STAGE 1 -- gmp-related installation
                STAGE 2 -- create the core library, extensions, samples
                STAGE 3 -- run tests and timings
        The screen output from the individual steps in these stages
        are stored in the files ${CORE_PATH}/tmp/DIAG_* for your diagnostics.

        But before any of these steps, you must choose your PLATFORM.
        PLATFORM is a combination of OS plus compiler.
        This variable is set in the Make.config file:

            % cd $(CORE_PATH)
            % vi Make.config -- use "vi" or your favorite editor to edit
                                the file ``Make.config''.   
                             -- Follow the instructions in the file.
                             -- For most users, you only need to set the
                                PLATFORM variable.
  
        To see what your chosen options are, do:
            % make opt[ions] -- this will show the various global settings
                             -- e.g. PLATFORM=gnu, LINKAGE=static, VAR=, etc.

   3.4) STAGE 1: INSTALLING GMP 

        PRELIMINARY STEP:   For most Unix-like OS (e.g., Solaris, Linux),
        gmp will automatically build BOTH a static and a dynamic library.  
        In this case, most compilers will link to the dynamic gmp library.
        Therefore, you need to add the path of your dynamic gmp library to
        the environmental variable LD_LIBRARY_PATH.
        
        E.g., in csh/tcsh,
        
            % setenv LD_LIBRARY_PATH ${LD_LIBRARY_PATH}:${your_gmp_install_dir}/lib
               
        E.g., in bash,
        
            % export LD_LIBRARY_PATH=${LD_LIBRARY_PATH}:${your_gmp_install_dir}/lib


        In option b) below, there is an example where ${your_gmp_install_dir}=/usr/local.

        NOW we are ready to proceed with installing gmp.
        Choose one of the following three situations that apply to you:

        a) You already have GMP header files and library files on 
        your system directory, AND they can be found by your
        C++ compiler.  In this case, there is nothing to do.
        In any case, if you want to quickly check if you are in this
        best case situation, do the following:

                % cd ${CORE_PATH} 
                % make testgmp

        This test simply computes 12345 * 67890.  If the answer
        838102050 is shown, you have passed this test and 
        you may go to STAGE 2.


        b) If you have compiled and installed GMP in some 
        directory which cannot be found by your compiler, then make a 
        symbolic link from ${CORE_PATH}/gmp using the following command:

            % cd ${CORE_PATH}
            % ln -s ${your_gmp_install_dir} gmp
            % make testgmp

        If you pass this test, you can go to STAGE 2.

        E.g., The default gmp installation will install the
        header file and library files in /usr/local/include
        and /usr/local/lib (respectively).  Hence, in this case,
        ${your_gmp_install_dir}=/usr/local.

        c) If you need to install gmp, and assuming you have downloaded
        our full distribution, follow the following steps:

            % cd ${CORE_PATH}
            % make first     -- this is equivalent to "make configure"
                             -- it uses the configuration program in gmp
                             -- it searches for system information
                                (compiler, CPU, files, etc).
                             -- screen output from this process is placed 
                                in the file ${CORE_PATH}/tmp/DIAG_CONFIG.
                                (E.g., if you do not have m4, the error will
                                be detected here.)
            % make second    -- this is equivalent to "make gmp"
                             -- this compiles gmp
                             -- screen output from this process is placed
                                in the file ${CORE_PATH}/tmp/DIAG_GMP
            % make third     -- this installs gmp
                             -- screen output from this process is placed
                                in the file ${CORE_PATH}/tmp/DIAG_GMPINSTALL
            % make testgmp   -- you must pass this test to continue
                                in the file ${CORE_PATH}/tmp/DIAG_TESTGMP

        IMPORTANT: Our top level make file is written for GNU's gmake.
        The remaining make files in subdirectories should work with other
        make programs.  The first and second steps takes 10-20 minutes.

   3.5) STAGE 2: BUILD CORE LIBRARY.

            % cd ${CORE_PATH}
            % make fourth    -- this is equivalent to a plain "make", or
                                "make core", or "make corelib; make corex; 
                                make demo".

                             -- screen output is placed in the files
                                ${CORE_PATH}/tmp/DIAG_X where X = CORELIB,
                                COREX or BUILD_DEMO.

        This creates the library files "libcore++.a", "libcorex++_level1.a"
        and "libcorex++_level3.a", and store them under ${CORE_PATH}/lib.

        The source files for the Core Library are found in
        ${CORE_PATH}/src.  If you only want to make "libcore++.a", type
        "make" while in ${CORE_PATH}/src.

        IMPORTANT: the compilation settings for STAGE 2 are found in
        ${CORE_PATH}/Make.config. See the Make.config file and also 
        step 3.9) below.

   3.6) STAGE 3: TESTING AND TIMING.
        If you had chosen LINKAGE to be "shared" above, then make sure
        that your LD_LIBRARY_PATH contains the directory ${CORE_PATH}/lib
        (see 3.9(4) below).

            % cd ${CORE_PATH}
            % make fifth     -- equivalent to "make test".  Screen output is
                                placed in the file ${CORE_PATH}/tmp/DIAG_TEST_DEMO

        This tests all the previously compiled programs 
        in ${CORE_PATH}/progs.  Many of the programs are self-validating:
        if an unexpected value is computed, it will output "ERROR!"
        instead of "CORRECT!".  Sometimes, the output says "INCORRECT!" but this
        is not considered an error (e.g., with Level I accuracy, this
        is expected).  You can browse the output in the DIAG_TEST_DEMO file
        (search for the word "ERROR" to catch obvious errors).
        You can also time it:

            % make sixth       -- equivalent to "make time"; it uses the "time"
                                  utility to measure the time "make test" 
                               -- screen output is placed in 
                                  the file ${CORE_PATH}/tmp/DIAG_TIME

   3.7) USING CORE LIBRARY.
        Assume that you have a stand alone C++ program "foo.cpp".
        In the ideal case, you only have to insert the preamble:

             #ifndef CORE_LEVEL
             #   define CORE_LEVEL N   // N=1,2,3.  Defaults to N=3 if omitted
             #endif
             #include "CORE/CORE.h"  

        This should be placed after your standard include
        files (e.g., <iostream.h>).  You can now compile it as usual:

             g++   -I${CORE_PATH}/inc -I${CORE_PATH}/gmp/include \ 
                   foo.cpp -o foo \                       
                   -L${CORE_PATH}/lib -L${CORE_PATH}/gmp/lib \
                   -lcore${VAR} -lgmp -lm                      

        For more information, please go to ${CORE_PATH}/progs/generic for
        samples, and also read the tutorial in ${CORE_PATH}/doc.

   3.8) PLATFORMS.
        Version 1.7 has been tested on

        sun solaris 5.8         --  g++-2.95.3, g++-3.2, g++-3.3, g++-3.4
                                --  (gmp 3.1.1, gmp 4.0.1, gmp 4.1, gmp 4.1.2)
                                --  (gmp 4.1.3, gmp 4.1.4)
                                --  Sun's WorkShop 6 (C++ 5.3)
        Debian Linux 2.4.9      --  gcc version 2.95
        cygwin                  --  g++-3.2, g++-3.3, g++-3.4
        mingw                   --  g++-3.2, g++-3.3, g++-3.4
        Windows                 --  Visual C++, version 6.0, 7.0, 7.1 

        NOTE : for users who prefer a unix/linux type environment that is
        embedded within the Windows' world, we highly recommend the Cygwin
        platform as an easy-to-use environment.  Cygwin and Windows
        can freely access each other's files (a big bonus).

   3.9) VARIANT INSTALLATIONS

        (1) INSTALLING BASE DISTRIBUTION:
        This assumes you already have an installed gmp.

          -- Download the file core_vX.Y.tgz (for version X.Y) from our
             website, http://cs.nyu.edu/exact/core.   This version has no
             gmp and no documentation.
          -- Do the UNPACK STEP (Step 3.2) above.  This creates the files
             under ${CORE_PATH} as described above.

        At this point there are two possibilities.
        You may not have to do anything.  To test this, try the following:

                % cd ${CORE_PATH}
                % make testgmp

        If this compiles a test program and prints an encouraging message,
        you may continue from STAGE 2 (Step 3.5) above.
        Otherwise assume that your gmp is installed at $(MY_GMP_DIR).  For 
        instance, if you have installed a full version of Core 
        Library at $(MY_CORELIB) then $(MY_GMP_DIR)=$(MY_CORELIB)/gmp.

          -- Link Core Library to pre-installed gmp by performing these steps:

                % cd ${CORE_PATH}
                % ln -s $(MY_GMP_PATH) gmp
                % make testgmp

        This should compiles and prints an encouraging message. 
        Continue from STAGE 2 (Step 3.5) above.

        
        (2) INSTALLATION FOR WINDOWS PLATFORM
        If you use cygwin on your windows platform, then the installation
        is same as on Unix platform as described above. 
        But if you use Visual C++ instead, then follow these steps.

          -- Download the file core_vX.Y_full.tgz (for version X.Y) from our
             website. (We recommend the Full Distribution since it contains
             gmp already and you cannot easily link to preinstalled gmp)
          -- Unpack it into some directory ${CORE_PATH}. 
          -- Unpack ${CORE_PATH}\gmp-xxx.tar.gz into ${CORE_PATH}\win32: this
             creates a subdirectory ${CORE_PATH}\win32\gmp-xxx. Rename this
             to plain ${CORE_PATH}\win32\gmp.
          -- Install gmp patches
                
                c:\>cd ${CORE_PATH}\win32\patches
                c:\>patch xxx      // where "xxx" is the gmp version;
                                   // (xxx = "3.1.1", "4.0.1", "4.1-static",
                                   //  and  "4.1-dynamic" available)
                                   // for GMP 4.1.2, you still can choose
                                   // "4.1-static" or "4.1-dynamic".

          -- Open a "Command Prompt" window and run "vcvars32.bat" to setup
             Visual C++ command line environment. File vcvars32.bat is
             automatically created by your Visual C++.  E.g., sometimes it is
             found in C:\"Microsoft Visual Studio"\vc98\Bin.

          -- Compile gmp and the Core Library: 
                
                c:\>cd ${CORE_PATH}\win32
                c:\>nmake
          
             This nmake also creates the Core Extension libraries and 
             and all the demo programs.

          -- Optional: Testing (for the demo programs)

                c:\>cd ${CORE_PATH}\win32
                c:\>set PATH=%PATH%;${CORE_PATH}\win32\lib
                c:\>nmake test
      
          -- Alternatively, use Visual Studio IDE to compile the Core Library
             and Core Extensions.  E.g., to compile Core Library, open the 
             project file "core.dsw" under ${CORE_PATH}\win32\corelib, and 
             compile.  To compile Core Extensions, open the project file "
             corex.dsw" under ${CORE_PATH}\win32\ext, and compile.

        (3) CORE USAGE FOR WINDOWS PLATFORM
        If you want to create your own Visual C++ project file, do the
        following steps:
 
          -- add "${CORE_PATH}\inc", "${CORE_PATH}\win32\gmp" into "Include Path".
          -- add "${CORE_PATH}\win32\lib" into "Lib Path".
          -- Enable "Run-Time Type Information" in your project settings. 

        (4) SHARED OR STATIC LIBRARY LINKAGE:
        In Make.config, you can set the LINKAGE variable to "shared" or
        "static".  The default is "static" for simplicity; but the
        executables will be fairly large (over 1MB each).
        To run programs using the static library there is nothing
        special to do;  to run the dynamic version of the Core Library,
        you could move your compiled CORE, gmp, etc, libraries 
        into the standard library paths (e.g., /lib or /usr/lib).
        Alternatively, you can set the environment
        variable LD_LIBRARY_PATH as follows:

        for "csh/tcsh",  
            % setenv LD_LIBRARY_PATH \
                ${CORE_PATH}/lib:${CORE_PATH}/gmp/lib:${LD_LIBRARY_PATH}.
        
        for "bash",
            $ export LD_LIBRARY_PATH= \
                ${CORE_PATH}/lib:${CORE_PATH}/gmp/lib:${LD_LIBRARY_PATH}.

        If gmp is not installed in ${CORE_PATH}, adjust accordingly.

        (5) RECOMPILATION OF THE CORE LIBRARY:
        Sometimes you may want to recompile the Core Library (perhaps after
        changing a file in ${CORE_PATH}/src or $(CORE_PATH)/inc).  
        The simplest is to go into ${CORE_PATH}/src and type
        "make clean; make".  This will automatically
        update the files libcore++.a and/or libcore++.so in ${CORE_PATH}/lib. 
        But for experimental purposes, we may want to keep two or more
        versions of libcore++.a around.  In this case, we suggest using the
        VAR variable described next.

        (6) DEBUGGING AND OTHER VERSIONS OF CORE LIBRARY: 
        It may be useful to have different compiled versions of the Core 
        Library around.  For this, you must edit file ${CORE_PATH}/Make.config.
        This file defines the compilation flags, depending on the platform.
        There are two main variables to set: VAR and PLATFORM.

        VAR indicates the "variant" of the library you want to compile.
        The Makefile creates the library file "libcore++$(VAR).a", which will be
        placed in ${CORE_PATH}/lib/.  Since the default value of VAR is
        the empty string, the default library is the plain "libcore++.a".

        Here are two useful variants, Debug variant and NoOpt variant:

        (a) VAR=Debug: you need this variant to run the GNU debugger, gdb.
           If you set VAR=Debug in Make.config, and then re-do STAGE 2 above
           (STAGE 1 does not have to be re-done), you will create the debugging
           variant of the library, namely "libcore++Debug.a".    The other stages
           will similarly create the Debug variants, e.g., Debug versions
           Core Extension libraries, sample programs, etc.
        (b) VAR=NoOpt: this version turns off all compiler optimizations.
           Try this if you find mysterious bugs, and want to rule out the
           possibility that they are caused by aggressive compiler optimizations.

        PLATFORM is used to define various variables that are platform-
        and compiler-specific.  It defaults to "gnu".  
        Other possible values are "sun", "cyg", "mingw", "sgi".
        The "sgi" option has not been tested in the latest library.

  3.10) CORE EXTENSIONS.

        Under ${CORE_PATH}/ext, you will find extensions of Core Library
        to encode knowledge of algebraic and geometric domains.  These
        "CORE Extensions" (COREX) are quite rudimentary at present, but 
        feel free to contribute.   

        For instance, there is a geometry2d and geometry3d.  We compile a
        Level 1 and Level 3 versions of these libraries, so that you can
        compile your application in either of these two accuracy levels.

  3.11) HOUSEKEEPING AND UNINSTALL

        To uninstall the library, simple delete all the files under
        ${CORE_PATH} (i.e., we do not put files anywhere).
        
        In every directory, we have a Makefile with two targets called
        "clean" and "veryclean".  If you want to save space, you can type
        "make clean" in any directory to remove temporary files.
        E.g., *.o files.  If you type "make veryclean", this will,
        in addition, remove more files (in particular, all executable files).
        NOTE: both targets are recursively propagated into subdirectories.


*************************************************************
4) NEWS, PLANS AND BUGS
   NEW in Version 1.7:
   -- Introduction of plane algebraic curves and bi-variate polynomials 
         The main capability is to plot curves and do basic
         intersection tests.  See CORE_PATH/progs/curves/.
   -- Introduced "InCore", an interactive version of Core Library 
         based on Python (this has to be downloaded separately)
   -- Enhancement of the univariate polynomial and real algebraic
        number facilities. New methods such as
        polynomial GCD, resultant, square free part, primitive part, etc.
        * Polynomial<NT> can now work with all choices of NT
                NT = BigInt, int, BigRat, Expr, BigFloat
          But not all functionality are fully available for
          NT=BigFloat and NT=Expr (e.g., rootbounds).
        * Sturm<NT> can now work with NT=BigFloat
        * To support the above, various new methods are added to the
          BigInt, BigRat, BigFloat and Real classes (isDivisible, gcd, etc).
        * Polynomials now accept string inputs. 
            E.g., Polynomial<BigInt> p = "x^3 - 2x^2 + 17x - 4";
   -- Compatibility with gmp 4.1, and gcc 3.3

   -- Introduced a common Reference Counting facility for all
         Core number types, encoded in the two templated classes:
                RCRepImpl<class N>
      to create Reps of the class N.  The basic functions provided by
      this class is reference counting, and gives us the "Reps" of
      each number type (e.g., BigIntRep is derived from RCRepImpl).  
      The other class is
                RCImpl<class T>
      which is the actual number type (e.g., BigInt is derived
      from RCImpl<BigIntRep>).  As a result former Rep Files
      such as RealRep.h can be removed, and the code size is reduced.
      Also, BigInt and BigRat now have reference counting in
      their Rep classes (none before).
   -- Speedup from reorganization of Core Library number classes.
      We wrote wrappers around gmp's C function library.
      We also tested the possibility of using gmp's C++ classes (since
      gmp 4.1) which are template based.  CORE's interface are not fully
      compatible with gmp since since we have exact algebraic representation
      and precision bounds.
      We compared three versions of Core Library:
           (A) -- old code: version 1.6
           (B) -- new code: some optimization
           (C) -- new code: optimzation + using gmp C++ class
      Here are the running times on two machines:
   
      Test              Pentium III (1G Memory)        Jinai (Solaris)
      =======================================================
      > A               64.12s                         1m:07s
      > B               56.52s                         52.6s
      > C               50.71s                         50.4s
      > Speedup         20%                            25%
    
      Although the use of gmp C++ classes (which use expression template
      to eliminate temporary variables) is faster, it is
      incompatiable with visual C++ (not sure about Sun CC).
      So we added as an option for compiling the Core Library:
      to turn on gmp C++ classes, uncomment macro CORE_USE_GMPXX
      in CoreImpl.h and recompile Core Library; there is no need to compile
      GMP C++ library since all necessory code are in Core Library already.

   -- Updated Core Library Tutorial
   -- Simple openGL display for curves: see CORE_PATH/ext/graphics/
   -- Bug fixes
          * rootOf(P,i) now works properly when P have multiple roots
            (reason: we assumed the endpoints of isolating intervals
            have distinct signs)
          * Fixed bugs in Newton and Sturm methods
          * Expr::doubleValue() is now correctly implemented.
            E.g., suppose you compute
                double s = sqrt(n);
                double ss = sqrt(Expr(n)).doubleValue();
            Then we guarantee that |s-ss| has relative error at
            most 4*CORE_EPS = 4.44089e-16 (CORE_EPS is machine epsilon). 
            This factor of 4 is essentially the best possible (see
            CORE_PATH/progs/testIO/testSqrt.cpp).
          * fixed Expr::degreeBound().  Previously it always returned 1 at
            leaves.  But with algebraic numbers, it must return d_e()).  This
            has dramatic improvement in speed. Ron Wein's program for
            intersecting two ellipses used to take overnight, but now take
            0.4 sec.
          * Fixed an output bug that has been around since Core 1.4.
            BigFloat can print an output whose exponent is off by 1.
                E.g., sqrt(100) = 9.999e0 but BigFloatRep::round(...),
                an internal function, returns the string "1.0000e0"
                instead of "1.0000e1".  Thanks to Blazi for noticing this.
   -- Miscellaneous:
          * Previously, the library version numbers have two numbers
            (e.g., "1" and "6" in Version 1.6).  Between official releases,
            we call it Version 1.6x.  Thus "Version 1.6x" refers to any
            number of unofficial releases between 1.6 and 1.7.
            We now have a third number.  E.g., this official release
            is Wersion 1.7.0.
          * CORE::core_error() is enhanced to write its results
            into a file "Core_Diagnostics" but also writes errors to
            std::cerr (as before).  
          * We introduce new versions of the BigFloat::makeExact(), namely,
            makeCeilExact() and makeFloorExact().
          * Upgraded Core Library to be compatible with the latest gmp
            4.1.3 (released 4/28/2004).
          * Use the program "astyle" to beautify all our code, so the
            files are more consistent and readable.  Tab are converted
            to spaces, use k&r style, etc):
                       ./astyle --style=kr -s2 filename
          * More use of BigFloats to replace Expr, when possible.  E.g.
            CauchyLowerBound() and CauchyUpperBound() rewritten using
            BigFloat instead of Expr (30% improvement here).
          * In CORE_PATH, you can type "make options" 
            to see all your currently selected CORE ENVIRONMENT VARIABLES.
            If you type "make alloptions", this will also show
            all possible alternatives that you could have chosen.
          * Simple timing facility (see src/Timer.h)
   -- Acknowledgements:  Thanks for feedback and bug reports from
            Janos Blazi, Arno Eigenwillig, Ovidiu Daescu,
            Andreas Fabri, Michael Hemmer, Athanasios Kakargias,
            Daniel Russell, Ron Wein.

   
   PLANS:
       -- improved precision-sensitive algorithm
       -- improved bounds (measure of Sekigawa, etc)
       -- better floating point filters
       -- optimized determinant primitive and filters
       -- compilation and optimization of expressions
       -- Expressions should have the ability to output exact values
                in case of integers or rational numbers.  Currently,
                only bigFloat values are output.
       -- complex numbers
       -- better implementation of relative precision bounds
       -- Newton-based algorithms for elementary functions
       -- development of Core Extensions (geometry, algebra, meshes, etc)
       -- graphical support and interface
       -- File I/O of Core Objects (e.g., expressions)
       -- CORE versions of "printf" and "scanf" (this will reduce the fuss to
                CORE-ize a standard C program).
       -- the exponent of a bigFloat number is represented by 
             a machine long.  This should not be a problem in practice.  An
             improvement is to use machine double for the exponent,
             yielding 53 bits of precision.
   
   BUGS:
       -- To report a bug, please send email to exact@cs.nyu.edu, with as
             much details as possible (including your platform/compiler).
       -- Let r = 54.  Suppose you convert a rational p/q to a BigFloat bf 
             using r bits of relative precision.  Next convert bf to a machine
             double md,
                       double md = (double)bf;
             This md should be equal to rounding "p/q" to the nearest machine
             double.  Turns out (Core 1.4) this may not be true!  
             But if r=59, our tests indicated that md does equal the machine
             rounding of p/q.  This bug is not too serious since,
             for any particular inputs, it can be removed by increasing r.
             Tests suggest that r=59 is sufficient for
             all p/q.  See ${CORE_PATH}/src/test/ for details.
       -- we should allow defOutputDigits to be CORE_INFTY, and when
             a rational number is printed in this case, we ought to print
             it with no errors.  Currently, we let defBigFloatOutputDigits
             control this output; since this value is never infinite,
             the printed value may have error.
       -- level II is not fully supported
       -- level IV is not fully defined 


*************************************************************
5) ACKNOWLEDGEMENT and BRIEF HISTORY

   This work has been supported by a National Science Foundation
        Grant \#CCR 9402464 and \#CCR 0082056 (an ITR grant).
   The Real/Expr Package (1994-96) was developed by
        Chee Yap and Tom Dube.  
   Koji Ouchi and Chee Yap further improved the Real/Expr Package with
        its concept of composite precision bounds.
        The new algorithms for BigFloat with automatic error bounds
        is documented in Koji's masters thesis.
   A Numerical Accuracy API (the 4 levels of accuracy) was 
        proposed by Chee Yap in Oct 1998.
   Core Library Version 1.1 (Jan 1999) was adapted from Real/Expr by
        Chee Yap, Vijay Karamcheti, Igor Pechtchanski and Chen Li to
        implement the Numerical Accuracy API.
        Compiler-based optimizations techniques were investigated.
   Version 1.2 (Sep 1999) is a debugged and improved version.
        The BFMS root bound was incorporated. 
   Version 1.3 (Sep 2000) is significantly
        faster than its predecessor because of new improved root 
        bounds and adoption of LiDIA/CLN's bignumber as default kernel.
   Version 1.4 (Aug 2001) moved from LiDIA/CLN to gmp as the main kernel.
        Incremental square roots, improved precision-sensitivity algorithms,
        simple floating point filters, hypergeometry package.  
   Version 1.5 (Aug 2002) improvements in speed and root bounds (k-ary bounds),
        CGAL compatibility changes, file I/O for large mathematical constants
        (BigInt, BigFloat, BigRat), improved hypergeometric package,
   Version 1.6 (June 2003) introduced arbitrary
        real algebraic numbers in Expr's, incorporated Polynomial and Sturm
        classes into Core Library.  CORE is now distributed with CGAL,
        and issued under the QPL agreement.
   Version 1.7 (Nov 2004) introduced algebraic curves and bivariate 
       polynomials.  An interactive version of Core Library called "InCore"
       is available.  Beginning graphic capability for display of curves.

*************************************************************
6)  LICENSE INFORMATION

   Core Library is now under the terms of the Q Public License
   version 1.0. See the file LICENSE.QPL distributed with CORE.
*************************************************************

*************************************************************
*  CONTACT AND FURTHER INFORMATION:
*       For comments and bug report, send email to:
*               exact@cs.nyu.edu.
*       Core Library Homepage:
*               http://cs.nyu.edu/exact/
*       CGAL Homepage:
*               http://www.cgal.org/
*       GEOMETRY FACTORY Homepage:
*               http://www.geometryfactory.com/
*       GNU/gmp Homepage:
*               http://www.gnu.org/software/gmp/gmp.html
*               http://www.gnu.org/home.html
*************************************************************