THIS IS A MODIFIED VERSION OF GMP-2.0.2.  THE MODIFICATIONS WERE MADE
TO INTEGRATE THIS CODE TO THE SSH SOFTWARE PACKAGE.  PLEASE CONTACT
ssh-bugs@cs.hut.fi IF MORE INFORMATION IS NEEDED.
-------------------------------------------------------------------------
			THE GNU MP LIBRARY


GNU MP is a library for arbitrary precision arithmetic, operating on signed
integers, rational numbers, and floating point numbers.  It has a rich set
of functions, and the functions have a regular interface.

GNU MP is designed to be as fast as possible, both for small operands and for
huge operands.  The speed is achieved by using fullwords as the basic
arithmetic type, by using fast algorithms, by carefully optimized assembly
code for the most common inner loops for a lots of CPUs, and by a general
emphasis on speed (instead of simplicity or elegance).

The speed of GNU MP is believed to be faster than any other similar library.
The advantage for GNU MP increases with the operand sizes for certain
operations, since GNU MP in many cases has asymptotically faster algorithms.


			GETTING STARTED

First, you have to configure and compiler GNU MP.  Simply typing

	./configure; make

will normally do a reasonable job, but will not give optimal library
execution speed.  So unless you're very unpatient, please read the detailed
instructions in the file INSTALL or in gmp.texi.

Once you have compiled the library, you should write some small example, and
make sure you can compile them.  A typical compilation command is this:

	gcc -g your-file.c -I<gmp-source-dir> <gmp-bin-dir>libgmp.a -lm

If you have installed the library, you can simply do:

	gcc -g your-file.c -lgmp -lm

The -lm is normally not needed, since only a few functions in GNU MP use the
math library.

Here is a sample program that declares 2 variables, initializes them as
required, and sets one of them from a signed integer, and the other from a
string of digits.  It then prints the product of the two numbers in base 10.

  #include <stdio.h>
  #include "gmp.h"

  main ()
  {
    mpz_t a, b, p;

    mpz_init (a);			/* initialize variables */
    mpz_init (b);
    mpz_init (p);

    mpz_set_si (a, 756839);		/* assign variables */
    mpz_set_str (b, "314159265358979323846", 0);
    mpz_mul (p, a, b);			/* generate product */
    mpz_out_str (stdout, 10, p);	/* print number without newline */
    puts ("");				/* print newline */

    mpz_clear (a);			/* clear out variables */
    mpz_clear (b);
    mpz_clear (p);

    exit (0);
  }

This might look tedious, with all initializing and clearing.  Fortunately
some of these operations can be combined, and other operations can often be
avoided.  The example above would be written differently by an experienced
GNU MP user:

  #include <stdio.h>
  #include "gmp.h"

  main ()
  {
    mpz_t b, p;

    mpz_init (p);

    mpz_init_set_str (b, "314159265358979323846", 0);
    mpz_mul_ui (p, b, 756839);		/* generate product */
    mpz_out_str (stdout, 10, p);	/* print number without newline */
    puts ("");				/* print newline */

    exit (0);
  }


			OVERVIEW OF GNU MP

There are five classes of functions in GNU MP.

 1. Signed integer arithmetic functions, mpz_*.  These functions are intended
    to be easy to use, with their regular interface.  The associated type is
    `mpz_t'.

 2. Rational arithmetic functions, mpq_*.  For now, just a small set of
    functions necessary for basic rational arithmetics.  The associated type
    is `mpq_t'.

 3. Floating-point arithmetic functions, mpf_*.  If the C type `double'
    doesn't give enough precision for your application, declare your
    variables as `mpf_t' instead, set the precision to any number desired,
    and call the functions in the mpf class for the arithmetic operations.

 4. Positive-integer, hard-to-use, very low overhead functions are in the
    mpn_* class.  No memory management is performed.  The caller must ensure
    enough space is available for the results.  The set of functions is not
    regular, nor is the calling interface.  These functions accept input
    arguments in the form of pairs consisting of a pointer to the least
    significant word, and a integral size telling how many limbs (= words)
    the pointer points to.

    Almost all calculations, in the entire package, are made by calling these
    low-level functions.

 5. Berkeley MP compatible functions.

    To use these functions, include the file "mp.h".  You can test if you are
    using the GNU version by testing if the symbol __GNU_MP__ is defined.

For more information on how to use GNU MP, please refer to the documentation.
It is composed from the file gmp.texi, and can be displayed on the screen or
printed.  How to do that, as well how to build the library, is described in
the INSTALL file in this directory.


			REPORTING BUGS

If you find a bug in the library, please make sure to tell us about it!

Report bugs and propose modifications and enhancements to
bug-gmp@prep.ai.mit.edu.  What information is needed in a good bug report is
described in the manual.
