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+\input texinfo    @c -*-texinfo-*-
+@c %**start of header
+@setfilename gmp.info
+@settitle GNU MP 2.0
+@synindex tp fn
+@iftex
+@afourpaper
+@end iftex
+@comment %**end of header
+
+@ifinfo
+@format
+START-INFO-DIR-ENTRY
+* gmp: (gmp.info).               GNU Multiple Precision Arithmetic Library.
+END-INFO-DIR-ENTRY
+@end format
+@end ifinfo
+
+@c smallbook
+
+@iftex
+@finalout
+@end iftex
+
+@c Note: the edition number is listed in *three* places; please update
+@c all three.  Also, update the month and year where appropriate.
+
+@c ==> Update edition number for settitle and subtitle, and in the
+@c ==> following paragraph; update date, too.
+
+
+@ifinfo
+This file documents GNU MP, a library for arbitrary-precision arithmetic.
+
+This is a draft edition of the documentation, last updated April 1996.
+
+Copyright (C) 1991, 1993, 1994, 1995, 1996 Free Software Foundation, Inc.
+
+Permission is granted to make and distribute verbatim copies of
+this manual provided the copyright notice and this permission notice
+are preserved on all copies.
+
+@ignore
+Permission is granted to process this file through TeX and print the
+results, provided the printed document carries copying permission
+notice identical to this one except for the removal of this paragraph
+(this paragraph not being relevant to the printed manual).
+
+@end ignore
+Permission is granted to copy and distribute modified versions of this
+manual under the conditions for verbatim copying, provided that the entire
+resulting derived work is distributed under the terms of a permission
+notice identical to this one.
+
+Permission is granted to copy and distribute translations of this manual
+into another language, under the above conditions for modified versions,
+except that this permission notice may be stated in a translation approved
+by the Foundation.
+@end ifinfo
+
+@setchapternewpage on
+@headings double
+@titlepage
+@c  use the new format for titles
+
+@title GNU MP
+@subtitle The GNU Multiple Precision Arithmetic Library
+@subtitle Edition 2.0
+@subtitle April 1996
+
+@author by Torbj@"orn Granlund, TMG Datakonsult
+
+@c Include the Distribution inside the titlepage so
+@c that headings are turned off.
+
+@tex
+\global\parindent=0pt
+\global\parskip=6pt
+\global\baselineskip=13pt
+@end tex
+
+@page
+@vskip 0pt plus 1filll
+Copyright @copyright{} 1991, 1993, 1994, 1995, 1996 Free Software Foundation, Inc.
+
+@sp 2
+
+Published by the Free Software Foundation @*
+59 Temple Place - Suite 330 @*
+Boston, MA 02111-1307, USA @*
+
+Permission is granted to make and distribute verbatim copies of
+this manual provided the copyright notice and this permission notice
+are preserved on all copies.
+
+Permission is granted to copy and distribute modified versions of this
+manual under the conditions for verbatim copying, provided that the entire
+resulting derived work is distributed under the terms of a permission
+notice identical to this one.
+
+Permission is granted to copy and distribute translations of this manual
+into another language, under the above conditions for modified versions,
+except that this permission notice may be stated in a translation approved
+by the Foundation.
+@end titlepage
+
+@ifinfo
+@node Top, Copying, (dir), (dir)
+
+@top GNU MP
+
+This manual documents how to install and use the GNU Multiple Precision
+Arithmetic Library, version 2.0.
+
+@end ifinfo
+
+@menu
+* Copying::                   GMP Copying Conditions (LGPL).
+* Introduction to MP::        Brief introduction to GNU MP.
+* Installing MP::             How to configure and compile the MP library.
+* MP Basics::                 What every MP user should now.
+* Reporting Bugs::            How to usefully report bugs.
+* Integer Functions::         Functions for arithmetic on signed integers.
+* Rational Number Functions:: Functions for arithmetic on rational numbers.
+* Floating-point Functions::  Functions for arithmetic on floats.
+* Low-level Functions::       Fast functions for natural numbers.
+* BSD Compatible Functions::  All functions found in BSD MP.
+* Custom Allocation::         How to customize the internal allocation.
+
+* Contributors::
+* References::
+* Concept Index::
+* Function Index::
+@end menu
+
+@node Copying, Introduction to MP, Top, Top
+@comment  node-name, next, previous,  up
+@unnumbered GNU MP Copying Conditions
+@cindex Copying conditions
+@cindex Conditions for copying GNU MP
+
+This library is @dfn{free}; this means that everyone is free to use it and
+free to redistribute it on a free basis.  The library is not in the public
+domain; it is copyrighted and there are restrictions on its distribution, but
+these restrictions are designed to permit everything that a good cooperating
+citizen would want to do.  What is not allowed is to try to prevent others
+from further sharing any version of this library that they might get from
+you.@refill
+
+Specifically, we want to make sure that you have the right to give away copies
+of the library, that you receive source code or else can get it if you want
+it, that you can change this library or use pieces of it in new free programs,
+and that you know you can do these things.@refill
+
+To make sure that everyone has such rights, we have to forbid you to deprive
+anyone else of these rights.  For example, if you distribute copies of the GNU
+MP library, you must give the recipients all the rights that you have.  You
+must make sure that they, too, receive or can get the source code.  And you
+must tell them their rights.@refill
+
+Also, for our own protection, we must make certain that everyone finds out
+that there is no warranty for the GNU MP library.  If it is modified by
+someone else and passed on, we want their recipients to know that what they
+have is not what we distributed, so that any problems introduced by others
+will not reflect on our reputation.@refill
+
+The precise conditions of the license for the GNU MP library are found in the
+Library General Public License that accompany the source code.@refill
+
+@node Introduction to MP, Installing MP, Copying, Top
+@comment  node-name,  next,  previous,  up
+@chapter Introduction to GNU MP
+
+
+GNU MP is a portable library written in C for arbitrary precision arithmetic
+on integers, rational numbers, and floating-point numbers.  It aims to provide
+the fastest possible arithmetic for all applications that need higher
+precision than is directly supported by the basic C types.
+
+Many applications use just a few hundred bits of precision; but some
+applications may need thousands or even millions of bits.  MP is designed to
+give good performance for both, by choosing algorithms based on the sizes of
+the operands, and by carefully keeping the overhead at a minimum.
+
+The speed of MP is achieved by using fullwords as the basic arithmetic type,
+by using sophisticated algorithms, by including carefully optimized assembly
+code for the most common inner loops for many different CPUs, and by a general
+emphasis on speed (as opposed to simplicity or elegance).
+
+There is carefully optimized assembly code for these CPUs: DEC Alpha, Amd
+29000, HPPA 1.0 and 1.1, Intel Pentium and generic x86, Intel i960, Motorola
+MC68000, MC68020, MC88100, and MC88110, Motorola/IBM PowerPC, National
+NS32000, IBM POWER, MIPS R3000, R4000, SPARCv7, SuperSPARC, generic SPARCv8,
+and DEC VAX.  Some optimizations also for ARM, Clipper, IBM ROMP (RT), and
+Pyramid AP/XP.
+
+This version of MP is released under a more liberal license than previous
+versions.  It is now permitted to link MP to non-free programs, as long as MP
+source code is provided when distributing the non-free program.
+
+
+@section How to use this Manual
+
+Everyone should read @ref{MP Basics}.  If you need to install the library
+yourself, you need to read @ref{Installing MP}, too.
+
+The rest of the manual can be used for later reference, although it is
+probably a good idea too glance through it.
+
+
+@node Installing MP, MP Basics, Introduction to MP, Top
+@comment  node-name,  next,  previous,  up
+@chapter Installing MP
+@cindex Installation
+
+To build MP, you first have to configure it for your CPU and operating system.
+You need a C compiler, preferably GCC, but any reasonable compiler should
+work.  And you need a standard Unix @samp{make} program, plus some other
+standard Unix utility programs.
+
+(If you're on a MS-DOS machine, your can build MP using @file{make.bat}.  It
+requires that djgpp is installed.  It does not require configuration, nor is
+@samp{make} needed; @file{make.bat} both configures and builds the library.)
+
+Here are the steps needed to install the library on Unix systems:
+
+@enumerate
+@item
+In most cases, @samp{./configure --target=cpu-vendor-os}, should work both for
+native and cross-compilation.  If you get error messages, your machine might
+not be supported.
+
+If you want to compile in a separate object directory, cd to that directory,
+and prefix the configure command with the path to the MP source directory.
+Not all @samp{make} programs have the necessary features to support this.  In
+particular, SunOS and Slowaris @samp{make} have bugs that makes them unable to
+build from a separate object directory.  Use GNU @samp{make} instead.
+
+In addition to the standard cpu-vendor-os tuples, MP recognizes sparc8 and
+supersparc as valid CPU names.  Specifying these CPU names for relevant
+systems will improve performance significantly.
+
+In general, if you want a library that runs as fast as possible, you should
+make sure you configure MP for the exact CPU type your system uses.
+
+If you have @code{gcc} in your @code{PATH}, it will be used by default.  To
+override this, pass @samp{-with-gcc=no} to @file{configure}.
+
+@item
+@samp{make}
+
+This will compile MP, and create a library archive file @file{libgmp.a} in the
+working directory.
+
+@item
+@samp{make check}
+
+This will make sure MP was built correctly.  If you get error messages, please
+report this to @samp{bug-gmp@@prep.ai.mit.edu}.  (@xref{Reporting Bugs}, for
+information on what to include in useful bug reports.)
+
+@item
+@samp{make install}
+
+This will copy the file @file{gmp.h} and @file{libgmp.a}, as well as the info
+files, to @file{/usr/local} (or if you passed the @samp{--prefix} option to
+@file{configure}, to the directory given as argument to @samp{--prefix}).
+@end enumerate
+
+@noindent
+If you wish to build and install the BSD MP compatible functions, use
+@samp{make libmp.a} and @samp{make install-bsdmp}.
+
+There are some other useful make targets:
+
+@itemize @bullet
+@item
+@samp{doc}
+
+Create a DVI version of the manual, in @file{gmp.dvi} and a set of info files,
+in @file{gmp.info}, @file{gmp.info-1}, @file{gmp.info-2}, etc.
+
+@item
+@samp{ps}
+
+Create a Postscript version of the manual, in @file{gmp.ps}.
+
+@item
+@samp{html}
+
+Create a HTML version of the manual, in @file{gmp.html}.
+
+@item
+@samp{clean}
+
+Delete all object files and archive files, but not the configuration files.
+
+@item
+@samp{distclean}
+
+Delete all files not included in the distribution.
+
+@item
+@samp{uninstall}
+
+Delete all files copied by @samp{make install}.
+@end itemize
+
+
+@section Known Build Problems
+
+GCC 2.7.2 (as well as 2.6.3) for the RS/6000 and PowerPC can not be used to
+compile MP, due to a bug in GCC.  If you want to use GCC for these machines,
+you need to apply the patch below to GCC, or use a later version of the
+compiler.
+
+If you are on a Sequent Symmetry, use the GNU assembler instead of the
+system's assembler, since the latter has serious bugs.
+
+The system compiler on NeXT is a massacred and old gcc, even if the compiler
+calls itself @file{cc}.  This compiler cannot be used to build MP.  You need
+to get a real gcc, and install that before you compile MP.  (NeXT might have
+fixed this in newer releases of their system.)
+
+Please report other problems to @samp{bug-gmp@@prep.ai.mit.edu}.
+@xref{Reporting Bugs}.
+
+
+Patch to apply to GCC 2.6.3 and 2.7.2:
+
+@example
+*** config/rs6000/rs6000.md	Sun Feb 11 08:22:11 1996
+--- config/rs6000/rs6000.md.new	Sun Feb 18 03:33:37 1996
+***************
+*** 920,926 ****
+     (set (match_operand:SI 0 "gpc_reg_operand" "=r")
+  	(not:SI (match_dup 1)))]
+    ""
+!   "nor. %0,%2,%1"
+    [(set_attr "type" "compare")])
+  
+  (define_insn ""
+--- 920,926 ----
+     (set (match_operand:SI 0 "gpc_reg_operand" "=r")
+  	(not:SI (match_dup 1)))]
+    ""
+!   "nor. %0,%1,%1"
+    [(set_attr "type" "compare")])
+  
+  (define_insn ""
+@end example
+
+@node MP Basics, Reporting Bugs, Installing MP, Top
+@comment  node-name,  next,  previous,  up
+@chapter MP Basics
+
+
+@cindex @file{gmp.h}
+All declarations needed to use MP are collected in the include file
+@file{gmp.h}.  It is designed to work with both C and C++ compilers.
+
+
+@section Nomenclature and Types
+
+@cindex Integer
+@tindex @code{mpz_t}
+@noindent
+In this manual, @dfn{integer} usually means a multiple precision integer, as
+defined by the MP library.  The C data type for such integers is @code{mpz_t}.
+Here are some examples of how to declare such integers:
+
+@example
+mpz_t sum;
+
+struct foo @{ mpz_t x, y; @};
+
+mpz_t vec[20];
+@end example
+
+@cindex Rational number
+@tindex @code{mpq_t}
+@noindent
+@dfn{Rational number} means a multiple precision fraction.  The C data type
+for these fractions is @code{mpq_t}.  For example:
+
+@example
+mpq_t quotient;
+@end example
+
+@cindex Floating-point number
+@tindex @code{mpf_t}
+@noindent
+@dfn{Floating point number} or @dfn{Float} for short, is an arbitrary precision
+mantissa with an limited precision exponent.  The C data type for such objects
+is @code{mpf_t}.
+
+@cindex Limb
+@tindex @code{mp_limb_t}
+@noindent
+A @dfn{limb} means the part of a multi-precision number that fits in a single
+word.  (We chose this word because a limb of the human body is analogous to a
+digit, only larger, and containing several digits.)  Normally a limb contains
+32 or 64 bits.  The C data type for a limb is @code{mp_limb_t}.
+
+
+@section Function Classes
+
+There are six classes of functions in the MP library:
+
+@enumerate
+@item
+Functions for signed integer arithmetic, with names beginning with
+@code{mpz_}.  The associated type is @code{mpz_t}.  There are about 100
+functions in this class.
+
+@item
+Functions for rational number arithmetic, with names beginning with
+@code{mpq_}.  The associated type is @code{mpq_t}.  There are about 20
+functions in this class, but the functions in the previous class can be used
+for performing arithmetic on the numerator and denominator separately.
+
+@item
+Functions for floating-point arithmetic, with names beginning with
+@code{mpf_}.  The associated type is @code{mpf_t}.  There are about 50
+functions is this class.
+
+@item
+Functions compatible with Berkeley MP, such as @code{itom}, @code{madd}, and
+@code{mult}.  The associated type is @code{MINT}.
+
+@item
+Fast low-level functions that operate on natural numbers.  These are used by
+the functions in the preceding groups, and you can also call them directly
+from very time-critical user programs.  These functions' names begin with
+@code{mpn_}.  There are about 30 (hard-to-use) functions in this class.
+
+The associated type is array of @code{mp_limb_t}.
+
+@item
+Miscellaneous functions.  Functions for setting up custom allocation.
+@end enumerate
+
+
+@section MP Variable Conventions
+
+As a general rule, all MP functions expect output arguments before input
+arguments.  This notation is based on an analogy with the assignment operator.
+(The BSD MP compatibility functions disobey this rule, having the output
+argument(s) last.)
+
+MP allows you to use the same variable for both input and output in the same
+expression.  For example, the main function for integer multiplication,
+@code{mpz_mul}, can be used like this: @code{mpz_mul (x, x, x);}.  This
+computes the square of @var{x} and put the result back in @var{x}.
+
+Before you can assign to an MP variable, you need to initialize it by calling
+one of the special initialization functions.  When you're done with a
+variable, you need to clear it out, using one of the functions for that
+purpose.  Which function to use depends on the type of variable.  See the
+chapters on integer functions, rational number functions, and floating-point
+functions for details.
+
+A variable should only be initialized once, or at least cleared out between
+each initialization.  After a variable has been initialized, it may be
+assigned to any number of times.
+
+For efficiency reasons, avoid to initialize and clear out a variable in loops.
+Instead, initialize it before entering the loop, and clear it out after the
+loop has exited.
+
+You don't need to be concerned about allocating additional space for MP
+variables.  All functions in MP automatically allocate additional space when a
+variable does not already have enough space.  They do not, however, reduce the
+space when a smaller number is stored in the object.  Most of the time, this
+policy is best, since it avoids frequent re-allocation.
+
+
+@section Useful Macros and Constants
+
+@deftypevr {Global Constant} {const int} mp_bits_per_limb
+The number of bits per limb.
+@end deftypevr
+
+@defmac __GNU_MP_VERSION
+@defmacx __GNU_MP_VERSION_MINOR
+The major and minor MP version, respectively, as integers.
+@end defmac
+
+@section Compatibility with Version 1.x
+
+This version of MP is upward compatible with previous versions of MP, with a
+few exceptions.
+
+@enumerate
+@item Integer division functions round the result differently.  The old
+functions (@code{mpz_div}, @code{mpz_divmod}, @code{mpz_mdiv},
+@code{mpz_mdivmod}, etc) now all use floor rounding (i.e., they round the
+quotient to @minus{}infinity).  There are a lot of new functions for integer
+division, giving the user better control over the rounding.
+
+@item The function @code{mpz_mod} now compute the true @strong{mod} function.
+
+@item The functions @code{mpz_powm} and @code{mpz_powm_ui} now use
+@strong{mod} for reduction.
+
+@item The assignment functions for rational numbers do no longer canonicalize
+their results.  In the case a non-canonical result could arise from an
+assignment, the user need to insert an explicit call to
+@code{mpq_canonicalize}.  This change was made for efficiency.
+
+@item Output generated by @code{mpz_out_raw} in this release cannot be read
+by @code{mpz_inp_raw} in previous releases.  This change was made for making
+the file format truly portable between machines with different word sizes.
+
+@item Several @code{mpn} functions have changed.  But they were intentionally
+undocumented in previous releases.
+
+@end enumerate
+
+
+@section Getting the Latest Version of MP
+
+The latest version of the MP library is available by anonymous ftp from from
+@samp{prep.ai.mit.edu}.  The file name is @file{/pub/gnu/gmp-M.N.tar.gz}.
+Many sites around the world mirror @samp{prep}; please use a mirror site near
+you.
+
+@node Reporting Bugs, Integer Functions, MP Basics, Top
+@comment  node-name,  next,  previous,  up
+@chapter Reporting Bugs
+@cindex Reporting bugs
+
+If you think you have found a bug in the MP library, please investigate it and
+report it.  We have made this library available to you, and it is not to ask
+too much from you, to ask you to report the bugs that you find.
+
+There are a few things you should think about when you put your bug report
+together.
+
+You have to send us a test case that makes it possible for us to reproduce the
+bug.  Include instructions on how to run the test case.
+
+You also have to explain what is wrong; if you get a crash, or if the results
+printed are incorrect and in that case, in what way.
+
+It is not uncommon that an observed problem is actually due to a bug in the
+compiler used when building MP; the MP code tends to explore interesting
+corners in compilers.  Therefore, please include compiler version information
+in your bug report.  This can be extracted using @samp{what `which cc`}, or,
+if you're using gcc, @samp{gcc -v}.  Also, include the output from @samp{uname
+-a}.
+
+If your bug report is good, we will do our best to help you to get a corrected
+version of the library; if the bug report is poor, we won't do anything about
+it (aside of chiding you to send better bug reports).
+
+Send your bug report to: @samp{bug-gmp@@prep.ai.mit.edu}.
+
+If you think something in this manual is unclear, or downright incorrect, or if
+the language needs to be improved, please send a note to the same address.
+
+
+@node Integer Functions, Rational Number Functions, Reporting Bugs, Top
+@comment  node-name,  next,  previous,  up
+@chapter Integer Functions
+@cindex Integer functions
+
+This chapter describes the MP functions for performing integer arithmetic.
+These functions start with the prefix @code{mpz_}.
+
+Arbitrary precision integers are stored in objects of type @code{mpz_t}.
+
+@menu
+* Initializing Integers::
+* Assigning Integers::
+* Simultaneous Integer Init & Assign::
+* Converting Integers::
+* Integer Arithmetic::
+* Comparison Functions::
+* Integer Logic and Bit Fiddling::
+* I/O of Integers::
+* Miscellaneous Integer Functions::
+@end menu
+
+@node Initializing Integers, Assigning Integers, , Integer Functions
+@comment  node-name,  next,  previous,  up
+@section Initialization and Assignment Functions
+
+The functions for integer arithmetic assume that all integer objects are
+initialized.  You do that by calling the function @code{mpz_init}.
+
+@deftypefun void mpz_init (mpz_t @var{integer})
+Initialize @var{integer} with limb space and set the initial numeric value to
+0.  Each variable should normally only be initialized once, or at least cleared
+out (using @code{mpz_clear}) between each initialization.
+@end deftypefun
+
+Here is an example of using @code{mpz_init}:
+
+@example
+@{
+  mpz_t integ;
+  mpz_init (integ);
+  @dots{}
+  mpz_add (integ, @dots{});
+  @dots{}
+  mpz_sub (integ, @dots{});
+
+  /* Unless the program is about to exit, do ... */
+  mpz_clear (integ);
+@}
+@end example
+
+@noindent
+As you can see, you can store new values any number of times, once an
+object is initialized.
+
+@deftypefun void mpz_clear (mpz_t @var{integer})
+Free the limb space occupied by @var{integer}.  Make sure to call this
+function for all @code{mpz_t} variables when you are done with them.
+@end deftypefun
+
+@deftypefun {void *} _mpz_realloc (mpz_t @var{integer}, mp_size_t @var{new_alloc})
+Change the limb space allocation to @var{new_alloc} limbs.  This function is
+not normally called from user code, but it can be used to give memory back to
+the heap, or to increase the space of a variable to avoid repeated automatic
+re-allocation.
+@end deftypefun
+
+@deftypefun void mpz_array_init (mpz_t @var{integer_array}[], size_t @var{array_size}, mp_size_t @var{fixed_num_bits})
+Allocate @strong{fixed} limb space for all @var{array_size} integers in
+@var{integer_array}.  The fixed allocation for each integer in the array is
+enough to store @var{fixed_num_bits}.  If the fixed space will be insufficient
+for storing the result of a subsequent calculation, the result is
+unpredictable.
+
+This function is useful for decreasing the working set for some algorithms
+that use large integer arrays.
+
+There is no way to de-allocate the storage allocated by this function.
+Don't call @code{mpz_clear}!
+@end deftypefun
+
+
+@node Assigning Integers, Simultaneous Integer Init & Assign, Initializing Integers, Integer Functions
+@comment  node-name,  next,  previous,  up
+@subsection Assignment Functions
+@cindex Integer assignment functions
+
+These functions assign new values to already initialized integers
+(@pxref{Initializing Integers}).
+
+@deftypefun void mpz_set (mpz_t @var{rop}, mpz_t @var{op})
+@deftypefunx void mpz_set_ui (mpz_t @var{rop}, unsigned long int @var{op})
+@deftypefunx void mpz_set_si (mpz_t @var{rop}, signed long int @var{op})
+@deftypefunx void mpz_set_d (mpz_t @var{rop}, double @var{op})
+Set the value of @var{rop} from @var{op}.
+@end deftypefun
+
+@deftypefun int mpz_set_str (mpz_t @var{rop}, char *@var{str}, int @var{base})
+Set the value of @var{rop} from @var{str}, a '\0'-terminated C string in base
+@var{base}.  White space is allowed in the string, and is simply ignored.  The
+base may vary from 2 to 36.  If @var{base} is 0, the actual base is determined
+from the leading characters: if the first two characters are `0x' or `0X',
+hexadecimal is assumed, otherwise if the first character is `0', octal is
+assumed, otherwise decimal is assumed.
+
+This function returns 0 if the entire string up to the '\0' is a valid
+number in base @var{base}.  Otherwise it returns @minus{}1.
+@end deftypefun
+
+
+@node Simultaneous Integer Init & Assign, Converting Integers, Assigning Integers, Integer Functions
+@comment  node-name,  next,  previous,  up
+@subsection Combined Initialization and Assignment Functions
+@cindex Initialization and assignment functions
+
+For convenience, MP provides a parallel series of initialize-and-set functions
+which initialize the output and then store the value there.  These functions'
+names have the form @code{mpz_init_set@dots{}}
+
+Here is an example of using one:
+
+@example
+@{
+  mpz_t pie;
+  mpz_init_set_str (pie, "3141592653589793238462643383279502884", 10);
+  @dots{}
+  mpz_sub (pie, @dots{});
+  @dots{}
+  mpz_clear (pie);
+@}
+@end example
+
+@noindent
+Once the integer has been initialized by any of the @code{mpz_init_set@dots{}}
+functions, it can be used as the source or destination operand for the ordinary
+integer functions.  Don't use an initialize-and-set function on a variable
+already initialized!
+
+@deftypefun void mpz_init_set (mpz_t @var{rop}, mpz_t @var{op})
+@deftypefunx void mpz_init_set_ui (mpz_t @var{rop}, unsigned long int @var{op})
+@deftypefunx void mpz_init_set_si (mpz_t @var{rop}, signed long int @var{op})
+@deftypefunx void mpz_init_set_d (mpz_t @var{rop}, double @var{op})
+Initialize @var{rop} with limb space and set the initial numeric value from
+@var{op}.
+@end deftypefun
+
+@deftypefun int mpz_init_set_str (mpz_t @var{rop}, char *@var{str}, int @var{base})
+Initialize @var{rop} and set its value from @var{str}, a '\0'-terminated C
+string in base @var{base}.  White space is allowed in the string, and is simply
+ignored.  The base may vary from 2 to 36.  If @var{base} is 0, the actual base
+is determined from the leading characters: if the first two characters are `0x'
+or `0X', hexadecimal is assumed, otherwise if the first character is `0', octal
+is assumed, otherwise decimal is assumed.
+
+If the string is a correct base @var{base} number, the function returns 0;
+if an error occurs it returns @minus{}1.  @var{rop} is initialized even if
+an error occurs.  (I.e., you have to call @code{mpz_clear} for it.)
+@end deftypefun
+
+
+@node Converting Integers,  Integer Arithmetic, Simultaneous Integer Init & Assign, Integer Functions
+@comment  node-name,  next,  previous,  up
+@section Conversion Functions
+@cindex Integer conversion functions
+@cindex Conversion functions
+
+This section describes functions for converting arbitrary precision integers
+to standard C types.  Functions for converting @strong{to} arbitrary
+precision integers are described in @ref{Assigning Integers} and @ref{I/O of
+Integers}.
+
+@deftypefun {unsigned long int} mpz_get_ui (mpz_t @var{op})
+Return the least significant part from @var{op}.  This function combined
+with @* @code{mpz_tdiv_q_2exp(@dots{}, @var{op}, CHAR_BIT*sizeof(unsigned
+long int))} can be used to extract the limbs of an integer efficiently.
+@end deftypefun
+
+@deftypefun {signed long int} mpz_get_si (mpz_t @var{op})
+If @var{op} fits into a @code{signed long int} return the value of @var{op}.
+Otherwise return the least significant part of @var{op}, with the same sign
+as @var{op}.
+
+If @var{op} is too large to fit in a @code{signed long int}, the returned
+result is probably not very useful.  @c To find out if the value will fit, use
+@c the function @code{mpz_fits_si}.
+@end deftypefun
+
+@deftypefun {char *} mpz_get_str (char *@var{str}, int @var{base}, mpz_t @var{op})
+Convert @var{op} to a string of digits in base @var{base}.  The base may vary
+from 2 to 36.
+
+If @var{str} is NULL, space for the result string is allocated using the
+default allocation function, and a pointer to the string is returned.
+
+If @var{str} is not NULL, it should point to a block of storage enough large
+for the result.  To find out the right amount of space to provide for
+@var{str}, use @code{mpz_sizeinbase (@var{op}, @var{base}) + 2}.  The two
+extra bytes are for a possible minus sign, and for the terminating null
+character.
+@end deftypefun
+
+
+@need 2000
+@node Integer Arithmetic, Comparison Functions, Converting Integers, Integer Functions
+@comment  node-name,  next,  previous,  up
+@section Arithmetic Functions
+@cindex Integer arithmetic functions
+@cindex Arithmetic functions
+
+@deftypefun void mpz_add (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
+@deftypefunx void mpz_add_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
+Set @var{rop} to @var{op1} + @var{op2}.
+@end deftypefun
+
+@deftypefun void mpz_sub (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
+@deftypefunx void mpz_sub_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
+Set @var{rop} to @var{op1} @minus{} @var{op2}.
+@end deftypefun
+
+@deftypefun void mpz_mul (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
+@deftypefunx void mpz_mul_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
+Set @var{rop} to @var{op1} times @var{op2}.
+@end deftypefun
+
+Division is undefined if the divisor is zero, and passing a zero divisor to
+the divide or modulo functions, as well passing a zero mod argument to the
+@code{mpz_powm} and @code{mpz_powm_ui} functions, will make these functions
+intentionally divide by zero.  This gives the user the possibility to handle
+arithmetic exceptions in these functions in the same manner as other
+arithmetic exceptions.
+
+There are three main groups of division functions:
+@itemize @bullet
+@item
+Functions that truncate the quotient towards 0.  The names of these
+functions start with @code{mpz_tdiv}.  The @samp{t} in the name is short for
+@samp{truncate}.
+@item
+Functions that round the quotient towards @minus{}infinity.  The names of
+these routines start with @code{mpz_fdiv}.  The @samp{f} in the name is
+short for @samp{floor}.
+@item
+Functions that round the quotient towards +infinity.  The names of
+these routines start with @code{mpz_cdiv}.  The @samp{c} in the name is
+short for @samp{ceil}.
+@end itemize
+
+For each rounding mode, there are a couple of variants.  Here @samp{q} means
+that the quotient is computed, while @samp{r} means that the remainder is
+computed.  Functions that compute both the quotient and remainder have
+@samp{qr} in the name.
+
+@deftypefun void mpz_tdiv_q (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
+@deftypefunx void mpz_tdiv_q_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
+Set @var{rop} to [@var{op1} / @var{op2}].  The quotient is truncated towards
+0.
+@end deftypefun
+
+@deftypefun void mpz_tdiv_r (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
+@deftypefunx void mpz_tdiv_r_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
+Set @var{rop} to (@var{op1} - [@var{op1} / @var{op2}] * @var{op2}).
+Unless the remainder is zero, it has the same sign as the dividend.
+@end deftypefun
+
+@deftypefun void mpz_tdiv_qr (mpz_t @var{rop1}, mpz_t @var{rop2}, mpz_t @var{op1}, mpz_t @var{op2})
+@deftypefunx void mpz_tdiv_qr_ui (mpz_t @var{rop1}, mpz_t @var{rop2}, mpz_t @var{op1}, unsigned long int @var{op2})
+Divide @var{op1} by @var{op2} and put the quotient in @var{rop1} and the
+remainder in @var{rop2}.  The quotient is rounded towards 0.  Unless the
+remainder is zero, it has the same sign as the dividend.
+
+If @var{rop1} and @var{rop2} are the same variable, the results are
+undefined.
+@end deftypefun
+
+@deftypefun void mpz_fdiv_q (mpz_t @var{rop1}, mpz_t @var{op1}, mpz_t @var{op2})
+@deftypefunx void mpz_fdiv_q_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
+@ifinfo
+Set @var{rop} to @var{op1} / @var{op2}.  The quotient is rounded towards
+@minus{}infinity.
+@end ifinfo
+@iftex
+Set @var{rop} to
+@tex
+$\lfloor@var{op1} / @var{op2}\rfloor$.
+@end tex
+(I.e., round the quotient towards
+@tex
+$-\infty$.)
+@end tex
+@end iftex
+@end deftypefun
+
+@deftypefun void mpz_fdiv_r (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
+@deftypefunx {unsigned long int} mpz_fdiv_r_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
+Divide @var{op1} by @var{op2} and put the remainder in @var{rop}.  Unless
+the remainder is zero, it has the same sign as the divisor.
+
+For @code{mpz_fdiv_r_ui} the remainder is small enough to fit in an
+@code{unsigned long int}, and is therefore returned.
+@end deftypefun
+
+@deftypefun void mpz_fdiv_qr (mpz_t @var{rop1}, mpz_t @var{rop2}, mpz_t @var{op1}, mpz_t @var{op2})
+@deftypefunx {unsigned long int} mpz_fdiv_qr_ui (mpz_t @var{rop1}, mpz_t @var{rop2}, mpz_t @var{op1}, unsigned long int @var{op2})
+Divide @var{op1} by @var{op2} and put the quotient in @var{rop1} and the
+remainder in @var{rop2}.  The quotient is rounded towards @minus{}infinity.
+Unless the remainder is zero, it has the same sign as the divisor.
+
+For @code{mpz_fdiv_qr_ui} the remainder is small enough to fit in an
+@code{unsigned long int}, and is therefore returned.
+
+If @var{rop1} and @var{rop2} are the same variable, the results are
+undefined.
+@end deftypefun
+
+@deftypefun {unsigned long int} mpz_fdiv_ui (mpz_t @var{op1}, unsigned long int @var{op2})
+This function is similar to @code{mpz_fdiv_r_ui}, but the remainder is only
+returned; it is not stored anywhere.
+@end deftypefun
+
+@deftypefun void mpz_cdiv_q (mpz_t @var{rop1}, mpz_t @var{op1}, mpz_t @var{op2})
+@deftypefunx void mpz_cdiv_q_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
+@ifinfo
+Set @var{rop} to @var{op1} / @var{op2}.  The quotient is rounded towards
++infinity.
+@end ifinfo
+@iftex
+Set @var{rop} to
+@tex
+$\lceil@var{op1} / @var{op2}\rceil$.
+@end tex
+(I.e., round the quotient towards
+@tex
+$+\infty$.)
+@end tex
+@end iftex
+@end deftypefun
+
+@deftypefun void mpz_cdiv_r (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
+@deftypefunx {unsigned long int} mpz_cdiv_r_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
+Divide @var{op1} by @var{op2} and put the remainder in @var{rop}.  Unless
+the remainder is zero, it has the opposite sign as the divisor.
+
+For @code{mpz_cdiv_r_ui} the negated remainder is small enough to fit in an
+@code{unsigned long int}, and it is therefore returned.
+@end deftypefun
+
+@deftypefun void mpz_cdiv_qr (mpz_t @var{rop1}, mpz_t @var{rop2}, mpz_t @var{op1}, mpz_t @var{op2})
+@deftypefunx {unsigned long int} mpz_cdiv_qr_ui (mpz_t @var{rop1}, mpz_t @var{rop2}, mpz_t @var{op1}, unsigned long int @var{op2})
+Divide @var{op1} by @var{op2} and put the quotient in @var{rop1} and the
+remainder in @var{rop2}.  The quotient is rounded towards +infinity.  Unless
+the remainder is zero, it has the opposite sign as the divisor.
+
+For @code{mpz_cdiv_qr_ui} the negated remainder is small enough to fit in an
+@code{unsigned long int}, and it is therefore returned.
+
+If @var{rop1} and @var{rop2} are the same variable, the results are
+undefined.
+@end deftypefun
+
+@deftypefun {unsigned long int} mpz_cdiv_ui (mpz_t @var{op1}, unsigned long int @var{op2})
+Return the negated remainder, similar to @code{mpz_cdiv_r_ui}.  (The
+difference is that this function doesn't store the remainder anywhere.)
+@end deftypefun
+
+@deftypefun void mpz_mod (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
+@deftypefunx {unsigned long int} mpz_mod_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
+Set @var{rop} to @var{op1} @code{mod} @var{op2}.  The sign of the divisor is
+ignored, and the result is always non-negative.
+
+For @code{mpz_mod_ui} the remainder is small enough to fit in an
+@code{unsigned long int}, and is therefore returned.
+@end deftypefun
+
+@deftypefun void mpz_divexact (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
+Set @var{rop} to @var{op1} / @var{op2}.  This function produces correct
+results only when it is known in advance that @var{op2} divides
+@var{op1}.
+
+Since mpz_divexact is much faster than any of the other routines that produce
+the quotient (@pxref{References} Jebelean), it is the best choice for
+instances in which exact division is known to occur, such as reducing a
+rational to lowest terms.
+@end deftypefun
+
+@deftypefun void mpz_sqrt (mpz_t @var{rop}, mpz_t @var{op})
+@ifinfo
+Set @var{rop} to the truncated integer part of the square root of
+@var{op}.
+@end ifinfo
+@iftex
+Set @var{rop} to
+@tex
+$\lfloor\sqrt{@var{op}}\rfloor$, the truncated integer part of the square
+root of @var{op}.
+@end tex
+@end iftex
+@end deftypefun
+
+@deftypefun void mpz_sqrtrem (mpz_t @var{rop1}, mpz_t @var{rop2}, mpz_t @var{op})
+@ifinfo
+Set @var{rop1} to the truncated integer part of the square root of @var{op},
+like @code{mpz_sqrt}.  Set @var{rop2} to
+@var{op}@minus{}@var{rop1}*@var{rop1},
+@end ifinfo
+@iftex
+Set @var{rop1} to
+@tex
+$\lfloor\sqrt{@var{op}}\rfloor$,
+@end tex
+like @code{mpz_sqrt}.  Set @var{rop2} to
+@tex
+$(@var{op} - @var{rop1}^2)$,
+@end tex
+@end iftex
+(i.e., zero if @var{op} is a perfect square).
+
+If @var{rop1} and @var{rop2} are the same variable, the results are
+undefined.
+@end deftypefun
+
+@deftypefun int mpz_perfect_square_p (mpz_t @var{op})
+Return non-zero if @var{op} is a perfect square, i.e., if the square root of
+@var{op} is an integer.  Return zero otherwise.
+@end deftypefun
+
+@deftypefun int mpz_probab_prime_p (mpz_t @var{op}, int @var{reps})
+If this function returns 0, @var{op} is definitely not prime.  If it returns
+1, then @var{op} is `probably' prime.  The probability of a false positive is
+@ifinfo
+(1/4)**@var{reps}.
+@end ifinfo
+@iftex
+@tex
+$(1/4)^{{reps}}$.
+@end tex
+@end iftex
+A reasonable value of reps is 25.
+
+An implementation of the probabilistic primality test found in Seminumerical
+Algorithms (@pxref{References} Knuth).
+@end deftypefun
+
+@deftypefun void mpz_powm (mpz_t @var{rop}, mpz_t @var{base}, mpz_t @var{exp}, mpz_t @var{mod})
+@deftypefunx void mpz_powm_ui (mpz_t @var{rop}, mpz_t @var{base}, unsigned long int @var{exp}, mpz_t @var{mod})
+Set @var{rop} to (@var{base} raised to @var{exp}) @code{mod} @var{mod}.  If
+@var{exp} is negative, the result is undefined.
+@end deftypefun
+
+@deftypefun void mpz_pow_ui (mpz_t @var{rop}, mpz_t @var{base}, unsigned long int @var{exp})
+@deftypefunx void mpz_ui_pow_ui (mpz_t @var{rop}, unsigned long int @var{base}, unsigned long int @var{exp})
+Set @var{rop} to @var{base} raised to @var{exp}.
+@end deftypefun
+
+@deftypefun void mpz_fac_ui (mpz_t @var{rop}, unsigned long int @var{op})
+Set @var{rop} to @var{op}!, the factorial of @var{op}.
+@end deftypefun
+
+@deftypefun void mpz_gcd (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
+Set @var{rop} to the greatest common divisor of @var{op1} and @var{op2}.
+@end deftypefun
+
+@deftypefun {unsigned long int} mpz_gcd_ui (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
+Compute the greatest common divisor of @var{op1} and @var{op2}.  If
+@var{rop} is not NULL, store the result there.
+
+If the result is small enough to fit in an @code{unsigned long int}, it is
+returned.  If the result does not fit, 0 is returned, and the result is equal
+to the argument @var{op1}.  Note that the result will always fit if @var{op2}
+is non-zero.
+@end deftypefun
+
+@deftypefun void mpz_gcdext (mpz_t @var{g}, mpz_t @var{s}, mpz_t @var{t}, mpz_t @var{a}, mpz_t @var{b})
+Compute @var{g}, @var{s}, and @var{t}, such that @var{a}@var{s} +
+@var{b}@var{t} = @var{g} = @code{gcd} (@var{a}, @var{b}).  If @var{t} is
+NULL, that argument is not computed.
+@end deftypefun
+
+@deftypefun int mpz_invert (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
+Compute the inverse of @var{op1} modulo @var{op2} and put the result in
+@var{rop}.  Return non-zero if an inverse exist, zero otherwise.  When the
+function returns zero, do not assume anything about the value in @var{rop}.
+@end deftypefun
+
+@deftypefun void mpz_neg (mpz_t @var{rop}, mpz_t @var{op})
+Set @var{rop} to @minus{}@var{op}.
+@end deftypefun
+
+@deftypefun void mpz_abs (mpz_t @var{rop}, mpz_t @var{op})
+Set @var{rop} to the absolute value of @var{op}.
+@end deftypefun
+
+@deftypefun void mpz_mul_2exp (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
+Set @var{rop} to @var{op1} times 2 raised to @var{op2}.  This operation can
+also be defined as a left shift, @var{op2} steps.
+@end deftypefun
+
+@deftypefun void mpz_tdiv_q_2exp (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
+Set @var{rop} to @var{op1} divided by 2 raised to @var{op2}.  The quotient is
+rounded towards 0.
+@end deftypefun
+
+@deftypefun void mpz_fdiv_q_2exp (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
+Set @var{rop} to @var{op1} divided by 2 raised to @var{op2}.  The quotient is
+rounded towards @minus{}infinity.
+@end deftypefun
+
+@deftypefun void mpz_tdiv_r_2exp (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
+Divide @var{op1} by (2 raised to @var{op2}) and put the remainder in
+@var{rop}.  The sign of @var{rop} will have the same sign as @var{op1}, unless
+is becomes zero.
+@end deftypefun
+
+@deftypefun void mpz_fdiv_r_2exp (mpz_t @var{rop}, mpz_t @var{op1}, unsigned long int @var{op2})
+Divide @var{op1} by (2 raised to @var{op2}) and put the remainder in
+@var{rop}.  The sign of @var{rop} will always be positive.
+
+This operation can also be defined as masking of the @var{op2} least
+significant bits.
+@end deftypefun
+
+@node Comparison Functions, Integer Logic and Bit Fiddling, Integer Arithmetic, Integer Functions
+@comment  node-name,  next,  previous,  up
+@section Comparison Functions
+
+@deftypefun int mpz_cmp (mpz_t @var{op1}, mpz_t @var{op2})
+@deftypefunx int mpz_cmp_ui (mpz_t @var{op1}, unsigned long int @var{op2})
+@deftypefunx int mpz_cmp_si (mpz_t @var{op1}, signed long int @var{op2})
+Compare @var{op1} and @var{op2}.  Return a positive value if @var{op1} >
+@var{op2}, zero if @var{op1} = @var{op2}, and a negative value if @var{op1}
+< @var{op2}.
+@end deftypefun
+
+@deftypefun int mpz_sgn (mpz_t @var{op})
+Return +1 if @var{op} > 0, 0 if @var{op} = 0, and @minus{}1 if @var{op} < 0.
+@end deftypefun
+
+@node Integer Logic and Bit Fiddling, I/O of Integers, Comparison Functions, Integer Functions
+@comment  node-name,  next,  previous,  up
+@section Logical and Bit Manipulation Functions
+@cindex Logical functions
+@cindex Bit manipulation functions
+
+These functions behave as if two's complement arithmetic were used (although
+sign-magnitude is used by the actual implementation).
+
+@deftypefun void mpz_and (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
+Set @var{rop} to @var{op1} logical-and @var{op2}.
+@end deftypefun
+
+@deftypefun void mpz_ior (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
+Set @var{rop} to @var{op1} inclusive-or @var{op2}.
+@end deftypefun
+
+@c @deftypefun void mpz_xor (mpz_t @var{rop}, mpz_t @var{op1}, mpz_t @var{op2})
+@c Set @var{rop} to @var{op1} exclusive-or @var{op2}.
+@c @end deftypefun
+
+@deftypefun void mpz_com (mpz_t @var{rop}, mpz_t @var{op})
+Set @var{rop} to the one's complement of @var{op}.
+@end deftypefun
+
+@deftypefun {unsigned long int} mpz_popcount (mpz_t @var{op})
+For non-negative numbers, return the population count of @var{op}.  For
+negative numbers, return the largest possible value (@var{MAX_ULONG}).
+@end deftypefun
+
+@deftypefun {unsigned long int} mpz_hamdist (mpz_t @var{op1}, mpz_t @var{op2})
+If @var{op1} and @var{op2} are both non-negative, return the hamming distance
+between the two operands.  Otherwise, return the largest possible value
+(@var{MAX_ULONG}).
+
+It is possible to extend this function to return a useful value when the
+operands are both negative, but the current implementation returns
+@var{MAX_ULONG} in this case.  @strong{Do not depend on this behavior, since
+it will change in future versions of the library.}
+@end deftypefun
+
+@deftypefun {unsigned long int} mpz_scan0 (mpz_t @var{op}, unsigned long int @var{starting_bit})
+Scan @var{op}, starting with bit @var{starting_bit}, towards more significant
+bits, until the first clear bit is found.  Return the index of the found bit.
+@end deftypefun
+
+@deftypefun {unsigned long int} mpz_scan1 (mpz_t @var{op}, unsigned long int @var{starting_bit})
+Scan @var{op}, starting with bit @var{starting_bit}, towards more significant
+bits, until the first set bit is found.  Return the index of the found bit.
+@end deftypefun
+
+@deftypefun void mpz_setbit (mpz_t @var{rop}, unsigned long int @var{bit_index})
+Set bit @var{bit_index} in @var{op1}.
+@end deftypefun
+
+@deftypefun void mpz_clrbit (mpz_t @var{rop}, unsigned long int @var{bit_index})
+Clear bit @var{bit_index} in @var{op1}.
+@end deftypefun
+
+@node I/O of Integers, Miscellaneous Integer Functions, Integer Logic and Bit Fiddling, Integer Functions
+@comment  node-name,  next,  previous,  up
+@section Input and Output Functions
+@cindex Integer input and output functions
+@cindex Input functions
+@cindex Output functions
+@cindex I/O functions
+
+Functions that perform input from a stdio stream, and functions that output to
+a stdio stream.  Passing a NULL pointer for a @var{stream} argument to any of
+these functions will make them read from @code{stdin} and write to
+@code{stdout}, respectively.
+
+When using any of these functions, it is a good idea to include @file{stdio.h}
+before @file{gmp.h}, since that will allow @file{gmp.h} to define prototypes
+for these functions.
+
+@deftypefun size_t mpz_out_str (FILE *@var{stream}, int @var{base}, mpz_t @var{op})
+Output @var{op} on stdio stream @var{stream}, as a string of digits in base
+@var{base}.  The base may vary from 2 to 36.
+
+Return the number of bytes written, or if an error occurred, return 0.
+@end deftypefun
+
+@deftypefun size_t mpz_inp_str (mpz_t @var{rop}, FILE *@var{stream}, int @var{base})
+Input a possibly white-space preceded string in base @var{base} from stdio
+stream @var{stream}, and put the read integer in @var{rop}.  The base may vary
+from 2 to 36.  If @var{base} is 0, the actual base is determined from the
+leading characters: if the first two characters are `0x' or `0X', hexadecimal
+is assumed, otherwise if the first character is `0', octal is assumed,
+otherwise decimal is assumed.
+
+Return the number of bytes read, or if an error occurred, return 0.
+@end deftypefun
+
+@deftypefun size_t mpz_out_raw (FILE *@var{stream}, mpz_t @var{op})
+Output @var{op} on stdio stream @var{stream}, in raw binary format.  The
+integer is written in a portable format, with 4 bytes of size information, and
+that many bytes of limbs.  Both the size and the limbs are written in
+decreasing significance order (i.e., in big-endian).
+
+The output can be read with @code{mpz_inp_raw}.
+
+Return the number of bytes written, or if an error occurred, return 0.
+
+The output of this can not be read by @code{mpz_inp_raw} from GMP 1, because
+of changes necessary for compatibility between 32-bit and 64-bit machines.
+@end deftypefun
+
+@deftypefun size_t mpz_inp_raw (mpz_t @var{rop}, FILE *@var{stream})
+Input from stdio stream @var{stream} in the format written by
+@code{mpz_out_raw}, and put the result in @var{rop}.  Return the number of
+bytes read, or if an error occurred, return 0.
+
+This routine can read the output from @code{mpz_out_raw} also from GMP 1, in
+spite of changes necessary for compatibility between 32-bit and 64-bit
+machines.
+@end deftypefun
+
+
+@node Miscellaneous Integer Functions,, I/O of Integers, Integer Functions
+@comment  node-name,  next,  previous,  up
+@section Miscellaneous Functions
+@cindex Miscellaneous integer functions
+
+@deftypefun void mpz_random (mpz_t @var{rop}, mp_size_t @var{max_size})
+Generate a random integer of at most @var{max_size} limbs.  The generated
+random number doesn't satisfy any particular requirements of randomness.
+Negative random numbers are generated when @var{max_size} is negative.
+@end deftypefun
+
+@deftypefun void mpz_random2 (mpz_t @var{rop}, mp_size_t @var{max_size})
+Generate a random integer of at most @var{max_size} limbs, with long strings
+of zeros and ones in the binary representation.  Useful for testing functions
+and algorithms, since this kind of random numbers have proven to be more
+likely to trigger corner-case bugs.  Negative random numbers are generated
+when @var{max_size} is negative.
+@end deftypefun
+
+@deftypefun size_t mpz_size (mpz_t @var{op})
+Return the size of @var{op} measured in number of limbs.  If @var{op} is zero,
+the returned value will be zero.
+@c (@xref{Nomenclature}, for an explanation of the concept @dfn{limb}.)
+
+@strong{This function is obsolete.  It will disappear from future MP
+releases.}
+@end deftypefun
+
+@deftypefun size_t mpz_sizeinbase (mpz_t @var{op}, int @var{base})
+Return the size of @var{op} measured in number of digits in base @var{base}.
+The base may vary from 2 to 36.  The returned value will be exact or 1 too
+big.  If @var{base} is a power of 2, the returned value will always be exact.
+
+This function is useful in order to allocate the right amount of space before
+converting @var{op} to a string.  The right amount of allocation is normally
+two more than the value returned by @code{mpz_sizeinbase} (one extra for a
+minus sign and one for the terminating '\0').
+@end deftypefun
+
+
+@node Rational Number Functions, Floating-point Functions, Integer Functions, Top
+@comment  node-name,  next,  previous,  up
+@chapter Rational Number Functions
+@cindex Rational number functions
+
+This chapter describes the MP functions for performing arithmetic on rational
+numbers.  These functions start with the prefix @code{mpq_}.
+
+Rational numbers are stored in objects of type @code{mpq_t}.
+
+All rational arithmetic functions assume operands have a canonical form, and
+canonicalize their result.  The canonical from means that the denominator and
+the numerator have no common factors, and that the denominator is positive.
+Zero has the unique representation 0/1.
+
+Pure assignment functions do not canonicalize the assigned variable.  It is
+the responsibility of the user to canonicalize the assigned variable before
+any arithmetic operations are performed on that variable.  @strong{Note that
+this is an incompatible change from version 1 of the library.}
+
+@deftypefun void mpq_canonicalize (mpq_t @var{op})
+Remove any factors that are common to the numerator and denominator of
+@var{op}, and make the denominator positive.
+@end deftypefun
+
+@menu
+* Initializing Rationals::
+* Assigning Rationals::
+* Simultaneous Integer Init & Assign::
+* Comparing Rationals::
+* Applying Integer Functions::
+* Miscellaneous Rational Functions::
+@end menu
+
+@node Initializing Rationals, Assigning Rationals, Rational Number Functions, Rational Number Functions
+@comment  node-name,  next,  previous,  up
+@section Initialization and Assignment Functions
+
+@deftypefun void mpq_init (mpq_t @var{dest_rational})
+Initialize @var{dest_rational} and set it to 0/1.  Each variable should
+normally only be initialized once, or at least cleared out (using the function
+@code{mpq_clear}) between each initialization.
+@end deftypefun
+
+@deftypefun void mpq_clear (mpq_t @var{rational_number})
+Free the space occupied by @var{rational_number}.  Make sure to call this
+function for all @code{mpq_t} variables when you are done with them.
+@end deftypefun
+
+@deftypefun void mpq_set (mpq_t @var{rop}, mpq_t @var{op})
+Assign @var{rop} from @var{op}.
+@end deftypefun
+
+@deftypefun void mpq_set_ui (mpq_t @var{rop}, unsigned long int @var{op1}, unsigned long int @var{op2})
+@deftypefunx void mpq_set_si (mpq_t @var{rop}, signed long int @var{op1}, unsigned long int @var{op2})
+Set the value of @var{rop} to @var{op1}/@var{op2}.  Note that if @var{op1} and
+@var{op2} have common factors, @var{rop} has to be passed to
+@code{mpq_canonicalize} before any operations are performed on @var{rop}.
+@end deftypefun
+
+@node Assigning Rationals, Comparing Rationals, Initializing Rationals, Rational Number Functions
+@comment  node-name,  next,  previous,  up
+@section Arithmetic Functions
+
+@deftypefun void mpq_add (mpq_t @var{sum}, mpq_t @var{addend1}, mpq_t @var{addend2})
+Set @var{sum} to @var{addend1} + @var{addend2}.
+@end deftypefun
+
+@deftypefun void mpq_sub (mpq_t @var{difference}, mpq_t @var{minuend}, mpq_t @var{subtrahend})
+Set @var{difference} to @var{minuend} @minus{} @var{subtrahend}.
+@end deftypefun
+
+@deftypefun void mpq_mul (mpq_t @var{product}, mpq_t @var{multiplier}, mpq_t @var{multiplicand})
+Set @var{product} to @var{multiplier} times @var{multiplicand}
+@end deftypefun
+
+@deftypefun void mpq_div (mpq_t @var{quotient}, mpq_t @var{dividend}, mpq_t @var{divisor})
+Set @var{quotient} to @var{dividend} / @var{divisor}.
+@end deftypefun
+
+@deftypefun void mpq_neg (mpq_t @var{negated_operand}, mpq_t @var{operand})
+Set @var{negated_operand} to @minus{}@var{operand}.
+@end deftypefun
+
+@deftypefun void mpq_inv (mpq_t @var{inverted_number}, mpq_t @var{number})
+Set @var{inverted_number} to 1 / @var{number}.  If the new denominator is
+zero, this routine will divide by zero.
+@end deftypefun
+
+@node Comparing Rationals, Applying Integer Functions, Assigning Rationals, Rational Number Functions
+@comment  node-name,  next,  previous,  up
+@section Comparison Functions
+
+@deftypefun int mpq_cmp (mpq_t @var{op1}, mpq_t @var{op2})
+Compare @var{op1} and @var{op2}.  Return a positive value if @var{op1} >
+@var{op2}, zero if @var{op1} = @var{op2}, and a negative value if @var{op1} <
+@var{op2}.
+
+To determine if two rationals are equal, @code{mpq_equal} is faster than this
+@code{mpq_cmp}.
+@end deftypefun
+
+@deftypefun int mpq_cmp_ui (mpq_t @var{op1}, unsigned long int @var{num2}, unsigned long int @var{den2})
+Compare @var{op1} and @var{num2}/@var{den2}.  Return a positive value if
+@var{op1} > @var{num2}/@var{den2}, zero if @var{op1} = @var{num2}/@var{den2},
+and a negative value if @var{op1} < @var{num2}/@var{den2}.
+
+This routine allows that @var{num2} and @var{den2} have common factors.
+@end deftypefun
+
+@deftypefun int mpq_sgn (mpq_t @var{op})
+Return +1 if @var{op} > 0, 0 if @var{op} = 0, and @minus{}1 if @var{op} < 0.
+@end deftypefun
+
+@deftypefun int mpq_equal (mpq_t @var{op1}, mpq_t @var{op2})
+Return non-zero if @var{op1} and @var{op2} are equal, zero if they are
+non-equal.  Although @code{mpq_cmp} can be used for the same purpose, this
+function is much faster.
+@end deftypefun
+
+@node Applying Integer Functions, Miscellaneous Rational Functions, Comparing Rationals, Rational Number Functions
+@comment  node-name,  next,  previous,  up
+@section Applying Integer Functions to Rationals
+
+The set of @code{mpq} functions is quite small.  In particular, there are no
+functions for either input or output.  But there are two macros that allow us
+to apply any @code{mpz} function on the numerator or denominator of a rational
+number.  If these macros are used to assign to the rational number,
+@code{mpq_canonicalize} normally need to be called afterwards.
+
+@deftypefn Macro mpz_t mpq_numref (mpq_t @var{op})
+@deftypefnx Macro mpz_t mpq_denref (mpq_t @var{op})
+Return a reference to the numerator and denominator of @var{op}, respectively.
+The @code{mpz} functions can be used on the result of these macros.
+@end deftypefn
+
+@need 2000
+@node Miscellaneous Rational Functions, , Applying Integer Functions, Rational Number Functions
+@comment  node-name,  next,  previous,  up
+@section Miscellaneous Functions
+
+These functions assign between either the numerator or denominator of a
+rational, and an integer.  Instead of using these functions, it is preferable
+to use the more general mechanisms @code{mpq_numref} and @code{mpq_denref},
+together with @code{mpz_set}.
+
+@deftypefun void mpq_set_num (mpq_t @var{rational}, mpz_t @var{numerator})
+Copy @var{numerator} to the numerator of @var{rational}.  When this risks to
+make the numerator and denominator of @var{rational} have common factors, you
+have to pass @var{rational} to @code{mpq_canonicalize} before any operations
+are performed on @var{rational}.
+
+This function is equivalent to
+@code{mpz_set (mpq_numref (@var{rational}), @var{numerator})}.
+@end deftypefun
+
+@deftypefun void mpq_set_den (mpq_t @var{rational}, mpz_t @var{denominator})
+Copy @var{denominator} to the denominator of @var{rational}.  When this risks
+to make the numerator and denominator of @var{rational} have common factors,
+or if the denominator might be negative, you have to pass @var{rational} to
+@code{mpq_canonicalize} before any operations are performed on @var{rational}.
+
+@strong{In version 1 of the library, negative denominators were handled by
+copying the sign to the numerator.  That is no longer done.}
+
+This function is equivalent to
+@code{mpz_set (mpq_denref (@var{rational}), @var{denominators})}.
+@end deftypefun
+
+@deftypefun void mpq_get_num (mpz_t @var{numerator}, mpq_t @var{rational})
+Copy the numerator of @var{rational} to the integer @var{numerator}, to
+prepare for integer operations on the numerator.
+
+This function is equivalent to
+@code{mpz_set (@var{numerator}, mpq_numref (@var{rational}))}.
+@end deftypefun
+
+@deftypefun void mpq_get_den (mpz_t @var{denominator}, mpq_t @var{rational})
+Copy the denominator of @var{rational} to the integer @var{denominator}, to
+prepare for integer operations on the denominator.
+
+This function is equivalent to
+@code{mpz_set (@var{denominator}, mpq_denref (@var{rational}))}.
+@end deftypefun
+
+
+@node Floating-point Functions, Low-level Functions, Rational Number Functions, Top
+@comment  node-name,  next,  previous,  up
+@chapter Floating-point Functions
+@cindex Floating-point functions
+@cindex Float functions
+
+This is a description of the @emph{preliminary} interface for floating-point
+arithmetic in GNU MP 2.
+
+The floating-point functions expect arguments of type @code{mpf_t}.
+
+The MP floating-point functions have an interface that is similar to the MP
+integer functions.  The function prefix for floating-point operations is
+@code{mpf_}.
+
+There is one significant characteristic of floating-point numbers that has
+motivated a difference between this function class and other MP function
+classes: the inherent inexactness of floating point arithmetic.  The user has
+to specify the precision of each variable.  A computation that assigns a
+variable will take place with the precision of the assigned variable; the
+precision of variables used as input is ignored.
+
+@cindex User-defined precision
+The precision of a calculation is defined as follows: Compute the requested
+operation exactly (with ``infinite precision''), and truncate the result to
+the destination variable precision.  Even if the user has asked for a very
+high precision, MP will not calculate with superfluous digits.  For example,
+if two low-precision numbers of nearly equal magnitude are added, the
+precision of the result will be limited to what is required to represent the
+result accurately.
+
+The MP floating-point functions are @emph{not} intended as a smooth extension
+to the IEEE P754 arithmetic.  Specifically, the results obtained on one
+computer often differs from the results obtained on a computer with a
+different word size.
+
+@menu
+* Initializing Floats::
+* Assigning Floats::
+* Simultaneous Float Init & Assign::
+* Converting Floats::
+* Float Arithmetic::
+* Float Comparison::
+* I/O of Floats::
+* Miscellaneous Float Functions::
+@end menu
+
+@node Initializing Floats, Assigning Floats, , Floating-point Functions
+@comment  node-name,  next,  previous,  up
+@section Initialization and Assignment Functions
+
+@deftypefun void mpf_set_default_prec (unsigned long int @var{prec})
+Set the default precision to be @strong{at least} @var{prec} bits.  All
+subsequent calls to @code{mpf_init} will use this precision, but previously
+initialized variables are unaffected.
+@end deftypefun
+
+An @code{mpf_t} object must be initialized before storing the first value in
+it.  The functions @code{mpf_init} and @code{mpf_init2} are used for that
+purpose.
+
+@deftypefun void mpf_init (mpf_t @var{x})
+Initialize @var{x} to 0.  Normally, a variable should be initialized once only
+or at least be cleared, using @code{mpf_clear}, between initializations.  The
+precision of @var{x} is undefined unless a default precision has already been
+established by a call to @code{mpf_set_default_prec}.
+@end deftypefun
+
+@deftypefun void mpf_init2 (mpf_t @var{x}, unsigned long int @var{prec})
+Initialize @var{x} to 0 and set its precision to be @strong{at least}
+@var{prec} bits.  Normally, a variable should be initialized once only or at
+least be cleared, using @code{mpf_clear}, between initializations.
+@end deftypefun
+
+@deftypefun void mpf_clear (mpf_t @var{x})
+Free the space occupied by @var{x}.  Make sure to call this function for all
+@code{mpf_t} variables when you are done with them.
+@end deftypefun
+
+Here is an example on how to initialize floating-point variables:
+@example
+@{
+  mpf_t x, y;
+  mpf_init (x);			/* use default precision */
+  mpf_init2 (y, 256);		/* precision @emph{at least} 256 bits */
+  @dots{}
+  /* Unless the program is about to exit, do ... */
+  mpf_clear (x);
+  mpf_clear (y);
+@}
+@end example
+
+The following three functions are useful for changing the precision during a
+calculation.  A typical use would be for adjusting the precision gradually in
+iterative algorithms like Newton-Raphson, making the computation precision
+closely match the actual accurate part of the numbers.
+
+@deftypefun void mpf_set_prec (mpf_t @var{rop}, unsigned long int @var{prec})
+Set the precision of @var{rop} to be @strong{at least} @var{prec} bits.
+Since changing the precision involves calls to @code{realloc}, this routine
+should not be called in a tight loop.
+@end deftypefun
+
+@deftypefun {unsigned long int} mpf_get_prec (mpf_t @var{op})
+Return the precision actually used for assignments of @var{op}.
+@end deftypefun
+
+@deftypefun void mpf_set_prec_raw (mpf_t @var{rop}, unsigned long int @var{prec})
+Set the precision of @var{rop} to be @strong{at least} @var{prec} bits.  This
+is a low-level function that does not change the allocation.  The @var{prec}
+argument must not be larger that the precision previously returned by
+@code{mpf_get_prec}.  It is crucial that the precision of @var{rop} is
+ultimately reset to exactly the value returned by @code{mpf_get_prec}.
+@end deftypefun
+
+
+@node Assigning Floats, Simultaneous Float Init & Assign, Initializing Floats, Floating-point Functions
+@comment  node-name,  next,  previous,  up
+@subsection Assignment Functions
+@cindex Float assignment functions
+
+These functions assign new values to already initialized floats
+(@pxref{Initializing Floats}).
+
+@deftypefun void mpf_set (mpf_t @var{rop}, mpf_t @var{op})
+@deftypefunx void mpf_set_ui (mpf_t @var{rop}, unsigned long int @var{op})
+@deftypefunx void mpf_set_si (mpf_t @var{rop}, signed long int @var{op})
+@deftypefunx void mpf_set_d (mpf_t @var{rop}, double @var{op})
+Set the value of @var{rop} from @var{op}.
+@end deftypefun
+
+@deftypefun int mpf_set_str (mpf_t @var{rop}, char *@var{str}, int @var{base})
+Set the value of @var{rop} from the string in @var{str}.  The string is of the
+form @samp{M@@N} or, if the base is 10 or less, alternatively @samp{MeN}.
+@samp{M} is the mantissa and @samp{N} is the exponent.  The mantissa is always
+in the specified base.  The exponent is either in the specified base or, if
+@var{base} is negative, in decimal.
+
+The argument @var{base} may be in the ranges 2 to 36, or @minus{}36 to
+@minus{}2.  Negative values are used to specify that the exponent is in
+decimal.
+
+Unlike the corresponding @code{mpz} function, the base will not be determined
+from the leading characters of the string if @var{base} is 0.  This is so that
+numbers like @samp{0.23} are not interpreted as octal.
+
+White space is allowed in the string, and is simply ignored.
+
+This function returns 0 if the entire string up to the '\0' is a valid number
+in base @var{base}.  Otherwise it returns @minus{}1.
+@end deftypefun
+
+
+@node Simultaneous Float Init & Assign, Converting Floats, Assigning Floats, Floating-point Functions
+@comment  node-name,  next,  previous,  up
+@subsection Combined Initialization and Assignment Functions
+@cindex Initialization and assignment functions
+
+For convenience, MP provides a parallel series of initialize-and-set functions
+which initialize the output and then store the value there.  These functions'
+names have the form @code{mpf_init_set@dots{}}
+
+Once the float has been initialized by any of the @code{mpf_init_set@dots{}}
+functions, it can be used as the source or destination operand for the ordinary
+float functions.  Don't use an initialize-and-set function on a variable
+already initialized!
+
+@deftypefun void mpf_init_set (mpf_t @var{rop}, mpf_t @var{op})
+@deftypefunx void mpf_init_set_ui (mpf_t @var{rop}, unsigned long int @var{op})
+@deftypefunx void mpf_init_set_si (mpf_t @var{rop}, signed long int @var{op})
+@deftypefunx void mpf_init_set_d (mpf_t @var{rop}, double @var{op})
+Initialize @var{rop} and set its value from @var{op}.
+
+The precision of @var{rop} will be taken from the active default precision, as
+set by @code{mpf_set_default_prec}.
+@end deftypefun
+
+@deftypefun int mpf_init_set_str (mpf_t @var{rop}, char *@var{str}, int @var{base})
+Initialize @var{rop} and set its value from the string in @var{str}.  See
+@code{mpf_set_str} above for details on the assignment operation.
+
+Note that @var{rop} is initialized even if an error occurs.  (I.e., you have to
+call @code{mpf_clear} for it.)
+
+The precision of @var{rop} will be taken from the active default precision, as
+set by @code{mpf_set_default_prec}.
+@end deftypefun
+
+
+@node Converting Floats, Float Arithmetic, Simultaneous Float Init & Assign, Floating-point Functions
+@comment  node-name,  next,  previous,  up
+@section Conversion Functions
+@cindex Conversion functions
+
+@deftypefun {char *} mpf_get_str (char *@var{str}, mp_exp_t *@var{expptr}, int @var{base}, size_t @var{n_digits}, mpf_t @var{op})
+Convert @var{op} to a string of digits in base @var{base}.  The base may vary
+from 2 to 36.  Generate at most @var{n_digits} significant digits, or if
+@var{n_digits} is 0, the maximum number of digits accurately representable by
+@var{op}.
+
+If @var{str} is NULL, space for the mantissa is allocated using the default
+allocation function, and a pointer to the string is returned.
+
+If @var{str} is not NULL, it should point to a block of storage enough large
+for the mantissa, i.e., @var{n_digits} + 2.  The two extra bytes are for a
+possible minus sign, and for the terminating null character.
+
+The exponent is written through the pointer @var{expptr}.
+
+If @var{n_digits} is 0, the maximum number of digits meaningfully achievable
+from the precision of @var{op} will be generated.  Note that the space
+requirements for @var{str} in this case will be impossible for the user to
+predetermine.  Therefore, you need to pass NULL for the string argument
+whenever @var{n_digits} is 0.
+
+The generated string is a fraction, with an implicit radix point immediately
+to the left of the first digit.  For example, the number 3.1416 would be
+returned as "31416" in the string and 1 written at @var{expptr}.
+@end deftypefun
+
+
+@node Float Arithmetic, Float Comparison, Converting Floats, Floating-point Functions
+@comment  node-name,  next,  previous,  up
+@section Arithmetic Functions
+@cindex Float arithmetic functions
+@cindex Arithmetic functions
+
+@deftypefun void mpf_add (mpf_t @var{rop}, mpf_t @var{op1}, mpf_t @var{op2})
+@deftypefunx void mpf_add_ui (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
+Set @var{rop} to @var{op1} + @var{op2}.
+@end deftypefun
+
+@deftypefun void mpf_sub (mpf_t @var{rop}, mpf_t @var{op1}, mpf_t @var{op2})
+@deftypefunx void mpf_ui_sub (mpf_t @var{rop}, unsigned long int @var{op1}, mpf_t @var{op2})
+@deftypefunx void mpf_sub_ui (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
+Set @var{rop} to @var{op1} @minus{} @var{op2}.
+@end deftypefun
+
+@deftypefun void mpf_mul (mpf_t @var{rop}, mpf_t @var{op1}, mpf_t @var{op2})
+@deftypefunx void mpf_mul_ui (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
+Set @var{rop} to @var{op1} times @var{op2}.
+@end deftypefun
+
+Division is undefined if the divisor is zero, and passing a zero divisor to
+the divide functions will make these functions intentionally divide by zero.
+This gives the user the possibility to handle arithmetic exceptions in these
+functions in the same manner as other arithmetic exceptions.
+
+@deftypefun void mpf_div (mpf_t @var{rop}, mpf_t @var{op1}, mpf_t @var{op2})
+@deftypefunx void mpf_ui_div (mpf_t @var{rop}, unsigned long int @var{op1}, mpf_t @var{op2})
+@deftypefunx void mpf_div_ui (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
+Set @var{rop} to @var{op1} / @var{op2}.
+rounded towards 0.
+@end deftypefun
+
+@deftypefun void mpf_sqrt (mpf_t @var{rop}, mpf_t @var{op})
+@deftypefunx void mpf_sqrt_ui (mpf_t @var{rop}, unsigned long int @var{op})
+Set @var{rop} to the square root of @var{op}.
+@end deftypefun
+
+@deftypefun void mpf_pow_ui (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
+Set @var{rop} to @var{op1} raised to @var{op2}.
+@end deftypefun
+
+@deftypefun void mpf_neg (mpf_t @var{rop}, mpf_t @var{op})
+Set @var{rop} to @minus{}@var{op}.
+@end deftypefun
+
+@deftypefun void mpf_abs (mpf_t @var{rop}, mpf_t @var{op})
+Set @var{rop} to the absolute value of @var{op}.
+@end deftypefun
+
+@deftypefun void mpf_mul_2exp (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
+Set @var{rop} to @var{op1} times 2 raised to @var{op2}.
+@end deftypefun
+
+@deftypefun void mpf_div_2exp (mpf_t @var{rop}, mpf_t @var{op1}, unsigned long int @var{op2})
+Set @var{rop} to @var{op1} divided by 2 raised to @var{op2}.
+@end deftypefun
+
+@node Float Comparison, I/O of Floats, Float Arithmetic, Floating-point Functions
+@comment  node-name,  next,  previous,  up
+@section Comparison Functions
+@cindex Float comparisons functions
+@cindex Comparison functions
+
+@deftypefun int mpf_cmp (mpf_t @var{op1}, mpf_t @var{op2})
+@deftypefunx int mpf_cmp_ui (mpf_t @var{op1}, unsigned long int @var{op2})
+@deftypefunx int mpf_cmp_si (mpf_t @var{op1}, signed long int @var{op2})
+Compare @var{op1} and @var{op2}.  Return a positive value if @var{op1} >
+@var{op2}, zero if @var{op1} = @var{op2}, and a negative value if @var{op1} <
+@var{op2}.
+@end deftypefun
+
+@deftypefun int mpf_eq (mpf_t @var{op1}, mpf_t @var{op2}, unsigned long int op3)
+Return non-zero if the first @var{op3} bits of @var{op1} and @var{op2} are
+equal, zero otherwise.  I.e., test of @var{op1} and @var{op2} are
+approximately equal.
+@end deftypefun
+
+@deftypefun void mpf_reldiff (mpf_t @var{rop}, mpf_t @var{op1}, mpf_t @var{op2})
+Compute the relative difference between @var{op1} and @var{op2} and store the
+result in @var{rop}.
+@end deftypefun
+
+@deftypefun int mpf_sgn (mpf_t @var{op})
+Return +1 if @var{op} > 0, 0 if @var{op} = 0, and @minus{}1 if @var{op} < 0.
+@end deftypefun
+
+@node I/O of Floats, Miscellaneous Float Functions, Float Comparison, Floating-point Functions
+@comment  node-name,  next,  previous,  up
+@section Input and Output Functions
+@cindex Float input and output functions
+@cindex Input functions
+@cindex Output functions
+@cindex I/O functions
+
+Functions that perform input from a stdio stream, and functions that output to
+a stdio stream.  Passing a NULL pointer for a @var{stream} argument to any of
+these functions will make them read from @code{stdin} and write to
+@code{stdout}, respectively.
+
+When using any of these functions, it is a good idea to include @file{stdio.h}
+before @file{gmp.h}, since that will allow @file{gmp.h} to define prototypes
+for these functions.
+
+@deftypefun size_t mpf_out_str (FILE *@var{stream}, int @var{base}, size_t @var{n_digits}, mpf_t @var{op})
+Output @var{op} on stdio stream @var{stream}, as a string of digits in
+base @var{base}.  The base may vary from 2 to 36.  Print at most
+@var{n_digits} significant digits, or if @var{n_digits} is 0, the maximum
+number of digits accurately representable by @var{op}.
+
+In addition to the significant digits, a leading @samp{0.} and a trailing
+exponent, in the form @samp{@@NNN}, are printed.
+
+Return the number of bytes written, or if an error occurred, return 0.
+@end deftypefun
+
+@deftypefun size_t mpf_inp_str (mpf_t @var{rop}, FILE *@var{stream}, int @var{base})
+Input a string in base @var{base} from stdio stream @var{stream}, and put the
+read float in @var{rop}.  The string is of the form @samp{M@@N} or, if the
+base is 10 or less, alternatively @samp{MeN}.  @samp{M} is the mantissa and
+@samp{N} is the exponent.  The mantissa is always in the specified base.  The
+exponent is either in the specified base or, if @var{base} is negative, in
+decimal.
+
+The argument @var{base} may be in the ranges 2 to 36, or @minus{}36 to
+@minus{}2.  Negative values are used to specify that the exponent is in
+decimal.
+
+Unlike the corresponding @code{mpz} function, the base will not be determined
+from the leading characters of the string if @var{base} is 0.  This is so that
+numbers like @samp{0.23} are not interpreted as octal.
+
+Return the number of bytes read, or if an error occurred, return 0.
+@end deftypefun
+
+@c @deftypefun void mpf_out_raw (FILE *@var{stream}, mpf_t @var{float})
+@c Output @var{float} on stdio stream @var{stream}, in raw binary
+@c format.  The float is written in a portable format, with 4 bytes of
+@c size information, and that many bytes of limbs.  Both the size and the
+@c limbs are written in decreasing significance order.
+@c @end deftypefun
+
+@c @deftypefun void mpf_inp_raw (mpf_t @var{float}, FILE *@var{stream})
+@c Input from stdio stream @var{stream} in the format written by
+@c @code{mpf_out_raw}, and put the result in @var{float}.
+@c @end deftypefun
+
+
+@node Miscellaneous Float Functions, , I/O of Floats, Floating-point Functions
+@comment  node-name,  next,  previous,  up
+@section Miscellaneous Functions
+@cindex Miscellaneous float functions
+
+@deftypefun void mpf_random2 (mpf_t @var{rop}, mp_size_t @var{max_size}, mp_exp_t @var{max_exp})
+Generate a random float of at most @var{max_size} limbs, with long strings of
+zeros and ones in the binary representation.  The exponent of the number is in
+the interval @minus{}@var{exp} to @var{exp}.  This function is useful for
+testing functions and algorithms, since this kind of random numbers have
+proven to be more likely to trigger corner-case bugs.  Negative random numbers
+are generated when @var{max_size} is negative.
+@end deftypefun
+
+@c @deftypefun size_t mpf_size (mpf_t @var{op})
+@c Return the size of @var{op} measured in number of limbs.  If @var{op} is
+@c zero, the returned value will be zero.  (@xref{Nomenclature}, for an
+@c explanation of the concept @dfn{limb}.)
+@c
+@c @strong{This function is obsolete.  It will disappear from future MP
+@c releases.}
+@c @end deftypefun
+
+@node Low-level Functions, BSD Compatible Functions, Floating-point Functions, Top
+@comment  node-name,  next,  previous,  up
+@chapter Low-level Functions
+@cindex Low-level functions
+
+This chapter describes low-level MP functions, used to implement the high-level
+MP functions, but also intended for time-critical user code.
+
+These functions start with the prefix @code{mpn_}.
+
+@c 1. Some of these function clobber input operands.
+@c
+
+The @code{mpn} functions are designed to be as fast as possible, @strong{not}
+to provide a coherent calling interface.  The different functions have somewhat
+similar interfaces, but there are variations that make them hard to use.  These
+functions do as little as possible apart from the real multiple precision
+computation, so that no time is spent on things that not all callers need.
+
+A source operand is specified by a pointer to the least significant limb and a
+limb count.  A destination operand is specified by just a pointer.  It is the
+responsibility of the caller to ensure that the destination has enough space
+for storing the result.
+
+With this way of specifying operands, it is possible to perform computations
+on subranges of an argument, and store the result into a subrange of a
+destination.
+
+A common requirement for all functions is that each source area needs at least
+one limb.  No size argument may be zero.
+
+The @code{mpn} functions is the base for the implementation of the @code{mpz_},
+@code{mpf_}, and @code{mpq_} functions.
+
+This example adds the number beginning at @var{src1_ptr} and the number
+beginning at @var{src2_ptr} and writes the sum at @var{dest_ptr}.  All areas
+have @var{size} limbs.
+
+@example
+cy = mpn_add_n (dest_ptr, src1_ptr, src2_ptr, size)
+@end example
+
+@noindent
+In the notation used here, a source operand is identified by the pointer to
+the least significant limb, and the limb count in braces.  For example,
+@{s1_ptr, s1_size@}.
+
+@deftypefun mp_limb_t mpn_add_n (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, const mp_limb_t * @var{src2_ptr}, mp_size_t @var{size})
+Add @{@var{src1_ptr}, @var{size}@} and @{@var{src2_ptr}, @var{size}@}, and
+write the @var{size} least significant limbs of the result to @var{dest_ptr}.
+Return carry, either 0 or 1.
+
+This is the lowest-level function for addition.  It is the preferred function
+for addition, since it is written in assembly for most targets.  For addition
+of a variable to itself (i.e., @var{src1_ptr} equals @var{src2_ptr}, use
+@code{mpn_lshift} with a count of 1 for optimal speed.
+@end deftypefun
+
+@deftypefun mp_limb_t mpn_add_1 (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, mp_size_t @var{size}, mp_limb_t @var{src2_limb})
+Add @{@var{src1_ptr}, @var{size}@} and @var{src2_limb}, and write the
+@var{size} least significant limbs of the result to @var{dest_ptr}.  Return
+carry, either 0 or 1.
+@end deftypefun
+
+@deftypefun mp_limb_t mpn_add (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, mp_size_t @var{src1_size}, const mp_limb_t * @var{src2_ptr}, mp_size_t @var{src2_size})
+Add @{@var{src1_ptr}, @var{src1_size}@} and @{@var{src2_ptr},
+@var{src2_size}@}, and write the @var{src1_size} least significant limbs of
+the result to @var{dest_ptr}.  Return carry, either 0 or 1.
+
+This function requires that @var{src1_size} is greater than or equal to
+@var{src2_size}.
+@end deftypefun
+
+@deftypefun mp_limb_t mpn_sub_n (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, const mp_limb_t * @var{src2_ptr}, mp_size_t @var{size})
+Subtract @{@var{src2_ptr}, @var{src2_size}@} from @{@var{src1_ptr},
+@var{size}@}, and write the @var{size} least significant limbs of the result
+to @var{dest_ptr}.  Return borrow, either 0 or 1.
+
+This is the lowest-level function for subtraction.  It is the preferred
+function for subtraction, since it is written in assembly for most targets.
+@end deftypefun
+
+@deftypefun mp_limb_t mpn_sub_1 (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, mp_size_t @var{size}, mp_limb_t @var{src2_limb})
+Subtract @var{src2_limb} from @{@var{src1_ptr}, @var{size}@}, and write the
+@var{size} least significant limbs of the result to @var{dest_ptr}.  Return
+borrow, either 0 or 1.
+@end deftypefun
+
+@deftypefun mp_limb_t mpn_sub (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, mp_size_t @var{src1_size}, const mp_limb_t * @var{src2_ptr}, mp_size_t @var{src2_size})
+Subtract @{@var{src2_ptr}, @var{src2_size}@} from @{@var{src1_ptr},
+@var{src1_size}@}, and write the @var{src1_size} least significant limbs of
+the result to @var{dest_ptr}.  Return borrow, either 0 or 1.
+
+This function requires that @var{src1_size} is greater than or equal to
+@var{src2_size}.
+@end deftypefun
+
+@deftypefun void mpn_mul_n (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, const mp_limb_t * @var{src2_ptr}, mp_size_t @var{size})
+Multiply @{@var{src1_ptr}, @var{size}@} and @{@var{src2_ptr}, @var{size}@},
+and write the @strong{entire} result to @var{dest_ptr}.
+
+The destination has to have space for 2@var{size} limbs, even if the
+significant result might be one limb smaller.
+@end deftypefun
+
+@deftypefun mp_limb_t mpn_mul_1 (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, mp_size_t @var{size}, mp_limb_t @var{src2_limb})
+Multiply @{@var{src1_ptr}, @var{size}@} and @var{src2_limb}, and write the
+@var{size} least significant limbs of the product to @var{dest_ptr}.  Return
+the most significant limb of the product.
+
+This is a low-level function that is a building block for general
+multiplication as well as other operations in MP.  It is written in assembly
+for most targets.
+
+Don't call this function if @var{src2_limb} is a power of 2; use
+@code{mpn_lshift} with a count equal to the logarithm of @var{src2_limb}
+instead, for optimal speed.
+@end deftypefun
+
+@deftypefun mp_limb_t mpn_addmul_1 (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, mp_size_t @var{size}, mp_limb_t @var{src2_limb})
+Multiply @{@var{src1_ptr}, @var{size}@} and @var{src2_limb}, and add the
+@var{size} least significant limbs of the product to @{@var{dest_ptr},
+@var{size}@} and write the result to @var{dest_ptr} @var{dest_ptr}.  Return
+the most significant limb of the product, plus carry-out from the addition.
+
+This is a low-level function that is a building block for general
+multiplication as well as other operations in MP.  It is written in assembly
+for most targets.
+@end deftypefun
+
+@deftypefun mp_limb_t mpn_submul_1 (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, mp_size_t @var{size}, mp_limb_t @var{src2_limb})
+Multiply @{@var{src1_ptr}, @var{size}@} and @var{src2_limb}, and subtract the
+@var{size} least significant limbs of the product from @{@var{dest_ptr},
+@var{size}@} and write the result to @var{dest_ptr}.  Return the most
+significant limb of the product, minus borrow-out from the subtraction.
+
+This is a low-level function that is a building block for general
+multiplication and division as well as other operations in MP.  It is written
+in assembly for most targets.
+@end deftypefun
+
+@deftypefun mp_limb_t mpn_mul (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src1_ptr}, mp_size_t @var{src1_size}, const mp_limb_t * @var{src2_ptr}, mp_size_t @var{src2_size})
+Multiply @{@var{src1_ptr}, @var{src1_size}@} and @{@var{src2_ptr},
+@var{src2_size}@}, and write the result to @var{dest_ptr}.  Return the most
+significant limb of the result.
+
+The destination has to have space for @var{src1_size} + @var{src1_size}
+limbs, even if the result might be one limb smaller.
+
+This function requires that @var{src1_size} is greater than or equal to
+@var{src2_size}.  The destination must be distinct from either input operands.
+@end deftypefun
+
+@deftypefun mp_size_t mpn_divrem (mp_limb_t * @var{r1p}, mp_size_t @var{xsize}, mp_limb_t * @var{rs2p}, mp_size_t @var{rs2size}, const mp_limb_t * @var{s3p}, mp_size_t @var{s3size})
+Divide @{@var{rs2p}, @var{rs2size}@} by @{@var{s3p}, @var{s3size}@}, and
+write the quotient at @var{r1p}, with the exception of the most significant
+limb, which is returned.  The remainder replaces the dividend at @var{rs2p}.
+
+In addition to an integer quotient, @var{xsize} fraction limbs are developed,
+and stored after the integral limbs.  For most usages, @var{xsize} will be
+zero.
+
+It is required that @var{rs2size} is greater than or equal to @var{s3size}.
+It is required that the most significant bit of the divisor is set.
+
+If the quotient is not needed, pass @var{rs2p} + @var{s3size} as @var{r1p}.
+Aside from that special case, no overlap between arguments is permitted.
+
+Return the most significant limb of the quotient, either 0 or 1.
+
+The area at @var{r1p} needs to be @var{rs2size} @minus{} @var{s3size} +
+@var{xsize} limbs large.
+@end deftypefun
+
+@deftypefun mp_limb_t mpn_divrem_1 (mp_limb_t * @var{r1p}, mp_size_t @var{xsize}, mp_limb_t * @var{s2p}, mp_size_t @var{s2size}, mp_limb_t @var{s3limb})
+Divide @{@var{s2p}, @var{s2size}@} by @var{s3limb}, and write the quotient
+at @var{r1p}.  Return the remainder.
+
+In addition to an integer quotient, @var{xsize} fraction limbs are developed,
+and stored after the integral limbs.  For most usages, @var{xsize} will be
+zero.
+
+The areas at @var{r1p} and @var{s2p} have to be identical or completely
+separate, not partially overlapping.
+@end deftypefun
+
+@deftypefun mp_size_t mpn_divmod (mp_limb_t * @var{r1p}, mp_limb_t * @var{rs2p}, mp_size_t @var{rs2size}, const mp_limb_t * @var{s3p}, mp_size_t @var{s3size})
+@strong{This interface is obsolete.  It will disappear from future releases.
+Use @code{mpn_divrem} in its stead.}
+@end deftypefun
+
+@deftypefun mp_limb_t mpn_divmod_1 (mp_limb_t * @var{r1p}, mp_limb_t * @var{s2p}, mp_size_t @var{s2size}, mp_limb_t @var{s3limb})
+@strong{This interface is obsolete.  It will disappear from future releases.
+Use @code{mpn_divrem_1} in its stead.}
+@end deftypefun
+
+@deftypefun mp_limb_t mpn_mod_1 (mp_limb_t * @var{s1p}, mp_size_t @var{s1size}, mp_limb_t @var{s2limb})
+Divide @{@var{s1p}, @var{s1size}@} by @var{s2limb}, and return the remainder.
+@end deftypefun
+
+@deftypefun mp_limb_t mpn_pre_mod_1 (mp_limb_t * @var{s1p}, mp_size_t @var{s1size}, mp_limb_t @var{s2limb}, mp_limb_t @var{s3limb})
+@strong{This interface is obsolete.  It will disappear from future releases.
+Use @code{mpn_mod_1} in its stead.}
+@end deftypefun
+
+@deftypefun mp_limb_t mpn_bdivmod (mp_limb_t * @var{dest_ptr}, mp_limb_t * @var{s1p}, mp_size_t @var{s1size}, const mp_limb_t * @var{s2p}, mp_size_t @var{s2size}, unsigned long int @var{d})
+The function puts the low [@var{d} / @var{BITS_PER_MP_LIMB}] limbs of
+@var{q} =
+@{@var{s1p}, @var{s1size}@} / @{@var{s2p}, @var{s2size}@}
+mod 2^@var{d}
+at @var{dest_ptr},
+and returns the high @var{d} mod @var{BITS_PER_MP_LIMB} bits of @var{q}.
+
+@{@var{s1p}, @var{s1size}@} - @var{q} * @{@var{s2p}, @var{s2size}@}
+mod 2^(@var{s1size}*@var{BITS_PER_MP_LIMB})
+is placed at @var{s1p}.
+Since the low [@var{d} / @var{BITS_PER_MP_LIMB}] limbs of
+this difference are zero, it is possible to overwrite the low limbs at
+@var{s1p} with this difference,
+provided @var{dest_ptr} <= @var{s1p}.
+
+This function requires that @var{s1size} * @var{BITS_PER_MP_LIMB} >= @var{D},
+and that @{@var{s2p}, @var{s2size}@} is odd.
+
+@strong{This interface is preliminary.  It might change incompatibly in
+future revisions.}
+@end deftypefun
+
+@deftypefun mp_limb_t mpn_lshift (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src_ptr}, mp_size_t @var{src_size}, unsigned long int @var{count})
+Shift @{@var{src_ptr}, @var{src_size}@} @var{count} bits to the left, and
+write the @var{src_size} least significant limbs of the result to
+@var{dest_ptr}.  @var{count} might be in the range 1 to n @minus{} 1, on an
+n-bit machine. The bits shifted out to the left are returned.
+
+Overlapping of the destination space and the source space is allowed in this
+function, provided @var{dest_ptr} >= @var{src_ptr}.
+
+This function is written in assembly for most targets.
+@end deftypefun
+
+@deftypefun mp_limp_t mpn_rshift (mp_limb_t * @var{dest_ptr}, const mp_limb_t * @var{src_ptr}, mp_size_t @var{src_size}, unsigned long int @var{count})
+Shift @{@var{src_ptr}, @var{src_size}@} @var{count} bits to the right, and
+write the @var{src_size} most significant limbs of the result to
+@var{dest_ptr}.  @var{count} might be in the range 1 to n @minus{} 1, on an
+n-bit machine.  The bits shifted out to the right are returned.
+
+Overlapping of the destination space and the source space is allowed in this
+function, provided @var{dest_ptr} <= @var{src_ptr}.
+
+This function is written in assembly for most targets.
+@end deftypefun
+
+@deftypefun int mpn_cmp (const mp_limb_t * @var{src1_ptr}, const mp_limb_t * @var{src2_ptr}, mp_size_t @var{size})
+Compare @{@var{src1_ptr}, @var{size}@} and @{@var{src2_ptr}, @var{size}@} and
+return a positive value if src1 > src2, 0 of they are equal, and a negative
+value if src1 < src2.
+@end deftypefun
+
+@deftypefun mp_size_t mpn_gcd (mp_limb_t * @var{dest_ptr}, mp_limb_t * @var{src1_ptr}, mp_size_t @var{src1_size}, mp_limb_t * @var{src2_ptr}, mp_size_t @var{src2_size})
+Puts at @var{dest_ptr} the greatest common divisor of @{@var{src1_ptr},
+@var{src1_size}@} and @{@var{src2_ptr}, @var{src2_size}@}; both source
+operands are destroyed by the operation.  The size in limbs of the greatest
+common divisor is returned.
+
+@{@var{src1_ptr}, @var{src1_size}@} must be odd, and @{@var{src2_ptr},
+@var{src2_size}@} must have at least as many bits as @{@var{src1_ptr},
+@var{src1_size}@}.
+
+@strong{This interface is preliminary.  It might change incompatibly in
+future revisions.}
+@end deftypefun
+
+@deftypefun mp_limb_t mpn_gcd_1 (const mp_limb_t * @var{src1_ptr}, mp_size_t @var{src1_size}, mp_limb_t @var{src2_limb})
+Return the greatest common divisor of @{@var{src1_ptr}, @var{src1_size}@}
+and @var{src2_limb}, where @var{src2_limb} (as well as @var{src1_size})
+must be different from 0.
+@end deftypefun
+
+@deftypefun mp_size_t mpn_gcdext (mp_limb_t * @var{r1p}, mp_limb_t * @var{r2p}, mp_limb_t * @var{s1p}, mp_size_t @var{s1size}, mp_limb_t * @var{s2p}, mp_size_t @var{s2size})
+Puts at @var{r1p} the greatest common divisor of @{@var{s1p}, @var{s1size}@}
+and @{@var{s2p}, @var{s2size}@}.  The first cofactor is written at
+@var{r2p}.  Both source operands are destroyed by the operation.  The size
+in limbs of the greatest common divisor is returned.
+
+@strong{This interface is preliminary.  It might change incompatibly in
+future revisions.}
+@end deftypefun
+
+@deftypefun mp_size_t mpn_sqrtrem (mp_limb_t * @var{r1p}, mp_limb_t * @var{r2p}, const mp_limb_t * @var{sp}, mp_size_t @var{size})
+Compute the square root of @{@var{sp}, @var{size}@} and put the result at
+@var{r1p}.  Write the remainder at @var{r2p}, unless @var{r2p} is NULL.
+
+Return the size of the remainder, whether @var{r2p} was NULL or non-NULL.
+Iff the operand was a perfect square, the return value will be 0.
+
+The areas at @var{r1p} and @var{sp} have to be distinct.  The areas at
+@var{r2p} and @var{sp} have to be identical or completely separate, not
+partially overlapping.
+
+The area at @var{r1p} needs to be @var{size} / 2 limbs large.
+The area at @var{r2p} needs to be @var{size} limbs large.
+
+@strong{This interface is preliminary.  It might change incompatibly in
+future revisions.}
+@end deftypefun
+
+@deftypefun mp_size_t mpn_get_str (unsigned char *@var{str}, int @var{base}, mp_limb_t * @var{s1p}, mp_size_t @var{s1size})
+Convert @{@var{s1p}, @var{s1size}@} to a raw unsigned char array in base
+@var{base}.  The string is not in ASCII; to convert it to printable format,
+add the ASCII codes for @samp{0} or @samp{A}, depending on the base and
+range.  There may be leading zeros in the string.
+
+The area at @var{s1p} is clobbered.
+
+Return the number of characters in @var{str}.
+
+The area at @var{str} has to have space for the largest possible number
+represented by a @var{s1size} long limb array, plus one extra character.
+@end deftypefun
+
+@deftypefun mp_size_t mpn_set_str (mp_limb_t * @var{r1p}, const char *@var{str}, size_t {strsize}, int @var{base})
+Convert the raw unsigned char array at @var{str} of length @var{strsize} to
+a limb array @{@var{s1p}, @var{s1size}@}.  The base of @var{str} is
+@var{base}.
+
+Return the number of limbs stored in @var{r1p}.
+@end deftypefun
+
+@deftypefun {unsigned long int} mpn_scan0 (const mp_limb_t * @var{s1p}, unsigned long int @var{bit})
+Scan @var{s1p} from bit position @var{bit} for the next clear bit.
+
+It is required that there be a clear bit within the area at @var{s1p} at or
+beyond bit position @var{bit}, so that the function has something to return.
+
+@strong{This interface is preliminary.  It might change incompatibly in
+future revisions.}
+@end deftypefun
+
+@deftypefun {unsigned long int} mpn_scan1 (const mp_limb_t * @var{s1p}, unsigned long int @var{bit})
+Scan @var{s1p} from bit position @var{bit} for the next set bit.
+
+It is required that there be a set bit within the area at @var{s1p} at or
+beyond bit position @var{bit}, so that the function has something to return.
+
+@strong{This interface is preliminary.  It might change incompatibly in
+future revisions.}
+@end deftypefun
+
+@deftypefun void mpn_random2 (mp_limb_t * @var{r1p}, mp_size_t @var{r1size})
+Generate a random number of length @var{r1size} with long strings of zeros
+and ones in the binary representation, and store it at @var{r1p}.
+
+The generated random numbers are intended for testing the correctness of the
+implementation of the @code{mpn} routines.
+@end deftypefun
+
+@deftypefun {unsigned long int} mpn_popcount (const mp_limb_t * @var{s1p}, unsigned long int @var{size})
+Count the number of set bits in @{@var{s1p}, @var{size}@}.
+@end deftypefun
+
+@deftypefun {unsigned long int} mpn_hamdist (const mp_limb_t * @var{s1p}, const mp_limb_t * @var{s2p}, unsigned long int @var{size})
+Compute the hamming distance between @{@var{s1p}, @var{size}@} and
+@{@var{s2p}, @var{size}@}.
+@end deftypefun
+
+@deftypefun int mpn_perfect_square_p (const mp_limb_t * @var{s1p}, mp_size_t @var{size})
+Return non-zero iff @{@var{s1p}, @var{size}@} is a perfect square.
+@end deftypefun
+
+
+@node BSD Compatible Functions, Custom Allocation, Low-level Functions, Top
+@comment  node-name,  next,  previous,  up
+@chapter Berkeley MP Compatible Functions
+@cindex BSD MP compatible functions
+
+These functions are intended to be fully compatible with the Berkeley MP
+library which is available on many BSD derived U*ix systems.
+
+The original Berkeley MP library has a usage restriction: you cannot use the
+same variable as both source and destination in a single function call.  The
+compatible functions in GNU MP do not share this restriction---inputs and
+outputs may overlap.
+
+It is not recommended that new programs are written using these functions.
+Apart from the incomplete set of functions, the interface for initializing
+@code{MINT} objects is more error prone, and the @code{pow} function collides
+with @code{pow} in @file{libm.a}.
+
+@cindex @file{mp.h}
+Include the header @file{mp.h} to get the definition of the necessary types
+and functions.  If you are on a BSD derived system, make sure to include GNU
+@file{mp.h} if you are going to link the GNU @file{libmp.a} to you program.
+This means that you probably need to give the -I<dir> option to the compiler,
+where <dir> is the directory where you have GNU @file{mp.h}.
+
+@deftypefun {MINT *} itom (signed short int @var{initial_value})
+Allocate an integer consisting of a @code{MINT} object and dynamic limb space.
+Initialize the integer to @var{initial_value}.  Return a pointer to the
+@code{MINT} object.
+@end deftypefun
+
+@deftypefun {MINT *} xtom (char *@var{initial_value})
+Allocate an integer consisting of a @code{MINT} object and dynamic limb space.
+Initialize the integer from @var{initial_value}, a hexadecimal, '\0'-terminate
+C string.  Return a pointer to the @code{MINT} object.
+@end deftypefun
+
+@deftypefun void move (MINT *@var{src}, MINT *@var{dest})
+Set @var{dest} to @var{src} by copying.  Both variables must be previously
+initialized.
+@end deftypefun
+
+@deftypefun void madd (MINT *@var{src_1}, MINT *@var{src_2}, MINT *@var{destination})
+Add @var{src_1} and @var{src_2} and put the sum in @var{destination}.
+@end deftypefun
+
+@deftypefun void msub (MINT *@var{src_1}, MINT *@var{src_2}, MINT *@var{destination})
+Subtract @var{src_2} from @var{src_1} and put the difference in
+@var{destination}.
+@end deftypefun
+
+@deftypefun void mult (MINT *@var{src_1}, MINT *@var{src_2}, MINT *@var{destination})
+Multiply @var{src_1} and @var{src_2} and put the product in
+@var{destination}.
+@end deftypefun
+
+@deftypefun void mdiv (MINT *@var{dividend}, MINT *@var{divisor}, MINT *@var{quotient}, MINT *@var{remainder})
+@deftypefunx void sdiv (MINT *@var{dividend}, signed short int @var{divisor}, MINT *@var{quotient}, signed short int *@var{remainder})
+Set @var{quotient} to @var{dividend} / @var{divisor}, and @var{remainder} to
+@var{dividend} mod @var{divisor}.  The quotient is rounded towards zero; the
+remainder has the same sign as the dividend unless it is zero.
+
+Some implementations of these functions work differently---or not at all---for
+negative arguments.
+@end deftypefun
+
+@deftypefun void msqrt (MINT *@var{operand}, MINT *@var{root}, MINT *@var{remainder})
+@ifinfo
+Set @var{root} to the truncated integer part of the square root of
+@var{operand}.  Set @var{remainder} to
+@var{operand}@minus{}@var{root}*@var{root},
+@end ifinfo
+@iftex
+Set @var{root} to
+@tex
+$\lfloor\sqrt{@var{operand}}\rfloor$,
+@end tex
+like @code{mpz_sqrt}.  Set @var{remainder} to
+@tex
+$(operand - root^2)$,
+@end tex
+@end iftex
+(i.e., zero if @var{operand} is a perfect square).
+
+If @var{root} and @var{remainder} are the same variable, the results are
+undefined.
+@end deftypefun
+
+@deftypefun void pow (MINT *@var{base}, MINT *@var{exp}, MINT *@var{mod}, MINT *@var{dest})
+Set @var{dest} to (@var{base} raised to @var{exp}) modulo @var{mod}.
+@end deftypefun
+
+@deftypefun void rpow (MINT *@var{base}, signed short int @var{exp}, MINT *@var{dest})
+Set @var{dest} to @var{base} raised to @var{exp}.
+@end deftypefun
+
+@deftypefun void gcd (MINT *@var{operand1}, MINT *@var{operand2}, MINT *@var{res})
+Set @var{res} to the greatest common divisor of @var{operand1} and
+@var{operand2}.
+@end deftypefun
+
+@deftypefun int mcmp (MINT *@var{operand1}, MINT *@var{operand2})
+Compare @var{operand1} and @var{operand2}.  Return a positive value if
+@var{operand1} > @var{operand2}, zero if @var{operand1} =
+@var{operand2}, and a negative value if @var{operand1} < @var{operand2}.
+@end deftypefun
+
+@deftypefun void min (MINT *@var{dest})
+Input a decimal string from @code{stdin}, and put the read integer in
+@var{dest}.  SPC and TAB are allowed in the number string, and are ignored.
+@end deftypefun
+
+@deftypefun void mout (MINT *@var{src})
+Output @var{src} to @code{stdout}, as a decimal string.  Also output a newline.
+@end deftypefun
+
+@deftypefun {char *} mtox (MINT *@var{operand})
+Convert @var{operand} to a hexadecimal string, and return a pointer to the
+string.  The returned string is allocated using the default memory allocation
+function, @code{malloc} by default.
+@end deftypefun
+
+@deftypefun void mfree (MINT *@var{operand})
+De-allocate, the space used by @var{operand}.  @strong{This function should
+only be passed a value returned by @code{itom} or @code{xtom}.}
+@end deftypefun
+
+@node Custom Allocation, Contributors, BSD Compatible Functions, Top
+@comment  node-name,  next,  previous,  up
+@chapter Custom Allocation
+
+By default, the MP functions use @code{malloc}, @code{realloc}, and
+@code{free} for memory allocation.  If @code{malloc} or @code{realloc} fails,
+the MP library terminates execution after printing a fatal error message to
+standard error.
+
+For some applications, you may wish to allocate memory in other ways, or you
+may not want to have a fatal error when there is no more memory available.  To
+accomplish this, you can specify alternative memory allocation functions.
+
+@deftypefun void mp_set_memory_functions (@* void *(*@var{alloc_func_ptr}) (size_t), @* void *(*@var{realloc_func_ptr}) (void *, size_t, size_t), @* void (*@var{free_func_ptr}) (void *, size_t))
+Replace the current allocation functions from the arguments.  If an argument
+is NULL, the corresponding default function is retained.
+
+@strong{Make sure to call this function in such a way that there are no active
+MP objects that were allocated using the previously active allocation
+function!  Usually, that means that you have to call this function before any
+other MP function.}
+@end deftypefun
+
+The functions you supply should fit the following declarations:
+
+@deftypefun {void *} allocate_function (size_t @var{alloc_size})
+This function should return a pointer to newly allocated space with at least
+@var{alloc_size} storage units.
+@end deftypefun
+
+@deftypefun {void *} reallocate_function (void *@var{ptr}, size_t @var{old_size}, size_t @var{new_size})
+This function should return a pointer to newly allocated space of at least
+@var{new_size} storage units, after copying at least the first @var{old_size}
+storage units from @var{ptr}.  It should also de-allocate the space at
+@var{ptr}.
+
+You can assume that the space at @var{ptr} was formerly returned from
+@code{allocate_function} or @code{reallocate_function}, for a request for
+@var{old_size} storage units.
+@end deftypefun
+
+@deftypefun void deallocate_function (void *@var{ptr}, size_t @var{size})
+De-allocate the space pointed to by @var{ptr}.
+
+You can assume that the space at @var{ptr} was formerly returned from
+@code{allocate_function} or @code{reallocate_function}, for a request for
+@var{size} storage units.
+@end deftypefun
+
+(A @dfn{storage unit} is the unit in which the @code{sizeof} operator returns
+the size of an object, normally an 8 bit byte.)
+
+
+@node Contributors, References, Custom Allocation, Top
+@comment  node-name,  next,  previous,  up
+@unnumbered Contributors
+
+I would like to thank Gunnar Sjoedin and Hans Riesel for their help with
+mathematical problems, Richard Stallman for his help with design issues and
+for revising the first version of this manual, Brian Beuning and Doug Lea for
+their testing of early versions of the library.
+
+John Amanatides of York University in Canada contributed the function
+@code{mpz_probab_prime_p}.
+
+Ken Weber (Kent State University, Universidade Federal do Rio Grande do Sul)
+contributed @code{mpz_gcd}, @code{mpz_divexact}, @code{mpn_gcd}, and
+@code{mpn_bdivmod}, partially supported by CNPq (Brazil) grant 301314194-2.
+
+Per Bothner of Cygnus Support helped to set up MP to use Cygnus' configure.
+He has also made valuable suggestions and tested numerous intermediary
+releases.
+
+Joachim Hollman was involved in the design of the @code{mpf} interface, and in
+the @code{mpz} design revisions for version 2.
+
+Bennet Yee contributed the functions @code{mpz_jacobi} and
+@code{mpz_legendre}.
+
+Andreas Schwab contributed the files @code{m68k/lshift.S} and
+@code{m68k/rshift.S}.
+
+The development of floating point functions of GNU MP 2, were supported in
+part by the ESPRIT-BRA (Basic Research Activities) 6846 project POSSO
+(POlynomial System SOlving).
+
+GNU MP 2 was finished and released by TMG Datakonsult, Sodermannagatan 5, 116
+23 STOCKHOLM, SWEDEN, in cooperation with the IDA Center for Computing
+Sciences, USA.
+
+
+@node References, , Contributors, Top
+@comment  node-name,  next,  previous,  up
+@unnumbered References
+
+@itemize @bullet
+
+@item
+Donald E. Knuth, "The Art of Computer Programming", vol 2,
+"Seminumerical Algorithms", 2nd edition, Addison-Wesley, 1981.
+
+@item
+John D. Lipson, "Elements of Algebra and Algebraic Computing",
+The Benjamin Cummings Publishing Company Inc, 1981.
+
+@item
+Richard M. Stallman, "Using and Porting GCC", Free Software Foundation,
+1995.
+
+@item
+Peter L. Montgomery, "Modular Multiplication Without Trial Division", in
+Mathematics of Computation, volume 44, number 170, April 1985.
+
+@item
+Torbjorn Granlund and Peter L. Montgomery, "Division by Invariant
+Integers using Multiplication", in Proceedings of the SIGPLAN
+PLDI'94 Conference, June 1994.
+
+@item
+Tudor Jebelean,
+"An algorithm for exact division",
+Journal of Symbolic Computation,
+v. 15, 1993, pp. 169-180.
+
+@item
+Kenneth Weber, "The accelerated integer GCD algorithm",
+ACM Transactions on Mathematical Software,
+v. 21 (March), 1995, pp. 111-122.
+@end itemize
+
+@node Concept Index, , , Top
+@comment  node-name,  next,  previous,  up
+@unnumbered Concept Index
+@printindex cp
+
+@node Function Index, , , Top
+@comment  node-name,  next,  previous,  up
+@unnumbered Function and Type Index
+@printindex fn
+
+
+@contents
+@bye