1.2

2 files changed, 5519 insertions, 0 deletions

diff --git a/library/GMP/include/gmp.h b/library/GMP/include/gmp.h
new file mode 100644
index 00000000..1268c74d
--- /dev/null
+++ b/library/GMP/include/gmp.h
@@ -0,0 +1,2182 @@
+/* Definitions for GNU multiple precision functions.   -*- mode: c -*-
+
+Copyright 1991, 1993, 1994, 1995, 1996, 1997, 1999, 2000, 2001, 2002, 2003,
+2004, 2005, 2006, 2007 Free Software Foundation, Inc.
+
+This file is part of the GNU MP Library.
+
+The GNU MP Library is free software; you can redistribute it and/or modify
+it under the terms of the GNU Lesser General Public License as published by
+the Free Software Foundation; either version 3 of the License, or (at your
+option) any later version.
+
+The GNU MP Library is distributed in the hope that it will be useful, but
+WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
+License for more details.
+
+You should have received a copy of the GNU Lesser General Public License
+along with the GNU MP Library.  If not, see http://www.gnu.org/licenses/.  */
+
+#ifndef __GMP_H__
+
+#if defined (__cplusplus)
+#include <iosfwd>   /* for std::istream, std::ostream, std::string */
+#endif
+
+
+/* Instantiated by configure. */
+#if ! defined (__GMP_WITHIN_CONFIGURE)
+#define __GMP_BITS_PER_MP_LIMB             32
+#define __GMP_HAVE_HOST_CPU_FAMILY_power   0
+#define __GMP_HAVE_HOST_CPU_FAMILY_powerpc 0
+#define GMP_LIMB_BITS                      32
+#define GMP_NAIL_BITS                      0
+#endif
+#define GMP_NUMB_BITS     (GMP_LIMB_BITS - GMP_NAIL_BITS)
+#define GMP_NUMB_MASK     ((~ __GMP_CAST (mp_limb_t, 0)) >> GMP_NAIL_BITS)
+#define GMP_NUMB_MAX      GMP_NUMB_MASK
+#define GMP_NAIL_MASK     (~ GMP_NUMB_MASK)
+
+
+/* The following (everything under ifndef __GNU_MP__) must be identical in
+   gmp.h and mp.h to allow both to be included in an application or during
+   the library build.  */
+#ifndef __GNU_MP__
+#define __GNU_MP__ 4
+
+#define __need_size_t  /* tell gcc stddef.h we only want size_t */
+#if defined (__cplusplus)
+#include <cstddef>     /* for size_t */
+#else
+#include <stddef.h>    /* for size_t */
+#endif
+#undef __need_size_t
+
+/* Instantiated by configure. */
+#if ! defined (__GMP_WITHIN_CONFIGURE)
+/* #undef _LONG_LONG_LIMB */
+#define __GMP_LIBGMP_DLL  0
+#endif
+
+
+/* __STDC__ - some ANSI compilers define this only to 0, hence the use of
+       "defined" and not "__STDC__-0".  In particular Sun workshop C 5.0
+       sets __STDC__ to 0, but requires "##" for token pasting.
+
+   _AIX - gnu ansidecl.h asserts that all known AIX compilers are ANSI but
+       don't always define __STDC__.
+
+   __DECC - current versions of DEC C (5.9 for instance) for alpha are ANSI,
+       but don't define __STDC__ in their default mode.  Don't know if old
+       versions might have been K&R, but let's not worry about that unless
+       someone is still using one.
+
+   _mips - gnu ansidecl.h says the RISC/OS MIPS compiler is ANSI in SVR4
+       mode, but doesn't define __STDC__.
+
+   _MSC_VER - Microsoft C is ANSI, but __STDC__ is undefined unless the /Za
+       option is given (in which case it's 1).
+
+   _WIN32 - tested for by gnu ansidecl.h, no doubt on the assumption that
+      all w32 compilers are ansi.
+
+   Note: This same set of tests is used by gen-psqr.c and
+   demos/expr/expr-impl.h, so if anything needs adding, then be sure to
+   update those too.  */
+
+#if  defined (__STDC__)                                 \
+  || defined (__cplusplus)                              \
+  || defined (_AIX)                                     \
+  || defined (__DECC)                                   \
+  || (defined (__mips) && defined (_SYSTYPE_SVR4))      \
+  || defined (_MSC_VER)                                 \
+  || defined (_WIN32)
+#define __GMP_HAVE_CONST        1
+#define __GMP_HAVE_PROTOTYPES   1
+#define __GMP_HAVE_TOKEN_PASTE  1
+#else
+#define __GMP_HAVE_CONST        0
+#define __GMP_HAVE_PROTOTYPES   0
+#define __GMP_HAVE_TOKEN_PASTE  0
+#endif
+
+
+#if __GMP_HAVE_CONST
+#define __gmp_const   const
+#define __gmp_signed  signed
+#else
+#define __gmp_const
+#define __gmp_signed
+#endif
+
+
+/* __GMP_DECLSPEC supports Windows DLL versions of libgmp, and is empty in
+   all other circumstances.
+
+   When compiling objects for libgmp, __GMP_DECLSPEC is an export directive,
+   or when compiling for an application it's an import directive.  The two
+   cases are differentiated by __GMP_WITHIN_GMP defined by the GMP Makefiles
+   (and not defined from an application).
+
+   __GMP_DECLSPEC_XX is similarly used for libgmpxx.  __GMP_WITHIN_GMPXX
+   indicates when building libgmpxx, and in that case libgmpxx functions are
+   exports, but libgmp functions which might get called are imports.
+
+   libmp.la uses __GMP_DECLSPEC, just as if it were libgmp.la.  libgmp and
+   libmp don't call each other, so there's no conflict or confusion.
+
+   Libtool DLL_EXPORT define is not used.
+
+   There's no attempt to support GMP built both static and DLL.  Doing so
+   would mean applications would have to tell us which of the two is going
+   to be used when linking, and that seems very tedious and error prone if
+   using GMP by hand, and equally tedious from a package since autoconf and
+   automake don't give much help.
+
+   __GMP_DECLSPEC is required on all documented global functions and
+   variables, the various internals in gmp-impl.h etc can be left unadorned.
+   But internals used by the test programs or speed measuring programs
+   should have __GMP_DECLSPEC, and certainly constants or variables must
+   have it or the wrong address will be resolved.
+
+   In gcc __declspec can go at either the start or end of a prototype.
+
+   In Microsoft C __declspec must go at the start, or after the type like
+   void __declspec(...) *foo()".  There's no __dllexport or anything to
+   guard against someone foolish #defining dllexport.  _export used to be
+   available, but no longer.
+
+   In Borland C _export still exists, but needs to go after the type, like
+   "void _export foo();".  Would have to change the __GMP_DECLSPEC syntax to
+   make use of that.  Probably more trouble than it's worth.  */
+
+#if defined (__GNUC__)
+#define __GMP_DECLSPEC_EXPORT  __declspec(__dllexport__)
+#define __GMP_DECLSPEC_IMPORT  __declspec(__dllimport__)
+#endif
+#if defined (_MSC_VER) || defined (__BORLANDC__)
+#define __GMP_DECLSPEC_EXPORT  __declspec(dllexport)
+#define __GMP_DECLSPEC_IMPORT  __declspec(dllimport)
+#endif
+#ifdef __WATCOMC__
+#define __GMP_DECLSPEC_EXPORT  __export
+#define __GMP_DECLSPEC_IMPORT  __import
+#endif
+#ifdef __IBMC__
+#define __GMP_DECLSPEC_EXPORT  _Export
+#define __GMP_DECLSPEC_IMPORT  _Import
+#endif
+
+#if __GMP_LIBGMP_DLL
+#if __GMP_WITHIN_GMP
+/* compiling to go into a DLL libgmp */
+#define __GMP_DECLSPEC  __GMP_DECLSPEC_EXPORT
+#else
+/* compiling to go into an application which will link to a DLL libgmp */
+#define __GMP_DECLSPEC  __GMP_DECLSPEC_IMPORT
+#endif
+#else
+/* all other cases */
+#define __GMP_DECLSPEC
+#endif
+
+
+#ifdef __GMP_SHORT_LIMB
+typedef unsigned int		mp_limb_t;
+typedef int			mp_limb_signed_t;
+#else
+#ifdef _LONG_LONG_LIMB
+typedef unsigned long long int	mp_limb_t;
+typedef long long int		mp_limb_signed_t;
+#else
+typedef unsigned long int	mp_limb_t;
+typedef long int		mp_limb_signed_t;
+#endif
+#endif
+
+/* For reference, note that the name __mpz_struct gets into C++ mangled
+   function names, which means although the "__" suggests an internal, we
+   must leave this name for binary compatibility.  */
+typedef struct
+{
+    int _mp_alloc;		/* Number of *limbs* allocated and pointed
+				   to by the _mp_d field.  */
+    int _mp_size;			/* abs(_mp_size) is the number of limbs the
+				   last field points to.  If _mp_size is
+				   negative this is a negative number.  */
+    mp_limb_t *_mp_d;		/* Pointer to the limbs.  */
+} __mpz_struct;
+
+#endif /* __GNU_MP__ */
+
+
+typedef __mpz_struct MP_INT;    /* gmp 1 source compatibility */
+typedef __mpz_struct mpz_t[1];
+
+typedef mp_limb_t *		mp_ptr;
+typedef __gmp_const mp_limb_t *	mp_srcptr;
+#if defined (_CRAY) && ! defined (_CRAYMPP)
+/* plain `int' is much faster (48 bits) */
+#define __GMP_MP_SIZE_T_INT     1
+typedef int			mp_size_t;
+typedef int			mp_exp_t;
+#else
+#define __GMP_MP_SIZE_T_INT     0
+typedef long int		mp_size_t;
+typedef long int		mp_exp_t;
+#endif
+
+typedef struct
+{
+    __mpz_struct _mp_num;
+    __mpz_struct _mp_den;
+} __mpq_struct;
+
+typedef __mpq_struct MP_RAT;    /* gmp 1 source compatibility */
+typedef __mpq_struct mpq_t[1];
+
+typedef struct
+{
+    int _mp_prec;			/* Max precision, in number of `mp_limb_t's.
+				   Set by mpf_init and modified by
+				   mpf_set_prec.  The area pointed to by the
+				   _mp_d field contains `prec' + 1 limbs.  */
+    int _mp_size;			/* abs(_mp_size) is the number of limbs the
+				   last field points to.  If _mp_size is
+				   negative this is a negative number.  */
+    mp_exp_t _mp_exp;		/* Exponent, in the base of `mp_limb_t'.  */
+    mp_limb_t *_mp_d;		/* Pointer to the limbs.  */
+} __mpf_struct;
+
+/* typedef __mpf_struct MP_FLOAT; */
+typedef __mpf_struct mpf_t[1];
+
+/* Available random number generation algorithms.  */
+typedef enum
+{
+    GMP_RAND_ALG_DEFAULT = 0,
+    GMP_RAND_ALG_LC = GMP_RAND_ALG_DEFAULT /* Linear congruential.  */
+} gmp_randalg_t;
+
+/* Random state struct.  */
+typedef struct
+{
+    mpz_t _mp_seed;	  /* _mp_d member points to state of the generator. */
+    gmp_randalg_t _mp_alg;  /* Currently unused. */
+    union
+    {
+        void *_mp_lc;         /* Pointer to function pointers structure.  */
+    } _mp_algdata;
+} __gmp_randstate_struct;
+typedef __gmp_randstate_struct gmp_randstate_t[1];
+
+/* Types for function declarations in gmp files.  */
+/* ??? Should not pollute user name space with these ??? */
+typedef __gmp_const __mpz_struct *mpz_srcptr;
+typedef __mpz_struct *mpz_ptr;
+typedef __gmp_const __mpf_struct *mpf_srcptr;
+typedef __mpf_struct *mpf_ptr;
+typedef __gmp_const __mpq_struct *mpq_srcptr;
+typedef __mpq_struct *mpq_ptr;
+
+
+/* This is not wanted in mp.h, so put it outside the __GNU_MP__ common
+   section. */
+#if __GMP_LIBGMP_DLL
+#if __GMP_WITHIN_GMPXX
+/* compiling to go into a DLL libgmpxx */
+#define __GMP_DECLSPEC_XX  __GMP_DECLSPEC_EXPORT
+#else
+/* compiling to go into a application which will link to a DLL libgmpxx */
+#define __GMP_DECLSPEC_XX  __GMP_DECLSPEC_IMPORT
+#endif
+#else
+/* all other cases */
+#define __GMP_DECLSPEC_XX
+#endif
+
+
+#if __GMP_HAVE_PROTOTYPES
+#define __GMP_PROTO(x) x
+#else
+#define __GMP_PROTO(x) ()
+#endif
+
+#ifndef __MPN
+#if __GMP_HAVE_TOKEN_PASTE
+#define __MPN(x) __gmpn_##x
+#else
+#define __MPN(x) __gmpn_/**/x
+#endif
+#endif
+
+/* For reference, "defined(EOF)" cannot be used here.  In g++ 2.95.4,
+   <iostream> defines EOF but not FILE.  */
+#if defined (FILE)                                              \
+  || defined (H_STDIO)                                          \
+  || defined (_H_STDIO)               /* AIX */                 \
+  || defined (_STDIO_H)               /* glibc, Sun, SCO */     \
+  || defined (_STDIO_H_)              /* BSD, OSF */            \
+  || defined (__STDIO_H)              /* Borland */             \
+  || defined (__STDIO_H__)            /* IRIX */                \
+  || defined (_STDIO_INCLUDED)        /* HPUX */                \
+  || defined (__dj_include_stdio_h_)  /* DJGPP */               \
+  || defined (_FILE_DEFINED)          /* Microsoft */           \
+  || defined (__STDIO__)              /* Apple MPW MrC */       \
+  || defined (_MSL_STDIO_H)           /* Metrowerks */          \
+  || defined (_STDIO_H_INCLUDED)      /* QNX4 */		\
+  || defined (_ISO_STDIO_ISO_H)       /* Sun C++ */
+#define _GMP_H_HAVE_FILE 1
+#endif
+
+/* In ISO C, if a prototype involving "struct obstack *" is given without
+   that structure defined, then the struct is scoped down to just the
+   prototype, causing a conflict if it's subsequently defined for real.  So
+   only give prototypes if we've got obstack.h.  */
+#if defined (_OBSTACK_H)   /* glibc <obstack.h> */
+#define _GMP_H_HAVE_OBSTACK 1
+#endif
+
+/* The prototypes for gmp_vprintf etc are provided only if va_list is
+   available, via an application having included <stdarg.h> or <varargs.h>.
+   Usually va_list is a typedef so can't be tested directly, but C99
+   specifies that va_start is a macro (and it was normally a macro on past
+   systems too), so look for that.
+
+   <stdio.h> will define some sort of va_list for vprintf and vfprintf, but
+   let's not bother trying to use that since it's not standard and since
+   application uses for gmp_vprintf etc will almost certainly require the
+   whole <stdarg.h> or <varargs.h> anyway.  */
+
+#ifdef va_start
+#define _GMP_H_HAVE_VA_LIST 1
+#endif
+
+/* Test for gcc >= maj.min, as per __GNUC_PREREQ in glibc */
+#if defined (__GNUC__) && defined (__GNUC_MINOR__)
+#define __GMP_GNUC_PREREQ(maj, min) \
+  ((__GNUC__ << 16) + __GNUC_MINOR__ >= ((maj) << 16) + (min))
+#else
+#define __GMP_GNUC_PREREQ(maj, min)  0
+#endif
+
+/* "pure" is in gcc 2.96 and up, see "(gcc)Function Attributes".  Basically
+   it means a function does nothing but examine its arguments and memory
+   (global or via arguments) to generate a return value, but changes nothing
+   and has no side-effects.  __GMP_NO_ATTRIBUTE_CONST_PURE lets
+   tune/common.c etc turn this off when trying to write timing loops.  */
+#if __GMP_GNUC_PREREQ (2,96) && ! defined (__GMP_NO_ATTRIBUTE_CONST_PURE)
+#define __GMP_ATTRIBUTE_PURE   __attribute__ ((__pure__))
+#else
+#define __GMP_ATTRIBUTE_PURE
+#endif
+
+
+/* __GMP_CAST allows us to use static_cast in C++, so our macros are clean
+   to "g++ -Wold-style-cast".
+
+   Casts in "extern inline" code within an extern "C" block don't induce
+   these warnings, so __GMP_CAST only needs to be used on documented
+   macros.  */
+
+#ifdef __cplusplus
+#define __GMP_CAST(type, expr)  (static_cast<type> (expr))
+#else
+#define __GMP_CAST(type, expr)  ((type) (expr))
+#endif
+
+
+/* An empty "throw ()" means the function doesn't throw any C++ exceptions,
+   this can save some stack frame info in applications.
+
+   Currently it's given only on functions which never divide-by-zero etc,
+   don't allocate memory, and are expected to never need to allocate memory.
+   This leaves open the possibility of a C++ throw from a future GMP
+   exceptions scheme.
+
+   mpz_set_ui etc are omitted to leave open the lazy allocation scheme
+   described in doc/tasks.html.  mpz_get_d etc are omitted to leave open
+   exceptions for float overflows.
+
+   Note that __GMP_NOTHROW must be given on any inlines the same as on their
+   prototypes (for g++ at least, where they're used together).  Note also
+   that g++ 3.0 demands that __GMP_NOTHROW is before other attributes like
+   __GMP_ATTRIBUTE_PURE.  */
+
+#if defined (__cplusplus)
+#define __GMP_NOTHROW  throw ()
+#else
+#define __GMP_NOTHROW
+#endif
+
+
+/* PORTME: What other compilers have a useful "extern inline"?  "static
+   inline" would be an acceptable substitute if the compiler (or linker)
+   discards unused statics.  */
+
+/* gcc has __inline__ in all modes, including strict ansi.  Give a prototype
+   for an inline too, so as to correctly specify "dllimport" on windows, in
+   case the function is called rather than inlined.
+   GCC 4.3 and above with -std=c99 or -std=gnu99 implements ISO C99
+   inline semantics, unless -fgnu89-inline is used.  */
+#ifdef __GNUC__
+#ifdef __GNUC_STDC_INLINE__
+#define __GMP_EXTERN_INLINE extern __inline__ __attribute__ ((__gnu_inline__))
+#else
+#define __GMP_EXTERN_INLINE      extern __inline__
+#endif
+#define __GMP_INLINE_PROTOTYPES  1
+#endif
+
+/* DEC C (eg. version 5.9) supports "static __inline foo()", even in -std1
+   strict ANSI mode.  Inlining is done even when not optimizing (ie. -O0
+   mode, which is the default), but an unnecessary local copy of foo is
+   emitted unless -O is used.  "extern __inline" is accepted, but the
+   "extern" appears to be ignored, ie. it becomes a plain global function
+   but which is inlined within its file.  Don't know if all old versions of
+   DEC C supported __inline, but as a start let's do the right thing for
+   current versions.  */
+#ifdef __DECC
+#define __GMP_EXTERN_INLINE  static __inline
+#endif
+
+/* SCO OpenUNIX 8 cc supports "static inline foo()" but not in -Xc strict
+   ANSI mode (__STDC__ is 1 in that mode).  Inlining only actually takes
+   place under -O.  Without -O "foo" seems to be emitted whether it's used
+   or not, which is wasteful.  "extern inline foo()" isn't useful, the
+   "extern" is apparently ignored, so foo is inlined if possible but also
+   emitted as a global, which causes multiple definition errors when
+   building a shared libgmp.  */
+#ifdef __SCO_VERSION__
+#if __SCO_VERSION__ > 400000000 && __STDC__ != 1 \
+  && ! defined (__GMP_EXTERN_INLINE)
+#define __GMP_EXTERN_INLINE  static inline
+#endif
+#endif
+
+/* C++ always has "inline" and since it's a normal feature the linker should
+   discard duplicate non-inlined copies, or if it doesn't then that's a
+   problem for everyone, not just GMP.  */
+#if defined (__cplusplus) && ! defined (__GMP_EXTERN_INLINE)
+#define __GMP_EXTERN_INLINE  inline
+#endif
+
+/* Don't do any inlining within a configure run, since if the compiler ends
+   up emitting copies of the code into the object file it can end up
+   demanding the various support routines (like mpn_popcount) for linking,
+   making the "alloca" test and perhaps others fail.  And on hppa ia64 a
+   pre-release gcc 3.2 was seen not respecting the "extern" in "extern
+   __inline__", triggering this problem too.  */
+#if defined (__GMP_WITHIN_CONFIGURE) && ! __GMP_WITHIN_CONFIGURE_INLINE
+#undef __GMP_EXTERN_INLINE
+#endif
+
+/* By default, don't give a prototype when there's going to be an inline
+   version.  Note in particular that Cray C++ objects to the combination of
+   prototype and inline.  */
+#ifdef __GMP_EXTERN_INLINE
+#ifndef __GMP_INLINE_PROTOTYPES
+#define __GMP_INLINE_PROTOTYPES  0
+#endif
+#else
+#define __GMP_INLINE_PROTOTYPES  1
+#endif
+
+
+#define __GMP_ABS(x)   ((x) >= 0 ? (x) : -(x))
+#define __GMP_MAX(h,i) ((h) > (i) ? (h) : (i))
+
+/* __GMP_USHRT_MAX is not "~ (unsigned short) 0" because short is promoted
+   to int by "~".  */
+#define __GMP_UINT_MAX   (~ (unsigned) 0)
+#define __GMP_ULONG_MAX  (~ (unsigned long) 0)
+#define __GMP_USHRT_MAX  ((unsigned short) ~0)
+
+
+/* __builtin_expect is in gcc 3.0, and not in 2.95. */
+#if __GMP_GNUC_PREREQ (3,0)
+#define __GMP_LIKELY(cond)    __builtin_expect ((cond) != 0, 1)
+#define __GMP_UNLIKELY(cond)  __builtin_expect ((cond) != 0, 0)
+#else
+#define __GMP_LIKELY(cond)    (cond)
+#define __GMP_UNLIKELY(cond)  (cond)
+#endif
+
+#ifdef _CRAY
+#define __GMP_CRAY_Pragma(str)  _Pragma (str)
+#else
+#define __GMP_CRAY_Pragma(str)
+#endif
+
+
+/* Allow direct user access to numerator and denominator of a mpq_t object.  */
+#define mpq_numref(Q) (&((Q)->_mp_num))
+#define mpq_denref(Q) (&((Q)->_mp_den))
+
+
+#if defined (__cplusplus)
+extern "C"
+{
+#ifdef _GMP_H_HAVE_FILE
+    using std::FILE;
+#endif
+#endif
+
+#define mp_set_memory_functions __gmp_set_memory_functions
+    __GMP_DECLSPEC void mp_set_memory_functions __GMP_PROTO ((void *(*) (size_t),
+            void *(*) (void *, size_t, size_t),
+            void (*) (void *, size_t))) __GMP_NOTHROW;
+
+#define mp_get_memory_functions __gmp_get_memory_functions
+    __GMP_DECLSPEC void mp_get_memory_functions __GMP_PROTO ((void *(**) (size_t),
+            void *(**) (void *, size_t, size_t),
+            void (**) (void *, size_t))) __GMP_NOTHROW;
+
+#define mp_bits_per_limb __gmp_bits_per_limb
+    __GMP_DECLSPEC extern __gmp_const int mp_bits_per_limb;
+
+#define gmp_errno __gmp_errno
+    __GMP_DECLSPEC extern int gmp_errno;
+
+#define gmp_version __gmp_version
+    __GMP_DECLSPEC extern __gmp_const char * __gmp_const gmp_version;
+
+
+    /**************** Random number routines.  ****************/
+
+    /* obsolete */
+#define gmp_randinit __gmp_randinit
+    __GMP_DECLSPEC void gmp_randinit __GMP_PROTO ((gmp_randstate_t, gmp_randalg_t, ...));
+
+#define gmp_randinit_default __gmp_randinit_default
+    __GMP_DECLSPEC void gmp_randinit_default __GMP_PROTO ((gmp_randstate_t));
+
+#define gmp_randinit_lc_2exp __gmp_randinit_lc_2exp
+    __GMP_DECLSPEC void gmp_randinit_lc_2exp __GMP_PROTO ((gmp_randstate_t,
+            mpz_srcptr, unsigned long int,
+            unsigned long int));
+
+#define gmp_randinit_lc_2exp_size __gmp_randinit_lc_2exp_size
+    __GMP_DECLSPEC int gmp_randinit_lc_2exp_size __GMP_PROTO ((gmp_randstate_t, unsigned long));
+
+#define gmp_randinit_mt __gmp_randinit_mt
+    __GMP_DECLSPEC void gmp_randinit_mt __GMP_PROTO ((gmp_randstate_t));
+
+#define gmp_randinit_set __gmp_randinit_set
+    void gmp_randinit_set __GMP_PROTO ((gmp_randstate_t, __gmp_const __gmp_randstate_struct *));
+
+#define gmp_randseed __gmp_randseed
+    __GMP_DECLSPEC void gmp_randseed __GMP_PROTO ((gmp_randstate_t, mpz_srcptr));
+
+#define gmp_randseed_ui __gmp_randseed_ui
+    __GMP_DECLSPEC void gmp_randseed_ui __GMP_PROTO ((gmp_randstate_t, unsigned long int));
+
+#define gmp_randclear __gmp_randclear
+    __GMP_DECLSPEC void gmp_randclear __GMP_PROTO ((gmp_randstate_t));
+
+#define gmp_urandomb_ui __gmp_urandomb_ui
+    unsigned long gmp_urandomb_ui __GMP_PROTO ((gmp_randstate_t, unsigned long));
+
+#define gmp_urandomm_ui __gmp_urandomm_ui
+    unsigned long gmp_urandomm_ui __GMP_PROTO ((gmp_randstate_t, unsigned long));
+
+
+    /**************** Formatted output routines.  ****************/
+
+#define gmp_asprintf __gmp_asprintf
+    __GMP_DECLSPEC int gmp_asprintf __GMP_PROTO ((char **, __gmp_const char *, ...));
+
+#define gmp_fprintf __gmp_fprintf
+#ifdef _GMP_H_HAVE_FILE
+    __GMP_DECLSPEC int gmp_fprintf __GMP_PROTO ((FILE *, __gmp_const char *, ...));
+#endif
+
+#define gmp_obstack_printf __gmp_obstack_printf
+#if defined (_GMP_H_HAVE_OBSTACK)
+    __GMP_DECLSPEC int gmp_obstack_printf __GMP_PROTO ((struct obstack *, __gmp_const char *, ...));
+#endif
+
+#define gmp_obstack_vprintf __gmp_obstack_vprintf
+#if defined (_GMP_H_HAVE_OBSTACK) && defined (_GMP_H_HAVE_VA_LIST)
+    __GMP_DECLSPEC int gmp_obstack_vprintf __GMP_PROTO ((struct obstack *, __gmp_const char *, va_list));
+#endif
+
+#define gmp_printf __gmp_printf
+    __GMP_DECLSPEC int gmp_printf __GMP_PROTO ((__gmp_const char *, ...));
+
+#define gmp_snprintf __gmp_snprintf
+    __GMP_DECLSPEC int gmp_snprintf __GMP_PROTO ((char *, size_t, __gmp_const char *, ...));
+
+#define gmp_sprintf __gmp_sprintf
+    __GMP_DECLSPEC int gmp_sprintf __GMP_PROTO ((char *, __gmp_const char *, ...));
+
+#define gmp_vasprintf __gmp_vasprintf
+#if defined (_GMP_H_HAVE_VA_LIST)
+    __GMP_DECLSPEC int gmp_vasprintf __GMP_PROTO ((char **, __gmp_const char *, va_list));
+#endif
+
+#define gmp_vfprintf __gmp_vfprintf
+#if defined (_GMP_H_HAVE_FILE) && defined (_GMP_H_HAVE_VA_LIST)
+    __GMP_DECLSPEC int gmp_vfprintf __GMP_PROTO ((FILE *, __gmp_const char *, va_list));
+#endif
+
+#define gmp_vprintf __gmp_vprintf
+#if defined (_GMP_H_HAVE_VA_LIST)
+    __GMP_DECLSPEC int gmp_vprintf __GMP_PROTO ((__gmp_const char *, va_list));
+#endif
+
+#define gmp_vsnprintf __gmp_vsnprintf
+#if defined (_GMP_H_HAVE_VA_LIST)
+    __GMP_DECLSPEC int gmp_vsnprintf __GMP_PROTO ((char *, size_t, __gmp_const char *, va_list));
+#endif
+
+#define gmp_vsprintf __gmp_vsprintf
+#if defined (_GMP_H_HAVE_VA_LIST)
+    __GMP_DECLSPEC int gmp_vsprintf __GMP_PROTO ((char *, __gmp_const char *, va_list));
+#endif
+
+
+    /**************** Formatted input routines.  ****************/
+
+#define gmp_fscanf __gmp_fscanf
+#ifdef _GMP_H_HAVE_FILE
+    __GMP_DECLSPEC int gmp_fscanf __GMP_PROTO ((FILE *, __gmp_const char *, ...));
+#endif
+
+#define gmp_scanf __gmp_scanf
+    __GMP_DECLSPEC int gmp_scanf __GMP_PROTO ((__gmp_const char *, ...));
+
+#define gmp_sscanf __gmp_sscanf
+    __GMP_DECLSPEC int gmp_sscanf __GMP_PROTO ((__gmp_const char *, __gmp_const char *, ...));
+
+#define gmp_vfscanf __gmp_vfscanf
+#if defined (_GMP_H_HAVE_FILE) && defined (_GMP_H_HAVE_VA_LIST)
+    __GMP_DECLSPEC int gmp_vfscanf __GMP_PROTO ((FILE *, __gmp_const char *, va_list));
+#endif
+
+#define gmp_vscanf __gmp_vscanf
+#if defined (_GMP_H_HAVE_VA_LIST)
+    __GMP_DECLSPEC int gmp_vscanf __GMP_PROTO ((__gmp_const char *, va_list));
+#endif
+
+#define gmp_vsscanf __gmp_vsscanf
+#if defined (_GMP_H_HAVE_VA_LIST)
+    __GMP_DECLSPEC int gmp_vsscanf __GMP_PROTO ((__gmp_const char *, __gmp_const char *, va_list));
+#endif
+
+
+    /**************** Integer (i.e. Z) routines.  ****************/
+
+#define _mpz_realloc __gmpz_realloc
+#define mpz_realloc __gmpz_realloc
+    __GMP_DECLSPEC void *_mpz_realloc __GMP_PROTO ((mpz_ptr, mp_size_t));
+
+#define mpz_abs __gmpz_abs
+#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_abs)
+    __GMP_DECLSPEC void mpz_abs __GMP_PROTO ((mpz_ptr, mpz_srcptr));
+#endif
+
+#define mpz_add __gmpz_add
+    __GMP_DECLSPEC void mpz_add __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
+
+#define mpz_add_ui __gmpz_add_ui
+    __GMP_DECLSPEC void mpz_add_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
+
+#define mpz_addmul __gmpz_addmul
+    __GMP_DECLSPEC void mpz_addmul __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
+
+#define mpz_addmul_ui __gmpz_addmul_ui
+    __GMP_DECLSPEC void mpz_addmul_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
+
+#define mpz_and __gmpz_and
+    __GMP_DECLSPEC void mpz_and __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
+
+#define mpz_array_init __gmpz_array_init
+    __GMP_DECLSPEC void mpz_array_init __GMP_PROTO ((mpz_ptr, mp_size_t, mp_size_t));
+
+#define mpz_bin_ui __gmpz_bin_ui
+    __GMP_DECLSPEC void mpz_bin_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
+
+#define mpz_bin_uiui __gmpz_bin_uiui
+    __GMP_DECLSPEC void mpz_bin_uiui __GMP_PROTO ((mpz_ptr, unsigned long int, unsigned long int));
+
+#define mpz_cdiv_q __gmpz_cdiv_q
+    __GMP_DECLSPEC void mpz_cdiv_q __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
+
+#define mpz_cdiv_q_2exp __gmpz_cdiv_q_2exp
+    __GMP_DECLSPEC void mpz_cdiv_q_2exp __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long));
+
+#define mpz_cdiv_q_ui __gmpz_cdiv_q_ui
+    __GMP_DECLSPEC unsigned long int mpz_cdiv_q_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
+
+#define mpz_cdiv_qr __gmpz_cdiv_qr
+    __GMP_DECLSPEC void mpz_cdiv_qr __GMP_PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr, mpz_srcptr));
+
+#define mpz_cdiv_qr_ui __gmpz_cdiv_qr_ui
+    __GMP_DECLSPEC unsigned long int mpz_cdiv_qr_ui __GMP_PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr, unsigned long int));
+
+#define mpz_cdiv_r __gmpz_cdiv_r
+    __GMP_DECLSPEC void mpz_cdiv_r __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
+
+#define mpz_cdiv_r_2exp __gmpz_cdiv_r_2exp
+    __GMP_DECLSPEC void mpz_cdiv_r_2exp __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long));
+
+#define mpz_cdiv_r_ui __gmpz_cdiv_r_ui
+    __GMP_DECLSPEC unsigned long int mpz_cdiv_r_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
+
+#define mpz_cdiv_ui __gmpz_cdiv_ui
+    __GMP_DECLSPEC unsigned long int mpz_cdiv_ui __GMP_PROTO ((mpz_srcptr, unsigned long int)) __GMP_ATTRIBUTE_PURE;
+
+#define mpz_clear __gmpz_clear
+    __GMP_DECLSPEC void mpz_clear __GMP_PROTO ((mpz_ptr));
+
+#define mpz_clrbit __gmpz_clrbit
+    __GMP_DECLSPEC void mpz_clrbit __GMP_PROTO ((mpz_ptr, unsigned long int));
+
+#define mpz_cmp __gmpz_cmp
+    __GMP_DECLSPEC int mpz_cmp __GMP_PROTO ((mpz_srcptr, mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpz_cmp_d __gmpz_cmp_d
+    __GMP_DECLSPEC int mpz_cmp_d __GMP_PROTO ((mpz_srcptr, double)) __GMP_ATTRIBUTE_PURE;
+
+#define _mpz_cmp_si __gmpz_cmp_si
+    __GMP_DECLSPEC int _mpz_cmp_si __GMP_PROTO ((mpz_srcptr, signed long int)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define _mpz_cmp_ui __gmpz_cmp_ui
+    __GMP_DECLSPEC int _mpz_cmp_ui __GMP_PROTO ((mpz_srcptr, unsigned long int)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpz_cmpabs __gmpz_cmpabs
+    __GMP_DECLSPEC int mpz_cmpabs __GMP_PROTO ((mpz_srcptr, mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpz_cmpabs_d __gmpz_cmpabs_d
+    __GMP_DECLSPEC int mpz_cmpabs_d __GMP_PROTO ((mpz_srcptr, double)) __GMP_ATTRIBUTE_PURE;
+
+#define mpz_cmpabs_ui __gmpz_cmpabs_ui
+    __GMP_DECLSPEC int mpz_cmpabs_ui __GMP_PROTO ((mpz_srcptr, unsigned long int)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpz_com __gmpz_com
+    __GMP_DECLSPEC void mpz_com __GMP_PROTO ((mpz_ptr, mpz_srcptr));
+
+#define mpz_combit __gmpz_combit
+    __GMP_DECLSPEC void mpz_combit __GMP_PROTO ((mpz_ptr, unsigned long int));
+
+#define mpz_congruent_p __gmpz_congruent_p
+    __GMP_DECLSPEC int mpz_congruent_p __GMP_PROTO ((mpz_srcptr, mpz_srcptr, mpz_srcptr)) __GMP_ATTRIBUTE_PURE;
+
+#define mpz_congruent_2exp_p __gmpz_congruent_2exp_p
+    __GMP_DECLSPEC int mpz_congruent_2exp_p __GMP_PROTO ((mpz_srcptr, mpz_srcptr, unsigned long)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpz_congruent_ui_p __gmpz_congruent_ui_p
+    __GMP_DECLSPEC int mpz_congruent_ui_p __GMP_PROTO ((mpz_srcptr, unsigned long, unsigned long)) __GMP_ATTRIBUTE_PURE;
+
+#define mpz_divexact __gmpz_divexact
+    __GMP_DECLSPEC void mpz_divexact __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
+
+#define mpz_divexact_ui __gmpz_divexact_ui
+    __GMP_DECLSPEC void mpz_divexact_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long));
+
+#define mpz_divisible_p __gmpz_divisible_p
+    __GMP_DECLSPEC int mpz_divisible_p __GMP_PROTO ((mpz_srcptr, mpz_srcptr)) __GMP_ATTRIBUTE_PURE;
+
+#define mpz_divisible_ui_p __gmpz_divisible_ui_p
+    __GMP_DECLSPEC int mpz_divisible_ui_p __GMP_PROTO ((mpz_srcptr, unsigned long)) __GMP_ATTRIBUTE_PURE;
+
+#define mpz_divisible_2exp_p __gmpz_divisible_2exp_p
+    __GMP_DECLSPEC int mpz_divisible_2exp_p __GMP_PROTO ((mpz_srcptr, unsigned long)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpz_dump __gmpz_dump
+    __GMP_DECLSPEC void mpz_dump __GMP_PROTO ((mpz_srcptr));
+
+#define mpz_export __gmpz_export
+    __GMP_DECLSPEC void *mpz_export __GMP_PROTO ((void *, size_t *, int, size_t, int, size_t, mpz_srcptr));
+
+#define mpz_fac_ui __gmpz_fac_ui
+    __GMP_DECLSPEC void mpz_fac_ui __GMP_PROTO ((mpz_ptr, unsigned long int));
+
+#define mpz_fdiv_q __gmpz_fdiv_q
+    __GMP_DECLSPEC void mpz_fdiv_q __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
+
+#define mpz_fdiv_q_2exp __gmpz_fdiv_q_2exp
+    __GMP_DECLSPEC void mpz_fdiv_q_2exp __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
+
+#define mpz_fdiv_q_ui __gmpz_fdiv_q_ui
+    __GMP_DECLSPEC unsigned long int mpz_fdiv_q_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
+
+#define mpz_fdiv_qr __gmpz_fdiv_qr
+    __GMP_DECLSPEC void mpz_fdiv_qr __GMP_PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr, mpz_srcptr));
+
+#define mpz_fdiv_qr_ui __gmpz_fdiv_qr_ui
+    __GMP_DECLSPEC unsigned long int mpz_fdiv_qr_ui __GMP_PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr, unsigned long int));
+
+#define mpz_fdiv_r __gmpz_fdiv_r
+    __GMP_DECLSPEC void mpz_fdiv_r __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
+
+#define mpz_fdiv_r_2exp __gmpz_fdiv_r_2exp
+    __GMP_DECLSPEC void mpz_fdiv_r_2exp __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
+
+#define mpz_fdiv_r_ui __gmpz_fdiv_r_ui
+    __GMP_DECLSPEC unsigned long int mpz_fdiv_r_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
+
+#define mpz_fdiv_ui __gmpz_fdiv_ui
+    __GMP_DECLSPEC unsigned long int mpz_fdiv_ui __GMP_PROTO ((mpz_srcptr, unsigned long int)) __GMP_ATTRIBUTE_PURE;
+
+#define mpz_fib_ui __gmpz_fib_ui
+    __GMP_DECLSPEC void mpz_fib_ui __GMP_PROTO ((mpz_ptr, unsigned long int));
+
+#define mpz_fib2_ui __gmpz_fib2_ui
+    __GMP_DECLSPEC void mpz_fib2_ui __GMP_PROTO ((mpz_ptr, mpz_ptr, unsigned long int));
+
+#define mpz_fits_sint_p __gmpz_fits_sint_p
+    __GMP_DECLSPEC int mpz_fits_sint_p __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpz_fits_slong_p __gmpz_fits_slong_p
+    __GMP_DECLSPEC int mpz_fits_slong_p __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpz_fits_sshort_p __gmpz_fits_sshort_p
+    __GMP_DECLSPEC int mpz_fits_sshort_p __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpz_fits_uint_p __gmpz_fits_uint_p
+#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_fits_uint_p)
+    __GMP_DECLSPEC int mpz_fits_uint_p __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+#endif
+
+#define mpz_fits_ulong_p __gmpz_fits_ulong_p
+#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_fits_ulong_p)
+    __GMP_DECLSPEC int mpz_fits_ulong_p __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+#endif
+
+#define mpz_fits_ushort_p __gmpz_fits_ushort_p
+#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_fits_ushort_p)
+    __GMP_DECLSPEC int mpz_fits_ushort_p __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+#endif
+
+#define mpz_gcd __gmpz_gcd
+    __GMP_DECLSPEC void mpz_gcd __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
+
+#define mpz_gcd_ui __gmpz_gcd_ui
+    __GMP_DECLSPEC unsigned long int mpz_gcd_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
+
+#define mpz_gcdext __gmpz_gcdext
+    __GMP_DECLSPEC void mpz_gcdext __GMP_PROTO ((mpz_ptr, mpz_ptr, mpz_ptr, mpz_srcptr, mpz_srcptr));
+
+#define mpz_get_d __gmpz_get_d
+    __GMP_DECLSPEC double mpz_get_d __GMP_PROTO ((mpz_srcptr)) __GMP_ATTRIBUTE_PURE;
+
+#define mpz_get_d_2exp __gmpz_get_d_2exp
+    __GMP_DECLSPEC double mpz_get_d_2exp __GMP_PROTO ((signed long int *, mpz_srcptr));
+
+#define mpz_get_si __gmpz_get_si
+    __GMP_DECLSPEC /* signed */ long int mpz_get_si __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpz_get_str __gmpz_get_str
+    __GMP_DECLSPEC char *mpz_get_str __GMP_PROTO ((char *, int, mpz_srcptr));
+
+#define mpz_get_ui __gmpz_get_ui
+#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_get_ui)
+    __GMP_DECLSPEC unsigned long int mpz_get_ui __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+#endif
+
+#define mpz_getlimbn __gmpz_getlimbn
+#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_getlimbn)
+    __GMP_DECLSPEC mp_limb_t mpz_getlimbn __GMP_PROTO ((mpz_srcptr, mp_size_t)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+#endif
+
+#define mpz_hamdist __gmpz_hamdist
+    __GMP_DECLSPEC unsigned long int mpz_hamdist __GMP_PROTO ((mpz_srcptr, mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpz_import __gmpz_import
+    __GMP_DECLSPEC void mpz_import __GMP_PROTO ((mpz_ptr, size_t, int, size_t, int, size_t, __gmp_const void *));
+
+#define mpz_init __gmpz_init
+    __GMP_DECLSPEC void mpz_init __GMP_PROTO ((mpz_ptr));
+
+#define mpz_init2 __gmpz_init2
+    __GMP_DECLSPEC void mpz_init2 __GMP_PROTO ((mpz_ptr, unsigned long));
+
+#define mpz_init_set __gmpz_init_set
+    __GMP_DECLSPEC void mpz_init_set __GMP_PROTO ((mpz_ptr, mpz_srcptr));
+
+#define mpz_init_set_d __gmpz_init_set_d
+    __GMP_DECLSPEC void mpz_init_set_d __GMP_PROTO ((mpz_ptr, double));
+
+#define mpz_init_set_si __gmpz_init_set_si
+    __GMP_DECLSPEC void mpz_init_set_si __GMP_PROTO ((mpz_ptr, signed long int));
+
+#define mpz_init_set_str __gmpz_init_set_str
+    __GMP_DECLSPEC int mpz_init_set_str __GMP_PROTO ((mpz_ptr, __gmp_const char *, int));
+
+#define mpz_init_set_ui __gmpz_init_set_ui
+    __GMP_DECLSPEC void mpz_init_set_ui __GMP_PROTO ((mpz_ptr, unsigned long int));
+
+#define mpz_inp_raw __gmpz_inp_raw
+#ifdef _GMP_H_HAVE_FILE
+    __GMP_DECLSPEC size_t mpz_inp_raw __GMP_PROTO ((mpz_ptr, FILE *));
+#endif
+
+#define mpz_inp_str __gmpz_inp_str
+#ifdef _GMP_H_HAVE_FILE
+    __GMP_DECLSPEC size_t mpz_inp_str __GMP_PROTO ((mpz_ptr, FILE *, int));
+#endif
+
+#define mpz_invert __gmpz_invert
+    __GMP_DECLSPEC int mpz_invert __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
+
+#define mpz_ior __gmpz_ior
+    __GMP_DECLSPEC void mpz_ior __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
+
+#define mpz_jacobi __gmpz_jacobi
+    __GMP_DECLSPEC int mpz_jacobi __GMP_PROTO ((mpz_srcptr, mpz_srcptr)) __GMP_ATTRIBUTE_PURE;
+
+#define mpz_kronecker mpz_jacobi  /* alias */
+
+#define mpz_kronecker_si __gmpz_kronecker_si
+    __GMP_DECLSPEC int mpz_kronecker_si __GMP_PROTO ((mpz_srcptr, long)) __GMP_ATTRIBUTE_PURE;
+
+#define mpz_kronecker_ui __gmpz_kronecker_ui
+    __GMP_DECLSPEC int mpz_kronecker_ui __GMP_PROTO ((mpz_srcptr, unsigned long)) __GMP_ATTRIBUTE_PURE;
+
+#define mpz_si_kronecker __gmpz_si_kronecker
+    __GMP_DECLSPEC int mpz_si_kronecker __GMP_PROTO ((long, mpz_srcptr)) __GMP_ATTRIBUTE_PURE;
+
+#define mpz_ui_kronecker __gmpz_ui_kronecker
+    __GMP_DECLSPEC int mpz_ui_kronecker __GMP_PROTO ((unsigned long, mpz_srcptr)) __GMP_ATTRIBUTE_PURE;
+
+#define mpz_lcm __gmpz_lcm
+    __GMP_DECLSPEC void mpz_lcm __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
+
+#define mpz_lcm_ui __gmpz_lcm_ui
+    __GMP_DECLSPEC void mpz_lcm_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long));
+
+#define mpz_legendre mpz_jacobi  /* alias */
+
+#define mpz_lucnum_ui __gmpz_lucnum_ui
+    __GMP_DECLSPEC void mpz_lucnum_ui __GMP_PROTO ((mpz_ptr, unsigned long int));
+
+#define mpz_lucnum2_ui __gmpz_lucnum2_ui
+    __GMP_DECLSPEC void mpz_lucnum2_ui __GMP_PROTO ((mpz_ptr, mpz_ptr, unsigned long int));
+
+#define mpz_millerrabin __gmpz_millerrabin
+    __GMP_DECLSPEC int mpz_millerrabin __GMP_PROTO ((mpz_srcptr, int)) __GMP_ATTRIBUTE_PURE;
+
+#define mpz_mod __gmpz_mod
+    __GMP_DECLSPEC void mpz_mod __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
+
+#define mpz_mod_ui mpz_fdiv_r_ui /* same as fdiv_r because divisor unsigned */
+
+#define mpz_mul __gmpz_mul
+    __GMP_DECLSPEC void mpz_mul __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
+
+#define mpz_mul_2exp __gmpz_mul_2exp
+    __GMP_DECLSPEC void mpz_mul_2exp __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
+
+#define mpz_mul_si __gmpz_mul_si
+    __GMP_DECLSPEC void mpz_mul_si __GMP_PROTO ((mpz_ptr, mpz_srcptr, long int));
+
+#define mpz_mul_ui __gmpz_mul_ui
+    __GMP_DECLSPEC void mpz_mul_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
+
+#define mpz_neg __gmpz_neg
+#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_neg)
+    __GMP_DECLSPEC void mpz_neg __GMP_PROTO ((mpz_ptr, mpz_srcptr));
+#endif
+
+#define mpz_nextprime __gmpz_nextprime
+    __GMP_DECLSPEC void mpz_nextprime __GMP_PROTO ((mpz_ptr, mpz_srcptr));
+
+#define mpz_out_raw __gmpz_out_raw
+#ifdef _GMP_H_HAVE_FILE
+    __GMP_DECLSPEC size_t mpz_out_raw __GMP_PROTO ((FILE *, mpz_srcptr));
+#endif
+
+#define mpz_out_str __gmpz_out_str
+#ifdef _GMP_H_HAVE_FILE
+    __GMP_DECLSPEC size_t mpz_out_str __GMP_PROTO ((FILE *, int, mpz_srcptr));
+#endif
+
+#define mpz_perfect_power_p __gmpz_perfect_power_p
+    __GMP_DECLSPEC int mpz_perfect_power_p __GMP_PROTO ((mpz_srcptr)) __GMP_ATTRIBUTE_PURE;
+
+#define mpz_perfect_square_p __gmpz_perfect_square_p
+#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_perfect_square_p)
+    __GMP_DECLSPEC int mpz_perfect_square_p __GMP_PROTO ((mpz_srcptr)) __GMP_ATTRIBUTE_PURE;
+#endif
+
+#define mpz_popcount __gmpz_popcount
+#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_popcount)
+    __GMP_DECLSPEC unsigned long int mpz_popcount __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+#endif
+
+#define mpz_pow_ui __gmpz_pow_ui
+    __GMP_DECLSPEC void mpz_pow_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
+
+#define mpz_powm __gmpz_powm
+    __GMP_DECLSPEC void mpz_powm __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr, mpz_srcptr));
+
+#define mpz_powm_ui __gmpz_powm_ui
+    __GMP_DECLSPEC void mpz_powm_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int, mpz_srcptr));
+
+#define mpz_probab_prime_p __gmpz_probab_prime_p
+    __GMP_DECLSPEC int mpz_probab_prime_p __GMP_PROTO ((mpz_srcptr, int)) __GMP_ATTRIBUTE_PURE;
+
+#define mpz_random __gmpz_random
+    __GMP_DECLSPEC void mpz_random __GMP_PROTO ((mpz_ptr, mp_size_t));
+
+#define mpz_random2 __gmpz_random2
+    __GMP_DECLSPEC void mpz_random2 __GMP_PROTO ((mpz_ptr, mp_size_t));
+
+#define mpz_realloc2 __gmpz_realloc2
+    __GMP_DECLSPEC void mpz_realloc2 __GMP_PROTO ((mpz_ptr, unsigned long));
+
+#define mpz_remove __gmpz_remove
+    __GMP_DECLSPEC unsigned long int mpz_remove __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
+
+#define mpz_root __gmpz_root
+    __GMP_DECLSPEC int mpz_root __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
+
+#define mpz_rootrem __gmpz_rootrem
+    __GMP_DECLSPEC void mpz_rootrem __GMP_PROTO ((mpz_ptr,mpz_ptr, mpz_srcptr, unsigned long int));
+
+#define mpz_rrandomb __gmpz_rrandomb
+    __GMP_DECLSPEC void mpz_rrandomb __GMP_PROTO ((mpz_ptr, gmp_randstate_t, unsigned long int));
+
+#define mpz_scan0 __gmpz_scan0
+    __GMP_DECLSPEC unsigned long int mpz_scan0 __GMP_PROTO ((mpz_srcptr, unsigned long int)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpz_scan1 __gmpz_scan1
+    __GMP_DECLSPEC unsigned long int mpz_scan1 __GMP_PROTO ((mpz_srcptr, unsigned long int)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpz_set __gmpz_set
+    __GMP_DECLSPEC void mpz_set __GMP_PROTO ((mpz_ptr, mpz_srcptr));
+
+#define mpz_set_d __gmpz_set_d
+    __GMP_DECLSPEC void mpz_set_d __GMP_PROTO ((mpz_ptr, double));
+
+#define mpz_set_f __gmpz_set_f
+    __GMP_DECLSPEC void mpz_set_f __GMP_PROTO ((mpz_ptr, mpf_srcptr));
+
+#define mpz_set_q __gmpz_set_q
+#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_set_q)
+    __GMP_DECLSPEC void mpz_set_q __GMP_PROTO ((mpz_ptr, mpq_srcptr));
+#endif
+
+#define mpz_set_si __gmpz_set_si
+    __GMP_DECLSPEC void mpz_set_si __GMP_PROTO ((mpz_ptr, signed long int));
+
+#define mpz_set_str __gmpz_set_str
+    __GMP_DECLSPEC int mpz_set_str __GMP_PROTO ((mpz_ptr, __gmp_const char *, int));
+
+#define mpz_set_ui __gmpz_set_ui
+    __GMP_DECLSPEC void mpz_set_ui __GMP_PROTO ((mpz_ptr, unsigned long int));
+
+#define mpz_setbit __gmpz_setbit
+    __GMP_DECLSPEC void mpz_setbit __GMP_PROTO ((mpz_ptr, unsigned long int));
+
+#define mpz_size __gmpz_size
+#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_size)
+    __GMP_DECLSPEC size_t mpz_size __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+#endif
+
+#define mpz_sizeinbase __gmpz_sizeinbase
+    __GMP_DECLSPEC size_t mpz_sizeinbase __GMP_PROTO ((mpz_srcptr, int)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpz_sqrt __gmpz_sqrt
+    __GMP_DECLSPEC void mpz_sqrt __GMP_PROTO ((mpz_ptr, mpz_srcptr));
+
+#define mpz_sqrtrem __gmpz_sqrtrem
+    __GMP_DECLSPEC void mpz_sqrtrem __GMP_PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr));
+
+#define mpz_sub __gmpz_sub
+    __GMP_DECLSPEC void mpz_sub __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
+
+#define mpz_sub_ui __gmpz_sub_ui
+    __GMP_DECLSPEC void mpz_sub_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
+
+#define mpz_ui_sub __gmpz_ui_sub
+    __GMP_DECLSPEC void mpz_ui_sub __GMP_PROTO ((mpz_ptr, unsigned long int, mpz_srcptr));
+
+#define mpz_submul __gmpz_submul
+    __GMP_DECLSPEC void mpz_submul __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
+
+#define mpz_submul_ui __gmpz_submul_ui
+    __GMP_DECLSPEC void mpz_submul_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
+
+#define mpz_swap __gmpz_swap
+    __GMP_DECLSPEC void mpz_swap __GMP_PROTO ((mpz_ptr, mpz_ptr)) __GMP_NOTHROW;
+
+#define mpz_tdiv_ui __gmpz_tdiv_ui
+    __GMP_DECLSPEC unsigned long int mpz_tdiv_ui __GMP_PROTO ((mpz_srcptr, unsigned long int)) __GMP_ATTRIBUTE_PURE;
+
+#define mpz_tdiv_q __gmpz_tdiv_q
+    __GMP_DECLSPEC void mpz_tdiv_q __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
+
+#define mpz_tdiv_q_2exp __gmpz_tdiv_q_2exp
+    __GMP_DECLSPEC void mpz_tdiv_q_2exp __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
+
+#define mpz_tdiv_q_ui __gmpz_tdiv_q_ui
+    __GMP_DECLSPEC unsigned long int mpz_tdiv_q_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
+
+#define mpz_tdiv_qr __gmpz_tdiv_qr
+    __GMP_DECLSPEC void mpz_tdiv_qr __GMP_PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr, mpz_srcptr));
+
+#define mpz_tdiv_qr_ui __gmpz_tdiv_qr_ui
+    __GMP_DECLSPEC unsigned long int mpz_tdiv_qr_ui __GMP_PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr, unsigned long int));
+
+#define mpz_tdiv_r __gmpz_tdiv_r
+    __GMP_DECLSPEC void mpz_tdiv_r __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
+
+#define mpz_tdiv_r_2exp __gmpz_tdiv_r_2exp
+    __GMP_DECLSPEC void mpz_tdiv_r_2exp __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
+
+#define mpz_tdiv_r_ui __gmpz_tdiv_r_ui
+    __GMP_DECLSPEC unsigned long int mpz_tdiv_r_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int));
+
+#define mpz_tstbit __gmpz_tstbit
+    __GMP_DECLSPEC int mpz_tstbit __GMP_PROTO ((mpz_srcptr, unsigned long int)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpz_ui_pow_ui __gmpz_ui_pow_ui
+    __GMP_DECLSPEC void mpz_ui_pow_ui __GMP_PROTO ((mpz_ptr, unsigned long int, unsigned long int));
+
+#define mpz_urandomb __gmpz_urandomb
+    __GMP_DECLSPEC void mpz_urandomb __GMP_PROTO ((mpz_ptr, gmp_randstate_t, unsigned long int));
+
+#define mpz_urandomm __gmpz_urandomm
+    __GMP_DECLSPEC void mpz_urandomm __GMP_PROTO ((mpz_ptr, gmp_randstate_t, mpz_srcptr));
+
+#define mpz_xor __gmpz_xor
+#define mpz_eor __gmpz_xor
+    __GMP_DECLSPEC void mpz_xor __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr));
+
+
+    /**************** Rational (i.e. Q) routines.  ****************/
+
+#define mpq_abs __gmpq_abs
+#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpq_abs)
+    __GMP_DECLSPEC void mpq_abs __GMP_PROTO ((mpq_ptr, mpq_srcptr));
+#endif
+
+#define mpq_add __gmpq_add
+    __GMP_DECLSPEC void mpq_add __GMP_PROTO ((mpq_ptr, mpq_srcptr, mpq_srcptr));
+
+#define mpq_canonicalize __gmpq_canonicalize
+    __GMP_DECLSPEC void mpq_canonicalize __GMP_PROTO ((mpq_ptr));
+
+#define mpq_clear __gmpq_clear
+    __GMP_DECLSPEC void mpq_clear __GMP_PROTO ((mpq_ptr));
+
+#define mpq_cmp __gmpq_cmp
+    __GMP_DECLSPEC int mpq_cmp __GMP_PROTO ((mpq_srcptr, mpq_srcptr)) __GMP_ATTRIBUTE_PURE;
+
+#define _mpq_cmp_si __gmpq_cmp_si
+    __GMP_DECLSPEC int _mpq_cmp_si __GMP_PROTO ((mpq_srcptr, long, unsigned long)) __GMP_ATTRIBUTE_PURE;
+
+#define _mpq_cmp_ui __gmpq_cmp_ui
+    __GMP_DECLSPEC int _mpq_cmp_ui __GMP_PROTO ((mpq_srcptr, unsigned long int, unsigned long int)) __GMP_ATTRIBUTE_PURE;
+
+#define mpq_div __gmpq_div
+    __GMP_DECLSPEC void mpq_div __GMP_PROTO ((mpq_ptr, mpq_srcptr, mpq_srcptr));
+
+#define mpq_div_2exp __gmpq_div_2exp
+    __GMP_DECLSPEC void mpq_div_2exp __GMP_PROTO ((mpq_ptr, mpq_srcptr, unsigned long));
+
+#define mpq_equal __gmpq_equal
+    __GMP_DECLSPEC int mpq_equal __GMP_PROTO ((mpq_srcptr, mpq_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpq_get_num __gmpq_get_num
+    __GMP_DECLSPEC void mpq_get_num __GMP_PROTO ((mpz_ptr, mpq_srcptr));
+
+#define mpq_get_den __gmpq_get_den
+    __GMP_DECLSPEC void mpq_get_den __GMP_PROTO ((mpz_ptr, mpq_srcptr));
+
+#define mpq_get_d __gmpq_get_d
+    __GMP_DECLSPEC double mpq_get_d __GMP_PROTO ((mpq_srcptr)) __GMP_ATTRIBUTE_PURE;
+
+#define mpq_get_str __gmpq_get_str
+    __GMP_DECLSPEC char *mpq_get_str __GMP_PROTO ((char *, int, mpq_srcptr));
+
+#define mpq_init __gmpq_init
+    __GMP_DECLSPEC void mpq_init __GMP_PROTO ((mpq_ptr));
+
+#define mpq_inp_str __gmpq_inp_str
+#ifdef _GMP_H_HAVE_FILE
+    __GMP_DECLSPEC size_t mpq_inp_str __GMP_PROTO ((mpq_ptr, FILE *, int));
+#endif
+
+#define mpq_inv __gmpq_inv
+    __GMP_DECLSPEC void mpq_inv __GMP_PROTO ((mpq_ptr, mpq_srcptr));
+
+#define mpq_mul __gmpq_mul
+    __GMP_DECLSPEC void mpq_mul __GMP_PROTO ((mpq_ptr, mpq_srcptr, mpq_srcptr));
+
+#define mpq_mul_2exp __gmpq_mul_2exp
+    __GMP_DECLSPEC void mpq_mul_2exp __GMP_PROTO ((mpq_ptr, mpq_srcptr, unsigned long));
+
+#define mpq_neg __gmpq_neg
+#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpq_neg)
+    __GMP_DECLSPEC void mpq_neg __GMP_PROTO ((mpq_ptr, mpq_srcptr));
+#endif
+
+#define mpq_out_str __gmpq_out_str
+#ifdef _GMP_H_HAVE_FILE
+    __GMP_DECLSPEC size_t mpq_out_str __GMP_PROTO ((FILE *, int, mpq_srcptr));
+#endif
+
+#define mpq_set __gmpq_set
+    __GMP_DECLSPEC void mpq_set __GMP_PROTO ((mpq_ptr, mpq_srcptr));
+
+#define mpq_set_d __gmpq_set_d
+    __GMP_DECLSPEC void mpq_set_d __GMP_PROTO ((mpq_ptr, double));
+
+#define mpq_set_den __gmpq_set_den
+    __GMP_DECLSPEC void mpq_set_den __GMP_PROTO ((mpq_ptr, mpz_srcptr));
+
+#define mpq_set_f __gmpq_set_f
+    __GMP_DECLSPEC void mpq_set_f __GMP_PROTO ((mpq_ptr, mpf_srcptr));
+
+#define mpq_set_num __gmpq_set_num
+    __GMP_DECLSPEC void mpq_set_num __GMP_PROTO ((mpq_ptr, mpz_srcptr));
+
+#define mpq_set_si __gmpq_set_si
+    __GMP_DECLSPEC void mpq_set_si __GMP_PROTO ((mpq_ptr, signed long int, unsigned long int));
+
+#define mpq_set_str __gmpq_set_str
+    __GMP_DECLSPEC int mpq_set_str __GMP_PROTO ((mpq_ptr, __gmp_const char *, int));
+
+#define mpq_set_ui __gmpq_set_ui
+    __GMP_DECLSPEC void mpq_set_ui __GMP_PROTO ((mpq_ptr, unsigned long int, unsigned long int));
+
+#define mpq_set_z __gmpq_set_z
+    __GMP_DECLSPEC void mpq_set_z __GMP_PROTO ((mpq_ptr, mpz_srcptr));
+
+#define mpq_sub __gmpq_sub
+    __GMP_DECLSPEC void mpq_sub __GMP_PROTO ((mpq_ptr, mpq_srcptr, mpq_srcptr));
+
+#define mpq_swap __gmpq_swap
+    __GMP_DECLSPEC void mpq_swap __GMP_PROTO ((mpq_ptr, mpq_ptr)) __GMP_NOTHROW;
+
+
+    /**************** Float (i.e. F) routines.  ****************/
+
+#define mpf_abs __gmpf_abs
+    __GMP_DECLSPEC void mpf_abs __GMP_PROTO ((mpf_ptr, mpf_srcptr));
+
+#define mpf_add __gmpf_add
+    __GMP_DECLSPEC void mpf_add __GMP_PROTO ((mpf_ptr, mpf_srcptr, mpf_srcptr));
+
+#define mpf_add_ui __gmpf_add_ui
+    __GMP_DECLSPEC void mpf_add_ui __GMP_PROTO ((mpf_ptr, mpf_srcptr, unsigned long int));
+#define mpf_ceil __gmpf_ceil
+    __GMP_DECLSPEC void mpf_ceil __GMP_PROTO ((mpf_ptr, mpf_srcptr));
+
+#define mpf_clear __gmpf_clear
+    __GMP_DECLSPEC void mpf_clear __GMP_PROTO ((mpf_ptr));
+
+#define mpf_cmp __gmpf_cmp
+    __GMP_DECLSPEC int mpf_cmp __GMP_PROTO ((mpf_srcptr, mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpf_cmp_d __gmpf_cmp_d
+    __GMP_DECLSPEC int mpf_cmp_d __GMP_PROTO ((mpf_srcptr, double)) __GMP_ATTRIBUTE_PURE;
+
+#define mpf_cmp_si __gmpf_cmp_si
+    __GMP_DECLSPEC int mpf_cmp_si __GMP_PROTO ((mpf_srcptr, signed long int)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpf_cmp_ui __gmpf_cmp_ui
+    __GMP_DECLSPEC int mpf_cmp_ui __GMP_PROTO ((mpf_srcptr, unsigned long int)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpf_div __gmpf_div
+    __GMP_DECLSPEC void mpf_div __GMP_PROTO ((mpf_ptr, mpf_srcptr, mpf_srcptr));
+
+#define mpf_div_2exp __gmpf_div_2exp
+    __GMP_DECLSPEC void mpf_div_2exp __GMP_PROTO ((mpf_ptr, mpf_srcptr, unsigned long int));
+
+#define mpf_div_ui __gmpf_div_ui
+    __GMP_DECLSPEC void mpf_div_ui __GMP_PROTO ((mpf_ptr, mpf_srcptr, unsigned long int));
+
+#define mpf_dump __gmpf_dump
+    __GMP_DECLSPEC void mpf_dump __GMP_PROTO ((mpf_srcptr));
+
+#define mpf_eq __gmpf_eq
+    __GMP_DECLSPEC int mpf_eq __GMP_PROTO ((mpf_srcptr, mpf_srcptr, unsigned long int)) __GMP_ATTRIBUTE_PURE;
+
+#define mpf_fits_sint_p __gmpf_fits_sint_p
+    __GMP_DECLSPEC int mpf_fits_sint_p __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpf_fits_slong_p __gmpf_fits_slong_p
+    __GMP_DECLSPEC int mpf_fits_slong_p __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpf_fits_sshort_p __gmpf_fits_sshort_p
+    __GMP_DECLSPEC int mpf_fits_sshort_p __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpf_fits_uint_p __gmpf_fits_uint_p
+    __GMP_DECLSPEC int mpf_fits_uint_p __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpf_fits_ulong_p __gmpf_fits_ulong_p
+    __GMP_DECLSPEC int mpf_fits_ulong_p __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpf_fits_ushort_p __gmpf_fits_ushort_p
+    __GMP_DECLSPEC int mpf_fits_ushort_p __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpf_floor __gmpf_floor
+    __GMP_DECLSPEC void mpf_floor __GMP_PROTO ((mpf_ptr, mpf_srcptr));
+
+#define mpf_get_d __gmpf_get_d
+    __GMP_DECLSPEC double mpf_get_d __GMP_PROTO ((mpf_srcptr)) __GMP_ATTRIBUTE_PURE;
+
+#define mpf_get_d_2exp __gmpf_get_d_2exp
+    __GMP_DECLSPEC double mpf_get_d_2exp __GMP_PROTO ((signed long int *, mpf_srcptr));
+
+#define mpf_get_default_prec __gmpf_get_default_prec
+    __GMP_DECLSPEC unsigned long int mpf_get_default_prec __GMP_PROTO ((void)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpf_get_prec __gmpf_get_prec
+    __GMP_DECLSPEC unsigned long int mpf_get_prec __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpf_get_si __gmpf_get_si
+    __GMP_DECLSPEC long mpf_get_si __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpf_get_str __gmpf_get_str
+    __GMP_DECLSPEC char *mpf_get_str __GMP_PROTO ((char *, mp_exp_t *, int, size_t, mpf_srcptr));
+
+#define mpf_get_ui __gmpf_get_ui
+    __GMP_DECLSPEC unsigned long mpf_get_ui __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpf_init __gmpf_init
+    __GMP_DECLSPEC void mpf_init __GMP_PROTO ((mpf_ptr));
+
+#define mpf_init2 __gmpf_init2
+    __GMP_DECLSPEC void mpf_init2 __GMP_PROTO ((mpf_ptr, unsigned long int));
+
+#define mpf_init_set __gmpf_init_set
+    __GMP_DECLSPEC void mpf_init_set __GMP_PROTO ((mpf_ptr, mpf_srcptr));
+
+#define mpf_init_set_d __gmpf_init_set_d
+    __GMP_DECLSPEC void mpf_init_set_d __GMP_PROTO ((mpf_ptr, double));
+
+#define mpf_init_set_si __gmpf_init_set_si
+    __GMP_DECLSPEC void mpf_init_set_si __GMP_PROTO ((mpf_ptr, signed long int));
+
+#define mpf_init_set_str __gmpf_init_set_str
+    __GMP_DECLSPEC int mpf_init_set_str __GMP_PROTO ((mpf_ptr, __gmp_const char *, int));
+
+#define mpf_init_set_ui __gmpf_init_set_ui
+    __GMP_DECLSPEC void mpf_init_set_ui __GMP_PROTO ((mpf_ptr, unsigned long int));
+
+#define mpf_inp_str __gmpf_inp_str
+#ifdef _GMP_H_HAVE_FILE
+    __GMP_DECLSPEC size_t mpf_inp_str __GMP_PROTO ((mpf_ptr, FILE *, int));
+#endif
+
+#define mpf_integer_p __gmpf_integer_p
+    __GMP_DECLSPEC int mpf_integer_p __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpf_mul __gmpf_mul
+    __GMP_DECLSPEC void mpf_mul __GMP_PROTO ((mpf_ptr, mpf_srcptr, mpf_srcptr));
+
+#define mpf_mul_2exp __gmpf_mul_2exp
+    __GMP_DECLSPEC void mpf_mul_2exp __GMP_PROTO ((mpf_ptr, mpf_srcptr, unsigned long int));
+
+#define mpf_mul_ui __gmpf_mul_ui
+    __GMP_DECLSPEC void mpf_mul_ui __GMP_PROTO ((mpf_ptr, mpf_srcptr, unsigned long int));
+
+#define mpf_neg __gmpf_neg
+    __GMP_DECLSPEC void mpf_neg __GMP_PROTO ((mpf_ptr, mpf_srcptr));
+
+#define mpf_out_str __gmpf_out_str
+#ifdef _GMP_H_HAVE_FILE
+    __GMP_DECLSPEC size_t mpf_out_str __GMP_PROTO ((FILE *, int, size_t, mpf_srcptr));
+#endif
+
+#define mpf_pow_ui __gmpf_pow_ui
+    __GMP_DECLSPEC void mpf_pow_ui __GMP_PROTO ((mpf_ptr, mpf_srcptr, unsigned long int));
+
+#define mpf_random2 __gmpf_random2
+    __GMP_DECLSPEC void mpf_random2 __GMP_PROTO ((mpf_ptr, mp_size_t, mp_exp_t));
+
+#define mpf_reldiff __gmpf_reldiff
+    __GMP_DECLSPEC void mpf_reldiff __GMP_PROTO ((mpf_ptr, mpf_srcptr, mpf_srcptr));
+
+#define mpf_set __gmpf_set
+    __GMP_DECLSPEC void mpf_set __GMP_PROTO ((mpf_ptr, mpf_srcptr));
+
+#define mpf_set_d __gmpf_set_d
+    __GMP_DECLSPEC void mpf_set_d __GMP_PROTO ((mpf_ptr, double));
+
+#define mpf_set_default_prec __gmpf_set_default_prec
+    __GMP_DECLSPEC void mpf_set_default_prec __GMP_PROTO ((unsigned long int)) __GMP_NOTHROW;
+
+#define mpf_set_prec __gmpf_set_prec
+    __GMP_DECLSPEC void mpf_set_prec __GMP_PROTO ((mpf_ptr, unsigned long int));
+
+#define mpf_set_prec_raw __gmpf_set_prec_raw
+    __GMP_DECLSPEC void mpf_set_prec_raw __GMP_PROTO ((mpf_ptr, unsigned long int)) __GMP_NOTHROW;
+
+#define mpf_set_q __gmpf_set_q
+    __GMP_DECLSPEC void mpf_set_q __GMP_PROTO ((mpf_ptr, mpq_srcptr));
+
+#define mpf_set_si __gmpf_set_si
+    __GMP_DECLSPEC void mpf_set_si __GMP_PROTO ((mpf_ptr, signed long int));
+
+#define mpf_set_str __gmpf_set_str
+    __GMP_DECLSPEC int mpf_set_str __GMP_PROTO ((mpf_ptr, __gmp_const char *, int));
+
+#define mpf_set_ui __gmpf_set_ui
+    __GMP_DECLSPEC void mpf_set_ui __GMP_PROTO ((mpf_ptr, unsigned long int));
+
+#define mpf_set_z __gmpf_set_z
+    __GMP_DECLSPEC void mpf_set_z __GMP_PROTO ((mpf_ptr, mpz_srcptr));
+
+#define mpf_size __gmpf_size
+    __GMP_DECLSPEC size_t mpf_size __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpf_sqrt __gmpf_sqrt
+    __GMP_DECLSPEC void mpf_sqrt __GMP_PROTO ((mpf_ptr, mpf_srcptr));
+
+#define mpf_sqrt_ui __gmpf_sqrt_ui
+    __GMP_DECLSPEC void mpf_sqrt_ui __GMP_PROTO ((mpf_ptr, unsigned long int));
+
+#define mpf_sub __gmpf_sub
+    __GMP_DECLSPEC void mpf_sub __GMP_PROTO ((mpf_ptr, mpf_srcptr, mpf_srcptr));
+
+#define mpf_sub_ui __gmpf_sub_ui
+    __GMP_DECLSPEC void mpf_sub_ui __GMP_PROTO ((mpf_ptr, mpf_srcptr, unsigned long int));
+
+#define mpf_swap __gmpf_swap
+    __GMP_DECLSPEC void mpf_swap __GMP_PROTO ((mpf_ptr, mpf_ptr)) __GMP_NOTHROW;
+
+#define mpf_trunc __gmpf_trunc
+    __GMP_DECLSPEC void mpf_trunc __GMP_PROTO ((mpf_ptr, mpf_srcptr));
+
+#define mpf_ui_div __gmpf_ui_div
+    __GMP_DECLSPEC void mpf_ui_div __GMP_PROTO ((mpf_ptr, unsigned long int, mpf_srcptr));
+
+#define mpf_ui_sub __gmpf_ui_sub
+    __GMP_DECLSPEC void mpf_ui_sub __GMP_PROTO ((mpf_ptr, unsigned long int, mpf_srcptr));
+
+#define mpf_urandomb __gmpf_urandomb
+    __GMP_DECLSPEC void mpf_urandomb __GMP_PROTO ((mpf_t, gmp_randstate_t, unsigned long int));
+
+
+    /************ Low level positive-integer (i.e. N) routines.  ************/
+
+    /* This is ugly, but we need to make user calls reach the prefixed function. */
+
+#define mpn_add __MPN(add)
+#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpn_add)
+    __GMP_DECLSPEC mp_limb_t mpn_add __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr,mp_size_t));
+#endif
+
+#define mpn_add_1 __MPN(add_1)
+#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpn_add_1)
+    __GMP_DECLSPEC mp_limb_t mpn_add_1 __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t)) __GMP_NOTHROW;
+#endif
+
+#define mpn_add_n __MPN(add_n)
+    __GMP_DECLSPEC mp_limb_t mpn_add_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
+
+#define mpn_addmul_1 __MPN(addmul_1)
+    __GMP_DECLSPEC mp_limb_t mpn_addmul_1 __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t));
+
+#define mpn_bdivmod __MPN(bdivmod)
+    __GMP_DECLSPEC mp_limb_t mpn_bdivmod __GMP_PROTO ((mp_ptr, mp_ptr, mp_size_t, mp_srcptr, mp_size_t, unsigned long int));
+
+#define mpn_cmp __MPN(cmp)
+#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpn_cmp)
+    __GMP_DECLSPEC int mpn_cmp __GMP_PROTO ((mp_srcptr, mp_srcptr, mp_size_t)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+#endif
+
+#define mpn_divexact_by3(dst,src,size) \
+  mpn_divexact_by3c (dst, src, size, __GMP_CAST (mp_limb_t, 0))
+
+#define mpn_divexact_by3c __MPN(divexact_by3c)
+    __GMP_DECLSPEC mp_limb_t mpn_divexact_by3c __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t));
+
+#define mpn_divmod_1(qp,np,nsize,dlimb) \
+  mpn_divrem_1 (qp, __GMP_CAST (mp_size_t, 0), np, nsize, dlimb)
+
+#define mpn_divrem __MPN(divrem)
+    __GMP_DECLSPEC mp_limb_t mpn_divrem __GMP_PROTO ((mp_ptr, mp_size_t, mp_ptr, mp_size_t, mp_srcptr, mp_size_t));
+
+#define mpn_divrem_1 __MPN(divrem_1)
+    __GMP_DECLSPEC mp_limb_t mpn_divrem_1 __GMP_PROTO ((mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_limb_t));
+
+#define mpn_divrem_2 __MPN(divrem_2)
+    __GMP_DECLSPEC mp_limb_t mpn_divrem_2 __GMP_PROTO ((mp_ptr, mp_size_t, mp_ptr, mp_size_t, mp_srcptr));
+
+#define mpn_gcd __MPN(gcd)
+    __GMP_DECLSPEC mp_size_t mpn_gcd __GMP_PROTO ((mp_ptr, mp_ptr, mp_size_t, mp_ptr, mp_size_t));
+
+#define mpn_gcd_1 __MPN(gcd_1)
+    __GMP_DECLSPEC mp_limb_t mpn_gcd_1 __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t)) __GMP_ATTRIBUTE_PURE;
+
+#define mpn_gcdext __MPN(gcdext)
+    __GMP_DECLSPEC mp_size_t mpn_gcdext __GMP_PROTO ((mp_ptr, mp_ptr, mp_size_t *, mp_ptr, mp_size_t, mp_ptr, mp_size_t));
+
+#define mpn_get_str __MPN(get_str)
+    __GMP_DECLSPEC size_t mpn_get_str __GMP_PROTO ((unsigned char *, int, mp_ptr, mp_size_t));
+
+#define mpn_hamdist __MPN(hamdist)
+    __GMP_DECLSPEC unsigned long int mpn_hamdist __GMP_PROTO ((mp_srcptr, mp_srcptr, mp_size_t)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpn_lshift __MPN(lshift)
+    __GMP_DECLSPEC mp_limb_t mpn_lshift __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, unsigned int));
+
+#define mpn_mod_1 __MPN(mod_1)
+    __GMP_DECLSPEC mp_limb_t mpn_mod_1 __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t)) __GMP_ATTRIBUTE_PURE;
+
+#define mpn_mul __MPN(mul)
+    __GMP_DECLSPEC mp_limb_t mpn_mul __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t));
+
+#define mpn_mul_1 __MPN(mul_1)
+    __GMP_DECLSPEC mp_limb_t mpn_mul_1 __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t));
+
+#define mpn_mul_n __MPN(mul_n)
+    __GMP_DECLSPEC void mpn_mul_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
+
+#define mpn_perfect_square_p __MPN(perfect_square_p)
+    __GMP_DECLSPEC int mpn_perfect_square_p __GMP_PROTO ((mp_srcptr, mp_size_t)) __GMP_ATTRIBUTE_PURE;
+
+#define mpn_popcount __MPN(popcount)
+    __GMP_DECLSPEC unsigned long int mpn_popcount __GMP_PROTO ((mp_srcptr, mp_size_t)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
+
+#define mpn_pow_1 __MPN(pow_1)
+    __GMP_DECLSPEC mp_size_t mpn_pow_1 __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t, mp_ptr));
+
+    /* undocumented now, but retained here for upward compatibility */
+#define mpn_preinv_mod_1 __MPN(preinv_mod_1)
+    __GMP_DECLSPEC mp_limb_t mpn_preinv_mod_1 __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t)) __GMP_ATTRIBUTE_PURE;
+
+#define mpn_random __MPN(random)
+    __GMP_DECLSPEC void mpn_random __GMP_PROTO ((mp_ptr, mp_size_t));
+
+#define mpn_random2 __MPN(random2)
+    __GMP_DECLSPEC void mpn_random2 __GMP_PROTO ((mp_ptr, mp_size_t));
+
+#define mpn_rshift __MPN(rshift)
+    __GMP_DECLSPEC mp_limb_t mpn_rshift __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, unsigned int));
+
+#define mpn_scan0 __MPN(scan0)
+    __GMP_DECLSPEC unsigned long int mpn_scan0 __GMP_PROTO ((mp_srcptr, unsigned long int)) __GMP_ATTRIBUTE_PURE;
+
+#define mpn_scan1 __MPN(scan1)
+    __GMP_DECLSPEC unsigned long int mpn_scan1 __GMP_PROTO ((mp_srcptr, unsigned long int)) __GMP_ATTRIBUTE_PURE;
+
+#define mpn_set_str __MPN(set_str)
+    __GMP_DECLSPEC mp_size_t mpn_set_str __GMP_PROTO ((mp_ptr, __gmp_const unsigned char *, size_t, int));
+
+#define mpn_sqrtrem __MPN(sqrtrem)
+    __GMP_DECLSPEC mp_size_t mpn_sqrtrem __GMP_PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_size_t));
+
+#define mpn_sub __MPN(sub)
+#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpn_sub)
+    __GMP_DECLSPEC mp_limb_t mpn_sub __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr,mp_size_t));
+#endif
+
+#define mpn_sub_1 __MPN(sub_1)
+#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpn_sub_1)
+    __GMP_DECLSPEC mp_limb_t mpn_sub_1 __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t)) __GMP_NOTHROW;
+#endif
+
+#define mpn_sub_n __MPN(sub_n)
+    __GMP_DECLSPEC mp_limb_t mpn_sub_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
+
+#define mpn_submul_1 __MPN(submul_1)
+    __GMP_DECLSPEC mp_limb_t mpn_submul_1 __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t));
+
+#define mpn_tdiv_qr __MPN(tdiv_qr)
+    __GMP_DECLSPEC void mpn_tdiv_qr __GMP_PROTO ((mp_ptr, mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t));
+
+
+    /**************** mpz inlines ****************/
+
+    /* The following are provided as inlines where possible, but always exist as
+       library functions too, for binary compatibility.
+
+       Within gmp itself this inlining generally isn't relied on, since it
+       doesn't get done for all compilers, whereas if something is worth
+       inlining then it's worth arranging always.
+
+       There are two styles of inlining here.  When the same bit of code is
+       wanted for the inline as for the library version, then __GMP_FORCE_foo
+       arranges for that code to be emitted and the __GMP_EXTERN_INLINE
+       directive suppressed, eg. mpz_fits_uint_p.  When a different bit of code
+       is wanted for the inline than for the library version, then
+       __GMP_FORCE_foo arranges the inline to be suppressed, eg. mpz_abs.  */
+
+#if defined (__GMP_EXTERN_INLINE) && ! defined (__GMP_FORCE_mpz_abs)
+    __GMP_EXTERN_INLINE void
+    mpz_abs (mpz_ptr __gmp_w, mpz_srcptr __gmp_u)
+    {
+        if (__gmp_w != __gmp_u)
+            mpz_set (__gmp_w, __gmp_u);
+        __gmp_w->_mp_size = __GMP_ABS (__gmp_w->_mp_size);
+    }
+#endif
+
+#if GMP_NAIL_BITS == 0
+#define __GMPZ_FITS_UTYPE_P(z,maxval)					\
+  mp_size_t  __gmp_n = z->_mp_size;					\
+  mp_ptr  __gmp_p = z->_mp_d;						\
+  return (__gmp_n == 0 || (__gmp_n == 1 && __gmp_p[0] <= maxval));
+#else
+#define __GMPZ_FITS_UTYPE_P(z,maxval)					\
+  mp_size_t  __gmp_n = z->_mp_size;					\
+  mp_ptr  __gmp_p = z->_mp_d;						\
+  return (__gmp_n == 0 || (__gmp_n == 1 && __gmp_p[0] <= maxval)	\
+	  || (__gmp_n == 2 && __gmp_p[1] <= ((mp_limb_t) maxval >> GMP_NUMB_BITS)));
+#endif
+
+#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_fits_uint_p)
+#if ! defined (__GMP_FORCE_mpz_fits_uint_p)
+    __GMP_EXTERN_INLINE
+#endif
+    int
+    mpz_fits_uint_p (mpz_srcptr __gmp_z) __GMP_NOTHROW
+    {
+        __GMPZ_FITS_UTYPE_P (__gmp_z, __GMP_UINT_MAX);
+    }
+#endif
+
+#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_fits_ulong_p)
+#if ! defined (__GMP_FORCE_mpz_fits_ulong_p)
+    __GMP_EXTERN_INLINE
+#endif
+    int
+    mpz_fits_ulong_p (mpz_srcptr __gmp_z) __GMP_NOTHROW
+    {
+        __GMPZ_FITS_UTYPE_P (__gmp_z, __GMP_ULONG_MAX);
+    }
+#endif
+
+#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_fits_ushort_p)
+#if ! defined (__GMP_FORCE_mpz_fits_ushort_p)
+    __GMP_EXTERN_INLINE
+#endif
+    int
+    mpz_fits_ushort_p (mpz_srcptr __gmp_z) __GMP_NOTHROW
+    {
+        __GMPZ_FITS_UTYPE_P (__gmp_z, __GMP_USHRT_MAX);
+    }
+#endif
+
+#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_get_ui)
+#if ! defined (__GMP_FORCE_mpz_get_ui)
+    __GMP_EXTERN_INLINE
+#endif
+    unsigned long
+    mpz_get_ui (mpz_srcptr __gmp_z) __GMP_NOTHROW
+    {
+        mp_ptr __gmp_p = __gmp_z->_mp_d;
+        mp_size_t __gmp_n = __gmp_z->_mp_size;
+        mp_limb_t __gmp_l = __gmp_p[0];
+        /* This is a "#if" rather than a plain "if" so as to avoid gcc warnings
+           about "<< GMP_NUMB_BITS" exceeding the type size, and to avoid Borland
+           C++ 6.0 warnings about condition always true for something like
+           "__GMP_ULONG_MAX < GMP_NUMB_MASK".  */
+#if GMP_NAIL_BITS == 0 || defined (_LONG_LONG_LIMB)
+        /* limb==long and no nails, or limb==longlong, one limb is enough */
+        return (__gmp_n != 0 ? __gmp_l : 0);
+#else
+        /* limb==long and nails, need two limbs when available */
+        __gmp_n = __GMP_ABS (__gmp_n);
+        if (__gmp_n <= 1)
+            return (__gmp_n != 0 ? __gmp_l : 0);
+        else
+            return __gmp_l + (__gmp_p[1] << GMP_NUMB_BITS);
+#endif
+    }
+#endif
+
+#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_getlimbn)
+#if ! defined (__GMP_FORCE_mpz_getlimbn)
+    __GMP_EXTERN_INLINE
+#endif
+    mp_limb_t
+    mpz_getlimbn (mpz_srcptr __gmp_z, mp_size_t __gmp_n) __GMP_NOTHROW
+    {
+        mp_limb_t  __gmp_result = 0;
+        if (__GMP_LIKELY (__gmp_n >= 0 && __gmp_n < __GMP_ABS (__gmp_z->_mp_size)))
+            __gmp_result = __gmp_z->_mp_d[__gmp_n];
+        return __gmp_result;
+    }
+#endif
+
+#if defined (__GMP_EXTERN_INLINE) && ! defined (__GMP_FORCE_mpz_neg)
+    __GMP_EXTERN_INLINE void
+    mpz_neg (mpz_ptr __gmp_w, mpz_srcptr __gmp_u)
+    {
+        if (__gmp_w != __gmp_u)
+            mpz_set (__gmp_w, __gmp_u);
+        __gmp_w->_mp_size = - __gmp_w->_mp_size;
+    }
+#endif
+
+#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_perfect_square_p)
+#if ! defined (__GMP_FORCE_mpz_perfect_square_p)
+    __GMP_EXTERN_INLINE
+#endif
+    int
+    mpz_perfect_square_p (mpz_srcptr __gmp_a)
+    {
+        mp_size_t __gmp_asize;
+        int       __gmp_result;
+
+        __gmp_asize = __gmp_a->_mp_size;
+        __gmp_result = (__gmp_asize >= 0);  /* zero is a square, negatives are not */
+        if (__GMP_LIKELY (__gmp_asize > 0))
+            __gmp_result = mpn_perfect_square_p (__gmp_a->_mp_d, __gmp_asize);
+        return __gmp_result;
+    }
+#endif
+
+#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_popcount)
+#if ! defined (__GMP_FORCE_mpz_popcount)
+    __GMP_EXTERN_INLINE
+#endif
+    unsigned long
+    mpz_popcount (mpz_srcptr __gmp_u) __GMP_NOTHROW
+    {
+        mp_size_t      __gmp_usize;
+        unsigned long  __gmp_result;
+
+        __gmp_usize = __gmp_u->_mp_size;
+        __gmp_result = (__gmp_usize < 0 ? __GMP_ULONG_MAX : 0);
+        if (__GMP_LIKELY (__gmp_usize > 0))
+            __gmp_result =  mpn_popcount (__gmp_u->_mp_d, __gmp_usize);
+        return __gmp_result;
+    }
+#endif
+
+#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_set_q)
+#if ! defined (__GMP_FORCE_mpz_set_q)
+    __GMP_EXTERN_INLINE
+#endif
+    void
+    mpz_set_q (mpz_ptr __gmp_w, mpq_srcptr __gmp_u)
+    {
+        mpz_tdiv_q (__gmp_w, mpq_numref (__gmp_u), mpq_denref (__gmp_u));
+    }
+#endif
+
+#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_size)
+#if ! defined (__GMP_FORCE_mpz_size)
+    __GMP_EXTERN_INLINE
+#endif
+    size_t
+    mpz_size (mpz_srcptr __gmp_z) __GMP_NOTHROW
+    {
+        return __GMP_ABS (__gmp_z->_mp_size);
+    }
+#endif
+
+
+    /**************** mpq inlines ****************/
+
+#if defined (__GMP_EXTERN_INLINE) && ! defined (__GMP_FORCE_mpq_abs)
+    __GMP_EXTERN_INLINE void
+    mpq_abs (mpq_ptr __gmp_w, mpq_srcptr __gmp_u)
+    {
+        if (__gmp_w != __gmp_u)
+            mpq_set (__gmp_w, __gmp_u);
+        __gmp_w->_mp_num._mp_size = __GMP_ABS (__gmp_w->_mp_num._mp_size);
+    }
+#endif
+
+#if defined (__GMP_EXTERN_INLINE) && ! defined (__GMP_FORCE_mpq_neg)
+    __GMP_EXTERN_INLINE void
+    mpq_neg (mpq_ptr __gmp_w, mpq_srcptr __gmp_u)
+    {
+        if (__gmp_w != __gmp_u)
+            mpq_set (__gmp_w, __gmp_u);
+        __gmp_w->_mp_num._mp_size = - __gmp_w->_mp_num._mp_size;
+    }
+#endif
+
+
+    /**************** mpn inlines ****************/
+
+    /* The comments with __GMPN_ADD_1 below apply here too.
+
+       The test for FUNCTION returning 0 should predict well.  If it's assumed
+       {yp,ysize} will usually have a random number of bits then the high limb
+       won't be full and a carry out will occur a good deal less than 50% of the
+       time.
+
+       ysize==0 isn't a documented feature, but is used internally in a few
+       places.
+
+       Producing cout last stops it using up a register during the main part of
+       the calculation, though gcc (as of 3.0) on an "if (mpn_add (...))"
+       doesn't seem able to move the true and false legs of the conditional up
+       to the two places cout is generated.  */
+
+#define __GMPN_AORS(cout, wp, xp, xsize, yp, ysize, FUNCTION, TEST)     \
+  do {                                                                  \
+    mp_size_t  __gmp_i;                                                 \
+    mp_limb_t  __gmp_x;                                                 \
+                                                                        \
+    /* ASSERT ((ysize) >= 0); */                                        \
+    /* ASSERT ((xsize) >= (ysize)); */                                  \
+    /* ASSERT (MPN_SAME_OR_SEPARATE2_P (wp, xsize, xp, xsize)); */      \
+    /* ASSERT (MPN_SAME_OR_SEPARATE2_P (wp, xsize, yp, ysize)); */      \
+                                                                        \
+    __gmp_i = (ysize);                                                  \
+    if (__gmp_i != 0)                                                   \
+      {                                                                 \
+        if (FUNCTION (wp, xp, yp, __gmp_i))                             \
+          {                                                             \
+            do                                                          \
+              {                                                         \
+                if (__gmp_i >= (xsize))                                 \
+                  {                                                     \
+                    (cout) = 1;                                         \
+                    goto __gmp_done;                                    \
+                  }                                                     \
+                __gmp_x = (xp)[__gmp_i];                                \
+              }                                                         \
+            while (TEST);                                               \
+          }                                                             \
+      }                                                                 \
+    if ((wp) != (xp))                                                   \
+      __GMPN_COPY_REST (wp, xp, xsize, __gmp_i);                        \
+    (cout) = 0;                                                         \
+  __gmp_done:                                                           \
+    ;                                                                   \
+  } while (0)
+
+#define __GMPN_ADD(cout, wp, xp, xsize, yp, ysize)              \
+  __GMPN_AORS (cout, wp, xp, xsize, yp, ysize, mpn_add_n,       \
+               (((wp)[__gmp_i++] = (__gmp_x + 1) & GMP_NUMB_MASK) == 0))
+#define __GMPN_SUB(cout, wp, xp, xsize, yp, ysize)              \
+  __GMPN_AORS (cout, wp, xp, xsize, yp, ysize, mpn_sub_n,       \
+               (((wp)[__gmp_i++] = (__gmp_x - 1) & GMP_NUMB_MASK), __gmp_x == 0))
+
+
+    /* The use of __gmp_i indexing is designed to ensure a compile time src==dst
+       remains nice and clear to the compiler, so that __GMPN_COPY_REST can
+       disappear, and the load/add/store gets a chance to become a
+       read-modify-write on CISC CPUs.
+
+       Alternatives:
+
+       Using a pair of pointers instead of indexing would be possible, but gcc
+       isn't able to recognise compile-time src==dst in that case, even when the
+       pointers are incremented more or less together.  Other compilers would
+       very likely have similar difficulty.
+
+       gcc could use "if (__builtin_constant_p(src==dst) && src==dst)" or
+       similar to detect a compile-time src==dst.  This works nicely on gcc
+       2.95.x, it's not good on gcc 3.0 where __builtin_constant_p(p==p) seems
+       to be always false, for a pointer p.  But the current code form seems
+       good enough for src==dst anyway.
+
+       gcc on x86 as usual doesn't give particularly good flags handling for the
+       carry/borrow detection.  It's tempting to want some multi instruction asm
+       blocks to help it, and this was tried, but in truth there's only a few
+       instructions to save and any gain is all too easily lost by register
+       juggling setting up for the asm.  */
+
+#if GMP_NAIL_BITS == 0
+#define __GMPN_AORS_1(cout, dst, src, n, v, OP, CB)		\
+  do {								\
+    mp_size_t  __gmp_i;						\
+    mp_limb_t  __gmp_x, __gmp_r;                                \
+								\
+    /* ASSERT ((n) >= 1); */					\
+    /* ASSERT (MPN_SAME_OR_SEPARATE_P (dst, src, n)); */	\
+								\
+    __gmp_x = (src)[0];						\
+    __gmp_r = __gmp_x OP (v);                                   \
+    (dst)[0] = __gmp_r;						\
+    if (CB (__gmp_r, __gmp_x, (v)))                             \
+      {								\
+	(cout) = 1;						\
+	for (__gmp_i = 1; __gmp_i < (n);)                       \
+	  {							\
+	    __gmp_x = (src)[__gmp_i];                           \
+	    __gmp_r = __gmp_x OP 1;                             \
+	    (dst)[__gmp_i] = __gmp_r;                           \
+	    ++__gmp_i;						\
+	    if (!CB (__gmp_r, __gmp_x, 1))                      \
+	      {							\
+		if ((src) != (dst))				\
+		  __GMPN_COPY_REST (dst, src, n, __gmp_i);      \
+		(cout) = 0;					\
+		break;						\
+	      }							\
+	  }							\
+      }								\
+    else							\
+      {								\
+	if ((src) != (dst))					\
+	  __GMPN_COPY_REST (dst, src, n, 1);			\
+	(cout) = 0;						\
+      }								\
+  } while (0)
+#endif
+
+#if GMP_NAIL_BITS >= 1
+#define __GMPN_AORS_1(cout, dst, src, n, v, OP, CB)		\
+  do {								\
+    mp_size_t  __gmp_i;						\
+    mp_limb_t  __gmp_x, __gmp_r;				\
+								\
+    /* ASSERT ((n) >= 1); */					\
+    /* ASSERT (MPN_SAME_OR_SEPARATE_P (dst, src, n)); */	\
+								\
+    __gmp_x = (src)[0];						\
+    __gmp_r = __gmp_x OP (v);					\
+    (dst)[0] = __gmp_r & GMP_NUMB_MASK;				\
+    if (__gmp_r >> GMP_NUMB_BITS != 0)				\
+      {								\
+	(cout) = 1;						\
+	for (__gmp_i = 1; __gmp_i < (n);)			\
+	  {							\
+	    __gmp_x = (src)[__gmp_i];				\
+	    __gmp_r = __gmp_x OP 1;				\
+	    (dst)[__gmp_i] = __gmp_r & GMP_NUMB_MASK;		\
+	    ++__gmp_i;						\
+	    if (__gmp_r >> GMP_NUMB_BITS == 0)			\
+	      {							\
+		if ((src) != (dst))				\
+		  __GMPN_COPY_REST (dst, src, n, __gmp_i);	\
+		(cout) = 0;					\
+		break;						\
+	      }							\
+	  }							\
+      }								\
+    else							\
+      {								\
+	if ((src) != (dst))					\
+	  __GMPN_COPY_REST (dst, src, n, 1);			\
+	(cout) = 0;						\
+      }								\
+  } while (0)
+#endif
+
+#define __GMPN_ADDCB(r,x,y) ((r) < (y))
+#define __GMPN_SUBCB(r,x,y) ((x) < (y))
+
+#define __GMPN_ADD_1(cout, dst, src, n, v)	     \
+  __GMPN_AORS_1(cout, dst, src, n, v, +, __GMPN_ADDCB)
+#define __GMPN_SUB_1(cout, dst, src, n, v)	     \
+  __GMPN_AORS_1(cout, dst, src, n, v, -, __GMPN_SUBCB)
+
+
+    /* Compare {xp,size} and {yp,size}, setting "result" to positive, zero or
+       negative.  size==0 is allowed.  On random data usually only one limb will
+       need to be examined to get a result, so it's worth having it inline.  */
+#define __GMPN_CMP(result, xp, yp, size)                                \
+  do {                                                                  \
+    mp_size_t  __gmp_i;                                                 \
+    mp_limb_t  __gmp_x, __gmp_y;                                        \
+                                                                        \
+    /* ASSERT ((size) >= 0); */                                         \
+                                                                        \
+    (result) = 0;                                                       \
+    __gmp_i = (size);                                                   \
+    while (--__gmp_i >= 0)                                              \
+      {                                                                 \
+        __gmp_x = (xp)[__gmp_i];                                        \
+        __gmp_y = (yp)[__gmp_i];                                        \
+        if (__gmp_x != __gmp_y)                                         \
+          {                                                             \
+            /* Cannot use __gmp_x - __gmp_y, may overflow an "int" */   \
+            (result) = (__gmp_x > __gmp_y ? 1 : -1);                    \
+            break;                                                      \
+          }                                                             \
+      }                                                                 \
+  } while (0)
+
+
+#if defined (__GMPN_COPY) && ! defined (__GMPN_COPY_REST)
+#define __GMPN_COPY_REST(dst, src, size, start)                 \
+  do {                                                          \
+    /* ASSERT ((start) >= 0); */                                \
+    /* ASSERT ((start) <= (size)); */                           \
+    __GMPN_COPY ((dst)+(start), (src)+(start), (size)-(start)); \
+  } while (0)
+#endif
+
+    /* Copy {src,size} to {dst,size}, starting at "start".  This is designed to
+       keep the indexing dst[j] and src[j] nice and simple for __GMPN_ADD_1,
+       __GMPN_ADD, etc.  */
+#if ! defined (__GMPN_COPY_REST)
+#define __GMPN_COPY_REST(dst, src, size, start)                 \
+  do {                                                          \
+    mp_size_t __gmp_j;                                          \
+    /* ASSERT ((size) >= 0); */                                 \
+    /* ASSERT ((start) >= 0); */                                \
+    /* ASSERT ((start) <= (size)); */                           \
+    /* ASSERT (MPN_SAME_OR_SEPARATE_P (dst, src, size)); */     \
+    __GMP_CRAY_Pragma ("_CRI ivdep");                           \
+    for (__gmp_j = (start); __gmp_j < (size); __gmp_j++)        \
+      (dst)[__gmp_j] = (src)[__gmp_j];                          \
+  } while (0)
+#endif
+
+    /* Enhancement: Use some of the smarter code from gmp-impl.h.  Maybe use
+       mpn_copyi if there's a native version, and if we don't mind demanding
+       binary compatibility for it (on targets which use it).  */
+
+#if ! defined (__GMPN_COPY)
+#define __GMPN_COPY(dst, src, size)   __GMPN_COPY_REST (dst, src, size, 0)
+#endif
+
+
+#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpn_add)
+#if ! defined (__GMP_FORCE_mpn_add)
+    __GMP_EXTERN_INLINE
+#endif
+    mp_limb_t
+    mpn_add (mp_ptr __gmp_wp, mp_srcptr __gmp_xp, mp_size_t __gmp_xsize, mp_srcptr __gmp_yp, mp_size_t __gmp_ysize)
+    {
+        mp_limb_t  __gmp_c;
+        __GMPN_ADD (__gmp_c, __gmp_wp, __gmp_xp, __gmp_xsize, __gmp_yp, __gmp_ysize);
+        return __gmp_c;
+    }
+#endif
+
+#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpn_add_1)
+#if ! defined (__GMP_FORCE_mpn_add_1)
+    __GMP_EXTERN_INLINE
+#endif
+    mp_limb_t
+    mpn_add_1 (mp_ptr __gmp_dst, mp_srcptr __gmp_src, mp_size_t __gmp_size, mp_limb_t __gmp_n) __GMP_NOTHROW
+    {
+        mp_limb_t  __gmp_c;
+        __GMPN_ADD_1 (__gmp_c, __gmp_dst, __gmp_src, __gmp_size, __gmp_n);
+        return __gmp_c;
+    }
+#endif
+
+#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpn_cmp)
+#if ! defined (__GMP_FORCE_mpn_cmp)
+    __GMP_EXTERN_INLINE
+#endif
+    int
+    mpn_cmp (mp_srcptr __gmp_xp, mp_srcptr __gmp_yp, mp_size_t __gmp_size) __GMP_NOTHROW
+    {
+        int __gmp_result;
+        __GMPN_CMP (__gmp_result, __gmp_xp, __gmp_yp, __gmp_size);
+        return __gmp_result;
+    }
+#endif
+
+#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpn_sub)
+#if ! defined (__GMP_FORCE_mpn_sub)
+    __GMP_EXTERN_INLINE
+#endif
+    mp_limb_t
+    mpn_sub (mp_ptr __gmp_wp, mp_srcptr __gmp_xp, mp_size_t __gmp_xsize, mp_srcptr __gmp_yp, mp_size_t __gmp_ysize)
+    {
+        mp_limb_t  __gmp_c;
+        __GMPN_SUB (__gmp_c, __gmp_wp, __gmp_xp, __gmp_xsize, __gmp_yp, __gmp_ysize);
+        return __gmp_c;
+    }
+#endif
+
+#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpn_sub_1)
+#if ! defined (__GMP_FORCE_mpn_sub_1)
+    __GMP_EXTERN_INLINE
+#endif
+    mp_limb_t
+    mpn_sub_1 (mp_ptr __gmp_dst, mp_srcptr __gmp_src, mp_size_t __gmp_size, mp_limb_t __gmp_n) __GMP_NOTHROW
+    {
+        mp_limb_t  __gmp_c;
+        __GMPN_SUB_1 (__gmp_c, __gmp_dst, __gmp_src, __gmp_size, __gmp_n);
+        return __gmp_c;
+    }
+#endif
+
+#if defined (__cplusplus)
+}
+#endif
+
+
+/* Allow faster testing for negative, zero, and positive.  */
+#define mpz_sgn(Z) ((Z)->_mp_size < 0 ? -1 : (Z)->_mp_size > 0)
+#define mpf_sgn(F) ((F)->_mp_size < 0 ? -1 : (F)->_mp_size > 0)
+#define mpq_sgn(Q) ((Q)->_mp_num._mp_size < 0 ? -1 : (Q)->_mp_num._mp_size > 0)
+
+/* When using GCC, optimize certain common comparisons.  */
+#if defined (__GNUC__)
+#define mpz_cmp_ui(Z,UI) \
+  (__builtin_constant_p (UI) && (UI) == 0				\
+   ? mpz_sgn (Z) : _mpz_cmp_ui (Z,UI))
+#define mpz_cmp_si(Z,SI) \
+  (__builtin_constant_p (SI) && (SI) == 0 ? mpz_sgn (Z)			\
+   : __builtin_constant_p (SI) && (SI) > 0				\
+    ? _mpz_cmp_ui (Z, __GMP_CAST (unsigned long int, SI))		\
+   : _mpz_cmp_si (Z,SI))
+#define mpq_cmp_ui(Q,NUI,DUI) \
+  (__builtin_constant_p (NUI) && (NUI) == 0				\
+   ? mpq_sgn (Q) : _mpq_cmp_ui (Q,NUI,DUI))
+#define mpq_cmp_si(q,n,d)                       \
+  (__builtin_constant_p ((n) >= 0) && (n) >= 0  \
+   ? mpq_cmp_ui (q, __GMP_CAST (unsigned long, n), d) \
+   : _mpq_cmp_si (q, n, d))
+#else
+#define mpz_cmp_ui(Z,UI) _mpz_cmp_ui (Z,UI)
+#define mpz_cmp_si(Z,UI) _mpz_cmp_si (Z,UI)
+#define mpq_cmp_ui(Q,NUI,DUI) _mpq_cmp_ui (Q,NUI,DUI)
+#define mpq_cmp_si(q,n,d)  _mpq_cmp_si(q,n,d)
+#endif
+
+
+/* Using "&" rather than "&&" means these can come out branch-free.  Every
+   mpz_t has at least one limb allocated, so fetching the low limb is always
+   allowed.  */
+#define mpz_odd_p(z)   (((z)->_mp_size != 0) & __GMP_CAST (int, (z)->_mp_d[0]))
+#define mpz_even_p(z)  (! mpz_odd_p (z))
+
+
+/**************** C++ routines ****************/
+
+#ifdef __cplusplus
+__GMP_DECLSPEC_XX std::ostream& operator<< (std::ostream &, mpz_srcptr);
+__GMP_DECLSPEC_XX std::ostream& operator<< (std::ostream &, mpq_srcptr);
+__GMP_DECLSPEC_XX std::ostream& operator<< (std::ostream &, mpf_srcptr);
+__GMP_DECLSPEC_XX std::istream& operator>> (std::istream &, mpz_ptr);
+__GMP_DECLSPEC_XX std::istream& operator>> (std::istream &, mpq_ptr);
+__GMP_DECLSPEC_XX std::istream& operator>> (std::istream &, mpf_ptr);
+#endif
+
+
+/* Source-level compatibility with GMP 2 and earlier. */
+#define mpn_divmod(qp,np,nsize,dp,dsize) \
+  mpn_divrem (qp, __GMP_CAST (mp_size_t, 0), np, nsize, dp, dsize)
+
+/* Source-level compatibility with GMP 1.  */
+#define mpz_mdiv	mpz_fdiv_q
+#define mpz_mdivmod	mpz_fdiv_qr
+#define mpz_mmod	mpz_fdiv_r
+#define mpz_mdiv_ui	mpz_fdiv_q_ui
+#define mpz_mdivmod_ui(q,r,n,d) \
+  (((r) == 0) ? mpz_fdiv_q_ui (q,n,d) : mpz_fdiv_qr_ui (q,r,n,d))
+#define mpz_mmod_ui(r,n,d) \
+  (((r) == 0) ? mpz_fdiv_ui (n,d) : mpz_fdiv_r_ui (r,n,d))
+
+/* Useful synonyms, but not quite compatible with GMP 1.  */
+#define mpz_div		mpz_fdiv_q
+#define mpz_divmod	mpz_fdiv_qr
+#define mpz_div_ui	mpz_fdiv_q_ui
+#define mpz_divmod_ui	mpz_fdiv_qr_ui
+#define mpz_div_2exp	mpz_fdiv_q_2exp
+#define mpz_mod_2exp	mpz_fdiv_r_2exp
+
+enum
+{
+    GMP_ERROR_NONE = 0,
+    GMP_ERROR_UNSUPPORTED_ARGUMENT = 1,
+    GMP_ERROR_DIVISION_BY_ZERO = 2,
+    GMP_ERROR_SQRT_OF_NEGATIVE = 4,
+    GMP_ERROR_INVALID_ARGUMENT = 8
+};
+
+/* Major version number is the value of __GNU_MP__ too, above and in mp.h. */
+#define __GNU_MP_VERSION 4
+#define __GNU_MP_VERSION_MINOR 2
+#define __GNU_MP_VERSION_PATCHLEVEL 2
+
+#define __GMP_H__
+#endif /* __GMP_H__ */
diff --git a/library/GMP/include/gmpxx.h b/library/GMP/include/gmpxx.h
new file mode 100644
index 00000000..76a72678
--- /dev/null
+++ b/library/GMP/include/gmpxx.h
@@ -0,0 +1,3337 @@
+/* gmpxx.h -- C++ class wrapper for GMP types.  -*- C++ -*-
+
+Copyright 2001, 2002, 2003, 2006 Free Software Foundation, Inc.
+
+This file is part of the GNU MP Library.
+
+The GNU MP Library is free software; you can redistribute it and/or modify
+it under the terms of the GNU Lesser General Public License as published by
+the Free Software Foundation; either version 3 of the License, or (at your
+option) any later version.
+
+The GNU MP Library is distributed in the hope that it will be useful, but
+WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
+License for more details.
+
+You should have received a copy of the GNU Lesser General Public License
+along with the GNU MP Library.  If not, see http://www.gnu.org/licenses/.  */
+
+/* the C++ compiler must implement the following features:
+   - member templates
+   - partial specialization of templates
+   - namespace support
+   for g++, this means version 2.91 or higher
+   for other compilers, I don't know */
+#ifdef __GNUC__
+#if __GNUC__ < 2 || (__GNUC__ == 2 && __GNUC_MINOR__ < 91)
+#error gmpxx.h requires g++ version 2.91 (egcs 1.1.2) or higher
+#endif
+#endif
+
+#ifndef __GMP_PLUSPLUS__
+#define __GMP_PLUSPLUS__
+
+#include <iosfwd>
+
+#include <cstring>  /* for strlen */
+#include <string>
+#include <stdexcept>
+#include <gmp.h>
+
+
+/**************** Function objects ****************/
+/* Any evaluation of a __gmp_expr ends up calling one of these functions
+   all intermediate functions being inline, the evaluation should optimize
+   to a direct call to the relevant function, thus yielding no overhead
+   over the C interface. */
+
+struct __gmp_unary_plus
+{
+  static void eval(mpz_ptr z, mpz_srcptr w) { mpz_set(z, w); }
+  static void eval(mpq_ptr q, mpq_srcptr r) { mpq_set(q, r); }
+  static void eval(mpf_ptr f, mpf_srcptr g) { mpf_set(f, g); }
+};
+
+struct __gmp_unary_minus
+{
+  static void eval(mpz_ptr z, mpz_srcptr w) { mpz_neg(z, w); }
+  static void eval(mpq_ptr q, mpq_srcptr r) { mpq_neg(q, r); }
+  static void eval(mpf_ptr f, mpf_srcptr g) { mpf_neg(f, g); }
+};
+
+struct __gmp_unary_com
+{
+  static void eval(mpz_ptr z, mpz_srcptr w) { mpz_com(z, w); }
+};
+
+struct __gmp_binary_plus
+{
+  static void eval(mpz_ptr z, mpz_srcptr w, mpz_srcptr v)
+  { mpz_add(z, w, v); }
+
+  static void eval(mpz_ptr z, mpz_srcptr w, unsigned long int l)
+  { mpz_add_ui(z, w, l); }
+  static void eval(mpz_ptr z, unsigned long int l, mpz_srcptr w)
+  { mpz_add_ui(z, w, l); }
+  static void eval(mpz_ptr z, mpz_srcptr w, signed long int l)
+  {
+    if (l >= 0)
+      mpz_add_ui(z, w, l);
+    else
+      mpz_sub_ui(z, w, -l);
+  }
+  static void eval(mpz_ptr z, signed long int l, mpz_srcptr w)
+  {
+    if (l >= 0)
+      mpz_add_ui(z, w, l);
+    else
+      mpz_sub_ui(z, w, -l);
+  }
+  static void eval(mpz_ptr z, mpz_srcptr w, double d)
+  {
+    mpz_t temp;
+    mpz_init_set_d(temp, d);
+    mpz_add(z, w, temp);
+    mpz_clear(temp);
+  }
+  static void eval(mpz_ptr z, double d, mpz_srcptr w)
+  {
+    mpz_t temp;
+    mpz_init_set_d(temp, d);
+    mpz_add(z, temp, w);
+    mpz_clear(temp);
+  }
+
+  static void eval(mpq_ptr q, mpq_srcptr r, mpq_srcptr s)
+  { mpq_add(q, r, s); }
+
+  static void eval(mpq_ptr q, mpq_srcptr r, unsigned long int l)
+  { mpq_set(q, r); mpz_addmul_ui(mpq_numref(q), mpq_denref(q), l); }
+  static void eval(mpq_ptr q, unsigned long int l, mpq_srcptr r)
+  { mpq_set(q, r); mpz_addmul_ui(mpq_numref(q), mpq_denref(q), l); }
+  static void eval(mpq_ptr q, mpq_srcptr r, signed long int l)
+  {
+    mpq_set(q, r);
+    if (l >= 0)
+      mpz_addmul_ui(mpq_numref(q), mpq_denref(q), l);
+    else
+      mpz_submul_ui(mpq_numref(q), mpq_denref(q), -l);
+  }
+  static void eval(mpq_ptr q, signed long int l, mpq_srcptr r)
+  {
+    mpq_set(q, r);
+    if (l >= 0)
+      mpz_addmul_ui(mpq_numref(q), mpq_denref(q), l);
+    else
+      mpz_submul_ui(mpq_numref(q), mpq_denref(q), -l);
+  }
+  static void eval(mpq_ptr q, mpq_srcptr r, double d)
+  {
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_d(temp, d);
+    mpq_add(q, r, temp);
+    mpq_clear(temp);
+  }
+  static void eval(mpq_ptr q, double d, mpq_srcptr r)
+  {
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_d(temp, d);
+    mpq_add(q, temp, r);
+    mpq_clear(temp);
+  }
+
+  static void eval(mpq_ptr q, mpq_srcptr r, mpz_srcptr z)
+  { mpq_set(q, r); mpz_addmul(mpq_numref(q), mpq_denref(q), z); }
+  static void eval(mpq_ptr q, mpz_srcptr z, mpq_srcptr r)
+  { mpq_set(q, r); mpz_addmul(mpq_numref(q), mpq_denref(q), z); }
+
+  static void eval(mpf_ptr f, mpf_srcptr g, mpf_srcptr h)
+  { mpf_add(f, g, h); }
+
+  static void eval(mpf_ptr f, mpf_srcptr g, unsigned long int l)
+  { mpf_add_ui(f, g, l); }
+  static void eval(mpf_ptr f, unsigned long int l, mpf_srcptr g)
+  { mpf_add_ui(f, g, l); }
+  static void eval(mpf_ptr f, mpf_srcptr g, signed long int l)
+  {
+    if (l >= 0)
+      mpf_add_ui(f, g, l);
+    else
+      mpf_sub_ui(f, g, -l);
+  }
+  static void eval(mpf_ptr f, signed long int l, mpf_srcptr g)
+  {
+    if (l >= 0)
+      mpf_add_ui(f, g, l);
+    else
+      mpf_sub_ui(f, g, -l);
+  }
+  static void eval(mpf_ptr f, mpf_srcptr g, double d)
+  {
+    mpf_t temp;
+    mpf_init2(temp, 8*sizeof(double));
+    mpf_set_d(temp, d);
+    mpf_add(f, g, temp);
+    mpf_clear(temp);
+  }
+  static void eval(mpf_ptr f, double d, mpf_srcptr g)
+  {
+    mpf_t temp;
+    mpf_init2(temp, 8*sizeof(double));
+    mpf_set_d(temp, d);
+    mpf_add(f, temp, g);
+    mpf_clear(temp);
+  }
+};
+
+struct __gmp_binary_minus
+{
+  static void eval(mpz_ptr z, mpz_srcptr w, mpz_srcptr v)
+  { mpz_sub(z, w, v); }
+
+  static void eval(mpz_ptr z, mpz_srcptr w, unsigned long int l)
+  { mpz_sub_ui(z, w, l); }
+  static void eval(mpz_ptr z, unsigned long int l, mpz_srcptr w)
+  { mpz_ui_sub(z, l, w); }
+  static void eval(mpz_ptr z, mpz_srcptr w, signed long int l)
+  {
+    if (l >= 0)
+      mpz_sub_ui(z, w, l);
+    else
+      mpz_add_ui(z, w, -l);
+  }
+  static void eval(mpz_ptr z, signed long int l, mpz_srcptr w)
+  {
+    if (l >= 0)
+      mpz_ui_sub(z, l, w);
+    else
+      {
+        mpz_add_ui(z, w, -l);
+        mpz_neg(z, z);
+      }
+  }
+  static void eval(mpz_ptr z, mpz_srcptr w, double d)
+  {
+    mpz_t temp;
+    mpz_init_set_d(temp, d);
+    mpz_sub(z, w, temp);
+    mpz_clear(temp);
+  }
+  static void eval(mpz_ptr z, double d, mpz_srcptr w)
+  {
+    mpz_t temp;
+    mpz_init_set_d(temp, d);
+    mpz_sub(z, temp, w);
+    mpz_clear(temp);
+  }
+
+  static void eval(mpq_ptr q, mpq_srcptr r, mpq_srcptr s)
+  { mpq_sub(q, r, s); }
+
+  static void eval(mpq_ptr q, mpq_srcptr r, unsigned long int l)
+  { mpq_set(q, r); mpz_submul_ui(mpq_numref(q), mpq_denref(q), l); }
+  static void eval(mpq_ptr q, unsigned long int l, mpq_srcptr r)
+  { mpq_neg(q, r); mpz_addmul_ui(mpq_numref(q), mpq_denref(q), l); }
+  static void eval(mpq_ptr q, mpq_srcptr r, signed long int l)
+  {
+    mpq_set(q, r);
+    if (l >= 0)
+      mpz_submul_ui(mpq_numref(q), mpq_denref(q), l);
+    else
+      mpz_addmul_ui(mpq_numref(q), mpq_denref(q), -l);
+  }
+  static void eval(mpq_ptr q, signed long int l, mpq_srcptr r)
+  {
+    mpq_neg(q, r);
+    if (l >= 0)
+      mpz_addmul_ui(mpq_numref(q), mpq_denref(q), l);
+    else
+      mpz_submul_ui(mpq_numref(q), mpq_denref(q), -l);
+  }
+  static void eval(mpq_ptr q, mpq_srcptr r, double d)
+  {
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_d(temp, d);
+    mpq_sub(q, r, temp);
+    mpq_clear(temp);
+  }
+  static void eval(mpq_ptr q, double d, mpq_srcptr r)
+  {
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_d(temp, d);
+    mpq_sub(q, temp, r);
+    mpq_clear(temp);
+  }
+
+  static void eval(mpq_ptr q, mpq_srcptr r, mpz_srcptr z)
+  { mpq_set(q, r); mpz_submul(mpq_numref(q), mpq_denref(q), z); }
+  static void eval(mpq_ptr q, mpz_srcptr z, mpq_srcptr r)
+  { mpq_neg(q, r); mpz_addmul(mpq_numref(q), mpq_denref(q), z); }
+
+  static void eval(mpf_ptr f, mpf_srcptr g, mpf_srcptr h)
+  { mpf_sub(f, g, h); }
+
+  static void eval(mpf_ptr f, mpf_srcptr g, unsigned long int l)
+  { mpf_sub_ui(f, g, l); }
+  static void eval(mpf_ptr f, unsigned long int l, mpf_srcptr g)
+  { mpf_ui_sub(f, l, g); }
+  static void eval(mpf_ptr f, mpf_srcptr g, signed long int l)
+  {
+    if (l >= 0)
+      mpf_sub_ui(f, g, l);
+    else
+      mpf_add_ui(f, g, -l);
+  }
+  static void eval(mpf_ptr f, signed long int l, mpf_srcptr g)
+  {
+    if (l >= 0)
+      mpf_sub_ui(f, g, l);
+    else
+      mpf_add_ui(f, g, -l);
+    mpf_neg(f, f);
+  }
+  static void eval(mpf_ptr f, mpf_srcptr g, double d)
+  {
+    mpf_t temp;
+    mpf_init2(temp, 8*sizeof(double));
+    mpf_set_d(temp, d);
+    mpf_sub(f, g, temp);
+    mpf_clear(temp);
+  }
+  static void eval(mpf_ptr f, double d, mpf_srcptr g)
+  {
+    mpf_t temp;
+    mpf_init2(temp, 8*sizeof(double));
+    mpf_set_d(temp, d);
+    mpf_sub(f, temp, g);
+    mpf_clear(temp);
+  }
+};
+
+struct __gmp_binary_multiplies
+{
+  static void eval(mpz_ptr z, mpz_srcptr w, mpz_srcptr v)
+  { mpz_mul(z, w, v); }
+
+  static void eval(mpz_ptr z, mpz_srcptr w, unsigned long int l)
+  { mpz_mul_ui(z, w, l); }
+  static void eval(mpz_ptr z, unsigned long int l, mpz_srcptr w)
+  { mpz_mul_ui(z, w, l); }
+  static void eval(mpz_ptr z, mpz_srcptr w, signed long int l)
+  { mpz_mul_si (z, w, l); }
+  static void eval(mpz_ptr z, signed long int l, mpz_srcptr w)
+  { mpz_mul_si (z, w, l); }
+  static void eval(mpz_ptr z, mpz_srcptr w, double d)
+  {
+    mpz_t temp;
+    mpz_init_set_d(temp, d);
+    mpz_mul(z, w, temp);
+    mpz_clear(temp);
+  }
+  static void eval(mpz_ptr z, double d, mpz_srcptr w)
+  {
+    mpz_t temp;
+    mpz_init_set_d(temp, d);
+    mpz_mul(z, temp, w);
+    mpz_clear(temp);
+  }
+
+  static void eval(mpq_ptr q, mpq_srcptr r, mpq_srcptr s)
+  { mpq_mul(q, r, s); }
+
+  static void eval(mpq_ptr q, mpq_srcptr r, unsigned long int l)
+  {
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_ui(temp, l, 1);
+    mpq_mul(q, r, temp);
+    mpq_clear(temp);
+  }
+  static void eval(mpq_ptr q, unsigned long int l, mpq_srcptr r)
+  {
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_ui(temp, l, 1);
+    mpq_mul(q, temp, r);
+    mpq_clear(temp);
+  }
+  static void eval(mpq_ptr q, mpq_srcptr r, signed long int l)
+  {
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_si(temp, l, 1);
+    mpq_mul(q, r, temp);
+    mpq_clear(temp);
+  }
+  static void eval(mpq_ptr q, signed long int l, mpq_srcptr r)
+  {
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_si(temp, l, 1);
+    mpq_mul(q, temp, r);
+    mpq_clear(temp);
+  }
+  static void eval(mpq_ptr q, mpq_srcptr r, double d)
+  {
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_d(temp, d);
+    mpq_mul(q, r, temp);
+    mpq_clear(temp);
+  }
+  static void eval(mpq_ptr q, double d, mpq_srcptr r)
+  {
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_d(temp, d);
+    mpq_mul(q, temp, r);
+    mpq_clear(temp);
+  }
+
+  static void eval(mpf_ptr f, mpf_srcptr g, mpf_srcptr h)
+  { mpf_mul(f, g, h); }
+
+  static void eval(mpf_ptr f, mpf_srcptr g, unsigned long int l)
+  { mpf_mul_ui(f, g, l); }
+  static void eval(mpf_ptr f, unsigned long int l, mpf_srcptr g)
+  { mpf_mul_ui(f, g, l); }
+  static void eval(mpf_ptr f, mpf_srcptr g, signed long int l)
+  {
+    if (l >= 0)
+      mpf_mul_ui(f, g, l);
+    else
+      {
+	mpf_mul_ui(f, g, -l);
+	mpf_neg(f, f);
+      }
+  }
+  static void eval(mpf_ptr f, signed long int l, mpf_srcptr g)
+  {
+    if (l >= 0)
+      mpf_mul_ui(f, g, l);
+    else
+      {
+	mpf_mul_ui(f, g, -l);
+	mpf_neg(f, f);
+      }
+  }
+  static void eval(mpf_ptr f, mpf_srcptr g, double d)
+  {
+    mpf_t temp;
+    mpf_init2(temp, 8*sizeof(double));
+    mpf_set_d(temp, d);
+    mpf_mul(f, g, temp);
+    mpf_clear(temp);
+  }
+  static void eval(mpf_ptr f, double d, mpf_srcptr g)
+  {
+    mpf_t temp;
+    mpf_init2(temp, 8*sizeof(double));
+    mpf_set_d(temp, d);
+    mpf_mul(f, temp, g);
+    mpf_clear(temp);
+  }
+};
+
+struct __gmp_binary_divides
+{
+  static void eval(mpz_ptr z, mpz_srcptr w, mpz_srcptr v)
+  { mpz_tdiv_q(z, w, v); }
+
+  static void eval(mpz_ptr z, mpz_srcptr w, unsigned long int l)
+  { mpz_tdiv_q_ui(z, w, l); }
+  static void eval(mpz_ptr z, unsigned long int l, mpz_srcptr w)
+  {
+    if (mpz_sgn(w) >= 0)
+      {
+	if (mpz_fits_ulong_p(w))
+	  mpz_set_ui(z, l / mpz_get_ui(w));
+	else
+	  mpz_set_ui(z, 0);
+      }
+    else
+      {
+	mpz_neg(z, w);
+	if (mpz_fits_ulong_p(z))
+	  {
+	    mpz_set_ui(z, l / mpz_get_ui(z));
+	    mpz_neg(z, z);
+	  }
+	else
+	  mpz_set_ui(z, 0);
+      }
+  }
+  static void eval(mpz_ptr z, mpz_srcptr w, signed long int l)
+  {
+    if (l >= 0)
+      mpz_tdiv_q_ui(z, w, l);
+    else
+      {
+	mpz_tdiv_q_ui(z, w, -l);
+	mpz_neg(z, z);
+      }
+  }
+  static void eval(mpz_ptr z, signed long int l, mpz_srcptr w)
+  {
+    if (mpz_fits_slong_p(w))
+      mpz_set_si(z, l / mpz_get_si(w));
+    else
+      {
+        /* if w is bigger than a long then the quotient must be zero, unless
+           l==LONG_MIN and w==-LONG_MIN in which case the quotient is -1 */
+        mpz_set_si (z, (mpz_cmpabs_ui (w, (l >= 0 ? l : -l)) == 0 ? -1 : 0));
+      }
+  }
+  static void eval(mpz_ptr z, mpz_srcptr w, double d)
+  {
+    mpz_t temp;
+    mpz_init_set_d(temp, d);
+    mpz_tdiv_q(z, w, temp);
+    mpz_clear(temp);
+  }
+  static void eval(mpz_ptr z, double d, mpz_srcptr w)
+  {
+    mpz_t temp;
+    mpz_init_set_d(temp, d);
+    mpz_tdiv_q(z, temp, w);
+    mpz_clear(temp);
+  }
+
+  static void eval(mpq_ptr q, mpq_srcptr r, mpq_srcptr s)
+  { mpq_div(q, r, s); }
+
+  static void eval(mpq_ptr q, mpq_srcptr r, unsigned long int l)
+  {
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_ui(temp, l, 1);
+    mpq_div(q, r, temp);
+    mpq_clear(temp);
+  }
+  static void eval(mpq_ptr q, unsigned long int l, mpq_srcptr r)
+  {
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_ui(temp, l, 1);
+    mpq_div(q, temp, r);
+    mpq_clear(temp);
+  }
+  static void eval(mpq_ptr q, mpq_srcptr r, signed long int l)
+  {
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_si(temp, l, 1);
+    mpq_div(q, r, temp);
+    mpq_clear(temp);
+  }
+  static void eval(mpq_ptr q, signed long int l, mpq_srcptr r)
+  {
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_si(temp, l, 1);
+    mpq_div(q, temp, r);
+    mpq_clear(temp);
+  }
+  static void eval(mpq_ptr q, mpq_srcptr r, double d)
+  {
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_d(temp, d);
+    mpq_div(q, r, temp);
+    mpq_clear(temp);
+  }
+  static void eval(mpq_ptr q, double d, mpq_srcptr r)
+  {
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_d(temp, d);
+    mpq_div(q, temp, r);
+    mpq_clear(temp);
+  }
+
+  static void eval(mpf_ptr f, mpf_srcptr g, mpf_srcptr h)
+  { mpf_div(f, g, h); }
+
+  static void eval(mpf_ptr f, mpf_srcptr g, unsigned long int l)
+  { mpf_div_ui(f, g, l); }
+  static void eval(mpf_ptr f, unsigned long int l, mpf_srcptr g)
+  { mpf_ui_div(f, l, g); }
+  static void eval(mpf_ptr f, mpf_srcptr g, signed long int l)
+  {
+    if (l >= 0)
+      mpf_div_ui(f, g, l);
+    else
+      {
+	mpf_div_ui(f, g, -l);
+	mpf_neg(f, f);
+      }
+  }
+  static void eval(mpf_ptr f, signed long int l, mpf_srcptr g)
+  {
+    if (l >= 0)
+      mpf_ui_div(f, l, g);
+    else
+      {
+	mpf_ui_div(f, -l, g);
+	mpf_neg(f, f);
+      }
+  }
+  static void eval(mpf_ptr f, mpf_srcptr g, double d)
+  {
+    mpf_t temp;
+    mpf_init2(temp, 8*sizeof(double));
+    mpf_set_d(temp, d);
+    mpf_div(f, g, temp);
+    mpf_clear(temp);
+  }
+  static void eval(mpf_ptr f, double d, mpf_srcptr g)
+  {
+    mpf_t temp;
+    mpf_init2(temp, 8*sizeof(double));
+    mpf_set_d(temp, d);
+    mpf_div(f, temp, g);
+    mpf_clear(temp);
+  }
+};
+
+struct __gmp_binary_modulus
+{
+  static void eval(mpz_ptr z, mpz_srcptr w, mpz_srcptr v)
+  { mpz_tdiv_r(z, w, v); }
+
+  static void eval(mpz_ptr z, mpz_srcptr w, unsigned long int l)
+  { mpz_tdiv_r_ui(z, w, l); }
+  static void eval(mpz_ptr z, unsigned long int l, mpz_srcptr w)
+  {
+    if (mpz_sgn(w) >= 0)
+      {
+	if (mpz_fits_ulong_p(w))
+	  mpz_set_ui(z, l % mpz_get_ui(w));
+	else
+	  mpz_set_ui(z, l);
+      }
+    else
+      {
+	mpz_neg(z, w);
+	if (mpz_fits_ulong_p(z))
+	  mpz_set_ui(z, l % mpz_get_ui(z));
+	else
+	  mpz_set_ui(z, l);
+      }
+  }
+  static void eval(mpz_ptr z, mpz_srcptr w, signed long int l)
+  {
+    mpz_tdiv_r_ui (z, w, (l >= 0 ? l : -l));
+  }
+  static void eval(mpz_ptr z, signed long int l, mpz_srcptr w)
+  {
+    if (mpz_fits_slong_p(w))
+      mpz_set_si(z, l % mpz_get_si(w));
+    else
+      {
+        /* if w is bigger than a long then the remainder is l unchanged,
+           unless l==LONG_MIN and w==-LONG_MIN in which case it's 0 */
+        mpz_set_si (z, mpz_cmpabs_ui (w, (l >= 0 ? l : -l)) == 0 ? 0 : l);
+      }
+  }
+  static void eval(mpz_ptr z, mpz_srcptr w, double d)
+  {
+    mpz_t temp;
+    mpz_init_set_d(temp, d);
+    mpz_tdiv_r(z, w, temp);
+    mpz_clear(temp);
+  }
+  static void eval(mpz_ptr z, double d, mpz_srcptr w)
+  {
+    mpz_t temp;
+    mpz_init_set_d(temp, d);
+    mpz_tdiv_r(z, temp, w);
+    mpz_clear(temp);
+  }
+};
+
+struct __gmp_binary_and
+{
+  static void eval(mpz_ptr z, mpz_srcptr w, mpz_srcptr v)
+  { mpz_and(z, w, v); }
+};
+
+struct __gmp_binary_ior
+{
+  static void eval(mpz_ptr z, mpz_srcptr w, mpz_srcptr v)
+  { mpz_ior(z, w, v); }
+};
+
+struct __gmp_binary_xor
+{
+  static void eval(mpz_ptr z, mpz_srcptr w, mpz_srcptr v)
+  { mpz_xor(z, w, v); }
+};
+
+struct __gmp_binary_lshift
+{
+  static void eval(mpz_ptr z, mpz_srcptr w, unsigned long int l)
+  { mpz_mul_2exp(z, w, l); }
+  static void eval(mpq_ptr q, mpq_srcptr r, unsigned long int l)
+  { mpq_mul_2exp(q, r, l); }
+  static void eval(mpf_ptr f, mpf_srcptr g, unsigned long int l)
+  { mpf_mul_2exp(f, g, l); }
+};
+
+struct __gmp_binary_rshift
+{
+  static void eval(mpz_ptr z, mpz_srcptr w, unsigned long int l)
+  { mpz_tdiv_q_2exp(z, w, l); }
+  static void eval(mpq_ptr q, mpq_srcptr r, unsigned long int l)
+  { mpq_div_2exp(q, r, l); }
+  static void eval(mpf_ptr f, mpf_srcptr g, unsigned long int l)
+  { mpf_div_2exp(f, g, l); }
+};
+
+struct __gmp_binary_equal
+{
+  static bool eval(mpz_srcptr z, mpz_srcptr w) { return mpz_cmp(z, w) == 0; }
+
+  static bool eval(mpz_srcptr z, unsigned long int l)
+  { return mpz_cmp_ui(z, l) == 0; }
+  static bool eval(unsigned long int l, mpz_srcptr z)
+  { return mpz_cmp_ui(z, l) == 0; }
+  static bool eval(mpz_srcptr z, signed long int l)
+  { return mpz_cmp_si(z, l) == 0; }
+  static bool eval(signed long int l, mpz_srcptr z)
+  { return mpz_cmp_si(z, l) == 0; }
+  static bool eval(mpz_srcptr z, double d)
+  { return mpz_cmp_d(z, d) == 0; }
+  static bool eval(double d, mpz_srcptr z)
+  { return mpz_cmp_d(z, d) == 0; }
+
+  static bool eval(mpq_srcptr q, mpq_srcptr r)
+  { return mpq_equal(q, r) != 0; }
+
+  static bool eval(mpq_srcptr q, unsigned long int l)
+  { return mpq_cmp_ui(q, l, 1) == 0; }
+  static bool eval(unsigned long int l, mpq_srcptr q)
+  { return mpq_cmp_ui(q, l, 1) == 0; }
+  static bool eval(mpq_srcptr q, signed long int l)
+  { return mpq_cmp_si(q, l, 1) == 0; }
+  static bool eval(signed long int l, mpq_srcptr q)
+  { return mpq_cmp_si(q, l, 1) == 0; }
+  static bool eval(mpq_srcptr q, double d)
+  {
+    bool b;
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_d(temp, d);
+    b = (mpq_equal(q, temp) != 0);
+    mpq_clear(temp);
+    return b;
+  }
+  static bool eval(double d, mpq_srcptr q)
+  {
+    bool b;
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_d(temp, d);
+    b = (mpq_equal(temp, q) != 0);
+    mpq_clear(temp);
+    return b;
+  }
+
+  static bool eval(mpf_srcptr f, mpf_srcptr g) { return mpf_cmp(f, g) == 0; }
+
+  static bool eval(mpf_srcptr f, unsigned long int l)
+  { return mpf_cmp_ui(f, l) == 0; }
+  static bool eval(unsigned long int l, mpf_srcptr f)
+  { return mpf_cmp_ui(f, l) == 0; }
+  static bool eval(mpf_srcptr f, signed long int l)
+  { return mpf_cmp_si(f, l) == 0; }
+  static bool eval(signed long int l, mpf_srcptr f)
+  { return mpf_cmp_si(f, l) == 0; }
+  static bool eval(mpf_srcptr f, double d)
+  { return mpf_cmp_d(f, d) == 0; }
+  static bool eval(double d, mpf_srcptr f)
+  { return mpf_cmp_d(f, d) == 0; }
+};
+
+struct __gmp_binary_not_equal
+{
+  static bool eval(mpz_srcptr z, mpz_srcptr w) { return mpz_cmp(z, w) != 0; }
+
+  static bool eval(mpz_srcptr z, unsigned long int l)
+  { return mpz_cmp_ui(z, l) != 0; }
+  static bool eval(unsigned long int l, mpz_srcptr z)
+  { return mpz_cmp_ui(z, l) != 0; }
+  static bool eval(mpz_srcptr z, signed long int l)
+  { return mpz_cmp_si(z, l) != 0; }
+  static bool eval(signed long int l, mpz_srcptr z)
+  { return mpz_cmp_si(z, l) != 0; }
+  static bool eval(mpz_srcptr z, double d)
+  { return mpz_cmp_d(z, d) != 0; }
+  static bool eval(double d, mpz_srcptr z)
+  { return mpz_cmp_d(z, d) != 0; }
+
+  static bool eval(mpq_srcptr q, mpq_srcptr r)
+  { return mpq_equal(q, r) == 0; }
+
+  static bool eval(mpq_srcptr q, unsigned long int l)
+  { return mpq_cmp_ui(q, l, 1) != 0; }
+  static bool eval(unsigned long int l, mpq_srcptr q)
+  { return mpq_cmp_ui(q, l, 1) != 0; }
+  static bool eval(mpq_srcptr q, signed long int l)
+  { return mpq_cmp_si(q, l, 1) != 0; }
+  static bool eval(signed long int l, mpq_srcptr q)
+  { return mpq_cmp_si(q, l, 1) != 0; }
+  static bool eval(mpq_srcptr q, double d)
+  {
+    bool b;
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_d(temp, d);
+    b = (mpq_equal(q, temp) == 0);
+    mpq_clear(temp);
+    return b;
+  }
+  static bool eval(double d, mpq_srcptr q)
+  {
+    bool b;
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_d(temp, d);
+    b = (mpq_equal(temp, q) == 0);
+    mpq_clear(temp);
+    return b;
+  }
+
+  static bool eval(mpf_srcptr f, mpf_srcptr g) { return mpf_cmp(f, g) != 0; }
+
+  static bool eval(mpf_srcptr f, unsigned long int l)
+  { return mpf_cmp_ui(f, l) != 0; }
+  static bool eval(unsigned long int l, mpf_srcptr f)
+  { return mpf_cmp_ui(f, l) != 0; }
+  static bool eval(mpf_srcptr f, signed long int l)
+  { return mpf_cmp_si(f, l) != 0; }
+  static bool eval(signed long int l, mpf_srcptr f)
+  { return mpf_cmp_si(f, l) != 0; }
+  static bool eval(mpf_srcptr f, double d)
+  { return mpf_cmp_d(f, d) != 0; }
+  static bool eval(double d, mpf_srcptr f)
+  { return mpf_cmp_d(f, d) != 0; }
+};
+
+struct __gmp_binary_less
+{
+  static bool eval(mpz_srcptr z, mpz_srcptr w) { return mpz_cmp(z, w) < 0; }
+
+  static bool eval(mpz_srcptr z, unsigned long int l)
+  { return mpz_cmp_ui(z, l) < 0; }
+  static bool eval(unsigned long int l, mpz_srcptr z)
+  { return mpz_cmp_ui(z, l) > 0; }
+  static bool eval(mpz_srcptr z, signed long int l)
+  { return mpz_cmp_si(z, l) < 0; }
+  static bool eval(signed long int l, mpz_srcptr z)
+  { return mpz_cmp_si(z, l) > 0; }
+  static bool eval(mpz_srcptr z, double d)
+  { return mpz_cmp_d(z, d) < 0; }
+  static bool eval(double d, mpz_srcptr z)
+  { return mpz_cmp_d(z, d) > 0; }
+
+  static bool eval(mpq_srcptr q, mpq_srcptr r) { return mpq_cmp(q, r) < 0; }
+
+  static bool eval(mpq_srcptr q, unsigned long int l)
+  { return mpq_cmp_ui(q, l, 1) < 0; }
+  static bool eval(unsigned long int l, mpq_srcptr q)
+  { return mpq_cmp_ui(q, l, 1) > 0; }
+  static bool eval(mpq_srcptr q, signed long int l)
+  { return mpq_cmp_si(q, l, 1) < 0; }
+  static bool eval(signed long int l, mpq_srcptr q)
+  { return mpq_cmp_si(q, l, 1) > 0; }
+  static bool eval(mpq_srcptr q, double d)
+  {
+    bool b;
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_d(temp, d);
+    b = (mpq_cmp(q, temp) < 0);
+    mpq_clear(temp);
+    return b;
+  }
+  static bool eval(double d, mpq_srcptr q)
+  {
+    bool b;
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_d(temp, d);
+    b = (mpq_cmp(temp, q) < 0);
+    mpq_clear(temp);
+    return b;
+  }
+
+  static bool eval(mpf_srcptr f, mpf_srcptr g) { return mpf_cmp(f, g) < 0; }
+
+  static bool eval(mpf_srcptr f, unsigned long int l)
+  { return mpf_cmp_ui(f, l) < 0; }
+  static bool eval(unsigned long int l, mpf_srcptr f)
+  { return mpf_cmp_ui(f, l) > 0; }
+  static bool eval(mpf_srcptr f, signed long int l)
+  { return mpf_cmp_si(f, l) < 0; }
+  static bool eval(signed long int l, mpf_srcptr f)
+  { return mpf_cmp_si(f, l) > 0; }
+  static bool eval(mpf_srcptr f, double d)
+  { return mpf_cmp_d(f, d) < 0; }
+  static bool eval(double d, mpf_srcptr f)
+  { return mpf_cmp_d(f, d) > 0; }
+};
+
+struct __gmp_binary_less_equal
+{
+  static bool eval(mpz_srcptr z, mpz_srcptr w) { return mpz_cmp(z, w) <= 0; }
+
+  static bool eval(mpz_srcptr z, unsigned long int l)
+  { return mpz_cmp_ui(z, l) <= 0; }
+  static bool eval(unsigned long int l, mpz_srcptr z)
+  { return mpz_cmp_ui(z, l) >= 0; }
+  static bool eval(mpz_srcptr z, signed long int l)
+  { return mpz_cmp_si(z, l) <= 0; }
+  static bool eval(signed long int l, mpz_srcptr z)
+  { return mpz_cmp_si(z, l) >= 0; }
+  static bool eval(mpz_srcptr z, double d)
+  { return mpz_cmp_d(z, d) <= 0; }
+  static bool eval(double d, mpz_srcptr z)
+  { return mpz_cmp_d(z, d) >= 0; }
+
+  static bool eval(mpq_srcptr q, mpq_srcptr r) { return mpq_cmp(q, r) <= 0; }
+
+  static bool eval(mpq_srcptr q, unsigned long int l)
+  { return mpq_cmp_ui(q, l, 1) <= 0; }
+  static bool eval(unsigned long int l, mpq_srcptr q)
+  { return mpq_cmp_ui(q, l, 1) >= 0; }
+  static bool eval(mpq_srcptr q, signed long int l)
+  { return mpq_cmp_si(q, l, 1) <= 0; }
+  static bool eval(signed long int l, mpq_srcptr q)
+  { return mpq_cmp_si(q, l, 1) >= 0; }
+  static bool eval(mpq_srcptr q, double d)
+  {
+    bool b;
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_d(temp, d);
+    b = (mpq_cmp(q, temp) <= 0);
+    mpq_clear(temp);
+    return b;
+  }
+  static bool eval(double d, mpq_srcptr q)
+  {
+    bool b;
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_d(temp, d);
+    b = (mpq_cmp(temp, q) <= 0);
+    mpq_clear(temp);
+    return b;
+  }
+
+  static bool eval(mpf_srcptr f, mpf_srcptr g) { return mpf_cmp(f, g) <= 0; }
+
+  static bool eval(mpf_srcptr f, unsigned long int l)
+  { return mpf_cmp_ui(f, l) <= 0; }
+  static bool eval(unsigned long int l, mpf_srcptr f)
+  { return mpf_cmp_ui(f, l) >= 0; }
+  static bool eval(mpf_srcptr f, signed long int l)
+  { return mpf_cmp_si(f, l) <= 0; }
+  static bool eval(signed long int l, mpf_srcptr f)
+  { return mpf_cmp_si(f, l) >= 0; }
+  static bool eval(mpf_srcptr f, double d)
+  { return mpf_cmp_d(f, d) <= 0; }
+  static bool eval(double d, mpf_srcptr f)
+  { return mpf_cmp_d(f, d) >= 0; }
+};
+
+struct __gmp_binary_greater
+{
+  static bool eval(mpz_srcptr z, mpz_srcptr w) { return mpz_cmp(z, w) > 0; }
+
+  static bool eval(mpz_srcptr z, unsigned long int l)
+  { return mpz_cmp_ui(z, l) > 0; }
+  static bool eval(unsigned long int l, mpz_srcptr z)
+  { return mpz_cmp_ui(z, l) < 0; }
+  static bool eval(mpz_srcptr z, signed long int l)
+  { return mpz_cmp_si(z, l) > 0; }
+  static bool eval(signed long int l, mpz_srcptr z)
+  { return mpz_cmp_si(z, l) < 0; }
+  static bool eval(mpz_srcptr z, double d)
+  { return mpz_cmp_d(z, d) > 0; }
+  static bool eval(double d, mpz_srcptr z)
+  { return mpz_cmp_d(z, d) < 0; }
+
+  static bool eval(mpq_srcptr q, mpq_srcptr r) { return mpq_cmp(q, r) > 0; }
+
+  static bool eval(mpq_srcptr q, unsigned long int l)
+  { return mpq_cmp_ui(q, l, 1) > 0; }
+  static bool eval(unsigned long int l, mpq_srcptr q)
+  { return mpq_cmp_ui(q, l, 1) < 0; }
+  static bool eval(mpq_srcptr q, signed long int l)
+  { return mpq_cmp_si(q, l, 1) > 0; }
+  static bool eval(signed long int l, mpq_srcptr q)
+  { return mpq_cmp_si(q, l, 1) < 0; }
+  static bool eval(mpq_srcptr q, double d)
+  {
+    bool b;
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_d(temp, d);
+    b = (mpq_cmp(q, temp) > 0);
+    mpq_clear(temp);
+    return b;
+  }
+  static bool eval(double d, mpq_srcptr q)
+  {
+    bool b;
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_d(temp, d);
+    b = (mpq_cmp(temp, q) > 0);
+    mpq_clear(temp);
+    return b;
+  }
+
+  static bool eval(mpf_srcptr f, mpf_srcptr g) { return mpf_cmp(f, g) > 0; }
+
+  static bool eval(mpf_srcptr f, unsigned long int l)
+  { return mpf_cmp_ui(f, l) > 0; }
+  static bool eval(unsigned long int l, mpf_srcptr f)
+  { return mpf_cmp_ui(f, l) < 0; }
+  static bool eval(mpf_srcptr f, signed long int l)
+  { return mpf_cmp_si(f, l) > 0; }
+  static bool eval(signed long int l, mpf_srcptr f)
+  { return mpf_cmp_si(f, l) < 0; }
+  static bool eval(mpf_srcptr f, double d)
+  { return mpf_cmp_d(f, d) > 0; }
+  static bool eval(double d, mpf_srcptr f)
+  { return mpf_cmp_d(f, d) < 0; }
+};
+
+struct __gmp_binary_greater_equal
+{
+  static bool eval(mpz_srcptr z, mpz_srcptr w) { return mpz_cmp(z, w) >= 0; }
+
+  static bool eval(mpz_srcptr z, unsigned long int l)
+  { return mpz_cmp_ui(z, l) >= 0; }
+  static bool eval(unsigned long int l, mpz_srcptr z)
+  { return mpz_cmp_ui(z, l) <= 0; }
+  static bool eval(mpz_srcptr z, signed long int l)
+  { return mpz_cmp_si(z, l) >= 0; }
+  static bool eval(signed long int l, mpz_srcptr z)
+  { return mpz_cmp_si(z, l) <= 0; }
+  static bool eval(mpz_srcptr z, double d)
+  { return mpz_cmp_d(z, d) >= 0; }
+  static bool eval(double d, mpz_srcptr z)
+  { return mpz_cmp_d(z, d) <= 0; }
+
+  static bool eval(mpq_srcptr q, mpq_srcptr r) { return mpq_cmp(q, r) >= 0; }
+
+  static bool eval(mpq_srcptr q, unsigned long int l)
+  { return mpq_cmp_ui(q, l, 1) >= 0; }
+  static bool eval(unsigned long int l, mpq_srcptr q)
+  { return mpq_cmp_ui(q, l, 1) <= 0; }
+  static bool eval(mpq_srcptr q, signed long int l)
+  { return mpq_cmp_si(q, l, 1) >= 0; }
+  static bool eval(signed long int l, mpq_srcptr q)
+  { return mpq_cmp_si(q, l, 1) <= 0; }
+  static bool eval(mpq_srcptr q, double d)
+  {
+    bool b;
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_d(temp, d);
+    b = (mpq_cmp(q, temp) >= 0);
+    mpq_clear(temp);
+    return b;
+  }
+  static bool eval(double d, mpq_srcptr q)
+  {
+    bool b;
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_d(temp, d);
+    b = (mpq_cmp(temp, q) >= 0);
+    mpq_clear(temp);
+    return b;
+  }
+
+  static bool eval(mpf_srcptr f, mpf_srcptr g) { return mpf_cmp(f, g) >= 0; }
+
+  static bool eval(mpf_srcptr f, unsigned long int l)
+  { return mpf_cmp_ui(f, l) >= 0; }
+  static bool eval(unsigned long int l, mpf_srcptr f)
+  { return mpf_cmp_ui(f, l) <= 0; }
+  static bool eval(mpf_srcptr f, signed long int l)
+  { return mpf_cmp_si(f, l) >= 0; }
+  static bool eval(signed long int l, mpf_srcptr f)
+  { return mpf_cmp_si(f, l) <= 0; }
+  static bool eval(mpf_srcptr f, double d)
+  { return mpf_cmp_d(f, d) >= 0; }
+  static bool eval(double d, mpf_srcptr f)
+  { return mpf_cmp_d(f, d) <= 0; }
+};
+
+struct __gmp_unary_increment
+{
+  static void eval(mpz_ptr z) { mpz_add_ui(z, z, 1); }
+  static void eval(mpq_ptr q)
+  { mpz_add(mpq_numref(q), mpq_numref(q), mpq_denref(q)); }
+  static void eval(mpf_ptr f) { mpf_add_ui(f, f, 1); }
+};
+
+struct __gmp_unary_decrement
+{
+  static void eval(mpz_ptr z) { mpz_sub_ui(z, z, 1); }
+  static void eval(mpq_ptr q)
+  { mpz_sub(mpq_numref(q), mpq_numref(q), mpq_denref(q)); }
+  static void eval(mpf_ptr f) { mpf_sub_ui(f, f, 1); }
+};
+
+struct __gmp_abs_function
+{
+  static void eval(mpz_ptr z, mpz_srcptr w) { mpz_abs(z, w); }
+  static void eval(mpq_ptr q, mpq_srcptr r) { mpq_abs(q, r); }
+  static void eval(mpf_ptr f, mpf_srcptr g) { mpf_abs(f, g); }
+};
+
+struct __gmp_trunc_function
+{
+  static void eval(mpf_ptr f, mpf_srcptr g) { mpf_trunc(f, g); }
+};
+
+struct __gmp_floor_function
+{
+  static void eval(mpf_ptr f, mpf_srcptr g) { mpf_floor(f, g); }
+};
+
+struct __gmp_ceil_function
+{
+  static void eval(mpf_ptr f, mpf_srcptr g) { mpf_ceil(f, g); }
+};
+
+struct __gmp_sqrt_function
+{
+  static void eval(mpz_ptr z, mpz_srcptr w) { mpz_sqrt(z, w); }
+  static void eval(mpf_ptr f, mpf_srcptr g) { mpf_sqrt(f, g); }
+};
+
+struct __gmp_hypot_function
+{
+  static void eval(mpf_ptr f, mpf_srcptr g, mpf_srcptr h)
+  {
+    mpf_t temp;
+    mpf_init2(temp, mpf_get_prec(f));
+    mpf_mul(temp, g, g);
+    mpf_mul(f, h, h);
+    mpf_add(f, f, temp);
+    mpf_sqrt(f, f);
+    mpf_clear(temp);
+  }
+
+  static void eval(mpf_ptr f, mpf_srcptr g, unsigned long int l)
+  {
+    mpf_t temp;
+    mpf_init2(temp, mpf_get_prec(f));
+    mpf_mul(temp, g, g);
+    mpf_set_ui(f, l);
+    mpf_mul(f, f, f);
+    mpf_add(f, f, temp);
+    mpf_sqrt(f, f);
+    mpf_clear(temp);
+  }
+  static void eval(mpf_ptr f, unsigned long int l, mpf_srcptr g)
+  {
+    mpf_t temp;
+    mpf_init2(temp, mpf_get_prec(f));
+    mpf_mul(temp, g, g);
+    mpf_set_ui(f, l);
+    mpf_mul(f, f, f);
+    mpf_add(f, f, temp);
+    mpf_sqrt(f, f);
+    mpf_clear(temp);
+  }
+  static void eval(mpf_ptr f, mpf_srcptr g, signed long int l)
+  {
+    mpf_t temp;
+    mpf_init2(temp, mpf_get_prec(f));
+    mpf_mul(temp, g, g);
+    mpf_set_si(f, l);
+    mpf_mul(f, f, f);
+    mpf_add(f, f, temp);
+    mpf_sqrt(f, f);
+    mpf_clear(temp);
+  }
+  static void eval(mpf_ptr f, signed long int l, mpf_srcptr g)
+  {
+    mpf_t temp;
+    mpf_init2(temp, mpf_get_prec(f));
+    mpf_mul(temp, g, g);
+    mpf_set_si(f, l);
+    mpf_mul(f, f, f);
+    mpf_add(f, f, temp);
+    mpf_sqrt(f, f);
+    mpf_clear(temp);
+  }
+  static void eval(mpf_ptr f, mpf_srcptr g, double d)
+  {
+    mpf_t temp;
+    mpf_init2(temp, mpf_get_prec(f));
+    mpf_mul(temp, g, g);
+    mpf_set_d(f, d);
+    mpf_mul(f, f, f);
+    mpf_add(f, f, temp);
+    mpf_sqrt(f, f);
+    mpf_clear(temp);
+  }
+  static void eval(mpf_ptr f, double d, mpf_srcptr g)
+  {
+    mpf_t temp;
+    mpf_init2(temp, mpf_get_prec(f));
+    mpf_mul(temp, g, g);
+    mpf_set_d(f, d);
+    mpf_mul(f, f, f);
+    mpf_add(f, f, temp);
+    mpf_sqrt(f, f);
+    mpf_clear(temp);
+  }
+};
+
+struct __gmp_sgn_function
+{
+  static int eval(mpz_srcptr z) { return mpz_sgn(z); }
+  static int eval(mpq_srcptr q) { return mpq_sgn(q); }
+  static int eval(mpf_srcptr f) { return mpf_sgn(f); }
+};
+
+struct __gmp_cmp_function
+{
+  static int eval(mpz_srcptr z, mpz_srcptr w) { return mpz_cmp(z, w); }
+
+  static int eval(mpz_srcptr z, unsigned long int l)
+  { return mpz_cmp_ui(z, l); }
+  static int eval(unsigned long int l, mpz_srcptr z)
+  { return -mpz_cmp_ui(z, l); }
+  static int eval(mpz_srcptr z, signed long int l)
+  { return mpz_cmp_si(z, l); }
+  static int eval(signed long int l, mpz_srcptr z)
+  { return -mpz_cmp_si(z, l); }
+  static int eval(mpz_srcptr z, double d)
+  { return mpz_cmp_d(z, d); }
+  static int eval(double d, mpz_srcptr z)
+  { return -mpz_cmp_d(z, d); }
+
+  static int eval(mpq_srcptr q, mpq_srcptr r) { return mpq_cmp(q, r); }
+
+  static int eval(mpq_srcptr q, unsigned long int l)
+  { return mpq_cmp_ui(q, l, 1); }
+  static int eval(unsigned long int l, mpq_srcptr q)
+  { return -mpq_cmp_ui(q, l, 1); }
+  static int eval(mpq_srcptr q, signed long int l)
+  { return mpq_cmp_si(q, l, 1); }
+  static int eval(signed long int l, mpq_srcptr q)
+  { return -mpq_cmp_si(q, l, 1); }
+  static int eval(mpq_srcptr q, double d)
+  {
+    int i;
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_d(temp, d);
+    i = mpq_cmp(q, temp);
+    mpq_clear(temp);
+    return i;
+  }
+  static int eval(double d, mpq_srcptr q)
+  {
+    int i;
+    mpq_t temp;
+    mpq_init(temp);
+    mpq_set_d(temp, d);
+    i = mpq_cmp(temp, q);
+    mpq_clear(temp);
+    return i;
+  }
+
+  static int eval(mpf_srcptr f, mpf_srcptr g) { return mpf_cmp(f, g); }
+
+  static int eval(mpf_srcptr f, unsigned long int l)
+  { return mpf_cmp_ui(f, l); }
+  static int eval(unsigned long int l, mpf_srcptr f)
+  { return -mpf_cmp_ui(f, l); }
+  static int eval(mpf_srcptr f, signed long int l)
+  { return mpf_cmp_si(f, l); }
+  static int eval(signed long int l, mpf_srcptr f)
+  { return -mpf_cmp_si(f, l); }
+  static int eval(mpf_srcptr f, double d)
+  { return mpf_cmp_d(f, d); }
+  static int eval(double d, mpf_srcptr f)
+  { return -mpf_cmp_d(f, d); }
+};
+
+struct __gmp_rand_function
+{
+  static void eval(mpz_ptr z, gmp_randstate_t s, unsigned long int l)
+  { mpz_urandomb(z, s, l); }
+  static void eval(mpz_ptr z, gmp_randstate_t s, mpz_srcptr w)
+  { mpz_urandomm(z, s, w); }
+  static void eval(mpf_ptr f, gmp_randstate_t s, unsigned long int prec)
+  { mpf_urandomb(f, s, prec); }
+};
+
+
+/**************** Auxiliary classes ****************/
+
+/* this is much the same as gmp_allocated_string in gmp-impl.h
+   since gmp-impl.h is not publicly available, I redefine it here
+   I use a different name to avoid possible clashes */
+struct __gmp_alloc_cstring
+{
+  char *str;
+  __gmp_alloc_cstring(char *s) { str = s; }
+  ~__gmp_alloc_cstring()
+  {
+    void (*freefunc) (void *, size_t);
+    mp_get_memory_functions (NULL, NULL, &freefunc);
+    (*freefunc) (str, std::strlen(str)+1);
+  }
+};
+
+
+// general expression template class
+template <class T, class U>
+class __gmp_expr;
+
+
+// templates for resolving expression types
+template <class T>
+struct __gmp_resolve_ref
+{
+  typedef T ref_type;
+};
+
+template <class T, class U>
+struct __gmp_resolve_ref<__gmp_expr<T, U> >
+{
+  typedef const __gmp_expr<T, U> & ref_type;
+};
+
+
+template <class T, class U = T>
+struct __gmp_resolve_expr;
+
+template <>
+struct __gmp_resolve_expr<mpz_t>
+{
+  typedef mpz_t value_type;
+  typedef mpz_ptr ptr_type;
+};
+
+template <>
+struct __gmp_resolve_expr<mpq_t>
+{
+  typedef mpq_t value_type;
+  typedef mpq_ptr ptr_type;
+};
+
+template <>
+struct __gmp_resolve_expr<mpf_t>
+{
+  typedef mpf_t value_type;
+  typedef mpf_ptr ptr_type;
+};
+
+template <>
+struct __gmp_resolve_expr<mpz_t, mpq_t>
+{
+  typedef mpq_t value_type;
+};
+
+template <>
+struct __gmp_resolve_expr<mpq_t, mpz_t>
+{
+  typedef mpq_t value_type;
+};
+
+template <>
+struct __gmp_resolve_expr<mpz_t, mpf_t>
+{
+  typedef mpf_t value_type;
+};
+
+template <>
+struct __gmp_resolve_expr<mpf_t, mpz_t>
+{
+  typedef mpf_t value_type;
+};
+
+template <>
+struct __gmp_resolve_expr<mpq_t, mpf_t>
+{
+  typedef mpf_t value_type;
+};
+
+template <>
+struct __gmp_resolve_expr<mpf_t, mpq_t>
+{
+  typedef mpf_t value_type;
+};
+
+
+
+template <class T, class U, class V>
+struct __gmp_resolve_temp
+{
+  typedef __gmp_expr<T, T> temp_type;
+};
+
+template <class T>
+struct __gmp_resolve_temp<T, T, T>
+{
+  typedef const __gmp_expr<T, T> & temp_type;
+};
+
+
+// classes for evaluating unary and binary expressions
+template <class T, class Op>
+struct __gmp_unary_expr
+{
+  const T &val;
+
+  __gmp_unary_expr(const T &v) : val(v) { }
+private:
+  __gmp_unary_expr();
+};
+
+template <class T, class U, class Op>
+struct __gmp_binary_expr
+{
+  typename __gmp_resolve_ref<T>::ref_type val1;
+  typename __gmp_resolve_ref<U>::ref_type val2;
+
+  __gmp_binary_expr(const T &v1, const U &v2) : val1(v1), val2(v2) { }
+private:
+  __gmp_binary_expr();
+};
+
+
+// functions for evaluating expressions
+template <class T, class U>
+void __gmp_set_expr(mpz_ptr, const __gmp_expr<T, U> &);
+template <class T, class U>
+void __gmp_set_expr(mpq_ptr, const __gmp_expr<T, U> &);
+template <class T, class U>
+void __gmp_set_expr(mpf_ptr, const __gmp_expr<T, U> &);
+
+
+/**************** Macros for in-class declarations ****************/
+/* This is just repetitive code that is easier to maintain if it's written
+   only once */
+
+#define __GMPP_DECLARE_COMPOUND_OPERATOR(fun)                         \
+  template <class T, class U>                                         \
+  __gmp_expr<value_type, value_type> & fun(const __gmp_expr<T, U> &);
+
+#define __GMPN_DECLARE_COMPOUND_OPERATOR(fun) \
+  __gmp_expr & fun(signed char);              \
+  __gmp_expr & fun(unsigned char);            \
+  __gmp_expr & fun(signed int);               \
+  __gmp_expr & fun(unsigned int);             \
+  __gmp_expr & fun(signed short int);         \
+  __gmp_expr & fun(unsigned short int);       \
+  __gmp_expr & fun(signed long int);          \
+  __gmp_expr & fun(unsigned long int);        \
+  __gmp_expr & fun(float);                    \
+  __gmp_expr & fun(double);                   \
+  __gmp_expr & fun(long double);
+
+#define __GMP_DECLARE_COMPOUND_OPERATOR(fun) \
+__GMPP_DECLARE_COMPOUND_OPERATOR(fun)        \
+__GMPN_DECLARE_COMPOUND_OPERATOR(fun)
+
+#define __GMP_DECLARE_COMPOUND_OPERATOR_UI(fun) \
+  __gmp_expr & fun(unsigned long int);
+
+#define __GMP_DECLARE_INCREMENT_OPERATOR(fun) \
+  inline __gmp_expr & fun();                  \
+  inline __gmp_expr fun(int);
+
+
+/**************** mpz_class -- wrapper for mpz_t ****************/
+
+template <>
+class __gmp_expr<mpz_t, mpz_t>
+{
+private:
+  typedef mpz_t value_type;
+  value_type mp;
+public:
+  unsigned long int get_prec() const { return mpf_get_default_prec(); }
+
+  // constructors and destructor
+  __gmp_expr() { mpz_init(mp); }
+
+  __gmp_expr(const __gmp_expr &z) { mpz_init_set(mp, z.mp); }
+  template <class T, class U>
+  __gmp_expr(const __gmp_expr<T, U> &expr)
+  { mpz_init(mp); __gmp_set_expr(mp, expr); }
+
+  __gmp_expr(signed char c) { mpz_init_set_si(mp, c); }
+  __gmp_expr(unsigned char c) { mpz_init_set_ui(mp, c); }
+
+  __gmp_expr(signed int i) { mpz_init_set_si(mp, i); }
+  __gmp_expr(unsigned int i) { mpz_init_set_ui(mp, i); }
+
+  __gmp_expr(signed short int s) { mpz_init_set_si(mp, s); }
+  __gmp_expr(unsigned short int s) { mpz_init_set_ui(mp, s); }
+
+  __gmp_expr(signed long int l) { mpz_init_set_si(mp, l); }
+  __gmp_expr(unsigned long int l) { mpz_init_set_ui(mp, l); }
+
+  __gmp_expr(float f) { mpz_init_set_d(mp, f); }
+  __gmp_expr(double d) { mpz_init_set_d(mp, d); }
+  // __gmp_expr(long double ld) { mpz_init_set_d(mp, ld); }
+
+  explicit __gmp_expr(const char *s)
+  {
+    if (mpz_init_set_str (mp, s, 0) != 0)
+      {
+        mpz_clear (mp);
+        throw std::invalid_argument ("mpz_set_str");
+      }
+  }
+  __gmp_expr(const char *s, int base)
+  {
+    if (mpz_init_set_str (mp, s, base) != 0)
+      {
+        mpz_clear (mp);
+        throw std::invalid_argument ("mpz_set_str");
+      }
+  }
+  explicit __gmp_expr(const std::string &s)
+  {
+    if (mpz_init_set_str (mp, s.c_str(), 0) != 0)
+      {
+        mpz_clear (mp);
+        throw std::invalid_argument ("mpz_set_str");
+      }
+  }
+  __gmp_expr(const std::string &s, int base)
+  {
+    if (mpz_init_set_str(mp, s.c_str(), base) != 0)
+      {
+        mpz_clear (mp);
+        throw std::invalid_argument ("mpz_set_str");
+      }
+  }
+
+  explicit __gmp_expr(mpz_srcptr z) { mpz_init_set(mp, z); }
+
+  ~__gmp_expr() { mpz_clear(mp); }
+
+  // assignment operators
+  __gmp_expr & operator=(const __gmp_expr &z)
+  { mpz_set(mp, z.mp); return *this; }
+  template <class T, class U>
+  __gmp_expr<value_type, value_type> & operator=(const __gmp_expr<T, U> &expr)
+  { __gmp_set_expr(mp, expr); return *this; }
+
+  __gmp_expr & operator=(signed char c) { mpz_set_si(mp, c); return *this; }
+  __gmp_expr & operator=(unsigned char c) { mpz_set_ui(mp, c); return *this; }
+
+  __gmp_expr & operator=(signed int i) { mpz_set_si(mp, i); return *this; }
+  __gmp_expr & operator=(unsigned int i) { mpz_set_ui(mp, i); return *this; }
+
+  __gmp_expr & operator=(signed short int s)
+  { mpz_set_si(mp, s); return *this; }
+  __gmp_expr & operator=(unsigned short int s)
+  { mpz_set_ui(mp, s); return *this; }
+
+  __gmp_expr & operator=(signed long int l)
+  { mpz_set_si(mp, l); return *this; }
+  __gmp_expr & operator=(unsigned long int l)
+  { mpz_set_ui(mp, l); return *this; }
+
+  __gmp_expr & operator=(float f) { mpz_set_d(mp, f); return *this; }
+  __gmp_expr & operator=(double d) { mpz_set_d(mp, d); return *this; }
+  // __gmp_expr & operator=(long double ld)
+  // { mpz_set_ld(mp, ld); return *this; }
+
+  __gmp_expr & operator=(const char *s)
+  {
+    if (mpz_set_str (mp, s, 0) != 0)
+      throw std::invalid_argument ("mpz_set_str");
+    return *this;
+  }
+  __gmp_expr & operator=(const std::string &s)
+  {
+    if (mpz_set_str(mp, s.c_str(), 0) != 0)
+      throw std::invalid_argument ("mpz_set_str");
+    return *this;
+  }
+
+  // string input/output functions
+  int set_str(const char *s, int base)
+  { return mpz_set_str(mp, s, base); }
+  int set_str(const std::string &s, int base)
+  { return mpz_set_str(mp, s.c_str(), base); }
+  std::string get_str(int base = 10) const
+  {
+    __gmp_alloc_cstring temp(mpz_get_str(0, base, mp));
+    return std::string(temp.str);
+  }
+
+  // conversion functions
+  mpz_srcptr __get_mp() const { return mp; }
+  mpz_ptr __get_mp() { return mp; }
+  mpz_srcptr get_mpz_t() const { return mp; }
+  mpz_ptr get_mpz_t() { return mp; }
+
+  signed long int get_si() const { return mpz_get_si(mp); }
+  unsigned long int get_ui() const { return mpz_get_ui(mp); }
+  double get_d() const { return mpz_get_d(mp); }
+
+  // bool fits_schar_p() const { return mpz_fits_schar_p(mp); }
+  // bool fits_uchar_p() const { return mpz_fits_uchar_p(mp); }
+  bool fits_sint_p() const { return mpz_fits_sint_p(mp); }
+  bool fits_uint_p() const { return mpz_fits_uint_p(mp); }
+  bool fits_sshort_p() const { return mpz_fits_sshort_p(mp); }
+  bool fits_ushort_p() const { return mpz_fits_ushort_p(mp); }
+  bool fits_slong_p() const { return mpz_fits_slong_p(mp); }
+  bool fits_ulong_p() const { return mpz_fits_ulong_p(mp); }
+  // bool fits_float_p() const { return mpz_fits_float_p(mp); }
+  // bool fits_double_p() const { return mpz_fits_double_p(mp); }
+  // bool fits_ldouble_p() const { return mpz_fits_ldouble_p(mp); }
+
+  // member operators
+  __GMP_DECLARE_COMPOUND_OPERATOR(operator+=)
+  __GMP_DECLARE_COMPOUND_OPERATOR(operator-=)
+  __GMP_DECLARE_COMPOUND_OPERATOR(operator*=)
+  __GMP_DECLARE_COMPOUND_OPERATOR(operator/=)
+  __GMP_DECLARE_COMPOUND_OPERATOR(operator%=)
+
+  __GMPP_DECLARE_COMPOUND_OPERATOR(operator&=)
+  __GMPP_DECLARE_COMPOUND_OPERATOR(operator|=)
+  __GMPP_DECLARE_COMPOUND_OPERATOR(operator^=)
+
+  __GMP_DECLARE_COMPOUND_OPERATOR_UI(operator<<=)
+  __GMP_DECLARE_COMPOUND_OPERATOR_UI(operator>>=)
+
+  __GMP_DECLARE_INCREMENT_OPERATOR(operator++)
+  __GMP_DECLARE_INCREMENT_OPERATOR(operator--)
+};
+
+typedef __gmp_expr<mpz_t, mpz_t> mpz_class;
+
+
+/**************** mpq_class -- wrapper for mpq_t ****************/
+
+template <>
+class __gmp_expr<mpq_t, mpq_t>
+{
+private:
+  typedef mpq_t value_type;
+  value_type mp;
+public:
+  unsigned long int get_prec() const { return mpf_get_default_prec(); }
+  void canonicalize() { mpq_canonicalize(mp); }
+
+  // constructors and destructor
+  __gmp_expr() { mpq_init(mp); }
+
+  __gmp_expr(const __gmp_expr &q) { mpq_init(mp); mpq_set(mp, q.mp); }
+  template <class T, class U>
+  __gmp_expr(const __gmp_expr<T, U> &expr)
+  { mpq_init(mp); __gmp_set_expr(mp, expr); }
+
+  __gmp_expr(signed char c) { mpq_init(mp); mpq_set_si(mp, c, 1); }
+  __gmp_expr(unsigned char c) { mpq_init(mp); mpq_set_ui(mp, c, 1); }
+
+  __gmp_expr(signed int i) { mpq_init(mp); mpq_set_si(mp, i, 1); }
+  __gmp_expr(unsigned int i) { mpq_init(mp); mpq_set_ui(mp, i, 1); }
+
+  __gmp_expr(signed short int s) { mpq_init(mp); mpq_set_si(mp, s, 1); }
+  __gmp_expr(unsigned short int s) { mpq_init(mp); mpq_set_ui(mp, s, 1); }
+
+  __gmp_expr(signed long int l) { mpq_init(mp); mpq_set_si(mp, l, 1); }
+  __gmp_expr(unsigned long int l) { mpq_init(mp); mpq_set_ui(mp, l, 1); }
+
+  __gmp_expr(float f) { mpq_init(mp); mpq_set_d(mp, f); }
+  __gmp_expr(double d) { mpq_init(mp); mpq_set_d(mp, d); }
+  // __gmp_expr(long double ld) { mpq_init(mp); mpq_set_ld(mp, ld); }
+
+  explicit __gmp_expr(const char *s)
+  {
+    mpq_init (mp);
+    if (mpq_set_str (mp, s, 0) != 0)
+      {
+        mpq_clear (mp);
+        throw std::invalid_argument ("mpq_set_str");
+      }
+  }
+  __gmp_expr(const char *s, int base)
+  {
+    mpq_init (mp);
+    if (mpq_set_str(mp, s, base) != 0)
+      {
+        mpq_clear (mp);
+        throw std::invalid_argument ("mpq_set_str");
+      }
+  }
+  explicit __gmp_expr(const std::string &s)
+  {
+    mpq_init (mp);
+    if (mpq_set_str (mp, s.c_str(), 0) != 0)
+      {
+        mpq_clear (mp);
+        throw std::invalid_argument ("mpq_set_str");
+      }
+  }
+  __gmp_expr(const std::string &s, int base)
+  {
+    mpq_init(mp);
+    if (mpq_set_str (mp, s.c_str(), base) != 0)
+      {
+        mpq_clear (mp);
+        throw std::invalid_argument ("mpq_set_str");
+      }
+  }
+  explicit __gmp_expr(mpq_srcptr q) { mpq_init(mp); mpq_set(mp, q); }
+
+  __gmp_expr(const mpz_class &num, const mpz_class &den)
+  {
+    mpq_init(mp);
+    mpz_set(mpq_numref(mp), num.get_mpz_t());
+    mpz_set(mpq_denref(mp), den.get_mpz_t());
+  }
+
+  ~__gmp_expr() { mpq_clear(mp); }
+
+  // assignment operators
+  __gmp_expr & operator=(const __gmp_expr &q)
+  { mpq_set(mp, q.mp); return *this; }
+  template <class T, class U>
+  __gmp_expr<value_type, value_type> & operator=(const __gmp_expr<T, U> &expr)
+  { __gmp_set_expr(mp, expr); return *this; }
+
+  __gmp_expr & operator=(signed char c)
+  { mpq_set_si(mp, c, 1); return *this; }
+  __gmp_expr & operator=(unsigned char c)
+  { mpq_set_ui(mp, c, 1); return *this; }
+
+  __gmp_expr & operator=(signed int i) { mpq_set_si(mp, i, 1); return *this; }
+  __gmp_expr & operator=(unsigned int i)
+  { mpq_set_ui(mp, i, 1); return *this; }
+
+  __gmp_expr & operator=(signed short int s)
+  { mpq_set_si(mp, s, 1); return *this; }
+  __gmp_expr & operator=(unsigned short int s)
+  { mpq_set_ui(mp, s, 1); return *this; }
+
+  __gmp_expr & operator=(signed long int l)
+  { mpq_set_si(mp, l, 1); return *this; }
+  __gmp_expr & operator=(unsigned long int l)
+  { mpq_set_ui(mp, l, 1); return *this; }
+
+  __gmp_expr & operator=(float f) { mpq_set_d(mp, f); return *this; }
+  __gmp_expr & operator=(double d) { mpq_set_d(mp, d); return *this; }
+  // __gmp_expr & operator=(long double ld)
+  // { mpq_set_ld(mp, ld); return *this; }
+
+  __gmp_expr & operator=(const char *s)
+  {
+    if (mpq_set_str (mp, s, 0) != 0)
+      throw std::invalid_argument ("mpq_set_str");
+    return *this;
+  }
+  __gmp_expr & operator=(const std::string &s)
+  {
+    if (mpq_set_str(mp, s.c_str(), 0) != 0)
+      throw std::invalid_argument ("mpq_set_str");
+    return *this;
+  }
+
+  // string input/output functions
+  int set_str(const char *s, int base)
+  { return mpq_set_str(mp, s, base); }
+  int set_str(const std::string &s, int base)
+  { return mpq_set_str(mp, s.c_str(), base); }
+  std::string get_str(int base = 10) const
+  {
+    __gmp_alloc_cstring temp(mpq_get_str(0, base, mp));
+    return std::string(temp.str);
+  }
+
+  // conversion functions
+
+  // casting a reference to an mpz_t to mpz_class & is a dirty hack,
+  // but works because the internal representation of mpz_class is
+  // exactly an mpz_t
+  const mpz_class & get_num() const
+  { return reinterpret_cast<const mpz_class &>(*mpq_numref(mp)); }
+  mpz_class & get_num()
+  { return reinterpret_cast<mpz_class &>(*mpq_numref(mp)); }
+  const mpz_class & get_den() const
+  { return reinterpret_cast<const mpz_class &>(*mpq_denref(mp)); }
+  mpz_class & get_den()
+  { return reinterpret_cast<mpz_class &>(*mpq_denref(mp)); }
+
+  mpq_srcptr __get_mp() const { return mp; }
+  mpq_ptr __get_mp() { return mp; }
+  mpq_srcptr get_mpq_t() const { return mp; }
+  mpq_ptr get_mpq_t() { return mp; }
+
+  mpz_srcptr get_num_mpz_t() const { return mpq_numref(mp); }
+  mpz_ptr get_num_mpz_t() { return mpq_numref(mp); }
+  mpz_srcptr get_den_mpz_t() const { return mpq_denref(mp); }
+  mpz_ptr get_den_mpz_t() { return mpq_denref(mp); }
+
+  double get_d() const { return mpq_get_d(mp); }
+
+  // compound assignments
+  __GMP_DECLARE_COMPOUND_OPERATOR(operator+=)
+  __GMP_DECLARE_COMPOUND_OPERATOR(operator-=)
+  __GMP_DECLARE_COMPOUND_OPERATOR(operator*=)
+  __GMP_DECLARE_COMPOUND_OPERATOR(operator/=)
+
+  __GMP_DECLARE_COMPOUND_OPERATOR_UI(operator<<=)
+  __GMP_DECLARE_COMPOUND_OPERATOR_UI(operator>>=)
+
+  __GMP_DECLARE_INCREMENT_OPERATOR(operator++)
+  __GMP_DECLARE_INCREMENT_OPERATOR(operator--)
+};
+
+typedef __gmp_expr<mpq_t, mpq_t> mpq_class;
+
+
+/**************** mpf_class -- wrapper for mpf_t ****************/
+
+template <>
+class __gmp_expr<mpf_t, mpf_t>
+{
+private:
+  typedef mpf_t value_type;
+  value_type mp;
+public:
+  unsigned long int get_prec() const { return mpf_get_prec(mp); }
+
+  void set_prec(unsigned long int prec) { mpf_set_prec(mp, prec); }
+  void set_prec_raw(unsigned long int prec) { mpf_set_prec_raw(mp, prec); }
+
+  // constructors and destructor
+  __gmp_expr() { mpf_init(mp); }
+
+  __gmp_expr(const __gmp_expr &f)
+  { mpf_init2(mp, f.get_prec()); mpf_set(mp, f.mp); }
+  __gmp_expr(const __gmp_expr &f, unsigned long int prec)
+  { mpf_init2(mp, prec); mpf_set(mp, f.mp); }
+  template <class T, class U>
+  __gmp_expr(const __gmp_expr<T, U> &expr)
+  { mpf_init2(mp, expr.get_prec()); __gmp_set_expr(mp, expr); }
+  template <class T, class U>
+  __gmp_expr(const __gmp_expr<T, U> &expr, unsigned long int prec)
+  { mpf_init2(mp, prec); __gmp_set_expr(mp, expr); }
+
+  __gmp_expr(signed char c) { mpf_init_set_si(mp, c); }
+  __gmp_expr(signed char c, unsigned long int prec)
+  { mpf_init2(mp, prec); mpf_set_si(mp, c); }
+  __gmp_expr(unsigned char c) { mpf_init_set_ui(mp, c); }
+  __gmp_expr(unsigned char c, unsigned long int prec)
+  { mpf_init2(mp, prec); mpf_set_ui(mp, c); }
+
+  __gmp_expr(signed int i) { mpf_init_set_si(mp, i); }
+  __gmp_expr(signed int i, unsigned long int prec)
+  { mpf_init2(mp, prec); mpf_set_si(mp, i); }
+  __gmp_expr(unsigned int i) { mpf_init_set_ui(mp, i); }
+  __gmp_expr(unsigned int i, unsigned long int prec)
+  { mpf_init2(mp, prec); mpf_set_ui(mp, i); }
+
+  __gmp_expr(signed short int s) { mpf_init_set_si(mp, s); }
+  __gmp_expr(signed short int s, unsigned long int prec)
+  { mpf_init2(mp, prec); mpf_set_si(mp, s); }
+  __gmp_expr(unsigned short int s) { mpf_init_set_ui(mp, s); }
+  __gmp_expr(unsigned short int s, unsigned long int prec)
+  { mpf_init2(mp, prec); mpf_set_ui(mp, s); }
+
+  __gmp_expr(signed long int l) { mpf_init_set_si(mp, l); }
+  __gmp_expr(signed long int l, unsigned long int prec)
+  { mpf_init2(mp, prec); mpf_set_si(mp, l); }
+  __gmp_expr(unsigned long int l) { mpf_init_set_ui(mp, l); }
+  __gmp_expr(unsigned long int l, unsigned long int prec)
+  { mpf_init2(mp, prec); mpf_set_ui(mp, l); }
+
+  __gmp_expr(float f) { mpf_init_set_d(mp, f); }
+  __gmp_expr(float f, unsigned long int prec)
+  { mpf_init2(mp, prec); mpf_set_d(mp, f); }
+  __gmp_expr(double d) { mpf_init_set_d(mp, d); }
+  __gmp_expr(double d, unsigned long int prec)
+  { mpf_init2(mp, prec); mpf_set_d(mp, d); }
+  // __gmp_expr(long double ld) { mpf_init_set_d(mp, ld); }
+  // __gmp_expr(long double ld, unsigned long int prec)
+  // { mpf_init2(mp, prec); mpf_set_d(mp, ld); }
+
+  explicit __gmp_expr(const char *s)
+  {
+    if (mpf_init_set_str (mp, s, 0) != 0)
+      {
+        mpf_clear (mp);
+        throw std::invalid_argument ("mpf_set_str");
+      }
+  }
+  __gmp_expr(const char *s, unsigned long int prec, int base = 0)
+  {
+    mpf_init2(mp, prec);
+    if (mpf_set_str(mp, s, base) != 0)
+      {
+        mpf_clear (mp);
+        throw std::invalid_argument ("mpf_set_str");
+      }
+  }
+  explicit __gmp_expr(const std::string &s)
+  {
+    if (mpf_init_set_str(mp, s.c_str(), 0) != 0)
+      {
+        mpf_clear (mp);
+        throw std::invalid_argument ("mpf_set_str");
+      }
+  }
+  __gmp_expr(const std::string &s, unsigned long int prec, int base = 0)
+  {
+    mpf_init2(mp, prec);
+    if (mpf_set_str(mp, s.c_str(), base) != 0)
+      {
+        mpf_clear (mp);
+        throw std::invalid_argument ("mpf_set_str");
+      }
+  }
+
+  explicit __gmp_expr(mpf_srcptr f)
+  { mpf_init2(mp, mpf_get_prec(f)); mpf_set(mp, f); }
+  __gmp_expr(mpf_srcptr f, unsigned long int prec)
+  { mpf_init2(mp, prec); mpf_set(mp, f); }
+
+  ~__gmp_expr() { mpf_clear(mp); }
+
+  // assignment operators
+  __gmp_expr & operator=(const __gmp_expr &f)
+  { mpf_set(mp, f.mp); return *this; }
+  template <class T, class U>
+  __gmp_expr<value_type, value_type> & operator=(const __gmp_expr<T, U> &expr)
+  { __gmp_set_expr(mp, expr); return *this; }
+
+  __gmp_expr & operator=(signed char c) { mpf_set_si(mp, c); return *this; }
+  __gmp_expr & operator=(unsigned char c) { mpf_set_ui(mp, c); return *this; }
+
+  __gmp_expr & operator=(signed int i) { mpf_set_si(mp, i); return *this; }
+  __gmp_expr & operator=(unsigned int i) { mpf_set_ui(mp, i); return *this; }
+
+  __gmp_expr & operator=(signed short int s)
+  { mpf_set_si(mp, s); return *this; }
+  __gmp_expr & operator=(unsigned short int s)
+  { mpf_set_ui(mp, s); return *this; }
+
+  __gmp_expr & operator=(signed long int l)
+  { mpf_set_si(mp, l); return *this; }
+  __gmp_expr & operator=(unsigned long int l)
+  { mpf_set_ui(mp, l); return *this; }
+
+  __gmp_expr & operator=(float f) { mpf_set_d(mp, f); return *this; }
+  __gmp_expr & operator=(double d) { mpf_set_d(mp, d); return *this; }
+  // __gmp_expr & operator=(long double ld)
+  // { mpf_set_ld(mp, ld); return *this; }
+
+  __gmp_expr & operator=(const char *s)
+  {
+    if (mpf_set_str (mp, s, 0) != 0)
+      throw std::invalid_argument ("mpf_set_str");
+    return *this;
+  }
+  __gmp_expr & operator=(const std::string &s)
+  {
+    if (mpf_set_str(mp, s.c_str(), 0) != 0)
+      throw std::invalid_argument ("mpf_set_str");
+    return *this;
+  }
+
+  // string input/output functions
+  int set_str(const char *s, int base)
+  { return mpf_set_str(mp, s, base); }
+  int set_str(const std::string &s, int base)
+  { return mpf_set_str(mp, s.c_str(), base); }
+  std::string get_str(mp_exp_t &expo, int base = 10, size_t size = 0) const
+  {
+    __gmp_alloc_cstring temp(mpf_get_str(0, &expo, base, size, mp));
+    return std::string(temp.str);
+  }
+
+  // conversion functions
+  mpf_srcptr __get_mp() const { return mp; }
+  mpf_ptr __get_mp() { return mp; }
+  mpf_srcptr get_mpf_t() const { return mp; }
+  mpf_ptr get_mpf_t() { return mp; }
+
+  signed long int get_si() const { return mpf_get_si(mp); }
+  unsigned long int get_ui() const { return mpf_get_ui(mp); }
+  double get_d() const { return mpf_get_d(mp); }
+
+  // bool fits_schar_p() const { return mpf_fits_schar_p(mp); }
+  // bool fits_uchar_p() const { return mpf_fits_uchar_p(mp); }
+  bool fits_sint_p() const { return mpf_fits_sint_p(mp); }
+  bool fits_uint_p() const { return mpf_fits_uint_p(mp); }
+  bool fits_sshort_p() const { return mpf_fits_sshort_p(mp); }
+  bool fits_ushort_p() const { return mpf_fits_ushort_p(mp); }
+  bool fits_slong_p() const { return mpf_fits_slong_p(mp); }
+  bool fits_ulong_p() const { return mpf_fits_ulong_p(mp); }
+  // bool fits_float_p() const { return mpf_fits_float_p(mp); }
+  // bool fits_double_p() const { return mpf_fits_double_p(mp); }
+  // bool fits_ldouble_p() const { return mpf_fits_ldouble_p(mp); }
+
+  // compound assignments
+  __GMP_DECLARE_COMPOUND_OPERATOR(operator+=)
+  __GMP_DECLARE_COMPOUND_OPERATOR(operator-=)
+  __GMP_DECLARE_COMPOUND_OPERATOR(operator*=)
+  __GMP_DECLARE_COMPOUND_OPERATOR(operator/=)
+
+  __GMP_DECLARE_COMPOUND_OPERATOR_UI(operator<<=)
+  __GMP_DECLARE_COMPOUND_OPERATOR_UI(operator>>=)
+
+  __GMP_DECLARE_INCREMENT_OPERATOR(operator++)
+  __GMP_DECLARE_INCREMENT_OPERATOR(operator--)
+};
+
+typedef __gmp_expr<mpf_t, mpf_t> mpf_class;
+
+
+
+/**************** I/O operators ****************/
+
+// these should (and will) be provided separately
+
+template <class T>
+inline std::ostream & operator<<
+(std::ostream &o, const __gmp_expr<T, T> &expr)
+{
+  return o << expr.__get_mp();
+}
+
+template <class T, class U>
+inline std::ostream & operator<<
+(std::ostream &o, const __gmp_expr<T, U> &expr)
+{
+  __gmp_expr<T, T> temp(expr);
+  return o << temp.__get_mp();
+}
+
+
+template <class T>
+inline std::istream & operator>>(std::istream &i, __gmp_expr<T, T> &expr)
+{
+  return i >> expr.__get_mp();
+}
+
+inline std::istream & operator>>(std::istream &i, mpq_class &q)
+{
+  i >> q.get_mpq_t();
+  // q.canonicalize(); // you might want to uncomment this
+  return i;
+}
+
+
+/**************** Functions for type conversion ****************/
+
+template <>
+inline void __gmp_set_expr(mpz_ptr z, const mpz_class &w)
+{
+  mpz_set(z, w.get_mpz_t());
+}
+
+template <class T>
+inline void __gmp_set_expr(mpz_ptr z, const __gmp_expr<mpz_t, T> &expr)
+{
+  expr.eval(z);
+}
+
+template <>
+inline void __gmp_set_expr(mpz_ptr z, const mpq_class &q)
+{
+  mpz_set_q(z, q.get_mpq_t());
+}
+
+template <class T>
+inline void __gmp_set_expr(mpz_ptr z, const __gmp_expr<mpq_t, T> &expr)
+{
+  mpq_class temp(expr);
+  mpz_set_q(z, temp.get_mpq_t());
+}
+
+template <class T>
+inline void __gmp_set_expr(mpz_ptr z, const mpf_class &f)
+{
+  mpz_set_f(z, f.get_mpf_t());
+}
+
+template <class T>
+inline void __gmp_set_expr(mpz_ptr z, const __gmp_expr<mpf_t, T> &expr)
+{
+  mpf_class temp(expr);
+  mpz_set_f(z, temp.get_mpf_t());
+}
+
+template <>
+inline void __gmp_set_expr(mpq_ptr q, const mpz_class &z)
+{
+  mpq_set_z(q, z.get_mpz_t());
+}
+
+template <class T>
+inline void __gmp_set_expr(mpq_ptr q, const __gmp_expr<mpz_t, T> &expr)
+{
+  mpz_class temp(expr);
+  mpq_set_z(q, temp.get_mpz_t());
+}
+
+template <>
+inline void __gmp_set_expr(mpq_ptr q, const mpq_class &r)
+{
+  mpq_set(q, r.get_mpq_t());
+}
+
+template <class T>
+inline void __gmp_set_expr(mpq_ptr q, const __gmp_expr<mpq_t, T> &expr)
+{
+  expr.eval(q);
+}
+
+template <class T>
+inline void __gmp_set_expr(mpq_ptr q, const mpf_class &f)
+{
+  mpq_set_f(q, f.get_mpf_t());
+}
+
+template <class T>
+inline void __gmp_set_expr(mpq_ptr q, const __gmp_expr<mpf_t, T> &expr)
+{
+  mpf_class temp(expr);
+  mpq_set_f(q, temp.get_mpf_t());
+}
+
+template <class T>
+inline void __gmp_set_expr(mpf_ptr f, const mpz_class &z)
+{
+  mpf_set_z(f, z.get_mpz_t());
+}
+
+template <class T>
+inline void __gmp_set_expr(mpf_ptr f, const __gmp_expr<mpz_t, T> &expr)
+{
+  mpz_class temp(expr);
+  mpf_set_z(f, temp.get_mpz_t());
+}
+
+template <class T>
+inline void __gmp_set_expr(mpf_ptr f, const mpq_class &q)
+{
+  mpf_set_q(f, q.get_mpq_t());
+}
+
+template <class T>
+inline void __gmp_set_expr(mpf_ptr f, const __gmp_expr<mpq_t, T> &expr)
+{
+  mpq_class temp(expr);
+  mpf_set_q(f, temp.get_mpq_t());
+}
+
+template <>
+inline void __gmp_set_expr(mpf_ptr f, const mpf_class &g)
+{
+  mpf_set(f, g.get_mpf_t());
+}
+
+template <class T>
+inline void __gmp_set_expr(mpf_ptr f, const __gmp_expr<mpf_t, T> &expr)
+{
+  expr.eval(f, mpf_get_prec(f));
+}
+
+
+/**************** Specializations of __gmp_expr ****************/
+/* The eval() method of __gmp_expr<T, U> evaluates the corresponding
+   expression and assigns the result to its argument, which is either an
+   mpz_t, mpq_t, or mpf_t as specified by the T argument.
+   Compound expressions are evaluated recursively (temporaries are created
+   to hold intermediate values), while for simple expressions the eval()
+   method of the appropriate function object (available as the Op argument
+   of either __gmp_unary_expr<T, Op> or __gmp_binary_expr<T, U, Op>) is
+   called. */
+
+
+/**************** Unary expressions ****************/
+/* cases:
+   - simple:   argument is mp*_class, that is, __gmp_expr<T, T>
+   - compound: argument is __gmp_expr<T, U> (with U not equal to T) */
+
+
+// simple expressions
+
+template <class T, class Op>
+class __gmp_expr<T, __gmp_unary_expr<__gmp_expr<T, T>, Op> >
+{
+private:
+  typedef __gmp_expr<T, T> val_type;
+
+  __gmp_unary_expr<val_type, Op> expr;
+public:
+  __gmp_expr(const val_type &val) : expr(val) { }
+  void eval(typename __gmp_resolve_expr<T>::ptr_type p,
+	    unsigned long int = 0) const
+  { Op::eval(p, expr.val.__get_mp()); }
+  const val_type & get_val() const { return expr.val; }
+  unsigned long int get_prec() const { return expr.val.get_prec(); }
+};
+
+
+// compound expressions
+
+template <class T, class U, class Op>
+class __gmp_expr<T, __gmp_unary_expr<__gmp_expr<T, U>, Op> >
+{
+private:
+  typedef __gmp_expr<T, U> val_type;
+
+  __gmp_unary_expr<val_type, Op> expr;
+public:
+  __gmp_expr(const val_type &val) : expr(val) { }
+  void eval(typename __gmp_resolve_expr<T>::ptr_type p) const
+  { __gmp_expr<T, T> temp(expr.val); Op::eval(p, temp.__get_mp()); }
+  void eval(typename __gmp_resolve_expr<T>::ptr_type p,
+	    unsigned long int prec) const
+  { __gmp_expr<T, T> temp(expr.val, prec); Op::eval(p, temp.__get_mp()); }
+  const val_type & get_val() const { return expr.val; }
+  unsigned long int get_prec() const { return expr.val.get_prec(); }
+};
+
+
+/**************** Binary expressions ****************/
+/* simple:
+   - arguments are both mp*_class
+   - one argument is mp*_class, one is a built-in type
+   compound:
+   - one is mp*_class, one is __gmp_expr<T, U>
+   - one is __gmp_expr<T, U>, one is built-in
+   - both arguments are __gmp_expr<...> */
+
+
+// simple expressions
+
+template <class T, class Op>
+class __gmp_expr
+<T, __gmp_binary_expr<__gmp_expr<T, T>, __gmp_expr<T, T>, Op> >
+{
+private:
+  typedef __gmp_expr<T, T> val1_type;
+  typedef __gmp_expr<T, T> val2_type;
+
+  __gmp_binary_expr<val1_type, val2_type, Op> expr;
+public:
+  __gmp_expr(const val1_type &val1, const val2_type &val2)
+    : expr(val1, val2) { }
+  void eval(typename __gmp_resolve_expr<T>::ptr_type p,
+	    unsigned long int = 0) const
+  { Op::eval(p, expr.val1.__get_mp(), expr.val2.__get_mp()); }
+  const val1_type & get_val1() const { return expr.val1; }
+  const val2_type & get_val2() const { return expr.val2; }
+  unsigned long int get_prec() const
+  {
+    unsigned long int prec1 = expr.val1.get_prec(),
+      prec2 = expr.val2.get_prec();
+    return (prec1 > prec2) ? prec1 : prec2;
+  }
+};
+
+
+// simple expressions, T is a built-in numerical type
+
+template <class T, class U, class Op>
+class __gmp_expr<T, __gmp_binary_expr<__gmp_expr<T, T>, U, Op> >
+{
+private:
+  typedef __gmp_expr<T, T> val1_type;
+  typedef U val2_type;
+
+  __gmp_binary_expr<val1_type, val2_type, Op> expr;
+public:
+  __gmp_expr(const val1_type &val1, const val2_type &val2)
+    : expr(val1, val2) { }
+  void eval(typename __gmp_resolve_expr<T>::ptr_type p,
+	    unsigned long int = 0) const
+  { Op::eval(p, expr.val1.__get_mp(), expr.val2); }
+  const val1_type & get_val1() const { return expr.val1; }
+  const val2_type & get_val2() const { return expr.val2; }
+  unsigned long int get_prec() const { return expr.val1.get_prec(); }
+};
+
+template <class T, class U, class Op>
+class __gmp_expr<T, __gmp_binary_expr<U, __gmp_expr<T, T>, Op> >
+{
+private:
+  typedef U val1_type;
+  typedef __gmp_expr<T, T> val2_type;
+
+  __gmp_binary_expr<val1_type, val2_type, Op> expr;
+public:
+  __gmp_expr(const val1_type &val1, const val2_type &val2)
+    : expr(val1, val2) { }
+  void eval(typename __gmp_resolve_expr<T>::ptr_type p,
+	    unsigned long int = 0) const
+  { Op::eval(p, expr.val1, expr.val2.__get_mp()); }
+  const val1_type & get_val1() const { return expr.val1; }
+  const val2_type & get_val2() const { return expr.val2; }
+  unsigned long int get_prec() const { return expr.val2.get_prec(); }
+};
+
+
+// compound expressions, one argument is a subexpression
+
+template <class T, class U, class V, class Op>
+class __gmp_expr
+<T, __gmp_binary_expr<__gmp_expr<T, T>, __gmp_expr<U, V>, Op> >
+{
+private:
+  typedef __gmp_expr<T, T> val1_type;
+  typedef __gmp_expr<U, V> val2_type;
+
+  __gmp_binary_expr<val1_type, val2_type, Op> expr;
+public:
+  __gmp_expr(const val1_type &val1, const val2_type &val2)
+    : expr(val1, val2) { }
+  void eval(typename __gmp_resolve_expr<T>::ptr_type p) const
+  {
+    __gmp_expr<T, T> temp(expr.val2);
+    Op::eval(p, expr.val1.__get_mp(), temp.__get_mp());
+  }
+  void eval(typename __gmp_resolve_expr<T>::ptr_type p,
+	    unsigned long int prec) const
+  {
+    __gmp_expr<T, T> temp(expr.val2, prec);
+    Op::eval(p, expr.val1.__get_mp(), temp.__get_mp());
+  }
+  const val1_type & get_val1() const { return expr.val1; }
+  const val2_type & get_val2() const { return expr.val2; }
+  unsigned long int get_prec() const
+  {
+    unsigned long int prec1 = expr.val1.get_prec(),
+      prec2 = expr.val2.get_prec();
+    return (prec1 > prec2) ? prec1 : prec2;
+  }
+};
+
+template <class T, class U, class V, class Op>
+class __gmp_expr
+<T, __gmp_binary_expr<__gmp_expr<U, V>, __gmp_expr<T, T>, Op> >
+{
+private:
+  typedef __gmp_expr<U, V> val1_type;
+  typedef __gmp_expr<T, T> val2_type;
+
+  __gmp_binary_expr<val1_type, val2_type, Op> expr;
+public:
+  __gmp_expr(const val1_type &val1, const val2_type &val2)
+    : expr(val1, val2) { }
+  void eval(typename __gmp_resolve_expr<T>::ptr_type p) const
+  {
+    __gmp_expr<T, T> temp(expr.val1);
+    Op::eval(p, temp.__get_mp(), expr.val2.__get_mp());
+  }
+  void eval(typename __gmp_resolve_expr<T>::ptr_type p,
+	    unsigned long int prec) const
+  {
+    __gmp_expr<T, T> temp(expr.val1, prec);
+    Op::eval(p, temp.__get_mp(), expr.val2.__get_mp());
+  }
+  const val1_type & get_val1() const { return expr.val1; }
+  const val2_type & get_val2() const { return expr.val2; }
+  unsigned long int get_prec() const
+  {
+    unsigned long int prec1 = expr.val1.get_prec(),
+      prec2 = expr.val2.get_prec();
+    return (prec1 > prec2) ? prec1 : prec2;
+  }
+};
+
+template <class T, class U, class Op>
+class __gmp_expr
+<T, __gmp_binary_expr<__gmp_expr<T, T>, __gmp_expr<T, U>, Op> >
+{
+private:
+  typedef __gmp_expr<T, T> val1_type;
+  typedef __gmp_expr<T, U> val2_type;
+
+  __gmp_binary_expr<val1_type, val2_type, Op> expr;
+public:
+  __gmp_expr(const val1_type &val1, const val2_type &val2)
+    : expr(val1, val2) { }
+  void eval(typename __gmp_resolve_expr<T>::ptr_type p) const
+  {
+    __gmp_expr<T, T> temp(expr.val2);
+    Op::eval(p, expr.val1.__get_mp(), temp.__get_mp());
+  }
+  void eval(typename __gmp_resolve_expr<T>::ptr_type p,
+	    unsigned long int prec) const
+  {
+    __gmp_expr<T, T> temp(expr.val2, prec);
+    Op::eval(p, expr.val1.__get_mp(), temp.__get_mp());
+  }
+  const val1_type & get_val1() const { return expr.val1; }
+  const val2_type & get_val2() const { return expr.val2; }
+  unsigned long int get_prec() const
+  {
+    unsigned long int prec1 = expr.val1.get_prec(),
+      prec2 = expr.val2.get_prec();
+    return (prec1 > prec2) ? prec1 : prec2;
+  }
+};
+
+template <class T, class U, class Op>
+class __gmp_expr
+<T, __gmp_binary_expr<__gmp_expr<T, U>, __gmp_expr<T, T>, Op> >
+{
+private:
+  typedef __gmp_expr<T, U> val1_type;
+  typedef __gmp_expr<T, T> val2_type;
+
+  __gmp_binary_expr<val1_type, val2_type, Op> expr;
+public:
+  __gmp_expr(const val1_type &val1, const val2_type &val2)
+    : expr(val1, val2) { }
+  void eval(typename __gmp_resolve_expr<T>::ptr_type p) const
+  {
+    __gmp_expr<T, T> temp(expr.val1);
+    Op::eval(p, temp.__get_mp(), expr.val2.__get_mp());
+  }
+  void eval(typename __gmp_resolve_expr<T>::ptr_type p,
+	    unsigned long int prec) const
+  {
+    __gmp_expr<T, T> temp(expr.val1, prec);
+    Op::eval(p, temp.__get_mp(), expr.val2.__get_mp());
+  }
+  const val1_type & get_val1() const { return expr.val1; }
+  const val2_type & get_val2() const { return expr.val2; }
+  unsigned long int get_prec() const
+  {
+    unsigned long int prec1 = expr.val1.get_prec(),
+      prec2 = expr.val2.get_prec();
+    return (prec1 > prec2) ? prec1 : prec2;
+  }
+};
+
+
+// one argument is a subexpression, one is a built-in
+
+template <class T, class U, class V, class Op>
+class __gmp_expr<T, __gmp_binary_expr<__gmp_expr<T, U>, V, Op> >
+{
+private:
+  typedef __gmp_expr<T, U> val1_type;
+  typedef V val2_type;
+
+  __gmp_binary_expr<val1_type, val2_type, Op> expr;
+public:
+  __gmp_expr(const val1_type &val1, const val2_type &val2)
+    : expr(val1, val2) { }
+  void eval(typename __gmp_resolve_expr<T>::ptr_type p) const
+  {
+    __gmp_expr<T, T> temp(expr.val1);
+    Op::eval(p, temp.__get_mp(), expr.val2);
+  }
+  void eval(typename __gmp_resolve_expr<T>::ptr_type p,
+	    unsigned long int prec) const
+  {
+    __gmp_expr<T, T> temp(expr.val1, prec);
+    Op::eval(p, temp.__get_mp(), expr.val2);
+  }
+  const val1_type & get_val1() const { return expr.val1; }
+  const val2_type & get_val2() const { return expr.val2; }
+  unsigned long int get_prec() const { return expr.val1.get_prec(); }
+};
+
+template <class T, class U, class V, class Op>
+class __gmp_expr<T, __gmp_binary_expr<U, __gmp_expr<T, V>, Op> >
+{
+private:
+  typedef U val1_type;
+  typedef __gmp_expr<T, V> val2_type;
+
+  __gmp_binary_expr<val1_type, val2_type, Op> expr;
+public:
+  __gmp_expr(const val1_type &val1, const val2_type &val2)
+    : expr(val1, val2) { }
+  void eval(typename __gmp_resolve_expr<T>::ptr_type p) const
+  {
+    __gmp_expr<T, T> temp(expr.val2);
+    Op::eval(p, expr.val1, temp.__get_mp());
+  }
+  void eval(typename __gmp_resolve_expr<T>::ptr_type p,
+	    unsigned long int prec) const
+  {
+    __gmp_expr<T, T> temp(expr.val2, prec);
+    Op::eval(p, expr.val1, temp.__get_mp());
+  }
+  const val1_type & get_val1() const { return expr.val1; }
+  const val2_type & get_val2() const { return expr.val2; }
+  unsigned long int get_prec() const { return expr.val2.get_prec(); }
+};
+
+
+// both arguments are subexpressions
+
+template <class T, class U, class V, class W, class Op>
+class __gmp_expr
+<T, __gmp_binary_expr<__gmp_expr<T, U>, __gmp_expr<V, W>, Op> >
+{
+private:
+  typedef __gmp_expr<T, U> val1_type;
+  typedef __gmp_expr<V, W> val2_type;
+
+  __gmp_binary_expr<val1_type, val2_type, Op> expr;
+public:
+  __gmp_expr(const val1_type &val1, const val2_type &val2)
+    : expr(val1, val2) { }
+  void eval(typename __gmp_resolve_expr<T>::ptr_type p) const
+  {
+    __gmp_expr<T, T> temp1(expr.val1), temp2(expr.val2);
+    Op::eval(p, temp1.__get_mp(), temp2.__get_mp());
+  }
+  void eval(typename __gmp_resolve_expr<T>::ptr_type p,
+	    unsigned long int prec) const
+  {
+    __gmp_expr<T, T> temp1(expr.val1, prec), temp2(expr.val2, prec);
+    Op::eval(p, temp1.__get_mp(), temp2.__get_mp());
+  }
+  const val1_type & get_val1() const { return expr.val1; }
+  const val2_type & get_val2() const { return expr.val2; }
+  unsigned long int get_prec() const
+  {
+    unsigned long int prec1 = expr.val1.get_prec(),
+      prec2 = expr.val2.get_prec();
+    return (prec1 > prec2) ? prec1 : prec2;
+  }
+};
+
+template <class T, class U, class V, class W, class Op>
+class __gmp_expr
+<T, __gmp_binary_expr<__gmp_expr<U, V>, __gmp_expr<T, W>, Op> >
+{
+private:
+  typedef __gmp_expr<U, V> val1_type;
+  typedef __gmp_expr<T, W> val2_type;
+
+  __gmp_binary_expr<val1_type, val2_type, Op> expr;
+public:
+  __gmp_expr(const val1_type &val1, const val2_type &val2)
+    : expr(val1, val2) { }
+  void eval(typename __gmp_resolve_expr<T>::ptr_type p) const
+  {
+    __gmp_expr<T, T> temp1(expr.val1), temp2(expr.val2);
+    Op::eval(p, temp1.__get_mp(), temp2.__get_mp());
+  }
+  void eval(typename __gmp_resolve_expr<T>::ptr_type p,
+	    unsigned long int prec) const
+  {
+    __gmp_expr<T, T> temp1(expr.val1, prec), temp2(expr.val2, prec);
+    Op::eval(p, temp1.__get_mp(), temp2.__get_mp());
+  }
+  const val1_type & get_val1() const { return expr.val1; }
+  const val2_type & get_val2() const { return expr.val2; }
+  unsigned long int get_prec() const
+  {
+    unsigned long int prec1 = expr.val1.get_prec(),
+      prec2 = expr.val2.get_prec();
+    return (prec1 > prec2) ? prec1 : prec2;
+  }
+};
+
+template <class T, class U, class V, class Op>
+class __gmp_expr
+<T, __gmp_binary_expr<__gmp_expr<T, U>, __gmp_expr<T, V>, Op> >
+{
+private:
+  typedef __gmp_expr<T, U> val1_type;
+  typedef __gmp_expr<T, V> val2_type;
+
+  __gmp_binary_expr<val1_type, val2_type, Op> expr;
+public:
+  __gmp_expr(const val1_type &val1, const val2_type &val2)
+    : expr(val1, val2) { }
+  void eval(typename __gmp_resolve_expr<T>::ptr_type p) const
+  {
+    __gmp_expr<T, T> temp1(expr.val1), temp2(expr.val2);
+    Op::eval(p, temp1.__get_mp(), temp2.__get_mp());
+  }
+  void eval(typename __gmp_resolve_expr<T>::ptr_type p,
+	    unsigned long int prec) const
+  {
+    __gmp_expr<T, T> temp1(expr.val1, prec), temp2(expr.val2, prec);
+    Op::eval(p, temp1.__get_mp(), temp2.__get_mp());
+  }
+  const val1_type & get_val1() const { return expr.val1; }
+  const val2_type & get_val2() const { return expr.val2; }
+  unsigned long int get_prec() const
+  {
+    unsigned long int prec1 = expr.val1.get_prec(),
+      prec2 = expr.val2.get_prec();
+    return (prec1 > prec2) ? prec1 : prec2;
+  }
+};
+
+
+/**************** Special cases ****************/
+
+/* Some operations (i.e., add and subtract) with mixed mpz/mpq arguments
+   can be done directly without first converting the mpz to mpq.
+   Appropriate specializations of __gmp_expr are required. */
+
+
+#define __GMPZQ_DEFINE_EXPR(eval_fun)                                       \
+                                                                            \
+template <>                                                                 \
+class __gmp_expr<mpq_t, __gmp_binary_expr<mpz_class, mpq_class, eval_fun> > \
+{                                                                           \
+private:                                                                    \
+  typedef mpz_class val1_type;                                              \
+  typedef mpq_class val2_type;                                              \
+                                                                            \
+  __gmp_binary_expr<val1_type, val2_type, eval_fun> expr;                   \
+public:                                                                     \
+  __gmp_expr(const val1_type &val1, const val2_type &val2)                  \
+    : expr(val1, val2) { }                                                  \
+  void eval(mpq_ptr q) const                                                \
+  { eval_fun::eval(q, expr.val1.get_mpz_t(), expr.val2.get_mpq_t()); }      \
+  const val1_type & get_val1() const { return expr.val1; }                  \
+  const val2_type & get_val2() const { return expr.val2; }                  \
+  unsigned long int get_prec() const { return mpf_get_default_prec(); }     \
+};                                                                          \
+                                                                            \
+template <>                                                                 \
+class __gmp_expr<mpq_t, __gmp_binary_expr<mpq_class, mpz_class, eval_fun> > \
+{                                                                           \
+private:                                                                    \
+  typedef mpq_class val1_type;                                              \
+  typedef mpz_class val2_type;                                              \
+                                                                            \
+  __gmp_binary_expr<val1_type, val2_type, eval_fun> expr;                   \
+public:                                                                     \
+  __gmp_expr(const val1_type &val1, const val2_type &val2)                  \
+    : expr(val1, val2) { }                                                  \
+  void eval(mpq_ptr q) const                                                \
+  { eval_fun::eval(q, expr.val1.get_mpq_t(), expr.val2.get_mpz_t()); }      \
+  const val1_type & get_val1() const { return expr.val1; }                  \
+  const val2_type & get_val2() const { return expr.val2; }                  \
+  unsigned long int get_prec() const { return mpf_get_default_prec(); }     \
+};                                                                          \
+                                                                            \
+template <class T>                                                          \
+class __gmp_expr                                                            \
+<mpq_t, __gmp_binary_expr<mpz_class, __gmp_expr<mpq_t, T>, eval_fun> >      \
+{                                                                           \
+private:                                                                    \
+  typedef mpz_class val1_type;                                              \
+  typedef __gmp_expr<mpq_t, T> val2_type;                                   \
+                                                                            \
+  __gmp_binary_expr<val1_type, val2_type, eval_fun> expr;                   \
+public:                                                                     \
+  __gmp_expr(const val1_type &val1, const val2_type &val2)                  \
+    : expr(val1, val2) { }                                                  \
+  void eval(mpq_ptr q) const                                                \
+  {                                                                         \
+    mpq_class temp(expr.val2);                                              \
+    eval_fun::eval(q, expr.val1.get_mpz_t(), temp.get_mpq_t());             \
+  }                                                                         \
+  const val1_type & get_val1() const { return expr.val1; }                  \
+  const val2_type & get_val2() const { return expr.val2; }                  \
+  unsigned long int get_prec() const { return mpf_get_default_prec(); }     \
+};                                                                          \
+                                                                            \
+template <class T>                                                          \
+class __gmp_expr                                                            \
+<mpq_t, __gmp_binary_expr<mpq_class, __gmp_expr<mpz_t, T>, eval_fun> >      \
+{                                                                           \
+private:                                                                    \
+  typedef mpq_class val1_type;                                              \
+  typedef __gmp_expr<mpz_t, T> val2_type;                                   \
+                                                                            \
+  __gmp_binary_expr<val1_type, val2_type, eval_fun> expr;                   \
+public:                                                                     \
+  __gmp_expr(const val1_type &val1, const val2_type &val2)                  \
+    : expr(val1, val2) { }                                                  \
+  void eval(mpq_ptr q) const                                                \
+  {                                                                         \
+    mpz_class temp(expr.val2);                                              \
+    eval_fun::eval(q, expr.val1.get_mpq_t(), temp.get_mpz_t());             \
+  }                                                                         \
+  const val1_type & get_val1() const { return expr.val1; }                  \
+  const val2_type & get_val2() const { return expr.val2; }                  \
+  unsigned long int get_prec() const { return mpf_get_default_prec(); }     \
+};                                                                          \
+                                                                            \
+template <class T>                                                          \
+class __gmp_expr                                                            \
+<mpq_t, __gmp_binary_expr<__gmp_expr<mpz_t, T>, mpq_class, eval_fun> >      \
+{                                                                           \
+private:                                                                    \
+  typedef __gmp_expr<mpz_t, T> val1_type;                                   \
+  typedef mpq_class val2_type;                                              \
+                                                                            \
+  __gmp_binary_expr<val1_type, val2_type, eval_fun> expr;                   \
+public:                                                                     \
+  __gmp_expr(const val1_type &val1, const val2_type &val2)                  \
+    : expr(val1, val2) { }                                                  \
+  void eval(mpq_ptr q) const                                                \
+  {                                                                         \
+    mpz_class temp(expr.val1);                                              \
+    eval_fun::eval(q, temp.get_mpz_t(), expr.val2.get_mpq_t());             \
+  }                                                                         \
+  const val1_type & get_val1() const { return expr.val1; }                  \
+  const val2_type & get_val2() const { return expr.val2; }                  \
+  unsigned long int get_prec() const { return mpf_get_default_prec(); }     \
+};                                                                          \
+                                                                            \
+template <class T>                                                          \
+class __gmp_expr                                                            \
+<mpq_t, __gmp_binary_expr<__gmp_expr<mpq_t, T>, mpz_class, eval_fun> >      \
+{                                                                           \
+private:                                                                    \
+  typedef __gmp_expr<mpq_t, T> val1_type;                                   \
+  typedef mpz_class val2_type;                                              \
+                                                                            \
+  __gmp_binary_expr<val1_type, val2_type, eval_fun> expr;                   \
+public:                                                                     \
+  __gmp_expr(const val1_type &val1, const val2_type &val2)                  \
+    : expr(val1, val2) { }                                                  \
+  void eval(mpq_ptr q) const                                                \
+  {                                                                         \
+    mpq_class temp(expr.val1);                                              \
+    eval_fun::eval(q, temp.get_mpq_t(), expr.val2.get_mpz_t());             \
+  }                                                                         \
+  const val1_type & get_val1() const { return expr.val1; }                  \
+  const val2_type & get_val2() const { return expr.val2; }                  \
+  unsigned long int get_prec() const { return mpf_get_default_prec(); }     \
+};                                                                          \
+                                                                            \
+template <class T, class U>                                                 \
+class __gmp_expr<mpq_t, __gmp_binary_expr                                   \
+<__gmp_expr<mpz_t, T>, __gmp_expr<mpq_t, U>, eval_fun> >                    \
+{                                                                           \
+private:                                                                    \
+  typedef __gmp_expr<mpz_t, T> val1_type;                                   \
+  typedef __gmp_expr<mpq_t, U> val2_type;                                   \
+                                                                            \
+  __gmp_binary_expr<val1_type, val2_type, eval_fun> expr;                   \
+public:                                                                     \
+  __gmp_expr(const val1_type &val1, const val2_type &val2)                  \
+    : expr(val1, val2) { }                                                  \
+  void eval(mpq_ptr q) const                                                \
+  {                                                                         \
+    mpz_class temp1(expr.val1);                                             \
+    mpq_class temp2(expr.val2);                                             \
+    eval_fun::eval(q, temp1.get_mpz_t(), temp2.get_mpq_t());                \
+  }                                                                         \
+  const val1_type & get_val1() const { return expr.val1; }                  \
+  const val2_type & get_val2() const { return expr.val2; }                  \
+  unsigned long int get_prec() const { return mpf_get_default_prec(); }     \
+};                                                                          \
+                                                                            \
+template <class T, class U>                                                 \
+class __gmp_expr<mpq_t, __gmp_binary_expr                                   \
+<__gmp_expr<mpq_t, T>, __gmp_expr<mpz_t, U>, eval_fun> >                    \
+{                                                                           \
+private:                                                                    \
+  typedef __gmp_expr<mpq_t, T> val1_type;                                   \
+  typedef __gmp_expr<mpz_t, U> val2_type;                                   \
+                                                                            \
+  __gmp_binary_expr<val1_type, val2_type, eval_fun> expr;                   \
+public:                                                                     \
+  __gmp_expr(const val1_type &val1, const val2_type &val2)                  \
+    : expr(val1, val2) { }                                                  \
+  void eval(mpq_ptr q) const                                                \
+  {                                                                         \
+    mpq_class temp1(expr.val1);                                             \
+    mpz_class temp2(expr.val2);                                             \
+    eval_fun::eval(q, temp1.get_mpq_t(), temp2.get_mpz_t());                \
+  }                                                                         \
+  const val1_type & get_val1() const { return expr.val1; }                  \
+  const val2_type & get_val2() const { return expr.val2; }                  \
+  unsigned long int get_prec() const { return mpf_get_default_prec(); }     \
+};
+
+
+__GMPZQ_DEFINE_EXPR(__gmp_binary_plus)
+__GMPZQ_DEFINE_EXPR(__gmp_binary_minus)
+
+
+
+/**************** Macros for defining functions ****************/
+/* Results of operators and functions are instances of __gmp_expr<T, U>.
+   T determines the numerical type of the expression: it can be either
+   mpz_t, mpq_t, or mpf_t.  When the arguments of a binary
+   expression have different numerical types, __gmp_resolve_expr is used
+   to determine the "larger" type.
+   U is either __gmp_unary_expr<V, Op> or __gmp_binary_expr<V, W, Op>,
+   where V and W are the arguments' types -- they can in turn be
+   expressions, thus allowing to build compound expressions to any
+   degree of complexity.
+   Op is a function object that must have an eval() method accepting
+   appropriate arguments.
+   Actual evaluation of a __gmp_expr<T, U> object is done when it gets
+   assigned to an mp*_class ("lazy" evaluation): this is done by calling
+   its eval() method. */
+
+
+// non-member unary operators and functions
+
+#define __GMP_DEFINE_UNARY_FUNCTION(fun, eval_fun)                           \
+                                                                             \
+template <class T, class U>                                                  \
+inline __gmp_expr<T, __gmp_unary_expr<__gmp_expr<T, U>, eval_fun> >          \
+fun(const __gmp_expr<T, U> &expr)                                            \
+{                                                                            \
+  return __gmp_expr<T, __gmp_unary_expr<__gmp_expr<T, U>, eval_fun> >(expr); \
+}
+
+#define __GMP_DEFINE_UNARY_TYPE_FUNCTION(type, fun, eval_fun) \
+                                                              \
+template <class T, class U>                                   \
+inline type fun(const __gmp_expr<T, U> &expr)                 \
+{                                                             \
+  typename __gmp_resolve_temp<T, T, U>::temp_type temp(expr); \
+  return eval_fun::eval(temp.__get_mp());                     \
+}
+
+
+// non-member binary operators and functions
+
+#define __GMPP_DEFINE_BINARY_FUNCTION(fun, eval_fun)                   \
+                                                                       \
+template <class T, class U, class V, class W>                          \
+inline __gmp_expr<typename __gmp_resolve_expr<T, V>::value_type,       \
+__gmp_binary_expr<__gmp_expr<T, U>, __gmp_expr<V, W>, eval_fun> >      \
+fun(const __gmp_expr<T, U> &expr1, const __gmp_expr<V, W> &expr2)      \
+{                                                                      \
+  return __gmp_expr<typename __gmp_resolve_expr<T, V>::value_type,     \
+     __gmp_binary_expr<__gmp_expr<T, U>, __gmp_expr<V, W>, eval_fun> > \
+    (expr1, expr2);                                                    \
+}
+
+#define __GMPNN_DEFINE_BINARY_FUNCTION(fun, eval_fun, type, bigtype)       \
+                                                                           \
+template <class T, class U>                                                \
+inline __gmp_expr                                                          \
+<T, __gmp_binary_expr<__gmp_expr<T, U>, bigtype, eval_fun> >               \
+fun(const __gmp_expr<T, U> &expr, type t)                                  \
+{                                                                          \
+  return __gmp_expr                                                        \
+    <T, __gmp_binary_expr<__gmp_expr<T, U>, bigtype, eval_fun> >(expr, t); \
+}                                                                          \
+                                                                           \
+template <class T, class U>                                                \
+inline __gmp_expr                                                          \
+<T, __gmp_binary_expr<bigtype, __gmp_expr<T, U>, eval_fun> >               \
+fun(type t, const __gmp_expr<T, U> &expr)                                  \
+{                                                                          \
+  return __gmp_expr                                                        \
+    <T, __gmp_binary_expr<bigtype, __gmp_expr<T, U>, eval_fun> >(t, expr); \
+}
+
+#define __GMPNS_DEFINE_BINARY_FUNCTION(fun, eval_fun, type)          \
+__GMPNN_DEFINE_BINARY_FUNCTION(fun, eval_fun, type, signed long int)
+
+#define __GMPNU_DEFINE_BINARY_FUNCTION(fun, eval_fun, type)            \
+__GMPNN_DEFINE_BINARY_FUNCTION(fun, eval_fun, type, unsigned long int)
+
+#define __GMPND_DEFINE_BINARY_FUNCTION(fun, eval_fun, type) \
+__GMPNN_DEFINE_BINARY_FUNCTION(fun, eval_fun, type, double)
+
+#define __GMPNLD_DEFINE_BINARY_FUNCTION(fun, eval_fun, type)     \
+__GMPNN_DEFINE_BINARY_FUNCTION(fun, eval_fun, type, long double)
+
+#define __GMPN_DEFINE_BINARY_FUNCTION(fun, eval_fun)              \
+__GMPNS_DEFINE_BINARY_FUNCTION(fun, eval_fun, signed char)        \
+__GMPNU_DEFINE_BINARY_FUNCTION(fun, eval_fun, unsigned char)      \
+__GMPNS_DEFINE_BINARY_FUNCTION(fun, eval_fun, signed int)         \
+__GMPNU_DEFINE_BINARY_FUNCTION(fun, eval_fun, unsigned int)       \
+__GMPNS_DEFINE_BINARY_FUNCTION(fun, eval_fun, signed short int)   \
+__GMPNU_DEFINE_BINARY_FUNCTION(fun, eval_fun, unsigned short int) \
+__GMPNS_DEFINE_BINARY_FUNCTION(fun, eval_fun, signed long int)    \
+__GMPNU_DEFINE_BINARY_FUNCTION(fun, eval_fun, unsigned long int)  \
+__GMPND_DEFINE_BINARY_FUNCTION(fun, eval_fun, float)              \
+__GMPND_DEFINE_BINARY_FUNCTION(fun, eval_fun, double)             \
+__GMPNLD_DEFINE_BINARY_FUNCTION(fun, eval_fun, long double)
+
+#define __GMP_DEFINE_BINARY_FUNCTION(fun, eval_fun) \
+__GMPP_DEFINE_BINARY_FUNCTION(fun, eval_fun)        \
+__GMPN_DEFINE_BINARY_FUNCTION(fun, eval_fun)
+
+
+#define __GMP_DEFINE_BINARY_FUNCTION_UI(fun, eval_fun)                 \
+                                                                       \
+template <class T, class U>                                            \
+inline __gmp_expr                                                      \
+<T, __gmp_binary_expr<__gmp_expr<T, U>, unsigned long int, eval_fun> > \
+fun(const __gmp_expr<T, U> &expr, unsigned long int l)                 \
+{                                                                      \
+  return __gmp_expr<T, __gmp_binary_expr                               \
+    <__gmp_expr<T, U>, unsigned long int, eval_fun> >(expr, l);        \
+}
+
+
+#define __GMPP_DEFINE_BINARY_TYPE_FUNCTION(type, fun, eval_fun)         \
+                                                                        \
+template <class T, class U, class V, class W>                           \
+inline type fun(const __gmp_expr<T, U> &expr1,                          \
+		const __gmp_expr<V, W> &expr2)                          \
+{                                                                       \
+  typedef typename __gmp_resolve_expr<T, V>::value_type eval_type;      \
+  typename __gmp_resolve_temp<eval_type, T, U>::temp_type temp1(expr1); \
+  typename __gmp_resolve_temp<eval_type, V, W>::temp_type temp2(expr2); \
+  return eval_fun::eval(temp1.__get_mp(), temp2.__get_mp());            \
+}
+
+#define __GMPNN_DEFINE_BINARY_TYPE_FUNCTION(type, fun, eval_fun,   \
+					    type2, bigtype)        \
+                                                                   \
+template <class T, class U>                                        \
+inline type fun(const __gmp_expr<T, U> &expr, type2 t)             \
+{                                                                  \
+  typename __gmp_resolve_temp<T, T, U>::temp_type temp(expr);      \
+  return eval_fun::eval(temp.__get_mp(), static_cast<bigtype>(t)); \
+}                                                                  \
+                                                                   \
+template <class T, class U>                                        \
+inline type fun(type2 t, const __gmp_expr<T, U> &expr)             \
+{                                                                  \
+  typename __gmp_resolve_temp<T, T, U>::temp_type temp(expr);      \
+  return eval_fun::eval(static_cast<bigtype>(t), temp.__get_mp()); \
+}
+
+#define __GMPNS_DEFINE_BINARY_TYPE_FUNCTION(type, fun, eval_fun, type2) \
+__GMPNN_DEFINE_BINARY_TYPE_FUNCTION(type, fun, eval_fun,                \
+				    type2, signed long int)
+
+#define __GMPNU_DEFINE_BINARY_TYPE_FUNCTION(type, fun, eval_fun, type2) \
+__GMPNN_DEFINE_BINARY_TYPE_FUNCTION(type, fun, eval_fun,                \
+				    type2, unsigned long int)
+
+#define __GMPND_DEFINE_BINARY_TYPE_FUNCTION(type, fun, eval_fun, type2) \
+__GMPNN_DEFINE_BINARY_TYPE_FUNCTION(type, fun, eval_fun, type2, double)
+
+#define __GMPNLD_DEFINE_BINARY_TYPE_FUNCTION(type, fun, eval_fun, type2)     \
+__GMPNN_DEFINE_BINARY_TYPE_FUNCTION(type, fun, eval_fun, type2, long double)
+
+#define __GMPN_DEFINE_BINARY_TYPE_FUNCTION(type, fun, eval_fun)              \
+__GMPNS_DEFINE_BINARY_TYPE_FUNCTION(type, fun, eval_fun, signed char)        \
+__GMPNU_DEFINE_BINARY_TYPE_FUNCTION(type, fun, eval_fun, unsigned char)      \
+__GMPNS_DEFINE_BINARY_TYPE_FUNCTION(type, fun, eval_fun, signed int)         \
+__GMPNU_DEFINE_BINARY_TYPE_FUNCTION(type, fun, eval_fun, unsigned int)       \
+__GMPNS_DEFINE_BINARY_TYPE_FUNCTION(type, fun, eval_fun, signed short int)   \
+__GMPNU_DEFINE_BINARY_TYPE_FUNCTION(type, fun, eval_fun, unsigned short int) \
+__GMPNS_DEFINE_BINARY_TYPE_FUNCTION(type, fun, eval_fun, signed long int)    \
+__GMPNU_DEFINE_BINARY_TYPE_FUNCTION(type, fun, eval_fun, unsigned long int)  \
+__GMPND_DEFINE_BINARY_TYPE_FUNCTION(type, fun, eval_fun, float)              \
+__GMPND_DEFINE_BINARY_TYPE_FUNCTION(type, fun, eval_fun, double)             \
+__GMPNLD_DEFINE_BINARY_TYPE_FUNCTION(type, fun, eval_fun, long double)
+
+#define __GMP_DEFINE_BINARY_TYPE_FUNCTION(type, fun, eval_fun) \
+__GMPP_DEFINE_BINARY_TYPE_FUNCTION(type, fun, eval_fun)        \
+__GMPN_DEFINE_BINARY_TYPE_FUNCTION(type, fun, eval_fun)
+
+
+// member operators
+
+#define __GMPP_DEFINE_COMPOUND_OPERATOR(type, fun, eval_fun)                 \
+                                                                             \
+template <class T, class U>                                                  \
+inline type##_class & type##_class::fun(const __gmp_expr<T, U> &expr)        \
+{                                                                            \
+  __gmp_set_expr(mp, __gmp_expr<type##_t, __gmp_binary_expr                  \
+		 <type##_class, __gmp_expr<T, U>, eval_fun> >(*this, expr)); \
+  return *this;                                                              \
+}
+
+#define __GMPNN_DEFINE_COMPOUND_OPERATOR(type, fun, eval_fun,    \
+					 type2, bigtype)         \
+                                                                 \
+inline type##_class & type##_class::fun(type2 t)                 \
+{                                                                \
+  __gmp_set_expr(mp, __gmp_expr<type##_t, __gmp_binary_expr      \
+		 <type##_class, bigtype, eval_fun> >(*this, t)); \
+  return *this;                                                  \
+}
+
+#define __GMPNS_DEFINE_COMPOUND_OPERATOR(type, fun, eval_fun, type2) \
+__GMPNN_DEFINE_COMPOUND_OPERATOR(type, fun, eval_fun,                \
+				 type2, signed long int)
+
+#define __GMPNU_DEFINE_COMPOUND_OPERATOR(type, fun, eval_fun, type2) \
+__GMPNN_DEFINE_COMPOUND_OPERATOR(type, fun, eval_fun,                \
+				 type2, unsigned long int)
+
+#define __GMPND_DEFINE_COMPOUND_OPERATOR(type, fun, eval_fun, type2) \
+__GMPNN_DEFINE_COMPOUND_OPERATOR(type, fun, eval_fun, type2, double)
+
+#define __GMPNLD_DEFINE_COMPOUND_OPERATOR(type, fun, eval_fun, type2)     \
+__GMPNN_DEFINE_COMPOUND_OPERATOR(type, fun, eval_fun, type2, long double)
+
+#define __GMPN_DEFINE_COMPOUND_OPERATOR(type, fun, eval_fun)              \
+__GMPNS_DEFINE_COMPOUND_OPERATOR(type, fun, eval_fun, signed char)        \
+__GMPNU_DEFINE_COMPOUND_OPERATOR(type, fun, eval_fun, unsigned char)      \
+__GMPNS_DEFINE_COMPOUND_OPERATOR(type, fun, eval_fun, signed int)         \
+__GMPNU_DEFINE_COMPOUND_OPERATOR(type, fun, eval_fun, unsigned int)       \
+__GMPNS_DEFINE_COMPOUND_OPERATOR(type, fun, eval_fun, signed short int)   \
+__GMPNU_DEFINE_COMPOUND_OPERATOR(type, fun, eval_fun, unsigned short int) \
+__GMPNS_DEFINE_COMPOUND_OPERATOR(type, fun, eval_fun, signed long int)    \
+__GMPNU_DEFINE_COMPOUND_OPERATOR(type, fun, eval_fun, unsigned long int)  \
+__GMPND_DEFINE_COMPOUND_OPERATOR(type, fun, eval_fun, float)              \
+__GMPND_DEFINE_COMPOUND_OPERATOR(type, fun, eval_fun, double)             \
+/* __GMPNLD_DEFINE_COMPOUND_OPERATOR(type, fun, eval_fun, long double) */
+
+#define __GMP_DEFINE_COMPOUND_OPERATOR(type, fun, eval_fun) \
+__GMPP_DEFINE_COMPOUND_OPERATOR(type, fun, eval_fun)        \
+__GMPN_DEFINE_COMPOUND_OPERATOR(type, fun, eval_fun)
+
+#define __GMPZ_DEFINE_COMPOUND_OPERATOR(fun, eval_fun) \
+__GMP_DEFINE_COMPOUND_OPERATOR(mpz, fun, eval_fun)
+
+#define __GMPZZ_DEFINE_COMPOUND_OPERATOR(fun, eval_fun) \
+__GMPP_DEFINE_COMPOUND_OPERATOR(mpz, fun, eval_fun)
+
+#define __GMPQ_DEFINE_COMPOUND_OPERATOR(fun, eval_fun) \
+__GMP_DEFINE_COMPOUND_OPERATOR(mpq, fun, eval_fun)
+
+#define __GMPF_DEFINE_COMPOUND_OPERATOR(fun, eval_fun) \
+__GMP_DEFINE_COMPOUND_OPERATOR(mpf, fun, eval_fun)
+
+
+
+#define __GMP_DEFINE_COMPOUND_OPERATOR_UI(type, fun, eval_fun)  \
+                                                                \
+inline type##_class & type##_class::fun(unsigned long int l)    \
+{                                                               \
+  __gmp_set_expr(mp, __gmp_expr<type##_t, __gmp_binary_expr     \
+    <type##_class, unsigned long int, eval_fun> >(*this, l));   \
+  return *this;                                                 \
+}
+
+#define __GMPZ_DEFINE_COMPOUND_OPERATOR_UI(fun, eval_fun) \
+__GMP_DEFINE_COMPOUND_OPERATOR_UI(mpz, fun, eval_fun)
+
+#define __GMPQ_DEFINE_COMPOUND_OPERATOR_UI(fun, eval_fun) \
+__GMP_DEFINE_COMPOUND_OPERATOR_UI(mpq, fun, eval_fun)
+
+#define __GMPF_DEFINE_COMPOUND_OPERATOR_UI(fun, eval_fun) \
+__GMP_DEFINE_COMPOUND_OPERATOR_UI(mpf, fun, eval_fun)
+
+
+
+#define __GMP_DEFINE_INCREMENT_OPERATOR(type, fun, eval_fun) \
+                                                             \
+inline type##_class & type##_class::fun()                    \
+{                                                            \
+  eval_fun::eval(mp);                                        \
+  return *this;                                              \
+}                                                            \
+                                                             \
+inline type##_class type##_class::fun(int)                   \
+{                                                            \
+  type##_class temp(*this);                                  \
+  eval_fun::eval(mp);                                        \
+  return temp;                                               \
+}
+
+#define __GMPZ_DEFINE_INCREMENT_OPERATOR(fun, eval_fun) \
+__GMP_DEFINE_INCREMENT_OPERATOR(mpz, fun, eval_fun)
+
+#define __GMPQ_DEFINE_INCREMENT_OPERATOR(fun, eval_fun) \
+__GMP_DEFINE_INCREMENT_OPERATOR(mpq, fun, eval_fun)
+
+#define __GMPF_DEFINE_INCREMENT_OPERATOR(fun, eval_fun) \
+__GMP_DEFINE_INCREMENT_OPERATOR(mpf, fun, eval_fun)
+
+
+
+/**************** Arithmetic operators and functions ****************/
+
+// non-member operators and functions
+
+__GMP_DEFINE_UNARY_FUNCTION(operator+, __gmp_unary_plus)
+__GMP_DEFINE_UNARY_FUNCTION(operator-, __gmp_unary_minus)
+__GMP_DEFINE_UNARY_FUNCTION(operator~, __gmp_unary_com)
+
+__GMP_DEFINE_BINARY_FUNCTION(operator+, __gmp_binary_plus)
+__GMP_DEFINE_BINARY_FUNCTION(operator-, __gmp_binary_minus)
+__GMP_DEFINE_BINARY_FUNCTION(operator*, __gmp_binary_multiplies)
+__GMP_DEFINE_BINARY_FUNCTION(operator/, __gmp_binary_divides)
+__GMP_DEFINE_BINARY_FUNCTION(operator%, __gmp_binary_modulus)
+__GMP_DEFINE_BINARY_FUNCTION(operator&, __gmp_binary_and)
+__GMP_DEFINE_BINARY_FUNCTION(operator|, __gmp_binary_ior)
+__GMP_DEFINE_BINARY_FUNCTION(operator^, __gmp_binary_xor)
+
+__GMP_DEFINE_BINARY_FUNCTION_UI(operator<<, __gmp_binary_lshift)
+__GMP_DEFINE_BINARY_FUNCTION_UI(operator>>, __gmp_binary_rshift)
+
+__GMP_DEFINE_BINARY_TYPE_FUNCTION(bool, operator==, __gmp_binary_equal)
+__GMP_DEFINE_BINARY_TYPE_FUNCTION(bool, operator!=, __gmp_binary_not_equal)
+__GMP_DEFINE_BINARY_TYPE_FUNCTION(bool, operator<, __gmp_binary_less)
+__GMP_DEFINE_BINARY_TYPE_FUNCTION(bool, operator<=, __gmp_binary_less_equal)
+__GMP_DEFINE_BINARY_TYPE_FUNCTION(bool, operator>, __gmp_binary_greater)
+__GMP_DEFINE_BINARY_TYPE_FUNCTION(bool, operator>=, \
+                                  __gmp_binary_greater_equal)
+
+__GMP_DEFINE_UNARY_FUNCTION(abs, __gmp_abs_function)
+__GMP_DEFINE_UNARY_FUNCTION(trunc, __gmp_trunc_function)
+__GMP_DEFINE_UNARY_FUNCTION(floor, __gmp_floor_function)
+__GMP_DEFINE_UNARY_FUNCTION(ceil, __gmp_ceil_function)
+__GMP_DEFINE_UNARY_FUNCTION(sqrt, __gmp_sqrt_function)
+__GMP_DEFINE_BINARY_FUNCTION(hypot, __gmp_hypot_function)
+
+__GMP_DEFINE_UNARY_TYPE_FUNCTION(int, sgn, __gmp_sgn_function)
+__GMP_DEFINE_BINARY_TYPE_FUNCTION(int, cmp, __gmp_cmp_function)
+
+// member operators for mpz_class
+
+__GMPZ_DEFINE_COMPOUND_OPERATOR(operator+=, __gmp_binary_plus)
+__GMPZ_DEFINE_COMPOUND_OPERATOR(operator-=, __gmp_binary_minus)
+__GMPZ_DEFINE_COMPOUND_OPERATOR(operator*=, __gmp_binary_multiplies)
+__GMPZ_DEFINE_COMPOUND_OPERATOR(operator/=, __gmp_binary_divides)
+__GMPZ_DEFINE_COMPOUND_OPERATOR(operator%=, __gmp_binary_modulus)
+
+__GMPZZ_DEFINE_COMPOUND_OPERATOR(operator&=, __gmp_binary_and)
+__GMPZZ_DEFINE_COMPOUND_OPERATOR(operator|=, __gmp_binary_ior)
+__GMPZZ_DEFINE_COMPOUND_OPERATOR(operator^=, __gmp_binary_xor)
+
+__GMPZ_DEFINE_COMPOUND_OPERATOR_UI(operator<<=, __gmp_binary_lshift)
+__GMPZ_DEFINE_COMPOUND_OPERATOR_UI(operator>>=, __gmp_binary_rshift)
+
+__GMPZ_DEFINE_INCREMENT_OPERATOR(operator++, __gmp_unary_increment)
+__GMPZ_DEFINE_INCREMENT_OPERATOR(operator--, __gmp_unary_decrement)
+
+// member operators for mpq_class
+
+__GMPQ_DEFINE_COMPOUND_OPERATOR(operator+=, __gmp_binary_plus)
+__GMPQ_DEFINE_COMPOUND_OPERATOR(operator-=, __gmp_binary_minus)
+__GMPQ_DEFINE_COMPOUND_OPERATOR(operator*=, __gmp_binary_multiplies)
+__GMPQ_DEFINE_COMPOUND_OPERATOR(operator/=, __gmp_binary_divides)
+
+__GMPQ_DEFINE_COMPOUND_OPERATOR_UI(operator<<=, __gmp_binary_lshift)
+__GMPQ_DEFINE_COMPOUND_OPERATOR_UI(operator>>=, __gmp_binary_rshift)
+
+__GMPQ_DEFINE_INCREMENT_OPERATOR(operator++, __gmp_unary_increment)
+__GMPQ_DEFINE_INCREMENT_OPERATOR(operator--, __gmp_unary_decrement)
+
+// member operators for mpf_class
+
+__GMPF_DEFINE_COMPOUND_OPERATOR(operator+=, __gmp_binary_plus)
+__GMPF_DEFINE_COMPOUND_OPERATOR(operator-=, __gmp_binary_minus)
+__GMPF_DEFINE_COMPOUND_OPERATOR(operator*=, __gmp_binary_multiplies)
+__GMPF_DEFINE_COMPOUND_OPERATOR(operator/=, __gmp_binary_divides)
+
+__GMPF_DEFINE_COMPOUND_OPERATOR_UI(operator<<=, __gmp_binary_lshift)
+__GMPF_DEFINE_COMPOUND_OPERATOR_UI(operator>>=, __gmp_binary_rshift)
+
+__GMPF_DEFINE_INCREMENT_OPERATOR(operator++, __gmp_unary_increment)
+__GMPF_DEFINE_INCREMENT_OPERATOR(operator--, __gmp_unary_decrement)
+
+
+
+/**************** Class wrapper for gmp_randstate_t ****************/
+
+class __gmp_urandomb_value { };
+class __gmp_urandomm_value { };
+
+template <>
+class __gmp_expr<mpz_t, __gmp_urandomb_value>
+{
+private:
+  __gmp_randstate_struct *state;
+  unsigned long int bits;
+public:
+  __gmp_expr(gmp_randstate_t s, unsigned long int l) : state(s), bits(l) { }
+  void eval(mpz_ptr z) const { __gmp_rand_function::eval(z, state, bits); }
+  unsigned long int get_prec() const { return mpf_get_default_prec(); }
+};
+
+template <>
+class __gmp_expr<mpz_t, __gmp_urandomm_value>
+{
+private:
+  __gmp_randstate_struct *state;
+  mpz_class range;
+public:
+  __gmp_expr(gmp_randstate_t s, const mpz_class &z) : state(s), range(z) { }
+  void eval(mpz_ptr z) const
+  { __gmp_rand_function::eval(z, state, range.get_mpz_t()); }
+  unsigned long int get_prec() const { return mpf_get_default_prec(); }
+};
+
+template <>
+class __gmp_expr<mpf_t, __gmp_urandomb_value>
+{
+private:
+  __gmp_randstate_struct *state;
+  unsigned long int bits;
+public:
+  __gmp_expr(gmp_randstate_t s, unsigned long int l) : state(s), bits(l) { }
+  void eval(mpf_ptr f, unsigned long int prec) const
+  { __gmp_rand_function::eval(f, state, (bits>0) ? get_prec() : prec); }
+  unsigned long int get_prec() const
+  {
+    if (bits == 0)
+      return mpf_get_default_prec();
+    else
+      return bits;
+  }
+};
+
+extern "C" {
+  typedef void __gmp_randinit_default_t (gmp_randstate_t);
+  typedef void __gmp_randinit_lc_2exp_t (gmp_randstate_t, mpz_srcptr, unsigned long int, unsigned long int);
+  typedef int __gmp_randinit_lc_2exp_size_t (gmp_randstate_t, unsigned long int);
+}
+
+class gmp_randclass
+{
+private:
+  gmp_randstate_t state;
+
+  // copy construction and assignment not allowed
+  gmp_randclass(const gmp_randclass &);
+  void operator=(const gmp_randclass &);
+public:
+  // constructors and destructor
+  gmp_randclass(gmp_randalg_t alg, unsigned long int size)
+  {
+    switch (alg)
+      {
+      case GMP_RAND_ALG_LC: // no other cases for now
+      default:
+	gmp_randinit(state, alg, size);
+	break;
+      }
+  }
+
+  // gmp_randinit_default
+  gmp_randclass(__gmp_randinit_default_t* f) { f(state); }
+
+  // gmp_randinit_lc_2exp
+  gmp_randclass(__gmp_randinit_lc_2exp_t* f,
+		mpz_class z, unsigned long int l1, unsigned long int l2)
+  { f(state, z.get_mpz_t(), l1, l2); }
+
+  // gmp_randinit_lc_2exp_size
+  gmp_randclass(__gmp_randinit_lc_2exp_size_t* f,
+		unsigned long int size)
+  {
+    if (f (state, size) == 0)
+      throw std::length_error ("gmp_randinit_lc_2exp_size");
+  }
+
+  ~gmp_randclass() { gmp_randclear(state); }
+
+  // initialize
+  void seed(); // choose a random seed some way (?)
+  void seed(unsigned long int s) { gmp_randseed_ui(state, s); }
+  void seed(const mpz_class &z) { gmp_randseed(state, z.get_mpz_t()); }
+
+  // get random number
+  __gmp_expr<mpz_t, __gmp_urandomb_value> get_z_bits(unsigned long int l)
+  { return __gmp_expr<mpz_t, __gmp_urandomb_value>(state, l); }
+  __gmp_expr<mpz_t, __gmp_urandomb_value> get_z_bits(const mpz_class &z)
+  { return get_z_bits(z.get_ui()); }
+
+  __gmp_expr<mpz_t, __gmp_urandomm_value> get_z_range(const mpz_class &z)
+  { return __gmp_expr<mpz_t, __gmp_urandomm_value>(state, z); }
+
+  __gmp_expr<mpf_t, __gmp_urandomb_value> get_f(unsigned long int prec = 0)
+  { return __gmp_expr<mpf_t, __gmp_urandomb_value>(state, prec); }
+};
+
+
+/**************** #undef all private macros ****************/
+
+#undef __GMPP_DECLARE_COMPOUND_OPERATOR
+#undef __GMPN_DECLARE_COMPOUND_OPERATOR
+#undef __GMP_DECLARE_COMPOUND_OPERATOR
+#undef __GMP_DECLARE_COMPOUND_OPERATOR_UI
+#undef __GMP_DECLARE_INCREMENT_OPERATOR
+
+#undef __GMPZQ_DEFINE_EXPR
+#undef __GMP_DEFINE_TERNARY_EXPR
+
+#undef __GMP_DEFINE_UNARY_FUNCTION
+#undef __GMP_DEFINE_UNARY_TYPE_FUNCTION
+
+#undef __GMPP_DEFINE_BINARY_FUNCTION
+#undef __GMPNN_DEFINE_BINARY_FUNCTION
+#undef __GMPNS_DEFINE_BINARY_FUNCTION
+#undef __GMPNU_DEFINE_BINARY_FUNCTION
+#undef __GMPND_DEFINE_BINARY_FUNCTION
+#undef __GMPNLD_DEFINE_BINARY_FUNCTION
+#undef __GMPN_DEFINE_BINARY_FUNCTION
+#undef __GMP_DEFINE_BINARY_FUNCTION
+
+#undef __GMP_DEFINE_BINARY_FUNCTION_UI
+
+#undef __GMPP_DEFINE_BINARY_TYPE_FUNCTION
+#undef __GMPNN_DEFINE_BINARY_TYPE_FUNCTION
+#undef __GMPNS_DEFINE_BINARY_TYPE_FUNCTION
+#undef __GMPNU_DEFINE_BINARY_TYPE_FUNCTION
+#undef __GMPND_DEFINE_BINARY_TYPE_FUNCTION
+#undef __GMPNLD_DEFINE_BINARY_TYPE_FUNCTION
+#undef __GMPN_DEFINE_BINARY_TYPE_FUNCTION
+#undef __GMP_DEFINE_BINARY_TYPE_FUNCTION
+
+#undef __GMPP_DECLARE_COMPOUND_OPERATOR
+#undef __GMPN_DECLARE_COMPOUND_OPERATOR
+#undef __GMP_DECLARE_COMPOUND_OPERATOR
+
+#undef __GMP_DECLARE_COMPOUND_OPERATOR_UI
+#undef __GMP_DECLARE_INCREMENT_OPERATOR
+
+#undef __GMPZ_DEFINE_COMPOUND_OPERATOR
+#undef __GMPZZ_DEFINE_COMPOUND_OPERATOR
+#undef __GMPZN_DEFINE_COMPOUND_OPERATOR
+#undef __GMPZNN_DEFINE_COMPOUND_OPERATOR
+#undef __GMPZNS_DEFINE_COMPOUND_OPERATOR
+#undef __GMPZNU_DEFINE_COMPOUND_OPERATOR
+#undef __GMPZND_DEFINE_COMPOUND_OPERATOR
+#undef __GMPZNLD_DEFINE_COMPOUND_OPERATOR
+
+#undef __GMPP_DEFINE_COMPOUND_OPERATOR
+#undef __GMPNN_DEFINE_COMPOUND_OPERATOR
+#undef __GMPNS_DEFINE_COMPOUND_OPERATOR
+#undef __GMPNU_DEFINE_COMPOUND_OPERATOR
+#undef __GMPND_DEFINE_COMPOUND_OPERATOR
+#undef __GMPNLD_DEFINE_COMPOUND_OPERATOR
+#undef __GMPN_DEFINE_COMPOUND_OPERATOR
+#undef __GMP_DEFINE_COMPOUND_OPERATOR
+
+#undef __GMPZ_DEFINE_COMPOUND_OPERATOR
+#undef __GMPZZ_DEFINE_COMPOUND_OPERATOR
+#undef __GMPQ_DEFINE_COMPOUND_OPERATOR
+#undef __GMPF_DEFINE_COMPOUND_OPERATOR
+
+#undef __GMP_DEFINE_COMPOUND_OPERATOR_UI
+#undef __GMPZ_DEFINE_COMPOUND_OPERATOR_UI
+#undef __GMPQ_DEFINE_COMPOUND_OPERATOR_UI
+#undef __GMPF_DEFINE_COMPOUND_OPERATOR_UI
+
+#undef __GMP_DEFINE_INCREMENT_OPERATOR
+#undef __GMPZ_DEFINE_INCREMENT_OPERATOR
+#undef __GMPQ_DEFINE_INCREMENT_OPERATOR
+#undef __GMPF_DEFINE_INCREMENT_OPERATOR
+
+#endif /* __GMP_PLUSPLUS__ */