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mpir/gmp-impl.h
gladman 279323b5fd Update Windows build for latest changes
2009-04-02 11:00:00 +00:00

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/* Include file for internal GNU MP types and definitions.
THE CONTENTS OF THIS FILE ARE FOR INTERNAL USE AND ARE ALMOST CERTAIN TO
BE SUBJECT TO INCOMPATIBLE CHANGES IN FUTURE GNU MP RELEASES.
Copyright 1991, 1993, 1994, 1995, 1996, 1997, 1999, 2000, 2001, 2002, 2003,
2004, 2005, 2006 Free Software Foundation, Inc.
Copyright 2009 William Hart
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 2.1 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; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
MA 02110-1301, USA. */
/* __GMP_DECLSPEC must be given on any global data that will be accessed
from outside libmpir, meaning from the test or development programs, or
from libmpirxx. Failing to do this will result in an incorrect address
being used for the accesses. On functions __GMP_DECLSPEC makes calls
from outside libmpir more efficient, but they'll still work fine without
it. */
#ifndef __GMP_IMPL_H__
#define __GMP_IMPL_H__
#if defined _CRAY
#include <intrinsics.h> /* for _popcnt */
#endif
/* limits.h is not used in general, since it's an ANSI-ism, and since on
solaris gcc 2.95 under -mcpu=ultrasparc in ABI=32 ends up getting wrong
values (the ABI=64 values).
On Cray vector systems, however, we need the system limits.h since sizes
of signed and unsigned types can differ there, depending on compiler
options (eg. -hnofastmd), making our SHRT_MAX etc expressions fail. For
reference, int can be 46 or 64 bits, whereas uint is always 64 bits; and
short can be 24, 32, 46 or 64 bits, and different for ushort. */
#if defined _CRAY
#include <limits.h>
#endif
/* For fat.h and other fat binary stuff.
No need for __GMP_ATTRIBUTE_PURE or __GMP_NOTHROW, since functions
declared this way are only used to set function pointers in __gmp_cpuvec,
they're not called directly. */
#define DECL_add_n(name) \
mp_limb_t name __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t))
#define DECL_addmul_1(name) \
mp_limb_t name __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t))
#define DECL_copyd(name) \
void name __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t))
#define DECL_copyi(name) \
DECL_copyd (name)
#define DECL_divexact_1(name) \
void name __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t))
#define DECL_divexact_by3c(name) \
mp_limb_t name __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t))
#define DECL_divrem_1(name) \
mp_limb_t name __GMP_PROTO ((mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_limb_t))
#define DECL_gcd_1(name) \
mp_limb_t name __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t))
#define DECL_lshift(name) \
mp_limb_t name __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, unsigned))
#define DECL_mod_1(name) \
mp_limb_t name __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t))
#define DECL_mod_34lsub1(name) \
mp_limb_t name __GMP_PROTO ((mp_srcptr, mp_size_t))
#define DECL_modexact_1c_odd(name) \
mp_limb_t name __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t))
#define DECL_mul_1(name) \
DECL_addmul_1 (name)
#define DECL_mul_basecase(name) \
void name __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t))
#define DECL_preinv_divrem_1(name) \
mp_limb_t name __GMP_PROTO ((mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t, int))
#define DECL_preinv_mod_1(name) \
mp_limb_t name __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t))
#define DECL_redc_basecase(name) \
void name __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t, mp_ptr))
#define DECL_rshift(name) \
DECL_lshift (name)
#define DECL_sqr_basecase(name) \
void name __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t))
#define DECL_sub_n(name) \
DECL_add_n (name)
#define DECL_submul_1(name) \
DECL_addmul_1 (name)
#define DECL_sumdiff_n(name) \
mp_limb_t name __GMP_PROTO ((mp_ptr, mp_ptr, mp_srcptr,mp_srcptr,mp_size_t))
#if ! __GMP_WITHIN_CONFIGURE
#include "config.h"
#include "gmp-mparam.h"
#include "fib_table.h"
#include "mp_bases.h"
#if WANT_FAT_BINARY
#include "fat.h"
#endif
#endif
#if HAVE_INTTYPES_H /* for uint_least32_t */
# include <inttypes.h>
#else
# if HAVE_STDINT_H
# include <stdint.h>
# endif
#endif
#ifdef __cplusplus
#include <cstring> /* for strlen */
#include <string> /* for std::string */
#endif
#ifndef WANT_TMP_DEBUG /* for TMP_ALLOC_LIMBS_2 and others */
#define WANT_TMP_DEBUG 0
#endif
/* Might search and replace _PROTO to __GMP_PROTO internally one day, to
avoid two names for one thing, but no hurry for that. */
#define _PROTO(x) __GMP_PROTO(x)
/* The following tries to get a good version of alloca. The tests are
adapted from autoconf AC_FUNC_ALLOCA, with a couple of additions.
Whether this succeeds is tested by GMP_FUNC_ALLOCA and HAVE_ALLOCA will
be setup appropriately.
ifndef alloca - a cpp define might already exist.
glibc <stdlib.h> includes <alloca.h> which uses GCC __builtin_alloca.
HP cc +Olibcalls adds a #define of alloca to __builtin_alloca.
GCC __builtin_alloca - preferred whenever available.
_AIX pragma - IBM compilers need a #pragma in "each module that needs to
use alloca". Pragma indented to protect pre-ANSI cpp's. _IBMR2 was
used in past versions of GMP, retained still in case it matters.
The autoconf manual says this pragma needs to be at the start of a C
file, apart from comments and preprocessor directives. Is that true?
xlc on aix 4.xxx doesn't seem to mind it being after prototypes etc
from mpir.h.
*/
#ifndef alloca
# ifdef __GNUC__
# define alloca __builtin_alloca
# else
# ifdef __DECC
# define alloca(x) __ALLOCA(x)
# else
# ifdef _MSC_VER
# include <malloc.h>
# define alloca _alloca
# else
# if HAVE_ALLOCA_H
# include <alloca.h>
# else
# if defined (_AIX) || defined (_IBMR2)
#pragma alloca
# else
char *alloca ();
# endif
# endif
# endif
# endif
# endif
#endif
/* if not provided by gmp-mparam.h */
#ifndef BYTES_PER_MP_LIMB
#define BYTES_PER_MP_LIMB SIZEOF_MP_LIMB_T
#endif
#ifndef BITS_PER_MP_LIMB
#define BITS_PER_MP_LIMB (8 * SIZEOF_MP_LIMB_T)
#endif
#define BITS_PER_ULONG (8 * SIZEOF_UNSIGNED_LONG)
/* gmp_uint_least32_t is an unsigned integer type with at least 32 bits. */
#if HAVE_UINT_LEAST32_T
typedef uint_least32_t gmp_uint_least32_t;
#else
#if SIZEOF_UNSIGNED_SHORT >= 4
typedef unsigned short gmp_uint_least32_t;
#else
#if SIZEOF_UNSIGNED >= 4
typedef unsigned gmp_uint_least32_t;
#else
typedef unsigned long gmp_uint_least32_t;
#endif
#endif
#endif
/* const and signed must match __gmp_const and __gmp_signed, so follow the
decision made for those in mpir.h. */
#if ! __GMP_HAVE_CONST
#define const /* empty */
#define signed /* empty */
#endif
/* "const" basically means a function does nothing but examine its arguments
and give a return value, it doesn't read or write any memory (neither
global nor pointed to by arguments), and has no other side-effects. This
is more restrictive than "pure". See info node "(gcc)Function
Attributes". __GMP_NO_ATTRIBUTE_CONST_PURE lets tune/common.c etc turn
this off when trying to write timing loops. */
#if HAVE_ATTRIBUTE_CONST && ! defined (__GMP_NO_ATTRIBUTE_CONST_PURE) && !( defined (__cplusplus) && defined (__sun))
#define ATTRIBUTE_CONST __attribute__ ((const))
#else
#define ATTRIBUTE_CONST
#endif
#if HAVE_ATTRIBUTE_NORETURN && !( defined (__cplusplus) && defined (__sun))
#define ATTRIBUTE_NORETURN __attribute__ ((noreturn))
#else
#define ATTRIBUTE_NORETURN
#endif
/* "malloc" means a function behaves like malloc in that the pointer it
returns doesn't alias anything. */
#if HAVE_ATTRIBUTE_MALLOC && !( defined (__cplusplus) && defined (__sun))
#define ATTRIBUTE_MALLOC __attribute__ ((malloc))
#else
#define ATTRIBUTE_MALLOC
#endif
#if ! HAVE_STRCHR
#define strchr(s,c) index(s,c)
#endif
#if ! HAVE_MEMSET
#define memset(p, c, n) \
do { \
ASSERT ((n) >= 0); \
char *__memset__p = (p); \
int __i; \
for (__i = 0; __i < (n); __i++) \
__memset__p[__i] = (c); \
} while (0)
#endif
/* va_copy is standard in C99, and gcc provides __va_copy when in strict C89
mode. Falling back to a memcpy will give maximum portability, since it
works no matter whether va_list is a pointer, struct or array. */
#if ! defined (va_copy) && defined (__va_copy)
#define va_copy(dst,src) __va_copy(dst,src)
#endif
#if ! defined (va_copy)
#define va_copy(dst,src) \
do { memcpy (&(dst), &(src), sizeof (va_list)); } while (0)
#endif
/* HAVE_HOST_CPU_alpha_CIX is 1 on an alpha with the CIX instructions
(ie. ctlz, ctpop, cttz). */
#if HAVE_HOST_CPU_alphaev67 || HAVE_HOST_CPU_alphaev68 \
|| HAVE_HOST_CPU_alphaev7
#define HAVE_HOST_CPU_alpha_CIX 1
#endif
#if defined (__cplusplus)
extern "C" {
#endif
/* Usage: TMP_DECL;
TMP_MARK;
ptr = TMP_ALLOC (bytes);
TMP_FREE;
Small allocations should use TMP_SALLOC, big allocations should use
TMP_BALLOC. Allocations that might be small or big should use TMP_ALLOC.
Functions that use just TMP_SALLOC should use TMP_SDECL, TMP_SMARK, and
TMP_SFREE.
TMP_DECL just declares a variable, but might be empty and so must be last
in a list of variables. TMP_MARK must be done before any TMP_ALLOC.
TMP_ALLOC(0) is not allowed. TMP_FREE doesn't need to be done if a
TMP_MARK was made, but then no TMP_ALLOCs. */
/* The alignment in bytes, used for TMP_ALLOCed blocks, when alloca or
__gmp_allocate_func doesn't already determine it. Currently TMP_ALLOC
isn't used for "double"s, so that's not in the union. */
union tmp_align_t {
mp_limb_t l;
char *p;
};
#define __TMP_ALIGN sizeof (union tmp_align_t)
/* Return "a" rounded upwards to a multiple of "m", if it isn't already.
"a" must be an unsigned type.
This is designed for use with a compile-time constant "m".
The POW2 case is expected to be usual, and gcc 3.0 and up recognises
"(-(8*n))%8" or the like is always zero, which means the rounding up in
the WANT_TMP_NOTREENTRANT version of TMP_ALLOC below will be a noop. */
#define ROUND_UP_MULTIPLE(a,m) \
(POW2_P(m) ? (a) + (-(a))%(m) \
: (a)+(m)-1 - (((a)+(m)-1) % (m)))
#if defined (WANT_TMP_ALLOCA) || defined (WANT_TMP_REENTRANT)
struct tmp_reentrant_t {
struct tmp_reentrant_t *next;
size_t size; /* bytes, including header */
};
void *__gmp_tmp_reentrant_alloc _PROTO ((struct tmp_reentrant_t **, size_t)) ATTRIBUTE_MALLOC;
void __gmp_tmp_reentrant_free _PROTO ((struct tmp_reentrant_t *));
#endif
#if WANT_TMP_ALLOCA
#define TMP_SDECL
#define TMP_DECL struct tmp_reentrant_t *__tmp_marker
#define TMP_SMARK
#define TMP_MARK __tmp_marker = 0
#define TMP_SALLOC(n) alloca(n)
#define TMP_BALLOC(n) __gmp_tmp_reentrant_alloc (&__tmp_marker, n)
#define TMP_ALLOC(n) \
(LIKELY ((n) < 65536) ? TMP_SALLOC(n) : TMP_BALLOC(n))
#define TMP_SFREE
#define TMP_FREE \
do { \
if (UNLIKELY (__tmp_marker != 0)) __gmp_tmp_reentrant_free (__tmp_marker); \
} while (0)
#endif
#if WANT_TMP_REENTRANT
#define TMP_SDECL TMP_DECL
#define TMP_DECL struct tmp_reentrant_t *__tmp_marker
#define TMP_SMARK TMP_MARK
#define TMP_MARK __tmp_marker = 0
#define TMP_SALLOC(n) TMP_ALLOC(n)
#define TMP_BALLOC(n) TMP_ALLOC(n)
#define TMP_ALLOC(n) __gmp_tmp_reentrant_alloc (&__tmp_marker, n)
#define TMP_SFREE TMP_FREE
#define TMP_FREE __gmp_tmp_reentrant_free (__tmp_marker)
#endif
#if WANT_TMP_NOTREENTRANT
struct tmp_marker
{
struct tmp_stack *which_chunk;
void *alloc_point;
};
void *__gmp_tmp_alloc _PROTO ((unsigned long)) ATTRIBUTE_MALLOC;
void __gmp_tmp_mark _PROTO ((struct tmp_marker *));
void __gmp_tmp_free _PROTO ((struct tmp_marker *));
#define TMP_SDECL TMP_DECL
#define TMP_DECL struct tmp_marker __tmp_marker
#define TMP_SMARK TMP_MARK
#define TMP_MARK __gmp_tmp_mark (&__tmp_marker)
#define TMP_SALLOC(n) TMP_ALLOC(n)
#define TMP_BALLOC(n) TMP_ALLOC(n)
#define TMP_ALLOC(n) \
__gmp_tmp_alloc (ROUND_UP_MULTIPLE ((unsigned long) (n), __TMP_ALIGN))
#define TMP_SFREE TMP_FREE
#define TMP_FREE __gmp_tmp_free (&__tmp_marker)
#endif
#if WANT_TMP_DEBUG
/* See tal-debug.c for some comments. */
struct tmp_debug_t {
struct tmp_debug_entry_t *list;
const char *file;
int line;
};
struct tmp_debug_entry_t {
struct tmp_debug_entry_t *next;
char *block;
size_t size;
};
void __gmp_tmp_debug_mark _PROTO ((const char *, int, struct tmp_debug_t **,
struct tmp_debug_t *,
const char *, const char *));
void *__gmp_tmp_debug_alloc _PROTO ((const char *, int, int,
struct tmp_debug_t **, const char *,
size_t)) ATTRIBUTE_MALLOC;
void __gmp_tmp_debug_free _PROTO ((const char *, int, int,
struct tmp_debug_t **,
const char *, const char *));
#define TMP_SDECL TMP_DECL_NAME(__tmp_xmarker, "__tmp_marker")
#define TMP_DECL TMP_DECL_NAME(__tmp_xmarker, "__tmp_marker")
#define TMP_SMARK TMP_MARK_NAME(__tmp_xmarker, "__tmp_marker")
#define TMP_MARK TMP_MARK_NAME(__tmp_xmarker, "__tmp_marker")
#define TMP_SFREE TMP_FREE_NAME(__tmp_xmarker, "__tmp_marker")
#define TMP_FREE TMP_FREE_NAME(__tmp_xmarker, "__tmp_marker")
/* The marker variable is designed to provoke an uninitialized varialble
warning from the compiler if TMP_FREE is used without a TMP_MARK.
__tmp_marker_inscope does the same for TMP_ALLOC. Runtime tests pick
these things up too. */
#define TMP_DECL_NAME(marker, marker_name) \
int marker; \
int __tmp_marker_inscope; \
const char *__tmp_marker_name = marker_name; \
struct tmp_debug_t __tmp_marker_struct; \
/* don't demand NULL, just cast a zero */ \
struct tmp_debug_t *__tmp_marker = (struct tmp_debug_t *) 0
#define TMP_MARK_NAME(marker, marker_name) \
do { \
marker = 1; \
__tmp_marker_inscope = 1; \
__gmp_tmp_debug_mark (ASSERT_FILE, ASSERT_LINE, \
&__tmp_marker, &__tmp_marker_struct, \
__tmp_marker_name, marker_name); \
} while (0)
#define TMP_SALLOC(n) TMP_ALLOC(n)
#define TMP_BALLOC(n) TMP_ALLOC(n)
#define TMP_ALLOC(size) \
__gmp_tmp_debug_alloc (ASSERT_FILE, ASSERT_LINE, \
__tmp_marker_inscope, \
&__tmp_marker, __tmp_marker_name, size)
#define TMP_FREE_NAME(marker, marker_name) \
do { \
__gmp_tmp_debug_free (ASSERT_FILE, ASSERT_LINE, \
marker, &__tmp_marker, \
__tmp_marker_name, marker_name); \
} while (0)
#endif /* WANT_TMP_DEBUG */
/* Allocating various types. */
#define TMP_ALLOC_TYPE(n,type) ((type *) TMP_ALLOC ((n) * sizeof (type)))
#define TMP_SALLOC_TYPE(n,type) ((type *) TMP_SALLOC ((n) * sizeof (type)))
#define TMP_BALLOC_TYPE(n,type) ((type *) TMP_BALLOC ((n) * sizeof (type)))
#define TMP_ALLOC_LIMBS(n) TMP_ALLOC_TYPE(n,mp_limb_t)
#define TMP_SALLOC_LIMBS(n) TMP_SALLOC_TYPE(n,mp_limb_t)
#define TMP_BALLOC_LIMBS(n) TMP_BALLOC_TYPE(n,mp_limb_t)
#define TMP_ALLOC_MP_PTRS(n) TMP_ALLOC_TYPE(n,mp_ptr)
#define TMP_SALLOC_MP_PTRS(n) TMP_SALLOC_TYPE(n,mp_ptr)
#define TMP_BALLOC_MP_PTRS(n) TMP_BALLOC_TYPE(n,mp_ptr)
/* It's more efficient to allocate one block than two. This is certainly
true of the malloc methods, but it can even be true of alloca if that
involves copying a chunk of stack (various RISCs), or a call to a stack
bounds check (mingw). In any case, when debugging keep separate blocks
so a redzoning malloc debugger can protect each individually. */
#define TMP_ALLOC_LIMBS_2(xp,xsize, yp,ysize) \
do { \
if (WANT_TMP_DEBUG) \
{ \
(xp) = TMP_ALLOC_LIMBS (xsize); \
(yp) = TMP_ALLOC_LIMBS (ysize); \
} \
else \
{ \
(xp) = TMP_ALLOC_LIMBS ((xsize) + (ysize)); \
(yp) = (xp) + (xsize); \
} \
} while (0)
/* From mpir.h, nicer names for internal use. */
#define CRAY_Pragma(str) __GMP_CRAY_Pragma(str)
#define MPN_CMP(result, xp, yp, size) __GMPN_CMP(result, xp, yp, size)
#define LIKELY(cond) __GMP_LIKELY(cond)
#define UNLIKELY(cond) __GMP_UNLIKELY(cond)
#define ABS(x) ((x) >= 0 ? (x) : -(x))
#undef MIN
#define MIN(l,o) ((l) < (o) ? (l) : (o))
#undef MAX
#define MAX(h,i) ((h) > (i) ? (h) : (i))
#define numberof(x) (sizeof (x) / sizeof ((x)[0]))
/* Field access macros. */
#define SIZ(x) ((x)->_mp_size)
#define ABSIZ(x) ABS (SIZ (x))
#define PTR(x) ((x)->_mp_d)
#define LIMBS(x) ((x)->_mp_d)
#define EXP(x) ((x)->_mp_exp)
#define PREC(x) ((x)->_mp_prec)
#define ALLOC(x) ((x)->_mp_alloc)
/* n-1 inverts any low zeros and the lowest one bit. If n&(n-1) leaves zero
then that lowest one bit must have been the only bit set. n==0 will
return true though, so avoid that. */
#define POW2_P(n) (((n) & ((n) - 1)) == 0)
/* The "short" defines are a bit different because shorts are promoted to
ints by ~ or >> etc.
#ifndef's are used since on some systems (HP?) header files other than
limits.h setup these defines. We could forcibly #undef in that case, but
there seems no need to worry about that. */
#ifndef ULONG_MAX
#define ULONG_MAX __GMP_ULONG_MAX
#endif
#ifndef UINT_MAX
#define UINT_MAX __GMP_UINT_MAX
#endif
#ifndef USHRT_MAX
#define USHRT_MAX __GMP_USHRT_MAX
#endif
#define MP_LIMB_T_MAX (~ (mp_limb_t) 0)
/* Must cast ULONG_MAX etc to unsigned long etc, since they might not be
unsigned on a K&R compiler. In particular the HP-UX 10 bundled K&R cc
treats the plain decimal values in <limits.h> as signed. */
#define ULONG_HIGHBIT (ULONG_MAX ^ ((unsigned long) ULONG_MAX >> 1))
#define UINT_HIGHBIT (UINT_MAX ^ ((unsigned) UINT_MAX >> 1))
#define USHRT_HIGHBIT ((unsigned short) (USHRT_MAX ^ ((unsigned short) USHRT_MAX >> 1)))
#define GMP_LIMB_HIGHBIT (MP_LIMB_T_MAX ^ (MP_LIMB_T_MAX >> 1))
#ifndef LONG_MIN
#define LONG_MIN ((long) ULONG_HIGHBIT)
#endif
#ifndef LONG_MAX
#define LONG_MAX (-(LONG_MIN+1))
#endif
#ifndef INT_MIN
#define INT_MIN ((int) UINT_HIGHBIT)
#endif
#ifndef INT_MAX
#define INT_MAX (-(INT_MIN+1))
#endif
#ifndef SHRT_MIN
#define SHRT_MIN ((short) USHRT_HIGHBIT)
#endif
#ifndef SHRT_MAX
#define SHRT_MAX ((short) (-(SHRT_MIN+1)))
#endif
#if __GMP_MP_SIZE_T_INT
#define MP_SIZE_T_MAX INT_MAX
#define MP_SIZE_T_MIN INT_MIN
#else
#define MP_SIZE_T_MAX LONG_MAX
#define MP_SIZE_T_MIN LONG_MIN
#endif
/* mp_exp_t is the same as mp_size_t */
#define MP_EXP_T_MAX MP_SIZE_T_MAX
#define MP_EXP_T_MIN MP_SIZE_T_MIN
#define LONG_HIGHBIT LONG_MIN
#define INT_HIGHBIT INT_MIN
#define SHRT_HIGHBIT SHRT_MIN
#define GMP_NUMB_HIGHBIT (CNST_LIMB(1) << (GMP_NUMB_BITS-1))
#if GMP_NAIL_BITS == 0
#define GMP_NAIL_LOWBIT CNST_LIMB(0)
#else
#define GMP_NAIL_LOWBIT (CNST_LIMB(1) << GMP_NUMB_BITS)
#endif
#if GMP_NAIL_BITS != 0
/* Set various *_THRESHOLD values to be used for nails. Thus we avoid using
code that has not yet been qualified. */
#undef DIV_SB_PREINV_THRESHOLD
#undef DIV_DC_THRESHOLD
#undef POWM_THRESHOLD
#define DIV_SB_PREINV_THRESHOLD MP_SIZE_T_MAX
#define DIV_DC_THRESHOLD 50
#define POWM_THRESHOLD 0
#undef GCD_ACCEL_THRESHOLD
#define GCD_ACCEL_THRESHOLD 3
#undef DIVREM_1_NORM_THRESHOLD
#undef DIVREM_1_UNNORM_THRESHOLD
#undef MOD_1_NORM_THRESHOLD
#undef MOD_1_UNNORM_THRESHOLD
#undef USE_PREINV_DIVREM_1
#undef USE_PREINV_MOD_1
#undef DIVREM_2_THRESHOLD
#undef DIVEXACT_1_THRESHOLD
#undef MODEXACT_1_ODD_THRESHOLD
#define DIVREM_1_NORM_THRESHOLD MP_SIZE_T_MAX /* no preinv */
#define DIVREM_1_UNNORM_THRESHOLD MP_SIZE_T_MAX /* no preinv */
#define MOD_1_NORM_THRESHOLD MP_SIZE_T_MAX /* no preinv */
#define MOD_1_UNNORM_THRESHOLD MP_SIZE_T_MAX /* no preinv */
#define USE_PREINV_DIVREM_1 0 /* no preinv */
#define USE_PREINV_MOD_1 0 /* no preinv */
#define DIVREM_2_THRESHOLD MP_SIZE_T_MAX /* no preinv */
#undef GET_STR_DC_THRESHOLD
#undef GET_STR_PRECOMPUTE_THRESHOLD
#undef SET_STR_THRESHOLD
#define GET_STR_DC_THRESHOLD 22
#define GET_STR_PRECOMPUTE_THRESHOLD 42
#define SET_STR_THRESHOLD 3259
/* mpn/generic/mul_fft.c is not nails-capable. */
#undef MUL_FFT_THRESHOLD
#undef SQR_FFT_THRESHOLD
#define MUL_FFT_THRESHOLD MP_SIZE_T_MAX
#define SQR_FFT_THRESHOLD MP_SIZE_T_MAX
#endif
/* Swap macros. */
#define MP_LIMB_T_SWAP(x, y) \
do { \
mp_limb_t __mp_limb_t_swap__tmp = (x); \
(x) = (y); \
(y) = __mp_limb_t_swap__tmp; \
} while (0)
#define MP_SIZE_T_SWAP(x, y) \
do { \
mp_size_t __mp_size_t_swap__tmp = (x); \
(x) = (y); \
(y) = __mp_size_t_swap__tmp; \
} while (0)
#define MP_PTR_SWAP(x, y) \
do { \
mp_ptr __mp_ptr_swap__tmp = (x); \
(x) = (y); \
(y) = __mp_ptr_swap__tmp; \
} while (0)
#define MP_SRCPTR_SWAP(x, y) \
do { \
mp_srcptr __mp_srcptr_swap__tmp = (x); \
(x) = (y); \
(y) = __mp_srcptr_swap__tmp; \
} while (0)
#define MPN_PTR_SWAP(xp,xs, yp,ys) \
do { \
MP_PTR_SWAP (xp, yp); \
MP_SIZE_T_SWAP (xs, ys); \
} while(0)
#define MPN_SRCPTR_SWAP(xp,xs, yp,ys) \
do { \
MP_SRCPTR_SWAP (xp, yp); \
MP_SIZE_T_SWAP (xs, ys); \
} while(0)
#define MPZ_PTR_SWAP(x, y) \
do { \
mpz_ptr __mpz_ptr_swap__tmp = (x); \
(x) = (y); \
(y) = __mpz_ptr_swap__tmp; \
} while (0)
#define MPZ_SRCPTR_SWAP(x, y) \
do { \
mpz_srcptr __mpz_srcptr_swap__tmp = (x); \
(x) = (y); \
(y) = __mpz_srcptr_swap__tmp; \
} while (0)
/* Enhancement: __gmp_allocate_func could have "__attribute__ ((malloc))",
but current gcc (3.0) doesn't seem to support that. */
__GMP_DECLSPEC extern void * (*__gmp_allocate_func) __GMP_PROTO ((size_t));
__GMP_DECLSPEC extern void * (*__gmp_reallocate_func) __GMP_PROTO ((void *, size_t, size_t));
__GMP_DECLSPEC extern void (*__gmp_free_func) __GMP_PROTO ((void *, size_t));
void *__gmp_default_allocate _PROTO ((size_t));
void *__gmp_default_reallocate _PROTO ((void *, size_t, size_t));
void __gmp_default_free _PROTO ((void *, size_t));
#define __GMP_ALLOCATE_FUNC_TYPE(n,type) \
((type *) (*__gmp_allocate_func) ((n) * sizeof (type)))
#define __GMP_ALLOCATE_FUNC_LIMBS(n) __GMP_ALLOCATE_FUNC_TYPE (n, mp_limb_t)
#define __GMP_REALLOCATE_FUNC_TYPE(p, old_size, new_size, type) \
((type *) (*__gmp_reallocate_func) \
(p, (old_size) * sizeof (type), (new_size) * sizeof (type)))
#define __GMP_REALLOCATE_FUNC_LIMBS(p, old_size, new_size) \
__GMP_REALLOCATE_FUNC_TYPE(p, old_size, new_size, mp_limb_t)
#define __GMP_FREE_FUNC_TYPE(p,n,type) (*__gmp_free_func) (p, (n) * sizeof (type))
#define __GMP_FREE_FUNC_LIMBS(p,n) __GMP_FREE_FUNC_TYPE (p, n, mp_limb_t)
#define __GMP_REALLOCATE_FUNC_MAYBE(ptr, oldsize, newsize) \
do { \
if ((oldsize) != (newsize)) \
(ptr) = (*__gmp_reallocate_func) (ptr, oldsize, newsize); \
} while (0)
#define __GMP_REALLOCATE_FUNC_MAYBE_TYPE(ptr, oldsize, newsize, type) \
do { \
if ((oldsize) != (newsize)) \
(ptr) = (type *) (*__gmp_reallocate_func) \
(ptr, (oldsize) * sizeof (type), (newsize) * sizeof (type)); \
} while (0)
/* Dummy for non-gcc, code involving it will go dead. */
#if ! defined (__GNUC__) || __GNUC__ < 2
#define __builtin_constant_p(x) 0
#endif
/* In gcc 2.96 and up on i386, tail calls are optimized to jumps if the
stack usage is compatible. __attribute__ ((regparm (N))) helps by
putting leading parameters in registers, avoiding extra stack.
regparm cannot be used with calls going through the PLT, because the
binding code there may clobber the registers (%eax, %edx, %ecx) used for
the regparm parameters. Calls to local (ie. static) functions could
still use this, if we cared to differentiate locals and globals.
On athlon-unknown-freebsd4.9 with gcc 3.3.3, regparm cannot be used with
-p or -pg profiling, since that version of gcc doesn't realize the
.mcount calls will clobber the parameter registers. Other systems are
ok, like debian with glibc 2.3.2 (mcount doesn't clobber), but we don't
bother to try to detect this. regparm is only an optimization so we just
disable it when profiling (profiling being a slowdown anyway). */
#if HAVE_HOST_CPU_FAMILY_x86 && __GMP_GNUC_PREREQ (2,96) && ! defined (PIC) \
&& ! WANT_PROFILING_PROF && ! WANT_PROFILING_GPROF
#define USE_LEADING_REGPARM 1
#else
#define USE_LEADING_REGPARM 0
#endif
/* Macros for altering parameter order according to regparm usage. */
#if USE_LEADING_REGPARM
#define REGPARM_2_1(a,b,x) x,a,b
#define REGPARM_3_1(a,b,c,x) x,a,b,c
#define REGPARM_ATTR(n) __attribute__ ((regparm (n)))
#else
#define REGPARM_2_1(a,b,x) a,b,x
#define REGPARM_3_1(a,b,c,x) a,b,c,x
#define REGPARM_ATTR(n)
#endif
/* ASM_L gives a local label for a gcc asm block, for use when temporary
local labels like "1:" might not be available, which is the case for
instance on the x86s (the SCO assembler doesn't support them).
The label generated is made unique by including "%=" which is a unique
number for each insn. This ensures the same name can be used in multiple
asm blocks, perhaps via a macro. Since jumps between asm blocks are not
allowed there's no need for a label to be usable outside a single
block. */
#define ASM_L(name) LSYM_PREFIX "asm_%=_" #name
#if defined (__GNUC__) && HAVE_HOST_CPU_FAMILY_x86
#if 0
/* FIXME: Check that these actually improve things.
FIXME: Need a cld after each std.
FIXME: Can't have inputs in clobbered registers, must describe them as
dummy outputs, and add volatile. */
#define MPN_COPY_INCR(DST, SRC, N) \
__asm__ ("cld\n\trep\n\tmovsl" : : \
"D" (DST), "S" (SRC), "c" (N) : \
"cx", "di", "si", "memory")
#define MPN_COPY_DECR(DST, SRC, N) \
__asm__ ("std\n\trep\n\tmovsl" : : \
"D" ((DST) + (N) - 1), "S" ((SRC) + (N) - 1), "c" (N) : \
"cx", "di", "si", "memory")
#endif
#endif
void __gmpz_aorsmul_1 _PROTO ((REGPARM_3_1 (mpz_ptr w, mpz_srcptr u, mp_limb_t v, mp_size_t sub))) REGPARM_ATTR(1);
#define mpz_aorsmul_1(w,u,v,sub) __gmpz_aorsmul_1 (REGPARM_3_1 (w, u, v, sub))
#define mpz_n_pow_ui __gmpz_n_pow_ui
void mpz_n_pow_ui _PROTO ((mpz_ptr, mp_srcptr, mp_size_t, unsigned long));
#define mpn_add_nc __MPN(add_nc)
__GMP_DECLSPEC mp_limb_t mpn_add_nc __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t, mp_limb_t));
#define mpn_addmul_1c __MPN(addmul_1c)
__GMP_DECLSPEC mp_limb_t mpn_addmul_1c __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t));
#define mpn_addmul_2 __MPN(addmul_2)
__GMP_DECLSPEC mp_limb_t mpn_addmul_2 _PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr));
#define mpn_addmul_3 __MPN(addmul_3)
__GMP_DECLSPEC mp_limb_t mpn_addmul_3 _PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr));
#define mpn_addmul_4 __MPN(addmul_4)
__GMP_DECLSPEC mp_limb_t mpn_addmul_4 _PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr));
#define mpn_addmul_5 __MPN(addmul_5)
__GMP_DECLSPEC mp_limb_t mpn_addmul_5 _PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr));
#define mpn_addmul_6 __MPN(addmul_6)
__GMP_DECLSPEC mp_limb_t mpn_addmul_6 _PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr));
#define mpn_addmul_7 __MPN(addmul_7)
__GMP_DECLSPEC mp_limb_t mpn_addmul_7 _PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr));
#define mpn_addmul_8 __MPN(addmul_8)
__GMP_DECLSPEC mp_limb_t mpn_addmul_8 _PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr));
/* mpn_addlsh1_n(c,a,b,n), when it exists, sets {c,n} to {a,n}+2*{b,n}, and
returns the carry out (0, 1 or 2). */
#define mpn_addlsh1_n __MPN(addlsh1_n)
__GMP_DECLSPEC mp_limb_t mpn_addlsh1_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
/* mpn_sublsh1_n(c,a,b,n), when it exists, sets {c,n} to {a,n}-2*{b,n}, and
returns the borrow out (0, 1 or 2). */
#define mpn_sublsh1_n __MPN(sublsh1_n)
__GMP_DECLSPEC mp_limb_t mpn_sublsh1_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
/* mpn_rsh1add_n(c,a,b,n), when it exists, sets {c,n} to ({a,n} + {b,n}) >> 1,
and returns the bit rshifted out (0 or 1). */
#define mpn_rsh1add_n __MPN(rsh1add_n)
__GMP_DECLSPEC mp_limb_t mpn_rsh1add_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
/* mpn_rsh1sub_n(c,a,b,n), when it exists, sets {c,n} to ({a,n} - {b,n}) >> 1,
and returns the bit rshifted out (0 or 1). If there's a borrow from the
subtract, it's stored as a 1 in the high bit of c[n-1], like a twos
complement negative. */
#define mpn_rsh1sub_n __MPN(rsh1sub_n)
__GMP_DECLSPEC mp_limb_t mpn_rsh1sub_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
#define mpn_addadd_n __MPN(addadd_n)
__GMP_DECLSPEC mp_limb_t mpn_addadd_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_srcptr, mp_size_t));
#define mpn_addsub_n __MPN(addsub_n)
__GMP_DECLSPEC int mpn_addsub_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_srcptr, mp_size_t));
#define mpn_subadd_n __MPN(subadd_n)
__GMP_DECLSPEC mp_limb_t mpn_subadd_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_srcptr, mp_size_t));
#ifndef mpn_sumdiff_n /* if not done with cpuvec in a fat binary */
#define mpn_sumdiff_n __MPN(sumdiff_n)
__GMP_DECLSPEC mp_limb_t mpn_sumdiff_n __GMP_PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
#endif
#define mpn_sumdiff_nc __MPN(sumdiff_nc)
__GMP_DECLSPEC mp_limb_t mpn_sumdiff_nc __GMP_PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_srcptr, mp_size_t, mp_limb_t));
#define mpn_divexact_byff __MPN(divexact_byff)
__GMP_DECLSPEC mp_limb_t mpn_divexact_byff __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t));
#define mpn_divexact_byBm1of __MPN(divexact_byBm1of)
__GMP_DECLSPEC mp_limb_t mpn_divexact_byBm1of __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t,mp_limb_t,mp_limb_t));
#define mpn_divrem_1c __MPN(divrem_1c)
__GMP_DECLSPEC mp_limb_t mpn_divrem_1c __GMP_PROTO ((mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t));
#define mpn_dump __MPN(dump)
__GMP_DECLSPEC void mpn_dump __GMP_PROTO ((mp_srcptr, mp_size_t));
#define mpn_fib2_ui __MPN(fib2_ui)
mp_size_t mpn_fib2_ui _PROTO ((mp_ptr, mp_ptr, unsigned long));
/* Remap names of internal mpn functions. */
#define __clz_tab __MPN(clz_tab)
#define mpn_udiv_w_sdiv __MPN(udiv_w_sdiv)
#define mpn_gcd_finda __MPN(gcd_finda)
mp_limb_t mpn_gcd_finda _PROTO((const mp_limb_t cp[2])) __GMP_ATTRIBUTE_PURE;
#define mpn_jacobi_base __MPN(jacobi_base)
int mpn_jacobi_base _PROTO ((mp_limb_t a, mp_limb_t b, int result_bit1)) ATTRIBUTE_CONST;
#define mpn_mod_1c __MPN(mod_1c)
__GMP_DECLSPEC mp_limb_t mpn_mod_1c __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t)) __GMP_ATTRIBUTE_PURE;
#define mpn_mul_1c __MPN(mul_1c)
__GMP_DECLSPEC mp_limb_t mpn_mul_1c __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t));
#define mpn_mul_2 __MPN(mul_2)
mp_limb_t mpn_mul_2 _PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr));
#ifndef mpn_mul_basecase /* if not done with cpuvec in a fat binary */
#define mpn_mul_basecase __MPN(mul_basecase)
__GMP_DECLSPEC void mpn_mul_basecase __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t));
#endif
#define mpn_mullow_n __MPN(mullow_n)
__GMP_DECLSPEC void mpn_mullow_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
#define mpn_mullow_basecase __MPN(mullow_basecase)
__GMP_DECLSPEC void mpn_mullow_basecase __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
#ifndef mpn_redc_basecase /* if not done with cpuvec in a fat binary */
#define mpn_redc_basecase __MPN(redc_basecase)
__GMP_DECLSPEC void mpn_redc_basecase __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t,mp_limb_t , mp_ptr));
#endif
#define mpn_sqr_n __MPN(sqr_n)
__GMP_DECLSPEC void mpn_sqr_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t));
#ifndef mpn_sqr_basecase /* if not done with cpuvec in a fat binary */
#define mpn_sqr_basecase __MPN(sqr_basecase)
__GMP_DECLSPEC void mpn_sqr_basecase __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t));
#endif
#define mpn_sub_nc __MPN(sub_nc)
__GMP_DECLSPEC mp_limb_t mpn_sub_nc __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t, mp_limb_t));
#define mpn_submul_1c __MPN(submul_1c)
__GMP_DECLSPEC mp_limb_t mpn_submul_1c __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t));
#define mpn_invert_2exp __MPN(invert_2exp)
__GMP_DECLSPEC void mpn_invert_2exp __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_ptr));
#define mpn_redc_1 __MPN(redc_1)
__GMP_DECLSPEC void mpn_redc_1 __GMP_PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_size_t, mp_limb_t);)
#define mpn_redc_2 __MPN(redc_2)
__GMP_DECLSPEC void mpn_redc_2 __GMP_PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_size_t, mp_srcptr));
#define mpn_divrem_euclidean_qr_1 __MPN(divrem_euclidean_qr_1)
__GMP_DECLSPEC mp_limb_t mpn_divrem_euclidean_qr_1 __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t,mp_limb_t));
#define mpn_divrem_euclidean_r_1 __MPN(divrem_euclidean_r_1)
__GMP_DECLSPEC mp_limb_t mpn_divrem_euclidean_r_1 __GMP_PROTO ((mp_srcptr, mp_size_t,mp_limb_t));
typedef __gmp_randstate_struct *gmp_randstate_ptr;
typedef const __gmp_randstate_struct *gmp_randstate_srcptr;
/* Pseudo-random number generator function pointers structure. */
typedef struct {
void (*randseed_fn) __GMP_PROTO ((gmp_randstate_t rstate, mpz_srcptr seed));
void (*randget_fn) __GMP_PROTO ((gmp_randstate_t rstate, mp_ptr dest, unsigned long int nbits));
void (*randclear_fn) __GMP_PROTO ((gmp_randstate_t rstate));
void (*randiset_fn) __GMP_PROTO ((gmp_randstate_ptr, gmp_randstate_srcptr));
} gmp_randfnptr_t;
/* Macro to obtain a void pointer to the function pointers structure. */
#define RNG_FNPTR(rstate) ((rstate)->_mp_algdata._mp_lc)
/* Macro to obtain a pointer to the generator's state.
When used as a lvalue the rvalue needs to be cast to mp_ptr. */
#define RNG_STATE(rstate) ((rstate)->_mp_seed->_mp_d)
/* Write a given number of random bits to rp. */
#define _gmp_rand(rp, state, bits) \
do { \
gmp_randstate_ptr __rstate = (state); \
(*((gmp_randfnptr_t *) RNG_FNPTR (__rstate))->randget_fn) \
(__rstate, rp, bits); \
} while (0)
__GMP_DECLSPEC void __gmp_randinit_mt_noseed __GMP_PROTO ((gmp_randstate_t));
/* __gmp_rands is the global state for the old-style random functions, and
is also used in the test programs (hence the __GMP_DECLSPEC).
There's no seeding here, so mpz_random etc will generate the same
sequence every time. This is not unlike the C library random functions
if you don't seed them, so perhaps it's acceptable. Digging up a seed
from /dev/random or the like would work on many systems, but might
encourage a false confidence, since it'd be pretty much impossible to do
something that would work reliably everywhere. In any case the new style
functions are recommended to applications which care about randomness, so
the old functions aren't too important. */
__GMP_DECLSPEC extern char __gmp_rands_initialized;
__GMP_DECLSPEC extern gmp_randstate_t __gmp_rands;
#define RANDS \
((__gmp_rands_initialized ? 0 \
: (__gmp_rands_initialized = 1, \
__gmp_randinit_mt_noseed (__gmp_rands), 0)), \
__gmp_rands)
/* this is used by the test programs, to free memory */
#define RANDS_CLEAR() \
do { \
if (__gmp_rands_initialized) \
{ \
__gmp_rands_initialized = 0; \
gmp_randclear (__gmp_rands); \
} \
} while (0)
/* kara uses n+1 limbs of temporary space and then recurses with the balance,
so need (n+1) + (ceil(n/2)+1) + (ceil(n/4)+1) + ... This can be solved to
2n + o(n). Since n is very limited, o(n) in practice could be around 15.
For now, assume n is arbitrarily large. */
#define MPN_KARA_MUL_N_TSIZE(n) (2*(n) + 2*GMP_LIMB_BITS)
#define MPN_KARA_SQR_N_TSIZE(n) (2*(n) + 2*GMP_LIMB_BITS)
/* toom3 uses 2n + 2n/3 + o(n) limbs of temporary space if mpn_sublsh1_n is
unavailable, but just 2n + o(n) if mpn_sublsh1_n is available. It is hard
to pin down the value of o(n), since it is a complex function of
MUL_TOOM3_THRESHOLD and n. Normally toom3 is used between kara and fft; in
that case o(n) will be really limited. If toom3 is used for arbitrarily
large operands, o(n) will be larger. These definitions handle operands of
up to 8956264246117233 limbs. A single multiplication using toom3 on the
fastest hardware currently (2003) would need 100 million years, which
suggests that these limits are acceptable. */
#if WANT_FFT
#if HAVE_NATIVE_mpn_sublsh1_n
#define MPN_TOOM3_MUL_N_TSIZE(n) (2*(n) + 63)
#define MPN_TOOM3_SQR_N_TSIZE(n) (2*(n) + 63)
#else
#define MPN_TOOM3_MUL_N_TSIZE(n) (2*(n) + 2*(n/3) + 63)
#define MPN_TOOM3_SQR_N_TSIZE(n) (2*(n) + 2*(n/3) + 63)
#endif
#else /* WANT_FFT */
#if HAVE_NATIVE_mpn_sublsh1_n
#define MPN_TOOM3_MUL_N_TSIZE(n) (2*(n) + 255)
#define MPN_TOOM3_SQR_N_TSIZE(n) (2*(n) + 255)
#else
#define MPN_TOOM3_MUL_N_TSIZE(n) (2*(n) + 2*(n/3) + 255)
#define MPN_TOOM3_SQR_N_TSIZE(n) (2*(n) + 2*(n/3) + 255)
#endif
#define MPN_TOOM3_MAX_N 285405
#endif /* WANT_FFT */
/* need 2 so that n2>=1 */
#define MPN_KARA_MUL_N_MINSIZE 2
#define MPN_KARA_SQR_N_MINSIZE 2
/* Need l>=1, ls>=1, and 2*ls > l (the latter for the tD MPN_INCR_U) */
#define MPN_TOOM3_MUL_N_MINSIZE 17
#define MPN_TOOM4_MUL_N_MINSIZE 32
#define MPN_TOOM7_MUL_N_MINSIZE 56
#define MPN_TOOM3_SQR_N_MINSIZE 17
#ifdef _MSC_VER
#define MUL_TOOM4_INTERNAL_THRESHOLD 200
#define MUL_TOOM7_INTERNAL_THRESHOLD 300
#else
#define MUL_TOOM4_INTERNAL_THRESHOLD 550
#define MUL_TOOM7_INTERNAL_THRESHOLD 1000
#endif
#define mpn_sqr_diagonal __MPN(sqr_diagonal)
void mpn_sqr_diagonal _PROTO ((mp_ptr, mp_srcptr, mp_size_t));
#define mpn_kara_mul_n __MPN(kara_mul_n)
void mpn_kara_mul_n _PROTO((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t, mp_ptr));
#define mpn_kara_sqr_n __MPN(kara_sqr_n)
void mpn_kara_sqr_n _PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_ptr));
#define mpn_toom3_mul_n __MPN(toom3_mul_n)
void mpn_toom3_mul_n _PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t,mp_ptr));
#define mpn_toom4_mul_n __MPN(toom4_mul_n)
void mpn_toom4_mul_n _PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
#define mpn_toom7_mul_n __MPN(toom7_mul_n)
void mpn_toom7_mul_n _PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
#define mpn_toom3_sqr_n __MPN(toom3_sqr_n)
void mpn_toom3_sqr_n _PROTO((mp_ptr, mp_srcptr, mp_size_t, mp_ptr));
#define mpn_fft_best_k __MPN(fft_best_k)
int mpn_fft_best_k _PROTO ((mp_size_t n, int sqr)) ATTRIBUTE_CONST;
#define mpn_mul_fft __MPN(mul_fft)
int mpn_mul_fft _PROTO ((mp_ptr op, mp_size_t pl,
mp_srcptr n, mp_size_t nl,
mp_srcptr m, mp_size_t ml,
int k));
#define mpn_mul_fft_full __MPN(mul_fft_full)
void mpn_mul_fft_full _PROTO ((mp_ptr op,
mp_srcptr n, mp_size_t nl,
mp_srcptr m, mp_size_t ml));
#define mpn_fft_next_size __MPN(fft_next_size)
mp_size_t mpn_fft_next_size _PROTO ((mp_size_t pl, int k)) ATTRIBUTE_CONST;
#define mpn_sb_divrem_mn __MPN(sb_divrem_mn)
mp_limb_t mpn_sb_divrem_mn _PROTO ((mp_ptr, mp_ptr, mp_size_t,
mp_srcptr, mp_size_t));
#define mpn_dc_divrem_n __MPN(dc_divrem_n)
mp_limb_t mpn_dc_divrem_n _PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_size_t));
/* #define mpn_tdiv_q __MPN(tdiv_q) */
/* void mpn_tdiv_q _PROTO ((mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t)); */
#define mpz_divexact_gcd __gmpz_divexact_gcd
void mpz_divexact_gcd _PROTO ((mpz_ptr q, mpz_srcptr a, mpz_srcptr d));
#define mpz_inp_str_nowhite __gmpz_inp_str_nowhite
#ifdef _GMP_H_HAVE_FILE
size_t mpz_inp_str_nowhite _PROTO ((mpz_ptr x, FILE *stream, int base, int c, size_t nread));
#endif
#define mpn_divisible_p __MPN(divisible_p)
int mpn_divisible_p _PROTO ((mp_srcptr ap, mp_size_t asize,
mp_srcptr dp, mp_size_t dsize)) __GMP_ATTRIBUTE_PURE;
#define mpn_rootrem __MPN(rootrem)
mp_size_t mpn_rootrem _PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_size_t, mp_limb_t));
#if defined (_CRAY)
#define MPN_COPY_INCR(dst, src, n) \
do { \
int __i; /* Faster on some Crays with plain int */ \
_Pragma ("_CRI ivdep"); \
for (__i = 0; __i < (n); __i++) \
(dst)[__i] = (src)[__i]; \
} while (0)
#endif
/* used by test programs, hence __GMP_DECLSPEC */
#ifndef mpn_copyi /* if not done with cpuvec in a fat binary */
#define mpn_copyi __MPN(copyi)
__GMP_DECLSPEC void mpn_copyi _PROTO ((mp_ptr, mp_srcptr, mp_size_t));
#endif
#if ! defined (MPN_COPY_INCR) && HAVE_NATIVE_mpn_copyi
#define MPN_COPY_INCR(dst, src, size) \
do { \
ASSERT ((size) >= 0); \
ASSERT (MPN_SAME_OR_INCR_P (dst, src, size)); \
mpn_copyi (dst, src, size); \
} while (0)
#endif
/* Copy N limbs from SRC to DST incrementing, N==0 allowed. */
#if ! defined (MPN_COPY_INCR)
#define MPN_COPY_INCR(dst, src, n) \
do { \
ASSERT ((n) >= 0); \
ASSERT (MPN_SAME_OR_INCR_P (dst, src, n)); \
if ((n) != 0) \
{ \
mp_size_t __n = (n) - 1; \
mp_ptr __dst = (dst); \
mp_srcptr __src = (src); \
mp_limb_t __x; \
__x = *__src++; \
if (__n != 0) \
{ \
do \
{ \
*__dst++ = __x; \
__x = *__src++; \
} \
while (--__n); \
} \
*__dst++ = __x; \
} \
} while (0)
#endif
#if defined (_CRAY)
#define MPN_COPY_DECR(dst, src, n) \
do { \
int __i; /* Faster on some Crays with plain int */ \
_Pragma ("_CRI ivdep"); \
for (__i = (n) - 1; __i >= 0; __i--) \
(dst)[__i] = (src)[__i]; \
} while (0)
#endif
/* used by test programs, hence __GMP_DECLSPEC */
#ifndef mpn_copyd /* if not done with cpuvec in a fat binary */
#define mpn_copyd __MPN(copyd)
__GMP_DECLSPEC void mpn_copyd _PROTO ((mp_ptr, mp_srcptr, mp_size_t));
#endif
#if ! defined (MPN_COPY_DECR) && HAVE_NATIVE_mpn_copyd
#define MPN_COPY_DECR(dst, src, size) \
do { \
ASSERT ((size) >= 0); \
ASSERT (MPN_SAME_OR_DECR_P (dst, src, size)); \
mpn_copyd (dst, src, size); \
} while (0)
#endif
/* Copy N limbs from SRC to DST decrementing, N==0 allowed. */
#if ! defined (MPN_COPY_DECR)
#define MPN_COPY_DECR(dst, src, n) \
do { \
ASSERT ((n) >= 0); \
ASSERT (MPN_SAME_OR_DECR_P (dst, src, n)); \
if ((n) != 0) \
{ \
mp_size_t __n = (n) - 1; \
mp_ptr __dst = (dst) + __n; \
mp_srcptr __src = (src) + __n; \
mp_limb_t __x; \
__x = *__src--; \
if (__n != 0) \
{ \
do \
{ \
*__dst-- = __x; \
__x = *__src--; \
} \
while (--__n); \
} \
*__dst-- = __x; \
} \
} while (0)
#endif
#ifndef MPN_COPY
#define MPN_COPY(d,s,n) \
do { \
ASSERT (MPN_SAME_OR_SEPARATE_P (d, s, n)); \
MPN_COPY_INCR (d, s, n); \
} while (0)
#endif
/* Set {dst,size} to the limbs of {src,size} in reverse order. */
#define MPN_REVERSE(dst, src, size) \
do { \
mp_ptr __dst = (dst); \
mp_size_t __size = (size); \
mp_srcptr __src = (src) + __size - 1; \
mp_size_t __i; \
ASSERT ((size) >= 0); \
ASSERT (! MPN_OVERLAP_P (dst, size, src, size)); \
CRAY_Pragma ("_CRI ivdep"); \
for (__i = 0; __i < __size; __i++) \
{ \
*__dst = *__src; \
__dst++; \
__src--; \
} \
} while (0)
/* Zero n limbs at dst.
For power and powerpc we want an inline stu/bdnz loop for zeroing. On
ppc630 for instance this is optimal since it can sustain only 1 store per
cycle.
gcc 2.95.x (for powerpc64 -maix64, or powerpc32) doesn't recognise the
"for" loop in the generic code below can become stu/bdnz. The do/while
here helps it get to that. The same caveat about plain -mpowerpc64 mode
applies here as to __GMPN_COPY_INCR in mpir.h.
xlc 3.1 already generates stu/bdnz from the generic C, and does so from
this loop too.
Enhancement: GLIBC does some trickery with dcbz to zero whole cache lines
at a time. MPN_ZERO isn't all that important in GMP, so it might be more
trouble than it's worth to do the same, though perhaps a call to memset
would be good when on a GNU system. */
#if HAVE_HOST_CPU_FAMILY_power || HAVE_HOST_CPU_FAMILY_powerpc
#define MPN_ZERO(dst, n) \
do { \
ASSERT ((n) >= 0); \
if ((n) != 0) \
{ \
mp_ptr __dst = (dst) - 1; \
mp_size_t __n = (n); \
do \
*++__dst = 0; \
while (--__n); \
} \
} while (0)
#endif
#ifndef MPN_ZERO
#define MPN_ZERO(dst, n) \
do { \
ASSERT ((n) >= 0); \
if ((n) != 0) \
{ \
mp_ptr __dst = (dst); \
mp_size_t __n = (n); \
do \
*__dst++ = 0; \
while (--__n); \
} \
} while (0)
#endif
/* On the x86s repe/scasl doesn't seem useful, since it takes many cycles to
start up and would need to strip a lot of zeros before it'd be faster
than a simple cmpl loop. Here are some times in cycles for
std/repe/scasl/cld and cld/repe/scasl (the latter would be for stripping
low zeros).
std cld
P5 18 16
P6 46 38
K6 36 13
K7 21 20
*/
#ifndef MPN_NORMALIZE
#define MPN_NORMALIZE(DST, NLIMBS) \
do { \
while ((NLIMBS) > 0) \
{ \
if ((DST)[(NLIMBS) - 1] != 0) \
break; \
(NLIMBS)--; \
} \
} while (0)
#endif
#ifndef MPN_NORMALIZE_NOT_ZERO
#define MPN_NORMALIZE_NOT_ZERO(DST, NLIMBS) \
do { \
ASSERT ((NLIMBS) >= 1); \
while (1) \
{ \
if ((DST)[(NLIMBS) - 1] != 0) \
break; \
(NLIMBS)--; \
} \
} while (0)
#endif
/* Strip least significant zero limbs from {ptr,size} by incrementing ptr
and decrementing size. low should be ptr[0], and will be the new ptr[0]
on returning. The number in {ptr,size} must be non-zero, ie. size!=0 and
somewhere a non-zero limb. */
#define MPN_STRIP_LOW_ZEROS_NOT_ZERO(ptr, size, low) \
do { \
ASSERT ((size) >= 1); \
ASSERT ((low) == (ptr)[0]); \
\
while ((low) == 0) \
{ \
(size)--; \
ASSERT ((size) >= 1); \
(ptr)++; \
(low) = *(ptr); \
} \
} while (0)
/* Initialize X of type mpz_t with space for NLIMBS limbs. X should be a
temporary variable; it will be automatically cleared out at function
return. We use __x here to make it possible to accept both mpz_ptr and
mpz_t arguments. */
#define MPZ_TMP_INIT(X, NLIMBS) \
do { \
mpz_ptr __x = (X); \
ASSERT ((NLIMBS) >= 1); \
__x->_mp_alloc = (NLIMBS); \
__x->_mp_d = (mp_ptr) TMP_ALLOC ((NLIMBS) * BYTES_PER_MP_LIMB); \
} while (0)
/* Realloc for an mpz_t WHAT if it has less than NEEDED limbs. */
#define MPZ_REALLOC(z,n) (UNLIKELY ((n) > ALLOC(z)) \
? (mp_ptr) _mpz_realloc(z,n) \
: PTR(z))
#define MPZ_EQUAL_1_P(z) (SIZ(z)==1 && PTR(z)[0] == 1)
/* MPN_FIB2_SIZE(n) is the size in limbs required by mpn_fib2_ui for fp and
f1p.
From Knuth vol 1 section 1.2.8, F[n] = phi^n/sqrt(5) rounded to the
nearest integer, where phi=(1+sqrt(5))/2 is the golden ratio. So the
number of bits required is n*log_2((1+sqrt(5))/2) = n*0.6942419.
The multiplier used is 23/32=0.71875 for efficient calculation on CPUs
without good floating point. There's +2 for rounding up, and a further
+2 since at the last step x limbs are doubled into a 2x+1 limb region
whereas the actual F[2k] value might be only 2x-1 limbs.
Note that a division is done first, since on a 32-bit system it's at
least conceivable to go right up to n==ULONG_MAX. (F[2^32-1] would be
about 380Mbytes, plus temporary workspace of about 1.2Gbytes here and
whatever a multiply of two 190Mbyte numbers takes.)
Enhancement: When GMP_NUMB_BITS is not a power of 2 the division could be
worked into the multiplier. */
#define MPN_FIB2_SIZE(n) \
((mp_size_t) ((n) / 32 * 23 / GMP_NUMB_BITS) + 4)
/* FIB_TABLE(n) returns the Fibonacci number F[n]. Must have n in the range
-1 <= n <= FIB_TABLE_LIMIT (that constant in fib_table.h).
FIB_TABLE_LUCNUM_LIMIT (in fib_table.h) is the largest n for which L[n] =
F[n] + 2*F[n-1] fits in a limb. */
__GMP_DECLSPEC extern const mp_limb_t __gmp_fib_table[];
#define FIB_TABLE(n) (__gmp_fib_table[(n)+1])
/* For a threshold between algorithms A and B, size>=thresh is where B
should be used. Special value MP_SIZE_T_MAX means only ever use A, or
value 0 means only ever use B. The tests for these special values will
be compile-time constants, so the compiler should be able to eliminate
the code for the unwanted algorithm. */
#define ABOVE_THRESHOLD(size,thresh) \
((thresh) == 0 \
|| ((thresh) != MP_SIZE_T_MAX \
&& (size) >= (thresh)))
#define BELOW_THRESHOLD(size,thresh) (! ABOVE_THRESHOLD (size, thresh))
/* Usage: int use_foo = BELOW_THRESHOLD (size, FOO_THRESHOLD);
...
if (CACHED_BELOW_THRESHOLD (use_foo, size, FOO_THRESHOLD))
When "use_foo" is a constant (thresh is 0 or MP_SIZE_T), gcc prior to
version 3.3 doesn't optimize away a test "if (use_foo)" when within a
loop. CACHED_BELOW_THRESHOLD helps it do so. */
#define CACHED_ABOVE_THRESHOLD(cache, thresh) \
((thresh) == 0 || (thresh) == MP_SIZE_T_MAX \
? ABOVE_THRESHOLD (0, thresh) \
: (cache))
#define CACHED_BELOW_THRESHOLD(cache, thresh) \
((thresh) == 0 || (thresh) == MP_SIZE_T_MAX \
? BELOW_THRESHOLD (0, thresh) \
: (cache))
/* If MUL_KARATSUBA_THRESHOLD is not already defined, define it to a
value which is good on most machines. */
#ifndef MUL_KARATSUBA_THRESHOLD
#define MUL_KARATSUBA_THRESHOLD 32
#endif
/* If MUL_TOOM3_THRESHOLD is not already defined, define it to a
value which is good on most machines. */
#ifndef MUL_TOOM3_THRESHOLD
#define MUL_TOOM3_THRESHOLD 128
#endif
#ifndef MUL_TOOM4_THRESHOLD
#define MUL_TOOM4_THRESHOLD 550
#endif
#ifndef MUL_TOOM7_THRESHOLD
#define MUL_TOOM7_THRESHOLD 1000
#endif
/* MUL_KARATSUBA_THRESHOLD_LIMIT is the maximum for MUL_KARATSUBA_THRESHOLD.
In a normal build MUL_KARATSUBA_THRESHOLD is a constant and we use that.
In a fat binary or tune program build MUL_KARATSUBA_THRESHOLD is a
variable and a separate hard limit will have been defined. Similarly for
TOOM3. */
#ifndef MUL_KARATSUBA_THRESHOLD_LIMIT
#define MUL_KARATSUBA_THRESHOLD_LIMIT MUL_KARATSUBA_THRESHOLD
#endif
#ifndef MUL_TOOM3_THRESHOLD_LIMIT
#define MUL_TOOM3_THRESHOLD_LIMIT MUL_TOOM3_THRESHOLD
#endif
#ifndef MUL_TOOM4_THRESHOLD_LIMIT
#define MUL_TOOM4_THRESHOLD_LIMIT MUL_TOOM4_THRESHOLD
#endif
#ifndef MUL_TOOM7_THRESHOLD_LIMIT
#define MUL_TOOM7_THRESHOLD_LIMIT MUL_TOOM7_THRESHOLD
#endif
#ifndef MULLOW_BASECASE_THRESHOLD_LIMIT
#define MULLOW_BASECASE_THRESHOLD_LIMIT MULLOW_BASECASE_THRESHOLD
#endif
/* SQR_BASECASE_THRESHOLD is where mpn_sqr_basecase should take over from
mpn_mul_basecase in mpn_sqr_n. Default is to use mpn_sqr_basecase
always. (Note that we certainly always want it if there's a native
assembler mpn_sqr_basecase.)
If it turns out that mpn_kara_sqr_n becomes faster than mpn_mul_basecase
before mpn_sqr_basecase does, then SQR_BASECASE_THRESHOLD is the
karatsuba threshold and SQR_KARATSUBA_THRESHOLD is 0. This oddity arises
more or less because SQR_KARATSUBA_THRESHOLD represents the size up to
which mpn_sqr_basecase should be used, and that may be never. */
#ifndef SQR_BASECASE_THRESHOLD
#define SQR_BASECASE_THRESHOLD 0
#endif
#ifndef SQR_KARATSUBA_THRESHOLD
#define SQR_KARATSUBA_THRESHOLD (2*MUL_KARATSUBA_THRESHOLD)
#endif
#ifndef SQR_TOOM3_THRESHOLD
#define SQR_TOOM3_THRESHOLD 128
#endif
/* See comments above about MUL_TOOM3_THRESHOLD_LIMIT. */
#ifndef SQR_TOOM3_THRESHOLD_LIMIT
#define SQR_TOOM3_THRESHOLD_LIMIT SQR_TOOM3_THRESHOLD
#endif
/* First k to use for an FFT modF multiply. A modF FFT is an order
log(2^k)/log(2^(k-1)) algorithm, so k=3 is merely 1.5 like karatsuba,
whereas k=4 is 1.33 which is faster than toom3 at 1.485. */
#define FFT_FIRST_K 4
/* Threshold at which FFT should be used to do a modF NxN -> N multiply. */
#ifndef MUL_FFT_MODF_THRESHOLD
#define MUL_FFT_MODF_THRESHOLD (MUL_TOOM3_THRESHOLD * 3)
#endif
#ifndef SQR_FFT_MODF_THRESHOLD
#define SQR_FFT_MODF_THRESHOLD (SQR_TOOM3_THRESHOLD * 3)
#endif
/* Threshold at which FFT should be used to do an NxN -> 2N multiply. This
will be a size where FFT is using k=7 or k=8, since an FFT-k used for an
NxN->2N multiply and not recursing into itself is an order
log(2^k)/log(2^(k-2)) algorithm, so it'll be at least k=7 at 1.39 which
is the first better than toom3. */
#ifndef MUL_FFT_THRESHOLD
#define MUL_FFT_THRESHOLD (MUL_FFT_MODF_THRESHOLD * 10)
#endif
#ifndef SQR_FFT_THRESHOLD
#define SQR_FFT_THRESHOLD (SQR_FFT_MODF_THRESHOLD * 10)
#endif
/* Table of thresholds for successive modF FFT "k"s. The first entry is
where FFT_FIRST_K+1 should be used, the second FFT_FIRST_K+2,
etc. See mpn_fft_best_k(). */
#ifndef MUL_FFT_TABLE
#define MUL_FFT_TABLE \
{ MUL_TOOM3_THRESHOLD * 4, /* k=5 */ \
MUL_TOOM3_THRESHOLD * 8, /* k=6 */ \
MUL_TOOM3_THRESHOLD * 16, /* k=7 */ \
MUL_TOOM3_THRESHOLD * 32, /* k=8 */ \
MUL_TOOM3_THRESHOLD * 96, /* k=9 */ \
MUL_TOOM3_THRESHOLD * 288, /* k=10 */ \
0 }
#endif
#ifndef SQR_FFT_TABLE
#define SQR_FFT_TABLE \
{ SQR_TOOM3_THRESHOLD * 4, /* k=5 */ \
SQR_TOOM3_THRESHOLD * 8, /* k=6 */ \
SQR_TOOM3_THRESHOLD * 16, /* k=7 */ \
SQR_TOOM3_THRESHOLD * 32, /* k=8 */ \
SQR_TOOM3_THRESHOLD * 96, /* k=9 */ \
SQR_TOOM3_THRESHOLD * 288, /* k=10 */ \
0 }
#endif
#ifndef FFT_TABLE_ATTRS
#define FFT_TABLE_ATTRS static const
#endif
#define MPN_FFT_TABLE_SIZE 16
/* mpn_dc_divrem_n(n) calls 2*mul(n/2)+2*div(n/2), thus to be faster than
div(n) = 4*div(n/2), we need mul(n/2) to be faster than the classic way,
i.e. n/2 >= MUL_KARATSUBA_THRESHOLD
Measured values are between 2 and 4 times MUL_KARATSUBA_THRESHOLD, so go
for 3 as an average. */
#ifndef DIV_DC_THRESHOLD
#define DIV_DC_THRESHOLD (3 * MUL_KARATSUBA_THRESHOLD)
#endif
/* Return non-zero if xp,xsize and yp,ysize overlap.
If xp+xsize<=yp there's no overlap, or if yp+ysize<=xp there's no
overlap. If both these are false, there's an overlap. */
#define MPN_OVERLAP_P(xp, xsize, yp, ysize) \
((xp) + (xsize) > (yp) && (yp) + (ysize) > (xp))
#define MEM_OVERLAP_P(xp, xsize, yp, ysize) \
( (char *) (xp) + (xsize) > (char *) (yp) \
&& (char *) (yp) + (ysize) > (char *) (xp))
/* Return non-zero if xp,xsize and yp,ysize are either identical or not
overlapping. Return zero if they're partially overlapping. */
#define MPN_SAME_OR_SEPARATE_P(xp, yp, size) \
MPN_SAME_OR_SEPARATE2_P(xp, size, yp, size)
#define MPN_SAME_OR_SEPARATE2_P(xp, xsize, yp, ysize) \
((xp) == (yp) || ! MPN_OVERLAP_P (xp, xsize, yp, ysize))
/* Return non-zero if dst,dsize and src,ssize are either identical or
overlapping in a way suitable for an incrementing/decrementing algorithm.
Return zero if they're partially overlapping in an unsuitable fashion. */
#define MPN_SAME_OR_INCR2_P(dst, dsize, src, ssize) \
((dst) <= (src) || ! MPN_OVERLAP_P (dst, dsize, src, ssize))
#define MPN_SAME_OR_INCR_P(dst, src, size) \
MPN_SAME_OR_INCR2_P(dst, size, src, size)
#define MPN_SAME_OR_DECR2_P(dst, dsize, src, ssize) \
((dst) >= (src) || ! MPN_OVERLAP_P (dst, dsize, src, ssize))
#define MPN_SAME_OR_DECR_P(dst, src, size) \
MPN_SAME_OR_DECR2_P(dst, size, src, size)
/* ASSERT() is a private assertion checking scheme, similar to <assert.h>.
ASSERT() does the check only if WANT_ASSERT is selected, ASSERT_ALWAYS()
does it always. Generally assertions are meant for development, but
might help when looking for a problem later too.
Note that strings shouldn't be used within the ASSERT expression,
eg. ASSERT(strcmp(s,"notgood")!=0), since the quotes upset the "expr"
used in the !HAVE_STRINGIZE case (ie. K&R). */
#ifdef __LINE__
#define ASSERT_LINE __LINE__
#else
#define ASSERT_LINE -1
#endif
#ifdef __FILE__
#define ASSERT_FILE __FILE__
#else
#define ASSERT_FILE ""
#endif
void __gmp_assert_header _PROTO ((const char *filename, int linenum));
__GMP_DECLSPEC void __gmp_assert_fail _PROTO ((const char *filename, int linenum, const char *expr)) ATTRIBUTE_NORETURN;
#if HAVE_STRINGIZE
#define ASSERT_FAIL(expr) __gmp_assert_fail (ASSERT_FILE, ASSERT_LINE, #expr)
#else
#define ASSERT_FAIL(expr) __gmp_assert_fail (ASSERT_FILE, ASSERT_LINE, "expr")
#endif
#define ASSERT_ALWAYS(expr) \
do { \
if (!(expr)) \
ASSERT_FAIL (expr); \
} while (0)
#if WANT_ASSERT
#define ASSERT(expr) ASSERT_ALWAYS (expr)
#else
#define ASSERT(expr) do {} while (0)
#endif
/* ASSERT_CARRY checks the expression is non-zero, and ASSERT_NOCARRY checks
that it's zero. In both cases if assertion checking is disabled the
expression is still evaluated. These macros are meant for use with
routines like mpn_add_n() where the return value represents a carry or
whatever that should or shouldn't occur in some context. For example,
ASSERT_NOCARRY (mpn_add_n (rp, s1p, s2p, size)); */
#if WANT_ASSERT
#define ASSERT_CARRY(expr) ASSERT_ALWAYS ((expr) != 0)
#define ASSERT_NOCARRY(expr) ASSERT_ALWAYS ((expr) == 0)
#else
#define ASSERT_CARRY(expr) (expr)
#define ASSERT_NOCARRY(expr) (expr)
#endif
/* ASSERT_CODE includes code when assertion checking is wanted. This is the
same as writing "#if WANT_ASSERT", but more compact. */
#if WANT_ASSERT
#define ASSERT_CODE(expr) expr
#else
#define ASSERT_CODE(expr)
#endif
/* Test that an mpq_t is in fully canonical form. This can be used as
protection on routines like mpq_equal which give wrong results on
non-canonical inputs. */
#if WANT_ASSERT
#define ASSERT_MPQ_CANONICAL(q) \
do { \
ASSERT (q->_mp_den._mp_size > 0); \
if (q->_mp_num._mp_size == 0) \
{ \
/* zero should be 0/1 */ \
ASSERT (mpz_cmp_ui (mpq_denref(q), 1L) == 0); \
} \
else \
{ \
/* no common factors */ \
mpz_t __g; \
mpz_init (__g); \
mpz_gcd (__g, mpq_numref(q), mpq_denref(q)); \
ASSERT (mpz_cmp_ui (__g, 1) == 0); \
mpz_clear (__g); \
} \
} while (0)
#else
#define ASSERT_MPQ_CANONICAL(q) do {} while (0)
#endif
/* Check that the nail parts are zero. */
#define ASSERT_ALWAYS_LIMB(limb) \
do { \
mp_limb_t __nail = (limb) & GMP_NAIL_MASK; \
ASSERT_ALWAYS (__nail == 0); \
} while (0)
#define ASSERT_ALWAYS_MPN(ptr, size) \
do { \
/* let whole loop go dead when no nails */ \
if (GMP_NAIL_BITS != 0) \
{ \
mp_size_t __i; \
for (__i = 0; __i < (size); __i++) \
ASSERT_ALWAYS_LIMB ((ptr)[__i]); \
} \
} while (0)
#if WANT_ASSERT
#define ASSERT_LIMB(limb) ASSERT_ALWAYS_LIMB (limb)
#define ASSERT_MPN(ptr, size) ASSERT_ALWAYS_MPN (ptr, size)
#else
#define ASSERT_LIMB(limb) do {} while (0)
#define ASSERT_MPN(ptr, size) do {} while (0)
#endif
/* Assert that an mpn region {ptr,size} is zero, or non-zero.
size==0 is allowed, and in that case {ptr,size} considered to be zero. */
#if WANT_ASSERT
#define ASSERT_MPN_ZERO_P(ptr,size) \
do { \
mp_size_t __i; \
ASSERT ((size) >= 0); \
for (__i = 0; __i < (size); __i++) \
ASSERT ((ptr)[__i] == 0); \
} while (0)
#define ASSERT_MPN_NONZERO_P(ptr,size) \
do { \
mp_size_t __i; \
int __nonzero = 0; \
ASSERT ((size) >= 0); \
for (__i = 0; __i < (size); __i++) \
if ((ptr)[__i] != 0) \
{ \
__nonzero = 1; \
break; \
} \
ASSERT (__nonzero); \
} while (0)
#else
#define ASSERT_MPN_ZERO_P(ptr,size) do {} while (0)
#define ASSERT_MPN_NONZERO_P(ptr,size) do {} while (0)
#endif
#if HAVE_NATIVE_mpn_com_n
#define mpn_com_n __MPN(com_n)
void mpn_com_n _PROTO ((mp_ptr, mp_srcptr, mp_size_t));
#else
#define mpn_com_n(d,s,n) \
do { \
mp_ptr __d = (d); \
mp_srcptr __s = (s); \
mp_size_t __n = (n); \
ASSERT (__n >= 1); \
ASSERT (MPN_SAME_OR_SEPARATE_P (__d, __s, __n)); \
do \
*__d++ = (~ *__s++) & GMP_NUMB_MASK; \
while (--__n); \
} while (0)
#endif
#define MPN_LOGOPS_N_INLINE(d, s1, s2, n, operation) \
do { \
mp_ptr __d = (d); \
mp_srcptr __s1 = (s1); \
mp_srcptr __s2 = (s2); \
mp_size_t __n = (n); \
ASSERT (__n >= 1); \
ASSERT (MPN_SAME_OR_SEPARATE_P (__d, __s1, __n)); \
ASSERT (MPN_SAME_OR_SEPARATE_P (__d, __s2, __n)); \
do \
operation; \
while (--__n); \
} while (0)
#if HAVE_NATIVE_mpn_and_n
#define mpn_and_n __MPN(and_n)
void mpn_and_n _PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
#else
#define mpn_and_n(d, s1, s2, n) \
MPN_LOGOPS_N_INLINE (d, s1, s2, n, *__d++ = *__s1++ & *__s2++)
#endif
#if HAVE_NATIVE_mpn_andn_n
#define mpn_andn_n __MPN(andn_n)
void mpn_andn_n _PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
#else
#define mpn_andn_n(d, s1, s2, n) \
MPN_LOGOPS_N_INLINE (d, s1, s2, n, *__d++ = *__s1++ & ~*__s2++)
#endif
#if HAVE_NATIVE_mpn_nand_n
#define mpn_nand_n __MPN(nand_n)
void mpn_nand_n _PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
#else
#define mpn_nand_n(d, s1, s2, n) \
MPN_LOGOPS_N_INLINE (d, s1, s2, n, *__d++ = ~(*__s1++ & *__s2++) & GMP_NUMB_MASK)
#endif
#if HAVE_NATIVE_mpn_ior_n
#define mpn_ior_n __MPN(ior_n)
void mpn_ior_n _PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
#else
#define mpn_ior_n(d, s1, s2, n) \
MPN_LOGOPS_N_INLINE (d, s1, s2, n, *__d++ = *__s1++ | *__s2++)
#endif
#if HAVE_NATIVE_mpn_iorn_n
#define mpn_iorn_n __MPN(iorn_n)
void mpn_iorn_n _PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
#else
#define mpn_iorn_n(d, s1, s2, n) \
MPN_LOGOPS_N_INLINE (d, s1, s2, n, *__d++ = (*__s1++ | ~*__s2++) & GMP_NUMB_MASK)
#endif
#if HAVE_NATIVE_mpn_nior_n
#define mpn_nior_n __MPN(nior_n)
void mpn_nior_n _PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
#else
#define mpn_nior_n(d, s1, s2, n) \
MPN_LOGOPS_N_INLINE (d, s1, s2, n, *__d++ = ~(*__s1++ | *__s2++) & GMP_NUMB_MASK)
#endif
#if HAVE_NATIVE_mpn_xor_n
#define mpn_xor_n __MPN(xor_n)
void mpn_xor_n _PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
#else
#define mpn_xor_n(d, s1, s2, n) \
MPN_LOGOPS_N_INLINE (d, s1, s2, n, *__d++ = *__s1++ ^ *__s2++)
#endif
#if HAVE_NATIVE_mpn_xnor_n
#define mpn_xnor_n __MPN(xnor_n)
void mpn_xnor_n _PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
#else
#define mpn_xnor_n(d, s1, s2, n) \
MPN_LOGOPS_N_INLINE (d, s1, s2, n, *__d++ = ~(*__s1++ ^ *__s2++) & GMP_NUMB_MASK)
#endif
#if HAVE_NATIVE_mpn_lshift1
#define mpn_lshift1 __MPN(lshift1)
mp_limb_t mpn_lshift1 _PROTO ((mp_ptr,mp_srcptr,mp_size_t));
#else
#define mpn_lshift1(__xp,__yp,__n) mpn_lshift((__xp),(__yp),(__n),1)
#endif
#if HAVE_NATIVE_mpn_rshift1
#define mpn_rshift1 __MPN(rshift1)
mp_limb_t mpn_rshift1 _PROTO ((mp_ptr,mp_srcptr,mp_size_t));
#else
#define mpn_rshift1(__xp,__yp,__n) mpn_rshift((__xp),(__yp),(__n),1)
#endif
/* ADDC_LIMB sets w=x+y and cout to 0 or 1 for a carry from that addition. */
#if GMP_NAIL_BITS == 0
#define ADDC_LIMB(cout, w, x, y) \
do { \
mp_limb_t __x = (x); \
mp_limb_t __y = (y); \
mp_limb_t __w = __x + __y; \
(w) = __w; \
(cout) = __w < __x; \
} while (0)
#else
#define ADDC_LIMB(cout, w, x, y) \
do { \
mp_limb_t __w; \
ASSERT_LIMB (x); \
ASSERT_LIMB (y); \
__w = (x) + (y); \
(w) = __w & GMP_NUMB_MASK; \
(cout) = __w >> GMP_NUMB_BITS; \
} while (0)
#endif
/* SUBC_LIMB sets w=x-y and cout to 0 or 1 for a borrow from that
subtract. */
#if GMP_NAIL_BITS == 0
#define SUBC_LIMB(cout, w, x, y) \
do { \
mp_limb_t __x = (x); \
mp_limb_t __y = (y); \
mp_limb_t __w = __x - __y; \
(w) = __w; \
(cout) = __w > __x; \
} while (0)
#else
#define SUBC_LIMB(cout, w, x, y) \
do { \
mp_limb_t __w = (x) - (y); \
(w) = __w & GMP_NUMB_MASK; \
(cout) = __w >> (GMP_LIMB_BITS-1); \
} while (0)
#endif
/* MPN_INCR_U does {ptr,size} += n, MPN_DECR_U does {ptr,size} -= n, both
expecting no carry (or borrow) from that.
The size parameter is only for the benefit of assertion checking. In a
normal build it's unused and the carry/borrow is just propagated as far
as it needs to go.
On random data, usually only one or two limbs of {ptr,size} get updated,
so there's no need for any sophisticated looping, just something compact
and sensible.
FIXME: Switch all code from mpn_{incr,decr}_u to MPN_{INCR,DECR}_U,
declaring their operand sizes, then remove the former. This is purely
for the benefit of assertion checking. */
#if defined (__GNUC__) && HAVE_HOST_CPU_FAMILY_x86 && GMP_NAIL_BITS == 0 \
&& BITS_PER_MP_LIMB == 32 && ! defined (NO_ASM) && ! WANT_ASSERT
/* Better flags handling than the generic C gives on i386, saving a few
bytes of code and maybe a cycle or two. */
#define MPN_IORD_U(ptr, incr, aors) \
do { \
mp_ptr __ptr_dummy; \
if (__builtin_constant_p (incr) && (incr) == 1) \
{ \
__asm__ __volatile__ \
("\n" ASM_L(top) ":\n" \
"\t" aors " $1, (%0)\n" \
"\tleal 4(%0),%0\n" \
"\tjc " ASM_L(top) \
: "=r" (__ptr_dummy) \
: "0" (ptr) \
: "memory"); \
} \
else \
{ \
__asm__ __volatile__ \
( aors " %2,(%0)\n" \
"\tjnc " ASM_L(done) "\n" \
ASM_L(top) ":\n" \
"\t" aors " $1,4(%0)\n" \
"\tleal 4(%0),%0\n" \
"\tjc " ASM_L(top) "\n" \
ASM_L(done) ":\n" \
: "=r" (__ptr_dummy) \
: "0" (ptr), \
"ri" (incr) \
: "memory"); \
} \
} while (0)
#define MPN_INCR_U(ptr, size, incr) MPN_IORD_U (ptr, incr, "addl")
#define MPN_DECR_U(ptr, size, incr) MPN_IORD_U (ptr, incr, "subl")
#define mpn_incr_u(ptr, incr) MPN_INCR_U (ptr, 0, incr)
#define mpn_decr_u(ptr, incr) MPN_DECR_U (ptr, 0, incr)
#endif
#if GMP_NAIL_BITS == 0
#ifndef mpn_incr_u
#define mpn_incr_u(p,incr) \
do { \
mp_limb_t __x; \
mp_ptr __p = (p); \
if (__builtin_constant_p (incr) && (incr) == 1) \
{ \
while (++(*(__p++)) == 0) \
; \
} \
else \
{ \
__x = *__p + (incr); \
*__p = __x; \
if (__x < (incr)) \
while (++(*(++__p)) == 0) \
; \
} \
} while (0)
#endif
#ifndef mpn_decr_u
#define mpn_decr_u(p,incr) \
do { \
mp_limb_t __x; \
mp_ptr __p = (p); \
if (__builtin_constant_p (incr) && (incr) == 1) \
{ \
while ((*(__p++))-- == 0) \
; \
} \
else \
{ \
__x = *__p; \
*__p = __x - (incr); \
if (__x < (incr)) \
while ((*(++__p))-- == 0) \
; \
} \
} while (0)
#endif
#endif
#if GMP_NAIL_BITS >= 1
#ifndef mpn_incr_u
#define mpn_incr_u(p,incr) \
do { \
mp_limb_t __x; \
mp_ptr __p = (p); \
if (__builtin_constant_p (incr) && (incr) == 1) \
{ \
do \
{ \
__x = (*__p + 1) & GMP_NUMB_MASK; \
*__p++ = __x; \
} \
while (__x == 0); \
} \
else \
{ \
__x = (*__p + (incr)); \
*__p++ = __x & GMP_NUMB_MASK; \
if (__x >> GMP_NUMB_BITS != 0) \
{ \
do \
{ \
__x = (*__p + 1) & GMP_NUMB_MASK; \
*__p++ = __x; \
} \
while (__x == 0); \
} \
} \
} while (0)
#endif
#ifndef mpn_decr_u
#define mpn_decr_u(p,incr) \
do { \
mp_limb_t __x; \
mp_ptr __p = (p); \
if (__builtin_constant_p (incr) && (incr) == 1) \
{ \
do \
{ \
__x = *__p; \
*__p++ = (__x - 1) & GMP_NUMB_MASK; \
} \
while (__x == 0); \
} \
else \
{ \
__x = *__p - (incr); \
*__p++ = __x & GMP_NUMB_MASK; \
if (__x >> GMP_NUMB_BITS != 0) \
{ \
do \
{ \
__x = *__p; \
*__p++ = (__x - 1) & GMP_NUMB_MASK; \
} \
while (__x == 0); \
} \
} \
} while (0)
#endif
#endif
#ifndef MPN_INCR_U
#if WANT_ASSERT
#define MPN_INCR_U(ptr, size, n) \
do { \
ASSERT ((size) >= 1); \
ASSERT_NOCARRY (mpn_add_1 (ptr, ptr, size, n)); \
} while (0)
#else
#define MPN_INCR_U(ptr, size, n) mpn_incr_u (ptr, n)
#endif
#endif
#ifndef MPN_DECR_U
#if WANT_ASSERT
#define MPN_DECR_U(ptr, size, n) \
do { \
ASSERT ((size) >= 1); \
ASSERT_NOCARRY (mpn_sub_1 (ptr, ptr, size, n)); \
} while (0)
#else
#define MPN_DECR_U(ptr, size, n) mpn_decr_u (ptr, n)
#endif
#endif
/* Structure for conversion between internal binary format and
strings in base 2..36. */
struct bases
{
/* Number of digits in the conversion base that always fits in an mp_limb_t.
For example, for base 10 on a machine where a mp_limb_t has 32 bits this
is 9, since 10**9 is the largest number that fits into a mp_limb_t. */
int chars_per_limb;
/* log(2)/log(conversion_base) */
double chars_per_bit_exactly;
/* base**chars_per_limb, i.e. the biggest number that fits a word, built by
factors of base. Exception: For 2, 4, 8, etc, big_base is log2(base),
i.e. the number of bits used to represent each digit in the base. */
mp_limb_t big_base;
/* A BITS_PER_MP_LIMB bit approximation to 1/big_base, represented as a
fixed-point number. Instead of dividing by big_base an application can
choose to multiply by big_base_inverted. */
mp_limb_t big_base_inverted;
};
#define mp_bases __MPN(bases)
#define __mp_bases __MPN(bases)
__GMP_DECLSPEC extern const struct bases mp_bases[257];
/* For power of 2 bases this is exact. For other bases the result is either
exact or one too big.
To be exact always it'd be necessary to examine all the limbs of the
operand, since numbers like 100..000 and 99...999 generally differ only
in the lowest limb. It'd be possible to examine just a couple of high
limbs to increase the probability of being exact, but that doesn't seem
worth bothering with. */
#define MPN_SIZEINBASE(result, ptr, size, base) \
do { \
int __lb_base, __cnt; \
size_t __totbits; \
\
ASSERT ((size) >= 0); \
ASSERT ((base) >= 2); \
ASSERT ((base) < numberof (mp_bases)); \
\
/* Special case for X == 0. */ \
if ((size) == 0) \
(result) = 1; \
else \
{ \
/* Calculate the total number of significant bits of X. */ \
count_leading_zeros (__cnt, (ptr)[(size)-1]); \
__totbits = (size_t) (size) * GMP_NUMB_BITS - (__cnt - GMP_NAIL_BITS);\
\
if (POW2_P (base)) \
{ \
__lb_base = mp_bases[base].big_base; \
(result) = (__totbits + __lb_base - 1) / __lb_base; \
} \
else \
(result) = (size_t) \
(__totbits * mp_bases[base].chars_per_bit_exactly) + 1; \
} \
} while (0)
/* eliminate mp_bases lookups for base==16 */
#define MPN_SIZEINBASE_16(result, ptr, size) \
do { \
int __cnt; \
mp_size_t __totbits; \
\
ASSERT ((size) >= 0); \
\
/* Special case for X == 0. */ \
if ((size) == 0) \
(result) = 1; \
else \
{ \
/* Calculate the total number of significant bits of X. */ \
count_leading_zeros (__cnt, (ptr)[(size)-1]); \
__totbits = (size_t) (size) * GMP_NUMB_BITS - (__cnt - GMP_NAIL_BITS);\
(result) = (__totbits + 4 - 1) / 4; \
} \
} while (0)
/* bit count to limb count, rounding up */
#define BITS_TO_LIMBS(n) (((n) + (GMP_NUMB_BITS - 1)) / GMP_NUMB_BITS)
/* MPN_SET_UI sets an mpn (ptr, cnt) to given ui. MPZ_FAKE_UI creates fake
mpz_t from ui. The zp argument must have room for LIMBS_PER_ULONG limbs
in both cases (LIMBS_PER_ULONG is also defined here.) */
#if BITS_PER_ULONG <= GMP_NUMB_BITS /* need one limb per ulong */
#define LIMBS_PER_ULONG 1
#define MPN_SET_UI(zp, zn, u) \
(zp)[0] = (u); \
(zn) = ((zp)[0] != 0);
#define MPZ_FAKE_UI(z, zp, u) \
(zp)[0] = (u); \
PTR (z) = (zp); \
SIZ (z) = ((zp)[0] != 0); \
ASSERT_CODE (ALLOC (z) = 1);
#else /* need two limbs per ulong */
#define LIMBS_PER_ULONG 2
#define MPN_SET_UI(zp, zn, u) \
(zp)[0] = (u) & GMP_NUMB_MASK; \
(zp)[1] = (u) >> GMP_NUMB_BITS; \
(zn) = ((zp)[1] != 0 ? 2 : (zp)[0] != 0 ? 1 : 0);
#define MPZ_FAKE_UI(z, zp, u) \
(zp)[0] = (u) & GMP_NUMB_MASK; \
(zp)[1] = (u) >> GMP_NUMB_BITS; \
SIZ (z) = ((zp)[1] != 0 ? 2 : (zp)[0] != 0 ? 1 : 0); \
PTR (z) = (zp); \
ASSERT_CODE (ALLOC (z) = 2);
#endif
#if HAVE_HOST_CPU_FAMILY_x86
#define TARGET_REGISTER_STARVED 1
#else
#define TARGET_REGISTER_STARVED 0
#endif
/* LIMB_HIGHBIT_TO_MASK(n) examines the high bit of a limb value and turns 1
or 0 there into a limb 0xFF..FF or 0 respectively.
On most CPUs this is just an arithmetic right shift by GMP_LIMB_BITS-1,
but C99 doesn't guarantee signed right shifts are arithmetic, so we have
a little compile-time test and a fallback to a "? :" form. The latter is
necessary for instance on Cray vector systems.
Recent versions of gcc (eg. 3.3) will in fact optimize a "? :" like this
to an arithmetic right shift anyway, but it's good to get the desired
shift on past versions too (in particular since an important use of
LIMB_HIGHBIT_TO_MASK is in udiv_qrnnd_preinv). */
#define LIMB_HIGHBIT_TO_MASK(n) \
(((mp_limb_signed_t) -1 >> 1) < 0 \
? (mp_limb_signed_t) (n) >> (GMP_LIMB_BITS - 1) \
: (n) & GMP_LIMB_HIGHBIT ? MP_LIMB_T_MAX : CNST_LIMB(0))
/* Use a library function for invert_limb, if available. */
#define mpn_invert_limb __MPN(invert_limb)
mp_limb_t mpn_invert_limb _PROTO ((mp_limb_t)) ATTRIBUTE_CONST;
#if ! defined (invert_limb) && HAVE_NATIVE_mpn_invert_limb
#define invert_limb(invxl,xl) \
do { \
(invxl) = mpn_invert_limb (xl); \
} while (0)
#endif
#ifndef invert_limb
#define invert_limb(invxl,xl) \
do { \
mp_limb_t dummy; \
ASSERT ((xl) != 0); \
udiv_qrnnd (invxl, dummy, ~(xl), ~CNST_LIMB(0), xl); \
} while (0)
#endif
#ifndef udiv_qrnnd_preinv
#define udiv_qrnnd_preinv udiv_qrnnd_preinv2
#endif
/* Divide the two-limb number in (NH,,NL) by D, with DI being the largest
limb not larger than (2**(2*BITS_PER_MP_LIMB))/D - (2**BITS_PER_MP_LIMB).
If this would yield overflow, DI should be the largest possible number
(i.e., only ones). For correct operation, the most significant bit of D
has to be set. Put the quotient in Q and the remainder in R. */
#define udiv_qrnnd_preinv1(q, r, nh, nl, d, di) \
do { \
mp_limb_t _q, _ql, _r; \
mp_limb_t _xh, _xl; \
ASSERT ((d) != 0); \
umul_ppmm (_q, _ql, (nh), (di)); \
_q += (nh); /* Compensate, di is 2**GMP_LIMB_BITS too small */ \
umul_ppmm (_xh, _xl, _q, (d)); \
sub_ddmmss (_xh, _r, (nh), (nl), _xh, _xl); \
if (_xh != 0) \
{ \
sub_ddmmss (_xh, _r, _xh, _r, 0, (d)); \
_q += 1; \
if (_xh != 0) \
{ \
_r -= (d); \
_q += 1; \
} \
} \
if (_r >= (d)) \
{ \
_r -= (d); \
_q += 1; \
} \
(r) = _r; \
(q) = _q; \
} while (0)
/* Like udiv_qrnnd_preinv, but branch-free. */
#define udiv_qrnnd_preinv2(q, r, nh, nl, d, di) \
do { \
mp_limb_t _n2, _n10, _nmask, _nadj, _q1; \
mp_limb_t _xh, _xl; \
_n2 = (nh); \
_n10 = (nl); \
_nmask = LIMB_HIGHBIT_TO_MASK (_n10); \
_nadj = _n10 + (_nmask & (d)); \
umul_ppmm (_xh, _xl, di, _n2 - _nmask); \
add_ssaaaa (_xh, _xl, _xh, _xl, _n2, _nadj); \
_q1 = ~_xh; \
umul_ppmm (_xh, _xl, _q1, d); \
add_ssaaaa (_xh, _xl, _xh, _xl, nh, nl); \
_xh -= (d); /* xh = 0 or -1 */ \
(r) = _xl + ((d) & _xh); \
(q) = _xh - _q1; \
} while (0)
/* Like udiv_qrnnd_preinv2, but for for any value D. DNORM is D shifted left
so that its most significant bit is set. LGUP is ceil(log2(D)). */
#define udiv_qrnnd_preinv2gen(q, r, nh, nl, d, di, dnorm, lgup) \
do { \
mp_limb_t _n2, _n10, _nmask, _nadj, _q1; \
mp_limb_t _xh, _xl; \
_n2 = ((nh) << (BITS_PER_MP_LIMB - (lgup))) + ((nl) >> 1 >> (l - 1));\
_n10 = (nl) << (BITS_PER_MP_LIMB - (lgup)); \
_nmask = LIMB_HIGHBIT_TO_MASK (_n10); \
_nadj = _n10 + (_nmask & (dnorm)); \
umul_ppmm (_xh, _xl, di, _n2 - _nmask); \
add_ssaaaa (_xh, _xl, _xh, _xl, _n2, _nadj); \
_q1 = ~_xh; \
umul_ppmm (_xh, _xl, _q1, d); \
add_ssaaaa (_xh, _xl, _xh, _xl, nh, nl); \
_xh -= (d); \
(r) = _xl + ((d) & _xh); \
(q) = _xh - _q1; \
} while (0)
#ifndef mpn_preinv_divrem_1 /* if not done with cpuvec in a fat binary */
#define mpn_preinv_divrem_1 __MPN(preinv_divrem_1)
mp_limb_t mpn_preinv_divrem_1 _PROTO ((mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t, int));
#endif
/* USE_PREINV_DIVREM_1 is whether to use mpn_preinv_divrem_1, as opposed to
the plain mpn_divrem_1. Likewise USE_PREINV_MOD_1 chooses between
mpn_preinv_mod_1 and plain mpn_mod_1. The default for both is yes, since
the few CISC chips where preinv is not good have defines saying so. */
#ifndef USE_PREINV_DIVREM_1
#define USE_PREINV_DIVREM_1 1
#endif
#ifndef USE_PREINV_MOD_1
#define USE_PREINV_MOD_1 1
#endif
#if USE_PREINV_DIVREM_1
#define MPN_DIVREM_OR_PREINV_DIVREM_1(qp,xsize,ap,size,d,dinv,shift) \
mpn_preinv_divrem_1 (qp, xsize, ap, size, d, dinv, shift)
#else
#define MPN_DIVREM_OR_PREINV_DIVREM_1(qp,xsize,ap,size,d,dinv,shift) \
mpn_divrem_1 (qp, xsize, ap, size, d)
#endif
#if USE_PREINV_MOD_1
#define MPN_MOD_OR_PREINV_MOD_1(src,size,divisor,inverse) \
mpn_preinv_mod_1 (src, size, divisor, inverse)
#else
#define MPN_MOD_OR_PREINV_MOD_1(src,size,divisor,inverse) \
mpn_mod_1 (src, size, divisor)
#endif
#ifndef mpn_mod_34lsub1 /* if not done with cpuvec in a fat binary */
#define mpn_mod_34lsub1 __MPN(mod_34lsub1)
mp_limb_t mpn_mod_34lsub1 _PROTO ((mp_srcptr, mp_size_t)) __GMP_ATTRIBUTE_PURE;
#endif
/* DIVEXACT_1_THRESHOLD is at what size to use mpn_divexact_1, as opposed to
plain mpn_divrem_1. Likewise MODEXACT_1_ODD_THRESHOLD for
mpn_modexact_1_odd against plain mpn_mod_1. On most CPUs divexact and
modexact are faster at all sizes, so the defaults are 0. Those CPUs
where this is not right have a tuned threshold. */
#ifndef DIVEXACT_1_THRESHOLD
#define DIVEXACT_1_THRESHOLD 0
#endif
#ifndef MODEXACT_1_ODD_THRESHOLD
#define MODEXACT_1_ODD_THRESHOLD 0
#endif
#ifndef mpn_divexact_1 /* if not done with cpuvec in a fat binary */
#define mpn_divexact_1 __MPN(divexact_1)
void mpn_divexact_1 _PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t));
#endif
#define MPN_DIVREM_OR_DIVEXACT_1(dst, src, size, divisor) \
do { \
if (BELOW_THRESHOLD (size, DIVEXACT_1_THRESHOLD)) \
ASSERT_NOCARRY (mpn_divrem_1 (dst, (mp_size_t) 0, src, size, divisor)); \
else \
{ \
ASSERT (mpn_mod_1 (src, size, divisor) == 0); \
mpn_divexact_1 (dst, src, size, divisor); \
} \
} while (0)
#ifndef mpn_modexact_1c_odd /* if not done with cpuvec in a fat binary */
#define mpn_modexact_1c_odd __MPN(modexact_1c_odd)
mp_limb_t mpn_modexact_1c_odd _PROTO ((mp_srcptr src, mp_size_t size,
mp_limb_t divisor, mp_limb_t c)) __GMP_ATTRIBUTE_PURE;
#endif
#if HAVE_NATIVE_mpn_modexact_1_odd
#define mpn_modexact_1_odd __MPN(modexact_1_odd)
mp_limb_t mpn_modexact_1_odd _PROTO ((mp_srcptr src, mp_size_t size,
mp_limb_t divisor)) __GMP_ATTRIBUTE_PURE;
#else
#define mpn_modexact_1_odd(src,size,divisor) \
mpn_modexact_1c_odd (src, size, divisor, CNST_LIMB(0))
#endif
#define MPN_MOD_OR_MODEXACT_1_ODD(src,size,divisor) \
(ABOVE_THRESHOLD (size, MODEXACT_1_ODD_THRESHOLD) \
? mpn_modexact_1_odd (src, size, divisor) \
: mpn_mod_1 (src, size, divisor))
/* modlimb_invert() sets inv to the multiplicative inverse of n modulo
2^GMP_NUMB_BITS, ie. satisfying inv*n == 1 mod 2^GMP_NUMB_BITS.
n must be odd (otherwise such an inverse doesn't exist).
This is not to be confused with invert_limb(), which is completely
different.
The table lookup gives an inverse with the low 8 bits valid, and each
multiply step doubles the number of bits. See Jebelean "An algorithm for
exact division" end of section 4 (reference in gmp.texi).
Possible enhancement: Could use UHWtype until the last step, if half-size
multiplies are faster (might help under _LONG_LONG_LIMB).
Alternative: As noted in Granlund and Montgomery "Division by Invariant
Integers using Multiplication" (reference in gmp.texi), n itself gives a
3-bit inverse immediately, and could be used instead of a table lookup.
A 4-bit inverse can be obtained effectively from xoring bits 1 and 2 into
bit 3, for instance with (((n + 2) & 4) << 1) ^ n. */
#define modlimb_invert_table __gmp_modlimb_invert_table
__GMP_DECLSPEC extern const unsigned char modlimb_invert_table[128];
#define modlimb_invert(inv,n) \
do { \
mp_limb_t __n = (n); \
mp_limb_t __inv; \
ASSERT ((__n & 1) == 1); \
\
__inv = modlimb_invert_table[(__n/2) & 0x7F]; /* 8 */ \
if (GMP_NUMB_BITS > 8) __inv = 2 * __inv - __inv * __inv * __n; \
if (GMP_NUMB_BITS > 16) __inv = 2 * __inv - __inv * __inv * __n; \
if (GMP_NUMB_BITS > 32) __inv = 2 * __inv - __inv * __inv * __n; \
\
if (GMP_NUMB_BITS > 64) \
{ \
int __invbits = 64; \
do { \
__inv = 2 * __inv - __inv * __inv * __n; \
__invbits *= 2; \
} while (__invbits < GMP_NUMB_BITS); \
} \
\
ASSERT ((__inv * __n & GMP_NUMB_MASK) == 1); \
(inv) = __inv & GMP_NUMB_MASK; \
} while (0)
/* Multiplicative inverse of 3, modulo 2^GMP_NUMB_BITS.
Eg. 0xAAAAAAAB for 32 bits, 0xAAAAAAAAAAAAAAAB for 64 bits.
GMP_NUMB_MAX/3*2+1 is right when GMP_NUMB_BITS is even, but when it's odd
we need to start from GMP_NUMB_MAX>>1. */
#define MODLIMB_INVERSE_3 (((GMP_NUMB_MAX >> (GMP_NUMB_BITS % 2)) / 3) * 2 + 1)
/* ceil(GMP_NUMB_MAX/3) and ceil(2*GMP_NUMB_MAX/3).
These expressions work because GMP_NUMB_MAX%3 != 0 for all GMP_NUMB_BITS. */
#define GMP_NUMB_CEIL_MAX_DIV3 (GMP_NUMB_MAX / 3 + 1)
#define GMP_NUMB_CEIL_2MAX_DIV3 ((GMP_NUMB_MAX>>1) / 3 + 1 + GMP_NUMB_HIGHBIT)
/* Set r to -a mod d. a>=d is allowed. Can give r>d. All should be limbs.
It's not clear whether this is the best way to do this calculation.
Anything congruent to -a would be fine for the one limb congruence
tests. */
#define NEG_MOD(r, a, d) \
do { \
ASSERT ((d) != 0); \
ASSERT_LIMB (a); \
ASSERT_LIMB (d); \
\
if ((a) <= (d)) \
{ \
/* small a is reasonably likely */ \
(r) = (d) - (a); \
} \
else \
{ \
unsigned __twos; \
mp_limb_t __dnorm; \
count_leading_zeros (__twos, d); \
__twos -= GMP_NAIL_BITS; \
__dnorm = (d) << __twos; \
(r) = ((a) <= __dnorm ? __dnorm : 2*__dnorm) - (a); \
} \
\
ASSERT_LIMB (r); \
} while (0)
/* A bit mask of all the least significant zero bits of n, or -1 if n==0. */
#define LOW_ZEROS_MASK(n) (((n) & -(n)) - 1)
/* ULONG_PARITY sets "p" to 1 if there's an odd number of 1 bits in "n", or
to 0 if there's an even number. "n" should be an unsigned long and "p"
an int. */
#if defined (__GNUC__) && ! defined (NO_ASM) && HAVE_HOST_CPU_alpha_CIX
#define ULONG_PARITY(p, n) \
do { \
int __p; \
__asm__ ("ctpop %1, %0" : "=r" (__p) : "r" (n)); \
(p) = __p & 1; \
} while (0)
#endif
/* Cray intrinsic _popcnt. */
#ifdef _CRAY
#define ULONG_PARITY(p, n) \
do { \
(p) = _popcnt (n) & 1; \
} while (0)
#endif
#if defined (__GNUC__) && ! defined (__INTEL_COMPILER) \
&& ! defined (NO_ASM) && defined (__ia64)
/* unsigned long is either 32 or 64 bits depending on the ABI, zero extend
to a 64 bit unsigned long long for popcnt */
#define ULONG_PARITY(p, n) \
do { \
unsigned long long __n = (unsigned long) (n); \
int __p; \
__asm__ ("popcnt %0 = %1" : "=r" (__p) : "r" (__n)); \
(p) = __p & 1; \
} while (0)
#endif
#if defined (__GNUC__) && ! defined (NO_ASM) && HAVE_HOST_CPU_FAMILY_x86
#if __GMP_GNUC_PREREQ (3,1)
#define __GMP_qm "=Qm"
#define __GMP_q "=Q"
#else
#define __GMP_qm "=qm"
#define __GMP_q "=q"
#endif
#define ULONG_PARITY(p, n) \
do { \
char __p; \
unsigned long __n = (n); \
__n ^= (__n >> 16); \
__asm__ ("xorb %h1, %b1\n\t" \
"setpo %0" \
: __GMP_qm (__p), __GMP_q (__n) \
: "1" (__n)); \
(p) = __p; \
} while (0)
#endif
#if ! defined (ULONG_PARITY)
#define ULONG_PARITY(p, n) \
do { \
unsigned long __n = (n); \
int __p = 0; \
do \
{ \
__p ^= 0x96696996L >> (__n & 0x1F); \
__n >>= 5; \
} \
while (__n != 0); \
\
(p) = __p & 1; \
} while (0)
#endif
/* 3 cycles on 604 or 750 since shifts and rlwimi's can pair. gcc (as of
version 3.1 at least) doesn't seem to know how to generate rlwimi for
anything other than bit-fields, so use "asm". */
#if defined (__GNUC__) && ! defined (NO_ASM) \
&& HAVE_HOST_CPU_FAMILY_powerpc && BITS_PER_MP_LIMB == 32
#define BSWAP_LIMB(dst, src) \
do { \
mp_limb_t __bswapl_src = (src); \
mp_limb_t __tmp1 = __bswapl_src >> 24; /* low byte */ \
mp_limb_t __tmp2 = __bswapl_src << 24; /* high byte */ \
__asm__ ("rlwimi %0, %2, 24, 16, 23" /* 2nd low */ \
: "=r" (__tmp1) : "0" (__tmp1), "r" (__bswapl_src)); \
__asm__ ("rlwimi %0, %2, 8, 8, 15" /* 3nd high */ \
: "=r" (__tmp2) : "0" (__tmp2), "r" (__bswapl_src)); \
(dst) = __tmp1 | __tmp2; /* whole */ \
} while (0)
#endif
/* bswap is available on i486 and up and is fast. A combination rorw $8 /
roll $16 / rorw $8 is used in glibc for plain i386 (and in the linux
kernel with xchgb instead of rorw), but this is not done here, because
i386 means generic x86 and mixing word and dword operations will cause
partial register stalls on P6 chips. */
#if defined (__GNUC__) && ! defined (NO_ASM) \
&& HAVE_HOST_CPU_FAMILY_x86 && ! HAVE_HOST_CPU_i386 \
&& BITS_PER_MP_LIMB == 32
#define BSWAP_LIMB(dst, src) \
do { \
__asm__ ("bswap %0" : "=r" (dst) : "0" (src)); \
} while (0)
#endif
#if defined (__GNUC__) && ! defined (NO_ASM) \
&& defined (__amd64__) && BITS_PER_MP_LIMB == 64
#define BSWAP_LIMB(dst, src) \
do { \
__asm__ ("bswap %q0" : "=r" (dst) : "0" (src)); \
} while (0)
#endif
#if defined (__GNUC__) && ! defined (__INTEL_COMPILER) \
&& ! defined (NO_ASM) && defined (__ia64) && GMP_LIMB_BITS == 64
#define BSWAP_LIMB(dst, src) \
do { \
__asm__ ("mux1 %0 = %1, @rev" : "=r" (dst) : "r" (src)); \
} while (0)
#endif
/* As per glibc. */
#if defined (__GNUC__) && ! defined (NO_ASM) \
&& HAVE_HOST_CPU_FAMILY_m68k && BITS_PER_MP_LIMB == 32
#define BSWAP_LIMB(dst, src) \
do { \
mp_limb_t __bswapl_src = (src); \
__asm__ ("ror%.w %#8, %0\n\t" \
"swap %0\n\t" \
"ror%.w %#8, %0" \
: "=d" (dst) \
: "0" (__bswapl_src)); \
} while (0)
#endif
#if ! defined (BSWAP_LIMB)
#if BITS_PER_MP_LIMB == 8
#define BSWAP_LIMB(dst, src) \
do { (dst) = (src); } while (0)
#endif
#if BITS_PER_MP_LIMB == 16
#define BSWAP_LIMB(dst, src) \
do { \
(dst) = ((src) << 8) + ((src) >> 8); \
} while (0)
#endif
#if BITS_PER_MP_LIMB == 32
#define BSWAP_LIMB(dst, src) \
do { \
(dst) = \
((src) << 24) \
+ (((src) & 0xFF00) << 8) \
+ (((src) >> 8) & 0xFF00) \
+ ((src) >> 24); \
} while (0)
#endif
#if BITS_PER_MP_LIMB == 64
#define BSWAP_LIMB(dst, src) \
do { \
(dst) = \
((src) << 56) \
+ (((src) & 0xFF00) << 40) \
+ (((src) & 0xFF0000) << 24) \
+ (((src) & 0xFF000000) << 8) \
+ (((src) >> 8) & 0xFF000000) \
+ (((src) >> 24) & 0xFF0000) \
+ (((src) >> 40) & 0xFF00) \
+ ((src) >> 56); \
} while (0)
#endif
#endif
#if ! defined (BSWAP_LIMB)
#define BSWAP_LIMB(dst, src) \
do { \
mp_limb_t __bswapl_src = (src); \
mp_limb_t __dst = 0; \
int __i; \
for (__i = 0; __i < BYTES_PER_MP_LIMB; __i++) \
{ \
__dst = (__dst << 8) | (__bswapl_src & 0xFF); \
__bswapl_src >>= 8; \
} \
(dst) = __dst; \
} while (0)
#endif
/* Apparently lwbrx might be slow on some PowerPC chips, so restrict it to
those we know are fast. */
#if defined (__GNUC__) && ! defined (NO_ASM) \
&& BITS_PER_MP_LIMB == 32 && HAVE_LIMB_BIG_ENDIAN \
&& (HAVE_HOST_CPU_powerpc604 \
|| HAVE_HOST_CPU_powerpc604e \
|| HAVE_HOST_CPU_powerpc750 \
|| HAVE_HOST_CPU_powerpc7400)
#define BSWAP_LIMB_FETCH(limb, src) \
do { \
mp_srcptr __blf_src = (src); \
mp_limb_t __limb; \
__asm__ ("lwbrx %0, 0, %1" \
: "=r" (__limb) \
: "r" (__blf_src), \
"m" (*__blf_src)); \
(limb) = __limb; \
} while (0)
#endif
#if ! defined (BSWAP_LIMB_FETCH)
#define BSWAP_LIMB_FETCH(limb, src) BSWAP_LIMB (limb, *(src))
#endif
/* On the same basis that lwbrx might be slow, restrict stwbrx to those we
know are fast. FIXME: Is this necessary? */
#if defined (__GNUC__) && ! defined (NO_ASM) \
&& BITS_PER_MP_LIMB == 32 && HAVE_LIMB_BIG_ENDIAN \
&& (HAVE_HOST_CPU_powerpc604 \
|| HAVE_HOST_CPU_powerpc604e \
|| HAVE_HOST_CPU_powerpc750 \
|| HAVE_HOST_CPU_powerpc7400)
#define BSWAP_LIMB_STORE(dst, limb) \
do { \
mp_ptr __dst = (dst); \
mp_limb_t __limb = (limb); \
__asm__ ("stwbrx %1, 0, %2" \
: "=m" (*__dst) \
: "r" (__limb), \
"r" (__dst)); \
} while (0)
#endif
#if ! defined (BSWAP_LIMB_STORE)
#define BSWAP_LIMB_STORE(dst, limb) BSWAP_LIMB (*(dst), limb)
#endif
/* Byte swap limbs from {src,size} and store at {dst,size}. */
#define MPN_BSWAP(dst, src, size) \
do { \
mp_ptr __dst = (dst); \
mp_srcptr __src = (src); \
mp_size_t __size = (size); \
mp_size_t __i; \
ASSERT ((size) >= 0); \
ASSERT (MPN_SAME_OR_SEPARATE_P (dst, src, size)); \
CRAY_Pragma ("_CRI ivdep"); \
for (__i = 0; __i < __size; __i++) \
{ \
BSWAP_LIMB_FETCH (*__dst, __src); \
__dst++; \
__src++; \
} \
} while (0)
/* Byte swap limbs from {dst,size} and store in reverse order at {src,size}. */
#define MPN_BSWAP_REVERSE(dst, src, size) \
do { \
mp_ptr __dst = (dst); \
mp_size_t __size = (size); \
mp_srcptr __src = (src) + __size - 1; \
mp_size_t __i; \
ASSERT ((size) >= 0); \
ASSERT (! MPN_OVERLAP_P (dst, size, src, size)); \
CRAY_Pragma ("_CRI ivdep"); \
for (__i = 0; __i < __size; __i++) \
{ \
BSWAP_LIMB_FETCH (*__dst, __src); \
__dst++; \
__src--; \
} \
} while (0)
/* No processor claiming to be SPARC v9 compliant seems to
implement the POPC instruction. Disable pattern for now. */
#if 0
#if defined __GNUC__ && defined __sparc_v9__ && BITS_PER_MP_LIMB == 64
#define popc_limb(result, input) \
do { \
DItype __res; \
__asm__ ("popc %1,%0" : "=r" (result) : "rI" (input)); \
} while (0)
#endif
#endif
#if defined (__GNUC__) && ! defined (NO_ASM) && HAVE_HOST_CPU_alpha_CIX
#define popc_limb(result, input) \
do { \
__asm__ ("ctpop %1, %0" : "=r" (result) : "r" (input)); \
} while (0)
#endif
/* Cray intrinsic. */
#ifdef _CRAY
#define popc_limb(result, input) \
do { \
(result) = _popcnt (input); \
} while (0)
#endif
#if defined (__GNUC__) && ! defined (__INTEL_COMPILER) \
&& ! defined (NO_ASM) && defined (__ia64) && GMP_LIMB_BITS == 64
#define popc_limb(result, input) \
do { \
__asm__ ("popcnt %0 = %1" : "=r" (result) : "r" (input)); \
} while (0)
#endif
/* Cool population count of an mp_limb_t.
You have to figure out how this works, We won't tell you!
The constants could also be expressed as:
0x55... = [2^N / 3] = [(2^N-1)/3]
0x33... = [2^N / 5] = [(2^N-1)/5]
0x0f... = [2^N / 17] = [(2^N-1)/17]
(N is GMP_LIMB_BITS, [] denotes truncation.) */
#if ! defined (popc_limb) && GMP_LIMB_BITS == 8
#define popc_limb(result, input) \
do { \
mp_limb_t __x = (input); \
__x -= (__x >> 1) & MP_LIMB_T_MAX/3; \
__x = ((__x >> 2) & MP_LIMB_T_MAX/5) + (__x & MP_LIMB_T_MAX/5); \
__x = ((__x >> 4) + __x) & MP_LIMB_T_MAX/17; \
(result) = __x & 0xff; \
} while (0)
#endif
#if ! defined (popc_limb) && GMP_LIMB_BITS == 16
#define popc_limb(result, input) \
do { \
mp_limb_t __x = (input); \
__x -= (__x >> 1) & MP_LIMB_T_MAX/3; \
__x = ((__x >> 2) & MP_LIMB_T_MAX/5) + (__x & MP_LIMB_T_MAX/5); \
__x = ((__x >> 4) + __x) & MP_LIMB_T_MAX/17; \
if (GMP_LIMB_BITS > 8) \
__x = ((__x >> 8) + __x); \
(result) = __x & 0xff; \
} while (0)
#endif
#if ! defined (popc_limb) && GMP_LIMB_BITS == 32
#define popc_limb(result, input) \
do { \
mp_limb_t __x = (input); \
__x -= (__x >> 1) & MP_LIMB_T_MAX/3; \
__x = ((__x >> 2) & MP_LIMB_T_MAX/5) + (__x & MP_LIMB_T_MAX/5); \
__x = ((__x >> 4) + __x) & MP_LIMB_T_MAX/17; \
if (GMP_LIMB_BITS > 8) \
__x = ((__x >> 8) + __x); \
if (GMP_LIMB_BITS > 16) \
__x = ((__x >> 16) + __x); \
(result) = __x & 0xff; \
} while (0)
#endif
#if ! defined (popc_limb) && GMP_LIMB_BITS == 64
#define popc_limb(result, input) \
do { \
mp_limb_t __x = (input); \
__x -= (__x >> 1) & MP_LIMB_T_MAX/3; \
__x = ((__x >> 2) & MP_LIMB_T_MAX/5) + (__x & MP_LIMB_T_MAX/5); \
__x = ((__x >> 4) + __x) & MP_LIMB_T_MAX/17; \
if (GMP_LIMB_BITS > 8) \
__x = ((__x >> 8) + __x); \
if (GMP_LIMB_BITS > 16) \
__x = ((__x >> 16) + __x); \
if (GMP_LIMB_BITS > 32) \
__x = ((__x >> 32) + __x); \
(result) = __x & 0xff; \
} while (0)
#endif
/* Define stuff for longlong.h. */
#if HAVE_ATTRIBUTE_MODE && defined (__GNUC__)
typedef unsigned int UQItype __attribute__ ((mode (QI)));
typedef int SItype __attribute__ ((mode (SI)));
typedef unsigned int USItype __attribute__ ((mode (SI)));
typedef int DItype __attribute__ ((mode (DI)));
typedef unsigned int UDItype __attribute__ ((mode (DI)));
#else
typedef unsigned char UQItype;
typedef long SItype;
typedef unsigned long USItype;
#if HAVE_LONG_LONG
typedef long long int DItype;
typedef unsigned long long int UDItype;
#else /* Assume `long' gives us a wide enough type. Needed for hppa2.0w. */
typedef long int DItype;
typedef unsigned long int UDItype;
#endif
#endif
typedef mp_limb_t UWtype;
typedef unsigned int UHWtype;
#define W_TYPE_SIZE BITS_PER_MP_LIMB
/* Define ieee_double_extract and _GMP_IEEE_FLOATS.
Bit field packing is "implementation defined" according to C99, which
leaves us at the compiler's mercy here. For some systems packing is
defined in the ABI (eg. x86). In any case so far it seems universal that
little endian systems pack from low to high, and big endian from high to
low within the given type.
Within the fields we rely on the integer endianness being the same as the
float endianness, this is true everywhere we know of and it'd be a fairly
strange system that did anything else. */
#if HAVE_DOUBLE_IEEE_LITTLE_SWAPPED
#define _GMP_IEEE_FLOATS 1
union ieee_double_extract
{
struct
{
gmp_uint_least32_t manh:20;
gmp_uint_least32_t exp:11;
gmp_uint_least32_t sig:1;
gmp_uint_least32_t manl:32;
} s;
double d;
};
#endif
#if HAVE_DOUBLE_IEEE_LITTLE_ENDIAN
#define _GMP_IEEE_FLOATS 1
union ieee_double_extract
{
struct
{
gmp_uint_least32_t manl:32;
gmp_uint_least32_t manh:20;
gmp_uint_least32_t exp:11;
gmp_uint_least32_t sig:1;
} s;
double d;
};
#endif
#if HAVE_DOUBLE_IEEE_BIG_ENDIAN
#define _GMP_IEEE_FLOATS 1
union ieee_double_extract
{
struct
{
gmp_uint_least32_t sig:1;
gmp_uint_least32_t exp:11;
gmp_uint_least32_t manh:20;
gmp_uint_least32_t manl:32;
} s;
double d;
};
#endif
/* Use (4.0 * ...) instead of (2.0 * ...) to work around buggy compilers
that don't convert ulong->double correctly (eg. SunOS 4 native cc). */
#define MP_BASE_AS_DOUBLE (4.0 * ((mp_limb_t) 1 << (GMP_NUMB_BITS - 2)))
/* Maximum number of limbs it will take to store any `double'.
We assume doubles have 53 mantissam bits. */
#define LIMBS_PER_DOUBLE ((53 + GMP_NUMB_BITS - 1) / GMP_NUMB_BITS + 1)
int __gmp_extract_double _PROTO ((mp_ptr, double));
#define mpn_get_d __gmpn_get_d
double mpn_get_d __GMP_PROTO ((mp_srcptr, mp_size_t, mp_size_t, long)) __GMP_ATTRIBUTE_PURE;
/* DOUBLE_NAN_INF_ACTION executes code a_nan if x is a NaN, or executes
a_inf if x is an infinity. Both are considered unlikely values, for
branch prediction. */
#if _GMP_IEEE_FLOATS
#define DOUBLE_NAN_INF_ACTION(x, a_nan, a_inf) \
do { \
union ieee_double_extract u; \
u.d = (x); \
if (UNLIKELY (u.s.exp == 0x7FF)) \
{ \
if (u.s.manl == 0 && u.s.manh == 0) \
{ a_inf; } \
else \
{ a_nan; } \
} \
} while (0)
#endif
#if HAVE_DOUBLE_VAX_D || HAVE_DOUBLE_VAX_G || HAVE_DOUBLE_CRAY_CFP
/* no nans or infs in these formats */
#define DOUBLE_NAN_INF_ACTION(x, a_nan, a_inf) \
do { } while (0)
#endif
#ifndef DOUBLE_NAN_INF_ACTION
/* Unknown format, try something generic.
NaN should be "unordered", so x!=x.
Inf should be bigger than DBL_MAX. */
#define DOUBLE_NAN_INF_ACTION(x, a_nan, a_inf) \
do { \
{ \
if (UNLIKELY ((x) != (x))) \
{ a_nan; } \
else if (UNLIKELY ((x) > DBL_MAX || (x) < -DBL_MAX)) \
{ a_inf; } \
} \
} while (0)
#endif
/* On m68k, x86 and amd64, gcc (and maybe other compilers) can hold doubles
in the coprocessor, which means a bigger exponent range than normal, and
depending on the rounding mode, a bigger mantissa than normal. (See
"Disappointments" in the gcc manual.) FORCE_DOUBLE stores and fetches
"d" through memory to force any rounding and overflows to occur.
On amd64, and on x86s with SSE2, gcc (depending on options) uses the xmm
registers, where there's no such extra precision and no need for the
FORCE_DOUBLE. We don't bother to detect this since the present uses for
FORCE_DOUBLE are only in test programs and default generic C code.
Not quite sure that an "automatic volatile" will use memory, but it does
in gcc. An asm("":"=m"(d):"0"(d)) can't be used to trick gcc, since
apparently matching operands like "0" are only allowed on a register
output. gcc 3.4 warns about this, though in fact it and past versions
seem to put the operand through memory as hoped. */
#if (HAVE_HOST_CPU_FAMILY_m68k || HAVE_HOST_CPU_FAMILY_x86 \
|| defined (__amd64__))
#define FORCE_DOUBLE(d) \
do { volatile double __gmp_force = (d); (d) = __gmp_force; } while (0)
#else
#define FORCE_DOUBLE(d) do { } while (0)
#endif
extern int __gmp_junk;
extern const int __gmp_0;
void __gmp_exception _PROTO ((int)) ATTRIBUTE_NORETURN;
void __gmp_divide_by_zero _PROTO ((void)) ATTRIBUTE_NORETURN;
void __gmp_sqrt_of_negative _PROTO ((void)) ATTRIBUTE_NORETURN;
void __gmp_invalid_operation _PROTO ((void)) ATTRIBUTE_NORETURN;
#define GMP_ERROR(code) __gmp_exception (code)
#define DIVIDE_BY_ZERO __gmp_divide_by_zero ()
#define SQRT_OF_NEGATIVE __gmp_sqrt_of_negative ()
#if defined _LONG_LONG_LIMB
#if __GMP_HAVE_TOKEN_PASTE
#define CNST_LIMB(C) ((mp_limb_t) C##LL)
#else
#define CNST_LIMB(C) ((mp_limb_t) C/**/LL)
#endif
#else /* not _LONG_LONG_LIMB */
#if __GMP_HAVE_TOKEN_PASTE
#define CNST_LIMB(C) ((mp_limb_t) C##L)
#else
#define CNST_LIMB(C) ((mp_limb_t) C/**/L)
#endif
#endif /* _LONG_LONG_LIMB */
/* Stuff used by mpn/generic/perfsqr.c and mpz/prime_p.c */
#if GMP_NUMB_BITS == 2
#define PP 0x3 /* 3 */
#define PP_FIRST_OMITTED 5
#endif
#if GMP_NUMB_BITS == 4
#define PP 0xF /* 3 x 5 */
#define PP_FIRST_OMITTED 7
#endif
#if GMP_NUMB_BITS == 8
#define PP 0x69 /* 3 x 5 x 7 */
#define PP_FIRST_OMITTED 11
#endif
#if GMP_NUMB_BITS == 16
#define PP 0x3AA7 /* 3 x 5 x 7 x 11 x 13 */
#define PP_FIRST_OMITTED 17
#endif
#if GMP_NUMB_BITS == 32
#define PP 0xC0CFD797L /* 3 x 5 x 7 x 11 x ... x 29 */
#define PP_INVERTED 0x53E5645CL
#define PP_FIRST_OMITTED 31
#endif
#if GMP_NUMB_BITS == 64
#define PP CNST_LIMB(0xE221F97C30E94E1D) /* 3 x 5 x 7 x 11 x ... x 53 */
#define PP_INVERTED CNST_LIMB(0x21CFE6CFC938B36B)
#define PP_FIRST_OMITTED 59
#endif
#ifndef PP_FIRST_OMITTED
#define PP_FIRST_OMITTED 3
#endif
/* BIT1 means a result value in bit 1 (second least significant bit), with a
zero bit representing +1 and a one bit representing -1. Bits other than
bit 1 are garbage. These are meant to be kept in "int"s, and casts are
used to ensure the expressions are "int"s even if a and/or b might be
other types.
JACOBI_TWOS_U_BIT1 and JACOBI_RECIP_UU_BIT1 are used in mpn_jacobi_base
and their speed is important. Expressions are used rather than
conditionals to accumulate sign changes, which effectively means XORs
instead of conditional JUMPs. */
/* (a/0), with a signed; is 1 if a=+/-1, 0 otherwise */
#define JACOBI_S0(a) (((a) == 1) | ((a) == -1))
/* (a/0), with a unsigned; is 1 if a=+/-1, 0 otherwise */
#define JACOBI_U0(a) ((a) == 1)
/* (a/0), with a given by low and size;
is 1 if a=+/-1, 0 otherwise */
#define JACOBI_LS0(alow,asize) \
(((asize) == 1 || (asize) == -1) && (alow) == 1)
/* (a/0), with a an mpz_t;
fetch of low limb always valid, even if size is zero */
#define JACOBI_Z0(a) JACOBI_LS0 (PTR(a)[0], SIZ(a))
/* (0/b), with b unsigned; is 1 if b=1, 0 otherwise */
#define JACOBI_0U(b) ((b) == 1)
/* (0/b), with b unsigned; is 1 if b=+/-1, 0 otherwise */
#define JACOBI_0S(b) ((b) == 1 || (b) == -1)
/* (0/b), with b given by low and size; is 1 if b=+/-1, 0 otherwise */
#define JACOBI_0LS(blow,bsize) \
(((bsize) == 1 || (bsize) == -1) && (blow) == 1)
/* Convert a bit1 to +1 or -1. */
#define JACOBI_BIT1_TO_PN(result_bit1) \
(1 - ((int) (result_bit1) & 2))
/* (2/b), with b unsigned and odd;
is (-1)^((b^2-1)/8) which is 1 if b==1,7mod8 or -1 if b==3,5mod8 and
hence obtained from (b>>1)^b */
#define JACOBI_TWO_U_BIT1(b) \
((int) (((b) >> 1) ^ (b)))
/* (2/b)^twos, with b unsigned and odd */
#define JACOBI_TWOS_U_BIT1(twos, b) \
((int) ((twos) << 1) & JACOBI_TWO_U_BIT1 (b))
/* (2/b)^twos, with b unsigned and odd */
#define JACOBI_TWOS_U(twos, b) \
(JACOBI_BIT1_TO_PN (JACOBI_TWOS_U_BIT1 (twos, b)))
/* (-1/b), with b odd (signed or unsigned);
is (-1)^((b-1)/2) */
#define JACOBI_N1B_BIT1(b) \
((int) (b))
/* (a/b) effect due to sign of a: signed/unsigned, b odd;
is (-1/b) if a<0, or +1 if a>=0 */
#define JACOBI_ASGN_SU_BIT1(a, b) \
((((a) < 0) << 1) & JACOBI_N1B_BIT1(b))
/* (a/b) effect due to sign of b: signed/signed;
is -1 if a and b both negative, +1 otherwise */
#define JACOBI_BSGN_SS_BIT1(a, b) \
((((a)<0) & ((b)<0)) << 1)
/* (a/b) effect due to sign of b: signed/mpz;
is -1 if a and b both negative, +1 otherwise */
#define JACOBI_BSGN_SZ_BIT1(a, b) \
JACOBI_BSGN_SS_BIT1 (a, SIZ(b))
/* (a/b) effect due to sign of b: mpz/signed;
is -1 if a and b both negative, +1 otherwise */
#define JACOBI_BSGN_ZS_BIT1(a, b) \
JACOBI_BSGN_SZ_BIT1 (b, a)
/* (a/b) reciprocity to switch to (b/a), a,b both unsigned and odd;
is (-1)^((a-1)*(b-1)/4), which means +1 if either a,b==1mod4, or -1 if
both a,b==3mod4, achieved in bit 1 by a&b. No ASSERT()s about a,b odd
because this is used in a couple of places with only bit 1 of a or b
valid. */
#define JACOBI_RECIP_UU_BIT1(a, b) \
((int) ((a) & (b)))
/* Strip low zero limbs from {b_ptr,b_size} by incrementing b_ptr and
decrementing b_size. b_low should be b_ptr[0] on entry, and will be
updated for the new b_ptr. result_bit1 is updated according to the
factors of 2 stripped, as per (a/2). */
#define JACOBI_STRIP_LOW_ZEROS(result_bit1, a, b_ptr, b_size, b_low) \
do { \
ASSERT ((b_size) >= 1); \
ASSERT ((b_low) == (b_ptr)[0]); \
\
while (UNLIKELY ((b_low) == 0)) \
{ \
(b_size)--; \
ASSERT ((b_size) >= 1); \
(b_ptr)++; \
(b_low) = *(b_ptr); \
\
ASSERT (((a) & 1) != 0); \
if ((GMP_NUMB_BITS % 2) == 1) \
(result_bit1) ^= JACOBI_TWO_U_BIT1(a); \
} \
} while (0)
/* Set a_rem to {a_ptr,a_size} reduced modulo b, either using mod_1 or
modexact_1_odd, but in either case leaving a_rem<b. b must be odd and
unsigned. modexact_1_odd effectively calculates -a mod b, and
result_bit1 is adjusted for the factor of -1.
The way mpn_modexact_1_odd sometimes bases its remainder on a_size and
sometimes on a_size-1 means if GMP_NUMB_BITS is odd we can't know what
factor to introduce into result_bit1, so for that case use mpn_mod_1
unconditionally.
FIXME: mpn_modexact_1_odd is more efficient, so some way to get it used
for odd GMP_NUMB_BITS would be good. Perhaps it could mung its result,
or not skip a divide step, or something. */
#define JACOBI_MOD_OR_MODEXACT_1_ODD(result_bit1, a_rem, a_ptr, a_size, b) \
do { \
mp_srcptr __a_ptr = (a_ptr); \
mp_size_t __a_size = (a_size); \
mp_limb_t __b = (b); \
\
ASSERT (__a_size >= 1); \
ASSERT (__b & 1); \
\
if ((GMP_NUMB_BITS % 2) != 0 \
|| BELOW_THRESHOLD (__a_size, MODEXACT_1_ODD_THRESHOLD)) \
{ \
(a_rem) = mpn_mod_1 (__a_ptr, __a_size, __b); \
} \
else \
{ \
(result_bit1) ^= JACOBI_N1B_BIT1 (__b); \
(a_rem) = mpn_modexact_1_odd (__a_ptr, __a_size, __b); \
} \
} while (0)
/* HGCD definitions */
#define mpn_hgcd2 __MPN(hgcd2)
#define mpn_hgcd2_fix __MPN(hgcd2_fix)
#define mpn_hgcd2_lehmer_step __MPN(hgcd2_lehmer_step)
#define mpn_hgcd_max_recursion __MPN(hgcd_max_recursion)
#define mpn_hgcd_init_itch __MPN(hgcd_init_itch)
#define mpn_hgcd_init __MPN(hgcd_init)
#define mpn_hgcd_lehmer_itch __MPN(hgcd_lehmer_itch)
#define mpn_hgcd_lehmer __MPN(hgcd_lehmer)
#define mpn_hgcd_itch __MPN(hgcd_itch)
#define mpn_hgcd __MPN(hgcd)
#define mpn_hgcd_equal __MPN(hgcd_equal)
#define mpn_hgcd_fix __MPN(hgcd_fix)
struct hgcd2_row
{
/* r = (-)u a + (-)v b */
mp_limb_t u;
mp_limb_t v;
};
struct hgcd2
{
/* Sign of the first row, sign >= 0 implies that u >= 0 and v <= 0,
sign < 0 implies u <= 0, v >= 0 */
int sign;
struct hgcd2_row row[4];
/* The quotients r0/r1 and r1/r2. */
mp_limb_t q[2];
};
int
mpn_hgcd2 __GMP_PROTO ((struct hgcd2 *hgcd,
mp_limb_t ah, mp_limb_t al,
mp_limb_t bh, mp_limb_t bl));
mp_size_t
mpn_hgcd2_fix __GMP_PROTO ((mp_ptr rp, mp_size_t ralloc,
int sign,
mp_limb_t u, mp_srcptr ap, mp_size_t asize,
mp_limb_t v, mp_srcptr bp, mp_size_t bsize));
int
mpn_hgcd2_lehmer_step __GMP_PROTO ((struct hgcd2 *hgcd,
mp_srcptr ap, mp_size_t asize,
mp_srcptr bp, mp_size_t bsize));
unsigned
mpn_hgcd_max_recursion __GMP_PROTO ((mp_size_t n));
struct hgcd_row
{
/* [rp, rsize] should always be normalized. */
mp_ptr rp; mp_size_t rsize;
mp_ptr uvp[2];
};
struct hgcd
{
int sign;
/* Space allocated for the uv entries, for sanity checking */
mp_size_t alloc;
/* Size of the largest u,v entry, usually row[3].uvp[1]. This
element should be normalized. Smaller elements must be zero
padded, and all unused limbs (i.e. between size and alloc) must
be zero. */
mp_size_t size;
struct hgcd_row row[4];
/* The quotients r0/r1 and r1/r2. */
mp_size_t qsize[2];
mp_ptr qp[2];
};
mp_size_t
mpn_hgcd_init_itch __GMP_PROTO ((mp_size_t size));
mp_size_t
mpn_hgcd_quotients_init_itch (mp_size_t asize);
void
mpn_hgcd_quotients_init (struct hgcd *hgcd,
mp_size_t asize,
mp_limb_t *limbs);
void
mpn_hgcd_init __GMP_PROTO ((struct hgcd *hgcd,
mp_size_t asize,
mp_limb_t *limbs));
mp_size_t
mpn_hgcd_lehmer_itch __GMP_PROTO ((mp_size_t asize));
int
mpn_hgcd_lehmer __GMP_PROTO ((struct hgcd *hgcd,
mp_srcptr ap, mp_size_t asize,
mp_srcptr bp, mp_size_t bsize,
mp_ptr tp, mp_size_t talloc));
mp_size_t
mpn_hgcd_itch __GMP_PROTO ((mp_size_t size));
int
mpn_hgcd __GMP_PROTO ((struct hgcd *hgcd,
mp_srcptr ap, mp_size_t asize,
mp_srcptr bp, mp_size_t bsize,
mp_ptr tp, mp_size_t talloc));
int
mpn_hgcd_equal __GMP_PROTO ((const struct hgcd *A, const struct hgcd *B));
mp_size_t
mpn_hgcd_fix __GMP_PROTO ((mp_size_t k,
mp_ptr rp, mp_size_t ralloc,
int sign, mp_size_t uvsize,
const struct hgcd_row *s,
mp_srcptr ap, mp_srcptr bp,
mp_ptr tp, mp_size_t talloc));
/* bgcd definitions */
#define mpn_bgcd_matrix_init __MPN(bgcd_matrix_init)
#define mpn_hbgcd_n_itch __MPN(hbgcd_n_itch)
#define mpn_hbgcd_n __MPN(hbgcd_n)
struct bgcd_matrix
{
unsigned j;
/* For sanity checks only. The alloc - n limbs above n should always
be zero. The allocated space must always include one limb beyond
the maximum size. */
mp_size_t alloc;
/* Size of matrix elements */
mp_size_t n;
signed char sign[2][2];
mp_ptr R[2][2];
};
/* See comment in bgcd.c */
#define MPN_BGCD_MATRIX_ITCH(n) ((11 * (n) + 31) / 16)
void
mpn_bgcd_matrix_init (struct bgcd_matrix *m, mp_ptr limbs, mp_size_t alloc);
mp_size_t
mpn_hbgcd_n_itch (mp_size_t n);
mp_size_t
mpn_hbgcd_n (mp_ptr ap, mp_ptr bp, mp_size_t n, unsigned k,
struct bgcd_matrix *m, mp_ptr tp);
/* ngcd definitions */
#define mpn_ngcd2 __MPN (ngcd2)
#define mpn_ngcd_matrix1_vector __MPN (ngcd_matrix1_vector)
#define mpn_ngcd_matrix_init __MPN (ngcd_matrix_init)
#define mpn_ngcd_matrix_mul __MPN (ngcd_matrix_mul)
#define mpn_ngcd_matrix_adjust __MPN (ngcd_matrix_adjust)
#define mpn_ngcd_step __MPN (ngcd_step)
#define mpn_nhgcd_itch __MPN (nhgcd_itch)
#define mpn_nhgcd __MPN (nhgcd)
/* The matrix non-negative M = (u, u'; v,v') keeps track of the
reduction (a;b) = M (alpha; beta) where alpha, beta are smaller
than a, b. The determinant must always be one, so that M has an
inverse (v', -u'; -v, u). Elements always fit in GMP_NUMB_BITS - 1
bits. */
struct ngcd_matrix1
{
mp_limb_t u[2][2];
};
int
mpn_nhgcd2 (mp_limb_t ah, mp_limb_t al, mp_limb_t bh, mp_limb_t bl,
struct ngcd_matrix1 *M);
mp_size_t
mpn_ngcd_matrix1_vector (struct ngcd_matrix1 *M, mp_size_t n, mp_ptr ap, mp_ptr bp, mp_ptr tp);
struct ngcd_matrix
{
/* For sanity checking only */
mp_size_t alloc;
mp_size_t n;
mp_ptr p[2][2];
/* Temporary storage, of the same size as the elements */
mp_ptr tp;
};
#define MPN_NGCD_MATRIX_INIT_ITCH(n) (5 * ((n+1)/2))
void
mpn_ngcd_matrix_init (struct ngcd_matrix *M, mp_size_t n, mp_ptr p);
void
mpn_ngcd_matrix_mul (struct ngcd_matrix *M, const struct ngcd_matrix *M1,
mp_ptr tp);
mp_size_t
mpn_ngcd_matrix_adjust (struct ngcd_matrix *M,
mp_size_t n, mp_ptr ap, mp_ptr bp,
mp_size_t p, mp_ptr tp);
#define MPN_NGCD_STEP_ITCH(n) ((n) + 1)
mp_size_t
mpn_ngcd_step (mp_size_t n, mp_ptr ap, mp_ptr bp, mp_size_t s,
struct ngcd_matrix *M, mp_ptr tp);
mp_size_t
mpn_nhgcd_itch (mp_size_t n);
mp_size_t
mpn_nhgcd (mp_ptr ap, mp_ptr bp, mp_size_t n,
struct ngcd_matrix *M, mp_ptr tp);
/* lgcd definitions */
#define mpn_ngcd_subdiv_step __MPN(ngcd_subdiv_step)
#define mpn_ngcd_lehmer __MPN(ngcd_lehmer)
#define mpn_lgcd __MPN(lgcd)
/* Needs storage for the division */
#define MPN_NGCD_SUBDIV_STEP_ITCH(n) ((n)+1)
mp_size_t
mpn_ngcd_subdiv_step (mp_ptr gp, mp_size_t *gn,
mp_ptr ap, mp_ptr bp, mp_size_t n, mp_ptr tp);
#define MPN_NGCD_LEHMER_ITCH(n) (2*(n))
mp_size_t
mpn_ngcd_lehmer (mp_ptr gp, mp_ptr ap, mp_ptr bp, mp_size_t n, mp_ptr tp);
mp_size_t
mpn_ngcd (mp_ptr gp, mp_ptr ap, mp_size_t an, mp_ptr bp, mp_size_t n);
mp_size_t
mpn_lgcd (mp_ptr gp, mp_ptr ap, mp_size_t an, mp_ptr bp, mp_size_t bn);
mp_size_t
mpn_rgcd (mp_ptr gp, mp_ptr up, mp_size_t usize, mp_ptr vp, mp_size_t vsize);
mp_size_t
mpn_sgcd (mp_ptr gp, mp_ptr ap, mp_size_t an, mp_ptr bp, mp_size_t bn);
mp_size_t
mpn_bgcd (mp_ptr gp, mp_ptr ap, mp_size_t an, mp_ptr bp, mp_size_t bn);
mp_size_t
mpn_basic_gcd (mp_ptr gp, mp_ptr up, mp_size_t usize, mp_ptr vp, mp_size_t vsize);
/* Default HGCD_SCHOENHAGE_THRESHOLD and GCD_SCHOENHAGE_THRESHOLD are for x86/k7 */
#ifndef HGCD_SCHOENHAGE_THRESHOLD
#define HGCD_SCHOENHAGE_THRESHOLD 191
#endif
#ifndef GCD_SCHOENHAGE_THRESHOLD
#define GCD_SCHOENHAGE_THRESHOLD 951
#endif
#ifndef GCDEXT_SCHOENHAGE_THRESHOLD
#define GCDEXT_SCHOENHAGE_THRESHOLD 600
#endif
/* This isn't tuned properly, but half of HGCD_SCHOENHAGE_THRESHOLD
makes some sense. */
#ifndef SGCD_BASE_THRESHOLD
#define SGCD_BASE_THRESHOLD ((HGCD_SCHOENHAGE_THRESHOLD) /2)
#endif
#ifndef SGCD_THRESHOLD
#define SGCD_THRESHOLD 1193
#endif
#ifndef HBGCD_THRESHOLD
#define HBGCD_THRESHOLD 133
#endif
#ifndef BGCD_THRESHOLD
#define BGCD_THRESHOLD 1015
#endif
#ifndef NHGCD_THRESHOLD
#define NHGCD_THRESHOLD 159
#endif
#ifndef NGCD_THRESHOLD
#define NGCD_THRESHOLD 866
#endif
/* Must be at least 7 */
#ifndef NGCD_LEHMER_THRESHOLD
#define NGCD_LEHMER_THRESHOLD 7
#endif
/* __GMPF_BITS_TO_PREC applies a minimum 53 bits, rounds upwards to a whole
limb and adds an extra limb. __GMPF_PREC_TO_BITS drops that extra limb,
hence giving back the user's size in bits rounded up. Notice that
converting prec->bits->prec gives an unchanged value. */
#define __GMPF_BITS_TO_PREC(n) \
((mp_size_t) ((__GMP_MAX (53, n) + 2 * GMP_NUMB_BITS - 1) / GMP_NUMB_BITS))
#define __GMPF_PREC_TO_BITS(n) \
((unsigned long) (n) * GMP_NUMB_BITS - GMP_NUMB_BITS)
extern mp_size_t __gmp_default_fp_limb_precision;
/* Set n to the number of significant digits an mpf of the given _mp_prec
field, in the given base. This is a rounded up value, designed to ensure
there's enough digits to reproduce all the guaranteed part of the value.
There are prec many limbs, but the high might be only "1" so forget it
and just count prec-1 limbs into chars. +1 rounds that upwards, and a
further +1 is because the limbs usually won't fall on digit boundaries.
FIXME: If base is a power of 2 and the bits per digit divides
BITS_PER_MP_LIMB then the +2 is unnecessary. This happens always for
base==2, and in base==16 with the current 32 or 64 bit limb sizes. */
#define MPF_SIGNIFICANT_DIGITS(n, base, prec) \
do { \
ASSERT (base >= 2 && base < numberof (mp_bases)); \
(n) = 2 + (size_t) ((((size_t) (prec) - 1) * GMP_NUMB_BITS) \
* mp_bases[(base)].chars_per_bit_exactly); \
} while (0)
/* Decimal point string, from the current C locale. Needs <langinfo.h> for
nl_langinfo and constants, preferrably with _GNU_SOURCE defined to get
DECIMAL_POINT from glibc, and needs <locale.h> for localeconv, each under
their respective #if HAVE_FOO_H.
GLIBC recommends nl_langinfo because getting only one facet can be
faster, apparently. */
/* DECIMAL_POINT seems to need _GNU_SOURCE defined to get it from glibc. */
#if HAVE_NL_LANGINFO && defined (DECIMAL_POINT)
#define GMP_DECIMAL_POINT (nl_langinfo (DECIMAL_POINT))
#endif
/* RADIXCHAR is deprecated, still in unix98 or some such. */
#if HAVE_NL_LANGINFO && defined (RADIXCHAR) && ! defined (GMP_DECIMAL_POINT)
#define GMP_DECIMAL_POINT (nl_langinfo (RADIXCHAR))
#endif
/* localeconv is slower since it returns all locale stuff */
#if HAVE_LOCALECONV && ! defined (GMP_DECIMAL_POINT)
#define GMP_DECIMAL_POINT (localeconv()->decimal_point)
#endif
#if ! defined (GMP_DECIMAL_POINT)
#define GMP_DECIMAL_POINT (".")
#endif
#define DOPRNT_CONV_FIXED 1
#define DOPRNT_CONV_SCIENTIFIC 2
#define DOPRNT_CONV_GENERAL 3
#define DOPRNT_JUSTIFY_NONE 0
#define DOPRNT_JUSTIFY_LEFT 1
#define DOPRNT_JUSTIFY_RIGHT 2
#define DOPRNT_JUSTIFY_INTERNAL 3
#define DOPRNT_SHOWBASE_YES 1
#define DOPRNT_SHOWBASE_NO 2
#define DOPRNT_SHOWBASE_NONZERO 3
struct doprnt_params_t {
int base; /* negative for upper case */
int conv; /* choices above */
const char *expfmt; /* exponent format */
int exptimes4; /* exponent multiply by 4 */
char fill; /* character */
int justify; /* choices above */
int prec; /* prec field, or -1 for all digits */
int showbase; /* choices above */
int showpoint; /* if radix point always shown */
int showtrailing; /* if trailing zeros wanted */
char sign; /* '+', ' ', or '\0' */
int width; /* width field */
};
#if _GMP_H_HAVE_VA_LIST
typedef int (*doprnt_format_t) _PROTO ((void *data, const char *fmt, va_list ap));
typedef int (*doprnt_memory_t) _PROTO ((void *data, const char *str, size_t len));
typedef int (*doprnt_reps_t) _PROTO ((void *data, int c, int reps));
typedef int (*doprnt_final_t) _PROTO ((void *data));
struct doprnt_funs_t {
doprnt_format_t format;
doprnt_memory_t memory;
doprnt_reps_t reps;
doprnt_final_t final; /* NULL if not required */
};
extern const struct doprnt_funs_t __gmp_fprintf_funs;
extern const struct doprnt_funs_t __gmp_sprintf_funs;
extern const struct doprnt_funs_t __gmp_snprintf_funs;
extern const struct doprnt_funs_t __gmp_obstack_printf_funs;
extern const struct doprnt_funs_t __gmp_ostream_funs;
/* "buf" is a __gmp_allocate_func block of "alloc" many bytes. The first
"size" of these have been written. "alloc > size" is maintained, so
there's room to store a '\0' at the end. "result" is where the
application wants the final block pointer. */
struct gmp_asprintf_t {
char **result;
char *buf;
size_t size;
size_t alloc;
};
#define GMP_ASPRINTF_T_INIT(d, output) \
do { \
(d).result = (output); \
(d).alloc = 256; \
(d).buf = (char *) (*__gmp_allocate_func) ((d).alloc); \
(d).size = 0; \
} while (0)
/* If a realloc is necessary, use twice the size actually required, so as to
avoid repeated small reallocs. */
#define GMP_ASPRINTF_T_NEED(d, n) \
do { \
size_t alloc, newsize, newalloc; \
ASSERT ((d)->alloc >= (d)->size + 1); \
\
alloc = (d)->alloc; \
newsize = (d)->size + (n); \
if (alloc <= newsize) \
{ \
newalloc = 2*newsize; \
(d)->alloc = newalloc; \
(d)->buf = __GMP_REALLOCATE_FUNC_TYPE ((d)->buf, \
alloc, newalloc, char); \
} \
} while (0)
__GMP_DECLSPEC int __gmp_asprintf_memory _PROTO ((struct gmp_asprintf_t *d, const char *str, size_t len));
__GMP_DECLSPEC int __gmp_asprintf_reps _PROTO ((struct gmp_asprintf_t *d, int c, int reps));
__GMP_DECLSPEC int __gmp_asprintf_final _PROTO ((struct gmp_asprintf_t *d));
/* buf is where to write the next output, and size is how much space is left
there. If the application passed size==0 then that's what we'll have
here, and nothing at all should be written. */
struct gmp_snprintf_t {
char *buf;
size_t size;
};
/* Add the bytes printed by the call to the total retval, or bail out on an
error. */
#define DOPRNT_ACCUMULATE(call) \
do { \
int __ret; \
__ret = call; \
if (__ret == -1) \
goto error; \
retval += __ret; \
} while (0)
#define DOPRNT_ACCUMULATE_FUN(fun, params) \
do { \
ASSERT ((fun) != NULL); \
DOPRNT_ACCUMULATE ((*(fun)) params); \
} while (0)
#define DOPRNT_FORMAT(fmt, ap) \
DOPRNT_ACCUMULATE_FUN (funs->format, (data, fmt, ap))
#define DOPRNT_MEMORY(ptr, len) \
DOPRNT_ACCUMULATE_FUN (funs->memory, (data, ptr, len))
#define DOPRNT_REPS(c, n) \
DOPRNT_ACCUMULATE_FUN (funs->reps, (data, c, n))
#define DOPRNT_STRING(str) DOPRNT_MEMORY (str, strlen (str))
#define DOPRNT_REPS_MAYBE(c, n) \
do { \
if ((n) != 0) \
DOPRNT_REPS (c, n); \
} while (0)
#define DOPRNT_MEMORY_MAYBE(ptr, len) \
do { \
if ((len) != 0) \
DOPRNT_MEMORY (ptr, len); \
} while (0)
__GMP_DECLSPEC int __gmp_doprnt _PROTO ((const struct doprnt_funs_t *, void *, const char *, va_list));
__GMP_DECLSPEC int __gmp_doprnt_integer _PROTO ((const struct doprnt_funs_t *, void *, const struct doprnt_params_t *, const char *));
#define __gmp_doprnt_mpf __gmp_doprnt_mpf2
__GMP_DECLSPEC int __gmp_doprnt_mpf _PROTO ((const struct doprnt_funs_t *, void *, const struct doprnt_params_t *, const char *, mpf_srcptr));
int __gmp_replacement_vsnprintf _PROTO ((char *, size_t, const char *, va_list));
#endif /* _GMP_H_HAVE_VA_LIST */
typedef int (*gmp_doscan_scan_t) _PROTO ((void *, const char *, ...));
typedef void *(*gmp_doscan_step_t) _PROTO ((void *, int));
typedef int (*gmp_doscan_get_t) _PROTO ((void *));
typedef int (*gmp_doscan_unget_t) _PROTO ((int, void *));
struct gmp_doscan_funs_t {
gmp_doscan_scan_t scan;
gmp_doscan_step_t step;
gmp_doscan_get_t get;
gmp_doscan_unget_t unget;
};
extern const struct gmp_doscan_funs_t __gmp_fscanf_funs;
extern const struct gmp_doscan_funs_t __gmp_sscanf_funs;
#if _GMP_H_HAVE_VA_LIST
int __gmp_doscan _PROTO ((const struct gmp_doscan_funs_t *, void *,
const char *, va_list));
#endif
/* For testing and debugging. */
#define MPZ_CHECK_FORMAT(z) \
do { \
ASSERT_ALWAYS (SIZ(z) == 0 || PTR(z)[ABSIZ(z) - 1] != 0); \
ASSERT_ALWAYS (ALLOC(z) >= ABSIZ(z)); \
ASSERT_ALWAYS_MPN (PTR(z), ABSIZ(z)); \
} while (0)
#define MPQ_CHECK_FORMAT(q) \
do { \
MPZ_CHECK_FORMAT (mpq_numref (q)); \
MPZ_CHECK_FORMAT (mpq_denref (q)); \
ASSERT_ALWAYS (SIZ(mpq_denref(q)) >= 1); \
\
if (SIZ(mpq_numref(q)) == 0) \
{ \
/* should have zero as 0/1 */ \
ASSERT_ALWAYS (SIZ(mpq_denref(q)) == 1 \
&& PTR(mpq_denref(q))[0] == 1); \
} \
else \
{ \
/* should have no common factors */ \
mpz_t g; \
mpz_init (g); \
mpz_gcd (g, mpq_numref(q), mpq_denref(q)); \
ASSERT_ALWAYS (mpz_cmp_ui (g, 1) == 0); \
mpz_clear (g); \
} \
} while (0)
#define MPF_CHECK_FORMAT(f) \
do { \
ASSERT_ALWAYS (PREC(f) >= __GMPF_BITS_TO_PREC(53)); \
ASSERT_ALWAYS (ABSIZ(f) <= PREC(f)+1); \
if (SIZ(f) == 0) \
ASSERT_ALWAYS (EXP(f) == 0); \
if (SIZ(f) != 0) \
ASSERT_ALWAYS (PTR(f)[ABSIZ(f) - 1] != 0); \
} while (0)
#define MPZ_PROVOKE_REALLOC(z) \
do { ALLOC(z) = ABSIZ(z); } while (0)
/* Enhancement: The "mod" and "gcd_1" functions below could have
__GMP_ATTRIBUTE_PURE, but currently (gcc 3.3) that's not supported on
function pointers, only actual functions. It probably doesn't make much
difference to the gmp code, since hopefully we arrange calls so there's
no great need for the compiler to move things around. */
#if WANT_FAT_BINARY
/* NOTE: The function pointers in this struct are also in CPUVEC_FUNCS_LIST
in mpn/x86/x86-defs.m4 and in mpn/x86_64/x86_64-defs.m4. Be sure to
update them there when changing here. */
struct cpuvec_t {
DECL_add_n ((*add_n));
DECL_addmul_1 ((*addmul_1));
DECL_copyd ((*copyd));
DECL_copyi ((*copyi));
DECL_divexact_1 ((*divexact_1));
DECL_divexact_by3c ((*divexact_by3c));
DECL_divrem_1 ((*divrem_1));
DECL_gcd_1 ((*gcd_1));
DECL_lshift ((*lshift));
DECL_mod_1 ((*mod_1));
DECL_mod_34lsub1 ((*mod_34lsub1));
DECL_modexact_1c_odd ((*modexact_1c_odd));
DECL_mul_1 ((*mul_1));
DECL_mul_basecase ((*mul_basecase));
DECL_preinv_divrem_1 ((*preinv_divrem_1));
DECL_preinv_mod_1 ((*preinv_mod_1));
DECL_redc_basecase ((*redc_basecase));
DECL_rshift ((*rshift));
DECL_sqr_basecase ((*sqr_basecase));
DECL_sub_n ((*sub_n));
DECL_submul_1 ((*submul_1));
DECL_sumdiff_n ((*sumdiff_n));
int initialized;
mp_size_t mul_karatsuba_threshold;
mp_size_t mul_toom3_threshold;
mp_size_t sqr_karatsuba_threshold;
mp_size_t sqr_toom3_threshold;
};
__GMP_DECLSPEC extern struct cpuvec_t __gmpn_cpuvec;
#endif /* x86 fat binary */
void __gmpn_cpuvec_init __GMP_PROTO ((void));
/* Get a threshold "field" from __gmpn_cpuvec, running __gmpn_cpuvec_init()
if that hasn't yet been done (to establish the right values). */
#define CPUVEC_THRESHOLD(field) \
((LIKELY (__gmpn_cpuvec.initialized) ? 0 : (__gmpn_cpuvec_init (), 0)), \
__gmpn_cpuvec.field)
#if TUNE_PROGRAM_BUILD
/* Some extras wanted when recompiling some .c files for use by the tune
program. Not part of a normal build.
It's necessary to keep these thresholds as #defines (just to an
identically named variable), since various defaults are established based
on #ifdef in the .c files. For some this is not so (the defaults are
instead establshed above), but all are done this way for consistency. */
#undef MUL_KARATSUBA_THRESHOLD
#define MUL_KARATSUBA_THRESHOLD mul_karatsuba_threshold
extern mp_size_t mul_karatsuba_threshold;
#undef MUL_TOOM3_THRESHOLD
#define MUL_TOOM3_THRESHOLD mul_toom3_threshold
extern mp_size_t mul_toom3_threshold;
#undef MUL_TOOM4_THRESHOLD
#define MUL_TOOM4_THRESHOLD mul_toom4_threshold
extern mp_size_t mul_toom4_threshold;
#undef MUL_TOOM7_THRESHOLD
#define MUL_TOOM7_THRESHOLD mul_toom7_threshold
extern mp_size_t mul_toom7_threshold;
#undef MUL_FFT_THRESHOLD
#define MUL_FFT_THRESHOLD mul_fft_threshold
extern mp_size_t mul_fft_threshold;
#undef MUL_FFT_MODF_THRESHOLD
#define MUL_FFT_MODF_THRESHOLD mul_fft_modf_threshold
extern mp_size_t mul_fft_modf_threshold;
#undef MUL_FFT_TABLE
#define MUL_FFT_TABLE { 0 }
/* A native mpn_sqr_basecase is not tuned and SQR_BASECASE_THRESHOLD should
remain as zero (always use it). */
#if ! HAVE_NATIVE_mpn_sqr_basecase
#undef SQR_BASECASE_THRESHOLD
#define SQR_BASECASE_THRESHOLD sqr_basecase_threshold
extern mp_size_t sqr_basecase_threshold;
#endif
#if TUNE_PROGRAM_BUILD_SQR
#undef SQR_KARATSUBA_THRESHOLD
#define SQR_KARATSUBA_THRESHOLD SQR_KARATSUBA_MAX_GENERIC
#else
#undef SQR_KARATSUBA_THRESHOLD
#define SQR_KARATSUBA_THRESHOLD sqr_karatsuba_threshold
extern mp_size_t sqr_karatsuba_threshold;
#endif
#undef SQR_TOOM3_THRESHOLD
#define SQR_TOOM3_THRESHOLD sqr_toom3_threshold
extern mp_size_t sqr_toom3_threshold;
#undef SQR_FFT_THRESHOLD
#define SQR_FFT_THRESHOLD sqr_fft_threshold
extern mp_size_t sqr_fft_threshold;
#undef SQR_FFT_MODF_THRESHOLD
#define SQR_FFT_MODF_THRESHOLD sqr_fft_modf_threshold
extern mp_size_t sqr_fft_modf_threshold;
#undef SQR_FFT_TABLE
#define SQR_FFT_TABLE { 0 }
#undef MULLOW_BASECASE_THRESHOLD
#define MULLOW_BASECASE_THRESHOLD mullow_basecase_threshold
extern mp_size_t mullow_basecase_threshold;
#undef MULLOW_DC_THRESHOLD
#define MULLOW_DC_THRESHOLD mullow_dc_threshold
extern mp_size_t mullow_dc_threshold;
#undef MULLOW_MUL_N_THRESHOLD
#define MULLOW_MUL_N_THRESHOLD mullow_mul_n_threshold
extern mp_size_t mullow_mul_n_threshold;
#if ! UDIV_PREINV_ALWAYS
#undef DIV_SB_PREINV_THRESHOLD
#define DIV_SB_PREINV_THRESHOLD div_sb_preinv_threshold
extern mp_size_t div_sb_preinv_threshold;
#endif
#undef DIV_DC_THRESHOLD
#define DIV_DC_THRESHOLD div_dc_threshold
extern mp_size_t div_dc_threshold;
#undef POWM_THRESHOLD
#define POWM_THRESHOLD powm_threshold
extern mp_size_t powm_threshold;
#undef GCD_ACCEL_THRESHOLD
#define GCD_ACCEL_THRESHOLD gcd_accel_threshold
extern mp_size_t gcd_accel_threshold;
#undef GCDEXT_THRESHOLD
#define GCDEXT_THRESHOLD gcdext_threshold
extern mp_size_t gcdext_threshold;
#undef DIVREM_1_NORM_THRESHOLD
#define DIVREM_1_NORM_THRESHOLD divrem_1_norm_threshold
extern mp_size_t divrem_1_norm_threshold;
#undef DIVREM_1_UNNORM_THRESHOLD
#define DIVREM_1_UNNORM_THRESHOLD divrem_1_unnorm_threshold
extern mp_size_t divrem_1_unnorm_threshold;
#undef MOD_1_NORM_THRESHOLD
#define MOD_1_NORM_THRESHOLD mod_1_norm_threshold
extern mp_size_t mod_1_norm_threshold;
#undef MOD_1_UNNORM_THRESHOLD
#define MOD_1_UNNORM_THRESHOLD mod_1_unnorm_threshold
extern mp_size_t mod_1_unnorm_threshold;
#if ! UDIV_PREINV_ALWAYS
#undef DIVREM_2_THRESHOLD
#define DIVREM_2_THRESHOLD divrem_2_threshold
extern mp_size_t divrem_2_threshold;
#endif
#undef GET_STR_DC_THRESHOLD
#define GET_STR_DC_THRESHOLD get_str_dc_threshold
extern mp_size_t get_str_dc_threshold;
#undef GET_STR_PRECOMPUTE_THRESHOLD
#define GET_STR_PRECOMPUTE_THRESHOLD get_str_precompute_threshold
extern mp_size_t get_str_precompute_threshold;
#undef SET_STR_THRESHOLD
#define SET_STR_THRESHOLD set_str_threshold
extern mp_size_t SET_STR_THRESHOLD;
#undef FFT_TABLE_ATTRS
#define FFT_TABLE_ATTRS
extern mp_size_t mpn_fft_table[2][MPN_FFT_TABLE_SIZE];
/* Sizes the tune program tests up to, used in a couple of recompilations. */
#undef MUL_KARATSUBA_THRESHOLD_LIMIT
#undef MUL_TOOM3_THRESHOLD_LIMIT
#undef MUL_TOOM4_THRESHOLD_LIMIT
#undef MUL_TOOM7_THRESHOLD_LIMIT
#undef MULLOW_BASECASE_THRESHOLD_LIMIT
#undef SQR_TOOM3_THRESHOLD_LIMIT
#define SQR_KARATSUBA_MAX_GENERIC 200
#define MUL_KARATSUBA_THRESHOLD_LIMIT 700
#define MUL_TOOM3_THRESHOLD_LIMIT 700
#define MUL_TOOM4_THRESHOLD_LIMIT 40000
#define MUL_TOOM7_THRESHOLD_LIMIT 1000000
#define MULLOW_BASECASE_THRESHOLD_LIMIT 200
#define SQR_TOOM3_THRESHOLD_LIMIT 400
#define GET_STR_THRESHOLD_LIMIT 150
/* "thresh" will normally be a variable when tuning, so use the cached
result. This helps mpn_sb_divrem_mn for instance. */
#undef CACHED_ABOVE_THRESHOLD
#define CACHED_ABOVE_THRESHOLD(cache, thresh) (cache)
#undef CACHED_BELOW_THRESHOLD
#define CACHED_BELOW_THRESHOLD(cache, thresh) (cache)
#endif /* TUNE_PROGRAM_BUILD */
#if defined (__cplusplus)
}
#endif
#ifdef __cplusplus
/* A little helper for a null-terminated __gmp_allocate_func string.
The destructor ensures it's freed even if an exception is thrown.
The len field is needed by the destructor, and can be used by anyone else
to avoid a second strlen pass over the data.
Since our input is a C string, using strlen is correct. Perhaps it'd be
more C++-ish style to use std::char_traits<char>::length, but char_traits
isn't available in gcc 2.95.4. */
class gmp_allocated_string {
public:
char *str;
size_t len;
gmp_allocated_string(char *arg)
{
str = arg;
len = std::strlen (str);
}
~gmp_allocated_string()
{
(*__gmp_free_func) (str, len+1);
}
};
std::istream &__gmpz_operator_in_nowhite (std::istream &, mpz_ptr, char);
int __gmp_istream_set_base (std::istream &, char &, bool &, bool &);
void __gmp_istream_set_digits (std::string &, std::istream &, char &, bool &, int);
void __gmp_doprnt_params_from_ios (struct doprnt_params_t *p, std::ios &o);
std::ostream& __gmp_doprnt_integer_ostream (std::ostream &o, struct doprnt_params_t *p, char *s);
extern const struct doprnt_funs_t __gmp_asprintf_funs_noformat;
#endif /* __cplusplus */
#endif /* __GMP_IMPL_H__ */
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