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source: trunk/third/gmp/gmp-impl.h @ 18191

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Revision 18191, 119.0 KB checked in by ghudson, 22 years ago (diff)
This commit was generated by cvs2svn to compensate for changes in r18190, which included commits to RCS files with non-trunk default branches.

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1	/* Include file for internal GNU MP types and definitions.
2
3	THE CONTENTS OF THIS FILE ARE FOR INTERNAL USE AND ARE ALMOST CERTAIN TO
4	BE SUBJECT TO INCOMPATIBLE CHANGES IN FUTURE GNU MP RELEASES.
5
6	Copyright 1991, 1993, 1994, 1995, 1996, 1997, 1999, 2000, 2001, 2002 Free
7	Software Foundation, Inc.
8
9	This file is part of the GNU MP Library.
10
11	The GNU MP Library is free software; you can redistribute it and/or modify
12	it under the terms of the GNU Lesser General Public License as published by
13	the Free Software Foundation; either version 2.1 of the License, or (at your
14	option) any later version.
15
16	The GNU MP Library is distributed in the hope that it will be useful, but
17	WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
18	or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
19	License for more details.
20
21	You should have received a copy of the GNU Lesser General Public License
22	along with the GNU MP Library; see the file COPYING.LIB. If not, write to
23	the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
24	MA 02111-1307, USA. */
25
26
27	#ifndef __GMP_IMPL_H__
28	#define __GMP_IMPL_H__
29
30	/* On Cray vector systems "short" and "unsigned short" might not be the same
31	number of bits, making the SHRT_MAX defaults below fail. (This depends
32	on compiler options.) Instead use limits.h. */
33	#if defined _CRAY
34	#include <limits.h>
35	#endif
36
37	#if ! __GMP_WITHIN_CONFIGURE
38	#include "config.h"
39	#include "gmp-mparam.h"
40	#endif
41
42	#ifdef __cplusplus
43	#include <string>
44	#endif
45
46	/* Might search and replace _PROTO to __GMP_PROTO internally one day, to
47	avoid two names for one thing, but no hurry for that. */
48	#define _PROTO(x) __GMP_PROTO(x)
49
50	/* The following tries to get a good version of alloca. The tests are
51	adapted from autoconf AC_FUNC_ALLOCA, with a couple of additions.
52	Whether this succeeds is tested by GMP_FUNC_ALLOCA and HAVE_ALLOCA will
53	be setup appropriately.
54
55	ifndef alloca - a cpp define might already exist.
56	glibc <stdlib.h> includes <alloca.h> which uses GCC __builtin_alloca.
57	HP cc +Olibcalls adds a #define of alloca to __builtin_alloca.
58
59	GCC __builtin_alloca - preferred whenever available.
60
61	_AIX pragma - IBM compilers need a #pragma in "each module that needs to
62	use alloca". Pragma indented to protect pre-ANSI cpp's. _IBMR2 was
63	used in past versions of GMP, retained still in case it matters.
64
65	The autoconf manual says this pragma needs to be at the start of a C
66	file, apart from comments and preprocessor directives. Is that true?
67	xlc on aix 4.xxx doesn't seem to mind it being after prototypes etc
68	from gmp.h.
69	*/
70
71	#ifndef alloca
72	# ifdef __GNUC__
73	# define alloca __builtin_alloca
74	# else
75	# ifdef __DECC
76	# define alloca(x) __ALLOCA(x)
77	# else
78	# ifdef _MSC_VER
79	# include <malloc.h>
80	# define alloca _alloca
81	# else
82	# if HAVE_ALLOCA_H
83	# include <alloca.h>
84	# else
85	# if defined (_AIX) \|\| defined (_IBMR2)
86	#pragma alloca
87	# else
88	char *alloca ();
89	# endif
90	# endif
91	# endif
92	# endif
93	# endif
94	#endif
95
96
97	/* const and signed must match __gmp_const and __gmp_signed, so follow the
98	decision made for those in gmp.h. */
99	#if ! __GMP_HAVE_CONST
100	#define const /* empty */
101	#define signed /* empty */
102	#endif
103
104
105	/* "const" basically means a function does nothing but examine its arguments
106	and give a return value, it doesn't read or write any memory (neither
107	global nor pointed to by arguments), and has no other side-effects. This
108	is more restrictive than "pure". See info node "(gcc)Function
109	Attributes". */
110	#if HAVE_ATTRIBUTE_CONST
111	#define ATTRIBUTE_CONST __attribute__ ((const))
112	#else
113	#define ATTRIBUTE_CONST
114	#endif
115
116	#if HAVE_ATTRIBUTE_NORETURN
117	#define ATTRIBUTE_NORETURN __attribute__ ((noreturn))
118	#else
119	#define ATTRIBUTE_NORETURN
120	#endif
121
122	/* "malloc" means a function behaves like malloc in that the pointer it
123	returns doesn't alias anything. */
124	#if HAVE_ATTRIBUTE_MALLOC
125	#define ATTRIBUTE_MALLOC __attribute__ ((malloc))
126	#else
127	#define ATTRIBUTE_MALLOC
128	#endif
129
130	#ifdef _CRAY
131	#define CRAY_Pragma(str) _Pragma (str)
132	#else
133	#define CRAY_Pragma(str)
134	#endif
135
136
137	#if ! HAVE_STRCHR
138	#define strchr(s,c) index(s,c)
139	#endif
140
141	#if ! HAVE_MEMSET
142	#define memset(p, c, n) \
143	do { \
144	ASSERT (n >= 0); \
145	int __i; \
146	for (__i = 0; __i < (n); __i++) \
147	(p)[__i] = (c); \
148	} while (0)
149	#endif
150
151	/* va_copy is standard in C99, and gcc provides __va_copy when in strict C89
152	mode. Falling back to a memcpy will give maximum portability, since it
153	works no matter whether va_list is a pointer, struct or array. */
154	#if ! defined (va_copy) && defined (__va_copy)
155	#define va_copy(dst,src) __va_copy(dst,src)
156	#endif
157	#if ! defined (va_copy)
158	#define va_copy(dst,src) \
159	do { memcpy (&(dst), &(src), sizeof (va_list)); } while (0)
160	#endif
161
162
163	#if defined (__cplusplus)
164	extern "C" {
165	#endif
166
167
168	/* Usage: TMP_DECL (marker);
169	TMP_MARK (marker);
170	ptr = TMP_ALLOC (bytes);
171	TMP_FREE (marker);
172
173	TMP_DECL just declares a variable, but might be empty and so must be last
174	in a list of variables. TMP_MARK must be done before any TMP_ALLOC.
175	TMP_ALLOC(0) is not allowed. TMP_FREE doesn't need to be done if a
176	TMP_MARK was made, but then no TMP_ALLOCs.
177
178	The name "marker" isn't used by the malloc-reentrant and debug methods,
179	instead they hardcode a name which TMP_ALLOC will know. For that reason
180	two TMP_DECLs are not allowed, unless one is in a nested "{ }" block, and
181	in that case TMP_MARK, TMP_ALLOC and TMP_FREE will refer to the TMP_DECL
182	which is in scope, irrespective of the marker name given. */
183
184	/* The alignment in bytes, used for TMP_ALLOCed blocks, when alloca or
185	__gmp_allocate_func doesn't already determine it. Currently TMP_ALLOC
186	isn't used for "double"s, so that's not in the union. */
187	union tmp_align_t {
188	mp_limb_t l;
189	char *p;
190	};
191	#define __TMP_ALIGN sizeof (union tmp_align_t)
192
193	/* Return "a" rounded upwards to a multiple of "m", if it isn't already.
194	"a" must be an unsigned type. */
195	#define ROUND_UP_MULTIPLE(a,m) ((a) + (-(a))%(m))
196
197	#if WANT_TMP_ALLOCA
198	/* Each TMP_ALLOC is simply an alloca(), and nothing else is needed.
199	This is the preferred method. */
200	#define TMP_DECL(m)
201	#define TMP_ALLOC(x) alloca(x)
202	#define TMP_MARK(m)
203	#define TMP_FREE(m)
204	#endif
205
206	#if WANT_TMP_REENTRANT
207	/* See tal-reent.c for some comments. */
208	struct tmp_reentrant_t {
209	struct tmp_reentrant_t *next;
210	size_t size; /* bytes, including header */
211	};
212	void __gmp_tmp_reentrant_alloc _PROTO ((struct tmp_reentrant_t *, size_t)) ATTRIBUTE_MALLOC;
213	void __gmp_tmp_reentrant_free _PROTO ((struct tmp_reentrant_t *));
214	#define TMP_DECL(marker) struct tmp_reentrant_t *__tmp_marker
215	/* don't demand NULL, just cast a zero */
216	#define TMP_MARK(marker) \
217	do { __tmp_marker = (struct tmp_reentrant_t *) 0; } while (0)
218	#define TMP_ALLOC(size) __gmp_tmp_reentrant_alloc (&__tmp_marker, size)
219	#define TMP_FREE(marker) __gmp_tmp_reentrant_free (__tmp_marker)
220	#endif
221
222	#if WANT_TMP_NOTREENTRANT
223	/* See tal-notreent.c for some comments. */
224	struct tmp_marker
225	{
226	struct tmp_stack *which_chunk;
227	void *alloc_point;
228	};
229	typedef struct tmp_marker tmp_marker;
230	void *__gmp_tmp_alloc _PROTO ((unsigned long)) ATTRIBUTE_MALLOC;
231	void __gmp_tmp_mark _PROTO ((tmp_marker *));
232	void __gmp_tmp_free _PROTO ((tmp_marker *));
233	#define TMP_DECL(marker) tmp_marker marker
234	/* gcc recognises "(-(8*n))%8" or the like is always zero, which means the
235	rounding up is a noop for allocs of whole limbs. */
236	#define TMP_ALLOC(size) \
237	__gmp_tmp_alloc (ROUND_UP_MULTIPLE ((unsigned long) (size), __TMP_ALIGN))
238	#define TMP_MARK(marker) __gmp_tmp_mark (&marker)
239	#define TMP_FREE(marker) __gmp_tmp_free (&marker)
240	#endif
241
242	#if WANT_TMP_DEBUG
243	/* See tal-debug.c for some comments. */
244	struct tmp_debug_t {
245	struct tmp_debug_entry_t *list;
246	const char *file;
247	int line;
248	};
249	struct tmp_debug_entry_t {
250	struct tmp_debug_entry_t *next;
251	char *block;
252	size_t size;
253	};
254	void __gmp_tmp_debug_mark _PROTO ((const char , int, struct tmp_debug_t *,
255	struct tmp_debug_t *,
256	const char , const char ));
257	void __gmp_tmp_debug_alloc _PROTO ((const char , int, int,
258	struct tmp_debug_t *, const char ,
259	size_t)) ATTRIBUTE_MALLOC;
260	void __gmp_tmp_debug_free _PROTO ((const char *, int, int,
261	struct tmp_debug_t **,
262	const char , const char ));
263	#if HAVE_STRINGIZE
264	#define TMP_DECL(marker) TMP_DECL_NAME(marker, #marker)
265	#define TMP_MARK(marker) TMP_MARK_NAME(marker, #marker)
266	#define TMP_FREE(marker) TMP_FREE_NAME(marker, #marker)
267	#else
268	#define TMP_DECL(marker) TMP_DECL_NAME(marker, "marker")
269	#define TMP_MARK(marker) TMP_MARK_NAME(marker, "marker")
270	#define TMP_FREE(marker) TMP_FREE_NAME(marker, "marker")
271	#endif
272	/* The marker variable is designed to provoke an uninitialized varialble
273	warning from the compiler if TMP_FREE is used without a TMP_MARK.
274	__tmp_marker_inscope does the same for TMP_ALLOC. Runtime tests pick
275	these things up too. */
276	#define TMP_DECL_NAME(marker, marker_name) \
277	int marker; \
278	int __tmp_marker_inscope; \
279	const char *__tmp_marker_name = marker_name; \
280	struct tmp_debug_t __tmp_marker_struct; \
281	/* don't demand NULL, just cast a zero */ \
282	struct tmp_debug_t __tmp_marker = (struct tmp_debug_t ) 0
283	#define TMP_MARK_NAME(marker, marker_name) \
284	do { \
285	marker = 1; \
286	__tmp_marker_inscope = 1; \
287	__gmp_tmp_debug_mark (ASSERT_FILE, ASSERT_LINE, \
288	&__tmp_marker, &__tmp_marker_struct, \
289	__tmp_marker_name, marker_name); \
290	} while (0)
291	#define TMP_ALLOC(size) \
292	__gmp_tmp_debug_alloc (ASSERT_FILE, ASSERT_LINE, \
293	__tmp_marker_inscope, \
294	&__tmp_marker, __tmp_marker_name, size)
295	#define TMP_FREE_NAME(marker, marker_name) \
296	do { \
297	__gmp_tmp_debug_free (ASSERT_FILE, ASSERT_LINE, \
298	marker, &__tmp_marker, \
299	__tmp_marker_name, marker_name); \
300	} while (0)
301	#endif
302
303
304	/* Allocating various types. */
305	#define TMP_ALLOC_TYPE(n,type) ((type ) TMP_ALLOC ((n) sizeof (type)))
306	#define TMP_ALLOC_LIMBS(n) TMP_ALLOC_TYPE(n,mp_limb_t)
307	#define TMP_ALLOC_MP_PTRS(n) TMP_ALLOC_TYPE(n,mp_ptr)
308
309	/* It's more efficient to allocate one block than two. This is certainly
310	true of the malloc methods, but it can even be true of alloca if that
311	involves copying a chunk of stack (various RISCs), or a call to a stack
312	bounds check (mingw). In any case, when debugging keep separate blocks
313	so a redzoning malloc debugger can protect each individually. */
314	#if WANT_TMP_DEBUG
315	#define TMP_ALLOC_LIMBS_2(xp,xsize, yp,ysize) \
316	do { \
317	(xp) = TMP_ALLOC_LIMBS (xsize); \
318	(yp) = TMP_ALLOC_LIMBS (ysize); \
319	} while (0)
320	#else
321	#define TMP_ALLOC_LIMBS_2(xp,xsize, yp,ysize) \
322	do { \
323	(xp) = TMP_ALLOC_LIMBS ((xsize) + (ysize)); \
324	(yp) = (xp) + (xsize); \
325	} while (0)
326	#endif
327
328
329	/* From gmp.h, nicer names for internal use. */
330	#define MPN_CMP(result, xp, yp, size) __GMPN_CMP(result, xp, yp, size)
331
332	#define ABS(x) ((x) >= 0 ? (x) : -(x))
333	#define MIN(l,o) ((l) < (o) ? (l) : (o))
334	#define MAX(h,i) ((h) > (i) ? (h) : (i))
335	#define numberof(x) (sizeof (x) / sizeof ((x)[0]))
336
337	/* Field access macros. */
338	#define SIZ(x) ((x)->_mp_size)
339	#define ABSIZ(x) ABS (SIZ (x))
340	#define PTR(x) ((x)->_mp_d)
341	#define LIMBS(x) ((x)->_mp_d)
342	#define EXP(x) ((x)->_mp_exp)
343	#define PREC(x) ((x)->_mp_prec)
344	#define ALLOC(x) ((x)->_mp_alloc)
345
346	/* n-1 inverts any low zeros and the lowest one bit. If n&(n-1) leaves zero
347	then that lowest one bit must have been the only bit set. n==0 will
348	return true though, so avoid that. */
349	#define POW2_P(n) (((n) & ((n) - 1)) == 0)
350
351
352	/* Might be already defined by gmp-mparam.h, otherwise use what's in gmp.h. */
353	#ifndef BITS_PER_MP_LIMB
354	#define BITS_PER_MP_LIMB __GMP_BITS_PER_MP_LIMB
355	#endif
356
357
358	/* The "short" defines are a bit different because shorts are promoted to
359	ints by ~ or >> etc. */
360
361	#ifndef ULONG_MAX
362	#define ULONG_MAX __GMP_ULONG_MAX
363	#endif
364	#ifndef UINT_MAX
365	#define UINT_MAX __GMP_UINT_MAX
366	#endif
367	#ifndef USHRT_MAX
368	#define USHRT_MAX __GMP_USHRT_MAX
369	#endif
370	#define MP_LIMB_T_MAX (~ (mp_limb_t) 0)
371
372	/* Must cast ULONG_MAX etc to unsigned long etc, since they might not be
373	unsigned on a K&R compiler. In particular the HP-UX 10 bundled K&R cc
374	treats the plain decimal values in <limits.h> as signed. */
375	#define ULONG_HIGHBIT (ULONG_MAX ^ ((unsigned long) ULONG_MAX >> 1))
376	#define UINT_HIGHBIT (UINT_MAX ^ ((unsigned) UINT_MAX >> 1))
377	#define USHRT_HIGHBIT ((unsigned short) (USHRT_MAX ^ ((unsigned short) USHRT_MAX >> 1)))
378	#define GMP_LIMB_HIGHBIT (MP_LIMB_T_MAX ^ (MP_LIMB_T_MAX >> 1))
379
380	#ifndef LONG_MIN
381	#define LONG_MIN ((long) ULONG_HIGHBIT)
382	#endif
383	#ifndef LONG_MAX
384	#define LONG_MAX (-(LONG_MIN+1))
385	#endif
386
387	#ifndef INT_MIN
388	#define INT_MIN ((int) UINT_HIGHBIT)
389	#endif
390	#ifndef INT_MAX
391	#define INT_MAX (-(INT_MIN+1))
392	#endif
393
394	#ifndef SHRT_MIN
395	#define SHRT_MIN ((short) USHRT_HIGHBIT)
396	#endif
397	#ifndef SHRT_MAX
398	#define SHRT_MAX ((short) (-(SHRT_MIN+1)))
399	#endif
400
401	#if __GMP_MP_SIZE_T_INT
402	#define MP_SIZE_T_MAX INT_MAX
403	#define MP_SIZE_T_MIN INT_MIN
404	#else
405	#define MP_SIZE_T_MAX LONG_MAX
406	#define MP_SIZE_T_MIN LONG_MIN
407	#endif
408
409	#define LONG_HIGHBIT LONG_MIN
410	#define INT_HIGHBIT INT_MIN
411	#define SHRT_HIGHBIT SHRT_MIN
412
413
414	#define GMP_NUMB_HIGHBIT (CNST_LIMB(1) << (GMP_NUMB_BITS-1))
415
416	#if GMP_NAIL_BITS == 0
417	#define GMP_NAIL_LOWBIT CNST_LIMB(0)
418	#else
419	#define GMP_NAIL_LOWBIT (CNST_LIMB(1) << GMP_NUMB_BITS)
420	#endif
421
422	#if GMP_NAIL_BITS != 0
423	/* Set various *_THRESHOLD values to be used for nails. Thus we avoid using
424	code that has not yet been qualified. */
425
426	#undef DIV_SB_PREINV_THRESHOLD
427	#undef DIV_DC_THRESHOLD
428	#undef POWM_THRESHOLD
429	#define DIV_SB_PREINV_THRESHOLD MP_SIZE_T_MAX
430	#define DIV_DC_THRESHOLD 50
431	#define POWM_THRESHOLD 0
432
433	#undef GCD_ACCEL_THRESHOLD
434	#undef GCDEXT_THRESHOLD
435	#define GCD_ACCEL_THRESHOLD 3
436	#define GCDEXT_THRESHOLD 20
437
438	#undef DIVREM_1_NORM_THRESHOLD
439	#undef DIVREM_1_UNNORM_THRESHOLD
440	#undef MOD_1_NORM_THRESHOLD
441	#undef MOD_1_UNNORM_THRESHOLD
442	#undef USE_PREINV_DIVREM_1
443	#undef USE_PREINV_MOD_1
444	#undef DIVREM_2_THRESHOLD
445	#undef DIVEXACT_1_THRESHOLD
446	#undef MODEXACT_1_ODD_THRESHOLD
447	#define DIVREM_1_NORM_THRESHOLD MP_SIZE_T_MAX /* preinv always */
448	#define DIVREM_1_UNNORM_THRESHOLD MP_SIZE_T_MAX /* always */
449	#define MOD_1_NORM_THRESHOLD MP_SIZE_T_MAX /* always */
450	#define MOD_1_UNNORM_THRESHOLD MP_SIZE_T_MAX /* always */
451	#define USE_PREINV_DIVREM_1 0 /* preinv never */
452	#define USE_PREINV_MOD_1 0 /* preinv never */
453	#define DIVREM_2_THRESHOLD MP_SIZE_T_MAX /* preinv never */
454	#define DIVEXACT_1_THRESHOLD MP_SIZE_T_MAX /* always */
455	#define MODEXACT_1_ODD_THRESHOLD MP_SIZE_T_MAX /* always */
456
457	#undef GET_STR_DC_THRESHOLD
458	#undef GET_STR_PRECOMPUTE_THRESHOLD
459	#undef SET_STR_THRESHOLD
460	#define GET_STR_DC_THRESHOLD 22
461	#define GET_STR_PRECOMPUTE_THRESHOLD 42
462	#define SET_STR_THRESHOLD 3259
463
464	#undef MUL_FFT_TABLE
465	#undef MUL_FFT_MODF_THRESHOLD
466	#undef MUL_FFT_THRESHOLD
467	#define MUL_FFT_TABLE { 400, 928, 1856, 3840, 7168, 20480, 0 }
468	#define MUL_FFT_MODF_THRESHOLD 416
469	#define MUL_FFT_THRESHOLD MP_SIZE_T_MAX
470
471	#undef SQR_FFT_TABLE
472	#undef SQR_FFT_MODF_THRESHOLD
473	#undef SQR_FFT_THRESHOLD
474	#define SQR_FFT_TABLE { 400, 992, 1984, 3840, 9216, 20480, 0 }
475	#define SQR_FFT_MODF_THRESHOLD 416
476	#define SQR_FFT_THRESHOLD MP_SIZE_T_MAX
477
478	#endif
479
480	/* Swap macros. */
481
482	#define MP_LIMB_T_SWAP(x, y) \
483	do { \
484	mp_limb_t __mp_limb_t_swap__tmp = (x); \
485	(x) = (y); \
486	(y) = __mp_limb_t_swap__tmp; \
487	} while (0)
488	#define MP_SIZE_T_SWAP(x, y) \
489	do { \
490	mp_size_t __mp_size_t_swap__tmp = (x); \
491	(x) = (y); \
492	(y) = __mp_size_t_swap__tmp; \
493	} while (0)
494
495	#define MP_PTR_SWAP(x, y) \
496	do { \
497	mp_ptr __mp_ptr_swap__tmp = (x); \
498	(x) = (y); \
499	(y) = __mp_ptr_swap__tmp; \
500	} while (0)
501	#define MP_SRCPTR_SWAP(x, y) \
502	do { \
503	mp_srcptr __mp_srcptr_swap__tmp = (x); \
504	(x) = (y); \
505	(y) = __mp_srcptr_swap__tmp; \
506	} while (0)
507
508	#define MPN_PTR_SWAP(xp,xs, yp,ys) \
509	do { \
510	MP_PTR_SWAP (xp, yp); \
511	MP_SIZE_T_SWAP (xs, ys); \
512	} while(0)
513	#define MPN_SRCPTR_SWAP(xp,xs, yp,ys) \
514	do { \
515	MP_SRCPTR_SWAP (xp, yp); \
516	MP_SIZE_T_SWAP (xs, ys); \
517	} while(0)
518
519	#define MPZ_PTR_SWAP(x, y) \
520	do { \
521	mpz_ptr __mpz_ptr_swap__tmp = (x); \
522	(x) = (y); \
523	(y) = __mpz_ptr_swap__tmp; \
524	} while (0)
525	#define MPZ_SRCPTR_SWAP(x, y) \
526	do { \
527	mpz_srcptr __mpz_srcptr_swap__tmp = (x); \
528	(x) = (y); \
529	(y) = __mpz_srcptr_swap__tmp; \
530	} while (0)
531
532
533	void *__gmp_default_allocate _PROTO ((size_t));
534	void __gmp_default_reallocate _PROTO ((void , size_t, size_t));
535	void __gmp_default_free _PROTO ((void *, size_t));
536
537	#define __GMP_ALLOCATE_FUNC_TYPE(n,type) \
538	((type ) (__gmp_allocate_func) ((n) * sizeof (type)))
539	#define __GMP_ALLOCATE_FUNC_LIMBS(n) __GMP_ALLOCATE_FUNC_TYPE (n, mp_limb_t)
540
541	#define __GMP_REALLOCATE_FUNC_TYPE(p, old_size, new_size, type) \
542	((type ) (__gmp_reallocate_func) \
543	(p, (old_size) * sizeof (type), (new_size) * sizeof (type)))
544	#define __GMP_REALLOCATE_FUNC_LIMBS(p, old_size, new_size) \
545	__GMP_REALLOCATE_FUNC_TYPE(p, old_size, new_size, mp_limb_t)
546
547	#define __GMP_FREE_FUNC_TYPE(p,n,type) (__gmp_free_func) (p, (n) sizeof (type))
548	#define __GMP_FREE_FUNC_LIMBS(p,n) __GMP_FREE_FUNC_TYPE (p, n, mp_limb_t)
549
550	#define __GMP_REALLOCATE_FUNC_MAYBE(ptr, oldsize, newsize) \
551	do { \
552	if ((oldsize) != (newsize)) \
553	(ptr) = (*__gmp_reallocate_func) (ptr, oldsize, newsize); \
554	} while (0)
555
556	#define __GMP_REALLOCATE_FUNC_MAYBE_TYPE(ptr, oldsize, newsize, type) \
557	do { \
558	if ((oldsize) != (newsize)) \
559	(ptr) = (type ) (__gmp_reallocate_func) \
560	(ptr, (oldsize) * sizeof (type), (newsize) * sizeof (type)); \
561	} while (0)
562
563
564	/* Dummy for non-gcc, code involving it will go dead. */
565	#ifndef __GNUC__
566	#define __builtin_constant_p(x) 0
567	#endif
568
569
570	/* In gcc 2.96 and up on i386, tail calls are optimized to jumps if the
571	stack usage is compatible. __attribute__ ((regparm (N))) helps by
572	putting leading parameters in registers, avoiding extra stack. */
573
574	#if HAVE_HOST_CPU_FAMILY_x86 && __GMP_GNUC_PREREQ (2,96)
575	#define USE_LEADING_REGPARM 1
576	#else
577	#define USE_LEADING_REGPARM 0
578	#endif
579
580	/* Macros for altering parameter order according to regparm usage. */
581	#if USE_LEADING_REGPARM
582	#define REGPARM_2_1(a,b,x) x,a,b
583	#define REGPARM_3_1(a,b,c,x) x,a,b,c
584	#define REGPARM_ATTR(n) __attribute__ ((regparm (n)))
585	#else
586	#define REGPARM_2_1(a,b,x) a,b,x
587	#define REGPARM_3_1(a,b,c,x) a,b,c,x
588	#define REGPARM_ATTR(n)
589	#endif
590
591
592	/* ASM_L gives a local label for a gcc asm block, for use when temporary
593	local labels like "1:" might not be available, which is the case for
594	instance on the x86s (the SCO assembler doesn't support them).
595
596	The label generated is made unique by including "%=" which is a unique
597	number for each insn. This ensures the same name can be used in multiple
598	asm blocks, perhaps via a macro. Since jumps between asm blocks are not
599	allowed there's no need for a label to be usable outside a single
600	block. */
601
602	#define ASM_L(name) LSYM_PREFIX "asm_%=_" #name
603
604
605	#if defined (__GNUC__) && HAVE_HOST_CPU_FAMILY_x86
606	#if 0
607	/* FIXME: Check that these actually improve things.
608	FIXME: Need a cld after each std.
609	FIXME: Can't have inputs in clobbered registers, must describe them as
610	dummy outputs, and add volatile. */
611	#define MPN_COPY_INCR(DST, SRC, N) \
612	__asm__ ("cld\n\trep\n\tmovsl" : : \
613	"D" (DST), "S" (SRC), "c" (N) : \
614	"cx", "di", "si", "memory")
615	#define MPN_COPY_DECR(DST, SRC, N) \
616	__asm__ ("std\n\trep\n\tmovsl" : : \
617	"D" ((DST) + (N) - 1), "S" ((SRC) + (N) - 1), "c" (N) : \
618	"cx", "di", "si", "memory")
619	#endif
620	#endif
621
622
623	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);
624	#define mpz_aorsmul_1(w,u,v,sub) __gmpz_aorsmul_1 (REGPARM_3_1 (w, u, v, sub))
625
626	#define mpz_n_pow_ui __gmpz_n_pow_ui
627	void mpz_n_pow_ui _PROTO ((mpz_ptr, mp_srcptr, mp_size_t, unsigned long));
628
629
630	#define mpn_add_nc __MPN(add_nc)
631	__GMP_DECLSPEC mp_limb_t mpn_add_nc __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t, mp_limb_t));
632
633	#define mpn_addmul_1c __MPN(addmul_1c)
634	__GMP_DECLSPEC mp_limb_t mpn_addmul_1c __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t));
635
636	#define mpn_addsub_n __MPN(addsub_n)
637	__GMP_DECLSPEC mp_limb_t mpn_addsub_n __GMP_PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
638
639	#define mpn_addsub_nc __MPN(addsub_nc)
640	__GMP_DECLSPEC mp_limb_t mpn_addsub_nc __GMP_PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_srcptr, mp_size_t, mp_limb_t));
641
642	#define mpn_divrem_1c __MPN(divrem_1c)
643	__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));
644
645	#define mpn_dump __MPN(dump)
646	__GMP_DECLSPEC void mpn_dump __GMP_PROTO ((mp_srcptr, mp_size_t));
647
648	#define mpn_fib2_ui __MPN(fib2_ui)
649	mp_size_t mpn_fib2_ui _PROTO ((mp_ptr, mp_ptr, unsigned long));
650
651	/* Remap names of internal mpn functions. */
652	#define __clz_tab __MPN(clz_tab)
653	#define mpn_udiv_w_sdiv __MPN(udiv_w_sdiv)
654
655	#define mpn_gcd_finda __MPN(gcd_finda)
656	mp_limb_t mpn_gcd_finda _PROTO((const mp_limb_t cp[2])) __GMP_ATTRIBUTE_PURE;
657
658	#define mpn_jacobi_base __MPN(jacobi_base)
659	int mpn_jacobi_base _PROTO ((mp_limb_t a, mp_limb_t b, int result_bit1)) ATTRIBUTE_CONST;
660
661	#define mpn_mod_1c __MPN(mod_1c)
662	__GMP_DECLSPEC mp_limb_t mpn_mod_1c __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t)) __GMP_ATTRIBUTE_PURE;
663
664	#define mpn_mul_1c __MPN(mul_1c)
665	__GMP_DECLSPEC mp_limb_t mpn_mul_1c __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t));
666
667	#define mpn_mul_2 __MPN(mul_2)
668	mp_limb_t mpn_mul_2 _PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr));
669
670	#define mpn_mul_basecase __MPN(mul_basecase)
671	__GMP_DECLSPEC void mpn_mul_basecase __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t));
672
673	#define mpn_sqr_n __MPN(sqr_n)
674	__GMP_DECLSPEC void mpn_sqr_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t));
675
676	#define mpn_sqr_basecase __MPN(sqr_basecase)
677	__GMP_DECLSPEC void mpn_sqr_basecase __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t));
678
679	#define mpn_sub_nc __MPN(sub_nc)
680	__GMP_DECLSPEC mp_limb_t mpn_sub_nc __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t, mp_limb_t));
681
682	#define mpn_submul_1c __MPN(submul_1c)
683	__GMP_DECLSPEC mp_limb_t mpn_submul_1c __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t));
684
685
686	typedef __gmp_randstate_struct *gmp_randstate_ptr;
687
688	#define _gmp_rand __gmp_rand
689	__GMP_DECLSPEC void _gmp_rand _PROTO ((mp_ptr, gmp_randstate_t, unsigned long int));
690
691
692	/* __gmp_rands is the global state for the old-style random functions, and
693	is also used in the test programs (hence the __GMP_DECLSPEC).
694
695	There's no seeding here, so mpz_random etc will generate the same
696	sequence every time. This is not unlike the C library random functions
697	if you don't seed them, so perhaps it's acceptable. Digging up a seed
698	from /dev/random or the like would work on many systems, but might
699	encourage a false confidence, since it'd be pretty much impossible to do
700	something that would work reliably everywhere. In any case the new style
701	functions are recommended to applications which care about randomness, so
702	the old functions aren't too important. */
703
704	__GMP_DECLSPEC extern char __gmp_rands_initialized;
705	__GMP_DECLSPEC extern gmp_randstate_t __gmp_rands;
706
707	#define RANDS \
708	((__gmp_rands_initialized ? 0 \
709	: (__gmp_rands_initialized = 1, \
710	gmp_randinit_default (__gmp_rands), 0)), \
711	__gmp_rands)
712
713	/* this is used by the test programs, to free memory */
714	#define RANDS_CLEAR() \
715	do { \
716	if (__gmp_rands_initialized) \
717	{ \
718	__gmp_rands_initialized = 0; \
719	gmp_randclear (__gmp_rands); \
720	} \
721	} while (0)
722
723
724	/* kara uses n+1 limbs of temporary space and then recurses with the
725	balance, so need (n+1) + (ceil(n/2)+1) + (ceil(n/4)+1) + ... */
726	#define MPN_KARA_MUL_N_TSIZE(n) (2*((n)+BITS_PER_MP_LIMB))
727	#define MPN_KARA_SQR_N_TSIZE(n) (2*((n)+BITS_PER_MP_LIMB))
728
729	/* toom3 uses 4*(ceil(n/3)) of temporary space and then recurses with the
730	balance either into itself or kara. The following might be
731	overestimates. */
732	#define MPN_TOOM3_MUL_N_TSIZE(n) (2(n) + 3BITS_PER_MP_LIMB)
733	#define MPN_TOOM3_SQR_N_TSIZE(n) (2(n) + 3BITS_PER_MP_LIMB)
734
735	/* need 2 so that n2>=1 */
736	#define MPN_KARA_MUL_N_MINSIZE 2
737	#define MPN_KARA_SQR_N_MINSIZE 2
738
739	/* Need l>=1, ls>=1, and 2ls > l (the latter for the tD MPN_INCR_U) /
740	#define MPN_TOOM3_MUL_N_MINSIZE 11
741	#define MPN_TOOM3_SQR_N_MINSIZE 11
742
743	#define mpn_sqr_diagonal __MPN(sqr_diagonal)
744	void mpn_sqr_diagonal _PROTO ((mp_ptr, mp_srcptr, mp_size_t));
745
746	#define mpn_kara_mul_n __MPN(kara_mul_n)
747	void mpn_kara_mul_n _PROTO((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t, mp_ptr));
748
749	#define mpn_kara_sqr_n __MPN(kara_sqr_n)
750	void mpn_kara_sqr_n _PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_ptr));
751
752	#define mpn_toom3_mul_n __MPN(toom3_mul_n)
753	void mpn_toom3_mul_n _PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t,mp_ptr));
754
755	#define mpn_toom3_sqr_n __MPN(toom3_sqr_n)
756	void mpn_toom3_sqr_n _PROTO((mp_ptr, mp_srcptr, mp_size_t, mp_ptr));
757
758
759	#define mpn_fft_best_k __MPN(fft_best_k)
760	int mpn_fft_best_k _PROTO ((mp_size_t n, int sqr)) ATTRIBUTE_CONST;
761
762	#define mpn_mul_fft __MPN(mul_fft)
763	void mpn_mul_fft _PROTO ((mp_ptr op, mp_size_t pl,
764	mp_srcptr n, mp_size_t nl,
765	mp_srcptr m, mp_size_t ml,
766	int k));
767
768	#define mpn_mul_fft_full __MPN(mul_fft_full)
769	void mpn_mul_fft_full _PROTO ((mp_ptr op,
770	mp_srcptr n, mp_size_t nl,
771	mp_srcptr m, mp_size_t ml));
772
773	#define mpn_fft_next_size __MPN(fft_next_size)
774	mp_size_t mpn_fft_next_size _PROTO ((mp_size_t pl, int k)) ATTRIBUTE_CONST;
775
776	#define mpn_sb_divrem_mn __MPN(sb_divrem_mn)
777	mp_limb_t mpn_sb_divrem_mn _PROTO ((mp_ptr, mp_ptr, mp_size_t,
778	mp_srcptr, mp_size_t));
779
780	#define mpn_dc_divrem_n __MPN(dc_divrem_n)
781	mp_limb_t mpn_dc_divrem_n _PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_size_t));
782
783	/* #define mpn_tdiv_q __MPN(tdiv_q) */
784	/* void mpn_tdiv_q _PROTO ((mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t)); */
785
786	#define mpz_divexact_gcd __gmpz_divexact_gcd
787	void mpz_divexact_gcd _PROTO ((mpz_ptr q, mpz_srcptr a, mpz_srcptr d));
788
789	#define mpz_inp_str_nowhite __gmpz_inp_str_nowhite
790	#ifdef _GMP_H_HAVE_FILE
791	size_t mpz_inp_str_nowhite _PROTO ((mpz_ptr x, FILE *stream, int base, int c, size_t nread));
792	#endif
793
794	#define mpn_divisible_p __MPN(divisible_p)
795	int mpn_divisible_p _PROTO ((mp_srcptr ap, mp_size_t asize,
796	mp_srcptr dp, mp_size_t dsize)) __GMP_ATTRIBUTE_PURE;
797
798	#define mpn_rootrem __gmpn_rootrem
799	mp_size_t mpn_rootrem _PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_size_t, mp_limb_t));
800
801
802	/* from gmp.h */
803	#if HAVE_HOST_CPU_FAMILY_power \|\| HAVE_HOST_CPU_FAMILY_powerpc
804	#define MPN_COPY_INCR(dst, src, size) \
805	do { \
806	ASSERT ((size) >= 0); \
807	ASSERT (MPN_SAME_OR_INCR_P (dst, src, size)); \
808	__GMPN_COPY_INCR (dst, src, size); \
809	} while (0)
810	#endif
811
812	#if defined (_CRAY)
813	#define MPN_COPY_INCR(dst, src, n) \
814	do { \
815	int __i; /* Faster on some Crays with plain int */ \
816	_Pragma ("_CRI ivdep"); \
817	for (__i = 0; __i < (n); __i++) \
818	(dst)[__i] = (src)[__i]; \
819	} while (0)
820	#endif
821
822	#define mpn_copyi __MPN(copyi)
823	void mpn_copyi _PROTO ((mp_ptr, mp_srcptr, mp_size_t));
824
825	#if ! defined (MPN_COPY_INCR) && HAVE_NATIVE_mpn_copyi
826	#define MPN_COPY_INCR(dst, src, size) \
827	do { \
828	ASSERT ((size) >= 0); \
829	ASSERT (MPN_SAME_OR_INCR_P (dst, src, size)); \
830	mpn_copyi (dst, src, size); \
831	} while (0)
832	#endif
833
834	/* Copy N limbs from SRC to DST incrementing, N==0 allowed. */
835	#if ! defined (MPN_COPY_INCR)
836	#define MPN_COPY_INCR(dst, src, n) \
837	do { \
838	ASSERT ((n) >= 0); \
839	ASSERT (MPN_SAME_OR_INCR_P (dst, src, n)); \
840	if ((n) != 0) \
841	{ \
842	mp_size_t __n = (n) - 1; \
843	mp_ptr __dst = (dst); \
844	mp_srcptr __src = (src); \
845	mp_limb_t __x; \
846	__x = *__src++; \
847	if (__n != 0) \
848	{ \
849	do \
850	{ \
851	*__dst++ = __x; \
852	__x = *__src++; \
853	} \
854	while (--__n); \
855	} \
856	*__dst++ = __x; \
857	} \
858	} while (0)
859	#endif
860
861
862	/* As per __GMPN_COPY_INCR in gmp.h. */
863	#if HAVE_HOST_CPU_FAMILY_power \|\| HAVE_HOST_CPU_FAMILY_powerpc
864	#define MPN_COPY_DECR(dst, src, size) \
865	do { \
866	ASSERT ((size) >= 0); \
867	ASSERT (MPN_SAME_OR_DECR_P (dst, src, size)); \
868	if ((size) != 0) \
869	{ \
870	mp_ptr __dst = (dst) + (size); \
871	mp_srcptr __src = (src) + (size); \
872	mp_size_t __size = (size); \
873	do \
874	--__dst = --__src; \
875	while (--__size != 0); \
876	} \
877	} while (0)
878	#endif
879
880	#if defined (_CRAY)
881	#define MPN_COPY_DECR(dst, src, n) \
882	do { \
883	int __i; /* Faster on some Crays with plain int */ \
884	_Pragma ("_CRI ivdep"); \
885	for (__i = (n) - 1; __i >= 0; __i--) \
886	(dst)[__i] = (src)[__i]; \
887	} while (0)
888	#endif
889
890	#define mpn_copyd __MPN(copyd)
891	void mpn_copyd _PROTO ((mp_ptr, mp_srcptr, mp_size_t));
892
893	#if ! defined (MPN_COPY_DECR) && HAVE_NATIVE_mpn_copyd
894	#define MPN_COPY_DECR(dst, src, size) \
895	do { \
896	ASSERT ((size) >= 0); \
897	ASSERT (MPN_SAME_OR_DECR_P (dst, src, size)); \
898	mpn_copyd (dst, src, size); \
899	} while (0)
900	#endif
901
902	/* Copy N limbs from SRC to DST decrementing, N==0 allowed. */
903	#if ! defined (MPN_COPY_DECR)
904	#define MPN_COPY_DECR(dst, src, n) \
905	do { \
906	ASSERT ((n) >= 0); \
907	ASSERT (MPN_SAME_OR_DECR_P (dst, src, n)); \
908	if ((n) != 0) \
909	{ \
910	mp_size_t __n = (n) - 1; \
911	mp_ptr __dst = (dst) + __n; \
912	mp_srcptr __src = (src) + __n; \
913	mp_limb_t __x; \
914	__x = *__src--; \
915	if (__n != 0) \
916	{ \
917	do \
918	{ \
919	*__dst-- = __x; \
920	__x = *__src--; \
921	} \
922	while (--__n); \
923	} \
924	*__dst-- = __x; \
925	} \
926	} while (0)
927	#endif
928
929
930	#ifndef MPN_COPY
931	#define MPN_COPY(d,s,n) \
932	do { \
933	ASSERT (MPN_SAME_OR_SEPARATE_P (d, s, n)); \
934	MPN_COPY_INCR (d, s, n); \
935	} while (0)
936	#endif
937
938
939	/* Set {dst,size} to the limbs of {src,size} in reverse order. */
940	#define MPN_REVERSE(dst, src, size) \
941	do { \
942	mp_ptr __dst = (dst); \
943	mp_size_t __size = (size); \
944	mp_srcptr __src = (src) + __size - 1; \
945	mp_size_t __i; \
946	ASSERT ((size) >= 0); \
947	ASSERT (! MPN_OVERLAP_P (dst, size, src, size)); \
948	CRAY_Pragma ("_CRI ivdep"); \
949	for (__i = 0; __i < __size; __i++) \
950	{ \
951	__dst = __src; \
952	__dst++; \
953	__src--; \
954	} \
955	} while (0)
956
957
958	/* Zero n limbs at dst.
959
960	For power and powerpc we want an inline stu/bdnz loop for zeroing. On
961	ppc630 for instance this is optimal since it can sustain only 1 store per
962	cycle.
963
964	gcc 2.95.x (for powerpc64 -maix64, or powerpc32) doesn't recognise the
965	"for" loop in the generic code below can become stu/bdnz. The do/while
966	here helps it get to that. The same caveat about plain -mpowerpc64 mode
967	applies here as to __GMPN_COPY_INCR in gmp.h.
968
969	xlc 3.1 already generates stu/bdnz from the generic C, and does so from
970	this loop too.
971
972	Enhancement: GLIBC does some trickery with dcbz to zero whole cache lines
973	at a time. MPN_ZERO isn't all that important in GMP, so it might be more
974	trouble than it's worth to do the same, though perhaps a call to memset
975	would be good when on a GNU system. */
976
977	#if HAVE_HOST_CPU_FAMILY_power \|\| HAVE_HOST_CPU_FAMILY_powerpc
978	#define MPN_ZERO(dst, n) \
979	do { \
980	ASSERT ((n) >= 0); \
981	if ((n) != 0) \
982	{ \
983	mp_ptr __dst = (dst) - 1; \
984	mp_size_t __n = (n); \
985	do \
986	*++__dst = 0; \
987	while (--__n); \
988	} \
989	} while (0)
990	#endif
991
992	#ifndef MPN_ZERO
993	#define MPN_ZERO(dst, n) \
994	do { \
995	ASSERT ((n) >= 0); \
996	if ((n) != 0) \
997	{ \
998	mp_ptr __dst = (dst); \
999	mp_size_t __n = (n); \
1000	do \
1001	*__dst++ = 0; \
1002	while (--__n); \
1003	} \
1004	} while (0)
1005	#endif
1006
1007
1008	/* On the x86s repe/scasl doesn't seem useful, since it takes many cycles to
1009	start up and would need to strip a lot of zeros before it'd be faster
1010	than a simple cmpl loop. Here are some times in cycles for
1011	std/repe/scasl/cld and cld/repe/scasl (the latter would be for stripping
1012	low zeros).
1013
1014	std cld
1015	P5 18 16
1016	P6 46 38
1017	K6 36 13
1018	K7 21 20
1019	*/
1020	#ifndef MPN_NORMALIZE
1021	#define MPN_NORMALIZE(DST, NLIMBS) \
1022	do { \
1023	while (NLIMBS > 0) \
1024	{ \
1025	if ((DST)[(NLIMBS) - 1] != 0) \
1026	break; \
1027	NLIMBS--; \
1028	} \
1029	} while (0)
1030	#endif
1031	#ifndef MPN_NORMALIZE_NOT_ZERO
1032	#define MPN_NORMALIZE_NOT_ZERO(DST, NLIMBS) \
1033	do { \
1034	ASSERT ((NLIMBS) >= 1); \
1035	while (1) \
1036	{ \
1037	if ((DST)[(NLIMBS) - 1] != 0) \
1038	break; \
1039	NLIMBS--; \
1040	} \
1041	} while (0)
1042	#endif
1043
1044	/* Strip least significant zero limbs from {ptr,size} by incrementing ptr
1045	and decrementing size. low should be ptr[0], and will be the new ptr[0]
1046	on returning. The number in {ptr,size} must be non-zero, ie. size!=0 and
1047	somewhere a non-zero limb. */
1048	#define MPN_STRIP_LOW_ZEROS_NOT_ZERO(ptr, size, low) \
1049	do { \
1050	ASSERT ((size) >= 1); \
1051	ASSERT ((low) == (ptr)[0]); \
1052	\
1053	while ((low) == 0) \
1054	{ \
1055	(size)--; \
1056	ASSERT ((size) >= 1); \
1057	(ptr)++; \
1058	(low) = *(ptr); \
1059	} \
1060	} while (0)
1061
1062	/* Initialize X of type mpz_t with space for NLIMBS limbs. X should be a
1063	temporary variable; it will be automatically cleared out at function
1064	return. We use __x here to make it possible to accept both mpz_ptr and
1065	mpz_t arguments. */
1066	#define MPZ_TMP_INIT(X, NLIMBS) \
1067	do { \
1068	mpz_ptr __x = (X); \
1069	ASSERT ((NLIMBS) >= 1); \
1070	__x->_mp_alloc = (NLIMBS); \
1071	__x->_mp_d = (mp_ptr) TMP_ALLOC ((NLIMBS) * BYTES_PER_MP_LIMB); \
1072	} while (0)
1073
1074	/* Realloc for an mpz_t WHAT if it has less than NEEDED limbs. */
1075	#define MPZ_REALLOC(z,n) ((n) > ALLOC(z) ? _mpz_realloc(z,n) : PTR(z))
1076
1077	#define MPZ_EQUAL_1_P(z) (SIZ(z)==1 && PTR(z)[0] == 1)
1078
1079
1080	/* MPN_FIB2_SIZE(n) is the size in limbs required by mpn_fib2_ui for fp and
1081	f1p.
1082
1083	From Knuth vol 1 section 1.2.8, F[n] = phi^n/sqrt(5) rounded to the
1084	nearest integer, where phi=(1+sqrt(5))/2 is the golden ratio. So the
1085	number of bits required is nlog_2((1+sqrt(5))/2) = n0.6942419.
1086
1087	The multiplier used is 23/32=0.71875 for efficient calculation on CPUs
1088	without good floating point. There's +2 for rounding up, and a further
1089	+2 since at the last step x limbs are doubled into a 2x+1 limb region
1090	whereas the actual F[2k] value might be only 2x-1 limbs.
1091
1092	Note that a division is done first, since on a 32-bit system it's at
1093	least conceivable to go right up to n==ULONG_MAX. (F[2^32-1] would be
1094	about 380Mbytes, plus temporary workspace of about 1.2Gbytes here and
1095	whatever a multiply of two 190Mbyte numbers takes.)
1096
1097	Enhancement: When GMP_NUMB_BITS is not a power of 2 the division could be
1098	worked into the multiplier. */
1099
1100	#define MPN_FIB2_SIZE(n) \
1101	((mp_size_t) ((n) / 32 * 23 / GMP_NUMB_BITS) + 4)
1102
1103
1104	/* FIB_TABLE(n) returns the Fibonacci number F[n]. Must have n in the range
1105	-1 <= n <= FIB_TABLE_LIMIT.
1106
1107	FIB_TABLE_LUCNUM_LIMIT is the largest n for which L[n] = F[n] + 2*F[n-1]
1108	fits in a limb.
1109
1110	This data generated by code at the end of mpn/generic/fib2_ui.c. */
1111
1112	extern const mp_limb_t __gmp_fib_table[];
1113	#define FIB_TABLE(n) (__gmp_fib_table[(n)+1])
1114
1115	#if GMP_NUMB_BITS >= 64
1116	#define FIB_TABLE_LIMIT 93
1117	#define FIB_TABLE_LUCNUM_LIMIT 92
1118	#else
1119	#if GMP_NUMB_BITS >= 32
1120	#define FIB_TABLE_LIMIT 47
1121	#define FIB_TABLE_LUCNUM_LIMIT 46
1122	#else
1123	#if GMP_NUMB_BITS >= 16
1124	#define FIB_TABLE_LIMIT 24
1125	#define FIB_TABLE_LUCNUM_LIMIT 23
1126	#else
1127	#if GMP_NUMB_BITS >= 8
1128	#define FIB_TABLE_LIMIT 13
1129	#define FIB_TABLE_LUCNUM_LIMIT 11
1130	#else
1131	#if GMP_NUMB_BITS >= 4
1132	#define FIB_TABLE_LIMIT 7
1133	#define FIB_TABLE_LUCNUM_LIMIT 5
1134	#endif /* 4 */
1135	#endif /* 8 */
1136	#endif /* 16 */
1137	#endif /* 32 */
1138	#endif /* 64 */
1139
1140
1141	/* For a threshold between algorithms A and B, size>=thresh is where B
1142	should be used. Special value MP_SIZE_T_MAX means only ever use A, or
1143	value 0 means only ever use B. The tests for these special values will
1144	be compile-time constants, so the compiler should be able to eliminate
1145	the code for the unwanted algorithm. */
1146
1147	#define ABOVE_THRESHOLD(size,thresh) \
1148	((thresh) == 0 \
1149	\|\| ((thresh) != MP_SIZE_T_MAX \
1150	&& (size) >= (thresh)))
1151	#define BELOW_THRESHOLD(size,thresh) (! ABOVE_THRESHOLD (size, thresh))
1152
1153
1154	/* If MUL_KARATSUBA_THRESHOLD is not already defined, define it to a
1155	value which is good on most machines. */
1156	#ifndef MUL_KARATSUBA_THRESHOLD
1157	#define MUL_KARATSUBA_THRESHOLD 32
1158	#endif
1159
1160	/* If MUL_TOOM3_THRESHOLD is not already defined, define it to a
1161	value which is good on most machines. */
1162	#ifndef MUL_TOOM3_THRESHOLD
1163	#define MUL_TOOM3_THRESHOLD 256
1164	#endif
1165
1166	/* This is the threshold at which mpn_sqr_basecase should take over from
1167	mpn_mul_basecase in mpn_sqr_n. Default is to use mpn_sqr_basecase
1168	always.
1169
1170	If it turns out that mpn_kara_sqr_n becomes faster than mpn_mul_basecase
1171	before mpn_sqr_basecase does, then SQR_BASECASE_THRESHOLD is the
1172	karatsuba threshold and SQR_KARATSUBA_THRESHOLD is 0. This oddity arises
1173	more or less because SQR_KARATSUBA_THRESHOLD represents the size up to
1174	which mpn_sqr_basecase should be used, and that may be never. */
1175
1176	#ifndef SQR_BASECASE_THRESHOLD
1177	#define SQR_BASECASE_THRESHOLD 0
1178	#endif
1179
1180	#ifndef SQR_KARATSUBA_THRESHOLD
1181	#define SQR_KARATSUBA_THRESHOLD (2*MUL_KARATSUBA_THRESHOLD)
1182	#endif
1183
1184	#ifndef SQR_TOOM3_THRESHOLD
1185	#define SQR_TOOM3_THRESHOLD (2*MUL_TOOM3_THRESHOLD)
1186	#endif
1187
1188	/* First k to use for an FFT modF multiply. A modF FFT is an order
1189	log(2^k)/log(2^(k-1)) algorithm, so k=3 is merely 1.5 like karatsuba,
1190	whereas k=4 is 1.33 which is faster than toom3 at 1.485. */
1191	#define FFT_FIRST_K 4
1192
1193	/* Threshold at which FFT should be used to do a modF NxN -> N multiply. */
1194	#ifndef MUL_FFT_MODF_THRESHOLD
1195	#define MUL_FFT_MODF_THRESHOLD (MUL_TOOM3_THRESHOLD * 3)
1196	#endif
1197	#ifndef SQR_FFT_MODF_THRESHOLD
1198	#define SQR_FFT_MODF_THRESHOLD (SQR_TOOM3_THRESHOLD * 3)
1199	#endif
1200
1201	/* Threshold at which FFT should be used to do an NxN -> 2N multiply. This
1202	will be a size where FFT is using k=7 or k=8, since an FFT-k used for an
1203	NxN->2N multiply and not recursing into itself is an order
1204	log(2^k)/log(2^(k-2)) algorithm, so it'll be at least k=7 at 1.39 which
1205	is the first better than toom3. */
1206	#ifndef MUL_FFT_THRESHOLD
1207	#define MUL_FFT_THRESHOLD (MUL_FFT_MODF_THRESHOLD * 10)
1208	#endif
1209	#ifndef SQR_FFT_THRESHOLD
1210	#define SQR_FFT_THRESHOLD (SQR_FFT_MODF_THRESHOLD * 10)
1211	#endif
1212
1213	/* Table of thresholds for successive modF FFT "k"s. The first entry is
1214	where FFT_FIRST_K+1 should be used, the second FFT_FIRST_K+2,
1215	etc. See mpn_fft_best_k(). */
1216	#ifndef MUL_FFT_TABLE
1217	#define MUL_FFT_TABLE \
1218	{ MUL_TOOM3_THRESHOLD * 4, /* k=5 */ \
1219	MUL_TOOM3_THRESHOLD * 8, /* k=6 */ \
1220	MUL_TOOM3_THRESHOLD * 16, /* k=7 */ \
1221	MUL_TOOM3_THRESHOLD * 32, /* k=8 */ \
1222	MUL_TOOM3_THRESHOLD * 96, /* k=9 */ \
1223	MUL_TOOM3_THRESHOLD * 288, /* k=10 */ \
1224	0 }
1225	#endif
1226	#ifndef SQR_FFT_TABLE
1227	#define SQR_FFT_TABLE \
1228	{ SQR_TOOM3_THRESHOLD * 4, /* k=5 */ \
1229	SQR_TOOM3_THRESHOLD * 8, /* k=6 */ \
1230	SQR_TOOM3_THRESHOLD * 16, /* k=7 */ \
1231	SQR_TOOM3_THRESHOLD * 32, /* k=8 */ \
1232	SQR_TOOM3_THRESHOLD * 96, /* k=9 */ \
1233	SQR_TOOM3_THRESHOLD * 288, /* k=10 */ \
1234	0 }
1235	#endif
1236
1237	#ifndef FFT_TABLE_ATTRS
1238	#define FFT_TABLE_ATTRS static const
1239	#endif
1240
1241	#define MPN_FFT_TABLE_SIZE 16
1242
1243
1244	/* mpn_dc_divrem_n(n) calls 2mul(n/2)+2div(n/2), thus to be faster than
1245	div(n) = 4*div(n/2), we need mul(n/2) to be faster than the classic way,
1246	i.e. n/2 >= MUL_KARATSUBA_THRESHOLD
1247
1248	Measured values are between 2 and 4 times MUL_KARATSUBA_THRESHOLD, so go
1249	for 3 as an average. */
1250
1251	#ifndef DIV_DC_THRESHOLD
1252	#define DIV_DC_THRESHOLD (3 * MUL_KARATSUBA_THRESHOLD)
1253	#endif
1254
1255
1256	/* Return non-zero if xp,xsize and yp,ysize overlap.
1257	If xp+xsize<=yp there's no overlap, or if yp+ysize<=xp there's no
1258	overlap. If both these are false, there's an overlap. */
1259	#define MPN_OVERLAP_P(xp, xsize, yp, ysize) \
1260	((xp) + (xsize) > (yp) && (yp) + (ysize) > (xp))
1261	#define MEM_OVERLAP_P(xp, xsize, yp, ysize) \
1262	( (char ) (xp) + (xsize) > (char ) (yp) \
1263	&& (char ) (yp) + (ysize) > (char ) (xp))
1264
1265	/* Return non-zero if xp,xsize and yp,ysize are either identical or not
1266	overlapping. Return zero if they're partially overlapping. */
1267	#define MPN_SAME_OR_SEPARATE_P(xp, yp, size) \
1268	MPN_SAME_OR_SEPARATE2_P(xp, size, yp, size)
1269	#define MPN_SAME_OR_SEPARATE2_P(xp, xsize, yp, ysize) \
1270	((xp) == (yp) \|\| ! MPN_OVERLAP_P (xp, xsize, yp, ysize))
1271
1272	/* Return non-zero if dst,dsize and src,ssize are either identical or
1273	overlapping in a way suitable for an incrementing/decrementing algorithm.
1274	Return zero if they're partially overlapping in an unsuitable fashion. */
1275	#define MPN_SAME_OR_INCR2_P(dst, dsize, src, ssize) \
1276	((dst) <= (src) \|\| ! MPN_OVERLAP_P (dst, dsize, src, ssize))
1277	#define MPN_SAME_OR_INCR_P(dst, src, size) \
1278	MPN_SAME_OR_INCR2_P(dst, size, src, size)
1279	#define MPN_SAME_OR_DECR2_P(dst, dsize, src, ssize) \
1280	((dst) >= (src) \|\| ! MPN_OVERLAP_P (dst, dsize, src, ssize))
1281	#define MPN_SAME_OR_DECR_P(dst, src, size) \
1282	MPN_SAME_OR_DECR2_P(dst, size, src, size)
1283
1284
1285	/* ASSERT() is a private assertion checking scheme, similar to <assert.h>.
1286	ASSERT() does the check only if WANT_ASSERT is selected, ASSERT_ALWAYS()
1287	does it always. Generally assertions are meant for development, but
1288	might help when looking for a problem later too.
1289
1290	Note that strings shouldn't be used within the ASSERT expression,
1291	eg. ASSERT(strcmp(s,"notgood")!=0), since the quotes upset the "expr"
1292	used in the !HAVE_STRINGIZE case (ie. K&R). */
1293
1294	#ifdef __LINE__
1295	#define ASSERT_LINE __LINE__
1296	#else
1297	#define ASSERT_LINE -1
1298	#endif
1299
1300	#ifdef __FILE__
1301	#define ASSERT_FILE __FILE__
1302	#else
1303	#define ASSERT_FILE ""
1304	#endif
1305
1306	void __gmp_assert_header _PROTO ((const char *filename, int linenum));
1307	__GMP_DECLSPEC void __gmp_assert_fail _PROTO ((const char filename, int linenum, const char expr)) ATTRIBUTE_NORETURN;
1308
1309	#if HAVE_STRINGIZE
1310	#define ASSERT_FAIL(expr) __gmp_assert_fail (ASSERT_FILE, ASSERT_LINE, #expr)
1311	#else
1312	#define ASSERT_FAIL(expr) __gmp_assert_fail (ASSERT_FILE, ASSERT_LINE, "expr")
1313	#endif
1314
1315	#define ASSERT_ALWAYS(expr) \
1316	do { \
1317	if (!(expr)) \
1318	ASSERT_FAIL (expr); \
1319	} while (0)
1320
1321	#if WANT_ASSERT
1322	#define ASSERT(expr) ASSERT_ALWAYS (expr)
1323	#else
1324	#define ASSERT(expr) do {} while (0)
1325	#endif
1326
1327
1328	/* ASSERT_CARRY checks the expression is non-zero, and ASSERT_NOCARRY checks
1329	that it's zero. In both cases if assertion checking is disabled the
1330	expression is still evaluated. These macros are meant for use with
1331	routines like mpn_add_n() where the return value represents a carry or
1332	whatever that should or shouldn't occur in some context. For example,
1333	ASSERT_NOCARRY (mpn_add_n (rp, s1p, s2p, size)); */
1334	#if WANT_ASSERT
1335	#define ASSERT_CARRY(expr) ASSERT_ALWAYS ((expr) != 0)
1336	#define ASSERT_NOCARRY(expr) ASSERT_ALWAYS ((expr) == 0)
1337	#else
1338	#define ASSERT_CARRY(expr) (expr)
1339	#define ASSERT_NOCARRY(expr) (expr)
1340	#endif
1341
1342
1343	/* ASSERT_CODE includes code when assertion checking is wanted. This is the
1344	same as writing "#if WANT_ASSERT", but more compact. */
1345	#if WANT_ASSERT
1346	#define ASSERT_CODE(expr) expr
1347	#else
1348	#define ASSERT_CODE(expr)
1349	#endif
1350
1351
1352	/* Test that an mpq_t is in fully canonical form. This can be used as
1353	protection on routines like mpq_equal which give wrong results on
1354	non-canonical inputs. */
1355	#if WANT_ASSERT
1356	#define ASSERT_MPQ_CANONICAL(q) \
1357	do { \
1358	ASSERT (q->_mp_den._mp_size > 0); \
1359	if (q->_mp_num._mp_size == 0) \
1360	{ \
1361	/* zero should be 0/1 */ \
1362	ASSERT (mpz_cmp_ui (mpq_denref(q), 1L) == 0); \
1363	} \
1364	else \
1365	{ \
1366	/* no common factors */ \
1367	mpz_t __g; \
1368	mpz_init (__g); \
1369	mpz_gcd (__g, mpq_numref(q), mpq_denref(q)); \
1370	ASSERT (mpz_cmp_ui (__g, 1) == 0); \
1371	mpz_clear (__g); \
1372	} \
1373	} while (0)
1374	#else
1375	#define ASSERT_MPQ_CANONICAL(q) do {} while (0)
1376	#endif
1377
1378	/* Check that the nail parts are zero. */
1379	#define ASSERT_ALWAYS_LIMB(limb) \
1380	do { \
1381	mp_limb_t __nail = (limb) & GMP_NAIL_MASK; \
1382	ASSERT_ALWAYS (__nail == 0); \
1383	} while (0)
1384	#define ASSERT_ALWAYS_MPN(ptr, size) \
1385	do { \
1386	/* let whole loop go dead when no nails */ \
1387	if (GMP_NAIL_BITS != 0) \
1388	{ \
1389	mp_size_t __i; \
1390	for (__i = 0; __i < (size); __i++) \
1391	ASSERT_ALWAYS_LIMB ((ptr)[__i]); \
1392	} \
1393	} while (0)
1394	#if WANT_ASSERT
1395	#define ASSERT_LIMB(limb) ASSERT_ALWAYS_LIMB (limb)
1396	#define ASSERT_MPN(ptr, size) ASSERT_ALWAYS_MPN (ptr, size)
1397	#else
1398	#define ASSERT_LIMB(limb) do {} while (0)
1399	#define ASSERT_MPN(ptr, size) do {} while (0)
1400	#endif
1401
1402
1403	/* Assert that an mpn region {ptr,size} is zero, or non-zero.
1404	size==0 is allowed, and in that case {ptr,size} considered to be zero. */
1405	#if WANT_ASSERT
1406	#define ASSERT_MPN_ZERO_P(ptr,size) \
1407	do { \
1408	mp_size_t __i; \
1409	ASSERT ((size) >= 0); \
1410	for (__i = 0; __i < (size); __i++) \
1411	ASSERT ((ptr)[__i] == 0); \
1412	} while (0)
1413	#define ASSERT_MPN_NONZERO_P(ptr,size) \
1414	do { \
1415	mp_size_t __i; \
1416	int __nonzero = 0; \
1417	ASSERT ((size) >= 0); \
1418	for (__i = 0; __i < (size); __i++) \
1419	if ((ptr)[__i] != 0) \
1420	{ \
1421	__nonzero = 1; \
1422	break; \
1423	} \
1424	ASSERT (__nonzero); \
1425	} while (0)
1426	#else
1427	#define ASSERT_MPN_ZERO_P(ptr,size) do {} while (0)
1428	#define ASSERT_MPN_NONZERO_P(ptr,size) do {} while (0)
1429	#endif
1430
1431
1432	#if HAVE_NATIVE_mpn_com_n
1433	#define mpn_com_n __MPN(com_n)
1434	void mpn_com_n _PROTO ((mp_ptr, mp_srcptr, mp_size_t));
1435	#else
1436	#define mpn_com_n(d,s,n) \
1437	do { \
1438	mp_ptr __d = (d); \
1439	mp_srcptr __s = (s); \
1440	mp_size_t __n = (n); \
1441	ASSERT (__n >= 1); \
1442	ASSERT (MPN_SAME_OR_SEPARATE_P (__d, __s, __n)); \
1443	do \
1444	__d++ = (~ __s++) & GMP_NUMB_MASK; \
1445	while (--__n); \
1446	} while (0)
1447	#endif
1448
1449	#define MPN_LOGOPS_N_INLINE(d, s1, s2, n, operation) \
1450	do { \
1451	mp_ptr __d = (d); \
1452	mp_srcptr __s1 = (s1); \
1453	mp_srcptr __s2 = (s2); \
1454	mp_size_t __n = (n); \
1455	ASSERT (__n >= 1); \
1456	ASSERT (MPN_SAME_OR_SEPARATE_P (__d, __s1, __n)); \
1457	ASSERT (MPN_SAME_OR_SEPARATE_P (__d, __s2, __n)); \
1458	do \
1459	operation; \
1460	while (--__n); \
1461	} while (0)
1462
1463	#if HAVE_NATIVE_mpn_and_n
1464	#define mpn_and_n __MPN(and_n)
1465	void mpn_and_n _PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
1466	#else
1467	#define mpn_and_n(d, s1, s2, n) \
1468	MPN_LOGOPS_N_INLINE (d, s1, s2, n, __d++ = __s1++ & *__s2++)
1469	#endif
1470
1471	#if HAVE_NATIVE_mpn_andn_n
1472	#define mpn_andn_n __MPN(andn_n)
1473	void mpn_andn_n _PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
1474	#else
1475	#define mpn_andn_n(d, s1, s2, n) \
1476	MPN_LOGOPS_N_INLINE (d, s1, s2, n, __d++ = __s1++ & ~*__s2++)
1477	#endif
1478
1479	#if HAVE_NATIVE_mpn_nand_n
1480	#define mpn_nand_n __MPN(nand_n)
1481	void mpn_nand_n _PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
1482	#else
1483	#define mpn_nand_n(d, s1, s2, n) \
1484	MPN_LOGOPS_N_INLINE (d, s1, s2, n, __d++ = ~ (__s1++ & *__s2++))
1485	#endif
1486
1487	#if HAVE_NATIVE_mpn_ior_n
1488	#define mpn_ior_n __MPN(ior_n)
1489	void mpn_ior_n _PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
1490	#else
1491	#define mpn_ior_n(d, s1, s2, n) \
1492	MPN_LOGOPS_N_INLINE (d, s1, s2, n, __d++ = __s1++ \| *__s2++)
1493	#endif
1494
1495	#if HAVE_NATIVE_mpn_iorn_n
1496	#define mpn_iorn_n __MPN(iorn_n)
1497	void mpn_iorn_n _PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
1498	#else
1499	#define mpn_iorn_n(d, s1, s2, n) \
1500	MPN_LOGOPS_N_INLINE (d, s1, s2, n, __d++ = __s1++ \| ~*__s2++)
1501	#endif
1502
1503	#if HAVE_NATIVE_mpn_nior_n
1504	#define mpn_nior_n __MPN(nior_n)
1505	void mpn_nior_n _PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
1506	#else
1507	#define mpn_nior_n(d, s1, s2, n) \
1508	MPN_LOGOPS_N_INLINE (d, s1, s2, n, __d++ = ~ (__s1++ \| *__s2++))
1509	#endif
1510
1511	#if HAVE_NATIVE_mpn_xor_n
1512	#define mpn_xor_n __MPN(xor_n)
1513	void mpn_xor_n _PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
1514	#else
1515	#define mpn_xor_n(d, s1, s2, n) \
1516	MPN_LOGOPS_N_INLINE (d, s1, s2, n, __d++ = __s1++ ^ *__s2++)
1517	#endif
1518
1519	#if HAVE_NATIVE_mpn_xnor_n
1520	#define mpn_xnor_n __MPN(xnor_n)
1521	void mpn_xnor_n _PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
1522	#else
1523	#define mpn_xnor_n(d, s1, s2, n) \
1524	MPN_LOGOPS_N_INLINE (d, s1, s2, n, __d++ = ~ (__s1++ ^ *__s2++))
1525	#endif
1526
1527
1528	/* SUBC_LIMB sets w=x-y and cout to 0 or 1 for a borrow from that
1529	subtract. */
1530	#if GMP_NAIL_BITS == 0
1531	#define SUBC_LIMB(cout, w, x, y) \
1532	do { \
1533	mp_limb_t __x = (x); \
1534	mp_limb_t __y = (y); \
1535	mp_limb_t __w = __x - __y; \
1536	(w) = __w; \
1537	(cout) = __w > __x; \
1538	} while (0)
1539	#else
1540	#define SUBC_LIMB(cout, w, x, y) \
1541	do { \
1542	mp_limb_t __w = (x) - (y); \
1543	(w) = __w & GMP_NUMB_MASK; \
1544	(cout) = __w >> (GMP_LIMB_BITS-1); \
1545	} while (0)
1546	#endif
1547
1548
1549	/* MPN_INCR_U does {ptr,size} += n, MPN_DECR_U does {ptr,size} -= n, both
1550	expecting no carry (or borrow) from that.
1551
1552	The size parameter is only for the benefit of assertion checking. In a
1553	normal build it's unused and the carry/borrow is just propagated as far
1554	as it needs to go.
1555
1556	On random data, usually only one or two limbs of {ptr,size} get updated,
1557	so there's no need for any sophisticated looping, just something compact
1558	and sensible.
1559
1560	FIXME: Do the generic MPN_{INCR,DECR}_U with a block of code like
1561	mpn_incr_u but with the assertions built in, rather than the separate
1562	add_1 and sub_1 when assertion checking.
1563
1564	FIXME: Switch all code from mpn_{incr,decr}_u to MPN_{INCR,DECR}_U,
1565	declaring their operand sizes, then remove the former. This is purely
1566	for the benefit of assertion checking. */
1567
1568	#if defined (__GNUC__) && HAVE_HOST_CPU_FAMILY_x86 && GMP_NAIL_BITS == 0 \
1569	&& BITS_PER_MP_LIMB == 32 && ! defined (NO_ASM) && ! WANT_ASSERT
1570	/* Better flags handling than the generic C gives on i386, saving a few
1571	bytes of code and maybe a cycle or two. */
1572
1573	#define MPN_IORD_U(ptr, incr, aors) \
1574	do { \
1575	mp_ptr __ptr_dummy; \
1576	if (__builtin_constant_p (incr) && (incr) == 1) \
1577	{ \
1578	__asm__ __volatile__ \
1579	("\n" ASM_L(top) ":\n" \
1580	"\t" aors " $1, (%0)\n" \
1581	"\tleal 4(%0),%0\n" \
1582	"\tjc " ASM_L(top) \
1583	: "=r" (__ptr_dummy) \
1584	: "0" (ptr) \
1585	: "memory"); \
1586	} \
1587	else \
1588	{ \
1589	__asm__ __volatile__ \
1590	( aors " %2,(%0)\n" \
1591	"\tjnc " ASM_L(done) "\n" \
1592	ASM_L(top) ":\n" \
1593	"\t" aors " $1,4(%0)\n" \
1594	"\tleal 4(%0),%0\n" \
1595	"\tjc " ASM_L(top) "\n" \
1596	ASM_L(done) ":\n" \
1597	: "=r" (__ptr_dummy) \
1598	: "0" (ptr), \
1599	"ri" (incr) \
1600	: "memory"); \
1601	} \
1602	} while (0)
1603
1604	#define MPN_INCR_U(ptr, size, incr) MPN_IORD_U (ptr, incr, "addl")
1605	#define MPN_DECR_U(ptr, size, incr) MPN_IORD_U (ptr, incr, "subl")
1606	#define mpn_incr_u(ptr, incr) MPN_INCR_U (ptr, 0, incr)
1607	#define mpn_decr_u(ptr, incr) MPN_DECR_U (ptr, 0, incr)
1608	#endif
1609
1610	#if GMP_NAIL_BITS == 0
1611	#ifndef mpn_incr_u
1612	#define mpn_incr_u(p,incr) \
1613	do { \
1614	mp_limb_t __x; \
1615	mp_ptr __p = (p); \
1616	if (__builtin_constant_p (incr) && (incr) == 1) \
1617	{ \
1618	while (++(*(__p++)) == 0) \
1619	; \
1620	} \
1621	else \
1622	{ \
1623	__x = *__p + (incr); \
1624	*__p = __x; \
1625	if (__x < (incr)) \
1626	while (++(*(++__p)) == 0) \
1627	; \
1628	} \
1629	} while (0)
1630	#endif
1631	#ifndef mpn_decr_u
1632	#define mpn_decr_u(p,incr) \
1633	do { \
1634	mp_limb_t __x; \
1635	mp_ptr __p = (p); \
1636	if (__builtin_constant_p (incr) && (incr) == 1) \
1637	{ \
1638	while ((*(__p++))-- == 0) \
1639	; \
1640	} \
1641	else \
1642	{ \
1643	__x = *__p; \
1644	*__p = __x - (incr); \
1645	if (__x < (incr)) \
1646	while ((*(++__p))-- == 0) \
1647	; \
1648	} \
1649	} while (0)
1650	#endif
1651	#endif
1652
1653	#if GMP_NAIL_BITS >= 1
1654	#ifndef mpn_incr_u
1655	#define mpn_incr_u(p,incr) \
1656	do { \
1657	mp_limb_t __x; \
1658	mp_ptr __p = (p); \
1659	if (__builtin_constant_p (incr) && (incr) == 1) \
1660	{ \
1661	do \
1662	{ \
1663	__x = (*__p + 1) & GMP_NUMB_MASK; \
1664	*__p++ = __x; \
1665	} \
1666	while (__x == 0); \
1667	} \
1668	else \
1669	{ \
1670	__x = (*__p + (incr)); \
1671	*__p++ = __x & GMP_NUMB_MASK; \
1672	if (__x >> GMP_NUMB_BITS != 0) \
1673	{ \
1674	do \
1675	{ \
1676	__x = (*__p + 1) & GMP_NUMB_MASK; \
1677	*__p++ = __x; \
1678	} \
1679	while (__x == 0); \
1680	} \
1681	} \
1682	} while (0)
1683	#endif
1684	#ifndef mpn_decr_u
1685	#define mpn_decr_u(p,incr) \
1686	do { \
1687	mp_limb_t __x; \
1688	mp_ptr __p = (p); \
1689	if (__builtin_constant_p (incr) && (incr) == 1) \
1690	{ \
1691	do \
1692	{ \
1693	__x = *__p; \
1694	*__p++ = (__x - 1) & GMP_NUMB_MASK; \
1695	} \
1696	while (__x == 0); \
1697	} \
1698	else \
1699	{ \
1700	__x = *__p - (incr); \
1701	*__p++ = __x & GMP_NUMB_MASK; \
1702	if (__x >> GMP_NUMB_BITS != 0) \
1703	{ \
1704	do \
1705	{ \
1706	__x = *__p; \
1707	*__p++ = (__x - 1) & GMP_NUMB_MASK; \
1708	} \
1709	while (__x == 0); \
1710	} \
1711	} \
1712	} while (0)
1713	#endif
1714	#endif
1715
1716	#ifndef MPN_INCR_U
1717	#if WANT_ASSERT
1718	#define MPN_INCR_U(ptr, size, n) \
1719	do { \
1720	ASSERT ((size) >= 1); \
1721	ASSERT_NOCARRY (mpn_add_1 (ptr, ptr, size, n)); \
1722	} while (0)
1723	#else
1724	#define MPN_INCR_U(ptr, size, n) mpn_incr_u (ptr, n)
1725	#endif
1726	#endif
1727
1728	#ifndef MPN_DECR_U
1729	#if WANT_ASSERT
1730	#define MPN_DECR_U(ptr, size, n) \
1731	do { \
1732	ASSERT ((size) >= 1); \
1733	ASSERT_NOCARRY (mpn_sub_1 (ptr, ptr, size, n)); \
1734	} while (0)
1735	#else
1736	#define MPN_DECR_U(ptr, size, n) mpn_decr_u (ptr, n)
1737	#endif
1738	#endif
1739
1740
1741	/* Structure for conversion between internal binary format and
1742	strings in base 2..36. */
1743	struct bases
1744	{
1745	/* Number of digits in the conversion base that always fits in an mp_limb_t.
1746	For example, for base 10 on a machine where a mp_limb_t has 32 bits this
1747	is 9, since 10*9 is the largest number that fits into a mp_limb_t. /
1748	int chars_per_limb;
1749
1750	/* log(2)/log(conversion_base) */
1751	double chars_per_bit_exactly;
1752
1753	/* base**chars_per_limb, i.e. the biggest number that fits a word, built by
1754	factors of base. Exception: For 2, 4, 8, etc, big_base is log2(base),
1755	i.e. the number of bits used to represent each digit in the base. */
1756	mp_limb_t big_base;
1757
1758	/* A BITS_PER_MP_LIMB bit approximation to 1/big_base, represented as a
1759	fixed-point number. Instead of dividing by big_base an application can
1760	choose to multiply by big_base_inverted. */
1761	mp_limb_t big_base_inverted;
1762	};
1763
1764	#define mp_bases __MPN(bases)
1765	#define __mp_bases __MPN(bases)
1766	__GMP_DECLSPEC extern const struct bases mp_bases[257];
1767
1768	/* mp_bases[10] values, generated by mpn/mp_bases.c */
1769	#if GMP_NUMB_BITS == 4
1770	#define MP_BASES_CHARS_PER_LIMB_10 1
1771	#define MP_BASES_BIG_BASE_10 CNST_LIMB(0xa)
1772	#define MP_BASES_BIG_BASE_INVERTED_10 CNST_LIMB(0x9)
1773	#define MP_BASES_NORMALIZATION_STEPS_10 0
1774	#endif
1775	#if GMP_NUMB_BITS == 8
1776	#define MP_BASES_CHARS_PER_LIMB_10 2
1777	#define MP_BASES_BIG_BASE_10 CNST_LIMB(0x64)
1778	#define MP_BASES_BIG_BASE_INVERTED_10 CNST_LIMB(0x47)
1779	#define MP_BASES_NORMALIZATION_STEPS_10 1
1780	#endif
1781	#if GMP_NUMB_BITS == 16
1782	#define MP_BASES_CHARS_PER_LIMB_10 4
1783	#define MP_BASES_BIG_BASE_10 CNST_LIMB(0x2710)
1784	#define MP_BASES_BIG_BASE_INVERTED_10 CNST_LIMB(0xa36e)
1785	#define MP_BASES_NORMALIZATION_STEPS_10 2
1786	#endif
1787	#if GMP_NUMB_BITS == 28
1788	#define MP_BASES_CHARS_PER_LIMB_10 8
1789	#define MP_BASES_BIG_BASE_10 CNST_LIMB(0x5f5e100)
1790	#define MP_BASES_BIG_BASE_INVERTED_10 CNST_LIMB(0x5798ee23)
1791	#define MP_BASES_NORMALIZATION_STEPS_10 5
1792	#endif
1793	#if GMP_NUMB_BITS == 30
1794	#define MP_BASES_CHARS_PER_LIMB_10 9
1795	#define MP_BASES_BIG_BASE_10 CNST_LIMB(0x3b9aca00)
1796	#define MP_BASES_BIG_BASE_INVERTED_10 CNST_LIMB(0x12e0be82)
1797	#define MP_BASES_NORMALIZATION_STEPS_10 2
1798	#endif
1799	#if GMP_NUMB_BITS == 32
1800	#define MP_BASES_CHARS_PER_LIMB_10 9
1801	#define MP_BASES_BIG_BASE_10 CNST_LIMB(0x3b9aca00)
1802	#define MP_BASES_BIG_BASE_INVERTED_10 CNST_LIMB(0x12e0be82)
1803	#define MP_BASES_NORMALIZATION_STEPS_10 2
1804	#endif
1805	#if GMP_NUMB_BITS == 60
1806	#define MP_BASES_CHARS_PER_LIMB_10 18
1807	#define MP_BASES_BIG_BASE_10 CNST_LIMB(0xde0b6b3a7640000)
1808	#define MP_BASES_BIG_BASE_INVERTED_10 CNST_LIMB(0x2725dd1d243aba0e)
1809	#define MP_BASES_NORMALIZATION_STEPS_10 4
1810	#endif
1811	#if GMP_NUMB_BITS == 62
1812	#define MP_BASES_CHARS_PER_LIMB_10 18
1813	#define MP_BASES_BIG_BASE_10 CNST_LIMB(0xde0b6b3a7640000)
1814	#define MP_BASES_BIG_BASE_INVERTED_10 CNST_LIMB(0x2725dd1d243aba0e)
1815	#define MP_BASES_NORMALIZATION_STEPS_10 4
1816	#endif
1817	#if GMP_NUMB_BITS == 64
1818	#define MP_BASES_CHARS_PER_LIMB_10 19
1819	#define MP_BASES_BIG_BASE_10 CNST_LIMB(0x8ac7230489e80000)
1820	#define MP_BASES_BIG_BASE_INVERTED_10 CNST_LIMB(0xd83c94fb6d2ac34a)
1821	#define MP_BASES_NORMALIZATION_STEPS_10 0
1822	#endif
1823
1824
1825	/* For power of 2 bases this is exact. For other bases the result is either
1826	exact or one too big.
1827
1828	To be exact always it'd be necessary to examine all the limbs of the
1829	operand, since numbers like 100..000 and 99...999 generally differ only
1830	in the lowest limb. It'd be possible to examine just a couple of high
1831	limbs to increase the probability of being exact, but that doesn't seem
1832	worth bothering with. */
1833
1834	#define MPN_SIZEINBASE(result, ptr, size, base) \
1835	do { \
1836	int __lb_base, __cnt; \
1837	mp_size_t __totbits; \
1838	\
1839	ASSERT ((size) >= 0); \
1840	ASSERT ((base) >= 2); \
1841	ASSERT ((base) < numberof (mp_bases)); \
1842	\
1843	/* Special case for X == 0. */ \
1844	if ((size) == 0) \
1845	(result) = 1; \
1846	else \
1847	{ \
1848	/* Calculate the total number of significant bits of X. */ \
1849	count_leading_zeros (__cnt, (ptr)[(size)-1]); \
1850	__totbits = (size) * GMP_NUMB_BITS - (__cnt - GMP_NAIL_BITS); \
1851	\
1852	if (POW2_P (base)) \
1853	{ \
1854	__lb_base = mp_bases[base].big_base; \
1855	(result) = (__totbits + __lb_base - 1) / __lb_base; \
1856	} \
1857	else \
1858	(result) = (size_t) \
1859	(__totbits * mp_bases[base].chars_per_bit_exactly) + 1; \
1860	} \
1861	} while (0)
1862
1863	/* eliminate mp_bases lookups for base==16 */
1864	#define MPN_SIZEINBASE_16(result, ptr, size) \
1865	do { \
1866	int __cnt; \
1867	mp_size_t __totbits; \
1868	\
1869	ASSERT ((size) >= 0); \
1870	\
1871	/* Special case for X == 0. */ \
1872	if ((size) == 0) \
1873	(result) = 1; \
1874	else \
1875	{ \
1876	/* Calculate the total number of significant bits of X. */ \
1877	count_leading_zeros (__cnt, (ptr)[(size)-1]); \
1878	__totbits = (size) * GMP_NUMB_BITS - (__cnt - GMP_NAIL_BITS); \
1879	(result) = (__totbits + 4 - 1) / 4; \
1880	} \
1881	} while (0)
1882
1883
1884	#if HAVE_HOST_CPU_FAMILY_x86
1885	#define TARGET_REGISTER_STARVED 1
1886	#else
1887	#define TARGET_REGISTER_STARVED 0
1888	#endif
1889
1890	/* Use a library function for invert_limb, if available. */
1891	#if ! defined (invert_limb) && HAVE_NATIVE_mpn_invert_limb
1892	#define mpn_invert_limb __MPN(invert_limb)
1893	mp_limb_t mpn_invert_limb _PROTO ((mp_limb_t)) ATTRIBUTE_CONST;
1894	#define invert_limb(invxl,xl) (invxl = mpn_invert_limb (xl))
1895	#endif
1896
1897	#ifndef invert_limb
1898	#define invert_limb(invxl,xl) \
1899	do { \
1900	mp_limb_t dummy; \
1901	ASSERT ((xl) != 0); \
1902	if (xl << 1 == 0) \
1903	invxl = ~(mp_limb_t) 0; \
1904	else \
1905	udiv_qrnnd (invxl, dummy, -xl, 0, xl); \
1906	} while (0)
1907	#endif
1908
1909	/* Divide the two-limb number in (NH,,NL) by D, with DI being the largest
1910	limb not larger than (2*(2BITS_PER_MP_LIMB))/D - (2**BITS_PER_MP_LIMB).
1911	If this would yield overflow, DI should be the largest possible number
1912	(i.e., only ones). For correct operation, the most significant bit of D
1913	has to be set. Put the quotient in Q and the remainder in R. */
1914	#define udiv_qrnnd_preinv(q, r, nh, nl, d, di) \
1915	do { \
1916	mp_limb_t _q, _ql, _r; \
1917	mp_limb_t _xh, _xl; \
1918	ASSERT ((d) != 0); \
1919	umul_ppmm (_q, _ql, (nh), (di)); \
1920	_q += (nh); /* DI is 2*BITS_PER_MP_LIMB too small / \
1921	umul_ppmm (_xh, _xl, _q, (d)); \
1922	sub_ddmmss (_xh, _r, (nh), (nl), _xh, _xl); \
1923	if (_xh != 0) \
1924	{ \
1925	sub_ddmmss (_xh, _r, _xh, _r, 0, (d)); \
1926	_q += 1; \
1927	if (_xh != 0) \
1928	{ \
1929	_r -= (d); \
1930	_q += 1; \
1931	} \
1932	} \
1933	if (_r >= (d)) \
1934	{ \
1935	_r -= (d); \
1936	_q += 1; \
1937	} \
1938	(r) = _r; \
1939	(q) = _q; \
1940	} while (0)
1941	/* Like udiv_qrnnd_preinv, but for for any value D. DNORM is D shifted left
1942	so that its most significant bit is set. LGUP is ceil(log2(D)). */
1943	#define udiv_qrnnd_preinv2gen(q, r, nh, nl, d, di, dnorm, lgup) \
1944	do { \
1945	mp_limb_t _n2, _n10, _n1, _nadj, _q1; \
1946	mp_limb_t _xh, _xl; \
1947	_n2 = ((nh) << (BITS_PER_MP_LIMB - (lgup))) + ((nl) >> 1 >> (l - 1));\
1948	_n10 = (nl) << (BITS_PER_MP_LIMB - (lgup)); \
1949	_n1 = ((mp_limb_signed_t) _n10 >> (BITS_PER_MP_LIMB - 1)); \
1950	_nadj = _n10 + (_n1 & (dnorm)); \
1951	umul_ppmm (_xh, _xl, di, _n2 - _n1); \
1952	add_ssaaaa (_xh, _xl, _xh, _xl, 0, _nadj); \
1953	_q1 = ~(_n2 + _xh); \
1954	umul_ppmm (_xh, _xl, _q1, d); \
1955	add_ssaaaa (_xh, _xl, _xh, _xl, nh, nl); \
1956	_xh -= (d); \
1957	(r) = _xl + ((d) & _xh); \
1958	(q) = _xh - _q1; \
1959	} while (0)
1960	/* Exactly like udiv_qrnnd_preinv, but branch-free. It is not clear which
1961	version to use. */
1962	#define udiv_qrnnd_preinv2norm(q, r, nh, nl, d, di) \
1963	do { \
1964	mp_limb_t _n2, _n10, _n1, _nadj, _q1; \
1965	mp_limb_t _xh, _xl; \
1966	_n2 = (nh); \
1967	_n10 = (nl); \
1968	_n1 = ((mp_limb_signed_t) _n10 >> (BITS_PER_MP_LIMB - 1)); \
1969	_nadj = _n10 + (_n1 & (d)); \
1970	umul_ppmm (_xh, _xl, di, _n2 - _n1); \
1971	add_ssaaaa (_xh, _xl, _xh, _xl, 0, _nadj); \
1972	_q1 = ~(_n2 + _xh); \
1973	umul_ppmm (_xh, _xl, _q1, d); \
1974	add_ssaaaa (_xh, _xl, _xh, _xl, nh, nl); \
1975	_xh -= (d); \
1976	(r) = _xl + ((d) & _xh); \
1977	(q) = _xh - _q1; \
1978	} while (0)
1979
1980
1981	#define mpn_preinv_divrem_1 __MPN(preinv_divrem_1)
1982	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));
1983
1984
1985	/* USE_PREINV_DIVREM_1 is whether to use mpn_preinv_divrem_1, as opposed to
1986	the plain mpn_divrem_1. Likewise USE_PREINV_MOD_1 chooses between
1987	mpn_preinv_mod_1 and plain mpn_mod_1. The default for both is yes, since
1988	the few CISC chips where preinv is not good have defines saying so. */
1989	#ifndef USE_PREINV_DIVREM_1
1990	#define USE_PREINV_DIVREM_1 1
1991	#endif
1992	#ifndef USE_PREINV_MOD_1
1993	#define USE_PREINV_MOD_1 1
1994	#endif
1995
1996	#if USE_PREINV_DIVREM_1
1997	#define MPN_DIVREM_OR_PREINV_DIVREM_1(qp,xsize,ap,size,d,dinv,shift) \
1998	mpn_preinv_divrem_1 (qp, xsize, ap, size, d, dinv, shift)
1999	#else
2000	#define MPN_DIVREM_OR_PREINV_DIVREM_1(qp,xsize,ap,size,d,dinv,shift) \
2001	mpn_divrem_1 (qp, xsize, ap, size, d)
2002	#endif
2003
2004	#if USE_PREINV_MOD_1
2005	#define MPN_MOD_OR_PREINV_MOD_1(src,size,divisor,inverse) \
2006	mpn_preinv_mod_1 (src, size, divisor, inverse)
2007	#else
2008	#define MPN_MOD_OR_PREINV_MOD_1(src,size,divisor,inverse) \
2009	mpn_mod_1 (src, size, divisor)
2010	#endif
2011
2012
2013	#define mpn_mod_34lsub1 __MPN(mod_34lsub1)
2014	mp_limb_t mpn_mod_34lsub1 _PROTO ((mp_srcptr, mp_size_t)) __GMP_ATTRIBUTE_PURE;
2015
2016
2017	/* DIVEXACT_1_THRESHOLD is at what size to use mpn_divexact_1, as opposed to
2018	plain mpn_divrem_1. Likewise MODEXACT_1_ODD_THRESHOLD for
2019	mpn_modexact_1_odd against plain mpn_mod_1. On most CPUs divexact and
2020	modexact are faster at all sizes, so the defaults are 0. Those CPUs
2021	where this is not right have a tuned threshold. */
2022	#ifndef DIVEXACT_1_THRESHOLD
2023	#define DIVEXACT_1_THRESHOLD 0
2024	#endif
2025	#ifndef MODEXACT_1_ODD_THRESHOLD
2026	#define MODEXACT_1_ODD_THRESHOLD 0
2027	#endif
2028
2029	#define mpn_divexact_1 __MPN(divexact_1)
2030	void mpn_divexact_1 _PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t));
2031
2032	#define MPN_DIVREM_OR_DIVEXACT_1(dst, src, size, divisor) \
2033	do { \
2034	if (BELOW_THRESHOLD (size, DIVEXACT_1_THRESHOLD)) \
2035	ASSERT_NOCARRY (mpn_divrem_1 (dst, (mp_size_t) 0, src, size, divisor)); \
2036	else \
2037	{ \
2038	ASSERT (mpn_mod_1 (src, size, divisor) == 0); \
2039	mpn_divexact_1 (dst, src, size, divisor); \
2040	} \
2041	} while (0)
2042
2043	#define mpn_modexact_1c_odd __MPN(modexact_1c_odd)
2044	mp_limb_t mpn_modexact_1c_odd _PROTO ((mp_srcptr src, mp_size_t size,
2045	mp_limb_t divisor, mp_limb_t c)) __GMP_ATTRIBUTE_PURE;
2046
2047	#if HAVE_NATIVE_mpn_modexact_1_odd
2048	#define mpn_modexact_1_odd __MPN(modexact_1_odd)
2049	mp_limb_t mpn_modexact_1_odd _PROTO ((mp_srcptr src, mp_size_t size,
2050	mp_limb_t divisor)) __GMP_ATTRIBUTE_PURE;
2051	#else
2052	#define mpn_modexact_1_odd(src,size,divisor) \
2053	mpn_modexact_1c_odd (src, size, divisor, CNST_LIMB(0))
2054	#endif
2055
2056	#define MPN_MOD_OR_MODEXACT_1_ODD(src,size,divisor) \
2057	(ABOVE_THRESHOLD (size, MODEXACT_1_ODD_THRESHOLD) \
2058	? mpn_modexact_1_odd (src, size, divisor) \
2059	: mpn_mod_1 (src, size, divisor))
2060
2061
2062	/* modlimb_invert() sets inv to the multiplicative inverse of n modulo
2063	2^BITS_PER_MP_LIMB, ie. satisfying inv*n == 1 mod 2^BITS_PER_MP_LIMB.
2064	n must be odd (otherwise such an inverse doesn't exist).
2065
2066	This is not to be confused with invert_limb(), which is completely
2067	different.
2068
2069	The table lookup gives an inverse with the low 8 bits valid, and each
2070	multiply step doubles the number of bits. See Jebelean "An algorithm for
2071	exact division" end of section 4 (reference in gmp.texi).
2072
2073	Possible enhancement: Could use UHWtype until the last step, if half-size
2074	multiplies are faster (might help under _LONG_LONG_LIMB).
2075
2076	Alternative: As noted in Granlund and Montgomery "Division by Invariant
2077	Integers using Multiplication" (reference in gmp.texi), n itself gives a
2078	3-bit inverse immediately, and could be used instead of a table lookup.
2079	A 4-bit inverse can be obtained effectively from xoring bits 1 and 2 into
2080	bit 3, for instance with (((n + 2) & 4) << 1) ^ n. */
2081
2082	#define modlimb_invert_table __gmp_modlimb_invert_table
2083	__GMP_DECLSPEC extern const unsigned char modlimb_invert_table[128];
2084
2085	#if BITS_PER_MP_LIMB <= 8
2086	#define modlimb_invert(inv,n) \
2087	do { \
2088	mp_limb_t __n = (n); \
2089	mp_limb_t __inv; \
2090	ASSERT ((__n & 1) == 1); \
2091	__inv = modlimb_invert_table[(__n/2) & 0x7F]; /* 8 */ \
2092	ASSERT ((__inv * __n & GMP_NUMB_MASK) == 1); \
2093	(inv) = __inv & GMP_NUMB_MASK; \
2094	} while (0)
2095	#else
2096	#if BITS_PER_MP_LIMB <= 16
2097	#define modlimb_invert(inv,n) \
2098	do { \
2099	mp_limb_t __n = (n); \
2100	mp_limb_t __inv; \
2101	ASSERT ((__n & 1) == 1); \
2102	__inv = modlimb_invert_table[(__n/2) & 0x7F]; /* 8 */ \
2103	__inv = 2 * __inv - __inv * __inv * __n; /* 16 */ \
2104	ASSERT ((__inv * __n & GMP_NUMB_MASK) == 1); \
2105	(inv) = __inv & GMP_NUMB_MASK; \
2106	} while (0)
2107	#else
2108	#if BITS_PER_MP_LIMB <= 32
2109	#define modlimb_invert(inv,n) \
2110	do { \
2111	mp_limb_t __n = (n); \
2112	mp_limb_t __inv; \
2113	ASSERT ((__n & 1) == 1); \
2114	__inv = modlimb_invert_table[(__n/2) & 0x7F]; /* 8 */ \
2115	__inv = 2 * __inv - __inv * __inv * __n; /* 16 */ \
2116	__inv = 2 * __inv - __inv * __inv * __n; /* 32 */ \
2117	ASSERT ((__inv * __n & GMP_NUMB_MASK) == 1); \
2118	(inv) = __inv & GMP_NUMB_MASK; \
2119	} while (0)
2120	#else
2121	#if BITS_PER_MP_LIMB <= 64
2122	#define modlimb_invert(inv,n) \
2123	do { \
2124	mp_limb_t __n = (n); \
2125	mp_limb_t __inv; \
2126	ASSERT ((__n & 1) == 1); \
2127	__inv = modlimb_invert_table[(__n/2) & 0x7F]; /* 8 */ \
2128	__inv = 2 * __inv - __inv * __inv * __n; /* 16 */ \
2129	__inv = 2 * __inv - __inv * __inv * __n; /* 32 */ \
2130	__inv = 2 * __inv - __inv * __inv * __n; /* 64 */ \
2131	ASSERT ((__inv * __n & GMP_NUMB_MASK) == 1); \
2132	(inv) = __inv & GMP_NUMB_MASK; \
2133	} while (0)
2134	#endif /* 64 */
2135	#endif /* 32 */
2136	#endif /* 16 */
2137	#endif /* 8 */
2138
2139
2140	/* Multiplicative inverse of 3, modulo 2^BITS_PER_MP_LIMB.
2141	0xAAAAAAAB for 32 bits, 0xAAAAAAAAAAAAAAAB for 64 bits. */
2142	#define MODLIMB_INVERSE_3 ((GMP_NUMB_MAX / 3) * 2 + 1)
2143
2144
2145	/* Set r to -a mod d. a>=d is allowed. Can give r>d. All should be limbs.
2146
2147	It's not clear whether this is the best way to do this calculation.
2148	Anything congruent to -a would be fine for the one limb congruence
2149	tests. */
2150
2151	#define NEG_MOD(r, a, d) \
2152	do { \
2153	ASSERT ((d) != 0); \
2154	ASSERT_LIMB (a); \
2155	ASSERT_LIMB (d); \
2156	\
2157	if ((a) <= (d)) \
2158	{ \
2159	/* small a is reasonably likely */ \
2160	(r) = (d) - (a); \
2161	} \
2162	else \
2163	{ \
2164	unsigned __twos; \
2165	mp_limb_t __dnorm; \
2166	count_leading_zeros (__twos, d); \
2167	__twos -= GMP_NAIL_BITS; \
2168	__dnorm = (d) << __twos; \
2169	(r) = ((a) <= __dnorm ? __dnorm : 2*__dnorm) - (a); \
2170	} \
2171	\
2172	ASSERT_LIMB (r); \
2173	} while (0)
2174
2175	/* A bit mask of all the least significant zero bits of n, or -1 if n==0. */
2176	#define LOW_ZEROS_MASK(n) (((n) & -(n)) - 1)
2177
2178
2179	/* Set "p" to 1 if there's an odd number of 1 bits in "n", or to 0 if
2180	there's an even number. */
2181
2182	#if defined (__GNUC__) && ! defined (NO_ASM) && HAVE_HOST_CPU_FAMILY_x86
2183	#define ULONG_PARITY(p, n) \
2184	do { \
2185	char __p; \
2186	unsigned long __n = (n); \
2187	__n ^= (__n >> 16); \
2188	asm ("xorb %h1, %b1\n" \
2189	"setpo %0\n" \
2190	: "=qm" (__p), "=q" (__n) \
2191	: "1" (__n)); \
2192	(p) = __p; \
2193	} while (0)
2194	#else
2195	#define ULONG_PARITY(p, n) \
2196	do { \
2197	unsigned long __n = (n); \
2198	int __p = 0; \
2199	do \
2200	{ \
2201	__p ^= 0x96696996L >> (__n & 0x1F); \
2202	__n >>= 5; \
2203	} \
2204	while (__n != 0); \
2205	\
2206	(p) = __p; \
2207	} while (0)
2208	#endif
2209
2210
2211	/* bswap is available on i486 and up and is fast. A combination rorw $8 /
2212	roll $16 / rorw $8 is used in glibc for plain i386 (and in the linux
2213	kernel with xchgb instead of rorw), but this is not done here, because
2214	i386 means generic x86 and mixing word and dword operations will cause
2215	partial register stalls on P6 chips. */
2216	#if defined (__GNUC__) && ! defined (NO_ASM) \
2217	&& HAVE_HOST_CPU_FAMILY_x86 && ! HAVE_HOST_CPU_i386 \
2218	&& BITS_PER_MP_LIMB == 32
2219	#define BSWAP_LIMB(dst, src) \
2220	do { \
2221	asm ("bswap %0" : "=r" (dst) : "0" (src)); \
2222	} while (0)
2223	#endif /* x86 */
2224
2225	#if defined (__GNUC__) && ! defined (NO_ASM) \
2226	&& defined (__ia64) && BITS_PER_MP_LIMB == 64
2227	#define BSWAP_LIMB(dst, src) \
2228	do { \
2229	asm ("mux1 %0 = %1, @rev" : "=r" (dst) : "r" (src)); \
2230	} while (0)
2231	#endif
2232
2233	#if ! defined (BSWAP_LIMB)
2234	#if BITS_PER_MP_LIMB == 8
2235	#define BSWAP_LIMB(dst, src) \
2236	do { (dst) = (src); } while (0)
2237	#endif
2238	#if BITS_PER_MP_LIMB == 16
2239	#define BSWAP_LIMB(dst, src) \
2240	do { \
2241	(dst) = ((src) << 8) + ((src) >> 8); \
2242	} while (0)
2243	#endif
2244	#if BITS_PER_MP_LIMB == 32
2245	#define BSWAP_LIMB(dst, src) \
2246	do { \
2247	(dst) = \
2248	((src) << 24) \
2249	+ (((src) & 0xFF00) << 8) \
2250	+ (((src) >> 8) & 0xFF00) \
2251	+ ((src) >> 24); \
2252	} while (0)
2253	#endif
2254	#if BITS_PER_MP_LIMB == 64
2255	#define BSWAP_LIMB(dst, src) \
2256	do { \
2257	(dst) = \
2258	((src) << 56) \
2259	+ (((src) & 0xFF00) << 40) \
2260	+ (((src) & 0xFF0000) << 24) \
2261	+ (((src) & 0xFF000000) << 8) \
2262	+ (((src) >> 8) & 0xFF000000) \
2263	+ (((src) >> 24) & 0xFF0000) \
2264	+ (((src) >> 40) & 0xFF00) \
2265	+ ((src) >> 56); \
2266	} while (0)
2267	#endif
2268	#endif
2269
2270
2271	/* Apparently lwbrx might be slow on some PowerPC chips, so restrict it to
2272	those we know are fast. */
2273	#if defined (__GNUC__) && ! defined (NO_ASM) \
2274	&& BITS_PER_MP_LIMB == 32 && HAVE_LIMB_BIG_ENDIAN \
2275	&& (HAVE_HOST_CPU_powerpc604 \
2276	\|\| HAVE_HOST_CPU_powerpc604e \
2277	\|\| HAVE_HOST_CPU_powerpc750 \
2278	\|\| HAVE_HOST_CPU_powerpc7400)
2279	#define BSWAP_LIMB_FETCH(limb, src) \
2280	do { \
2281	mp_srcptr __blf_src = (src); \
2282	mp_limb_t __limb; \
2283	__asm__ ("lwbrx %0, 0, %1" \
2284	: "=r" (__limb) \
2285	: "r" (__blf_src), \
2286	"m" (*__blf_src)); \
2287	(limb) = __limb; \
2288	} while (0)
2289	#endif
2290
2291	#if ! defined (BSWAP_LIMB_FETCH)
2292	#define BSWAP_LIMB_FETCH(limb, src) BSWAP_LIMB (limb, *(src))
2293	#endif
2294
2295
2296	/* On the same basis that lwbrx might be slow, restrict stwbrx to those we
2297	know are fast. FIXME: Is this necessary? */
2298	#if defined (__GNUC__) && ! defined (NO_ASM) \
2299	&& BITS_PER_MP_LIMB == 32 && HAVE_LIMB_BIG_ENDIAN \
2300	&& (HAVE_HOST_CPU_powerpc604 \
2301	\|\| HAVE_HOST_CPU_powerpc604e \
2302	\|\| HAVE_HOST_CPU_powerpc750 \
2303	\|\| HAVE_HOST_CPU_powerpc7400)
2304	#define BSWAP_LIMB_STORE(dst, limb) \
2305	do { \
2306	mp_ptr __dst = (dst); \
2307	mp_limb_t __limb = (limb); \
2308	__asm__ ("stwbrx %1, 0, %2" \
2309	: "=m" (*__dst) \
2310	: "r" (__limb), \
2311	"r" (__dst)); \
2312	} while (0)
2313	#endif
2314
2315	#if ! defined (BSWAP_LIMB_STORE)
2316	#define BSWAP_LIMB_STORE(dst, limb) BSWAP_LIMB (*(dst), limb)
2317	#endif
2318
2319
2320	/* Byte swap limbs from {src,size} and store at {dst,size}. */
2321	#define MPN_BSWAP(dst, src, size) \
2322	do { \
2323	mp_ptr __dst = (dst); \
2324	mp_srcptr __src = (src); \
2325	mp_size_t __size = (size); \
2326	mp_size_t __i; \
2327	ASSERT ((size) >= 0); \
2328	ASSERT (MPN_SAME_OR_SEPARATE_P (dst, src, size)); \
2329	CRAY_Pragma ("_CRI ivdep"); \
2330	for (__i = 0; __i < __size; __i++) \
2331	{ \
2332	BSWAP_LIMB_FETCH (*__dst, __src); \
2333	__dst++; \
2334	__src++; \
2335	} \
2336	} while (0)
2337
2338	/* Byte swap limbs from {dst,size} and store in reverse order at {src,size}. */
2339	#define MPN_BSWAP_REVERSE(dst, src, size) \
2340	do { \
2341	mp_ptr __dst = (dst); \
2342	mp_size_t __size = (size); \
2343	mp_srcptr __src = (src) + __size - 1; \
2344	mp_size_t __i; \
2345	ASSERT ((size) >= 0); \
2346	ASSERT (! MPN_OVERLAP_P (dst, size, src, size)); \
2347	CRAY_Pragma ("_CRI ivdep"); \
2348	for (__i = 0; __i < __size; __i++) \
2349	{ \
2350	BSWAP_LIMB_FETCH (*__dst, __src); \
2351	__dst++; \
2352	__src--; \
2353	} \
2354	} while (0)
2355
2356
2357	/* No processor claiming to be SPARC v9 compliant seems to
2358	implement the POPC instruction. Disable pattern for now. */
2359	#if 0
2360	#if defined __GNUC__ && defined __sparc_v9__ && BITS_PER_MP_LIMB == 64
2361	#define popc_limb(result, input) \
2362	do { \
2363	DItype __res; \
2364	asm ("popc %1,%0" : "=r" (result) : "rI" (input)); \
2365	} while (0)
2366	#endif
2367	#endif
2368
2369	/* Cool population count of an mp_limb_t.
2370	You have to figure out how this works, We won't tell you!
2371
2372	The constants could also be expressed as:
2373	0xAA... = [2^(N+1) / 3] = [(2^N-1)/3*2]
2374	0x33... = [2^N / 5] = [(2^N-1)/5]
2375	0x0f... = [2^N / 17] = [(2^N-1)/17]
2376	(N is BITS_PER_MP_LIMB, [] denotes truncation.) */
2377
2378	#if ! defined (popc_limb) && BITS_PER_MP_LIMB == 64
2379	#define popc_limb(result, input) \
2380	do { \
2381	mp_limb_t __x = (input); \
2382	__x -= (__x & CNST_LIMB(0xaaaaaaaaaaaaaaaa)) >> 1; \
2383	__x = ((__x >> 2) & CNST_LIMB(0x3333333333333333)) \
2384	+ (__x & CNST_LIMB(0x3333333333333333)); \
2385	__x = ((__x >> 4) + __x) & CNST_LIMB(0x0f0f0f0f0f0f0f0f); \
2386	__x = ((__x >> 8) + __x); \
2387	__x = ((__x >> 16) + __x); \
2388	__x = ((__x >> 32) + __x) & 0xff; \
2389	(result) = __x; \
2390	} while (0)
2391	#endif
2392	#if ! defined (popc_limb) && BITS_PER_MP_LIMB == 32
2393	#define popc_limb(result, input) \
2394	do { \
2395	mp_limb_t __x = (input); \
2396	__x -= (__x & 0xaaaaaaaaL) >> 1; \
2397	__x = ((__x >> 2) & 0x33333333L) + (__x & 0x33333333L); \
2398	__x = ((__x >> 4) + __x) & 0x0f0f0f0fL; \
2399	__x = ((__x >> 8) + __x); \
2400	__x = ((__x >> 16) + __x) & 0xff; \
2401	(result) = __x; \
2402	} while (0)
2403	#endif
2404	#if ! defined (popc_limb) && BITS_PER_MP_LIMB == 16
2405	#define popc_limb(result, input) \
2406	do { \
2407	mp_limb_t __x = (input); \
2408	__x -= (__x & 0xaaaa) >> 1; \
2409	__x = ((__x >> 2) & 0x3333) + (__x & 0x3333); \
2410	__x = ((__x >> 4) + __x) & 0x0f0f; \
2411	__x = ((__x >> 8) + __x) & 0xff; \
2412	(result) = __x; \
2413	} while (0)
2414	#endif
2415	#if ! defined (popc_limb) && BITS_PER_MP_LIMB == 8
2416	#define popc_limb(result, input) \
2417	do { \
2418	mp_limb_t __x = (input); \
2419	__x -= (__x & 0xaa) >> 1; \
2420	__x = ((__x >> 2) & 0x33) + (__x & 0x33); \
2421	__x = ((__x >> 4) + __x) & 0xf; \
2422	(result) = __x; \
2423	} while (0)
2424	#endif
2425	#if ! defined (popc_limb) && BITS_PER_MP_LIMB == 4
2426	#define popc_limb(result, input) \
2427	do { \
2428	mp_limb_t __x = (input); \
2429	__x = (__x & 1) + ((__x >> 1) & 1) + ((__x >> 2) & 1) + ((__x >> 3) & 1); \
2430	(result) = __x; \
2431	} while (0)
2432	#endif
2433
2434
2435	/* Define stuff for longlong.h. */
2436	#if HAVE_ATTRIBUTE_MODE
2437	typedef unsigned int UQItype __attribute__ ((mode (QI)));
2438	typedef int SItype __attribute__ ((mode (SI)));
2439	typedef unsigned int USItype __attribute__ ((mode (SI)));
2440	typedef int DItype __attribute__ ((mode (DI)));
2441	typedef unsigned int UDItype __attribute__ ((mode (DI)));
2442	#else
2443	typedef unsigned char UQItype;
2444	typedef long SItype;
2445	typedef unsigned long USItype;
2446	#if HAVE_LONG_LONG
2447	typedef long long int DItype;
2448	typedef unsigned long long int UDItype;
2449	#else /* Assume `long' gives us a wide enough type. Needed for hppa2.0w. */
2450	typedef long int DItype;
2451	typedef unsigned long int UDItype;
2452	#endif
2453	#endif
2454
2455	typedef mp_limb_t UWtype;
2456	typedef unsigned int UHWtype;
2457	#define W_TYPE_SIZE BITS_PER_MP_LIMB
2458
2459	/* Define ieee_double_extract and _GMP_IEEE_FLOATS. */
2460
2461	#if (defined (__arm__) && (defined (__ARMWEL__) \|\| defined (__linux__)))
2462	/* Special case for little endian ARM since floats remain in big-endian. */
2463	#define _GMP_IEEE_FLOATS 1
2464	union ieee_double_extract
2465	{
2466	struct
2467	{
2468	unsigned int manh:20;
2469	unsigned int exp:11;
2470	unsigned int sig:1;
2471	unsigned int manl:32;
2472	} s;
2473	double d;
2474	};
2475	#else
2476	#if defined (_LITTLE_ENDIAN) \|\| defined (__LITTLE_ENDIAN__) \
2477	\|\| defined (__alpha) \
2478	\|\| defined (__clipper__) \
2479	\|\| defined (__cris) \
2480	\|\| defined (__i386__) \
2481	\|\| defined (__x86_64__) \
2482	\|\| defined (__i860__) \
2483	\|\| defined (__i960__) \
2484	\|\| defined (__ia64) \
2485	\|\| defined (MIPSEL) \|\| defined (_MIPSEL) \
2486	\|\| defined (__ns32000__) \
2487	\|\| defined (__WINNT) \|\| defined (_WIN32)
2488	#define _GMP_IEEE_FLOATS 1
2489	union ieee_double_extract
2490	{
2491	struct
2492	{
2493	unsigned int manl:32;
2494	unsigned int manh:20;
2495	unsigned int exp:11;
2496	unsigned int sig:1;
2497	} s;
2498	double d;
2499	};
2500	#else /* Need this as an #else since the tests aren't made exclusive. */
2501	#if defined (__mc68000__) \|\| defined (__mc68020__) \|\| defined (__m68k__)\
2502	\|\| defined(mc68020)
2503	#define _GMP_IEEE_FLOATS 1
2504	union ieee_double_extract
2505	{
2506	struct
2507	{
2508	/* "int" might be only 16 bits, so use "long" */
2509	unsigned long sig:1;
2510	unsigned long exp:11;
2511	unsigned long manh:20;
2512	unsigned long manl:32;
2513	} s;
2514	double d;
2515	};
2516	#else
2517	#if defined (_BIG_ENDIAN) \|\| defined (__BIG_ENDIAN__) \
2518	\|\| defined (__a29k__) \|\| defined (_AM29K) \
2519	\|\| defined (__arm__) \
2520	\|\| (defined (__convex__) && defined (_IEEE_FLOAT_)) \
2521	\|\| defined (_CRAYMPP) \|\| defined (_CRAYIEEE) \
2522	\|\| defined (__i370__) \|\| defined (__mvs__) \
2523	\|\| defined (__m88000__) \
2524	\|\| defined (MIPSEB) \|\| defined (_MIPSEB) \
2525	\|\| defined (__hppa) \|\| defined (__hppa__) \
2526	\|\| defined (__pyr__) \
2527	\|\| defined (__ibm032__) \
2528	\|\| defined (_IBMR2) \|\| defined (_ARCH_PPC) \
2529	\|\| defined (__sh__) \
2530	\|\| defined (__sparc) \|\| defined (sparc) \|\| defined (__sparc__) \
2531	\|\| defined (__we32k__)
2532	#define _GMP_IEEE_FLOATS 1
2533	union ieee_double_extract
2534	{
2535	struct
2536	{
2537	unsigned int sig:1;
2538	unsigned int exp:11;
2539	unsigned int manh:20;
2540	unsigned int manl:32;
2541	} s;
2542	double d;
2543	};
2544	#endif
2545	#endif
2546	#endif
2547	#endif
2548
2549	/* Use (4.0 * ...) instead of (2.0 * ...) to work around buggy compilers
2550	that don't convert ulong->double correctly (eg. SunOS 4 native cc). */
2551	#define MP_BASE_AS_DOUBLE (4.0 * ((mp_limb_t) 1 << (GMP_NUMB_BITS - 2)))
2552	/* Maximum number of limbs it will take to store any `double'.
2553	We assume doubles have 53 mantissam bits. */
2554	#define LIMBS_PER_DOUBLE ((53 + GMP_NUMB_BITS - 1) / GMP_NUMB_BITS + 1)
2555
2556	double __gmp_scale2 _PROTO ((double, int)) ATTRIBUTE_CONST;
2557	int __gmp_extract_double _PROTO ((mp_ptr, double));
2558
2559	extern int __gmp_junk;
2560	extern const int __gmp_0;
2561	void __gmp_exception _PROTO ((int)) ATTRIBUTE_NORETURN;
2562	void __gmp_divide_by_zero _PROTO ((void)) ATTRIBUTE_NORETURN;
2563	void __gmp_sqrt_of_negative _PROTO ((void)) ATTRIBUTE_NORETURN;
2564	#define GMP_ERROR(code) __gmp_exception (code)
2565	#define DIVIDE_BY_ZERO __gmp_divide_by_zero ()
2566	#define SQRT_OF_NEGATIVE __gmp_sqrt_of_negative ()
2567
2568	#if defined _LONG_LONG_LIMB
2569	#if __GMP_HAVE_TOKEN_PASTE
2570	#define CNST_LIMB(C) ((mp_limb_t) C##LL)
2571	#else
2572	#define CNST_LIMB(C) ((mp_limb_t) C/**/LL)
2573	#endif
2574	#else /* not _LONG_LONG_LIMB */
2575	#if __GMP_HAVE_TOKEN_PASTE
2576	#define CNST_LIMB(C) ((mp_limb_t) C##L)
2577	#else
2578	#define CNST_LIMB(C) ((mp_limb_t) C/**/L)
2579	#endif
2580	#endif /* _LONG_LONG_LIMB */
2581
2582	/* Stuff used by mpn/generic/perfsqr.c and mpz/prime_p.c */
2583	#if GMP_NUMB_BITS == 2
2584	#define PP 0x3 /* 3 */
2585	#define PP_FIRST_OMITTED 5
2586	#endif
2587	#if GMP_NUMB_BITS == 4
2588	#define PP 0xF /* 3 x 5 */
2589	#define PP_FIRST_OMITTED 7
2590	#endif
2591	#if GMP_NUMB_BITS == 8
2592	#define PP 0x69 /* 3 x 5 x 7 */
2593	#define PP_FIRST_OMITTED 11
2594	#endif
2595	#if GMP_NUMB_BITS == 16
2596	#define PP 0x3AA7 /* 3 x 5 x 7 x 11 x 13 */
2597	#define PP_FIRST_OMITTED 17
2598	#endif
2599	#if GMP_NUMB_BITS == 32
2600	#define PP 0xC0CFD797L /* 3 x 5 x 7 x 11 x ... x 29 */
2601	#define PP_INVERTED 0x53E5645CL
2602	#define PP_FIRST_OMITTED 31
2603	#endif
2604	#if GMP_NUMB_BITS == 64
2605	#define PP CNST_LIMB(0xE221F97C30E94E1D) /* 3 x 5 x 7 x 11 x ... x 53 */
2606	#define PP_INVERTED CNST_LIMB(0x21CFE6CFC938B36B)
2607	#define PP_FIRST_OMITTED 59
2608	#endif
2609	#ifndef PP_FIRST_OMITTED
2610	#define PP_FIRST_OMITTED 3
2611	#endif
2612
2613
2614
2615	/* BIT1 means a result value in bit 1 (second least significant bit), with a
2616	zero bit representing +1 and a one bit representing -1. Bits other than
2617	bit 1 are garbage. These are meant to be kept in "int"s, and casts are
2618	used to ensure the expressions are "int"s even if a and/or b might be
2619	other types.
2620
2621	JACOBI_TWOS_U_BIT1 and JACOBI_RECIP_UU_BIT1 are used in mpn_jacobi_base
2622	and their speed is important. Expressions are used rather than
2623	conditionals to accumulate sign changes, which effectively means XORs
2624	instead of conditional JUMPs. */
2625
2626	/* (a/0), with a signed; is 1 if a=+/-1, 0 otherwise */
2627	#define JACOBI_S0(a) (((a) == 1) \| ((a) == -1))
2628
2629	/* (a/0), with a unsigned; is 1 if a=+/-1, 0 otherwise */
2630	#define JACOBI_U0(a) ((a) == 1)
2631
2632	/* (a/0), with a given by low and size;
2633	is 1 if a=+/-1, 0 otherwise */
2634	#define JACOBI_LS0(alow,asize) \
2635	(((asize) == 1 \|\| (asize) == -1) && (alow) == 1)
2636
2637	/* (a/0), with a an mpz_t;
2638	fetch of low limb always valid, even if size is zero */
2639	#define JACOBI_Z0(a) JACOBI_LS0 (PTR(a)[0], SIZ(a))
2640
2641	/* (0/b), with b unsigned; is 1 if b=+/-1, 0 otherwise */
2642	#define JACOBI_0U(b) ((b) == 1)
2643
2644	/* (0/b), with b unsigned; is 1 if b=+/-1, 0 otherwise */
2645	#define JACOBI_0S(b) ((b) == 1 \|\| (b) == -1)
2646
2647	/* (0/b), with b given by low and size; is 1 if b=+/-1, 0 otherwise */
2648	#define JACOBI_0LS(blow,bsize) \
2649	(((bsize) == 1 \|\| (bsize) == -1) && (blow) == 1)
2650
2651	/* Convert a bit1 to +1 or -1. */
2652	#define JACOBI_BIT1_TO_PN(result_bit1) \
2653	(1 - ((int) (result_bit1) & 2))
2654
2655	/* (2/b), with b unsigned and odd;
2656	is (-1)^((b^2-1)/8) which is 1 if b==1,7mod8 or -1 if b==3,5mod8 and
2657	hence obtained from (b>>1)^b */
2658	#define JACOBI_TWO_U_BIT1(b) \
2659	((int) (((b) >> 1) ^ (b)))
2660
2661	/* (2/b)^twos, with b unsigned and odd */
2662	#define JACOBI_TWOS_U_BIT1(twos, b) \
2663	((int) ((twos) << 1) & JACOBI_TWO_U_BIT1 (b))
2664
2665	/* (2/b)^twos, with b unsigned and odd */
2666	#define JACOBI_TWOS_U(twos, b) \
2667	(JACOBI_BIT1_TO_PN (JACOBI_TWOS_U_BIT1 (twos, b)))
2668
2669	/* (-1/b), with b odd (signed or unsigned);
2670	is (-1)^((b-1)/2) */
2671	#define JACOBI_N1B_BIT1(b) \
2672	((int) (b))
2673
2674	/* (a/b) effect due to sign of a: signed/unsigned, b odd;
2675	is (-1/b) if a<0, or +1 if a>=0 */
2676	#define JACOBI_ASGN_SU_BIT1(a, b) \
2677	((((a) < 0) << 1) & JACOBI_N1B_BIT1(b))
2678
2679	/* (a/b) effect due to sign of b: signed/signed;
2680	is -1 if a and b both negative, +1 otherwise */
2681	#define JACOBI_BSGN_SS_BIT1(a, b) \
2682	((((a)<0) & ((b)<0)) << 1)
2683
2684	/* (a/b) effect due to sign of b: signed/mpz;
2685	is -1 if a and b both negative, +1 otherwise */
2686	#define JACOBI_BSGN_SZ_BIT1(a, b) \
2687	JACOBI_BSGN_SS_BIT1 (a, SIZ(b))
2688
2689	/* (a/b) effect due to sign of b: mpz/signed;
2690	is -1 if a and b both negative, +1 otherwise */
2691	#define JACOBI_BSGN_ZS_BIT1(a, b) \
2692	JACOBI_BSGN_SZ_BIT1 (b, a)
2693
2694	/* (a/b) reciprocity to switch to (b/a), a,b both unsigned and odd;
2695	is (-1)^((a-1)*(b-1)/4), which means +1 if either a,b==1mod4, or -1 if
2696	both a,b==3mod4, achieved in bit 1 by a&b. No ASSERT()s about a,b odd
2697	because this is used in a couple of places with only bit 1 of a or b
2698	valid. */
2699	#define JACOBI_RECIP_UU_BIT1(a, b) \
2700	((int) ((a) & (b)))
2701
2702
2703	/* Set a_rem to {a_ptr,a_size} reduced modulo b, either using mod_1 or
2704	modexact_1_odd, but in either case leaving a_rem<b. b must be odd and
2705	unsigned. modexact_1_odd effectively calculates -a mod b, and
2706	result_bit1 is adjusted for the factor of -1.
2707
2708	The way mpn_modexact_1_odd sometimes bases its remainder on a_size and
2709	sometimes on a_size-1 means if GMP_NUMB_BITS is odd we can't know what
2710	factor to introduce into result_bit1, so for that case use mpn_mod_1
2711	unconditionally.
2712
2713	FIXME: mpn_modexact_1_odd is more efficient, so some way to get it used
2714	for odd GMP_NUMB_BITS would be good. Perhaps it could mung its result,
2715	or not skip a divide step, or something. */
2716
2717	#define JACOBI_MOD_OR_MODEXACT_1_ODD(result_bit1, a_rem, a_ptr, a_size, b) \
2718	do { \
2719	mp_srcptr __a_ptr = (a_ptr); \
2720	mp_size_t __a_size = (a_size); \
2721	mp_limb_t __b = (b); \
2722	\
2723	ASSERT (__a_size >= 1); \
2724	ASSERT (__b & 1); \
2725	\
2726	if ((GMP_NUMB_BITS % 2) != 0 \
2727	\|\| BELOW_THRESHOLD (__a_size, MODEXACT_1_ODD_THRESHOLD)) \
2728	{ \
2729	(a_rem) = mpn_mod_1 (__a_ptr, __a_size, __b); \
2730	} \
2731	else \
2732	{ \
2733	(result_bit1) ^= JACOBI_N1B_BIT1 (__b); \
2734	(a_rem) = mpn_modexact_1_odd (__a_ptr, __a_size, __b); \
2735	} \
2736	} while (0)
2737
2738
2739	/* __GMPF_BITS_TO_PREC applies a minimum 53 bits, rounds upwards to a whole
2740	limb and adds an extra limb. __GMPF_PREC_TO_BITS drops that extra limb,
2741	hence giving back the user's size in bits rounded up. Notice that
2742	converting prec->bits->prec gives an unchanged value. */
2743	#define __GMPF_BITS_TO_PREC(n) \
2744	((mp_size_t) ((__GMP_MAX (53, n) + 2 * GMP_NUMB_BITS - 1) / GMP_NUMB_BITS))
2745	#define __GMPF_PREC_TO_BITS(n) \
2746	((unsigned long) (n) * GMP_NUMB_BITS - GMP_NUMB_BITS)
2747
2748	extern mp_size_t __gmp_default_fp_limb_precision;
2749
2750
2751	/* Set n to the number of significant digits an mpf of the given _mp_prec
2752	field, in the given base. This is a rounded up value, designed to ensure
2753	there's enough digits to reproduce all the guaranteed part of the value.
2754
2755	There are prec many limbs, but the high might be only "1" so forget it
2756	and just count prec-1 limbs into chars. +1 rounds that upwards, and a
2757	further +1 is because the limbs usually won't fall on digit boundaries.
2758
2759	FIXME: If base is a power of 2 and the bits per digit divides
2760	BITS_PER_MP_LIMB then the +2 is unnecessary. This happens always for
2761	base==2, and in base==16 with the current 32 or 64 bit limb sizes. */
2762
2763	#define MPF_SIGNIFICANT_DIGITS(n, base, prec) \
2764	do { \
2765	ASSERT (base >= 2 && base < numberof (mp_bases)); \
2766	(n) = 2 + (size_t) ((((prec) - 1) * BITS_PER_MP_LIMB) \
2767	* mp_bases[(base)].chars_per_bit_exactly); \
2768	} while (0)
2769
2770
2771	#define DOPRNT_CONV_FIXED 1
2772	#define DOPRNT_CONV_SCIENTIFIC 2
2773	#define DOPRNT_CONV_GENERAL 3
2774
2775	#define DOPRNT_JUSTIFY_NONE 0
2776	#define DOPRNT_JUSTIFY_LEFT 1
2777	#define DOPRNT_JUSTIFY_RIGHT 2
2778	#define DOPRNT_JUSTIFY_INTERNAL 3
2779
2780	#define DOPRNT_SHOWBASE_YES 1
2781	#define DOPRNT_SHOWBASE_NO 2
2782	#define DOPRNT_SHOWBASE_NONZERO 3
2783
2784	struct doprnt_params_t {
2785	int base; /* negative for upper case */
2786	int conv; /* choices above */
2787	const char expfmt; / exponent format */
2788	int exptimes4; /* exponent multiply by 4 */
2789	char fill; /* character */
2790	int justify; /* choices above */
2791	int prec; /* prec field, or -1 for all digits */
2792	int showbase; /* choices above */
2793	int showpoint; /* if radix point always shown */
2794	int showtrailing; /* if trailing zeros wanted */
2795	char sign; /* '+', ' ', or '\0' */
2796	int width; /* width field */
2797	};
2798
2799	#if _GMP_H_HAVE_VA_LIST
2800
2801	typedef int (doprnt_format_t) _PROTO ((void data, const char *fmt, va_list ap));
2802	typedef int (doprnt_memory_t) _PROTO ((void data, const char *str, size_t len));
2803	typedef int (doprnt_reps_t) _PROTO ((void data, int c, int reps));
2804	typedef int (doprnt_final_t) _PROTO ((void data));
2805
2806	struct doprnt_funs_t {
2807	doprnt_format_t format;
2808	doprnt_memory_t memory;
2809	doprnt_reps_t reps;
2810	doprnt_final_t final; /* NULL if not required */
2811	};
2812
2813	extern const struct doprnt_funs_t __gmp_fprintf_funs;
2814	extern const struct doprnt_funs_t __gmp_sprintf_funs;
2815	extern const struct doprnt_funs_t __gmp_snprintf_funs;
2816	extern const struct doprnt_funs_t __gmp_obstack_printf_funs;
2817	extern const struct doprnt_funs_t __gmp_ostream_funs;
2818
2819	/* "buf" is a __gmp_allocate_func block of "alloc" many bytes. The first
2820	"size" of these have been written. "alloc > size" is maintained, so
2821	there's room to store a '\0' at the end. "result" is where the
2822	application wants the final block pointer. */
2823	struct gmp_asprintf_t {
2824	char **result;
2825	char *buf;
2826	size_t size;
2827	size_t alloc;
2828	};
2829
2830	#define GMP_ASPRINTF_T_INIT(d, output) \
2831	do { \
2832	(d).result = (output); \
2833	(d).alloc = 256; \
2834	(d).buf = (char ) (__gmp_allocate_func) ((d).alloc); \
2835	(d).size = 0; \
2836	} while (0)
2837
2838	/* If a realloc is necessary, use twice the size actually required, so as to
2839	avoid repeated small reallocs. */
2840	#define GMP_ASPRINTF_T_NEED(d, n) \
2841	do { \
2842	size_t alloc, newsize, newalloc; \
2843	ASSERT ((d)->alloc >= (d)->size + 1); \
2844	\
2845	alloc = (d)->alloc; \
2846	newsize = (d)->size + (n); \
2847	if (alloc <= newsize) \
2848	{ \
2849	newalloc = 2*newsize; \
2850	(d)->alloc = newalloc; \
2851	(d)->buf = __GMP_REALLOCATE_FUNC_TYPE ((d)->buf, \
2852	alloc, newalloc, char); \
2853	} \
2854	} while (0)
2855
2856	__GMP_DECLSPEC int __gmp_asprintf_memory _PROTO ((struct gmp_asprintf_t d, const char str, size_t len));
2857	__GMP_DECLSPEC int __gmp_asprintf_reps _PROTO ((struct gmp_asprintf_t *d, int c, int reps));
2858	__GMP_DECLSPEC int __gmp_asprintf_final _PROTO ((struct gmp_asprintf_t *d));
2859
2860	/* buf is where to write the next output, and size is how much space is left
2861	there. If the application passed size==0 then that's what we'll have
2862	here, and nothing at all should be written. */
2863	struct gmp_snprintf_t {
2864	char *buf;
2865	size_t size;
2866	};
2867
2868	/* Add the bytes printed by the call to the total retval, or bail out on an
2869	error. */
2870	#define DOPRNT_ACCUMULATE(call) \
2871	do { \
2872	int __ret; \
2873	__ret = call; \
2874	if (__ret == -1) \
2875	goto error; \
2876	retval += __ret; \
2877	} while (0)
2878	#define DOPRNT_ACCUMULATE_FUN(fun, params) \
2879	do { \
2880	ASSERT ((fun) != NULL); \
2881	DOPRNT_ACCUMULATE ((*(fun)) params); \
2882	} while (0)
2883
2884	#define DOPRNT_FORMAT(fmt, ap) \
2885	DOPRNT_ACCUMULATE_FUN (funs->format, (data, fmt, ap))
2886	#define DOPRNT_MEMORY(ptr, len) \
2887	DOPRNT_ACCUMULATE_FUN (funs->memory, (data, ptr, len))
2888	#define DOPRNT_REPS(c, n) \
2889	DOPRNT_ACCUMULATE_FUN (funs->reps, (data, c, n))
2890
2891	#define DOPRNT_STRING(str) DOPRNT_MEMORY (str, strlen (str))
2892
2893	#define DOPRNT_REPS_MAYBE(c, n) \
2894	do { \
2895	if ((n) != 0) \
2896	DOPRNT_REPS (c, n); \
2897	} while (0)
2898	#define DOPRNT_MEMORY_MAYBE(ptr, len) \
2899	do { \
2900	if ((len) != 0) \
2901	DOPRNT_MEMORY (ptr, len); \
2902	} while (0)
2903
2904	__GMP_DECLSPEC int __gmp_doprnt _PROTO ((const struct doprnt_funs_t , void , const char *, va_list));
2905	__GMP_DECLSPEC int __gmp_doprnt_integer _PROTO ((const struct doprnt_funs_t , void , const struct doprnt_params_t , const char ));
2906	__GMP_DECLSPEC int __gmp_doprnt_mpf _PROTO ((const struct doprnt_funs_t , void , const struct doprnt_params_t *, mpf_srcptr));
2907	/* why no __GMP_DECLSPEC here??? */
2908	int __gmp_replacement_vsnprintf _PROTO ((char , size_t, const char , va_list));
2909	#endif /* _GMP_H_HAVE_VA_LIST */
2910
2911
2912	typedef int (gmp_doscan_scan_t) _PROTO ((void , const char *, ...));
2913	typedef void (gmp_doscan_step_t) _PROTO ((void *, int));
2914	typedef int (gmp_doscan_get_t) _PROTO ((void ));
2915	typedef int (gmp_doscan_unget_t) _PROTO ((int, void ));
2916
2917	struct gmp_doscan_funs_t {
2918	gmp_doscan_scan_t scan;
2919	gmp_doscan_step_t step;
2920	gmp_doscan_get_t get;
2921	gmp_doscan_unget_t unget;
2922	};
2923	extern const struct gmp_doscan_funs_t __gmp_fscanf_funs;
2924	extern const struct gmp_doscan_funs_t __gmp_sscanf_funs;
2925
2926	#if _GMP_H_HAVE_VA_LIST
2927	int __gmp_doscan _PROTO ((const struct gmp_doscan_funs_t , void ,
2928	const char *, va_list));
2929	#endif
2930
2931
2932	/* For testing and debugging. */
2933	#define MPZ_CHECK_FORMAT(z) \
2934	do { \
2935	ASSERT_ALWAYS (SIZ(z) == 0 \|\| PTR(z)[ABSIZ(z) - 1] != 0); \
2936	ASSERT_ALWAYS (ALLOC(z) >= ABSIZ(z)); \
2937	ASSERT_ALWAYS_MPN (PTR(z), ABSIZ(z)); \
2938	} while (0)
2939
2940	#define MPQ_CHECK_FORMAT(q) \
2941	do { \
2942	MPZ_CHECK_FORMAT (mpq_numref (q)); \
2943	MPZ_CHECK_FORMAT (mpq_denref (q)); \
2944	ASSERT_ALWAYS (SIZ(mpq_denref(q)) >= 1); \
2945	\
2946	if (SIZ(mpq_numref(q)) == 0) \
2947	{ \
2948	/* should have zero as 0/1 */ \
2949	ASSERT_ALWAYS (SIZ(mpq_denref(q)) == 1 \
2950	&& PTR(mpq_denref(q))[0] == 1); \
2951	} \
2952	else \
2953	{ \
2954	/* should have no common factors */ \
2955	mpz_t g; \
2956	mpz_init (g); \
2957	mpz_gcd (g, mpq_numref(q), mpq_denref(q)); \
2958	ASSERT_ALWAYS (mpz_cmp_ui (g, 1) == 0); \
2959	mpz_clear (g); \
2960	} \
2961	} while (0)
2962
2963	#define MPF_CHECK_FORMAT(f) \
2964	do { \
2965	ASSERT_ALWAYS (PREC(f) >= __GMPF_BITS_TO_PREC(53)); \
2966	ASSERT_ALWAYS (ABSIZ(f) <= PREC(f)+1); \
2967	if (SIZ(f) == 0) \
2968	ASSERT_ALWAYS (EXP(f) == 0); \
2969	if (SIZ(f) != 0) \
2970	ASSERT_ALWAYS (PTR(f)[ABSIZ(f) - 1] != 0); \
2971	} while (0)
2972
2973
2974	#define MPZ_PROVOKE_REALLOC(z) \
2975	do { ALLOC(z) = ABSIZ(z); } while (0)
2976
2977
2978	#if TUNE_PROGRAM_BUILD
2979	/* Some extras wanted when recompiling some .c files for use by the tune
2980	program. Not part of a normal build. */
2981
2982	extern mp_size_t mul_threshold[];
2983	extern mp_size_t fft_modf_mul_threshold;
2984	extern mp_size_t sqr_threshold[];
2985	extern mp_size_t fft_modf_sqr_threshold;
2986	extern mp_size_t sb_preinv_threshold[];
2987	extern mp_size_t dc_threshold[];
2988	extern mp_size_t powm_threshold[];
2989	extern mp_size_t gcd_accel_threshold[];
2990	extern mp_size_t gcdext_threshold[];
2991	extern mp_size_t divrem_1_norm_threshold[];
2992	extern mp_size_t divrem_1_unnorm_threshold[];
2993	extern mp_size_t divrem_2_threshold[];
2994	extern mp_size_t mod_1_norm_threshold[];
2995	extern mp_size_t mod_1_unnorm_threshold[];
2996	extern mp_size_t get_str_basecase_threshold[];
2997	extern mp_size_t get_str_precompute_threshold[];
2998
2999	#undef MUL_KARATSUBA_THRESHOLD
3000	#undef MUL_TOOM3_THRESHOLD
3001	#undef MUL_FFT_TABLE
3002	#undef MUL_FFT_THRESHOLD
3003	#undef MUL_FFT_MODF_THRESHOLD
3004	#undef SQR_BASECASE_THRESHOLD
3005	#undef SQR_KARATSUBA_THRESHOLD
3006	#undef SQR_TOOM3_THRESHOLD
3007	#undef SQR_FFT_TABLE
3008	#undef SQR_FFT_THRESHOLD
3009	#undef SQR_FFT_MODF_THRESHOLD
3010	#undef DIV_DC_THRESHOLD
3011	#undef POWM_THRESHOLD
3012	#undef GCD_ACCEL_THRESHOLD
3013	#undef GCDEXT_THRESHOLD
3014	#undef DIVREM_1_NORM_THRESHOLD
3015	#undef DIVREM_1_UNNORM_THRESHOLD
3016	#undef MOD_1_NORM_THRESHOLD
3017	#undef MOD_1_UNNORM_THRESHOLD
3018	#undef GET_STR_DC_THRESHOLD
3019	#undef GET_STR_PRECOMPUTE_THRESHOLD
3020
3021	#define MUL_KARATSUBA_THRESHOLD mul_threshold[0]
3022	#define MUL_TOOM3_THRESHOLD mul_threshold[1]
3023	#define MUL_FFT_TABLE { 0 }
3024	#define MUL_FFT_THRESHOLD mul_threshold[2]
3025	#define MUL_FFT_MODF_THRESHOLD fft_modf_mul_threshold
3026	#define SQR_BASECASE_THRESHOLD sqr_threshold[0]
3027	#define SQR_KARATSUBA_THRESHOLD sqr_threshold[1]
3028	#define SQR_TOOM3_THRESHOLD sqr_threshold[2]
3029	#define SQR_FFT_TABLE { 0 }
3030	#define SQR_FFT_THRESHOLD sqr_threshold[3]
3031	#define SQR_FFT_MODF_THRESHOLD fft_modf_sqr_threshold
3032	#define DIV_DC_THRESHOLD dc_threshold[0]
3033	#define POWM_THRESHOLD powm_threshold[0]
3034	#define GCD_ACCEL_THRESHOLD gcd_accel_threshold[0]
3035	#define GCDEXT_THRESHOLD gcdext_threshold[0]
3036	#define DIVREM_1_NORM_THRESHOLD divrem_1_norm_threshold[0]
3037	#define DIVREM_1_UNNORM_THRESHOLD divrem_1_unnorm_threshold[0]
3038	#define MOD_1_NORM_THRESHOLD mod_1_norm_threshold[0]
3039	#define MOD_1_UNNORM_THRESHOLD mod_1_unnorm_threshold[0]
3040	#define GET_STR_DC_THRESHOLD get_str_basecase_threshold[0]
3041	#define GET_STR_PRECOMPUTE_THRESHOLD get_str_precompute_threshold[0]
3042
3043	#if ! UDIV_PREINV_ALWAYS
3044	#undef DIV_SB_PREINV_THRESHOLD
3045	#undef DIVREM_2_THRESHOLD
3046	#define DIV_SB_PREINV_THRESHOLD sb_preinv_threshold[0]
3047	#define DIVREM_2_THRESHOLD divrem_2_threshold[0]
3048	#endif
3049
3050	/* Sizes the tune program tests up to, used in a couple of recompilations. */
3051	#define SQR_KARATSUBA_MAX_GENERIC 200
3052	#define MUL_TOOM3_THRESHOLD_LIMIT 700
3053	#define GET_STR_THRESHOLD_LIMIT 500
3054
3055	#undef FFT_TABLE_ATTRS
3056	#define FFT_TABLE_ATTRS
3057	extern mp_size_t mpn_fft_table[2][MPN_FFT_TABLE_SIZE];
3058
3059	#if TUNE_PROGRAM_BUILD_SQR
3060	#undef SQR_KARATSUBA_THRESHOLD
3061	#define SQR_KARATSUBA_THRESHOLD SQR_KARATSUBA_MAX_GENERIC
3062	#endif
3063
3064	#endif /* TUNE_PROGRAM_BUILD */
3065
3066	#if defined (__cplusplus)
3067	}
3068	#endif
3069
3070
3071	#ifdef __cplusplus
3072
3073	/* A little helper for a null-terminated __gmp_allocate_func string.
3074	The destructor ensures it's freed even if an exception is thrown. */
3075	class gmp_allocated_string {
3076	public:
3077	char *str;
3078	gmp_allocated_string(char *arg) { str = arg; }
3079	~gmp_allocated_string() { (*__gmp_free_func) (str, strlen(str)+1); }
3080	};
3081
3082	int __gmp_istream_set_base (std::istream &, char &, bool &, bool &);
3083	void __gmp_istream_set_digits (std::string &, std::istream &, char &, bool &, int);
3084	void __gmp_doprnt_params_from_ios (struct doprnt_params_t *p, std::ios &o);
3085	std::ostream& __gmp_doprnt_integer_ostream (std::ostream &o, struct doprnt_params_t p, char s);
3086	extern const struct doprnt_funs_t __gmp_asprintf_funs_noformat;
3087
3088	#endif /* __cplusplus */
3089
3090	#endif /* __GMP_IMPL_H__ */

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