| blob | b424f9dd0a26800b736be00094a013fe16b52630 |
1 /* Include file for internal GNU MP types and definitions.
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.
6 Copyright 1991, 1993, 1994, 1995, 1996, 1997, 1999, 2000, 2001, 2002, 2003,
7 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012 Free Software Foundation,
8 Inc.
10 This file is part of the GNU MP Library.
12 The GNU MP Library is free software; you can redistribute it and/or modify
13 it under the terms of the GNU Lesser General Public License as published by
14 the Free Software Foundation; either version 3 of the License, or (at your
15 option) any later version.
17 The GNU MP Library is distributed in the hope that it will be useful, but
18 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
19 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
20 License for more details.
22 You should have received a copy of the GNU Lesser General Public License
23 along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
26 /* __GMP_DECLSPEC must be given on any global data that will be accessed
27 from outside libgmp, meaning from the test or development programs, or
28 from libgmpxx. Failing to do this will result in an incorrect address
29 being used for the accesses. On functions __GMP_DECLSPEC makes calls
30 from outside libgmp more efficient, but they'll still work fine without
31 it. */
34 #ifndef __GMP_IMPL_H__
35 #define __GMP_IMPL_H__
37 #if defined _CRAY
39 #endif
41 /* limits.h is not used in general, since it's an ANSI-ism, and since on
42 solaris gcc 2.95 under -mcpu=ultrasparc in ABI=32 ends up getting wrong
43 values (the ABI=64 values).
45 On Cray vector systems, however, we need the system limits.h since sizes
46 of signed and unsigned types can differ there, depending on compiler
47 options (eg. -hnofastmd), making our SHRT_MAX etc expressions fail. For
48 reference, int can be 46 or 64 bits, whereas uint is always 64 bits; and
49 short can be 24, 32, 46 or 64 bits, and different for ushort. */
51 #if defined _CRAY
52 #include <limits.h>
53 #endif
55 /* For fat.h and other fat binary stuff.
56 No need for __GMP_ATTRIBUTE_PURE or __GMP_NOTHROW, since functions
57 declared this way are only used to set function pointers in __gmp_cpuvec,
58 they're not called directly. */
59 #define DECL_add_n(name) \
60 __GMP_DECLSPEC mp_limb_t name __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t))
61 #define DECL_addmul_1(name) \
62 __GMP_DECLSPEC mp_limb_t name __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t))
63 #define DECL_copyd(name) \
64 __GMP_DECLSPEC void name __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t))
65 #define DECL_copyi(name) \
66 DECL_copyd (name)
67 #define DECL_divexact_1(name) \
68 __GMP_DECLSPEC void name __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t))
69 #define DECL_divexact_by3c(name) \
70 __GMP_DECLSPEC mp_limb_t name __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t))
71 #define DECL_divrem_1(name) \
72 __GMP_DECLSPEC mp_limb_t name __GMP_PROTO ((mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_limb_t))
73 #define DECL_gcd_1(name) \
74 __GMP_DECLSPEC mp_limb_t name __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t))
75 #define DECL_lshift(name) \
76 __GMP_DECLSPEC mp_limb_t name __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, unsigned))
77 #define DECL_mod_1(name) \
78 __GMP_DECLSPEC mp_limb_t name __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t))
79 #define DECL_mod_34lsub1(name) \
80 __GMP_DECLSPEC mp_limb_t name __GMP_PROTO ((mp_srcptr, mp_size_t))
81 #define DECL_modexact_1c_odd(name) \
82 __GMP_DECLSPEC mp_limb_t name __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t))
83 #define DECL_mul_1(name) \
84 DECL_addmul_1 (name)
85 #define DECL_mul_basecase(name) \
86 __GMP_DECLSPEC void name __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t))
87 #define DECL_preinv_divrem_1(name) \
88 __GMP_DECLSPEC mp_limb_t name __GMP_PROTO ((mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t, int))
89 #define DECL_preinv_mod_1(name) \
90 __GMP_DECLSPEC mp_limb_t name __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t))
91 #define DECL_rshift(name) \
92 DECL_lshift (name)
93 #define DECL_sqr_basecase(name) \
94 __GMP_DECLSPEC void name __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t))
95 #define DECL_sub_n(name) \
96 DECL_add_n (name)
97 #define DECL_submul_1(name) \
98 DECL_addmul_1 (name)
100 #if ! __GMP_WITHIN_CONFIGURE
105 #if WANT_FAT_BINARY
107 #endif
108 #endif
111 # include <inttypes.h>
112 #else
113 # if HAVE_STDINT_H
114 # include <stdint.h>
115 # endif
116 #endif
118 #ifdef __cplusplus
121 #endif
125 #define WANT_TMP_DEBUG 0
126 #endif
128 /* The following tries to get a good version of alloca. The tests are
129 adapted from autoconf AC_FUNC_ALLOCA, with a couple of additions.
130 Whether this succeeds is tested by GMP_FUNC_ALLOCA and HAVE_ALLOCA will
131 be setup appropriately.
133 ifndef alloca - a cpp define might already exist.
134 glibc <stdlib.h> includes <alloca.h> which uses GCC __builtin_alloca.
135 HP cc +Olibcalls adds a #define of alloca to __builtin_alloca.
137 GCC __builtin_alloca - preferred whenever available.
139 _AIX pragma - IBM compilers need a #pragma in "each module that needs to
140 use alloca". Pragma indented to protect pre-ANSI cpp's. _IBMR2 was
141 used in past versions of GMP, retained still in case it matters.
143 The autoconf manual says this pragma needs to be at the start of a C
144 file, apart from comments and preprocessor directives. Is that true?
145 xlc on aix 4.xxx doesn't seem to mind it being after prototypes etc
146 from gmp.h.
147 */
149 #ifndef alloca
150 # ifdef __GNUC__
151 # define alloca __builtin_alloca
152 # else
153 # ifdef __DECC
154 # define alloca(x) __ALLOCA(x)
155 # else
156 # ifdef _MSC_VER
157 # include <malloc.h>
158 # define alloca _alloca
159 # else
160 # if HAVE_ALLOCA_H
161 # include <alloca.h>
162 # else
163 # if defined (_AIX) || defined (_IBMR2)
164 #pragma alloca
165 # else
167 # endif
168 # endif
169 # endif
170 # endif
171 # endif
172 #endif
175 /* if not provided by gmp-mparam.h */
176 #ifndef BYTES_PER_MP_LIMB
177 #define BYTES_PER_MP_LIMB SIZEOF_MP_LIMB_T
178 #endif
179 #define GMP_LIMB_BYTES BYTES_PER_MP_LIMB
180 #ifndef GMP_LIMB_BITS
181 #define GMP_LIMB_BITS (8 * SIZEOF_MP_LIMB_T)
182 #endif
184 #define BITS_PER_ULONG (8 * SIZEOF_UNSIGNED_LONG)
187 /* gmp_uint_least32_t is an unsigned integer type with at least 32 bits. */
188 #if HAVE_UINT_LEAST32_T
190 #else
191 #if SIZEOF_UNSIGNED_SHORT >= 4
193 #else
194 #if SIZEOF_UNSIGNED >= 4
196 #else
198 #endif
199 #endif
200 #endif
203 /* gmp_intptr_t, for pointer to integer casts */
204 #if HAVE_INTPTR_T
208 #endif
211 /* pre-inverse types for truncating division and modulo */
216 /* const and signed must match __gmp_const and __gmp_signed, so follow the
217 decision made for those in gmp.h. */
218 #if ! __GMP_HAVE_CONST
221 #endif
223 /* "const" basically means a function does nothing but examine its arguments
224 and give a return value, it doesn't read or write any memory (neither
225 global nor pointed to by arguments), and has no other side-effects. This
226 is more restrictive than "pure". See info node "(gcc)Function
227 Attributes". __GMP_NO_ATTRIBUTE_CONST_PURE lets tune/common.c etc turn
228 this off when trying to write timing loops. */
229 #if HAVE_ATTRIBUTE_CONST && ! defined (__GMP_NO_ATTRIBUTE_CONST_PURE)
230 #define ATTRIBUTE_CONST __attribute__ ((const))
231 #else
232 #define ATTRIBUTE_CONST
233 #endif
235 #if HAVE_ATTRIBUTE_NORETURN
236 #define ATTRIBUTE_NORETURN __attribute__ ((noreturn))
237 #else
238 #define ATTRIBUTE_NORETURN
239 #endif
241 /* "malloc" means a function behaves like malloc in that the pointer it
242 returns doesn't alias anything. */
243 #if HAVE_ATTRIBUTE_MALLOC
244 #define ATTRIBUTE_MALLOC __attribute__ ((malloc))
245 #else
246 #define ATTRIBUTE_MALLOC
247 #endif
250 #if ! HAVE_STRCHR
251 #define strchr(s,c) index(s,c)
252 #endif
254 #if ! HAVE_MEMSET
255 #define memset(p, c, n) \
256 do { \
257 ASSERT ((n) >= 0); \
258 char *__memset__p = (p); \
259 int __i; \
260 for (__i = 0; __i < (n); __i++) \
261 __memset__p[__i] = (c); \
262 } while (0)
263 #endif
265 /* va_copy is standard in C99, and gcc provides __va_copy when in strict C89
266 mode. Falling back to a memcpy will give maximum portability, since it
267 works no matter whether va_list is a pointer, struct or array. */
268 #if ! defined (va_copy) && defined (__va_copy)
269 #define va_copy(dst,src) __va_copy(dst,src)
270 #endif
271 #if ! defined (va_copy)
272 #define va_copy(dst,src) \
273 do { memcpy (&(dst), &(src), sizeof (va_list)); } while (0)
274 #endif
277 /* HAVE_HOST_CPU_alpha_CIX is 1 on an alpha with the CIX instructions
278 (ie. ctlz, ctpop, cttz). */
279 #if HAVE_HOST_CPU_alphaev67 || HAVE_HOST_CPU_alphaev68 \
280 || HAVE_HOST_CPU_alphaev7
281 #define HAVE_HOST_CPU_alpha_CIX 1
282 #endif
285 #if defined (__cplusplus)
287 #endif
290 /* Usage: TMP_DECL;
291 TMP_MARK;
292 ptr = TMP_ALLOC (bytes);
293 TMP_FREE;
295 Small allocations should use TMP_SALLOC, big allocations should use
296 TMP_BALLOC. Allocations that might be small or big should use TMP_ALLOC.
298 Functions that use just TMP_SALLOC should use TMP_SDECL, TMP_SMARK, and
299 TMP_SFREE.
301 TMP_DECL just declares a variable, but might be empty and so must be last
302 in a list of variables. TMP_MARK must be done before any TMP_ALLOC.
303 TMP_ALLOC(0) is not allowed. TMP_FREE doesn't need to be done if a
304 TMP_MARK was made, but then no TMP_ALLOCs. */
306 /* The alignment in bytes, used for TMP_ALLOCed blocks, when alloca or
307 __gmp_allocate_func doesn't already determine it. Currently TMP_ALLOC
308 isn't used for "double"s, so that's not in the union. */
310 mp_limb_t l;
312 };
313 #define __TMP_ALIGN sizeof (union tmp_align_t)
315 /* Return "a" rounded upwards to a multiple of "m", if it isn't already.
316 "a" must be an unsigned type.
317 This is designed for use with a compile-time constant "m".
318 The POW2 case is expected to be usual, and gcc 3.0 and up recognises
319 "(-(8*n))%8" or the like is always zero, which means the rounding up in
320 the WANT_TMP_NOTREENTRANT version of TMP_ALLOC below will be a noop. */
321 #define ROUND_UP_MULTIPLE(a,m) \
322 (POW2_P(m) ? (a) + (-(a))%(m) \
323 : (a)+(m)-1 - (((a)+(m)-1) % (m)))
325 #if defined (WANT_TMP_ALLOCA) || defined (WANT_TMP_REENTRANT)
329 };
330 __GMP_DECLSPEC void *__gmp_tmp_reentrant_alloc __GMP_PROTO ((struct tmp_reentrant_t **, size_t)) ATTRIBUTE_MALLOC;
332 #endif
334 #if WANT_TMP_ALLOCA
335 #define TMP_SDECL
336 #define TMP_DECL struct tmp_reentrant_t *__tmp_marker
337 #define TMP_SMARK
338 #define TMP_MARK __tmp_marker = 0
339 #define TMP_SALLOC(n) alloca(n)
340 #define TMP_BALLOC(n) __gmp_tmp_reentrant_alloc (&__tmp_marker, n)
341 #define TMP_ALLOC(n) \
342 (LIKELY ((n) < 65536) ? TMP_SALLOC(n) : TMP_BALLOC(n))
343 #define TMP_SFREE
344 #define TMP_FREE \
345 do { \
346 if (UNLIKELY (__tmp_marker != 0)) __gmp_tmp_reentrant_free (__tmp_marker); \
347 } while (0)
348 #endif
350 #if WANT_TMP_REENTRANT
351 #define TMP_SDECL TMP_DECL
352 #define TMP_DECL struct tmp_reentrant_t *__tmp_marker
353 #define TMP_SMARK TMP_MARK
354 #define TMP_MARK __tmp_marker = 0
355 #define TMP_SALLOC(n) TMP_ALLOC(n)
356 #define TMP_BALLOC(n) TMP_ALLOC(n)
357 #define TMP_ALLOC(n) __gmp_tmp_reentrant_alloc (&__tmp_marker, n)
358 #define TMP_SFREE TMP_FREE
359 #define TMP_FREE __gmp_tmp_reentrant_free (__tmp_marker)
360 #endif
362 #if WANT_TMP_NOTREENTRANT
363 struct tmp_marker
364 {
367 };
371 #define TMP_SDECL TMP_DECL
372 #define TMP_DECL struct tmp_marker __tmp_marker
373 #define TMP_SMARK TMP_MARK
374 #define TMP_MARK __gmp_tmp_mark (&__tmp_marker)
375 #define TMP_SALLOC(n) TMP_ALLOC(n)
376 #define TMP_BALLOC(n) TMP_ALLOC(n)
377 #define TMP_ALLOC(n) \
378 __gmp_tmp_alloc (ROUND_UP_MULTIPLE ((unsigned long) (n), __TMP_ALIGN))
379 #define TMP_SFREE TMP_FREE
380 #define TMP_FREE __gmp_tmp_free (&__tmp_marker)
381 #endif
383 #if WANT_TMP_DEBUG
384 /* See tal-debug.c for some comments. */
389 };
394 };
395 __GMP_DECLSPEC void __gmp_tmp_debug_mark __GMP_PROTO ((const char *, int, struct tmp_debug_t **,
410 /* The marker variable is designed to provoke an uninitialized variable
411 warning from the compiler if TMP_FREE is used without a TMP_MARK.
412 __tmp_marker_inscope does the same for TMP_ALLOC. Runtime tests pick
413 these things up too. */
414 #define TMP_DECL_NAME(marker, marker_name) \
415 int marker; \
416 int __tmp_marker_inscope; \
417 const char *__tmp_marker_name = marker_name; \
418 struct tmp_debug_t __tmp_marker_struct; \
420 struct tmp_debug_t *__tmp_marker = (struct tmp_debug_t *) 0
421 #define TMP_MARK_NAME(marker, marker_name) \
422 do { \
423 marker = 1; \
424 __tmp_marker_inscope = 1; \
425 __gmp_tmp_debug_mark (ASSERT_FILE, ASSERT_LINE, \
426 &__tmp_marker, &__tmp_marker_struct, \
427 __tmp_marker_name, marker_name); \
428 } while (0)
429 #define TMP_SALLOC(n) TMP_ALLOC(n)
430 #define TMP_BALLOC(n) TMP_ALLOC(n)
431 #define TMP_ALLOC(size) \
432 __gmp_tmp_debug_alloc (ASSERT_FILE, ASSERT_LINE, \
433 __tmp_marker_inscope, \
434 &__tmp_marker, __tmp_marker_name, size)
435 #define TMP_FREE_NAME(marker, marker_name) \
436 do { \
437 __gmp_tmp_debug_free (ASSERT_FILE, ASSERT_LINE, \
438 marker, &__tmp_marker, \
439 __tmp_marker_name, marker_name); \
440 } while (0)
444 /* Allocating various types. */
445 #define TMP_ALLOC_TYPE(n,type) ((type *) TMP_ALLOC ((n) * sizeof (type)))
446 #define TMP_SALLOC_TYPE(n,type) ((type *) TMP_SALLOC ((n) * sizeof (type)))
447 #define TMP_BALLOC_TYPE(n,type) ((type *) TMP_BALLOC ((n) * sizeof (type)))
448 #define TMP_ALLOC_LIMBS(n) TMP_ALLOC_TYPE(n,mp_limb_t)
449 #define TMP_SALLOC_LIMBS(n) TMP_SALLOC_TYPE(n,mp_limb_t)
450 #define TMP_BALLOC_LIMBS(n) TMP_BALLOC_TYPE(n,mp_limb_t)
451 #define TMP_ALLOC_MP_PTRS(n) TMP_ALLOC_TYPE(n,mp_ptr)
452 #define TMP_SALLOC_MP_PTRS(n) TMP_SALLOC_TYPE(n,mp_ptr)
453 #define TMP_BALLOC_MP_PTRS(n) TMP_BALLOC_TYPE(n,mp_ptr)
455 /* It's more efficient to allocate one block than two. This is certainly
456 true of the malloc methods, but it can even be true of alloca if that
457 involves copying a chunk of stack (various RISCs), or a call to a stack
458 bounds check (mingw). In any case, when debugging keep separate blocks
459 so a redzoning malloc debugger can protect each individually. */
460 #define TMP_ALLOC_LIMBS_2(xp,xsize, yp,ysize) \
461 do { \
462 if (WANT_TMP_DEBUG) \
463 { \
464 (xp) = TMP_ALLOC_LIMBS (xsize); \
465 (yp) = TMP_ALLOC_LIMBS (ysize); \
466 } \
467 else \
468 { \
469 (xp) = TMP_ALLOC_LIMBS ((xsize) + (ysize)); \
470 (yp) = (xp) + (xsize); \
471 } \
472 } while (0)
475 /* From gmp.h, nicer names for internal use. */
476 #define CRAY_Pragma(str) __GMP_CRAY_Pragma(str)
477 #define MPN_CMP(result, xp, yp, size) __GMPN_CMP(result, xp, yp, size)
478 #define LIKELY(cond) __GMP_LIKELY(cond)
479 #define UNLIKELY(cond) __GMP_UNLIKELY(cond)
481 #define ABS(x) ((x) >= 0 ? (x) : -(x))
482 #define ABS_CAST(T,x) ((x) >= 0 ? (T)(x) : -((T)((x) + 1) - 1))
483 #undef MIN
484 #define MIN(l,o) ((l) < (o) ? (l) : (o))
485 #undef MAX
486 #define MAX(h,i) ((h) > (i) ? (h) : (i))
487 #define numberof(x) (sizeof (x) / sizeof ((x)[0]))
489 /* Field access macros. */
490 #define SIZ(x) ((x)->_mp_size)
491 #define ABSIZ(x) ABS (SIZ (x))
492 #define PTR(x) ((x)->_mp_d)
493 #define LIMBS(x) ((x)->_mp_d)
494 #define EXP(x) ((x)->_mp_exp)
495 #define PREC(x) ((x)->_mp_prec)
496 #define ALLOC(x) ((x)->_mp_alloc)
498 /* n-1 inverts any low zeros and the lowest one bit. If n&(n-1) leaves zero
499 then that lowest one bit must have been the only bit set. n==0 will
500 return true though, so avoid that. */
501 #define POW2_P(n) (((n) & ((n) - 1)) == 0)
504 /* The "short" defines are a bit different because shorts are promoted to
505 ints by ~ or >> etc.
507 #ifndef's are used since on some systems (HP?) header files other than
508 limits.h setup these defines. We could forcibly #undef in that case, but
509 there seems no need to worry about that. */
511 #ifndef ULONG_MAX
512 #define ULONG_MAX __GMP_ULONG_MAX
513 #endif
514 #ifndef UINT_MAX
515 #define UINT_MAX __GMP_UINT_MAX
516 #endif
517 #ifndef USHRT_MAX
518 #define USHRT_MAX __GMP_USHRT_MAX
519 #endif
520 #define MP_LIMB_T_MAX (~ (mp_limb_t) 0)
522 /* Must cast ULONG_MAX etc to unsigned long etc, since they might not be
523 unsigned on a K&R compiler. In particular the HP-UX 10 bundled K&R cc
524 treats the plain decimal values in <limits.h> as signed. */
525 #define ULONG_HIGHBIT (ULONG_MAX ^ ((unsigned long) ULONG_MAX >> 1))
526 #define UINT_HIGHBIT (UINT_MAX ^ ((unsigned) UINT_MAX >> 1))
527 #define USHRT_HIGHBIT ((unsigned short) (USHRT_MAX ^ ((unsigned short) USHRT_MAX >> 1)))
528 #define GMP_LIMB_HIGHBIT (MP_LIMB_T_MAX ^ (MP_LIMB_T_MAX >> 1))
530 #ifndef LONG_MIN
531 #define LONG_MIN ((long) ULONG_HIGHBIT)
532 #endif
533 #ifndef LONG_MAX
534 #define LONG_MAX (-(LONG_MIN+1))
535 #endif
537 #ifndef INT_MIN
538 #define INT_MIN ((int) UINT_HIGHBIT)
539 #endif
540 #ifndef INT_MAX
541 #define INT_MAX (-(INT_MIN+1))
542 #endif
544 #ifndef SHRT_MIN
545 #define SHRT_MIN ((short) USHRT_HIGHBIT)
546 #endif
547 #ifndef SHRT_MAX
548 #define SHRT_MAX ((short) (-(SHRT_MIN+1)))
549 #endif
551 #if __GMP_MP_SIZE_T_INT
552 #define MP_SIZE_T_MAX INT_MAX
553 #define MP_SIZE_T_MIN INT_MIN
554 #else
555 #define MP_SIZE_T_MAX LONG_MAX
556 #define MP_SIZE_T_MIN LONG_MIN
557 #endif
559 /* mp_exp_t is the same as mp_size_t */
560 #define MP_EXP_T_MAX MP_SIZE_T_MAX
561 #define MP_EXP_T_MIN MP_SIZE_T_MIN
563 #define LONG_HIGHBIT LONG_MIN
564 #define INT_HIGHBIT INT_MIN
565 #define SHRT_HIGHBIT SHRT_MIN
568 #define GMP_NUMB_HIGHBIT (CNST_LIMB(1) << (GMP_NUMB_BITS-1))
570 #if GMP_NAIL_BITS == 0
571 #define GMP_NAIL_LOWBIT CNST_LIMB(0)
572 #else
573 #define GMP_NAIL_LOWBIT (CNST_LIMB(1) << GMP_NUMB_BITS)
574 #endif
576 #if GMP_NAIL_BITS != 0
577 /* Set various *_THRESHOLD values to be used for nails. Thus we avoid using
578 code that has not yet been qualified. */
580 #undef DC_DIV_QR_THRESHOLD
581 #define DC_DIV_QR_THRESHOLD 50
583 #undef DIVREM_1_NORM_THRESHOLD
584 #undef DIVREM_1_UNNORM_THRESHOLD
585 #undef MOD_1_NORM_THRESHOLD
586 #undef MOD_1_UNNORM_THRESHOLD
587 #undef USE_PREINV_DIVREM_1
588 #undef DIVREM_2_THRESHOLD
589 #undef DIVEXACT_1_THRESHOLD
597 /* mpn/generic/mul_fft.c is not nails-capable. */
598 #undef MUL_FFT_THRESHOLD
599 #undef SQR_FFT_THRESHOLD
600 #define MUL_FFT_THRESHOLD MP_SIZE_T_MAX
601 #define SQR_FFT_THRESHOLD MP_SIZE_T_MAX
602 #endif
604 /* Swap macros. */
606 #define MP_LIMB_T_SWAP(x, y) \
607 do { \
608 mp_limb_t __mp_limb_t_swap__tmp = (x); \
609 (x) = (y); \
610 (y) = __mp_limb_t_swap__tmp; \
611 } while (0)
612 #define MP_SIZE_T_SWAP(x, y) \
613 do { \
614 mp_size_t __mp_size_t_swap__tmp = (x); \
615 (x) = (y); \
616 (y) = __mp_size_t_swap__tmp; \
617 } while (0)
619 #define MP_PTR_SWAP(x, y) \
620 do { \
621 mp_ptr __mp_ptr_swap__tmp = (x); \
622 (x) = (y); \
623 (y) = __mp_ptr_swap__tmp; \
624 } while (0)
625 #define MP_SRCPTR_SWAP(x, y) \
626 do { \
627 mp_srcptr __mp_srcptr_swap__tmp = (x); \
628 (x) = (y); \
629 (y) = __mp_srcptr_swap__tmp; \
630 } while (0)
632 #define MPN_PTR_SWAP(xp,xs, yp,ys) \
633 do { \
634 MP_PTR_SWAP (xp, yp); \
635 MP_SIZE_T_SWAP (xs, ys); \
636 } while(0)
637 #define MPN_SRCPTR_SWAP(xp,xs, yp,ys) \
638 do { \
639 MP_SRCPTR_SWAP (xp, yp); \
640 MP_SIZE_T_SWAP (xs, ys); \
641 } while(0)
643 #define MPZ_PTR_SWAP(x, y) \
644 do { \
645 mpz_ptr __mpz_ptr_swap__tmp = (x); \
646 (x) = (y); \
647 (y) = __mpz_ptr_swap__tmp; \
648 } while (0)
649 #define MPZ_SRCPTR_SWAP(x, y) \
650 do { \
651 mpz_srcptr __mpz_srcptr_swap__tmp = (x); \
652 (x) = (y); \
653 (y) = __mpz_srcptr_swap__tmp; \
654 } while (0)
657 /* Enhancement: __gmp_allocate_func could have "__attribute__ ((malloc))",
658 but current gcc (3.0) doesn't seem to support that. */
667 #define __GMP_ALLOCATE_FUNC_TYPE(n,type) \
668 ((type *) (*__gmp_allocate_func) ((n) * sizeof (type)))
669 #define __GMP_ALLOCATE_FUNC_LIMBS(n) __GMP_ALLOCATE_FUNC_TYPE (n, mp_limb_t)
671 #define __GMP_REALLOCATE_FUNC_TYPE(p, old_size, new_size, type) \
672 ((type *) (*__gmp_reallocate_func) \
673 (p, (old_size) * sizeof (type), (new_size) * sizeof (type)))
674 #define __GMP_REALLOCATE_FUNC_LIMBS(p, old_size, new_size) \
675 __GMP_REALLOCATE_FUNC_TYPE(p, old_size, new_size, mp_limb_t)
677 #define __GMP_FREE_FUNC_TYPE(p,n,type) (*__gmp_free_func) (p, (n) * sizeof (type))
678 #define __GMP_FREE_FUNC_LIMBS(p,n) __GMP_FREE_FUNC_TYPE (p, n, mp_limb_t)
680 #define __GMP_REALLOCATE_FUNC_MAYBE(ptr, oldsize, newsize) \
681 do { \
682 if ((oldsize) != (newsize)) \
683 (ptr) = (*__gmp_reallocate_func) (ptr, oldsize, newsize); \
684 } while (0)
686 #define __GMP_REALLOCATE_FUNC_MAYBE_TYPE(ptr, oldsize, newsize, type) \
687 do { \
688 if ((oldsize) != (newsize)) \
689 (ptr) = (type *) (*__gmp_reallocate_func) \
690 (ptr, (oldsize) * sizeof (type), (newsize) * sizeof (type)); \
691 } while (0)
694 /* Dummy for non-gcc, code involving it will go dead. */
695 #if ! defined (__GNUC__) || __GNUC__ < 2
696 #define __builtin_constant_p(x) 0
697 #endif
700 /* In gcc 2.96 and up on i386, tail calls are optimized to jumps if the
701 stack usage is compatible. __attribute__ ((regparm (N))) helps by
702 putting leading parameters in registers, avoiding extra stack.
704 regparm cannot be used with calls going through the PLT, because the
705 binding code there may clobber the registers (%eax, %edx, %ecx) used for
706 the regparm parameters. Calls to local (ie. static) functions could
707 still use this, if we cared to differentiate locals and globals.
709 On athlon-unknown-freebsd4.9 with gcc 3.3.3, regparm cannot be used with
710 -p or -pg profiling, since that version of gcc doesn't realize the
711 .mcount calls will clobber the parameter registers. Other systems are
712 ok, like debian with glibc 2.3.2 (mcount doesn't clobber), but we don't
713 bother to try to detect this. regparm is only an optimization so we just
714 disable it when profiling (profiling being a slowdown anyway). */
716 #if HAVE_HOST_CPU_FAMILY_x86 && __GMP_GNUC_PREREQ (2,96) && ! defined (PIC) \
717 && ! WANT_PROFILING_PROF && ! WANT_PROFILING_GPROF
718 #define USE_LEADING_REGPARM 1
719 #else
720 #define USE_LEADING_REGPARM 0
721 #endif
723 /* Macros for altering parameter order according to regparm usage. */
724 #if USE_LEADING_REGPARM
725 #define REGPARM_2_1(a,b,x) x,a,b
726 #define REGPARM_3_1(a,b,c,x) x,a,b,c
727 #define REGPARM_ATTR(n) __attribute__ ((regparm (n)))
728 #else
729 #define REGPARM_2_1(a,b,x) a,b,x
730 #define REGPARM_3_1(a,b,c,x) a,b,c,x
731 #define REGPARM_ATTR(n)
732 #endif
735 /* ASM_L gives a local label for a gcc asm block, for use when temporary
736 local labels like "1:" might not be available, which is the case for
737 instance on the x86s (the SCO assembler doesn't support them).
739 The label generated is made unique by including "%=" which is a unique
740 number for each insn. This ensures the same name can be used in multiple
741 asm blocks, perhaps via a macro. Since jumps between asm blocks are not
742 allowed there's no need for a label to be usable outside a single
743 block. */
748 #if defined (__GNUC__) && HAVE_HOST_CPU_FAMILY_x86
749 #if 0
750 /* FIXME: Check that these actually improve things.
751 FIXME: Need a cld after each std.
752 FIXME: Can't have inputs in clobbered registers, must describe them as
753 dummy outputs, and add volatile. */
754 #define MPN_COPY_INCR(DST, SRC, N) \
758 #define MPN_COPY_DECR(DST, SRC, N) \
762 #endif
763 #endif
766 __GMP_DECLSPEC void __gmpz_aorsmul_1 __GMP_PROTO ((REGPARM_3_1 (mpz_ptr, mpz_srcptr, mp_limb_t, mp_size_t))) REGPARM_ATTR(1);
767 #define mpz_aorsmul_1(w,u,v,sub) __gmpz_aorsmul_1 (REGPARM_3_1 (w, u, v, sub))
769 #define mpz_n_pow_ui __gmpz_n_pow_ui
773 #define mpn_addmul_1c __MPN(addmul_1c)
774 __GMP_DECLSPEC mp_limb_t mpn_addmul_1c __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t));
776 #define mpn_addmul_2 __MPN(addmul_2)
779 #define mpn_addmul_3 __MPN(addmul_3)
782 #define mpn_addmul_4 __MPN(addmul_4)
785 #define mpn_addmul_5 __MPN(addmul_5)
788 #define mpn_addmul_6 __MPN(addmul_6)
791 #define mpn_addmul_7 __MPN(addmul_7)
794 #define mpn_addmul_8 __MPN(addmul_8)
797 /* mpn_addlsh1_n(c,a,b,n), when it exists, sets {c,n} to {a,n}+2*{b,n}, and
798 returns the carry out (0, 1 or 2). */
799 #define mpn_addlsh1_n __MPN(addlsh1_n)
802 /* mpn_addlsh2_n(c,a,b,n), when it exists, sets {c,n} to {a,n}+4*{b,n}, and
803 returns the carry out (0, ..., 4). */
804 #define mpn_addlsh2_n __MPN(addlsh2_n)
807 /* mpn_addlsh_n(c,a,b,n,k), when it exists, sets {c,n} to {a,n}+2^k*{b,n}, and
808 returns the carry out (0, ..., 2^k). */
809 #define mpn_addlsh_n __MPN(addlsh_n)
810 __GMP_DECLSPEC mp_limb_t mpn_addlsh_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t, unsigned int));
812 /* mpn_sublsh1_n(c,a,b,n), when it exists, sets {c,n} to {a,n}-2*{b,n}, and
813 returns the borrow out (0, 1 or 2). */
814 #define mpn_sublsh1_n __MPN(sublsh1_n)
817 /* mpn_rsblsh1_n(c,a,b,n), when it exists, sets {c,n} to 2*{b,n}-{a,n}, and
818 returns the carry out (-1, 0, 1). */
819 #define mpn_rsblsh1_n __MPN(rsblsh1_n)
820 __GMP_DECLSPEC mp_limb_signed_t mpn_rsblsh1_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
822 /* mpn_sublsh2_n(c,a,b,n), when it exists, sets {c,n} to {a,n}-4*{b,n}, and
823 returns the borrow out (FIXME 0, 1, 2 or 3). */
824 #define mpn_sublsh2_n __MPN(sublsh2_n)
827 /* mpn_rsblsh2_n(c,a,b,n), when it exists, sets {c,n} to 4*{b,n}-{a,n}, and
828 returns the carry out (-1, ..., 3). */
829 #define mpn_rsblsh2_n __MPN(rsblsh2_n)
830 __GMP_DECLSPEC mp_limb_signed_t mpn_rsblsh2_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
832 /* mpn_rsblsh_n(c,a,b,n,k), when it exists, sets {c,n} to 2^k*{b,n}-{a,n}, and
833 returns the carry out (-1, 0, ..., 2^k-1). */
834 #define mpn_rsblsh_n __MPN(rsblsh_n)
835 __GMP_DECLSPEC mp_limb_signed_t mpn_rsblsh_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t, unsigned int));
837 /* mpn_rsh1add_n(c,a,b,n), when it exists, sets {c,n} to ({a,n} + {b,n}) >> 1,
838 and returns the bit rshifted out (0 or 1). */
839 #define mpn_rsh1add_n __MPN(rsh1add_n)
841 #define mpn_rsh1add_nc __MPN(rsh1add_nc)
842 __GMP_DECLSPEC mp_limb_t mpn_rsh1add_nc __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t, mp_limb_t));
844 /* mpn_rsh1sub_n(c,a,b,n), when it exists, sets {c,n} to ({a,n} - {b,n}) >> 1,
845 and returns the bit rshifted out (0 or 1). If there's a borrow from the
846 subtract, it's stored as a 1 in the high bit of c[n-1], like a twos
847 complement negative. */
848 #define mpn_rsh1sub_n __MPN(rsh1sub_n)
850 #define mpn_rsh1sub_nc __MPN(rsh1sub_nc)
851 __GMP_DECLSPEC mp_limb_t mpn_rsh1sub_nc __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t, mp_limb_t));
853 #define mpn_lshiftc __MPN(lshiftc)
854 __GMP_DECLSPEC mp_limb_t mpn_lshiftc __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, unsigned int));
856 #define mpn_add_n_sub_n __MPN(add_n_sub_n)
857 __GMP_DECLSPEC mp_limb_t mpn_add_n_sub_n __GMP_PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_srcptr, mp_size_t));
859 #define mpn_add_n_sub_nc __MPN(add_n_sub_nc)
860 __GMP_DECLSPEC mp_limb_t mpn_add_n_sub_nc __GMP_PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_srcptr, mp_size_t, mp_limb_t));
862 #define mpn_addaddmul_1msb0 __MPN(addaddmul_1msb0)
863 __GMP_DECLSPEC mp_limb_t mpn_addaddmul_1msb0 __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t));
865 #define mpn_divrem_1c __MPN(divrem_1c)
866 __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));
868 #define mpn_dump __MPN(dump)
871 #define mpn_fib2_ui __MPN(fib2_ui)
874 /* Remap names of internal mpn functions. */
875 #define __clz_tab __MPN(clz_tab)
876 #define mpn_udiv_w_sdiv __MPN(udiv_w_sdiv)
878 #define mpn_jacobi_base __MPN(jacobi_base)
881 #define mpn_mod_1c __MPN(mod_1c)
882 __GMP_DECLSPEC mp_limb_t mpn_mod_1c __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t)) __GMP_ATTRIBUTE_PURE;
884 #define mpn_mul_1c __MPN(mul_1c)
885 __GMP_DECLSPEC mp_limb_t mpn_mul_1c __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t));
887 #define mpn_mul_2 __MPN(mul_2)
890 #define mpn_mul_3 __MPN(mul_3)
893 #define mpn_mul_4 __MPN(mul_4)
897 #define mpn_mul_basecase __MPN(mul_basecase)
898 __GMP_DECLSPEC void mpn_mul_basecase __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t));
899 #endif
901 #define mpn_mullo_n __MPN(mullo_n)
904 #define mpn_mullo_basecase __MPN(mullo_basecase)
907 #define mpn_sqr __MPN(sqr)
911 #define mpn_sqr_basecase __MPN(sqr_basecase)
913 #endif
915 #define mpn_submul_1c __MPN(submul_1c)
916 __GMP_DECLSPEC mp_limb_t mpn_submul_1c __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t));
918 #define mpn_redc_1 __MPN(redc_1)
921 #define mpn_redc_2 __MPN(redc_2)
923 #define mpn_redc_n __MPN(redc_n)
927 #define mpn_mod_1_1p_cps __MPN(mod_1_1p_cps)
929 #define mpn_mod_1_1p __MPN(mod_1_1p)
930 __GMP_DECLSPEC mp_limb_t mpn_mod_1_1p __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t [4])) __GMP_ATTRIBUTE_PURE;
932 #define mpn_mod_1s_2p_cps __MPN(mod_1s_2p_cps)
934 #define mpn_mod_1s_2p __MPN(mod_1s_2p)
935 __GMP_DECLSPEC mp_limb_t mpn_mod_1s_2p __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t [5])) __GMP_ATTRIBUTE_PURE;
937 #define mpn_mod_1s_3p_cps __MPN(mod_1s_3p_cps)
939 #define mpn_mod_1s_3p __MPN(mod_1s_3p)
940 __GMP_DECLSPEC mp_limb_t mpn_mod_1s_3p __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t [6])) __GMP_ATTRIBUTE_PURE;
942 #define mpn_mod_1s_4p_cps __MPN(mod_1s_4p_cps)
944 #define mpn_mod_1s_4p __MPN(mod_1s_4p)
945 __GMP_DECLSPEC mp_limb_t mpn_mod_1s_4p __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t [7])) __GMP_ATTRIBUTE_PURE;
947 #define mpn_bc_mulmod_bnm1 __MPN(bc_mulmod_bnm1)
948 __GMP_DECLSPEC void mpn_bc_mulmod_bnm1 __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t, mp_ptr));
949 #define mpn_mulmod_bnm1 __MPN(mulmod_bnm1)
950 __GMP_DECLSPEC void mpn_mulmod_bnm1 __GMP_PROTO ((mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr));
951 #define mpn_mulmod_bnm1_next_size __MPN(mulmod_bnm1_next_size)
960 }
962 #define mpn_sqrmod_bnm1 __MPN(sqrmod_bnm1)
963 __GMP_DECLSPEC void mpn_sqrmod_bnm1 __GMP_PROTO ((mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr));
964 #define mpn_sqrmod_bnm1_next_size __MPN(sqrmod_bnm1_next_size)
973 }
978 /* Pseudo-random number generator function pointers structure. */
986 /* Macro to obtain a void pointer to the function pointers structure. */
987 #define RNG_FNPTR(rstate) ((rstate)->_mp_algdata._mp_lc)
989 /* Macro to obtain a pointer to the generator's state.
990 When used as a lvalue the rvalue needs to be cast to mp_ptr. */
991 #define RNG_STATE(rstate) ((rstate)->_mp_seed->_mp_d)
993 /* Write a given number of random bits to rp. */
994 #define _gmp_rand(rp, state, bits) \
995 do { \
996 gmp_randstate_ptr __rstate = (state); \
997 (*((gmp_randfnptr_t *) RNG_FNPTR (__rstate))->randget_fn) \
998 (__rstate, rp, bits); \
999 } while (0)
1004 /* __gmp_rands is the global state for the old-style random functions, and
1005 is also used in the test programs (hence the __GMP_DECLSPEC).
1007 There's no seeding here, so mpz_random etc will generate the same
1008 sequence every time. This is not unlike the C library random functions
1009 if you don't seed them, so perhaps it's acceptable. Digging up a seed
1010 from /dev/random or the like would work on many systems, but might
1011 encourage a false confidence, since it'd be pretty much impossible to do
1012 something that would work reliably everywhere. In any case the new style
1013 functions are recommended to applications which care about randomness, so
1014 the old functions aren't too important. */
1019 #define RANDS \
1020 ((__gmp_rands_initialized ? 0 \
1021 : (__gmp_rands_initialized = 1, \
1022 __gmp_randinit_mt_noseed (__gmp_rands), 0)), \
1023 __gmp_rands)
1025 /* this is used by the test programs, to free memory */
1026 #define RANDS_CLEAR() \
1027 do { \
1028 if (__gmp_rands_initialized) \
1029 { \
1030 __gmp_rands_initialized = 0; \
1031 gmp_randclear (__gmp_rands); \
1032 } \
1033 } while (0)
1036 /* For a threshold between algorithms A and B, size>=thresh is where B
1037 should be used. Special value MP_SIZE_T_MAX means only ever use A, or
1038 value 0 means only ever use B. The tests for these special values will
1039 be compile-time constants, so the compiler should be able to eliminate
1040 the code for the unwanted algorithm. */
1042 #define ABOVE_THRESHOLD(size,thresh) \
1043 ((thresh) == 0 \
1044 || ((thresh) != MP_SIZE_T_MAX \
1045 && (size) >= (thresh)))
1046 #define BELOW_THRESHOLD(size,thresh) (! ABOVE_THRESHOLD (size, thresh))
1048 #define MPN_TOOM22_MUL_MINSIZE 4
1049 #define MPN_TOOM2_SQR_MINSIZE 4
1051 #define MPN_TOOM33_MUL_MINSIZE 17
1052 #define MPN_TOOM3_SQR_MINSIZE 17
1054 #define MPN_TOOM44_MUL_MINSIZE 30
1055 #define MPN_TOOM4_SQR_MINSIZE 30
1057 #define MPN_TOOM6H_MUL_MINSIZE 46
1058 #define MPN_TOOM6_SQR_MINSIZE 46
1060 #define MPN_TOOM8H_MUL_MINSIZE 86
1061 #define MPN_TOOM8_SQR_MINSIZE 86
1063 #define MPN_TOOM32_MUL_MINSIZE 10
1064 #define MPN_TOOM42_MUL_MINSIZE 10
1067 #define MPN_TOOM63_MUL_MINSIZE 49
1069 #define mpn_sqr_diagonal __MPN(sqr_diagonal)
1072 #define mpn_toom_interpolate_5pts __MPN(toom_interpolate_5pts)
1073 __GMP_DECLSPEC void mpn_toom_interpolate_5pts __GMP_PROTO ((mp_ptr, mp_ptr, mp_ptr, mp_size_t, mp_size_t, int, mp_limb_t));
1076 #define mpn_toom_interpolate_6pts __MPN(toom_interpolate_6pts)
1077 __GMP_DECLSPEC void mpn_toom_interpolate_6pts __GMP_PROTO ((mp_ptr, mp_size_t, enum toom6_flags, mp_ptr, mp_ptr, mp_ptr, mp_size_t));
1080 #define mpn_toom_interpolate_7pts __MPN(toom_interpolate_7pts)
1081 __GMP_DECLSPEC void mpn_toom_interpolate_7pts __GMP_PROTO ((mp_ptr, mp_size_t, enum toom7_flags, mp_ptr, mp_ptr, mp_ptr, mp_ptr, mp_size_t, mp_ptr));
1083 #define mpn_toom_interpolate_8pts __MPN(toom_interpolate_8pts)
1084 __GMP_DECLSPEC void mpn_toom_interpolate_8pts __GMP_PROTO ((mp_ptr, mp_size_t, mp_ptr, mp_ptr, mp_size_t, mp_ptr));
1086 #define mpn_toom_interpolate_12pts __MPN(toom_interpolate_12pts)
1087 __GMP_DECLSPEC void mpn_toom_interpolate_12pts __GMP_PROTO ((mp_ptr, mp_ptr, mp_ptr, mp_ptr, mp_size_t, mp_size_t, int, mp_ptr));
1089 #define mpn_toom_interpolate_16pts __MPN(toom_interpolate_16pts)
1090 __GMP_DECLSPEC void mpn_toom_interpolate_16pts __GMP_PROTO ((mp_ptr, mp_ptr, mp_ptr, mp_ptr, mp_ptr, mp_size_t, mp_size_t, int, mp_ptr));
1092 #define mpn_toom_couple_handling __MPN(toom_couple_handling)
1093 __GMP_DECLSPEC void mpn_toom_couple_handling __GMP_PROTO ((mp_ptr, mp_size_t, mp_ptr, int, mp_size_t, int, int));
1095 #define mpn_toom_eval_dgr3_pm1 __MPN(toom_eval_dgr3_pm1)
1096 __GMP_DECLSPEC int mpn_toom_eval_dgr3_pm1 __GMP_PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_size_t, mp_size_t, mp_ptr));
1098 #define mpn_toom_eval_dgr3_pm2 __MPN(toom_eval_dgr3_pm2)
1099 __GMP_DECLSPEC int mpn_toom_eval_dgr3_pm2 __GMP_PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_size_t, mp_size_t, mp_ptr));
1101 #define mpn_toom_eval_pm1 __MPN(toom_eval_pm1)
1102 __GMP_DECLSPEC int mpn_toom_eval_pm1 __GMP_PROTO ((mp_ptr, mp_ptr, unsigned, mp_srcptr, mp_size_t, mp_size_t, mp_ptr));
1104 #define mpn_toom_eval_pm2 __MPN(toom_eval_pm2)
1105 __GMP_DECLSPEC int mpn_toom_eval_pm2 __GMP_PROTO ((mp_ptr, mp_ptr, unsigned, mp_srcptr, mp_size_t, mp_size_t, mp_ptr));
1107 #define mpn_toom_eval_pm2exp __MPN(toom_eval_pm2exp)
1108 __GMP_DECLSPEC int mpn_toom_eval_pm2exp __GMP_PROTO ((mp_ptr, mp_ptr, unsigned, mp_srcptr, mp_size_t, mp_size_t, unsigned, mp_ptr));
1110 #define mpn_toom_eval_pm2rexp __MPN(toom_eval_pm2rexp)
1111 __GMP_DECLSPEC int mpn_toom_eval_pm2rexp __GMP_PROTO ((mp_ptr, mp_ptr, unsigned, mp_srcptr, mp_size_t, mp_size_t, unsigned, mp_ptr));
1113 #define mpn_toom22_mul __MPN(toom22_mul)
1114 __GMP_DECLSPEC void mpn_toom22_mul __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr));
1116 #define mpn_toom32_mul __MPN(toom32_mul)
1117 __GMP_DECLSPEC void mpn_toom32_mul __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr));
1119 #define mpn_toom42_mul __MPN(toom42_mul)
1120 __GMP_DECLSPEC void mpn_toom42_mul __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr));
1122 #define mpn_toom52_mul __MPN(toom52_mul)
1123 __GMP_DECLSPEC void mpn_toom52_mul __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr));
1125 #define mpn_toom62_mul __MPN(toom62_mul)
1126 __GMP_DECLSPEC void mpn_toom62_mul __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr));
1128 #define mpn_toom2_sqr __MPN(toom2_sqr)
1131 #define mpn_toom33_mul __MPN(toom33_mul)
1132 __GMP_DECLSPEC void mpn_toom33_mul __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr));
1134 #define mpn_toom43_mul __MPN(toom43_mul)
1135 __GMP_DECLSPEC void mpn_toom43_mul __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr));
1137 #define mpn_toom53_mul __MPN(toom53_mul)
1138 __GMP_DECLSPEC void mpn_toom53_mul __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr));
1140 #define mpn_toom63_mul __MPN(toom63_mul)
1141 __GMP_DECLSPEC void mpn_toom63_mul __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr));
1143 #define mpn_toom3_sqr __MPN(toom3_sqr)
1146 #define mpn_toom44_mul __MPN(toom44_mul)
1147 __GMP_DECLSPEC void mpn_toom44_mul __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr));
1149 #define mpn_toom4_sqr __MPN(toom4_sqr)
1152 #define mpn_toom6h_mul __MPN(toom6h_mul)
1153 __GMP_DECLSPEC void mpn_toom6h_mul __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr));
1155 #define mpn_toom6_sqr __MPN(toom6_sqr)
1158 #define mpn_toom8h_mul __MPN(toom8h_mul)
1159 __GMP_DECLSPEC void mpn_toom8h_mul __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr));
1161 #define mpn_toom8_sqr __MPN(toom8_sqr)
1164 #define mpn_fft_best_k __MPN(fft_best_k)
1167 #define mpn_mul_fft __MPN(mul_fft)
1168 __GMP_DECLSPEC mp_limb_t mpn_mul_fft __GMP_PROTO ((mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, int));
1170 #define mpn_mul_fft_full __MPN(mul_fft_full)
1171 __GMP_DECLSPEC void mpn_mul_fft_full __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t));
1173 #define mpn_nussbaumer_mul __MPN(nussbaumer_mul)
1174 __GMP_DECLSPEC void mpn_nussbaumer_mul __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t));
1176 #define mpn_fft_next_size __MPN(fft_next_size)
1179 #define mpn_sbpi1_div_qr __MPN(sbpi1_div_qr)
1180 __GMP_DECLSPEC mp_limb_t mpn_sbpi1_div_qr __GMP_PROTO ((mp_ptr, mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_limb_t));
1182 #define mpn_sbpi1_div_q __MPN(sbpi1_div_q)
1183 __GMP_DECLSPEC mp_limb_t mpn_sbpi1_div_q __GMP_PROTO ((mp_ptr, mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_limb_t));
1185 #define mpn_sbpi1_divappr_q __MPN(sbpi1_divappr_q)
1186 __GMP_DECLSPEC mp_limb_t mpn_sbpi1_divappr_q __GMP_PROTO ((mp_ptr, mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_limb_t));
1188 #define mpn_dcpi1_div_qr __MPN(dcpi1_div_qr)
1189 __GMP_DECLSPEC mp_limb_t mpn_dcpi1_div_qr __GMP_PROTO ((mp_ptr, mp_ptr, mp_size_t, mp_srcptr, mp_size_t, gmp_pi1_t *));
1190 #define mpn_dcpi1_div_qr_n __MPN(dcpi1_div_qr_n)
1191 __GMP_DECLSPEC mp_limb_t mpn_dcpi1_div_qr_n __GMP_PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_size_t, gmp_pi1_t *, mp_ptr));
1193 #define mpn_dcpi1_div_q __MPN(dcpi1_div_q)
1194 __GMP_DECLSPEC mp_limb_t mpn_dcpi1_div_q __GMP_PROTO ((mp_ptr, mp_ptr, mp_size_t, mp_srcptr, mp_size_t, gmp_pi1_t *));
1196 #define mpn_dcpi1_divappr_q __MPN(dcpi1_divappr_q)
1197 __GMP_DECLSPEC mp_limb_t mpn_dcpi1_divappr_q __GMP_PROTO ((mp_ptr, mp_ptr, mp_size_t, mp_srcptr, mp_size_t, gmp_pi1_t *));
1198 #define mpn_dcpi1_divappr_q_n __MPN(dcpi1_divappr_q_n)
1199 __GMP_DECLSPEC mp_limb_t mpn_dcpi1_divappr_q_n __GMP_PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_size_t, gmp_pi1_t *, mp_ptr));
1201 #define mpn_mu_div_qr __MPN(mu_div_qr)
1202 __GMP_DECLSPEC mp_limb_t mpn_mu_div_qr __GMP_PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr));
1203 #define mpn_mu_div_qr_itch __MPN(mu_div_qr_itch)
1205 #define mpn_mu_div_qr_choose_in __MPN(mu_div_qr_choose_in)
1208 #define mpn_preinv_mu_div_qr __MPN(preinv_mu_div_qr)
1209 __GMP_DECLSPEC mp_limb_t mpn_preinv_mu_div_qr __GMP_PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr));
1210 #define mpn_preinv_mu_div_qr_itch __MPN(preinv_mu_div_qr_itch)
1211 __GMP_DECLSPEC mp_size_t mpn_preinv_mu_div_qr_itch __GMP_PROTO ((mp_size_t, mp_size_t, mp_size_t));
1213 #define mpn_mu_divappr_q __MPN(mu_divappr_q)
1214 __GMP_DECLSPEC mp_limb_t mpn_mu_divappr_q __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr));
1215 #define mpn_mu_divappr_q_itch __MPN(mu_divappr_q_itch)
1217 #define mpn_mu_divappr_q_choose_in __MPN(mu_divappr_q_choose_in)
1220 #define mpn_preinv_mu_divappr_q __MPN(preinv_mu_divappr_q)
1221 __GMP_DECLSPEC mp_limb_t mpn_preinv_mu_divappr_q __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr));
1223 #define mpn_mu_div_q __MPN(mu_div_q)
1224 __GMP_DECLSPEC mp_limb_t mpn_mu_div_q __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr));
1225 #define mpn_mu_div_q_itch __MPN(mu_div_q_itch)
1228 #define mpn_div_q __MPN(div_q)
1229 __GMP_DECLSPEC void mpn_div_q __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr));
1231 #define mpn_invert __MPN(invert)
1233 #define mpn_invert_itch(n) mpn_invertappr_itch(n)
1235 #define mpn_ni_invertappr __MPN(ni_invertappr)
1236 __GMP_DECLSPEC mp_limb_t mpn_ni_invertappr __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_ptr));
1237 #define mpn_invertappr __MPN(invertappr)
1239 #define mpn_invertappr_itch(n) (3 * (n) + 2)
1241 #define mpn_binvert __MPN(binvert)
1243 #define mpn_binvert_itch __MPN(binvert_itch)
1246 #define mpn_bdiv_q_1 __MPN(bdiv_q_1)
1249 #define mpn_pi1_bdiv_q_1 __MPN(pi1_bdiv_q_1)
1250 __GMP_DECLSPEC mp_limb_t mpn_pi1_bdiv_q_1 __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t, int));
1252 #define mpn_sbpi1_bdiv_qr __MPN(sbpi1_bdiv_qr)
1253 __GMP_DECLSPEC mp_limb_t mpn_sbpi1_bdiv_qr __GMP_PROTO ((mp_ptr, mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_limb_t));
1255 #define mpn_sbpi1_bdiv_q __MPN(sbpi1_bdiv_q)
1256 __GMP_DECLSPEC void mpn_sbpi1_bdiv_q __GMP_PROTO ((mp_ptr, mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_limb_t));
1258 #define mpn_dcpi1_bdiv_qr __MPN(dcpi1_bdiv_qr)
1259 __GMP_DECLSPEC mp_limb_t mpn_dcpi1_bdiv_qr __GMP_PROTO ((mp_ptr, mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_limb_t));
1260 #define mpn_dcpi1_bdiv_qr_n_itch __MPN(dcpi1_bdiv_qr_n_itch)
1263 #define mpn_dcpi1_bdiv_qr_n __MPN(dcpi1_bdiv_qr_n)
1264 __GMP_DECLSPEC mp_limb_t mpn_dcpi1_bdiv_qr_n __GMP_PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_size_t, mp_limb_t, mp_ptr));
1265 #define mpn_dcpi1_bdiv_q __MPN(dcpi1_bdiv_q)
1266 __GMP_DECLSPEC void mpn_dcpi1_bdiv_q __GMP_PROTO ((mp_ptr, mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_limb_t));
1268 #define mpn_dcpi1_bdiv_q_n_itch __MPN(dcpi1_bdiv_q_n_itch)
1270 #define mpn_dcpi1_bdiv_q_n __MPN(dcpi1_bdiv_q_n)
1271 __GMP_DECLSPEC void mpn_dcpi1_bdiv_q_n __GMP_PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_size_t, mp_limb_t, mp_ptr));
1273 #define mpn_mu_bdiv_qr __MPN(mu_bdiv_qr)
1274 __GMP_DECLSPEC mp_limb_t mpn_mu_bdiv_qr __GMP_PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr));
1275 #define mpn_mu_bdiv_qr_itch __MPN(mu_bdiv_qr_itch)
1278 #define mpn_mu_bdiv_q __MPN(mu_bdiv_q)
1279 __GMP_DECLSPEC void mpn_mu_bdiv_q __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr));
1280 #define mpn_mu_bdiv_q_itch __MPN(mu_bdiv_q_itch)
1283 #define mpn_bdiv_qr __MPN(bdiv_qr)
1284 __GMP_DECLSPEC mp_limb_t mpn_bdiv_qr __GMP_PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr));
1285 #define mpn_bdiv_qr_itch __MPN(bdiv_qr_itch)
1288 #define mpn_bdiv_q __MPN(bdiv_q)
1289 __GMP_DECLSPEC void mpn_bdiv_q __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr));
1290 #define mpn_bdiv_q_itch __MPN(bdiv_q_itch)
1293 #define mpn_divexact __MPN(divexact)
1294 __GMP_DECLSPEC void mpn_divexact __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t));
1295 #define mpn_divexact_itch __MPN(divexact_itch)
1298 #define mpn_bdiv_dbm1c __MPN(bdiv_dbm1c)
1299 __GMP_DECLSPEC mp_limb_t mpn_bdiv_dbm1c __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t));
1300 #define mpn_bdiv_dbm1(dst, src, size, divisor) \
1301 mpn_bdiv_dbm1c (dst, src, size, divisor, __GMP_CAST (mp_limb_t, 0))
1303 #define mpn_powm __MPN(powm)
1304 __GMP_DECLSPEC void mpn_powm __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr));
1305 #define mpn_powlo __MPN(powlo)
1306 __GMP_DECLSPEC void mpn_powlo __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t, mp_size_t, mp_ptr));
1307 #define mpn_powm_sec __MPN(powm_sec)
1308 __GMP_DECLSPEC void mpn_powm_sec __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr));
1309 #define mpn_powm_sec_itch __MPN(powm_sec_itch)
1311 #define mpn_subcnd_n __MPN(subcnd_n)
1312 __GMP_DECLSPEC mp_limb_t mpn_subcnd_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t, mp_limb_t));
1313 #define mpn_tabselect __MPN(tabselect)
1314 __GMP_DECLSPEC void mpn_tabselect __GMP_PROTO ((volatile mp_limb_t *, volatile mp_limb_t *, mp_size_t, mp_size_t, mp_size_t));
1315 #define mpn_redc_1_sec __MPN(redc_1_sec)
1316 __GMP_DECLSPEC void mpn_redc_1_sec __GMP_PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_size_t, mp_limb_t));
1318 #ifndef DIVEXACT_BY3_METHOD
1319 #if GMP_NUMB_BITS % 2 == 0 && ! defined (HAVE_NATIVE_mpn_divexact_by3c)
1321 #else
1322 #define DIVEXACT_BY3_METHOD 1
1323 #endif
1324 #endif
1326 #if DIVEXACT_BY3_METHOD == 0
1327 #undef mpn_divexact_by3
1328 #define mpn_divexact_by3(dst,src,size) \
1329 (3 & mpn_bdiv_dbm1 (dst, src, size, __GMP_CAST (mp_limb_t, GMP_NUMB_MASK / 3)))
1330 /* override mpn_divexact_by3c defined in gmp.h */
1331 /*
1332 #undef mpn_divexact_by3c
1333 #define mpn_divexact_by3c(dst,src,size,cy) \
1334 (3 & mpn_bdiv_dbm1c (dst, src, size, __GMP_CAST (mp_limb_t, GMP_NUMB_MASK / 3, GMP_NUMB_MASK / 3 * cy)))
1335 */
1336 #endif
1338 #if GMP_NUMB_BITS % 4 == 0
1339 #define mpn_divexact_by5(dst,src,size) \
1340 (7 & 3 * mpn_bdiv_dbm1 (dst, src, size, __GMP_CAST (mp_limb_t, GMP_NUMB_MASK / 5)))
1341 #endif
1343 #if GMP_NUMB_BITS % 6 == 0
1344 #define mpn_divexact_by7(dst,src,size) \
1345 (7 & 1 * mpn_bdiv_dbm1 (dst, src, size, __GMP_CAST (mp_limb_t, GMP_NUMB_MASK / 7)))
1346 #endif
1348 #if GMP_NUMB_BITS % 6 == 0
1349 #define mpn_divexact_by9(dst,src,size) \
1350 (15 & 7 * mpn_bdiv_dbm1 (dst, src, size, __GMP_CAST (mp_limb_t, GMP_NUMB_MASK / 9)))
1351 #endif
1353 #if GMP_NUMB_BITS % 10 == 0
1354 #define mpn_divexact_by11(dst,src,size) \
1355 (15 & 5 * mpn_bdiv_dbm1 (dst, src, size, __GMP_CAST (mp_limb_t, GMP_NUMB_MASK / 11)))
1356 #endif
1358 #if GMP_NUMB_BITS % 12 == 0
1359 #define mpn_divexact_by13(dst,src,size) \
1360 (15 & 3 * mpn_bdiv_dbm1 (dst, src, size, __GMP_CAST (mp_limb_t, GMP_NUMB_MASK / 13)))
1361 #endif
1363 #if GMP_NUMB_BITS % 4 == 0
1364 #define mpn_divexact_by15(dst,src,size) \
1365 (15 & 1 * mpn_bdiv_dbm1 (dst, src, size, __GMP_CAST (mp_limb_t, GMP_NUMB_MASK / 15)))
1366 #endif
1368 #define mpz_divexact_gcd __gmpz_divexact_gcd
1371 #define mpz_inp_str_nowhite __gmpz_inp_str_nowhite
1372 #ifdef _GMP_H_HAVE_FILE
1374 #endif
1376 #define mpn_divisible_p __MPN(divisible_p)
1377 __GMP_DECLSPEC int mpn_divisible_p __GMP_PROTO ((mp_srcptr, mp_size_t, mp_srcptr, mp_size_t)) __GMP_ATTRIBUTE_PURE;
1379 #define mpn_rootrem __MPN(rootrem)
1380 __GMP_DECLSPEC mp_size_t mpn_rootrem __GMP_PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_size_t, mp_limb_t));
1383 #if defined (_CRAY)
1384 #define MPN_COPY_INCR(dst, src, n) \
1385 do { \
1388 for (__i = 0; __i < (n); __i++) \
1389 (dst)[__i] = (src)[__i]; \
1390 } while (0)
1391 #endif
1393 /* used by test programs, hence __GMP_DECLSPEC */
1395 #define mpn_copyi __MPN(copyi)
1397 #endif
1399 #if ! defined (MPN_COPY_INCR) && HAVE_NATIVE_mpn_copyi
1400 #define MPN_COPY_INCR(dst, src, size) \
1401 do { \
1402 ASSERT ((size) >= 0); \
1403 ASSERT (MPN_SAME_OR_INCR_P (dst, src, size)); \
1404 mpn_copyi (dst, src, size); \
1405 } while (0)
1406 #endif
1408 /* Copy N limbs from SRC to DST incrementing, N==0 allowed. */
1409 #if ! defined (MPN_COPY_INCR)
1410 #define MPN_COPY_INCR(dst, src, n) \
1411 do { \
1412 ASSERT ((n) >= 0); \
1413 ASSERT (MPN_SAME_OR_INCR_P (dst, src, n)); \
1414 if ((n) != 0) \
1415 { \
1416 mp_size_t __n = (n) - 1; \
1417 mp_ptr __dst = (dst); \
1418 mp_srcptr __src = (src); \
1419 mp_limb_t __x; \
1420 __x = *__src++; \
1421 if (__n != 0) \
1422 { \
1423 do \
1424 { \
1425 *__dst++ = __x; \
1426 __x = *__src++; \
1427 } \
1428 while (--__n); \
1429 } \
1430 *__dst++ = __x; \
1431 } \
1432 } while (0)
1433 #endif
1436 #if defined (_CRAY)
1437 #define MPN_COPY_DECR(dst, src, n) \
1438 do { \
1441 for (__i = (n) - 1; __i >= 0; __i--) \
1442 (dst)[__i] = (src)[__i]; \
1443 } while (0)
1444 #endif
1446 /* used by test programs, hence __GMP_DECLSPEC */
1448 #define mpn_copyd __MPN(copyd)
1450 #endif
1452 #if ! defined (MPN_COPY_DECR) && HAVE_NATIVE_mpn_copyd
1453 #define MPN_COPY_DECR(dst, src, size) \
1454 do { \
1455 ASSERT ((size) >= 0); \
1456 ASSERT (MPN_SAME_OR_DECR_P (dst, src, size)); \
1457 mpn_copyd (dst, src, size); \
1458 } while (0)
1459 #endif
1461 /* Copy N limbs from SRC to DST decrementing, N==0 allowed. */
1462 #if ! defined (MPN_COPY_DECR)
1463 #define MPN_COPY_DECR(dst, src, n) \
1464 do { \
1465 ASSERT ((n) >= 0); \
1466 ASSERT (MPN_SAME_OR_DECR_P (dst, src, n)); \
1467 if ((n) != 0) \
1468 { \
1469 mp_size_t __n = (n) - 1; \
1470 mp_ptr __dst = (dst) + __n; \
1471 mp_srcptr __src = (src) + __n; \
1472 mp_limb_t __x; \
1473 __x = *__src--; \
1474 if (__n != 0) \
1475 { \
1476 do \
1477 { \
1478 *__dst-- = __x; \
1479 __x = *__src--; \
1480 } \
1481 while (--__n); \
1482 } \
1483 *__dst-- = __x; \
1484 } \
1485 } while (0)
1486 #endif
1489 #ifndef MPN_COPY
1490 #define MPN_COPY(d,s,n) \
1491 do { \
1492 ASSERT (MPN_SAME_OR_SEPARATE_P (d, s, n)); \
1493 MPN_COPY_INCR (d, s, n); \
1494 } while (0)
1495 #endif
1498 /* Set {dst,size} to the limbs of {src,size} in reverse order. */
1499 #define MPN_REVERSE(dst, src, size) \
1500 do { \
1501 mp_ptr __dst = (dst); \
1502 mp_size_t __size = (size); \
1503 mp_srcptr __src = (src) + __size - 1; \
1504 mp_size_t __i; \
1505 ASSERT ((size) >= 0); \
1506 ASSERT (! MPN_OVERLAP_P (dst, size, src, size)); \
1508 for (__i = 0; __i < __size; __i++) \
1509 { \
1510 *__dst = *__src; \
1511 __dst++; \
1512 __src--; \
1513 } \
1514 } while (0)
1517 /* Zero n limbs at dst.
1519 For power and powerpc we want an inline stu/bdnz loop for zeroing. On
1520 ppc630 for instance this is optimal since it can sustain only 1 store per
1521 cycle.
1523 gcc 2.95.x (for powerpc64 -maix64, or powerpc32) doesn't recognise the
1524 "for" loop in the generic code below can become stu/bdnz. The do/while
1525 here helps it get to that. The same caveat about plain -mpowerpc64 mode
1526 applies here as to __GMPN_COPY_INCR in gmp.h.
1528 xlc 3.1 already generates stu/bdnz from the generic C, and does so from
1529 this loop too.
1531 Enhancement: GLIBC does some trickery with dcbz to zero whole cache lines
1532 at a time. MPN_ZERO isn't all that important in GMP, so it might be more
1533 trouble than it's worth to do the same, though perhaps a call to memset
1534 would be good when on a GNU system. */
1536 #if HAVE_HOST_CPU_FAMILY_power || HAVE_HOST_CPU_FAMILY_powerpc
1537 #define MPN_ZERO(dst, n) \
1538 do { \
1539 ASSERT ((n) >= 0); \
1540 if ((n) != 0) \
1541 { \
1542 mp_ptr __dst = (dst) - 1; \
1543 mp_size_t __n = (n); \
1544 do \
1545 *++__dst = 0; \
1546 while (--__n); \
1547 } \
1548 } while (0)
1549 #endif
1551 #ifndef MPN_ZERO
1552 #define MPN_ZERO(dst, n) \
1553 do { \
1554 ASSERT ((n) >= 0); \
1555 if ((n) != 0) \
1556 { \
1557 mp_ptr __dst = (dst); \
1558 mp_size_t __n = (n); \
1559 do \
1560 *__dst++ = 0; \
1561 while (--__n); \
1562 } \
1563 } while (0)
1564 #endif
1567 /* On the x86s repe/scasl doesn't seem useful, since it takes many cycles to
1568 start up and would need to strip a lot of zeros before it'd be faster
1569 than a simple cmpl loop. Here are some times in cycles for
1570 std/repe/scasl/cld and cld/repe/scasl (the latter would be for stripping
1571 low zeros).
1573 std cld
1574 P5 18 16
1575 P6 46 38
1576 K6 36 13
1577 K7 21 20
1578 */
1579 #ifndef MPN_NORMALIZE
1580 #define MPN_NORMALIZE(DST, NLIMBS) \
1581 do { \
1582 while ((NLIMBS) > 0) \
1583 { \
1584 if ((DST)[(NLIMBS) - 1] != 0) \
1585 break; \
1586 (NLIMBS)--; \
1587 } \
1588 } while (0)
1589 #endif
1590 #ifndef MPN_NORMALIZE_NOT_ZERO
1591 #define MPN_NORMALIZE_NOT_ZERO(DST, NLIMBS) \
1592 do { \
1593 ASSERT ((NLIMBS) >= 1); \
1594 while (1) \
1595 { \
1596 if ((DST)[(NLIMBS) - 1] != 0) \
1597 break; \
1598 (NLIMBS)--; \
1599 } \
1600 } while (0)
1601 #endif
1603 /* Strip least significant zero limbs from {ptr,size} by incrementing ptr
1604 and decrementing size. low should be ptr[0], and will be the new ptr[0]
1605 on returning. The number in {ptr,size} must be non-zero, ie. size!=0 and
1606 somewhere a non-zero limb. */
1607 #define MPN_STRIP_LOW_ZEROS_NOT_ZERO(ptr, size, low) \
1608 do { \
1609 ASSERT ((size) >= 1); \
1610 ASSERT ((low) == (ptr)[0]); \
1611 \
1612 while ((low) == 0) \
1613 { \
1614 (size)--; \
1615 ASSERT ((size) >= 1); \
1616 (ptr)++; \
1617 (low) = *(ptr); \
1618 } \
1619 } while (0)
1621 /* Initialize X of type mpz_t with space for NLIMBS limbs. X should be a
1622 temporary variable; it will be automatically cleared out at function
1623 return. We use __x here to make it possible to accept both mpz_ptr and
1624 mpz_t arguments. */
1625 #define MPZ_TMP_INIT(X, NLIMBS) \
1626 do { \
1627 mpz_ptr __x = (X); \
1628 ASSERT ((NLIMBS) >= 1); \
1629 __x->_mp_alloc = (NLIMBS); \
1630 __x->_mp_d = TMP_ALLOC_LIMBS (NLIMBS); \
1631 } while (0)
1633 /* Realloc for an mpz_t WHAT if it has less than NEEDED limbs. */
1634 #define MPZ_REALLOC(z,n) (UNLIKELY ((n) > ALLOC(z)) \
1635 ? (mp_ptr) _mpz_realloc(z,n) \
1636 : PTR(z))
1638 #define MPZ_EQUAL_1_P(z) (SIZ(z)==1 && PTR(z)[0] == 1)
1641 /* MPN_FIB2_SIZE(n) is the size in limbs required by mpn_fib2_ui for fp and
1642 f1p.
1644 From Knuth vol 1 section 1.2.8, F[n] = phi^n/sqrt(5) rounded to the
1645 nearest integer, where phi=(1+sqrt(5))/2 is the golden ratio. So the
1646 number of bits required is n*log_2((1+sqrt(5))/2) = n*0.6942419.
1648 The multiplier used is 23/32=0.71875 for efficient calculation on CPUs
1649 without good floating point. There's +2 for rounding up, and a further
1650 +2 since at the last step x limbs are doubled into a 2x+1 limb region
1651 whereas the actual F[2k] value might be only 2x-1 limbs.
1653 Note that a division is done first, since on a 32-bit system it's at
1654 least conceivable to go right up to n==ULONG_MAX. (F[2^32-1] would be
1655 about 380Mbytes, plus temporary workspace of about 1.2Gbytes here and
1656 whatever a multiply of two 190Mbyte numbers takes.)
1658 Enhancement: When GMP_NUMB_BITS is not a power of 2 the division could be
1659 worked into the multiplier. */
1661 #define MPN_FIB2_SIZE(n) \
1662 ((mp_size_t) ((n) / 32 * 23 / GMP_NUMB_BITS) + 4)
1665 /* FIB_TABLE(n) returns the Fibonacci number F[n]. Must have n in the range
1666 -1 <= n <= FIB_TABLE_LIMIT (that constant in fib_table.h).
1668 FIB_TABLE_LUCNUM_LIMIT (in fib_table.h) is the largest n for which L[n] =
1669 F[n] + 2*F[n-1] fits in a limb. */
1672 #define FIB_TABLE(n) (__gmp_fib_table[(n)+1])
1676 {
1683 #define gmp_init_primesieve __gmp_init_primesieve
1686 #define gmp_nextprime __gmp_nextprime
1690 #ifndef MUL_TOOM22_THRESHOLD
1691 #define MUL_TOOM22_THRESHOLD 30
1692 #endif
1694 #ifndef MUL_TOOM33_THRESHOLD
1695 #define MUL_TOOM33_THRESHOLD 100
1696 #endif
1698 #ifndef MUL_TOOM44_THRESHOLD
1699 #define MUL_TOOM44_THRESHOLD 300
1700 #endif
1702 #ifndef MUL_TOOM6H_THRESHOLD
1703 #define MUL_TOOM6H_THRESHOLD 350
1704 #endif
1706 #ifndef SQR_TOOM6_THRESHOLD
1707 #define SQR_TOOM6_THRESHOLD MUL_TOOM6H_THRESHOLD
1708 #endif
1710 #ifndef MUL_TOOM8H_THRESHOLD
1711 #define MUL_TOOM8H_THRESHOLD 450
1712 #endif
1714 #ifndef SQR_TOOM8_THRESHOLD
1715 #define SQR_TOOM8_THRESHOLD MUL_TOOM8H_THRESHOLD
1716 #endif
1718 #ifndef MUL_TOOM32_TO_TOOM43_THRESHOLD
1719 #define MUL_TOOM32_TO_TOOM43_THRESHOLD 100
1720 #endif
1722 #ifndef MUL_TOOM32_TO_TOOM53_THRESHOLD
1723 #define MUL_TOOM32_TO_TOOM53_THRESHOLD 110
1724 #endif
1726 #ifndef MUL_TOOM42_TO_TOOM53_THRESHOLD
1727 #define MUL_TOOM42_TO_TOOM53_THRESHOLD 100
1728 #endif
1730 #ifndef MUL_TOOM42_TO_TOOM63_THRESHOLD
1731 #define MUL_TOOM42_TO_TOOM63_THRESHOLD 110
1732 #endif
1734 /* MUL_TOOM22_THRESHOLD_LIMIT is the maximum for MUL_TOOM22_THRESHOLD. In a
1735 normal build MUL_TOOM22_THRESHOLD is a constant and we use that. In a fat
1736 binary or tune program build MUL_TOOM22_THRESHOLD is a variable and a
1737 separate hard limit will have been defined. Similarly for TOOM3. */
1738 #ifndef MUL_TOOM22_THRESHOLD_LIMIT
1739 #define MUL_TOOM22_THRESHOLD_LIMIT MUL_TOOM22_THRESHOLD
1740 #endif
1741 #ifndef MUL_TOOM33_THRESHOLD_LIMIT
1742 #define MUL_TOOM33_THRESHOLD_LIMIT MUL_TOOM33_THRESHOLD
1743 #endif
1744 #ifndef MULLO_BASECASE_THRESHOLD_LIMIT
1745 #define MULLO_BASECASE_THRESHOLD_LIMIT MULLO_BASECASE_THRESHOLD
1746 #endif
1748 /* SQR_BASECASE_THRESHOLD is where mpn_sqr_basecase should take over from
1749 mpn_mul_basecase. Default is to use mpn_sqr_basecase from 0. (Note that we
1750 certainly always want it if there's a native assembler mpn_sqr_basecase.)
1752 If it turns out that mpn_toom2_sqr becomes faster than mpn_mul_basecase
1753 before mpn_sqr_basecase does, then SQR_BASECASE_THRESHOLD is the toom2
1754 threshold and SQR_TOOM2_THRESHOLD is 0. This oddity arises more or less
1755 because SQR_TOOM2_THRESHOLD represents the size up to which mpn_sqr_basecase
1756 should be used, and that may be never. */
1758 #ifndef SQR_BASECASE_THRESHOLD
1759 #define SQR_BASECASE_THRESHOLD 0
1760 #endif
1762 #ifndef SQR_TOOM2_THRESHOLD
1763 #define SQR_TOOM2_THRESHOLD 50
1764 #endif
1766 #ifndef SQR_TOOM3_THRESHOLD
1767 #define SQR_TOOM3_THRESHOLD 120
1768 #endif
1770 #ifndef SQR_TOOM4_THRESHOLD
1771 #define SQR_TOOM4_THRESHOLD 400
1772 #endif
1774 /* See comments above about MUL_TOOM33_THRESHOLD_LIMIT. */
1775 #ifndef SQR_TOOM3_THRESHOLD_LIMIT
1776 #define SQR_TOOM3_THRESHOLD_LIMIT SQR_TOOM3_THRESHOLD
1777 #endif
1779 #ifndef DC_DIV_QR_THRESHOLD
1780 #define DC_DIV_QR_THRESHOLD 50
1781 #endif
1783 #ifndef DC_DIVAPPR_Q_THRESHOLD
1784 #define DC_DIVAPPR_Q_THRESHOLD 200
1785 #endif
1787 #ifndef DC_BDIV_QR_THRESHOLD
1788 #define DC_BDIV_QR_THRESHOLD 50
1789 #endif
1791 #ifndef DC_BDIV_Q_THRESHOLD
1792 #define DC_BDIV_Q_THRESHOLD 180
1793 #endif
1795 #ifndef DIVEXACT_JEB_THRESHOLD
1796 #define DIVEXACT_JEB_THRESHOLD 25
1797 #endif
1799 #ifndef INV_MULMOD_BNM1_THRESHOLD
1800 #define INV_MULMOD_BNM1_THRESHOLD (5*MULMOD_BNM1_THRESHOLD)
1801 #endif
1803 #ifndef INV_APPR_THRESHOLD
1804 #define INV_APPR_THRESHOLD INV_NEWTON_THRESHOLD
1805 #endif
1807 #ifndef INV_NEWTON_THRESHOLD
1808 #define INV_NEWTON_THRESHOLD 200
1809 #endif
1811 #ifndef BINV_NEWTON_THRESHOLD
1812 #define BINV_NEWTON_THRESHOLD 300
1813 #endif
1815 #ifndef MU_DIVAPPR_Q_THRESHOLD
1816 #define MU_DIVAPPR_Q_THRESHOLD 2000
1817 #endif
1819 #ifndef MU_DIV_QR_THRESHOLD
1820 #define MU_DIV_QR_THRESHOLD 2000
1821 #endif
1823 #ifndef MUPI_DIV_QR_THRESHOLD
1824 #define MUPI_DIV_QR_THRESHOLD 200
1825 #endif
1827 #ifndef MU_BDIV_Q_THRESHOLD
1828 #define MU_BDIV_Q_THRESHOLD 2000
1829 #endif
1831 #ifndef MU_BDIV_QR_THRESHOLD
1832 #define MU_BDIV_QR_THRESHOLD 2000
1833 #endif
1835 #ifndef MULMOD_BNM1_THRESHOLD
1836 #define MULMOD_BNM1_THRESHOLD 16
1837 #endif
1839 #ifndef SQRMOD_BNM1_THRESHOLD
1840 #define SQRMOD_BNM1_THRESHOLD 16
1841 #endif
1843 #ifndef MUL_TO_MULMOD_BNM1_FOR_2NXN_THRESHOLD
1844 #define MUL_TO_MULMOD_BNM1_FOR_2NXN_THRESHOLD (INV_MULMOD_BNM1_THRESHOLD/2)
1845 #endif
1847 #if HAVE_NATIVE_mpn_addmul_2 || HAVE_NATIVE_mpn_redc_2
1849 #ifndef REDC_1_TO_REDC_2_THRESHOLD
1850 #define REDC_1_TO_REDC_2_THRESHOLD 15
1851 #endif
1852 #ifndef REDC_2_TO_REDC_N_THRESHOLD
1853 #define REDC_2_TO_REDC_N_THRESHOLD 100
1854 #endif
1856 #else
1858 #ifndef REDC_1_TO_REDC_N_THRESHOLD
1859 #define REDC_1_TO_REDC_N_THRESHOLD 100
1860 #endif
1865 /* First k to use for an FFT modF multiply. A modF FFT is an order
1866 log(2^k)/log(2^(k-1)) algorithm, so k=3 is merely 1.5 like karatsuba,
1867 whereas k=4 is 1.33 which is faster than toom3 at 1.485. */
1868 #define FFT_FIRST_K 4
1870 /* Threshold at which FFT should be used to do a modF NxN -> N multiply. */
1871 #ifndef MUL_FFT_MODF_THRESHOLD
1872 #define MUL_FFT_MODF_THRESHOLD (MUL_TOOM33_THRESHOLD * 3)
1873 #endif
1874 #ifndef SQR_FFT_MODF_THRESHOLD
1875 #define SQR_FFT_MODF_THRESHOLD (SQR_TOOM3_THRESHOLD * 3)
1876 #endif
1878 /* Threshold at which FFT should be used to do an NxN -> 2N multiply. This
1879 will be a size where FFT is using k=7 or k=8, since an FFT-k used for an
1880 NxN->2N multiply and not recursing into itself is an order
1881 log(2^k)/log(2^(k-2)) algorithm, so it'll be at least k=7 at 1.39 which
1882 is the first better than toom3. */
1883 #ifndef MUL_FFT_THRESHOLD
1884 #define MUL_FFT_THRESHOLD (MUL_FFT_MODF_THRESHOLD * 10)
1885 #endif
1886 #ifndef SQR_FFT_THRESHOLD
1887 #define SQR_FFT_THRESHOLD (SQR_FFT_MODF_THRESHOLD * 10)
1888 #endif
1890 /* Table of thresholds for successive modF FFT "k"s. The first entry is
1891 where FFT_FIRST_K+1 should be used, the second FFT_FIRST_K+2,
1892 etc. See mpn_fft_best_k(). */
1893 #ifndef MUL_FFT_TABLE
1894 #define MUL_FFT_TABLE \
1901 0 }
1902 #endif
1903 #ifndef SQR_FFT_TABLE
1904 #define SQR_FFT_TABLE \
1911 0 }
1912 #endif
1914 struct fft_table_nk
1915 {
1918 };
1920 #ifndef FFT_TABLE_ATTRS
1921 #define FFT_TABLE_ATTRS static const
1922 #endif
1924 #define MPN_FFT_TABLE_SIZE 16
1927 #ifndef DC_DIV_QR_THRESHOLD
1928 #define DC_DIV_QR_THRESHOLD (3 * MUL_TOOM22_THRESHOLD)
1929 #endif
1931 #ifndef GET_STR_DC_THRESHOLD
1932 #define GET_STR_DC_THRESHOLD 18
1933 #endif
1935 #ifndef GET_STR_PRECOMPUTE_THRESHOLD
1936 #define GET_STR_PRECOMPUTE_THRESHOLD 35
1937 #endif
1939 #ifndef SET_STR_DC_THRESHOLD
1940 #define SET_STR_DC_THRESHOLD 750
1941 #endif
1943 #ifndef SET_STR_PRECOMPUTE_THRESHOLD
1944 #define SET_STR_PRECOMPUTE_THRESHOLD 2000
1945 #endif
1947 /* Return non-zero if xp,xsize and yp,ysize overlap.
1948 If xp+xsize<=yp there's no overlap, or if yp+ysize<=xp there's no
1949 overlap. If both these are false, there's an overlap. */
1950 #define MPN_OVERLAP_P(xp, xsize, yp, ysize) \
1951 ((xp) + (xsize) > (yp) && (yp) + (ysize) > (xp))
1952 #define MEM_OVERLAP_P(xp, xsize, yp, ysize) \
1953 ( (char *) (xp) + (xsize) > (char *) (yp) \
1954 && (char *) (yp) + (ysize) > (char *) (xp))
1956 /* Return non-zero if xp,xsize and yp,ysize are either identical or not
1957 overlapping. Return zero if they're partially overlapping. */
1958 #define MPN_SAME_OR_SEPARATE_P(xp, yp, size) \
1959 MPN_SAME_OR_SEPARATE2_P(xp, size, yp, size)
1960 #define MPN_SAME_OR_SEPARATE2_P(xp, xsize, yp, ysize) \
1961 ((xp) == (yp) || ! MPN_OVERLAP_P (xp, xsize, yp, ysize))
1963 /* Return non-zero if dst,dsize and src,ssize are either identical or
1964 overlapping in a way suitable for an incrementing/decrementing algorithm.
1965 Return zero if they're partially overlapping in an unsuitable fashion. */
1966 #define MPN_SAME_OR_INCR2_P(dst, dsize, src, ssize) \
1967 ((dst) <= (src) || ! MPN_OVERLAP_P (dst, dsize, src, ssize))
1968 #define MPN_SAME_OR_INCR_P(dst, src, size) \
1969 MPN_SAME_OR_INCR2_P(dst, size, src, size)
1970 #define MPN_SAME_OR_DECR2_P(dst, dsize, src, ssize) \
1971 ((dst) >= (src) || ! MPN_OVERLAP_P (dst, dsize, src, ssize))
1972 #define MPN_SAME_OR_DECR_P(dst, src, size) \
1973 MPN_SAME_OR_DECR2_P(dst, size, src, size)
1976 /* ASSERT() is a private assertion checking scheme, similar to <assert.h>.
1977 ASSERT() does the check only if WANT_ASSERT is selected, ASSERT_ALWAYS()
1978 does it always. Generally assertions are meant for development, but
1979 might help when looking for a problem later too.
1981 Note that strings shouldn't be used within the ASSERT expression,
1982 eg. ASSERT(strcmp(s,"notgood")!=0), since the quotes upset the "expr"
1983 used in the !HAVE_STRINGIZE case (ie. K&R). */
1985 #ifdef __LINE__
1986 #define ASSERT_LINE __LINE__
1987 #else
1988 #define ASSERT_LINE -1
1989 #endif
1991 #ifdef __FILE__
1992 #define ASSERT_FILE __FILE__
1993 #else
1995 #endif
1998 __GMP_DECLSPEC void __gmp_assert_fail __GMP_PROTO ((const char *, int, const char *)) ATTRIBUTE_NORETURN;
2000 #if HAVE_STRINGIZE
2001 #define ASSERT_FAIL(expr) __gmp_assert_fail (ASSERT_FILE, ASSERT_LINE, #expr)
2002 #else
2004 #endif
2006 #define ASSERT_ALWAYS(expr) \
2007 do { \
2008 if (!(expr)) \
2009 ASSERT_FAIL (expr); \
2010 } while (0)
2012 #if WANT_ASSERT
2013 #define ASSERT(expr) ASSERT_ALWAYS (expr)
2014 #else
2015 #define ASSERT(expr) do {} while (0)
2016 #endif
2019 /* ASSERT_CARRY checks the expression is non-zero, and ASSERT_NOCARRY checks
2020 that it's zero. In both cases if assertion checking is disabled the
2021 expression is still evaluated. These macros are meant for use with
2022 routines like mpn_add_n() where the return value represents a carry or
2023 whatever that should or shouldn't occur in some context. For example,
2024 ASSERT_NOCARRY (mpn_add_n (rp, s1p, s2p, size)); */
2025 #if WANT_ASSERT
2026 #define ASSERT_CARRY(expr) ASSERT_ALWAYS ((expr) != 0)
2027 #define ASSERT_NOCARRY(expr) ASSERT_ALWAYS ((expr) == 0)
2028 #else
2029 #define ASSERT_CARRY(expr) (expr)
2030 #define ASSERT_NOCARRY(expr) (expr)
2031 #endif
2034 /* ASSERT_CODE includes code when assertion checking is wanted. This is the
2035 same as writing "#if WANT_ASSERT", but more compact. */
2036 #if WANT_ASSERT
2037 #define ASSERT_CODE(expr) expr
2038 #else
2039 #define ASSERT_CODE(expr)
2040 #endif
2043 /* Test that an mpq_t is in fully canonical form. This can be used as
2044 protection on routines like mpq_equal which give wrong results on
2045 non-canonical inputs. */
2046 #if WANT_ASSERT
2047 #define ASSERT_MPQ_CANONICAL(q) \
2048 do { \
2049 ASSERT (q->_mp_den._mp_size > 0); \
2050 if (q->_mp_num._mp_size == 0) \
2051 { \
2053 ASSERT (mpz_cmp_ui (mpq_denref(q), 1L) == 0); \
2054 } \
2055 else \
2056 { \
2058 mpz_t __g; \
2059 mpz_init (__g); \
2060 mpz_gcd (__g, mpq_numref(q), mpq_denref(q)); \
2061 ASSERT (mpz_cmp_ui (__g, 1) == 0); \
2062 mpz_clear (__g); \
2063 } \
2064 } while (0)
2065 #else
2066 #define ASSERT_MPQ_CANONICAL(q) do {} while (0)
2067 #endif
2069 /* Check that the nail parts are zero. */
2070 #define ASSERT_ALWAYS_LIMB(limb) \
2071 do { \
2072 mp_limb_t __nail = (limb) & GMP_NAIL_MASK; \
2073 ASSERT_ALWAYS (__nail == 0); \
2074 } while (0)
2075 #define ASSERT_ALWAYS_MPN(ptr, size) \
2076 do { \
2078 if (GMP_NAIL_BITS != 0) \
2079 { \
2080 mp_size_t __i; \
2081 for (__i = 0; __i < (size); __i++) \
2082 ASSERT_ALWAYS_LIMB ((ptr)[__i]); \
2083 } \
2084 } while (0)
2085 #if WANT_ASSERT
2086 #define ASSERT_LIMB(limb) ASSERT_ALWAYS_LIMB (limb)
2087 #define ASSERT_MPN(ptr, size) ASSERT_ALWAYS_MPN (ptr, size)
2088 #else
2089 #define ASSERT_LIMB(limb) do {} while (0)
2090 #define ASSERT_MPN(ptr, size) do {} while (0)
2091 #endif
2094 /* Assert that an mpn region {ptr,size} is zero, or non-zero.
2095 size==0 is allowed, and in that case {ptr,size} considered to be zero. */
2096 #if WANT_ASSERT
2097 #define ASSERT_MPN_ZERO_P(ptr,size) \
2098 do { \
2099 mp_size_t __i; \
2100 ASSERT ((size) >= 0); \
2101 for (__i = 0; __i < (size); __i++) \
2102 ASSERT ((ptr)[__i] == 0); \
2103 } while (0)
2104 #define ASSERT_MPN_NONZERO_P(ptr,size) \
2105 do { \
2106 mp_size_t __i; \
2107 int __nonzero = 0; \
2108 ASSERT ((size) >= 0); \
2109 for (__i = 0; __i < (size); __i++) \
2110 if ((ptr)[__i] != 0) \
2111 { \
2112 __nonzero = 1; \
2113 break; \
2114 } \
2115 ASSERT (__nonzero); \
2116 } while (0)
2117 #else
2118 #define ASSERT_MPN_ZERO_P(ptr,size) do {} while (0)
2119 #define ASSERT_MPN_NONZERO_P(ptr,size) do {} while (0)
2120 #endif
2123 #if ! HAVE_NATIVE_mpn_com
2124 #undef mpn_com
2125 #define mpn_com(d,s,n) \
2126 do { \
2127 mp_ptr __d = (d); \
2128 mp_srcptr __s = (s); \
2129 mp_size_t __n = (n); \
2130 ASSERT (__n >= 1); \
2131 ASSERT (MPN_SAME_OR_SEPARATE_P (__d, __s, __n)); \
2132 do \
2133 *__d++ = (~ *__s++) & GMP_NUMB_MASK; \
2134 while (--__n); \
2135 } while (0)
2136 #endif
2138 #define MPN_LOGOPS_N_INLINE(rp, up, vp, n, operation) \
2139 do { \
2140 mp_srcptr __up = (up); \
2141 mp_srcptr __vp = (vp); \
2142 mp_ptr __rp = (rp); \
2143 mp_size_t __n = (n); \
2144 mp_limb_t __a, __b; \
2145 ASSERT (__n > 0); \
2146 ASSERT (MPN_SAME_OR_SEPARATE_P (__rp, __up, __n)); \
2147 ASSERT (MPN_SAME_OR_SEPARATE_P (__rp, __vp, __n)); \
2148 __up += __n; \
2149 __vp += __n; \
2150 __rp += __n; \
2151 __n = -__n; \
2152 do { \
2153 __a = __up[__n]; \
2154 __b = __vp[__n]; \
2155 __rp[__n] = operation; \
2156 } while (++__n); \
2157 } while (0)
2160 #if ! HAVE_NATIVE_mpn_and_n
2161 #undef mpn_and_n
2162 #define mpn_and_n(rp, up, vp, n) \
2163 MPN_LOGOPS_N_INLINE (rp, up, vp, n, __a & __b)
2164 #endif
2166 #if ! HAVE_NATIVE_mpn_andn_n
2167 #undef mpn_andn_n
2168 #define mpn_andn_n(rp, up, vp, n) \
2169 MPN_LOGOPS_N_INLINE (rp, up, vp, n, __a & ~__b)
2170 #endif
2172 #if ! HAVE_NATIVE_mpn_nand_n
2173 #undef mpn_nand_n
2174 #define mpn_nand_n(rp, up, vp, n) \
2175 MPN_LOGOPS_N_INLINE (rp, up, vp, n, ~(__a & __b) & GMP_NUMB_MASK)
2176 #endif
2178 #if ! HAVE_NATIVE_mpn_ior_n
2179 #undef mpn_ior_n
2180 #define mpn_ior_n(rp, up, vp, n) \
2181 MPN_LOGOPS_N_INLINE (rp, up, vp, n, __a | __b)
2182 #endif
2184 #if ! HAVE_NATIVE_mpn_iorn_n
2185 #undef mpn_iorn_n
2186 #define mpn_iorn_n(rp, up, vp, n) \
2187 MPN_LOGOPS_N_INLINE (rp, up, vp, n, (__a | ~__b) & GMP_NUMB_MASK)
2188 #endif
2190 #if ! HAVE_NATIVE_mpn_nior_n
2191 #undef mpn_nior_n
2192 #define mpn_nior_n(rp, up, vp, n) \
2193 MPN_LOGOPS_N_INLINE (rp, up, vp, n, ~(__a | __b) & GMP_NUMB_MASK)
2194 #endif
2196 #if ! HAVE_NATIVE_mpn_xor_n
2197 #undef mpn_xor_n
2198 #define mpn_xor_n(rp, up, vp, n) \
2199 MPN_LOGOPS_N_INLINE (rp, up, vp, n, __a ^ __b)
2200 #endif
2202 #if ! HAVE_NATIVE_mpn_xnor_n
2203 #undef mpn_xnor_n
2204 #define mpn_xnor_n(rp, up, vp, n) \
2205 MPN_LOGOPS_N_INLINE (rp, up, vp, n, ~(__a ^ __b) & GMP_NUMB_MASK)
2206 #endif
2208 #define mpn_trialdiv __MPN(trialdiv)
2211 #define mpn_remove __MPN(remove)
2212 __GMP_DECLSPEC mp_bitcnt_t mpn_remove __GMP_PROTO ((mp_ptr, mp_size_t *, mp_ptr, mp_size_t, mp_ptr, mp_size_t, mp_bitcnt_t));
2215 /* ADDC_LIMB sets w=x+y and cout to 0 or 1 for a carry from that addition. */
2216 #if GMP_NAIL_BITS == 0
2217 #define ADDC_LIMB(cout, w, x, y) \
2218 do { \
2219 mp_limb_t __x = (x); \
2220 mp_limb_t __y = (y); \
2221 mp_limb_t __w = __x + __y; \
2222 (w) = __w; \
2223 (cout) = __w < __x; \
2224 } while (0)
2225 #else
2226 #define ADDC_LIMB(cout, w, x, y) \
2227 do { \
2228 mp_limb_t __w; \
2229 ASSERT_LIMB (x); \
2230 ASSERT_LIMB (y); \
2231 __w = (x) + (y); \
2232 (w) = __w & GMP_NUMB_MASK; \
2233 (cout) = __w >> GMP_NUMB_BITS; \
2234 } while (0)
2235 #endif
2237 /* SUBC_LIMB sets w=x-y and cout to 0 or 1 for a borrow from that
2238 subtract. */
2239 #if GMP_NAIL_BITS == 0
2240 #define SUBC_LIMB(cout, w, x, y) \
2241 do { \
2242 mp_limb_t __x = (x); \
2243 mp_limb_t __y = (y); \
2244 mp_limb_t __w = __x - __y; \
2245 (w) = __w; \
2246 (cout) = __w > __x; \
2247 } while (0)
2248 #else
2249 #define SUBC_LIMB(cout, w, x, y) \
2250 do { \
2251 mp_limb_t __w = (x) - (y); \
2252 (w) = __w & GMP_NUMB_MASK; \
2253 (cout) = __w >> (GMP_LIMB_BITS-1); \
2254 } while (0)
2255 #endif
2258 /* MPN_INCR_U does {ptr,size} += n, MPN_DECR_U does {ptr,size} -= n, both
2259 expecting no carry (or borrow) from that.
2261 The size parameter is only for the benefit of assertion checking. In a
2262 normal build it's unused and the carry/borrow is just propagated as far
2263 as it needs to go.
2265 On random data, usually only one or two limbs of {ptr,size} get updated,
2266 so there's no need for any sophisticated looping, just something compact
2267 and sensible.
2269 FIXME: Switch all code from mpn_{incr,decr}_u to MPN_{INCR,DECR}_U,
2270 declaring their operand sizes, then remove the former. This is purely
2271 for the benefit of assertion checking. */
2273 #if defined (__GNUC__) && HAVE_HOST_CPU_FAMILY_x86 && GMP_NAIL_BITS == 0 \
2274 && GMP_LIMB_BITS == 32 && ! defined (NO_ASM) && ! WANT_ASSERT
2275 /* Better flags handling than the generic C gives on i386, saving a few
2276 bytes of code and maybe a cycle or two. */
2278 #define MPN_IORD_U(ptr, incr, aors) \
2279 do { \
2280 mp_ptr __ptr_dummy; \
2281 if (__builtin_constant_p (incr) && (incr) == 1) \
2282 { \
2283 __asm__ __volatile__ \
2291 } \
2292 else \
2293 { \
2294 __asm__ __volatile__ \
2306 } \
2307 } while (0)
2311 #define mpn_incr_u(ptr, incr) MPN_INCR_U (ptr, 0, incr)
2312 #define mpn_decr_u(ptr, incr) MPN_DECR_U (ptr, 0, incr)
2313 #endif
2315 #if GMP_NAIL_BITS == 0
2316 #ifndef mpn_incr_u
2317 #define mpn_incr_u(p,incr) \
2318 do { \
2319 mp_limb_t __x; \
2320 mp_ptr __p = (p); \
2321 if (__builtin_constant_p (incr) && (incr) == 1) \
2322 { \
2323 while (++(*(__p++)) == 0) \
2324 ; \
2325 } \
2326 else \
2327 { \
2328 __x = *__p + (incr); \
2329 *__p = __x; \
2330 if (__x < (incr)) \
2331 while (++(*(++__p)) == 0) \
2332 ; \
2333 } \
2334 } while (0)
2335 #endif
2336 #ifndef mpn_decr_u
2337 #define mpn_decr_u(p,incr) \
2338 do { \
2339 mp_limb_t __x; \
2340 mp_ptr __p = (p); \
2341 if (__builtin_constant_p (incr) && (incr) == 1) \
2342 { \
2343 while ((*(__p++))-- == 0) \
2344 ; \
2345 } \
2346 else \
2347 { \
2348 __x = *__p; \
2349 *__p = __x - (incr); \
2350 if (__x < (incr)) \
2351 while ((*(++__p))-- == 0) \
2352 ; \
2353 } \
2354 } while (0)
2355 #endif
2356 #endif
2358 #if GMP_NAIL_BITS >= 1
2359 #ifndef mpn_incr_u
2360 #define mpn_incr_u(p,incr) \
2361 do { \
2362 mp_limb_t __x; \
2363 mp_ptr __p = (p); \
2364 if (__builtin_constant_p (incr) && (incr) == 1) \
2365 { \
2366 do \
2367 { \
2368 __x = (*__p + 1) & GMP_NUMB_MASK; \
2369 *__p++ = __x; \
2370 } \
2371 while (__x == 0); \
2372 } \
2373 else \
2374 { \
2375 __x = (*__p + (incr)); \
2376 *__p++ = __x & GMP_NUMB_MASK; \
2377 if (__x >> GMP_NUMB_BITS != 0) \
2378 { \
2379 do \
2380 { \
2381 __x = (*__p + 1) & GMP_NUMB_MASK; \
2382 *__p++ = __x; \
2383 } \
2384 while (__x == 0); \
2385 } \
2386 } \
2387 } while (0)
2388 #endif
2389 #ifndef mpn_decr_u
2390 #define mpn_decr_u(p,incr) \
2391 do { \
2392 mp_limb_t __x; \
2393 mp_ptr __p = (p); \
2394 if (__builtin_constant_p (incr) && (incr) == 1) \
2395 { \
2396 do \
2397 { \
2398 __x = *__p; \
2399 *__p++ = (__x - 1) & GMP_NUMB_MASK; \
2400 } \
2401 while (__x == 0); \
2402 } \
2403 else \
2404 { \
2405 __x = *__p - (incr); \
2406 *__p++ = __x & GMP_NUMB_MASK; \
2407 if (__x >> GMP_NUMB_BITS != 0) \
2408 { \
2409 do \
2410 { \
2411 __x = *__p; \
2412 *__p++ = (__x - 1) & GMP_NUMB_MASK; \
2413 } \
2414 while (__x == 0); \
2415 } \
2416 } \
2417 } while (0)
2418 #endif
2419 #endif
2421 #ifndef MPN_INCR_U
2422 #if WANT_ASSERT
2423 #define MPN_INCR_U(ptr, size, n) \
2424 do { \
2425 ASSERT ((size) >= 1); \
2426 ASSERT_NOCARRY (mpn_add_1 (ptr, ptr, size, n)); \
2427 } while (0)
2428 #else
2429 #define MPN_INCR_U(ptr, size, n) mpn_incr_u (ptr, n)
2430 #endif
2431 #endif
2433 #ifndef MPN_DECR_U
2434 #if WANT_ASSERT
2435 #define MPN_DECR_U(ptr, size, n) \
2436 do { \
2437 ASSERT ((size) >= 1); \
2438 ASSERT_NOCARRY (mpn_sub_1 (ptr, ptr, size, n)); \
2439 } while (0)
2440 #else
2441 #define MPN_DECR_U(ptr, size, n) mpn_decr_u (ptr, n)
2442 #endif
2443 #endif
2446 /* Structure for conversion between internal binary format and
2447 strings in base 2..36. */
2448 struct bases
2449 {
2450 /* Number of digits in the conversion base that always fits in an mp_limb_t.
2451 For example, for base 10 on a machine where a mp_limb_t has 32 bits this
2452 is 9, since 10**9 is the largest number that fits into a mp_limb_t. */
2455 /* log(2)/log(conversion_base) */
2458 /* base**chars_per_limb, i.e. the biggest number that fits a word, built by
2459 factors of base. Exception: For 2, 4, 8, etc, big_base is log2(base),
2460 i.e. the number of bits used to represent each digit in the base. */
2461 mp_limb_t big_base;
2463 /* A GMP_LIMB_BITS bit approximation to 1/big_base, represented as a
2464 fixed-point number. Instead of dividing by big_base an application can
2465 choose to multiply by big_base_inverted. */
2466 mp_limb_t big_base_inverted;
2467 };
2469 #define mp_bases __MPN(bases)
2473 /* For power of 2 bases this is exact. For other bases the result is either
2474 exact or one too big.
2476 To be exact always it'd be necessary to examine all the limbs of the
2477 operand, since numbers like 100..000 and 99...999 generally differ only
2478 in the lowest limb. It'd be possible to examine just a couple of high
2479 limbs to increase the probability of being exact, but that doesn't seem
2480 worth bothering with. */
2482 #define MPN_SIZEINBASE(result, ptr, size, base) \
2483 do { \
2484 int __lb_base, __cnt; \
2485 size_t __totbits; \
2486 \
2487 ASSERT ((size) >= 0); \
2488 ASSERT ((base) >= 2); \
2489 ASSERT ((base) < numberof (mp_bases)); \
2490 \
2492 if ((size) == 0) \
2493 (result) = 1; \
2494 else \
2495 { \
2497 count_leading_zeros (__cnt, (ptr)[(size)-1]); \
2498 __totbits = (size_t) (size) * GMP_NUMB_BITS - (__cnt - GMP_NAIL_BITS);\
2499 \
2500 if (POW2_P (base)) \
2501 { \
2502 __lb_base = mp_bases[base].big_base; \
2503 (result) = (__totbits + __lb_base - 1) / __lb_base; \
2504 } \
2505 else \
2506 (result) = (size_t) \
2507 (__totbits * mp_bases[base].chars_per_bit_exactly) + 1; \
2508 } \
2509 } while (0)
2511 /* eliminate mp_bases lookups for base==16 */
2512 #define MPN_SIZEINBASE_16(result, ptr, size) \
2513 do { \
2514 int __cnt; \
2515 mp_size_t __totbits; \
2516 \
2517 ASSERT ((size) >= 0); \
2518 \
2520 if ((size) == 0) \
2521 (result) = 1; \
2522 else \
2523 { \
2525 count_leading_zeros (__cnt, (ptr)[(size)-1]); \
2526 __totbits = (size_t) (size) * GMP_NUMB_BITS - (__cnt - GMP_NAIL_BITS);\
2527 (result) = (__totbits + 4 - 1) / 4; \
2528 } \
2529 } while (0)
2531 /* bit count to limb count, rounding up */
2532 #define BITS_TO_LIMBS(n) (((n) + (GMP_NUMB_BITS - 1)) / GMP_NUMB_BITS)
2534 /* MPN_SET_UI sets an mpn (ptr, cnt) to given ui. MPZ_FAKE_UI creates fake
2535 mpz_t from ui. The zp argument must have room for LIMBS_PER_ULONG limbs
2536 in both cases (LIMBS_PER_ULONG is also defined here.) */
2539 #define LIMBS_PER_ULONG 1
2540 #define MPN_SET_UI(zp, zn, u) \
2541 (zp)[0] = (u); \
2542 (zn) = ((zp)[0] != 0);
2543 #define MPZ_FAKE_UI(z, zp, u) \
2544 (zp)[0] = (u); \
2545 PTR (z) = (zp); \
2546 SIZ (z) = ((zp)[0] != 0); \
2547 ASSERT_CODE (ALLOC (z) = 1);
2551 #define LIMBS_PER_ULONG 2
2552 #define MPN_SET_UI(zp, zn, u) \
2553 (zp)[0] = (u) & GMP_NUMB_MASK; \
2554 (zp)[1] = (u) >> GMP_NUMB_BITS; \
2555 (zn) = ((zp)[1] != 0 ? 2 : (zp)[0] != 0 ? 1 : 0);
2556 #define MPZ_FAKE_UI(z, zp, u) \
2557 (zp)[0] = (u) & GMP_NUMB_MASK; \
2558 (zp)[1] = (u) >> GMP_NUMB_BITS; \
2559 SIZ (z) = ((zp)[1] != 0 ? 2 : (zp)[0] != 0 ? 1 : 0); \
2560 PTR (z) = (zp); \
2561 ASSERT_CODE (ALLOC (z) = 2);
2563 #endif
2566 #if HAVE_HOST_CPU_FAMILY_x86
2567 #define TARGET_REGISTER_STARVED 1
2568 #else
2569 #define TARGET_REGISTER_STARVED 0
2570 #endif
2573 /* LIMB_HIGHBIT_TO_MASK(n) examines the high bit of a limb value and turns 1
2574 or 0 there into a limb 0xFF..FF or 0 respectively.
2576 On most CPUs this is just an arithmetic right shift by GMP_LIMB_BITS-1,
2577 but C99 doesn't guarantee signed right shifts are arithmetic, so we have
2578 a little compile-time test and a fallback to a "? :" form. The latter is
2579 necessary for instance on Cray vector systems.
2581 Recent versions of gcc (eg. 3.3) will in fact optimize a "? :" like this
2582 to an arithmetic right shift anyway, but it's good to get the desired
2583 shift on past versions too (in particular since an important use of
2584 LIMB_HIGHBIT_TO_MASK is in udiv_qrnnd_preinv). */
2586 #define LIMB_HIGHBIT_TO_MASK(n) \
2587 (((mp_limb_signed_t) -1 >> 1) < 0 \
2588 ? (mp_limb_signed_t) (n) >> (GMP_LIMB_BITS - 1) \
2589 : (n) & GMP_LIMB_HIGHBIT ? MP_LIMB_T_MAX : CNST_LIMB(0))
2592 /* Use a library function for invert_limb, if available. */
2593 #define mpn_invert_limb __MPN(invert_limb)
2595 #if ! defined (invert_limb) && HAVE_NATIVE_mpn_invert_limb
2596 #define invert_limb(invxl,xl) \
2597 do { \
2598 (invxl) = mpn_invert_limb (xl); \
2599 } while (0)
2600 #endif
2602 #ifndef invert_limb
2603 #define invert_limb(invxl,xl) \
2604 do { \
2605 mp_limb_t dummy; \
2606 ASSERT ((xl) != 0); \
2607 udiv_qrnnd (invxl, dummy, ~(xl), ~CNST_LIMB(0), xl); \
2608 } while (0)
2609 #endif
2611 #define invert_pi1(dinv, d1, d0) \
2612 do { \
2613 mp_limb_t v, p, t1, t0, mask; \
2614 invert_limb (v, d1); \
2615 p = d1 * v; \
2616 p += d0; \
2617 if (p < d0) \
2618 { \
2619 v--; \
2620 mask = -(p >= d1); \
2621 p -= d1; \
2622 v += mask; \
2623 p -= mask & d1; \
2624 } \
2625 umul_ppmm (t1, t0, d0, v); \
2626 p += t1; \
2627 if (p < t1) \
2628 { \
2629 v--; \
2630 if (UNLIKELY (p >= d1)) \
2631 { \
2632 if (p > d1 || t0 >= d0) \
2633 v--; \
2634 } \
2635 } \
2636 (dinv).inv32 = v; \
2637 } while (0)
2640 #ifndef udiv_qrnnd_preinv
2641 #define udiv_qrnnd_preinv udiv_qrnnd_preinv3
2642 #endif
2644 /* Divide the two-limb number in (NH,,NL) by D, with DI being the largest
2645 limb not larger than (2**(2*GMP_LIMB_BITS))/D - (2**GMP_LIMB_BITS).
2646 If this would yield overflow, DI should be the largest possible number
2647 (i.e., only ones). For correct operation, the most significant bit of D
2648 has to be set. Put the quotient in Q and the remainder in R. */
2649 #define udiv_qrnnd_preinv1(q, r, nh, nl, d, di) \
2650 do { \
2651 mp_limb_t _q, _ql, _r; \
2652 mp_limb_t _xh, _xl; \
2653 ASSERT ((d) != 0); \
2654 umul_ppmm (_q, _ql, (nh), (di)); \
2656 umul_ppmm (_xh, _xl, _q, (d)); \
2657 sub_ddmmss (_xh, _r, (nh), (nl), _xh, _xl); \
2658 if (_xh != 0) \
2659 { \
2660 sub_ddmmss (_xh, _r, _xh, _r, 0, (d)); \
2661 _q += 1; \
2662 if (_xh != 0) \
2663 { \
2664 _r -= (d); \
2665 _q += 1; \
2666 } \
2667 } \
2668 if (_r >= (d)) \
2669 { \
2670 _r -= (d); \
2671 _q += 1; \
2672 } \
2673 (r) = _r; \
2674 (q) = _q; \
2675 } while (0)
2677 /* Like udiv_qrnnd_preinv, but branch-free. */
2678 #define udiv_qrnnd_preinv2(q, r, nh, nl, d, di) \
2679 do { \
2680 mp_limb_t _n2, _n10, _nmask, _nadj, _q1; \
2681 mp_limb_t _xh, _xl; \
2682 _n2 = (nh); \
2683 _n10 = (nl); \
2684 _nmask = LIMB_HIGHBIT_TO_MASK (_n10); \
2685 _nadj = _n10 + (_nmask & (d)); \
2686 umul_ppmm (_xh, _xl, di, _n2 - _nmask); \
2687 add_ssaaaa (_xh, _xl, _xh, _xl, _n2, _nadj); \
2688 _q1 = ~_xh; \
2689 umul_ppmm (_xh, _xl, _q1, d); \
2690 add_ssaaaa (_xh, _xl, _xh, _xl, nh, nl); \
2692 (r) = _xl + ((d) & _xh); \
2693 (q) = _xh - _q1; \
2694 } while (0)
2696 /* Like udiv_qrnnd_preinv2, but for for any value D. DNORM is D shifted left
2697 so that its most significant bit is set. LGUP is ceil(log2(D)). */
2698 #define udiv_qrnnd_preinv2gen(q, r, nh, nl, d, di, dnorm, lgup) \
2699 do { \
2700 mp_limb_t _n2, _n10, _nmask, _nadj, _q1; \
2701 mp_limb_t _xh, _xl; \
2702 _n2 = ((nh) << (GMP_LIMB_BITS - (lgup))) + ((nl) >> 1 >> (l - 1)); \
2703 _n10 = (nl) << (GMP_LIMB_BITS - (lgup)); \
2704 _nmask = LIMB_HIGHBIT_TO_MASK (_n10); \
2705 _nadj = _n10 + (_nmask & (dnorm)); \
2706 umul_ppmm (_xh, _xl, di, _n2 - _nmask); \
2707 add_ssaaaa (_xh, _xl, _xh, _xl, _n2, _nadj); \
2708 _q1 = ~_xh; \
2709 umul_ppmm (_xh, _xl, _q1, d); \
2710 add_ssaaaa (_xh, _xl, _xh, _xl, nh, nl); \
2711 _xh -= (d); \
2712 (r) = _xl + ((d) & _xh); \
2713 (q) = _xh - _q1; \
2714 } while (0)
2716 /* udiv_qrnnd_preinv3 -- Based on work by Niels Möller and Torbjörn Granlund.
2718 We write things strangely below, to help gcc. A more straightforward
2719 version:
2721 _r = (nl) - _qh * (d);
2722 _t = _r + (d);
2723 if (_r >= _ql)
2724 {
2725 _qh--;
2726 _r = _t;
2727 }
2729 For one operation shorter critical path, one may want to use this form:
2731 _p = _qh * (d)
2732 _s = (nl) + (d);
2733 _r = (nl) - _p;
2734 _t = _s - _p;
2735 if (_r >= _ql)
2736 {
2737 _qh--;
2738 _r = _t;
2739 }
2740 */
2741 #define udiv_qrnnd_preinv3(q, r, nh, nl, d, di) \
2742 do { \
2743 mp_limb_t _qh, _ql, _r; \
2744 umul_ppmm (_qh, _ql, (nh), (di)); \
2745 if (__builtin_constant_p (nl) && (nl) == 0) \
2746 _qh += (nh) + 1; \
2747 else \
2748 add_ssaaaa (_qh, _ql, _qh, _ql, (nh) + 1, (nl)); \
2749 _r = (nl) - _qh * (d); \
2751 { \
2752 _r += (d); \
2753 _qh--; \
2754 } \
2755 if (UNLIKELY (_r >= (d))) \
2756 { \
2757 _r -= (d); \
2758 _qh++; \
2759 } \
2760 (r) = _r; \
2761 (q) = _qh; \
2762 } while (0)
2764 /* Compute r = nh*B mod d, where di is the inverse of d. */
2765 #define udiv_rnd_preinv(r, nh, d, di) \
2766 do { \
2767 mp_limb_t _qh, _ql, _r; \
2768 umul_ppmm (_qh, _ql, (nh), (di)); \
2769 _qh += (nh) + 1; \
2770 _r = - _qh * (d); \
2771 if (_r > _ql) \
2772 _r += (d); \
2773 (r) = _r; \
2774 } while (0)
2776 /* Compute quotient the quotient and remainder for n / d. Requires d
2777 >= B^2 / 2 and n < d B. di is the inverse
2779 floor ((B^3 - 1) / (d0 + d1 B)) - B.
2781 NOTE: Output variables are updated multiple times. Only some inputs
2782 and outputs may overlap.
2783 */
2784 #define udiv_qr_3by2(q, r1, r0, n2, n1, n0, d1, d0, dinv) \
2785 do { \
2786 mp_limb_t _q0, _t1, _t0, _mask; \
2787 umul_ppmm ((q), _q0, (n2), (dinv)); \
2788 add_ssaaaa ((q), _q0, (q), _q0, (n2), (n1)); \
2789 \
2791 (r1) = (n1) - (d1) * (q); \
2792 (r0) = (n0); \
2793 sub_ddmmss ((r1), (r0), (r1), (r0), (d1), (d0)); \
2794 umul_ppmm (_t1, _t0, (d0), (q)); \
2795 sub_ddmmss ((r1), (r0), (r1), (r0), _t1, _t0); \
2796 (q)++; \
2797 \
2799 _mask = - (mp_limb_t) ((r1) >= _q0); \
2800 (q) += _mask; \
2801 add_ssaaaa ((r1), (r0), (r1), (r0), _mask & (d1), _mask & (d0)); \
2802 if (UNLIKELY ((r1) >= (d1))) \
2803 { \
2804 if ((r1) > (d1) || (r0) >= (d0)) \
2805 { \
2806 (q)++; \
2807 sub_ddmmss ((r1), (r0), (r1), (r0), (d1), (d0)); \
2808 } \
2809 } \
2810 } while (0)
2813 #define mpn_preinv_divrem_1 __MPN(preinv_divrem_1)
2814 __GMP_DECLSPEC mp_limb_t mpn_preinv_divrem_1 __GMP_PROTO ((mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t, int));
2815 #endif
2818 /* USE_PREINV_DIVREM_1 is whether to use mpn_preinv_divrem_1, as opposed to the
2819 plain mpn_divrem_1. The default is yes, since the few CISC chips where
2820 preinv is not good have defines saying so. */
2821 #ifndef USE_PREINV_DIVREM_1
2822 #define USE_PREINV_DIVREM_1 1
2823 #endif
2825 #if USE_PREINV_DIVREM_1
2826 #define MPN_DIVREM_OR_PREINV_DIVREM_1(qp,xsize,ap,size,d,dinv,shift) \
2827 mpn_preinv_divrem_1 (qp, xsize, ap, size, d, dinv, shift)
2828 #else
2829 #define MPN_DIVREM_OR_PREINV_DIVREM_1(qp,xsize,ap,size,d,dinv,shift) \
2830 mpn_divrem_1 (qp, xsize, ap, size, d)
2831 #endif
2833 #ifndef PREINV_MOD_1_TO_MOD_1_THRESHOLD
2834 #define PREINV_MOD_1_TO_MOD_1_THRESHOLD 10
2835 #endif
2837 /* This selection may seem backwards. The reason mpn_mod_1 typically takes
2838 over for larger sizes is that it uses the mod_1_1 function. */
2839 #define MPN_MOD_OR_PREINV_MOD_1(src,size,divisor,inverse) \
2840 (BELOW_THRESHOLD (size, PREINV_MOD_1_TO_MOD_1_THRESHOLD) \
2841 ? mpn_preinv_mod_1 (src, size, divisor, inverse) \
2842 : mpn_mod_1 (src, size, divisor))
2846 #define mpn_mod_34lsub1 __MPN(mod_34lsub1)
2847 __GMP_DECLSPEC mp_limb_t mpn_mod_34lsub1 __GMP_PROTO ((mp_srcptr, mp_size_t)) __GMP_ATTRIBUTE_PURE;
2848 #endif
2851 /* DIVEXACT_1_THRESHOLD is at what size to use mpn_divexact_1, as opposed to
2852 plain mpn_divrem_1. Likewise BMOD_1_TO_MOD_1_THRESHOLD for
2853 mpn_modexact_1_odd against plain mpn_mod_1. On most CPUs divexact and
2854 modexact are faster at all sizes, so the defaults are 0. Those CPUs
2855 where this is not right have a tuned threshold. */
2856 #ifndef DIVEXACT_1_THRESHOLD
2857 #define DIVEXACT_1_THRESHOLD 0
2858 #endif
2859 #ifndef BMOD_1_TO_MOD_1_THRESHOLD
2860 #define BMOD_1_TO_MOD_1_THRESHOLD 10
2861 #endif
2864 #define mpn_divexact_1 __MPN(divexact_1)
2866 #endif
2868 #define MPN_DIVREM_OR_DIVEXACT_1(dst, src, size, divisor) \
2869 do { \
2870 if (BELOW_THRESHOLD (size, DIVEXACT_1_THRESHOLD)) \
2871 ASSERT_NOCARRY (mpn_divrem_1 (dst, (mp_size_t) 0, src, size, divisor)); \
2872 else \
2873 { \
2874 ASSERT (mpn_mod_1 (src, size, divisor) == 0); \
2875 mpn_divexact_1 (dst, src, size, divisor); \
2876 } \
2877 } while (0)
2880 #define mpn_modexact_1c_odd __MPN(modexact_1c_odd)
2881 __GMP_DECLSPEC mp_limb_t mpn_modexact_1c_odd __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t)) __GMP_ATTRIBUTE_PURE;
2882 #endif
2884 #if HAVE_NATIVE_mpn_modexact_1_odd
2885 #define mpn_modexact_1_odd __MPN(modexact_1_odd)
2886 __GMP_DECLSPEC mp_limb_t mpn_modexact_1_odd __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t)) __GMP_ATTRIBUTE_PURE;
2887 #else
2888 #define mpn_modexact_1_odd(src,size,divisor) \
2889 mpn_modexact_1c_odd (src, size, divisor, CNST_LIMB(0))
2890 #endif
2892 #define MPN_MOD_OR_MODEXACT_1_ODD(src,size,divisor) \
2893 (BELOW_THRESHOLD (size, BMOD_1_TO_MOD_1_THRESHOLD) \
2894 ? mpn_modexact_1_odd (src, size, divisor) \
2895 : mpn_mod_1 (src, size, divisor))
2897 /* binvert_limb() sets inv to the multiplicative inverse of n modulo
2898 2^GMP_NUMB_BITS, ie. satisfying inv*n == 1 mod 2^GMP_NUMB_BITS.
2899 n must be odd (otherwise such an inverse doesn't exist).
2901 This is not to be confused with invert_limb(), which is completely
2902 different.
2904 The table lookup gives an inverse with the low 8 bits valid, and each
2905 multiply step doubles the number of bits. See Jebelean "An algorithm for
2906 exact division" end of section 4 (reference in gmp.texi).
2908 Possible enhancement: Could use UHWtype until the last step, if half-size
2909 multiplies are faster (might help under _LONG_LONG_LIMB).
2911 Alternative: As noted in Granlund and Montgomery "Division by Invariant
2912 Integers using Multiplication" (reference in gmp.texi), n itself gives a
2913 3-bit inverse immediately, and could be used instead of a table lookup.
2914 A 4-bit inverse can be obtained effectively from xoring bits 1 and 2 into
2915 bit 3, for instance with (((n + 2) & 4) << 1) ^ n. */
2917 #define binvert_limb_table __gmp_binvert_limb_table
2920 #define binvert_limb(inv,n) \
2921 do { \
2922 mp_limb_t __n = (n); \
2923 mp_limb_t __inv; \
2924 ASSERT ((__n & 1) == 1); \
2925 \
2927 if (GMP_NUMB_BITS > 8) __inv = 2 * __inv - __inv * __inv * __n; \
2928 if (GMP_NUMB_BITS > 16) __inv = 2 * __inv - __inv * __inv * __n; \
2929 if (GMP_NUMB_BITS > 32) __inv = 2 * __inv - __inv * __inv * __n; \
2930 \
2931 if (GMP_NUMB_BITS > 64) \
2932 { \
2933 int __invbits = 64; \
2934 do { \
2935 __inv = 2 * __inv - __inv * __inv * __n; \
2936 __invbits *= 2; \
2937 } while (__invbits < GMP_NUMB_BITS); \
2938 } \
2939 \
2940 ASSERT ((__inv * __n & GMP_NUMB_MASK) == 1); \
2941 (inv) = __inv & GMP_NUMB_MASK; \
2942 } while (0)
2945 /* Multiplicative inverse of 3, modulo 2^GMP_NUMB_BITS.
2946 Eg. 0xAAAAAAAB for 32 bits, 0xAAAAAAAAAAAAAAAB for 64 bits.
2947 GMP_NUMB_MAX/3*2+1 is right when GMP_NUMB_BITS is even, but when it's odd
2948 we need to start from GMP_NUMB_MAX>>1. */
2949 #define MODLIMB_INVERSE_3 (((GMP_NUMB_MAX >> (GMP_NUMB_BITS % 2)) / 3) * 2 + 1)
2951 /* ceil(GMP_NUMB_MAX/3) and ceil(2*GMP_NUMB_MAX/3).
2952 These expressions work because GMP_NUMB_MAX%3 != 0 for all GMP_NUMB_BITS. */
2953 #define GMP_NUMB_CEIL_MAX_DIV3 (GMP_NUMB_MAX / 3 + 1)
2954 #define GMP_NUMB_CEIL_2MAX_DIV3 ((GMP_NUMB_MAX>>1) / 3 + 1 + GMP_NUMB_HIGHBIT)
2957 /* Set r to -a mod d. a>=d is allowed. Can give r>d. All should be limbs.
2959 It's not clear whether this is the best way to do this calculation.
2960 Anything congruent to -a would be fine for the one limb congruence
2961 tests. */
2963 #define NEG_MOD(r, a, d) \
2964 do { \
2965 ASSERT ((d) != 0); \
2966 ASSERT_LIMB (a); \
2967 ASSERT_LIMB (d); \
2968 \
2969 if ((a) <= (d)) \
2970 { \
2972 (r) = (d) - (a); \
2973 } \
2974 else \
2975 { \
2976 unsigned __twos; \
2977 mp_limb_t __dnorm; \
2978 count_leading_zeros (__twos, d); \
2979 __twos -= GMP_NAIL_BITS; \
2980 __dnorm = (d) << __twos; \
2981 (r) = ((a) <= __dnorm ? __dnorm : 2*__dnorm) - (a); \
2982 } \
2983 \
2984 ASSERT_LIMB (r); \
2985 } while (0)
2987 /* A bit mask of all the least significant zero bits of n, or -1 if n==0. */
2988 #define LOW_ZEROS_MASK(n) (((n) & -(n)) - 1)
2991 /* ULONG_PARITY sets "p" to 1 if there's an odd number of 1 bits in "n", or
2992 to 0 if there's an even number. "n" should be an unsigned long and "p"
2993 an int. */
2995 #if defined (__GNUC__) && ! defined (NO_ASM) && HAVE_HOST_CPU_alpha_CIX
2996 #define ULONG_PARITY(p, n) \
2997 do { \
2998 int __p; \
3000 (p) = __p & 1; \
3001 } while (0)
3002 #endif
3004 /* Cray intrinsic _popcnt. */
3005 #ifdef _CRAY
3006 #define ULONG_PARITY(p, n) \
3007 do { \
3008 (p) = _popcnt (n) & 1; \
3009 } while (0)
3010 #endif
3012 #if defined (__GNUC__) && ! defined (__INTEL_COMPILER) \
3013 && ! defined (NO_ASM) && defined (__ia64)
3014 /* unsigned long is either 32 or 64 bits depending on the ABI, zero extend
3015 to a 64 bit unsigned long long for popcnt */
3016 #define ULONG_PARITY(p, n) \
3017 do { \
3018 unsigned long long __n = (unsigned long) (n); \
3019 int __p; \
3021 (p) = __p & 1; \
3022 } while (0)
3023 #endif
3025 #if defined (__GNUC__) && ! defined (__INTEL_COMPILER) \
3026 && ! defined (NO_ASM) && HAVE_HOST_CPU_FAMILY_x86
3027 #if __GMP_GNUC_PREREQ (3,1)
3030 #else
3033 #endif
3034 #define ULONG_PARITY(p, n) \
3035 do { \
3036 char __p; \
3037 unsigned long __n = (n); \
3038 __n ^= (__n >> 16); \
3041 : __GMP_qm (__p), __GMP_q (__n) \
3043 (p) = __p; \
3044 } while (0)
3045 #endif
3047 #if ! defined (ULONG_PARITY)
3048 #define ULONG_PARITY(p, n) \
3049 do { \
3050 unsigned long __n = (n); \
3051 int __p = 0; \
3052 do \
3053 { \
3054 __p ^= 0x96696996L >> (__n & 0x1F); \
3055 __n >>= 5; \
3056 } \
3057 while (__n != 0); \
3058 \
3059 (p) = __p & 1; \
3060 } while (0)
3061 #endif
3064 /* 3 cycles on 604 or 750 since shifts and rlwimi's can pair. gcc (as of
3065 version 3.1 at least) doesn't seem to know how to generate rlwimi for
3066 anything other than bit-fields, so use "asm". */
3067 #if defined (__GNUC__) && ! defined (NO_ASM) \
3068 && HAVE_HOST_CPU_FAMILY_powerpc && GMP_LIMB_BITS == 32
3069 #define BSWAP_LIMB(dst, src) \
3070 do { \
3071 mp_limb_t __bswapl_src = (src); \
3079 } while (0)
3080 #endif
3082 /* bswap is available on i486 and up and is fast. A combination rorw $8 /
3083 roll $16 / rorw $8 is used in glibc for plain i386 (and in the linux
3084 kernel with xchgb instead of rorw), but this is not done here, because
3085 i386 means generic x86 and mixing word and dword operations will cause
3086 partial register stalls on P6 chips. */
3087 #if defined (__GNUC__) && ! defined (NO_ASM) \
3088 && HAVE_HOST_CPU_FAMILY_x86 && ! HAVE_HOST_CPU_i386 \
3089 && GMP_LIMB_BITS == 32
3090 #define BSWAP_LIMB(dst, src) \
3091 do { \
3093 } while (0)
3094 #endif
3096 #if defined (__GNUC__) && ! defined (NO_ASM) \
3097 && defined (__amd64__) && GMP_LIMB_BITS == 64
3098 #define BSWAP_LIMB(dst, src) \
3099 do { \
3101 } while (0)
3102 #endif
3104 #if defined (__GNUC__) && ! defined (__INTEL_COMPILER) \
3105 && ! defined (NO_ASM) && defined (__ia64) && GMP_LIMB_BITS == 64
3106 #define BSWAP_LIMB(dst, src) \
3107 do { \
3109 } while (0)
3110 #endif
3112 /* As per glibc. */
3113 #if defined (__GNUC__) && ! defined (NO_ASM) \
3114 && HAVE_HOST_CPU_FAMILY_m68k && GMP_LIMB_BITS == 32
3115 #define BSWAP_LIMB(dst, src) \
3116 do { \
3117 mp_limb_t __bswapl_src = (src); \
3123 } while (0)
3124 #endif
3126 #if ! defined (BSWAP_LIMB)
3127 #if GMP_LIMB_BITS == 8
3128 #define BSWAP_LIMB(dst, src) \
3129 do { (dst) = (src); } while (0)
3130 #endif
3131 #if GMP_LIMB_BITS == 16
3132 #define BSWAP_LIMB(dst, src) \
3133 do { \
3134 (dst) = ((src) << 8) + ((src) >> 8); \
3135 } while (0)
3136 #endif
3137 #if GMP_LIMB_BITS == 32
3138 #define BSWAP_LIMB(dst, src) \
3139 do { \
3140 (dst) = \
3141 ((src) << 24) \
3142 + (((src) & 0xFF00) << 8) \
3143 + (((src) >> 8) & 0xFF00) \
3144 + ((src) >> 24); \
3145 } while (0)
3146 #endif
3147 #if GMP_LIMB_BITS == 64
3148 #define BSWAP_LIMB(dst, src) \
3149 do { \
3150 (dst) = \
3151 ((src) << 56) \
3152 + (((src) & 0xFF00) << 40) \
3153 + (((src) & 0xFF0000) << 24) \
3154 + (((src) & 0xFF000000) << 8) \
3155 + (((src) >> 8) & 0xFF000000) \
3156 + (((src) >> 24) & 0xFF0000) \
3157 + (((src) >> 40) & 0xFF00) \
3158 + ((src) >> 56); \
3159 } while (0)
3160 #endif
3161 #endif
3163 #if ! defined (BSWAP_LIMB)
3164 #define BSWAP_LIMB(dst, src) \
3165 do { \
3166 mp_limb_t __bswapl_src = (src); \
3167 mp_limb_t __dst = 0; \
3168 int __i; \
3169 for (__i = 0; __i < BYTES_PER_MP_LIMB; __i++) \
3170 { \
3171 __dst = (__dst << 8) | (__bswapl_src & 0xFF); \
3172 __bswapl_src >>= 8; \
3173 } \
3174 (dst) = __dst; \
3175 } while (0)
3176 #endif
3179 /* Apparently lwbrx might be slow on some PowerPC chips, so restrict it to
3180 those we know are fast. */
3181 #if defined (__GNUC__) && ! defined (NO_ASM) \
3182 && GMP_LIMB_BITS == 32 && HAVE_LIMB_BIG_ENDIAN \
3183 && (HAVE_HOST_CPU_powerpc604 \
3184 || HAVE_HOST_CPU_powerpc604e \
3185 || HAVE_HOST_CPU_powerpc750 \
3186 || HAVE_HOST_CPU_powerpc7400)
3187 #define BSWAP_LIMB_FETCH(limb, src) \
3188 do { \
3189 mp_srcptr __blf_src = (src); \
3190 mp_limb_t __limb; \
3195 (limb) = __limb; \
3196 } while (0)
3197 #endif
3199 #if ! defined (BSWAP_LIMB_FETCH)
3200 #define BSWAP_LIMB_FETCH(limb, src) BSWAP_LIMB (limb, *(src))
3201 #endif
3204 /* On the same basis that lwbrx might be slow, restrict stwbrx to those we
3205 know are fast. FIXME: Is this necessary? */
3206 #if defined (__GNUC__) && ! defined (NO_ASM) \
3207 && GMP_LIMB_BITS == 32 && HAVE_LIMB_BIG_ENDIAN \
3208 && (HAVE_HOST_CPU_powerpc604 \
3209 || HAVE_HOST_CPU_powerpc604e \
3210 || HAVE_HOST_CPU_powerpc750 \
3211 || HAVE_HOST_CPU_powerpc7400)
3212 #define BSWAP_LIMB_STORE(dst, limb) \
3213 do { \
3214 mp_ptr __dst = (dst); \
3215 mp_limb_t __limb = (limb); \
3220 } while (0)
3221 #endif
3223 #if ! defined (BSWAP_LIMB_STORE)
3224 #define BSWAP_LIMB_STORE(dst, limb) BSWAP_LIMB (*(dst), limb)
3225 #endif
3228 /* Byte swap limbs from {src,size} and store at {dst,size}. */
3229 #define MPN_BSWAP(dst, src, size) \
3230 do { \
3231 mp_ptr __dst = (dst); \
3232 mp_srcptr __src = (src); \
3233 mp_size_t __size = (size); \
3234 mp_size_t __i; \
3235 ASSERT ((size) >= 0); \
3236 ASSERT (MPN_SAME_OR_SEPARATE_P (dst, src, size)); \
3238 for (__i = 0; __i < __size; __i++) \
3239 { \
3240 BSWAP_LIMB_FETCH (*__dst, __src); \
3241 __dst++; \
3242 __src++; \
3243 } \
3244 } while (0)
3246 /* Byte swap limbs from {dst,size} and store in reverse order at {src,size}. */
3247 #define MPN_BSWAP_REVERSE(dst, src, size) \
3248 do { \
3249 mp_ptr __dst = (dst); \
3250 mp_size_t __size = (size); \
3251 mp_srcptr __src = (src) + __size - 1; \
3252 mp_size_t __i; \
3253 ASSERT ((size) >= 0); \
3254 ASSERT (! MPN_OVERLAP_P (dst, size, src, size)); \
3256 for (__i = 0; __i < __size; __i++) \
3257 { \
3258 BSWAP_LIMB_FETCH (*__dst, __src); \
3259 __dst++; \
3260 __src--; \
3261 } \
3262 } while (0)
3265 /* No processor claiming to be SPARC v9 compliant seems to
3266 implement the POPC instruction. Disable pattern for now. */
3267 #if 0
3268 #if defined __GNUC__ && defined __sparc_v9__ && GMP_LIMB_BITS == 64
3269 #define popc_limb(result, input) \
3270 do { \
3271 DItype __res; \
3273 } while (0)
3274 #endif
3275 #endif
3277 #if defined (__GNUC__) && ! defined (NO_ASM) && HAVE_HOST_CPU_alpha_CIX
3278 #define popc_limb(result, input) \
3279 do { \
3281 } while (0)
3282 #endif
3284 /* Cray intrinsic. */
3285 #ifdef _CRAY
3286 #define popc_limb(result, input) \
3287 do { \
3288 (result) = _popcnt (input); \
3289 } while (0)
3290 #endif
3292 #if defined (__GNUC__) && ! defined (__INTEL_COMPILER) \
3293 && ! defined (NO_ASM) && defined (__ia64) && GMP_LIMB_BITS == 64
3294 #define popc_limb(result, input) \
3295 do { \
3297 } while (0)
3298 #endif
3300 /* Cool population count of an mp_limb_t.
3301 You have to figure out how this works, We won't tell you!
3303 The constants could also be expressed as:
3304 0x55... = [2^N / 3] = [(2^N-1)/3]
3305 0x33... = [2^N / 5] = [(2^N-1)/5]
3306 0x0f... = [2^N / 17] = [(2^N-1)/17]
3307 (N is GMP_LIMB_BITS, [] denotes truncation.) */
3309 #if ! defined (popc_limb) && GMP_LIMB_BITS == 8
3310 #define popc_limb(result, input) \
3311 do { \
3312 mp_limb_t __x = (input); \
3313 __x -= (__x >> 1) & MP_LIMB_T_MAX/3; \
3314 __x = ((__x >> 2) & MP_LIMB_T_MAX/5) + (__x & MP_LIMB_T_MAX/5); \
3315 __x = ((__x >> 4) + __x) & MP_LIMB_T_MAX/17; \
3316 (result) = __x & 0xff; \
3317 } while (0)
3318 #endif
3320 #if ! defined (popc_limb) && GMP_LIMB_BITS == 16
3321 #define popc_limb(result, input) \
3322 do { \
3323 mp_limb_t __x = (input); \
3324 __x -= (__x >> 1) & MP_LIMB_T_MAX/3; \
3325 __x = ((__x >> 2) & MP_LIMB_T_MAX/5) + (__x & MP_LIMB_T_MAX/5); \
3326 __x = ((__x >> 4) + __x) & MP_LIMB_T_MAX/17; \
3327 __x = ((__x >> 8) + __x); \
3328 (result) = __x & 0xff; \
3329 } while (0)
3330 #endif
3332 #if ! defined (popc_limb) && GMP_LIMB_BITS == 32
3333 #define popc_limb(result, input) \
3334 do { \
3335 mp_limb_t __x = (input); \
3336 __x -= (__x >> 1) & MP_LIMB_T_MAX/3; \
3337 __x = ((__x >> 2) & MP_LIMB_T_MAX/5) + (__x & MP_LIMB_T_MAX/5); \
3338 __x = ((__x >> 4) + __x) & MP_LIMB_T_MAX/17; \
3339 __x = ((__x >> 8) + __x); \
3340 __x = ((__x >> 16) + __x); \
3341 (result) = __x & 0xff; \
3342 } while (0)
3343 #endif
3345 #if ! defined (popc_limb) && GMP_LIMB_BITS == 64
3346 #define popc_limb(result, input) \
3347 do { \
3348 mp_limb_t __x = (input); \
3349 __x -= (__x >> 1) & MP_LIMB_T_MAX/3; \
3350 __x = ((__x >> 2) & MP_LIMB_T_MAX/5) + (__x & MP_LIMB_T_MAX/5); \
3351 __x = ((__x >> 4) + __x) & MP_LIMB_T_MAX/17; \
3352 __x = ((__x >> 8) + __x); \
3353 __x = ((__x >> 16) + __x); \
3354 __x = ((__x >> 32) + __x); \
3355 (result) = __x & 0xff; \
3356 } while (0)
3357 #endif
3360 /* Define stuff for longlong.h. */
3361 #if HAVE_ATTRIBUTE_MODE
3367 #else
3371 #if HAVE_LONG_LONG
3377 #endif
3378 #endif
3382 #define W_TYPE_SIZE GMP_LIMB_BITS
3384 /* Define ieee_double_extract and _GMP_IEEE_FLOATS.
3386 Bit field packing is "implementation defined" according to C99, which
3387 leaves us at the compiler's mercy here. For some systems packing is
3388 defined in the ABI (eg. x86). In any case so far it seems universal that
3389 little endian systems pack from low to high, and big endian from high to
3390 low within the given type.
3392 Within the fields we rely on the integer endianness being the same as the
3393 float endianness, this is true everywhere we know of and it'd be a fairly
3394 strange system that did anything else. */
3396 #if HAVE_DOUBLE_IEEE_LITTLE_SWAPPED
3397 #define _GMP_IEEE_FLOATS 1
3398 union ieee_double_extract
3399 {
3400 struct
3401 {
3408 };
3409 #endif
3411 #if HAVE_DOUBLE_IEEE_LITTLE_ENDIAN
3412 #define _GMP_IEEE_FLOATS 1
3413 union ieee_double_extract
3414 {
3415 struct
3416 {
3423 };
3424 #endif
3426 #if HAVE_DOUBLE_IEEE_BIG_ENDIAN
3427 #define _GMP_IEEE_FLOATS 1
3428 union ieee_double_extract
3429 {
3430 struct
3431 {
3438 };
3439 #endif
3442 /* Use (4.0 * ...) instead of (2.0 * ...) to work around buggy compilers
3443 that don't convert ulong->double correctly (eg. SunOS 4 native cc). */
3444 #define MP_BASE_AS_DOUBLE (4.0 * ((mp_limb_t) 1 << (GMP_NUMB_BITS - 2)))
3445 /* Maximum number of limbs it will take to store any `double'.
3446 We assume doubles have 53 mantissa bits. */
3447 #define LIMBS_PER_DOUBLE ((53 + GMP_NUMB_BITS - 2) / GMP_NUMB_BITS + 1)
3451 #define mpn_get_d __gmpn_get_d
3452 __GMP_DECLSPEC double mpn_get_d __GMP_PROTO ((mp_srcptr, mp_size_t, mp_size_t, long)) __GMP_ATTRIBUTE_PURE;
3455 /* DOUBLE_NAN_INF_ACTION executes code a_nan if x is a NaN, or executes
3456 a_inf if x is an infinity. Both are considered unlikely values, for
3457 branch prediction. */
3459 #if _GMP_IEEE_FLOATS
3460 #define DOUBLE_NAN_INF_ACTION(x, a_nan, a_inf) \
3461 do { \
3462 union ieee_double_extract u; \
3463 u.d = (x); \
3464 if (UNLIKELY (u.s.exp == 0x7FF)) \
3465 { \
3466 if (u.s.manl == 0 && u.s.manh == 0) \
3467 { a_inf; } \
3468 else \
3469 { a_nan; } \
3470 } \
3471 } while (0)
3472 #endif
3474 #if HAVE_DOUBLE_VAX_D || HAVE_DOUBLE_VAX_G || HAVE_DOUBLE_CRAY_CFP
3475 /* no nans or infs in these formats */
3476 #define DOUBLE_NAN_INF_ACTION(x, a_nan, a_inf) \
3477 do { } while (0)
3478 #endif
3480 #ifndef DOUBLE_NAN_INF_ACTION
3481 /* Unknown format, try something generic.
3482 NaN should be "unordered", so x!=x.
3483 Inf should be bigger than DBL_MAX. */
3484 #define DOUBLE_NAN_INF_ACTION(x, a_nan, a_inf) \
3485 do { \
3486 { \
3487 if (UNLIKELY ((x) != (x))) \
3488 { a_nan; } \
3489 else if (UNLIKELY ((x) > DBL_MAX || (x) < -DBL_MAX)) \
3490 { a_inf; } \
3491 } \
3492 } while (0)
3493 #endif
3495 /* On m68k, x86 and amd64, gcc (and maybe other compilers) can hold doubles
3496 in the coprocessor, which means a bigger exponent range than normal, and
3497 depending on the rounding mode, a bigger mantissa than normal. (See
3498 "Disappointments" in the gcc manual.) FORCE_DOUBLE stores and fetches
3499 "d" through memory to force any rounding and overflows to occur.
3501 On amd64, and on x86s with SSE2, gcc (depending on options) uses the xmm
3502 registers, where there's no such extra precision and no need for the
3503 FORCE_DOUBLE. We don't bother to detect this since the present uses for
3504 FORCE_DOUBLE are only in test programs and default generic C code.
3506 Not quite sure that an "automatic volatile" will use memory, but it does
3507 in gcc. An asm("":"=m"(d):"0"(d)) can't be used to trick gcc, since
3508 apparently matching operands like "0" are only allowed on a register
3509 output. gcc 3.4 warns about this, though in fact it and past versions
3510 seem to put the operand through memory as hoped. */
3512 #if (HAVE_HOST_CPU_FAMILY_m68k || HAVE_HOST_CPU_FAMILY_x86 \
3513 || defined (__amd64__))
3514 #define FORCE_DOUBLE(d) \
3515 do { volatile double __gmp_force = (d); (d) = __gmp_force; } while (0)
3516 #else
3517 #define FORCE_DOUBLE(d) do { } while (0)
3518 #endif
3527 #define GMP_ERROR(code) __gmp_exception (code)
3528 #define DIVIDE_BY_ZERO __gmp_divide_by_zero ()
3529 #define SQRT_OF_NEGATIVE __gmp_sqrt_of_negative ()
3531 #if defined _LONG_LONG_LIMB
3532 #if __GMP_HAVE_TOKEN_PASTE
3533 #define CNST_LIMB(C) ((mp_limb_t) C##LL)
3534 #else
3536 #endif
3538 #if __GMP_HAVE_TOKEN_PASTE
3539 #define CNST_LIMB(C) ((mp_limb_t) C##L)
3540 #else
3542 #endif
3545 /* Stuff used by mpn/generic/perfsqr.c and mpz/prime_p.c */
3546 #if GMP_NUMB_BITS == 2
3548 #define PP_FIRST_OMITTED 5
3549 #endif
3550 #if GMP_NUMB_BITS == 4
3552 #define PP_FIRST_OMITTED 7
3553 #endif
3554 #if GMP_NUMB_BITS == 8
3556 #define PP_FIRST_OMITTED 11
3557 #endif
3558 #if GMP_NUMB_BITS == 16
3560 #define PP_FIRST_OMITTED 17
3561 #endif
3562 #if GMP_NUMB_BITS == 32
3564 #define PP_INVERTED 0x53E5645CL
3565 #define PP_FIRST_OMITTED 31
3566 #endif
3567 #if GMP_NUMB_BITS == 64
3569 #define PP_INVERTED CNST_LIMB(0x21CFE6CFC938B36B)
3570 #define PP_FIRST_OMITTED 59
3571 #endif
3572 #ifndef PP_FIRST_OMITTED
3573 #define PP_FIRST_OMITTED 3
3574 #endif
3578 /* BIT1 means a result value in bit 1 (second least significant bit), with a
3579 zero bit representing +1 and a one bit representing -1. Bits other than
3580 bit 1 are garbage. These are meant to be kept in "int"s, and casts are
3581 used to ensure the expressions are "int"s even if a and/or b might be
3582 other types.
3584 JACOBI_TWOS_U_BIT1 and JACOBI_RECIP_UU_BIT1 are used in mpn_jacobi_base
3585 and their speed is important. Expressions are used rather than
3586 conditionals to accumulate sign changes, which effectively means XORs
3587 instead of conditional JUMPs. */
3589 /* (a/0), with a signed; is 1 if a=+/-1, 0 otherwise */
3590 #define JACOBI_S0(a) (((a) == 1) | ((a) == -1))
3592 /* (a/0), with a unsigned; is 1 if a=+/-1, 0 otherwise */
3593 #define JACOBI_U0(a) ((a) == 1)
3595 /* (a/0), with a given by low and size;
3596 is 1 if a=+/-1, 0 otherwise */
3597 #define JACOBI_LS0(alow,asize) \
3598 (((asize) == 1 || (asize) == -1) && (alow) == 1)
3600 /* (a/0), with a an mpz_t;
3601 fetch of low limb always valid, even if size is zero */
3602 #define JACOBI_Z0(a) JACOBI_LS0 (PTR(a)[0], SIZ(a))
3604 /* (0/b), with b unsigned; is 1 if b=1, 0 otherwise */
3605 #define JACOBI_0U(b) ((b) == 1)
3607 /* (0/b), with b unsigned; is 1 if b=+/-1, 0 otherwise */
3608 #define JACOBI_0S(b) ((b) == 1 || (b) == -1)
3610 /* (0/b), with b given by low and size; is 1 if b=+/-1, 0 otherwise */
3611 #define JACOBI_0LS(blow,bsize) \
3612 (((bsize) == 1 || (bsize) == -1) && (blow) == 1)
3614 /* Convert a bit1 to +1 or -1. */
3615 #define JACOBI_BIT1_TO_PN(result_bit1) \
3616 (1 - ((int) (result_bit1) & 2))
3618 /* (2/b), with b unsigned and odd;
3619 is (-1)^((b^2-1)/8) which is 1 if b==1,7mod8 or -1 if b==3,5mod8 and
3620 hence obtained from (b>>1)^b */
3621 #define JACOBI_TWO_U_BIT1(b) \
3622 ((int) (((b) >> 1) ^ (b)))
3624 /* (2/b)^twos, with b unsigned and odd */
3625 #define JACOBI_TWOS_U_BIT1(twos, b) \
3626 ((int) ((twos) << 1) & JACOBI_TWO_U_BIT1 (b))
3628 /* (2/b)^twos, with b unsigned and odd */
3629 #define JACOBI_TWOS_U(twos, b) \
3630 (JACOBI_BIT1_TO_PN (JACOBI_TWOS_U_BIT1 (twos, b)))
3632 /* (-1/b), with b odd (signed or unsigned);
3633 is (-1)^((b-1)/2) */
3634 #define JACOBI_N1B_BIT1(b) \
3635 ((int) (b))
3637 /* (a/b) effect due to sign of a: signed/unsigned, b odd;
3638 is (-1/b) if a<0, or +1 if a>=0 */
3639 #define JACOBI_ASGN_SU_BIT1(a, b) \
3640 ((((a) < 0) << 1) & JACOBI_N1B_BIT1(b))
3642 /* (a/b) effect due to sign of b: signed/signed;
3643 is -1 if a and b both negative, +1 otherwise */
3644 #define JACOBI_BSGN_SS_BIT1(a, b) \
3645 ((((a)<0) & ((b)<0)) << 1)
3647 /* (a/b) effect due to sign of b: signed/mpz;
3648 is -1 if a and b both negative, +1 otherwise */
3649 #define JACOBI_BSGN_SZ_BIT1(a, b) \
3650 JACOBI_BSGN_SS_BIT1 (a, SIZ(b))
3652 /* (a/b) effect due to sign of b: mpz/signed;
3653 is -1 if a and b both negative, +1 otherwise */
3654 #define JACOBI_BSGN_ZS_BIT1(a, b) \
3655 JACOBI_BSGN_SZ_BIT1 (b, a)
3657 /* (a/b) reciprocity to switch to (b/a), a,b both unsigned and odd;
3658 is (-1)^((a-1)*(b-1)/4), which means +1 if either a,b==1mod4, or -1 if
3659 both a,b==3mod4, achieved in bit 1 by a&b. No ASSERT()s about a,b odd
3660 because this is used in a couple of places with only bit 1 of a or b
3661 valid. */
3662 #define JACOBI_RECIP_UU_BIT1(a, b) \
3663 ((int) ((a) & (b)))
3665 /* Strip low zero limbs from {b_ptr,b_size} by incrementing b_ptr and
3666 decrementing b_size. b_low should be b_ptr[0] on entry, and will be
3667 updated for the new b_ptr. result_bit1 is updated according to the
3668 factors of 2 stripped, as per (a/2). */
3669 #define JACOBI_STRIP_LOW_ZEROS(result_bit1, a, b_ptr, b_size, b_low) \
3670 do { \
3671 ASSERT ((b_size) >= 1); \
3672 ASSERT ((b_low) == (b_ptr)[0]); \
3673 \
3674 while (UNLIKELY ((b_low) == 0)) \
3675 { \
3676 (b_size)--; \
3677 ASSERT ((b_size) >= 1); \
3678 (b_ptr)++; \
3679 (b_low) = *(b_ptr); \
3680 \
3681 ASSERT (((a) & 1) != 0); \
3682 if ((GMP_NUMB_BITS % 2) == 1) \
3683 (result_bit1) ^= JACOBI_TWO_U_BIT1(a); \
3684 } \
3685 } while (0)
3687 /* Set a_rem to {a_ptr,a_size} reduced modulo b, either using mod_1 or
3688 modexact_1_odd, but in either case leaving a_rem<b. b must be odd and
3689 unsigned. modexact_1_odd effectively calculates -a mod b, and
3690 result_bit1 is adjusted for the factor of -1.
3692 The way mpn_modexact_1_odd sometimes bases its remainder on a_size and
3693 sometimes on a_size-1 means if GMP_NUMB_BITS is odd we can't know what
3694 factor to introduce into result_bit1, so for that case use mpn_mod_1
3695 unconditionally.
3697 FIXME: mpn_modexact_1_odd is more efficient, so some way to get it used
3698 for odd GMP_NUMB_BITS would be good. Perhaps it could mung its result,
3699 or not skip a divide step, or something. */
3701 #define JACOBI_MOD_OR_MODEXACT_1_ODD(result_bit1, a_rem, a_ptr, a_size, b) \
3702 do { \
3703 mp_srcptr __a_ptr = (a_ptr); \
3704 mp_size_t __a_size = (a_size); \
3705 mp_limb_t __b = (b); \
3706 \
3707 ASSERT (__a_size >= 1); \
3708 ASSERT (__b & 1); \
3709 \
3710 if ((GMP_NUMB_BITS % 2) != 0 \
3711 || ABOVE_THRESHOLD (__a_size, BMOD_1_TO_MOD_1_THRESHOLD)) \
3712 { \
3713 (a_rem) = mpn_mod_1 (__a_ptr, __a_size, __b); \
3714 } \
3715 else \
3716 { \
3717 (result_bit1) ^= JACOBI_N1B_BIT1 (__b); \
3718 (a_rem) = mpn_modexact_1_odd (__a_ptr, __a_size, __b); \
3719 } \
3720 } while (0)
3722 /* Matrix multiplication */
3723 #define mpn_matrix22_mul __MPN(matrix22_mul)
3724 __GMP_DECLSPEC void mpn_matrix22_mul __GMP_PROTO ((mp_ptr, mp_ptr, mp_ptr, mp_ptr, mp_size_t, mp_srcptr, mp_srcptr, mp_srcptr, mp_srcptr, mp_size_t, mp_ptr));
3725 #define mpn_matrix22_mul_strassen __MPN(matrix22_mul_strassen)
3726 __GMP_DECLSPEC void mpn_matrix22_mul_strassen __GMP_PROTO ((mp_ptr, mp_ptr, mp_ptr, mp_ptr, mp_size_t, mp_srcptr, mp_srcptr, mp_srcptr, mp_srcptr, mp_size_t, mp_ptr));
3727 #define mpn_matrix22_mul_itch __MPN(matrix22_mul_itch)
3730 #ifndef MATRIX22_STRASSEN_THRESHOLD
3731 #define MATRIX22_STRASSEN_THRESHOLD 30
3732 #endif
3734 /* HGCD definitions */
3736 /* Extract one numb, shifting count bits left
3737 ________ ________
3738 |___xh___||___xl___|
3739 |____r____|
3740 >count <
3742 The count includes any nail bits, so it should work fine if count
3743 is computed using count_leading_zeros. If GMP_NAIL_BITS > 0, all of
3744 xh, xl and r include nail bits. Must have 0 < count < GMP_LIMB_BITS.
3746 FIXME: Omit masking with GMP_NUMB_MASK, and let callers do that for
3747 those calls where the count high bits of xh may be non-zero.
3748 */
3750 #define MPN_EXTRACT_NUMB(count, xh, xl) \
3751 ((((xh) << ((count) - GMP_NAIL_BITS)) & GMP_NUMB_MASK) | \
3752 ((xl) >> (GMP_LIMB_BITS - (count))))
3755 /* The matrix non-negative M = (u, u'; v,v') keeps track of the
3756 reduction (a;b) = M (alpha; beta) where alpha, beta are smaller
3757 than a, b. The determinant must always be one, so that M has an
3758 inverse (v', -u'; -v, u). Elements always fit in GMP_NUMB_BITS - 1
3759 bits. */
3760 struct hgcd_matrix1
3761 {
3763 };
3765 #define mpn_hgcd2 __MPN (hgcd2)
3766 __GMP_DECLSPEC int mpn_hgcd2 __GMP_PROTO ((mp_limb_t, mp_limb_t, mp_limb_t, mp_limb_t, struct hgcd_matrix1 *));
3768 #define mpn_hgcd_mul_matrix1_vector __MPN (hgcd_mul_matrix1_vector)
3769 __GMP_DECLSPEC mp_size_t mpn_hgcd_mul_matrix1_vector __GMP_PROTO ((const struct hgcd_matrix1 *, mp_ptr, mp_srcptr, mp_ptr, mp_size_t));
3771 #define mpn_hgcd_mul_matrix1_inverse_vector __MPN (hgcd_mul_matrix1_inverse_vector)
3772 __GMP_DECLSPEC mp_size_t mpn_hgcd_mul_matrix1_inverse_vector __GMP_PROTO ((const struct hgcd_matrix1 *, mp_ptr, mp_srcptr, mp_ptr, mp_size_t));
3774 struct hgcd_matrix
3775 {
3777 mp_size_t n;
3779 };
3781 #define MPN_HGCD_MATRIX_INIT_ITCH(n) (4 * ((n+1)/2 + 1))
3783 #define mpn_hgcd_matrix_init __MPN (hgcd_matrix_init)
3784 __GMP_DECLSPEC void mpn_hgcd_matrix_init __GMP_PROTO ((struct hgcd_matrix *, mp_size_t, mp_ptr));
3786 #define mpn_hgcd_matrix_mul __MPN (hgcd_matrix_mul)
3787 __GMP_DECLSPEC void mpn_hgcd_matrix_mul __GMP_PROTO ((struct hgcd_matrix *, const struct hgcd_matrix *, mp_ptr));
3789 #define mpn_hgcd_matrix_adjust __MPN (hgcd_matrix_adjust)
3790 __GMP_DECLSPEC mp_size_t mpn_hgcd_matrix_adjust __GMP_PROTO ((struct hgcd_matrix *, mp_size_t, mp_ptr, mp_ptr, mp_size_t, mp_ptr));
3792 #define mpn_hgcd_itch __MPN (hgcd_itch)
3795 #define mpn_hgcd __MPN (hgcd)
3796 __GMP_DECLSPEC mp_size_t mpn_hgcd __GMP_PROTO ((mp_ptr, mp_ptr, mp_size_t, struct hgcd_matrix *, mp_ptr));
3798 #define MPN_HGCD_LEHMER_ITCH(n) (n)
3800 #define mpn_hgcd_lehmer __MPN (hgcd_lehmer)
3801 __GMP_DECLSPEC mp_size_t mpn_hgcd_lehmer __GMP_PROTO ((mp_ptr, mp_ptr, mp_size_t, struct hgcd_matrix *, mp_ptr));
3803 /* Needs storage for the quotient */
3804 #define MPN_GCD_SUBDIV_STEP_ITCH(n) (n)
3806 #define mpn_gcd_subdiv_step __MPN(gcd_subdiv_step)
3807 __GMP_DECLSPEC mp_size_t mpn_gcd_subdiv_step __GMP_PROTO ((mp_ptr, mp_size_t *, mp_ptr, mp_ptr, mp_size_t, mp_ptr));
3809 #define MPN_GCD_LEHMER_N_ITCH(n) (n)
3811 #define mpn_gcd_lehmer_n __MPN(gcd_lehmer_n)
3812 __GMP_DECLSPEC mp_size_t mpn_gcd_lehmer_n __GMP_PROTO ((mp_ptr, mp_ptr, mp_ptr, mp_size_t, mp_ptr));
3814 #define mpn_gcdext_subdiv_step __MPN(gcdext_subdiv_step)
3815 __GMP_DECLSPEC mp_size_t mpn_gcdext_subdiv_step __GMP_PROTO ((mp_ptr, mp_size_t *, mp_ptr, mp_size_t *, mp_ptr, mp_ptr, mp_size_t, mp_ptr, mp_ptr, mp_size_t *, mp_ptr, mp_ptr));
3817 #define MPN_GCDEXT_LEHMER_N_ITCH(n) (4*(n) + 3)
3819 #define mpn_gcdext_lehmer_n __MPN(gcdext_lehmer_n)
3820 __GMP_DECLSPEC mp_size_t mpn_gcdext_lehmer_n __GMP_PROTO ((mp_ptr, mp_ptr, mp_size_t *, mp_ptr, mp_ptr, mp_size_t, mp_ptr));
3822 /* 4*(an + 1) + 4*(bn + 1) + an */
3823 #define MPN_GCDEXT_LEHMER_ITCH(an, bn) (5*(an) + 4*(bn) + 8)
3825 #ifndef HGCD_THRESHOLD
3826 #define HGCD_THRESHOLD 400
3827 #endif
3829 #ifndef GCD_DC_THRESHOLD
3830 #define GCD_DC_THRESHOLD 1000
3831 #endif
3833 #ifndef GCDEXT_DC_THRESHOLD
3834 #define GCDEXT_DC_THRESHOLD 600
3835 #endif
3837 /* Definitions for mpn_set_str and mpn_get_str */
3838 struct powers
3839 {
3845 };
3847 #define mpn_dc_set_str_powtab_alloc(n) ((n) + GMP_LIMB_BITS)
3848 #define mpn_dc_set_str_itch(n) ((n) + GMP_LIMB_BITS)
3849 #define mpn_dc_get_str_powtab_alloc(n) ((n) + 2 * GMP_LIMB_BITS)
3850 #define mpn_dc_get_str_itch(n) ((n) + GMP_LIMB_BITS)
3852 #define mpn_dc_set_str __MPN(dc_set_str)
3853 __GMP_DECLSPEC mp_size_t mpn_dc_set_str __GMP_PROTO ((mp_ptr, const unsigned char *, size_t, const powers_t *, mp_ptr));
3854 #define mpn_bc_set_str __MPN(bc_set_str)
3855 __GMP_DECLSPEC mp_size_t mpn_bc_set_str __GMP_PROTO ((mp_ptr, const unsigned char *, size_t, int));
3856 #define mpn_set_str_compute_powtab __MPN(set_str_compute_powtab)
3857 __GMP_DECLSPEC void mpn_set_str_compute_powtab __GMP_PROTO ((powers_t *, mp_ptr, mp_size_t, int));
3860 /* __GMPF_BITS_TO_PREC applies a minimum 53 bits, rounds upwards to a whole
3861 limb and adds an extra limb. __GMPF_PREC_TO_BITS drops that extra limb,
3862 hence giving back the user's size in bits rounded up. Notice that
3863 converting prec->bits->prec gives an unchanged value. */
3864 #define __GMPF_BITS_TO_PREC(n) \
3865 ((mp_size_t) ((__GMP_MAX (53, n) + 2 * GMP_NUMB_BITS - 1) / GMP_NUMB_BITS))
3866 #define __GMPF_PREC_TO_BITS(n) \
3867 ((mp_bitcnt_t) (n) * GMP_NUMB_BITS - GMP_NUMB_BITS)
3872 /* Set n to the number of significant digits an mpf of the given _mp_prec
3873 field, in the given base. This is a rounded up value, designed to ensure
3874 there's enough digits to reproduce all the guaranteed part of the value.
3876 There are prec many limbs, but the high might be only "1" so forget it
3877 and just count prec-1 limbs into chars. +1 rounds that upwards, and a
3878 further +1 is because the limbs usually won't fall on digit boundaries.
3880 FIXME: If base is a power of 2 and the bits per digit divides
3881 GMP_LIMB_BITS then the +2 is unnecessary. This happens always for
3882 base==2, and in base==16 with the current 32 or 64 bit limb sizes. */
3884 #define MPF_SIGNIFICANT_DIGITS(n, base, prec) \
3885 do { \
3886 ASSERT (base >= 2 && base < numberof (mp_bases)); \
3887 (n) = 2 + (size_t) ((((size_t) (prec) - 1) * GMP_NUMB_BITS) \
3888 * mp_bases[(base)].chars_per_bit_exactly); \
3889 } while (0)
3892 /* Decimal point string, from the current C locale. Needs <langinfo.h> for
3893 nl_langinfo and constants, preferably with _GNU_SOURCE defined to get
3894 DECIMAL_POINT from glibc, and needs <locale.h> for localeconv, each under
3895 their respective #if HAVE_FOO_H.
3897 GLIBC recommends nl_langinfo because getting only one facet can be
3898 faster, apparently. */
3900 /* DECIMAL_POINT seems to need _GNU_SOURCE defined to get it from glibc. */
3901 #if HAVE_NL_LANGINFO && defined (DECIMAL_POINT)
3902 #define GMP_DECIMAL_POINT (nl_langinfo (DECIMAL_POINT))
3903 #endif
3904 /* RADIXCHAR is deprecated, still in unix98 or some such. */
3905 #if HAVE_NL_LANGINFO && defined (RADIXCHAR) && ! defined (GMP_DECIMAL_POINT)
3906 #define GMP_DECIMAL_POINT (nl_langinfo (RADIXCHAR))
3907 #endif
3908 /* localeconv is slower since it returns all locale stuff */
3909 #if HAVE_LOCALECONV && ! defined (GMP_DECIMAL_POINT)
3910 #define GMP_DECIMAL_POINT (localeconv()->decimal_point)
3911 #endif
3912 #if ! defined (GMP_DECIMAL_POINT)
3914 #endif
3917 #define DOPRNT_CONV_FIXED 1
3918 #define DOPRNT_CONV_SCIENTIFIC 2
3919 #define DOPRNT_CONV_GENERAL 3
3921 #define DOPRNT_JUSTIFY_NONE 0
3922 #define DOPRNT_JUSTIFY_LEFT 1
3923 #define DOPRNT_JUSTIFY_RIGHT 2
3924 #define DOPRNT_JUSTIFY_INTERNAL 3
3926 #define DOPRNT_SHOWBASE_YES 1
3927 #define DOPRNT_SHOWBASE_NO 2
3928 #define DOPRNT_SHOWBASE_NONZERO 3
3943 };
3945 #if _GMP_H_HAVE_VA_LIST
3953 doprnt_format_t format;
3954 doprnt_memory_t memory;
3955 doprnt_reps_t reps;
3957 };
3965 /* "buf" is a __gmp_allocate_func block of "alloc" many bytes. The first
3966 "size" of these have been written. "alloc > size" is maintained, so
3967 there's room to store a '\0' at the end. "result" is where the
3968 application wants the final block pointer. */
3974 };
3976 #define GMP_ASPRINTF_T_INIT(d, output) \
3977 do { \
3978 (d).result = (output); \
3979 (d).alloc = 256; \
3980 (d).buf = (char *) (*__gmp_allocate_func) ((d).alloc); \
3981 (d).size = 0; \
3982 } while (0)
3984 /* If a realloc is necessary, use twice the size actually required, so as to
3985 avoid repeated small reallocs. */
3986 #define GMP_ASPRINTF_T_NEED(d, n) \
3987 do { \
3988 size_t alloc, newsize, newalloc; \
3989 ASSERT ((d)->alloc >= (d)->size + 1); \
3990 \
3991 alloc = (d)->alloc; \
3992 newsize = (d)->size + (n); \
3993 if (alloc <= newsize) \
3994 { \
3995 newalloc = 2*newsize; \
3996 (d)->alloc = newalloc; \
3997 (d)->buf = __GMP_REALLOCATE_FUNC_TYPE ((d)->buf, \
3998 alloc, newalloc, char); \
3999 } \
4000 } while (0)
4002 __GMP_DECLSPEC int __gmp_asprintf_memory __GMP_PROTO ((struct gmp_asprintf_t *, const char *, size_t));
4006 /* buf is where to write the next output, and size is how much space is left
4007 there. If the application passed size==0 then that's what we'll have
4008 here, and nothing at all should be written. */
4012 };
4014 /* Add the bytes printed by the call to the total retval, or bail out on an
4015 error. */
4016 #define DOPRNT_ACCUMULATE(call) \
4017 do { \
4018 int __ret; \
4019 __ret = call; \
4020 if (__ret == -1) \
4021 goto error; \
4022 retval += __ret; \
4023 } while (0)
4024 #define DOPRNT_ACCUMULATE_FUN(fun, params) \
4025 do { \
4026 ASSERT ((fun) != NULL); \
4027 DOPRNT_ACCUMULATE ((*(fun)) params); \
4028 } while (0)
4030 #define DOPRNT_FORMAT(fmt, ap) \
4031 DOPRNT_ACCUMULATE_FUN (funs->format, (data, fmt, ap))
4032 #define DOPRNT_MEMORY(ptr, len) \
4033 DOPRNT_ACCUMULATE_FUN (funs->memory, (data, ptr, len))
4034 #define DOPRNT_REPS(c, n) \
4035 DOPRNT_ACCUMULATE_FUN (funs->reps, (data, c, n))
4037 #define DOPRNT_STRING(str) DOPRNT_MEMORY (str, strlen (str))
4039 #define DOPRNT_REPS_MAYBE(c, n) \
4040 do { \
4041 if ((n) != 0) \
4042 DOPRNT_REPS (c, n); \
4043 } while (0)
4044 #define DOPRNT_MEMORY_MAYBE(ptr, len) \
4045 do { \
4046 if ((len) != 0) \
4047 DOPRNT_MEMORY (ptr, len); \
4048 } while (0)
4050 __GMP_DECLSPEC int __gmp_doprnt __GMP_PROTO ((const struct doprnt_funs_t *, void *, const char *, va_list));
4051 __GMP_DECLSPEC int __gmp_doprnt_integer __GMP_PROTO ((const struct doprnt_funs_t *, void *, const struct doprnt_params_t *, const char *));
4053 #define __gmp_doprnt_mpf __gmp_doprnt_mpf2
4054 __GMP_DECLSPEC int __gmp_doprnt_mpf __GMP_PROTO ((const struct doprnt_funs_t *, void *, const struct doprnt_params_t *, const char *, mpf_srcptr));
4056 __GMP_DECLSPEC int __gmp_replacement_vsnprintf __GMP_PROTO ((char *, size_t, const char *, va_list));
4066 gmp_doscan_scan_t scan;
4067 gmp_doscan_step_t step;
4068 gmp_doscan_get_t get;
4069 gmp_doscan_unget_t unget;
4070 };
4074 #if _GMP_H_HAVE_VA_LIST
4075 __GMP_DECLSPEC int __gmp_doscan __GMP_PROTO ((const struct gmp_doscan_funs_t *, void *, const char *, va_list));
4076 #endif
4079 /* For testing and debugging. */
4080 #define MPZ_CHECK_FORMAT(z) \
4081 do { \
4082 ASSERT_ALWAYS (SIZ(z) == 0 || PTR(z)[ABSIZ(z) - 1] != 0); \
4083 ASSERT_ALWAYS (ALLOC(z) >= ABSIZ(z)); \
4084 ASSERT_ALWAYS_MPN (PTR(z), ABSIZ(z)); \
4085 } while (0)
4087 #define MPQ_CHECK_FORMAT(q) \
4088 do { \
4089 MPZ_CHECK_FORMAT (mpq_numref (q)); \
4090 MPZ_CHECK_FORMAT (mpq_denref (q)); \
4091 ASSERT_ALWAYS (SIZ(mpq_denref(q)) >= 1); \
4092 \
4093 if (SIZ(mpq_numref(q)) == 0) \
4094 { \
4096 ASSERT_ALWAYS (SIZ(mpq_denref(q)) == 1 \
4097 && PTR(mpq_denref(q))[0] == 1); \
4098 } \
4099 else \
4100 { \
4102 mpz_t g; \
4103 mpz_init (g); \
4104 mpz_gcd (g, mpq_numref(q), mpq_denref(q)); \
4105 ASSERT_ALWAYS (mpz_cmp_ui (g, 1) == 0); \
4106 mpz_clear (g); \
4107 } \
4108 } while (0)
4110 #define MPF_CHECK_FORMAT(f) \
4111 do { \
4112 ASSERT_ALWAYS (PREC(f) >= __GMPF_BITS_TO_PREC(53)); \
4113 ASSERT_ALWAYS (ABSIZ(f) <= PREC(f)+1); \
4114 if (SIZ(f) == 0) \
4115 ASSERT_ALWAYS (EXP(f) == 0); \
4116 if (SIZ(f) != 0) \
4117 ASSERT_ALWAYS (PTR(f)[ABSIZ(f) - 1] != 0); \
4118 } while (0)
4121 #define MPZ_PROVOKE_REALLOC(z) \
4122 do { ALLOC(z) = ABSIZ(z); } while (0)
4125 /* Enhancement: The "mod" and "gcd_1" functions below could have
4126 __GMP_ATTRIBUTE_PURE, but currently (gcc 3.3) that's not supported on
4127 function pointers, only actual functions. It probably doesn't make much
4128 difference to the gmp code, since hopefully we arrange calls so there's
4129 no great need for the compiler to move things around. */
4131 #if WANT_FAT_BINARY && (HAVE_HOST_CPU_FAMILY_x86 || HAVE_HOST_CPU_FAMILY_x86_64)
4132 /* NOTE: The function pointers in this struct are also in CPUVEC_FUNCS_LIST
4133 in mpn/x86/x86-defs.m4. Be sure to update that when changing here. */
4156 mp_size_t mul_toom22_threshold;
4157 mp_size_t mul_toom33_threshold;
4158 mp_size_t sqr_toom2_threshold;
4159 mp_size_t sqr_toom3_threshold;
4160 };
4166 /* Get a threshold "field" from __gmpn_cpuvec, running __gmpn_cpuvec_init()
4167 if that hasn't yet been done (to establish the right values). */
4168 #define CPUVEC_THRESHOLD(field) \
4169 ((LIKELY (__gmpn_cpuvec.initialized) ? 0 : (__gmpn_cpuvec_init (), 0)), \
4170 __gmpn_cpuvec.field)
4173 #if HAVE_NATIVE_mpn_add_nc
4174 #define mpn_add_nc __MPN(add_nc)
4175 __GMP_DECLSPEC mp_limb_t mpn_add_nc __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t, mp_limb_t));
4176 #else
4178 mp_limb_t
4180 {
4181 mp_limb_t co;
4185 }
4186 #endif
4188 #if HAVE_NATIVE_mpn_sub_nc
4189 #define mpn_sub_nc __MPN(sub_nc)
4190 __GMP_DECLSPEC mp_limb_t mpn_sub_nc __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t, mp_limb_t));
4191 #else
4194 {
4195 mp_limb_t co;
4199 }
4200 #endif
4204 {
4205 mp_size_t i;
4207 {
4210 }
4212 }
4214 #if TUNE_PROGRAM_BUILD
4215 /* Some extras wanted when recompiling some .c files for use by the tune
4216 program. Not part of a normal build.
4218 It's necessary to keep these thresholds as #defines (just to an
4219 identically named variable), since various defaults are established based
4220 on #ifdef in the .c files. For some this is not so (the defaults are
4221 instead established above), but all are done this way for consistency. */
4223 #undef MUL_TOOM22_THRESHOLD
4224 #define MUL_TOOM22_THRESHOLD mul_toom22_threshold
4227 #undef MUL_TOOM33_THRESHOLD
4228 #define MUL_TOOM33_THRESHOLD mul_toom33_threshold
4231 #undef MUL_TOOM44_THRESHOLD
4232 #define MUL_TOOM44_THRESHOLD mul_toom44_threshold
4235 #undef MUL_TOOM6H_THRESHOLD
4236 #define MUL_TOOM6H_THRESHOLD mul_toom6h_threshold
4239 #undef MUL_TOOM8H_THRESHOLD
4240 #define MUL_TOOM8H_THRESHOLD mul_toom8h_threshold
4243 #undef MUL_TOOM32_TO_TOOM43_THRESHOLD
4244 #define MUL_TOOM32_TO_TOOM43_THRESHOLD mul_toom32_to_toom43_threshold
4247 #undef MUL_TOOM32_TO_TOOM53_THRESHOLD
4248 #define MUL_TOOM32_TO_TOOM53_THRESHOLD mul_toom32_to_toom53_threshold
4251 #undef MUL_TOOM42_TO_TOOM53_THRESHOLD
4252 #define MUL_TOOM42_TO_TOOM53_THRESHOLD mul_toom42_to_toom53_threshold
4255 #undef MUL_TOOM42_TO_TOOM63_THRESHOLD
4256 #define MUL_TOOM42_TO_TOOM63_THRESHOLD mul_toom42_to_toom63_threshold
4259 #undef MUL_FFT_THRESHOLD
4260 #define MUL_FFT_THRESHOLD mul_fft_threshold
4263 #undef MUL_FFT_MODF_THRESHOLD
4264 #define MUL_FFT_MODF_THRESHOLD mul_fft_modf_threshold
4267 #undef MUL_FFT_TABLE
4268 #define MUL_FFT_TABLE { 0 }
4270 #undef MUL_FFT_TABLE3
4271 #define MUL_FFT_TABLE3 { {0,0} }
4273 /* A native mpn_sqr_basecase is not tuned and SQR_BASECASE_THRESHOLD should
4274 remain as zero (always use it). */
4275 #if ! HAVE_NATIVE_mpn_sqr_basecase
4276 #undef SQR_BASECASE_THRESHOLD
4277 #define SQR_BASECASE_THRESHOLD sqr_basecase_threshold
4279 #endif
4281 #if TUNE_PROGRAM_BUILD_SQR
4282 #undef SQR_TOOM2_THRESHOLD
4283 #define SQR_TOOM2_THRESHOLD SQR_TOOM2_MAX_GENERIC
4284 #else
4285 #undef SQR_TOOM2_THRESHOLD
4286 #define SQR_TOOM2_THRESHOLD sqr_toom2_threshold
4288 #endif
4290 #undef SQR_TOOM3_THRESHOLD
4291 #define SQR_TOOM3_THRESHOLD sqr_toom3_threshold
4294 #undef SQR_TOOM4_THRESHOLD
4295 #define SQR_TOOM4_THRESHOLD sqr_toom4_threshold
4298 #undef SQR_TOOM6_THRESHOLD
4299 #define SQR_TOOM6_THRESHOLD sqr_toom6_threshold
4302 #undef SQR_TOOM8_THRESHOLD
4303 #define SQR_TOOM8_THRESHOLD sqr_toom8_threshold
4306 #undef SQR_FFT_THRESHOLD
4307 #define SQR_FFT_THRESHOLD sqr_fft_threshold
4310 #undef SQR_FFT_MODF_THRESHOLD
4311 #define SQR_FFT_MODF_THRESHOLD sqr_fft_modf_threshold
4314 #undef SQR_FFT_TABLE
4315 #define SQR_FFT_TABLE { 0 }
4317 #undef SQR_FFT_TABLE3
4318 #define SQR_FFT_TABLE3 { {0,0} }
4320 #undef MULLO_BASECASE_THRESHOLD
4321 #define MULLO_BASECASE_THRESHOLD mullo_basecase_threshold
4324 #undef MULLO_DC_THRESHOLD
4325 #define MULLO_DC_THRESHOLD mullo_dc_threshold
4328 #undef MULLO_MUL_N_THRESHOLD
4329 #define MULLO_MUL_N_THRESHOLD mullo_mul_n_threshold
4332 #undef DC_DIV_QR_THRESHOLD
4333 #define DC_DIV_QR_THRESHOLD dc_div_qr_threshold
4336 #undef DC_DIVAPPR_Q_THRESHOLD
4337 #define DC_DIVAPPR_Q_THRESHOLD dc_divappr_q_threshold
4340 #undef DC_BDIV_Q_THRESHOLD
4341 #define DC_BDIV_Q_THRESHOLD dc_bdiv_q_threshold
4344 #undef DC_BDIV_QR_THRESHOLD
4345 #define DC_BDIV_QR_THRESHOLD dc_bdiv_qr_threshold
4348 #undef MU_DIV_QR_THRESHOLD
4349 #define MU_DIV_QR_THRESHOLD mu_div_qr_threshold
4352 #undef MU_DIVAPPR_Q_THRESHOLD
4353 #define MU_DIVAPPR_Q_THRESHOLD mu_divappr_q_threshold
4356 #undef MUPI_DIV_QR_THRESHOLD
4357 #define MUPI_DIV_QR_THRESHOLD mupi_div_qr_threshold
4360 #undef MU_BDIV_QR_THRESHOLD
4361 #define MU_BDIV_QR_THRESHOLD mu_bdiv_qr_threshold
4364 #undef MU_BDIV_Q_THRESHOLD
4365 #define MU_BDIV_Q_THRESHOLD mu_bdiv_q_threshold
4368 #undef INV_MULMOD_BNM1_THRESHOLD
4369 #define INV_MULMOD_BNM1_THRESHOLD inv_mulmod_bnm1_threshold
4372 #undef INV_NEWTON_THRESHOLD
4373 #define INV_NEWTON_THRESHOLD inv_newton_threshold
4376 #undef INV_APPR_THRESHOLD
4377 #define INV_APPR_THRESHOLD inv_appr_threshold
4380 #undef BINV_NEWTON_THRESHOLD
4381 #define BINV_NEWTON_THRESHOLD binv_newton_threshold
4384 #undef REDC_1_TO_REDC_2_THRESHOLD
4385 #define REDC_1_TO_REDC_2_THRESHOLD redc_1_to_redc_2_threshold
4388 #undef REDC_2_TO_REDC_N_THRESHOLD
4389 #define REDC_2_TO_REDC_N_THRESHOLD redc_2_to_redc_n_threshold
4392 #undef REDC_1_TO_REDC_N_THRESHOLD
4393 #define REDC_1_TO_REDC_N_THRESHOLD redc_1_to_redc_n_threshold
4396 #undef MATRIX22_STRASSEN_THRESHOLD
4397 #define MATRIX22_STRASSEN_THRESHOLD matrix22_strassen_threshold
4400 #undef HGCD_THRESHOLD
4401 #define HGCD_THRESHOLD hgcd_threshold
4404 #undef GCD_DC_THRESHOLD
4405 #define GCD_DC_THRESHOLD gcd_dc_threshold
4408 #undef GCDEXT_DC_THRESHOLD
4409 #define GCDEXT_DC_THRESHOLD gcdext_dc_threshold
4412 #undef DIVREM_1_NORM_THRESHOLD
4413 #define DIVREM_1_NORM_THRESHOLD divrem_1_norm_threshold
4416 #undef DIVREM_1_UNNORM_THRESHOLD
4417 #define DIVREM_1_UNNORM_THRESHOLD divrem_1_unnorm_threshold
4420 #undef MOD_1_NORM_THRESHOLD
4421 #define MOD_1_NORM_THRESHOLD mod_1_norm_threshold
4424 #undef MOD_1_UNNORM_THRESHOLD
4425 #define MOD_1_UNNORM_THRESHOLD mod_1_unnorm_threshold
4428 #undef MOD_1N_TO_MOD_1_1_THRESHOLD
4429 #define MOD_1N_TO_MOD_1_1_THRESHOLD mod_1n_to_mod_1_1_threshold
4432 #undef MOD_1U_TO_MOD_1_1_THRESHOLD
4433 #define MOD_1U_TO_MOD_1_1_THRESHOLD mod_1u_to_mod_1_1_threshold
4436 #undef MOD_1_1_TO_MOD_1_2_THRESHOLD
4437 #define MOD_1_1_TO_MOD_1_2_THRESHOLD mod_1_1_to_mod_1_2_threshold
4440 #undef MOD_1_2_TO_MOD_1_4_THRESHOLD
4441 #define MOD_1_2_TO_MOD_1_4_THRESHOLD mod_1_2_to_mod_1_4_threshold
4444 #undef PREINV_MOD_1_TO_MOD_1_THRESHOLD
4445 #define PREINV_MOD_1_TO_MOD_1_THRESHOLD preinv_mod_1_to_mod_1_threshold
4448 #if ! UDIV_PREINV_ALWAYS
4449 #undef DIVREM_2_THRESHOLD
4450 #define DIVREM_2_THRESHOLD divrem_2_threshold
4452 #endif
4454 #undef MULMOD_BNM1_THRESHOLD
4455 #define MULMOD_BNM1_THRESHOLD mulmod_bnm1_threshold
4458 #undef SQRMOD_BNM1_THRESHOLD
4459 #define SQRMOD_BNM1_THRESHOLD sqrmod_bnm1_threshold
4462 #undef GET_STR_DC_THRESHOLD
4463 #define GET_STR_DC_THRESHOLD get_str_dc_threshold
4466 #undef GET_STR_PRECOMPUTE_THRESHOLD
4467 #define GET_STR_PRECOMPUTE_THRESHOLD get_str_precompute_threshold
4470 #undef SET_STR_DC_THRESHOLD
4471 #define SET_STR_DC_THRESHOLD set_str_dc_threshold
4474 #undef SET_STR_PRECOMPUTE_THRESHOLD
4475 #define SET_STR_PRECOMPUTE_THRESHOLD set_str_precompute_threshold
4478 #undef FFT_TABLE_ATTRS
4479 #define FFT_TABLE_ATTRS
4484 /* Sizes the tune program tests up to, used in a couple of recompilations. */
4485 #undef MUL_TOOM22_THRESHOLD_LIMIT
4486 #undef MUL_TOOM33_THRESHOLD_LIMIT
4487 #undef MULLO_BASECASE_THRESHOLD_LIMIT
4488 #undef SQR_TOOM3_THRESHOLD_LIMIT
4489 #define SQR_TOOM2_MAX_GENERIC 200
4490 #define MUL_TOOM22_THRESHOLD_LIMIT 700
4491 #define MUL_TOOM33_THRESHOLD_LIMIT 700
4492 #define SQR_TOOM3_THRESHOLD_LIMIT 400
4493 #define MUL_TOOM44_THRESHOLD_LIMIT 1000
4494 #define SQR_TOOM4_THRESHOLD_LIMIT 1000
4495 #define MUL_TOOM6H_THRESHOLD_LIMIT 1100
4496 #define SQR_TOOM6_THRESHOLD_LIMIT 1100
4497 #define MUL_TOOM8H_THRESHOLD_LIMIT 1200
4498 #define SQR_TOOM8_THRESHOLD_LIMIT 1200
4499 #define MULLO_BASECASE_THRESHOLD_LIMIT 200
4500 #define GET_STR_THRESHOLD_LIMIT 150
4504 #if defined (__cplusplus)
4505 }
4506 #endif
4508 /* FIXME: Make these itch functions less conservative. Also consider making
4509 them dependent on just 'an', and compute the allocation directly from 'an'
4510 instead of via n. */
4512 /* toom22/toom2: Scratch need is 2*(an + k), k is the recursion depth.
4513 k is ths smallest k such that
4514 ceil(an/2^k) < MUL_TOOM22_THRESHOLD.
4515 which implies that
4516 k = bitsize of floor ((an-1)/(MUL_TOOM22_THRESHOLD-1))
4517 = 1 + floor (log_2 (floor ((an-1)/(MUL_TOOM22_THRESHOLD-1))))
4518 */
4519 #define mpn_toom22_mul_itch(an, bn) \
4520 (2 * ((an) + GMP_NUMB_BITS))
4521 #define mpn_toom2_sqr_itch(an) \
4522 (2 * ((an) + GMP_NUMB_BITS))
4524 /* toom33/toom3: Scratch need is 5an/2 + 10k, k is the recursion depth.
4525 We use 3an + C, so that we can use a smaller constant.
4526 */
4527 #define mpn_toom33_mul_itch(an, bn) \
4528 (3 * (an) + GMP_NUMB_BITS)
4529 #define mpn_toom3_sqr_itch(an) \
4530 (3 * (an) + GMP_NUMB_BITS)
4532 /* toom33/toom3: Scratch need is 8an/3 + 13k, k is the recursion depth.
4533 We use 3an + C, so that we can use a smaller constant.
4534 */
4535 #define mpn_toom44_mul_itch(an, bn) \
4536 (3 * (an) + GMP_NUMB_BITS)
4537 #define mpn_toom4_sqr_itch(an) \
4538 (3 * (an) + GMP_NUMB_BITS)
4540 #define mpn_toom6_sqr_itch(n) \
4541 ( ((n) - SQR_TOOM6_THRESHOLD)*2 + \
4542 MAX(SQR_TOOM6_THRESHOLD*2 + GMP_NUMB_BITS*6, \
4543 mpn_toom4_sqr_itch(SQR_TOOM6_THRESHOLD)) )
4545 #define mpn_toom6_mul_n_itch(n) \
4546 ( ((n) - MUL_TOOM6H_THRESHOLD)*2 + \
4547 MAX(MUL_TOOM6H_THRESHOLD*2 + GMP_NUMB_BITS*6, \
4548 mpn_toom44_mul_itch(MUL_TOOM6H_THRESHOLD,MUL_TOOM6H_THRESHOLD)) )
4552 mp_size_t estimatedN;
4555 }
4557 #define mpn_toom8_sqr_itch(n) \
4558 ( (((n)*15)>>3) - ((SQR_TOOM8_THRESHOLD*15)>>3) + \
4559 MAX(((SQR_TOOM8_THRESHOLD*15)>>3) + GMP_NUMB_BITS*6, \
4560 mpn_toom6_sqr_itch(SQR_TOOM8_THRESHOLD)) )
4562 #define mpn_toom8_mul_n_itch(n) \
4563 ( (((n)*15)>>3) - ((MUL_TOOM8H_THRESHOLD*15)>>3) + \
4564 MAX(((MUL_TOOM8H_THRESHOLD*15)>>3) + GMP_NUMB_BITS*6, \
4565 mpn_toom6_mul_n_itch(MUL_TOOM8H_THRESHOLD)) )
4569 mp_size_t estimatedN;
4572 }
4576 {
4581 }
4585 {
4588 }
4592 {
4596 }
4600 {
4603 }
4607 {
4610 }
4614 {
4617 }
4621 {
4624 }
4626 #if 0
4627 #define mpn_fft_mul mpn_mul_fft_full
4628 #else
4629 #define mpn_fft_mul mpn_nussbaumer_mul
4630 #endif
4632 #ifdef __cplusplus
4634 /* A little helper for a null-terminated __gmp_allocate_func string.
4635 The destructor ensures it's freed even if an exception is thrown.
4636 The len field is needed by the destructor, and can be used by anyone else
4637 to avoid a second strlen pass over the data.
4639 Since our input is a C string, using strlen is correct. Perhaps it'd be
4640 more C++-ish style to use std::char_traits<char>::length, but char_traits
4641 isn't available in gcc 2.95.4. */
4648 {
4651 }
4653 {
4655 }
4656 };
4662 std::ostream& __gmp_doprnt_integer_ostream (std::ostream &o, struct doprnt_params_t *p, char *s);