1 From da4e4f5db6561923ad239aa653660250aaeb5873 Mon Sep 17 00:00:00 2001
2 From: Steven Barth <cyrus@openwrt.org>
3 Date: Mon, 6 Oct 2014 07:26:13 +0200
4 Subject: [PATCH 2/2] build: allow building with mini-gmp instead of gmp
6 This introduces --without-libgmp which includes mini-gmp into nft
7 (adding ~30k) but avoids linking libgmp which is >400k.
9 This is useful for embedded distributions not using gmp otherwise.
11 Note: currently --without-libgmp must be used with --disable-debug.
13 Signed-off-by: Steven Barth <cyrus@openwrt.org>
16 include/bignum.h | 17 +
17 include/expression.h | 2 +-
18 include/gmputil.h | 2 +-
19 include/mini-gmp.h | 294 ++++
20 include/utils.h | 4 +-
26 src/mini-gmp-printf.c | 62 +
27 src/mini-gmp.c | 4386 +++++++++++++++++++++++++++++++++++++++++++++++++
28 13 files changed, 4790 insertions(+), 13 deletions(-)
29 create mode 100644 include/bignum.h
30 create mode 100644 include/mini-gmp.h
31 create mode 100644 src/mini-gmp-printf.c
32 create mode 100644 src/mini-gmp.c
36 @@ -68,8 +68,18 @@ AC_CHECK_LIB([mnl], [mnl_socket_open], ,
37 AC_CHECK_LIB([nftnl], [nft_rule_alloc], ,
38 AC_MSG_ERROR([No suitable version of libnftnl found]))
40 -AC_CHECK_LIB([gmp], [__gmpz_init], ,
41 - AC_MSG_ERROR([No suitable version of libgmp found]))
42 +AC_ARG_WITH([libgmp], [AS_HELP_STRING([--without-libgmp],
43 + [Disable libgmp support (use builtin mini-gmp)])], [],
45 +AS_IF([test "x$with_libgmp" != xno], [
46 +AC_CHECK_LIB([gmp],[__gmpz_init], , AC_MSG_ERROR([No suitable version of libgmp found]))
48 +AC_SUBST(with_libgmp)
51 +AS_IF([test "x$with_libgmp" != xyes -a "x$CONFIG_DEBUG" = xy], [
52 +AC_MSG_ERROR([--without-libgmp MUST be used with --disable-debug])
56 AC_ARG_WITH([libreadline], [AS_HELP_STRING([--without-libreadline],
58 +++ b/include/bignum.h
60 +#ifndef NFTABLES_BIGNUM_H
61 +#define NFTABLES_BIGNUM_H
68 +#include <mini-gmp.h>
72 +int gmp_printf(const char *format, const mpz_t value);
76 +#endif /* NFTABLES_BIGNUM_H */
77 --- a/include/expression.h
78 +++ b/include/expression.h
80 #define NFTABLES_EXPRESSION_H
85 #include <linux/netfilter/nf_tables.h>
88 --- a/include/gmputil.h
89 +++ b/include/gmputil.h
91 #ifndef NFTABLES_GMPUTIL_H
92 #define NFTABLES_GMPUTIL_H
96 #include <asm/byteorder.h>
100 +++ b/include/mini-gmp.h
102 +/* mini-gmp, a minimalistic implementation of a GNU GMP subset.
104 +Copyright 2011-2014 Free Software Foundation, Inc.
106 +This file is part of the GNU MP Library.
108 +The GNU MP Library is free software; you can redistribute it and/or modify
109 +it under the terms of either:
111 + * the GNU Lesser General Public License as published by the Free
112 + Software Foundation; either version 3 of the License, or (at your
113 + option) any later version.
117 + * the GNU General Public License as published by the Free Software
118 + Foundation; either version 2 of the License, or (at your option) any
121 +or both in parallel, as here.
123 +The GNU MP Library is distributed in the hope that it will be useful, but
124 +WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
125 +or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
128 +You should have received copies of the GNU General Public License and the
129 +GNU Lesser General Public License along with the GNU MP Library. If not,
130 +see https://www.gnu.org/licenses/. */
132 +/* About mini-gmp: This is a minimal implementation of a subset of the
133 + GMP interface. It is intended for inclusion into applications which
134 + have modest bignums needs, as a fallback when the real GMP library
137 + This file defines the public interface. */
139 +#ifndef __MINI_GMP_H__
140 +#define __MINI_GMP_H__
145 +#if defined (__cplusplus)
149 +void mp_set_memory_functions (void *(*) (size_t),
150 + void *(*) (void *, size_t, size_t),
151 + void (*) (void *, size_t));
153 +void mp_get_memory_functions (void *(**) (size_t),
154 + void *(**) (void *, size_t, size_t),
155 + void (**) (void *, size_t));
157 +typedef unsigned long mp_limb_t;
158 +typedef long mp_size_t;
159 +typedef unsigned long mp_bitcnt_t;
161 +typedef mp_limb_t *mp_ptr;
162 +typedef const mp_limb_t *mp_srcptr;
166 + int _mp_alloc; /* Number of *limbs* allocated and pointed
167 + to by the _mp_d field. */
168 + int _mp_size; /* abs(_mp_size) is the number of limbs the
169 + last field points to. If _mp_size is
170 + negative this is a negative number. */
171 + mp_limb_t *_mp_d; /* Pointer to the limbs. */
174 +typedef __mpz_struct mpz_t[1];
176 +typedef __mpz_struct *mpz_ptr;
177 +typedef const __mpz_struct *mpz_srcptr;
179 +extern const int mp_bits_per_limb;
181 +void mpn_copyi (mp_ptr, mp_srcptr, mp_size_t);
182 +void mpn_copyd (mp_ptr, mp_srcptr, mp_size_t);
183 +void mpn_zero (mp_ptr, mp_size_t);
185 +int mpn_cmp (mp_srcptr, mp_srcptr, mp_size_t);
187 +mp_limb_t mpn_add_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t);
188 +mp_limb_t mpn_add_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
189 +mp_limb_t mpn_add (mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t);
191 +mp_limb_t mpn_sub_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t);
192 +mp_limb_t mpn_sub_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
193 +mp_limb_t mpn_sub (mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t);
195 +mp_limb_t mpn_mul_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t);
196 +mp_limb_t mpn_addmul_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t);
197 +mp_limb_t mpn_submul_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t);
199 +mp_limb_t mpn_mul (mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t);
200 +void mpn_mul_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
201 +void mpn_sqr (mp_ptr, mp_srcptr, mp_size_t);
202 +int mpn_perfect_square_p (mp_srcptr, mp_size_t);
203 +mp_size_t mpn_sqrtrem (mp_ptr, mp_ptr, mp_srcptr, mp_size_t);
205 +mp_limb_t mpn_lshift (mp_ptr, mp_srcptr, mp_size_t, unsigned int);
206 +mp_limb_t mpn_rshift (mp_ptr, mp_srcptr, mp_size_t, unsigned int);
208 +mp_bitcnt_t mpn_scan0 (mp_srcptr, mp_bitcnt_t);
209 +mp_bitcnt_t mpn_scan1 (mp_srcptr, mp_bitcnt_t);
211 +mp_bitcnt_t mpn_popcount (mp_srcptr, mp_size_t);
213 +mp_limb_t mpn_invert_3by2 (mp_limb_t, mp_limb_t);
214 +#define mpn_invert_limb(x) mpn_invert_3by2 ((x), 0)
216 +size_t mpn_get_str (unsigned char *, int, mp_ptr, mp_size_t);
217 +mp_size_t mpn_set_str (mp_ptr, const unsigned char *, size_t, int);
219 +void mpz_init (mpz_t);
220 +void mpz_init2 (mpz_t, mp_bitcnt_t);
221 +void mpz_clear (mpz_t);
223 +#define mpz_odd_p(z) (((z)->_mp_size != 0) & (int) (z)->_mp_d[0])
224 +#define mpz_even_p(z) (! mpz_odd_p (z))
226 +int mpz_sgn (const mpz_t);
227 +int mpz_cmp_si (const mpz_t, long);
228 +int mpz_cmp_ui (const mpz_t, unsigned long);
229 +int mpz_cmp (const mpz_t, const mpz_t);
230 +int mpz_cmpabs_ui (const mpz_t, unsigned long);
231 +int mpz_cmpabs (const mpz_t, const mpz_t);
232 +int mpz_cmp_d (const mpz_t, double);
233 +int mpz_cmpabs_d (const mpz_t, double);
235 +void mpz_abs (mpz_t, const mpz_t);
236 +void mpz_neg (mpz_t, const mpz_t);
237 +void mpz_swap (mpz_t, mpz_t);
239 +void mpz_add_ui (mpz_t, const mpz_t, unsigned long);
240 +void mpz_add (mpz_t, const mpz_t, const mpz_t);
241 +void mpz_sub_ui (mpz_t, const mpz_t, unsigned long);
242 +void mpz_ui_sub (mpz_t, unsigned long, const mpz_t);
243 +void mpz_sub (mpz_t, const mpz_t, const mpz_t);
245 +void mpz_mul_si (mpz_t, const mpz_t, long int);
246 +void mpz_mul_ui (mpz_t, const mpz_t, unsigned long int);
247 +void mpz_mul (mpz_t, const mpz_t, const mpz_t);
248 +void mpz_mul_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
249 +void mpz_addmul_ui (mpz_t, const mpz_t, unsigned long int);
250 +void mpz_addmul (mpz_t, const mpz_t, const mpz_t);
251 +void mpz_submul_ui (mpz_t, const mpz_t, unsigned long int);
252 +void mpz_submul (mpz_t, const mpz_t, const mpz_t);
254 +void mpz_cdiv_qr (mpz_t, mpz_t, const mpz_t, const mpz_t);
255 +void mpz_fdiv_qr (mpz_t, mpz_t, const mpz_t, const mpz_t);
256 +void mpz_tdiv_qr (mpz_t, mpz_t, const mpz_t, const mpz_t);
257 +void mpz_cdiv_q (mpz_t, const mpz_t, const mpz_t);
258 +void mpz_fdiv_q (mpz_t, const mpz_t, const mpz_t);
259 +void mpz_tdiv_q (mpz_t, const mpz_t, const mpz_t);
260 +void mpz_cdiv_r (mpz_t, const mpz_t, const mpz_t);
261 +void mpz_fdiv_r (mpz_t, const mpz_t, const mpz_t);
262 +void mpz_tdiv_r (mpz_t, const mpz_t, const mpz_t);
264 +void mpz_cdiv_q_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
265 +void mpz_fdiv_q_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
266 +void mpz_tdiv_q_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
267 +void mpz_cdiv_r_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
268 +void mpz_fdiv_r_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
269 +void mpz_tdiv_r_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
271 +void mpz_mod (mpz_t, const mpz_t, const mpz_t);
273 +void mpz_divexact (mpz_t, const mpz_t, const mpz_t);
275 +int mpz_divisible_p (const mpz_t, const mpz_t);
276 +int mpz_congruent_p (const mpz_t, const mpz_t, const mpz_t);
278 +unsigned long mpz_cdiv_qr_ui (mpz_t, mpz_t, const mpz_t, unsigned long);
279 +unsigned long mpz_fdiv_qr_ui (mpz_t, mpz_t, const mpz_t, unsigned long);
280 +unsigned long mpz_tdiv_qr_ui (mpz_t, mpz_t, const mpz_t, unsigned long);
281 +unsigned long mpz_cdiv_q_ui (mpz_t, const mpz_t, unsigned long);
282 +unsigned long mpz_fdiv_q_ui (mpz_t, const mpz_t, unsigned long);
283 +unsigned long mpz_tdiv_q_ui (mpz_t, const mpz_t, unsigned long);
284 +unsigned long mpz_cdiv_r_ui (mpz_t, const mpz_t, unsigned long);
285 +unsigned long mpz_fdiv_r_ui (mpz_t, const mpz_t, unsigned long);
286 +unsigned long mpz_tdiv_r_ui (mpz_t, const mpz_t, unsigned long);
287 +unsigned long mpz_cdiv_ui (const mpz_t, unsigned long);
288 +unsigned long mpz_fdiv_ui (const mpz_t, unsigned long);
289 +unsigned long mpz_tdiv_ui (const mpz_t, unsigned long);
291 +unsigned long mpz_mod_ui (mpz_t, const mpz_t, unsigned long);
293 +void mpz_divexact_ui (mpz_t, const mpz_t, unsigned long);
295 +int mpz_divisible_ui_p (const mpz_t, unsigned long);
297 +unsigned long mpz_gcd_ui (mpz_t, const mpz_t, unsigned long);
298 +void mpz_gcd (mpz_t, const mpz_t, const mpz_t);
299 +void mpz_gcdext (mpz_t, mpz_t, mpz_t, const mpz_t, const mpz_t);
300 +void mpz_lcm_ui (mpz_t, const mpz_t, unsigned long);
301 +void mpz_lcm (mpz_t, const mpz_t, const mpz_t);
302 +int mpz_invert (mpz_t, const mpz_t, const mpz_t);
304 +void mpz_sqrtrem (mpz_t, mpz_t, const mpz_t);
305 +void mpz_sqrt (mpz_t, const mpz_t);
306 +int mpz_perfect_square_p (const mpz_t);
308 +void mpz_pow_ui (mpz_t, const mpz_t, unsigned long);
309 +void mpz_ui_pow_ui (mpz_t, unsigned long, unsigned long);
310 +void mpz_powm (mpz_t, const mpz_t, const mpz_t, const mpz_t);
311 +void mpz_powm_ui (mpz_t, const mpz_t, unsigned long, const mpz_t);
313 +void mpz_rootrem (mpz_t, mpz_t, const mpz_t, unsigned long);
314 +int mpz_root (mpz_t, const mpz_t, unsigned long);
316 +void mpz_fac_ui (mpz_t, unsigned long);
317 +void mpz_bin_uiui (mpz_t, unsigned long, unsigned long);
319 +int mpz_probab_prime_p (const mpz_t, int);
321 +int mpz_tstbit (const mpz_t, mp_bitcnt_t);
322 +void mpz_setbit (mpz_t, mp_bitcnt_t);
323 +void mpz_clrbit (mpz_t, mp_bitcnt_t);
324 +void mpz_combit (mpz_t, mp_bitcnt_t);
326 +void mpz_com (mpz_t, const mpz_t);
327 +void mpz_and (mpz_t, const mpz_t, const mpz_t);
328 +void mpz_ior (mpz_t, const mpz_t, const mpz_t);
329 +void mpz_xor (mpz_t, const mpz_t, const mpz_t);
331 +mp_bitcnt_t mpz_popcount (const mpz_t);
332 +mp_bitcnt_t mpz_hamdist (const mpz_t, const mpz_t);
333 +mp_bitcnt_t mpz_scan0 (const mpz_t, mp_bitcnt_t);
334 +mp_bitcnt_t mpz_scan1 (const mpz_t, mp_bitcnt_t);
336 +int mpz_fits_slong_p (const mpz_t);
337 +int mpz_fits_ulong_p (const mpz_t);
338 +long int mpz_get_si (const mpz_t);
339 +unsigned long int mpz_get_ui (const mpz_t);
340 +double mpz_get_d (const mpz_t);
341 +size_t mpz_size (const mpz_t);
342 +mp_limb_t mpz_getlimbn (const mpz_t, mp_size_t);
344 +void mpz_realloc2 (mpz_t, mp_bitcnt_t);
345 +mp_srcptr mpz_limbs_read (mpz_srcptr);
346 +mp_ptr mpz_limbs_modify (mpz_t, mp_size_t);
347 +mp_ptr mpz_limbs_write (mpz_t, mp_size_t);
348 +void mpz_limbs_finish (mpz_t, mp_size_t);
349 +mpz_srcptr mpz_roinit_n (mpz_t, mp_srcptr, mp_size_t);
351 +#define MPZ_ROINIT_N(xp, xs) {{0, (xs),(xp) }}
353 +void mpz_set_si (mpz_t, signed long int);
354 +void mpz_set_ui (mpz_t, unsigned long int);
355 +void mpz_set (mpz_t, const mpz_t);
356 +void mpz_set_d (mpz_t, double);
358 +void mpz_init_set_si (mpz_t, signed long int);
359 +void mpz_init_set_ui (mpz_t, unsigned long int);
360 +void mpz_init_set (mpz_t, const mpz_t);
361 +void mpz_init_set_d (mpz_t, double);
363 +size_t mpz_sizeinbase (const mpz_t, int);
364 +char *mpz_get_str (char *, int, const mpz_t);
365 +int mpz_set_str (mpz_t, const char *, int);
366 +int mpz_init_set_str (mpz_t, const char *, int);
368 +/* This long list taken from gmp.h. */
369 +/* For reference, "defined(EOF)" cannot be used here. In g++ 2.95.4,
370 + <iostream> defines EOF but not FILE. */
371 +#if defined (FILE) \
372 + || defined (H_STDIO) \
373 + || defined (_H_STDIO) /* AIX */ \
374 + || defined (_STDIO_H) /* glibc, Sun, SCO */ \
375 + || defined (_STDIO_H_) /* BSD, OSF */ \
376 + || defined (__STDIO_H) /* Borland */ \
377 + || defined (__STDIO_H__) /* IRIX */ \
378 + || defined (_STDIO_INCLUDED) /* HPUX */ \
379 + || defined (__dj_include_stdio_h_) /* DJGPP */ \
380 + || defined (_FILE_DEFINED) /* Microsoft */ \
381 + || defined (__STDIO__) /* Apple MPW MrC */ \
382 + || defined (_MSL_STDIO_H) /* Metrowerks */ \
383 + || defined (_STDIO_H_INCLUDED) /* QNX4 */ \
384 + || defined (_ISO_STDIO_ISO_H) /* Sun C++ */ \
385 + || defined (__STDIO_LOADED) /* VMS */
386 +size_t mpz_out_str (FILE *, int, const mpz_t);
389 +void mpz_import (mpz_t, size_t, int, size_t, int, size_t, const void *);
390 +void *mpz_export (void *, size_t *, int, size_t, int, size_t, const mpz_t);
392 +#if defined (__cplusplus)
395 +#endif /* __MINI_GMP_H__ */
396 --- a/include/utils.h
397 +++ b/include/utils.h
405 #define BITS_PER_BYTE 8
408 #define pr_debug(fmt, arg...) gmp_printf(fmt, ##arg)
410 -#define pr_debug(fmt, arg...) ({ if (false) gmp_printf(fmt, ##arg); 0; })
411 +#define pr_debug(fmt, arg...)
414 #define __fmtstring(x, y) __attribute__((format(printf, x, y)))
415 --- a/src/Makefile.in
416 +++ b/src/Makefile.in
417 @@ -31,3 +31,8 @@ nft-extra-clean-files += parser.c parser
420 nft-extra-clean-files += scanner.c scanner.h
422 +ifneq (@with_libgmp@,yes)
423 +nft-obj += mini-gmp.o
424 +nft-obj += mini-gmp-printf.o
428 @@ -252,11 +252,9 @@ static struct error_record *integer_type
435 - if (gmp_sscanf(sym->identifier, "%Zu%n", v, &len) != 1 ||
436 - (int)strlen(sym->identifier) != len) {
437 + if (mpz_set_str(v, sym->identifier, 0)) {
439 if (sym->dtype != &integer_type)
443 @@ -43,6 +43,7 @@ static void erec_destroy(struct error_re
447 +__attribute__((format(printf, 3, 0)))
448 struct error_record *erec_vcreate(enum error_record_types type,
449 const struct location *loc,
450 const char *fmt, va_list ap)
451 @@ -54,10 +55,11 @@ struct error_record *erec_vcreate(enum e
452 erec->num_locations = 0;
453 erec_add_location(erec, loc);
455 - gmp_vasprintf(&erec->msg, fmt, ap);
456 + if (vasprintf(&erec->msg, fmt, ap)) {}
460 +__attribute__((format(printf, 3, 4)))
461 struct error_record *erec_create(enum error_record_types type,
462 const struct location *loc,
463 const char *fmt, ...)
466 @@ -228,9 +228,13 @@ static int expr_evaluate_value(struct ev
468 mpz_init_bitmask(mask, ctx->ectx.len);
469 if (mpz_cmp((*expr)->value, mask) > 0) {
470 + char *valstr = mpz_get_str(NULL, 10, (*expr)->value);
471 + char *rangestr = mpz_get_str(NULL, 10, mask);
472 expr_error(ctx->msgs, *expr,
473 - "Value %Zu exceeds valid range 0-%Zu",
474 - (*expr)->value, mask);
475 + "Value %s exceeds valid range 0-%s",
490 #include <nftables.h>
491 #include <datatype.h>
493 +++ b/src/mini-gmp-printf.c
496 +#include <stdbool.h>
501 +// nftables mostly uses gmp_printf as below so we build a minimalistic
502 +// version to avoid the awkwardness of wrapping printf.
503 +// This requires rewriting other occurences of gmp_printf or
504 +// variants which are rare (only 1 so far).
505 +// Also we exclude pr_debug here since this is a rathole
506 +// and if debugging is desired then libgmp can be used.
508 +int gmp_printf(const char *f, const mpz_t value)
513 + if (fputc(*f, stdout) != *f)
518 + unsigned long prec = 0;
525 + prec = strtoul(++f, (char**)&f, 10);
532 + else if (*f == 'x')
537 + len = mpz_sizeinbase(value, base);
538 + while (--prec >= len) {
539 + if (fputc('0', stdout) != '0')
545 + str = mpz_get_str(NULL, base, value);
546 + ok = str && fwrite(str, 1, len, stdout) == len;
561 +/* mini-gmp, a minimalistic implementation of a GNU GMP subset.
563 + Contributed to the GNU project by Niels Möller
565 +Copyright 1991-1997, 1999-2014 Free Software Foundation, Inc.
567 +This file is part of the GNU MP Library.
569 +The GNU MP Library is free software; you can redistribute it and/or modify
570 +it under the terms of either:
572 + * the GNU Lesser General Public License as published by the Free
573 + Software Foundation; either version 3 of the License, or (at your
574 + option) any later version.
578 + * the GNU General Public License as published by the Free Software
579 + Foundation; either version 2 of the License, or (at your option) any
582 +or both in parallel, as here.
584 +The GNU MP Library is distributed in the hope that it will be useful, but
585 +WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
586 +or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
589 +You should have received copies of the GNU General Public License and the
590 +GNU Lesser General Public License along with the GNU MP Library. If not,
591 +see https://www.gnu.org/licenses/. */
593 +/* NOTE: All functions in this file which are not declared in
594 + mini-gmp.h are internal, and are not intended to be compatible
595 + neither with GMP nor with future versions of mini-gmp. */
597 +/* Much of the material copied from GMP files, including: gmp-impl.h,
598 + longlong.h, mpn/generic/add_n.c, mpn/generic/addmul_1.c,
599 + mpn/generic/lshift.c, mpn/generic/mul_1.c,
600 + mpn/generic/mul_basecase.c, mpn/generic/rshift.c,
601 + mpn/generic/sbpi1_div_qr.c, mpn/generic/sub_n.c,
602 + mpn/generic/submul_1.c. */
611 +#include "mini-gmp.h"
615 +#define GMP_LIMB_BITS (sizeof(mp_limb_t) * CHAR_BIT)
617 +#define GMP_LIMB_MAX (~ (mp_limb_t) 0)
618 +#define GMP_LIMB_HIGHBIT ((mp_limb_t) 1 << (GMP_LIMB_BITS - 1))
620 +#define GMP_HLIMB_BIT ((mp_limb_t) 1 << (GMP_LIMB_BITS / 2))
621 +#define GMP_LLIMB_MASK (GMP_HLIMB_BIT - 1)
623 +#define GMP_ULONG_BITS (sizeof(unsigned long) * CHAR_BIT)
624 +#define GMP_ULONG_HIGHBIT ((unsigned long) 1 << (GMP_ULONG_BITS - 1))
626 +#define GMP_ABS(x) ((x) >= 0 ? (x) : -(x))
627 +#define GMP_NEG_CAST(T,x) (-((T)((x) + 1) - 1))
629 +#define GMP_MIN(a, b) ((a) < (b) ? (a) : (b))
630 +#define GMP_MAX(a, b) ((a) > (b) ? (a) : (b))
632 +#define gmp_assert_nocarry(x) do { \
633 + mp_limb_t __cy = x; \
634 + assert (__cy == 0); \
637 +#define gmp_clz(count, x) do { \
638 + mp_limb_t __clz_x = (x); \
639 + unsigned __clz_c; \
640 + for (__clz_c = 0; \
641 + (__clz_x & ((mp_limb_t) 0xff << (GMP_LIMB_BITS - 8))) == 0; \
644 + for (; (__clz_x & GMP_LIMB_HIGHBIT) == 0; __clz_c++) \
646 + (count) = __clz_c; \
649 +#define gmp_ctz(count, x) do { \
650 + mp_limb_t __ctz_x = (x); \
651 + unsigned __ctz_c = 0; \
652 + gmp_clz (__ctz_c, __ctz_x & - __ctz_x); \
653 + (count) = GMP_LIMB_BITS - 1 - __ctz_c; \
656 +#define gmp_add_ssaaaa(sh, sl, ah, al, bh, bl) \
659 + __x = (al) + (bl); \
660 + (sh) = (ah) + (bh) + (__x < (al)); \
664 +#define gmp_sub_ddmmss(sh, sl, ah, al, bh, bl) \
667 + __x = (al) - (bl); \
668 + (sh) = (ah) - (bh) - ((al) < (bl)); \
672 +#define gmp_umul_ppmm(w1, w0, u, v) \
674 + mp_limb_t __x0, __x1, __x2, __x3; \
675 + unsigned __ul, __vl, __uh, __vh; \
676 + mp_limb_t __u = (u), __v = (v); \
678 + __ul = __u & GMP_LLIMB_MASK; \
679 + __uh = __u >> (GMP_LIMB_BITS / 2); \
680 + __vl = __v & GMP_LLIMB_MASK; \
681 + __vh = __v >> (GMP_LIMB_BITS / 2); \
683 + __x0 = (mp_limb_t) __ul * __vl; \
684 + __x1 = (mp_limb_t) __ul * __vh; \
685 + __x2 = (mp_limb_t) __uh * __vl; \
686 + __x3 = (mp_limb_t) __uh * __vh; \
688 + __x1 += __x0 >> (GMP_LIMB_BITS / 2);/* this can't give carry */ \
689 + __x1 += __x2; /* but this indeed can */ \
690 + if (__x1 < __x2) /* did we get it? */ \
691 + __x3 += GMP_HLIMB_BIT; /* yes, add it in the proper pos. */ \
693 + (w1) = __x3 + (__x1 >> (GMP_LIMB_BITS / 2)); \
694 + (w0) = (__x1 << (GMP_LIMB_BITS / 2)) + (__x0 & GMP_LLIMB_MASK); \
697 +#define gmp_udiv_qrnnd_preinv(q, r, nh, nl, d, di) \
699 + mp_limb_t _qh, _ql, _r, _mask; \
700 + gmp_umul_ppmm (_qh, _ql, (nh), (di)); \
701 + gmp_add_ssaaaa (_qh, _ql, _qh, _ql, (nh) + 1, (nl)); \
702 + _r = (nl) - _qh * (d); \
703 + _mask = -(mp_limb_t) (_r > _ql); /* both > and >= are OK */ \
705 + _r += _mask & (d); \
716 +#define gmp_udiv_qr_3by2(q, r1, r0, n2, n1, n0, d1, d0, dinv) \
718 + mp_limb_t _q0, _t1, _t0, _mask; \
719 + gmp_umul_ppmm ((q), _q0, (n2), (dinv)); \
720 + gmp_add_ssaaaa ((q), _q0, (q), _q0, (n2), (n1)); \
722 + /* Compute the two most significant limbs of n - q'd */ \
723 + (r1) = (n1) - (d1) * (q); \
724 + gmp_sub_ddmmss ((r1), (r0), (r1), (n0), (d1), (d0)); \
725 + gmp_umul_ppmm (_t1, _t0, (d0), (q)); \
726 + gmp_sub_ddmmss ((r1), (r0), (r1), (r0), _t1, _t0); \
729 + /* Conditionally adjust q and the remainders */ \
730 + _mask = - (mp_limb_t) ((r1) >= _q0); \
732 + gmp_add_ssaaaa ((r1), (r0), (r1), (r0), _mask & (d1), _mask & (d0)); \
733 + if ((r1) >= (d1)) \
735 + if ((r1) > (d1) || (r0) >= (d0)) \
738 + gmp_sub_ddmmss ((r1), (r0), (r1), (r0), (d1), (d0)); \
744 +#define MP_LIMB_T_SWAP(x, y) \
746 + mp_limb_t __mp_limb_t_swap__tmp = (x); \
748 + (y) = __mp_limb_t_swap__tmp; \
750 +#define MP_SIZE_T_SWAP(x, y) \
752 + mp_size_t __mp_size_t_swap__tmp = (x); \
754 + (y) = __mp_size_t_swap__tmp; \
756 +#define MP_BITCNT_T_SWAP(x,y) \
758 + mp_bitcnt_t __mp_bitcnt_t_swap__tmp = (x); \
760 + (y) = __mp_bitcnt_t_swap__tmp; \
762 +#define MP_PTR_SWAP(x, y) \
764 + mp_ptr __mp_ptr_swap__tmp = (x); \
766 + (y) = __mp_ptr_swap__tmp; \
768 +#define MP_SRCPTR_SWAP(x, y) \
770 + mp_srcptr __mp_srcptr_swap__tmp = (x); \
772 + (y) = __mp_srcptr_swap__tmp; \
775 +#define MPN_PTR_SWAP(xp,xs, yp,ys) \
777 + MP_PTR_SWAP (xp, yp); \
778 + MP_SIZE_T_SWAP (xs, ys); \
780 +#define MPN_SRCPTR_SWAP(xp,xs, yp,ys) \
782 + MP_SRCPTR_SWAP (xp, yp); \
783 + MP_SIZE_T_SWAP (xs, ys); \
786 +#define MPZ_PTR_SWAP(x, y) \
788 + mpz_ptr __mpz_ptr_swap__tmp = (x); \
790 + (y) = __mpz_ptr_swap__tmp; \
792 +#define MPZ_SRCPTR_SWAP(x, y) \
794 + mpz_srcptr __mpz_srcptr_swap__tmp = (x); \
796 + (y) = __mpz_srcptr_swap__tmp; \
799 +const int mp_bits_per_limb = GMP_LIMB_BITS;
802 +/* Memory allocation and other helper functions. */
804 +gmp_die (const char *msg)
806 + fprintf (stderr, "%s\n", msg);
811 +gmp_default_alloc (size_t size)
819 + gmp_die("gmp_default_alloc: Virtual memory exhausted.");
825 +gmp_default_realloc (void *old, size_t old_size, size_t new_size)
829 + p = realloc (old, new_size);
832 + gmp_die("gmp_default_realoc: Virtual memory exhausted.");
838 +gmp_default_free (void *p, size_t size)
843 +static void * (*gmp_allocate_func) (size_t) = gmp_default_alloc;
844 +static void * (*gmp_reallocate_func) (void *, size_t, size_t) = gmp_default_realloc;
845 +static void (*gmp_free_func) (void *, size_t) = gmp_default_free;
848 +mp_get_memory_functions (void *(**alloc_func) (size_t),
849 + void *(**realloc_func) (void *, size_t, size_t),
850 + void (**free_func) (void *, size_t))
853 + *alloc_func = gmp_allocate_func;
856 + *realloc_func = gmp_reallocate_func;
859 + *free_func = gmp_free_func;
863 +mp_set_memory_functions (void *(*alloc_func) (size_t),
864 + void *(*realloc_func) (void *, size_t, size_t),
865 + void (*free_func) (void *, size_t))
868 + alloc_func = gmp_default_alloc;
870 + realloc_func = gmp_default_realloc;
872 + free_func = gmp_default_free;
874 + gmp_allocate_func = alloc_func;
875 + gmp_reallocate_func = realloc_func;
876 + gmp_free_func = free_func;
879 +#define gmp_xalloc(size) ((*gmp_allocate_func)((size)))
880 +#define gmp_free(p) ((*gmp_free_func) ((p), 0))
883 +gmp_xalloc_limbs (mp_size_t size)
885 + return gmp_xalloc (size * sizeof (mp_limb_t));
889 +gmp_xrealloc_limbs (mp_ptr old, mp_size_t size)
892 + return (*gmp_reallocate_func) (old, 0, size * sizeof (mp_limb_t));
899 +mpn_copyi (mp_ptr d, mp_srcptr s, mp_size_t n)
902 + for (i = 0; i < n; i++)
907 +mpn_copyd (mp_ptr d, mp_srcptr s, mp_size_t n)
914 +mpn_cmp (mp_srcptr ap, mp_srcptr bp, mp_size_t n)
918 + if (ap[n] != bp[n])
919 + return ap[n] > bp[n] ? 1 : -1;
925 +mpn_cmp4 (mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
928 + return an < bn ? -1 : 1;
930 + return mpn_cmp (ap, bp, an);
934 +mpn_normalized_size (mp_srcptr xp, mp_size_t n)
936 + for (; n > 0 && xp[n-1] == 0; n--)
941 +#define mpn_zero_p(xp, n) (mpn_normalized_size ((xp), (n)) == 0)
944 +mpn_zero (mp_ptr rp, mp_size_t n)
948 + for (i = 0; i < n; i++)
953 +mpn_add_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b)
961 + mp_limb_t r = ap[i] + b;
972 +mpn_add_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
977 + for (i = 0, cy = 0; i < n; i++)
980 + a = ap[i]; b = bp[i];
991 +mpn_add (mp_ptr rp, mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
997 + cy = mpn_add_n (rp, ap, bp, bn);
999 + cy = mpn_add_1 (rp + bn, ap + bn, an - bn, cy);
1004 +mpn_sub_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b)
1013 + mp_limb_t a = ap[i];
1015 + mp_limb_t cy = a < b;;
1025 +mpn_sub_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
1030 + for (i = 0, cy = 0; i < n; i++)
1033 + a = ap[i]; b = bp[i];
1043 +mpn_sub (mp_ptr rp, mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
1047 + assert (an >= bn);
1049 + cy = mpn_sub_n (rp, ap, bp, bn);
1051 + cy = mpn_sub_1 (rp + bn, ap + bn, an - bn, cy);
1056 +mpn_mul_1 (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_limb_t vl)
1058 + mp_limb_t ul, cl, hpl, lpl;
1066 + gmp_umul_ppmm (hpl, lpl, ul, vl);
1069 + cl = (lpl < cl) + hpl;
1079 +mpn_addmul_1 (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_limb_t vl)
1081 + mp_limb_t ul, cl, hpl, lpl, rl;
1089 + gmp_umul_ppmm (hpl, lpl, ul, vl);
1092 + cl = (lpl < cl) + hpl;
1105 +mpn_submul_1 (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_limb_t vl)
1107 + mp_limb_t ul, cl, hpl, lpl, rl;
1115 + gmp_umul_ppmm (hpl, lpl, ul, vl);
1118 + cl = (lpl < cl) + hpl;
1131 +mpn_mul (mp_ptr rp, mp_srcptr up, mp_size_t un, mp_srcptr vp, mp_size_t vn)
1133 + assert (un >= vn);
1136 + /* We first multiply by the low order limb. This result can be
1137 + stored, not added, to rp. We also avoid a loop for zeroing this
1140 + rp[un] = mpn_mul_1 (rp, up, un, vp[0]);
1141 + rp += 1, vp += 1, vn -= 1;
1143 + /* Now accumulate the product of up[] and the next higher limb from
1148 + rp[un] = mpn_addmul_1 (rp, up, un, vp[0]);
1149 + rp += 1, vp += 1, vn -= 1;
1151 + return rp[un - 1];
1155 +mpn_mul_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
1157 + mpn_mul (rp, ap, n, bp, n);
1161 +mpn_sqr (mp_ptr rp, mp_srcptr ap, mp_size_t n)
1163 + mpn_mul (rp, ap, n, ap, n);
1167 +mpn_lshift (mp_ptr rp, mp_srcptr up, mp_size_t n, unsigned int cnt)
1169 + mp_limb_t high_limb, low_limb;
1175 + assert (cnt >= 1);
1176 + assert (cnt < GMP_LIMB_BITS);
1181 + tnc = GMP_LIMB_BITS - cnt;
1183 + retval = low_limb >> tnc;
1184 + high_limb = (low_limb << cnt);
1186 + for (i = n; --i != 0;)
1189 + *--rp = high_limb | (low_limb >> tnc);
1190 + high_limb = (low_limb << cnt);
1192 + *--rp = high_limb;
1198 +mpn_rshift (mp_ptr rp, mp_srcptr up, mp_size_t n, unsigned int cnt)
1200 + mp_limb_t high_limb, low_limb;
1206 + assert (cnt >= 1);
1207 + assert (cnt < GMP_LIMB_BITS);
1209 + tnc = GMP_LIMB_BITS - cnt;
1210 + high_limb = *up++;
1211 + retval = (high_limb << tnc);
1212 + low_limb = high_limb >> cnt;
1214 + for (i = n; --i != 0;)
1216 + high_limb = *up++;
1217 + *rp++ = low_limb | (high_limb << tnc);
1218 + low_limb = high_limb >> cnt;
1226 +mpn_common_scan (mp_limb_t limb, mp_size_t i, mp_srcptr up, mp_size_t un,
1231 + assert (ux == 0 || ux == GMP_LIMB_MAX);
1232 + assert (0 <= i && i <= un );
1238 + return (ux == 0 ? ~(mp_bitcnt_t) 0 : un * GMP_LIMB_BITS);
1239 + limb = ux ^ up[i];
1241 + gmp_ctz (cnt, limb);
1242 + return (mp_bitcnt_t) i * GMP_LIMB_BITS + cnt;
1246 +mpn_scan1 (mp_srcptr ptr, mp_bitcnt_t bit)
1249 + i = bit / GMP_LIMB_BITS;
1251 + return mpn_common_scan ( ptr[i] & (GMP_LIMB_MAX << (bit % GMP_LIMB_BITS)),
1256 +mpn_scan0 (mp_srcptr ptr, mp_bitcnt_t bit)
1259 + i = bit / GMP_LIMB_BITS;
1261 + return mpn_common_scan (~ptr[i] & (GMP_LIMB_MAX << (bit % GMP_LIMB_BITS)),
1262 + i, ptr, i, GMP_LIMB_MAX);
1266 +/* MPN division interface. */
1268 +mpn_invert_3by2 (mp_limb_t u1, mp_limb_t u0)
1270 + mp_limb_t r, p, m;
1274 + /* First, do a 2/1 inverse. */
1275 + /* The inverse m is defined as floor( (B^2 - 1 - u1)/u1 ), so that 0 <
1276 + * B^2 - (B + m) u1 <= u1 */
1277 + assert (u1 >= GMP_LIMB_HIGHBIT);
1279 + ul = u1 & GMP_LLIMB_MASK;
1280 + uh = u1 >> (GMP_LIMB_BITS / 2);
1283 + r = ((~u1 - (mp_limb_t) qh * uh) << (GMP_LIMB_BITS / 2)) | GMP_LLIMB_MASK;
1285 + p = (mp_limb_t) qh * ul;
1286 + /* Adjustment steps taken from udiv_qrnnd_c */
1291 + if (r >= u1) /* i.e. we didn't get carry when adding to r */
1300 + /* Do a 3/2 division (with half limb size) */
1301 + p = (r >> (GMP_LIMB_BITS / 2)) * qh + r;
1302 + ql = (p >> (GMP_LIMB_BITS / 2)) + 1;
1304 + /* By the 3/2 method, we don't need the high half limb. */
1305 + r = (r << (GMP_LIMB_BITS / 2)) + GMP_LLIMB_MASK - ql * u1;
1307 + if (r >= (p << (GMP_LIMB_BITS / 2)))
1312 + m = ((mp_limb_t) qh << (GMP_LIMB_BITS / 2)) + ql;
1334 + gmp_umul_ppmm (th, tl, u0, m);
1339 + m -= ((r > u1) | ((r == u1) & (tl > u0)));
1346 +struct gmp_div_inverse
1348 + /* Normalization shift count. */
1350 + /* Normalized divisor (d0 unused for mpn_div_qr_1) */
1352 + /* Inverse, for 2/1 or 3/2. */
1357 +mpn_div_qr_1_invert (struct gmp_div_inverse *inv, mp_limb_t d)
1362 + gmp_clz (shift, d);
1363 + inv->shift = shift;
1364 + inv->d1 = d << shift;
1365 + inv->di = mpn_invert_limb (inv->d1);
1369 +mpn_div_qr_2_invert (struct gmp_div_inverse *inv,
1370 + mp_limb_t d1, mp_limb_t d0)
1375 + gmp_clz (shift, d1);
1376 + inv->shift = shift;
1379 + d1 = (d1 << shift) | (d0 >> (GMP_LIMB_BITS - shift));
1384 + inv->di = mpn_invert_3by2 (d1, d0);
1388 +mpn_div_qr_invert (struct gmp_div_inverse *inv,
1389 + mp_srcptr dp, mp_size_t dn)
1394 + mpn_div_qr_1_invert (inv, dp[0]);
1396 + mpn_div_qr_2_invert (inv, dp[1], dp[0]);
1405 + gmp_clz (shift, d1);
1406 + inv->shift = shift;
1409 + d1 = (d1 << shift) | (d0 >> (GMP_LIMB_BITS - shift));
1410 + d0 = (d0 << shift) | (dp[dn-3] >> (GMP_LIMB_BITS - shift));
1414 + inv->di = mpn_invert_3by2 (d1, d0);
1418 +/* Not matching current public gmp interface, rather corresponding to
1419 + the sbpi1_div_* functions. */
1421 +mpn_div_qr_1_preinv (mp_ptr qp, mp_srcptr np, mp_size_t nn,
1422 + const struct gmp_div_inverse *inv)
1428 + if (inv->shift > 0)
1430 + tp = gmp_xalloc_limbs (nn);
1431 + r = mpn_lshift (tp, np, nn, inv->shift);
1443 + gmp_udiv_qrnnd_preinv (q, r, r, np[nn], d, di);
1447 + if (inv->shift > 0)
1450 + return r >> inv->shift;
1454 +mpn_div_qr_1 (mp_ptr qp, mp_srcptr np, mp_size_t nn, mp_limb_t d)
1458 + /* Special case for powers of two. */
1459 + if ((d & (d-1)) == 0)
1461 + mp_limb_t r = np[0] & (d-1);
1465 + mpn_copyi (qp, np, nn);
1469 + gmp_ctz (shift, d);
1470 + mpn_rshift (qp, np, nn, shift);
1477 + struct gmp_div_inverse inv;
1478 + mpn_div_qr_1_invert (&inv, d);
1479 + return mpn_div_qr_1_preinv (qp, np, nn, &inv);
1484 +mpn_div_qr_2_preinv (mp_ptr qp, mp_ptr rp, mp_srcptr np, mp_size_t nn,
1485 + const struct gmp_div_inverse *inv)
1489 + mp_limb_t d1, d0, di, r1, r0;
1493 + shift = inv->shift;
1500 + tp = gmp_xalloc_limbs (nn);
1501 + r1 = mpn_lshift (tp, np, nn, shift);
1514 + gmp_udiv_qr_3by2 (q, r1, r0, r1, r0, n0, d1, d0, di);
1523 + assert ((r0 << (GMP_LIMB_BITS - shift)) == 0);
1524 + r0 = (r0 >> shift) | (r1 << (GMP_LIMB_BITS - shift));
1536 +mpn_div_qr_2 (mp_ptr qp, mp_ptr rp, mp_srcptr np, mp_size_t nn,
1537 + mp_limb_t d1, mp_limb_t d0)
1539 + struct gmp_div_inverse inv;
1542 + mpn_div_qr_2_invert (&inv, d1, d0);
1543 + mpn_div_qr_2_preinv (qp, rp, np, nn, &inv);
1548 +mpn_div_qr_pi1 (mp_ptr qp,
1549 + mp_ptr np, mp_size_t nn, mp_limb_t n1,
1550 + mp_srcptr dp, mp_size_t dn,
1556 + mp_limb_t cy, cy1;
1560 + assert (nn >= dn);
1565 + assert ((d1 & GMP_LIMB_HIGHBIT) != 0);
1566 + /* Iteration variable is the index of the q limb.
1568 + * We divide <n1, np[dn-1+i], np[dn-2+i], np[dn-3+i],..., np[i]>
1569 + * by <d1, d0, dp[dn-3], ..., dp[0] >
1575 + mp_limb_t n0 = np[dn-1+i];
1577 + if (n1 == d1 && n0 == d0)
1580 + mpn_submul_1 (np+i, dp, dn, q);
1581 + n1 = np[dn-1+i]; /* update n1, last loop's value will now be invalid */
1585 + gmp_udiv_qr_3by2 (q, n1, n0, n1, n0, np[dn-2+i], d1, d0, dinv);
1587 + cy = mpn_submul_1 (np + i, dp, dn-2, q);
1597 + n1 += d1 + mpn_add_n (np + i, np + i, dp, dn - 1);
1611 +mpn_div_qr_preinv (mp_ptr qp, mp_ptr np, mp_size_t nn,
1612 + mp_srcptr dp, mp_size_t dn,
1613 + const struct gmp_div_inverse *inv)
1616 + assert (nn >= dn);
1619 + np[0] = mpn_div_qr_1_preinv (qp, np, nn, inv);
1621 + mpn_div_qr_2_preinv (qp, np, np, nn, inv);
1627 + assert (inv->d1 == dp[dn-1]);
1628 + assert (inv->d0 == dp[dn-2]);
1629 + assert ((inv->d1 & GMP_LIMB_HIGHBIT) != 0);
1631 + shift = inv->shift;
1633 + nh = mpn_lshift (np, np, nn, shift);
1637 + mpn_div_qr_pi1 (qp, np, nn, nh, dp, dn, inv->di);
1640 + gmp_assert_nocarry (mpn_rshift (np, np, dn, shift));
1645 +mpn_div_qr (mp_ptr qp, mp_ptr np, mp_size_t nn, mp_srcptr dp, mp_size_t dn)
1647 + struct gmp_div_inverse inv;
1651 + assert (nn >= dn);
1653 + mpn_div_qr_invert (&inv, dp, dn);
1654 + if (dn > 2 && inv.shift > 0)
1656 + tp = gmp_xalloc_limbs (dn);
1657 + gmp_assert_nocarry (mpn_lshift (tp, dp, dn, inv.shift));
1660 + mpn_div_qr_preinv (qp, np, nn, dp, dn, &inv);
1666 +/* MPN base conversion. */
1668 +mpn_base_power_of_two_p (unsigned b)
1675 + case 16: return 4;
1676 + case 32: return 5;
1677 + case 64: return 6;
1678 + case 128: return 7;
1679 + case 256: return 8;
1680 + default: return 0;
1684 +struct mpn_base_info
1686 + /* bb is the largest power of the base which fits in one limb, and
1687 + exp is the corresponding exponent. */
1693 +mpn_get_base_info (struct mpn_base_info *info, mp_limb_t b)
1699 + m = GMP_LIMB_MAX / b;
1700 + for (exp = 1, p = b; p <= m; exp++)
1708 +mpn_limb_size_in_base_2 (mp_limb_t u)
1713 + gmp_clz (shift, u);
1714 + return GMP_LIMB_BITS - shift;
1718 +mpn_get_str_bits (unsigned char *sp, unsigned bits, mp_srcptr up, mp_size_t un)
1720 + unsigned char mask;
1725 + sn = ((un - 1) * GMP_LIMB_BITS + mpn_limb_size_in_base_2 (up[un-1])
1726 + + bits - 1) / bits;
1728 + mask = (1U << bits) - 1;
1730 + for (i = 0, j = sn, shift = 0; j-- > 0;)
1732 + unsigned char digit = up[i] >> shift;
1736 + if (shift >= GMP_LIMB_BITS && ++i < un)
1738 + shift -= GMP_LIMB_BITS;
1739 + digit |= up[i] << (bits - shift);
1741 + sp[j] = digit & mask;
1746 +/* We generate digits from the least significant end, and reverse at
1749 +mpn_limb_get_str (unsigned char *sp, mp_limb_t w,
1750 + const struct gmp_div_inverse *binv)
1753 + for (i = 0; w > 0; i++)
1755 + mp_limb_t h, l, r;
1757 + h = w >> (GMP_LIMB_BITS - binv->shift);
1758 + l = w << binv->shift;
1760 + gmp_udiv_qrnnd_preinv (w, r, h, l, binv->d1, binv->di);
1761 + assert ( (r << (GMP_LIMB_BITS - binv->shift)) == 0);
1762 + r >>= binv->shift;
1770 +mpn_get_str_other (unsigned char *sp,
1771 + int base, const struct mpn_base_info *info,
1772 + mp_ptr up, mp_size_t un)
1774 + struct gmp_div_inverse binv;
1778 + mpn_div_qr_1_invert (&binv, base);
1784 + struct gmp_div_inverse bbinv;
1785 + mpn_div_qr_1_invert (&bbinv, info->bb);
1791 + w = mpn_div_qr_1_preinv (up, up, un, &bbinv);
1792 + un -= (up[un-1] == 0);
1793 + done = mpn_limb_get_str (sp + sn, w, &binv);
1795 + for (sn += done; done < info->exp; done++)
1800 + sn += mpn_limb_get_str (sp + sn, up[0], &binv);
1802 + /* Reverse order */
1803 + for (i = 0; 2*i + 1 < sn; i++)
1805 + unsigned char t = sp[i];
1806 + sp[i] = sp[sn - i - 1];
1807 + sp[sn - i - 1] = t;
1814 +mpn_get_str (unsigned char *sp, int base, mp_ptr up, mp_size_t un)
1819 + assert (up[un-1] > 0);
1821 + bits = mpn_base_power_of_two_p (base);
1823 + return mpn_get_str_bits (sp, bits, up, un);
1826 + struct mpn_base_info info;
1828 + mpn_get_base_info (&info, base);
1829 + return mpn_get_str_other (sp, base, &info, up, un);
1834 +mpn_set_str_bits (mp_ptr rp, const unsigned char *sp, size_t sn,
1841 + for (j = sn, rn = 0, shift = 0; j-- > 0; )
1850 + rp[rn-1] |= (mp_limb_t) sp[j] << shift;
1852 + if (shift >= GMP_LIMB_BITS)
1854 + shift -= GMP_LIMB_BITS;
1856 + rp[rn++] = (mp_limb_t) sp[j] >> (bits - shift);
1860 + rn = mpn_normalized_size (rp, rn);
1865 +mpn_set_str_other (mp_ptr rp, const unsigned char *sp, size_t sn,
1866 + mp_limb_t b, const struct mpn_base_info *info)
1873 + k = 1 + (sn - 1) % info->exp;
1878 + w = w * b + sp[j++];
1882 + for (rn = (w > 0); j < sn;)
1887 + for (k = 1; k < info->exp; k++)
1888 + w = w * b + sp[j++];
1890 + cy = mpn_mul_1 (rp, rp, rn, info->bb);
1891 + cy += mpn_add_1 (rp, rp, rn, w);
1901 +mpn_set_str (mp_ptr rp, const unsigned char *sp, size_t sn, int base)
1908 + bits = mpn_base_power_of_two_p (base);
1910 + return mpn_set_str_bits (rp, sp, sn, bits);
1913 + struct mpn_base_info info;
1915 + mpn_get_base_info (&info, base);
1916 + return mpn_set_str_other (rp, sp, sn, base, &info);
1921 +/* MPZ interface */
1927 + r->_mp_d = gmp_xalloc_limbs (1);
1930 +/* The utility of this function is a bit limited, since many functions
1931 + assigns the result variable using mpz_swap. */
1933 +mpz_init2 (mpz_t r, mp_bitcnt_t bits)
1937 + bits -= (bits != 0); /* Round down, except if 0 */
1938 + rn = 1 + bits / GMP_LIMB_BITS;
1940 + r->_mp_alloc = rn;
1942 + r->_mp_d = gmp_xalloc_limbs (rn);
1946 +mpz_clear (mpz_t r)
1948 + gmp_free (r->_mp_d);
1952 +mpz_realloc (mpz_t r, mp_size_t size)
1954 + size = GMP_MAX (size, 1);
1956 + r->_mp_d = gmp_xrealloc_limbs (r->_mp_d, size);
1957 + r->_mp_alloc = size;
1959 + if (GMP_ABS (r->_mp_size) > size)
1965 +/* Realloc for an mpz_t WHAT if it has less than NEEDED limbs. */
1966 +#define MPZ_REALLOC(z,n) ((n) > (z)->_mp_alloc \
1967 + ? mpz_realloc(z,n) \
1970 +/* MPZ assignment and basic conversions. */
1972 +mpz_set_si (mpz_t r, signed long int x)
1975 + mpz_set_ui (r, x);
1976 + else /* (x < 0) */
1979 + r->_mp_d[0] = GMP_NEG_CAST (unsigned long int, x);
1984 +mpz_set_ui (mpz_t r, unsigned long int x)
1996 +mpz_set (mpz_t r, const mpz_t x)
1998 + /* Allow the NOP r == x */
2004 + n = GMP_ABS (x->_mp_size);
2005 + rp = MPZ_REALLOC (r, n);
2007 + mpn_copyi (rp, x->_mp_d, n);
2008 + r->_mp_size = x->_mp_size;
2013 +mpz_init_set_si (mpz_t r, signed long int x)
2016 + mpz_set_si (r, x);
2020 +mpz_init_set_ui (mpz_t r, unsigned long int x)
2023 + mpz_set_ui (r, x);
2027 +mpz_init_set (mpz_t r, const mpz_t x)
2034 +mpz_fits_slong_p (const mpz_t u)
2036 + mp_size_t us = u->_mp_size;
2041 + return u->_mp_d[0] < GMP_LIMB_HIGHBIT;
2042 + else if (us == -1)
2043 + return u->_mp_d[0] <= GMP_LIMB_HIGHBIT;
2049 +mpz_fits_ulong_p (const mpz_t u)
2051 + mp_size_t us = u->_mp_size;
2053 + return (us == (us > 0));
2057 +mpz_get_si (const mpz_t u)
2059 + mp_size_t us = u->_mp_size;
2062 + return (long) (u->_mp_d[0] & ~GMP_LIMB_HIGHBIT);
2064 + return (long) (- u->_mp_d[0] | GMP_LIMB_HIGHBIT);
2070 +mpz_get_ui (const mpz_t u)
2072 + return u->_mp_size == 0 ? 0 : u->_mp_d[0];
2076 +mpz_size (const mpz_t u)
2078 + return GMP_ABS (u->_mp_size);
2082 +mpz_getlimbn (const mpz_t u, mp_size_t n)
2084 + if (n >= 0 && n < GMP_ABS (u->_mp_size))
2085 + return u->_mp_d[n];
2091 +mpz_realloc2 (mpz_t x, mp_bitcnt_t n)
2093 + mpz_realloc (x, 1 + (n - (n != 0)) / GMP_LIMB_BITS);
2097 +mpz_limbs_read (mpz_srcptr x)
2103 +mpz_limbs_modify (mpz_t x, mp_size_t n)
2106 + return MPZ_REALLOC (x, n);
2110 +mpz_limbs_write (mpz_t x, mp_size_t n)
2112 + return mpz_limbs_modify (x, n);
2116 +mpz_limbs_finish (mpz_t x, mp_size_t xs)
2119 + xn = mpn_normalized_size (x->_mp_d, GMP_ABS (xs));
2120 + x->_mp_size = xs < 0 ? -xn : xn;
2124 +mpz_roinit_n (mpz_t x, mp_srcptr xp, mp_size_t xs)
2127 + x->_mp_d = (mp_ptr) xp;
2128 + mpz_limbs_finish (x, xs);
2133 +/* Conversions and comparison to double. */
2135 +mpz_set_d (mpz_t r, double x)
2144 + /* x != x is true when x is a NaN, and x == x * 0.5 is true when x is
2145 + zero or infinity. */
2146 + if (x != x || x == x * 0.5)
2161 + B = 2.0 * (double) GMP_LIMB_HIGHBIT;
2163 + for (rn = 1; x >= B; rn++)
2166 + rp = MPZ_REALLOC (r, rn);
2168 + f = (mp_limb_t) x;
2176 + f = (mp_limb_t) x;
2182 + r->_mp_size = sign ? - rn : rn;
2186 +mpz_init_set_d (mpz_t r, double x)
2193 +mpz_get_d (const mpz_t u)
2197 + double B = 2.0 * (double) GMP_LIMB_HIGHBIT;
2199 + un = GMP_ABS (u->_mp_size);
2204 + x = u->_mp_d[--un];
2206 + x = B*x + u->_mp_d[--un];
2208 + if (u->_mp_size < 0)
2215 +mpz_cmpabs_d (const mpz_t x, double d)
2226 + xn = GMP_ABS (xn);
2228 + B = 2.0 * (double) GMP_LIMB_HIGHBIT;
2231 + /* Scale d so it can be compared with the top limb. */
2232 + for (i = 1; i < xn; i++)
2238 + /* Compare floor(d) to top limb, subtract and cancel when equal. */
2239 + for (i = xn; i-- > 0;)
2243 + f = (mp_limb_t) d;
2252 + return - (d > 0.0);
2256 +mpz_cmp_d (const mpz_t x, double d)
2258 + if (x->_mp_size < 0)
2263 + return -mpz_cmpabs_d (x, d);
2270 + return mpz_cmpabs_d (x, d);
2275 +/* MPZ comparisons and the like. */
2277 +mpz_sgn (const mpz_t u)
2279 + mp_size_t usize = u->_mp_size;
2281 + return (usize > 0) - (usize < 0);
2285 +mpz_cmp_si (const mpz_t u, long v)
2287 + mp_size_t usize = u->_mp_size;
2292 + return mpz_cmp_ui (u, v);
2293 + else if (usize >= 0)
2295 + else /* usize == -1 */
2297 + mp_limb_t ul = u->_mp_d[0];
2298 + if ((mp_limb_t)GMP_NEG_CAST (unsigned long int, v) < ul)
2301 + return (mp_limb_t)GMP_NEG_CAST (unsigned long int, v) > ul;
2306 +mpz_cmp_ui (const mpz_t u, unsigned long v)
2308 + mp_size_t usize = u->_mp_size;
2312 + else if (usize < 0)
2316 + mp_limb_t ul = (usize > 0) ? u->_mp_d[0] : 0;
2317 + return (ul > v) - (ul < v);
2322 +mpz_cmp (const mpz_t a, const mpz_t b)
2324 + mp_size_t asize = a->_mp_size;
2325 + mp_size_t bsize = b->_mp_size;
2327 + if (asize != bsize)
2328 + return (asize < bsize) ? -1 : 1;
2329 + else if (asize >= 0)
2330 + return mpn_cmp (a->_mp_d, b->_mp_d, asize);
2332 + return mpn_cmp (b->_mp_d, a->_mp_d, -asize);
2336 +mpz_cmpabs_ui (const mpz_t u, unsigned long v)
2338 + mp_size_t un = GMP_ABS (u->_mp_size);
2344 + ul = (un == 1) ? u->_mp_d[0] : 0;
2346 + return (ul > v) - (ul < v);
2350 +mpz_cmpabs (const mpz_t u, const mpz_t v)
2352 + return mpn_cmp4 (u->_mp_d, GMP_ABS (u->_mp_size),
2353 + v->_mp_d, GMP_ABS (v->_mp_size));
2357 +mpz_abs (mpz_t r, const mpz_t u)
2362 + r->_mp_size = GMP_ABS (r->_mp_size);
2366 +mpz_neg (mpz_t r, const mpz_t u)
2371 + r->_mp_size = -r->_mp_size;
2375 +mpz_swap (mpz_t u, mpz_t v)
2377 + MP_SIZE_T_SWAP (u->_mp_size, v->_mp_size);
2378 + MP_SIZE_T_SWAP (u->_mp_alloc, v->_mp_alloc);
2379 + MP_PTR_SWAP (u->_mp_d, v->_mp_d);
2383 +/* MPZ addition and subtraction */
2385 +/* Adds to the absolute value. Returns new size, but doesn't store it. */
2387 +mpz_abs_add_ui (mpz_t r, const mpz_t a, unsigned long b)
2393 + an = GMP_ABS (a->_mp_size);
2400 + rp = MPZ_REALLOC (r, an + 1);
2402 + cy = mpn_add_1 (rp, a->_mp_d, an, b);
2409 +/* Subtract from the absolute value. Returns new size, (or -1 on underflow),
2410 + but doesn't store it. */
2412 +mpz_abs_sub_ui (mpz_t r, const mpz_t a, unsigned long b)
2414 + mp_size_t an = GMP_ABS (a->_mp_size);
2415 + mp_ptr rp = MPZ_REALLOC (r, an);
2422 + else if (an == 1 && a->_mp_d[0] < b)
2424 + rp[0] = b - a->_mp_d[0];
2429 + gmp_assert_nocarry (mpn_sub_1 (rp, a->_mp_d, an, b));
2430 + return mpn_normalized_size (rp, an);
2435 +mpz_add_ui (mpz_t r, const mpz_t a, unsigned long b)
2437 + if (a->_mp_size >= 0)
2438 + r->_mp_size = mpz_abs_add_ui (r, a, b);
2440 + r->_mp_size = -mpz_abs_sub_ui (r, a, b);
2444 +mpz_sub_ui (mpz_t r, const mpz_t a, unsigned long b)
2446 + if (a->_mp_size < 0)
2447 + r->_mp_size = -mpz_abs_add_ui (r, a, b);
2449 + r->_mp_size = mpz_abs_sub_ui (r, a, b);
2453 +mpz_ui_sub (mpz_t r, unsigned long a, const mpz_t b)
2455 + if (b->_mp_size < 0)
2456 + r->_mp_size = mpz_abs_add_ui (r, b, a);
2458 + r->_mp_size = -mpz_abs_sub_ui (r, b, a);
2462 +mpz_abs_add (mpz_t r, const mpz_t a, const mpz_t b)
2464 + mp_size_t an = GMP_ABS (a->_mp_size);
2465 + mp_size_t bn = GMP_ABS (b->_mp_size);
2471 + MPZ_SRCPTR_SWAP (a, b);
2472 + MP_SIZE_T_SWAP (an, bn);
2475 + rp = MPZ_REALLOC (r, an + 1);
2476 + cy = mpn_add (rp, a->_mp_d, an, b->_mp_d, bn);
2484 +mpz_abs_sub (mpz_t r, const mpz_t a, const mpz_t b)
2486 + mp_size_t an = GMP_ABS (a->_mp_size);
2487 + mp_size_t bn = GMP_ABS (b->_mp_size);
2491 + cmp = mpn_cmp4 (a->_mp_d, an, b->_mp_d, bn);
2494 + rp = MPZ_REALLOC (r, an);
2495 + gmp_assert_nocarry (mpn_sub (rp, a->_mp_d, an, b->_mp_d, bn));
2496 + return mpn_normalized_size (rp, an);
2500 + rp = MPZ_REALLOC (r, bn);
2501 + gmp_assert_nocarry (mpn_sub (rp, b->_mp_d, bn, a->_mp_d, an));
2502 + return -mpn_normalized_size (rp, bn);
2509 +mpz_add (mpz_t r, const mpz_t a, const mpz_t b)
2513 + if ( (a->_mp_size ^ b->_mp_size) >= 0)
2514 + rn = mpz_abs_add (r, a, b);
2516 + rn = mpz_abs_sub (r, a, b);
2518 + r->_mp_size = a->_mp_size >= 0 ? rn : - rn;
2522 +mpz_sub (mpz_t r, const mpz_t a, const mpz_t b)
2526 + if ( (a->_mp_size ^ b->_mp_size) >= 0)
2527 + rn = mpz_abs_sub (r, a, b);
2529 + rn = mpz_abs_add (r, a, b);
2531 + r->_mp_size = a->_mp_size >= 0 ? rn : - rn;
2535 +/* MPZ multiplication */
2537 +mpz_mul_si (mpz_t r, const mpz_t u, long int v)
2541 + mpz_mul_ui (r, u, GMP_NEG_CAST (unsigned long int, v));
2545 + mpz_mul_ui (r, u, (unsigned long int) v);
2549 +mpz_mul_ui (mpz_t r, const mpz_t u, unsigned long int v)
2557 + if (us == 0 || v == 0)
2563 + un = GMP_ABS (us);
2565 + tp = MPZ_REALLOC (r, un + 1);
2566 + cy = mpn_mul_1 (tp, u->_mp_d, un, v);
2570 + r->_mp_size = (us < 0) ? - un : un;
2574 +mpz_mul (mpz_t r, const mpz_t u, const mpz_t v)
2577 + mp_size_t un, vn, rn;
2584 + if (un == 0 || vn == 0)
2590 + sign = (un ^ vn) < 0;
2592 + un = GMP_ABS (un);
2593 + vn = GMP_ABS (vn);
2595 + mpz_init2 (t, (un + vn) * GMP_LIMB_BITS);
2599 + mpn_mul (tp, u->_mp_d, un, v->_mp_d, vn);
2601 + mpn_mul (tp, v->_mp_d, vn, u->_mp_d, un);
2604 + rn -= tp[rn-1] == 0;
2606 + t->_mp_size = sign ? - rn : rn;
2612 +mpz_mul_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t bits)
2619 + un = GMP_ABS (u->_mp_size);
2626 + limbs = bits / GMP_LIMB_BITS;
2627 + shift = bits % GMP_LIMB_BITS;
2629 + rn = un + limbs + (shift > 0);
2630 + rp = MPZ_REALLOC (r, rn);
2633 + mp_limb_t cy = mpn_lshift (rp + limbs, u->_mp_d, un, shift);
2638 + mpn_copyd (rp + limbs, u->_mp_d, un);
2643 + r->_mp_size = (u->_mp_size < 0) ? - rn : rn;
2647 +mpz_addmul_ui (mpz_t r, const mpz_t u, unsigned long int v)
2651 + mpz_mul_ui (t, u, v);
2652 + mpz_add (r, r, t);
2657 +mpz_submul_ui (mpz_t r, const mpz_t u, unsigned long int v)
2661 + mpz_mul_ui (t, u, v);
2662 + mpz_sub (r, r, t);
2667 +mpz_addmul (mpz_t r, const mpz_t u, const mpz_t v)
2671 + mpz_mul (t, u, v);
2672 + mpz_add (r, r, t);
2677 +mpz_submul (mpz_t r, const mpz_t u, const mpz_t v)
2681 + mpz_mul (t, u, v);
2682 + mpz_sub (r, r, t);
2688 +enum mpz_div_round_mode { GMP_DIV_FLOOR, GMP_DIV_CEIL, GMP_DIV_TRUNC };
2690 +/* Allows q or r to be zero. Returns 1 iff remainder is non-zero. */
2692 +mpz_div_qr (mpz_t q, mpz_t r,
2693 + const mpz_t n, const mpz_t d, enum mpz_div_round_mode mode)
2695 + mp_size_t ns, ds, nn, dn, qs;
2700 + gmp_die("mpz_div_qr: Divide by zero.");
2711 + nn = GMP_ABS (ns);
2712 + dn = GMP_ABS (ds);
2718 + if (mode == GMP_DIV_CEIL && qs >= 0)
2720 + /* q = 1, r = n - d */
2722 + mpz_sub (r, n, d);
2724 + mpz_set_ui (q, 1);
2726 + else if (mode == GMP_DIV_FLOOR && qs < 0)
2728 + /* q = -1, r = n + d */
2730 + mpz_add (r, n, d);
2732 + mpz_set_si (q, -1);
2736 + /* q = 0, r = d */
2750 + mpz_init_set (tr, n);
2757 + mpz_init2 (tq, qn * GMP_LIMB_BITS);
2763 + mpn_div_qr (qp, np, nn, d->_mp_d, dn);
2767 + qn -= (qp[qn-1] == 0);
2769 + tq->_mp_size = qs < 0 ? -qn : qn;
2771 + rn = mpn_normalized_size (np, dn);
2772 + tr->_mp_size = ns < 0 ? - rn : rn;
2774 + if (mode == GMP_DIV_FLOOR && qs < 0 && rn != 0)
2777 + mpz_sub_ui (tq, tq, 1);
2779 + mpz_add (tr, tr, d);
2781 + else if (mode == GMP_DIV_CEIL && qs >= 0 && rn != 0)
2784 + mpz_add_ui (tq, tq, 1);
2786 + mpz_sub (tr, tr, d);
2804 +mpz_cdiv_qr (mpz_t q, mpz_t r, const mpz_t n, const mpz_t d)
2806 + mpz_div_qr (q, r, n, d, GMP_DIV_CEIL);
2810 +mpz_fdiv_qr (mpz_t q, mpz_t r, const mpz_t n, const mpz_t d)
2812 + mpz_div_qr (q, r, n, d, GMP_DIV_FLOOR);
2816 +mpz_tdiv_qr (mpz_t q, mpz_t r, const mpz_t n, const mpz_t d)
2818 + mpz_div_qr (q, r, n, d, GMP_DIV_TRUNC);
2822 +mpz_cdiv_q (mpz_t q, const mpz_t n, const mpz_t d)
2824 + mpz_div_qr (q, NULL, n, d, GMP_DIV_CEIL);
2828 +mpz_fdiv_q (mpz_t q, const mpz_t n, const mpz_t d)
2830 + mpz_div_qr (q, NULL, n, d, GMP_DIV_FLOOR);
2834 +mpz_tdiv_q (mpz_t q, const mpz_t n, const mpz_t d)
2836 + mpz_div_qr (q, NULL, n, d, GMP_DIV_TRUNC);
2840 +mpz_cdiv_r (mpz_t r, const mpz_t n, const mpz_t d)
2842 + mpz_div_qr (NULL, r, n, d, GMP_DIV_CEIL);
2846 +mpz_fdiv_r (mpz_t r, const mpz_t n, const mpz_t d)
2848 + mpz_div_qr (NULL, r, n, d, GMP_DIV_FLOOR);
2852 +mpz_tdiv_r (mpz_t r, const mpz_t n, const mpz_t d)
2854 + mpz_div_qr (NULL, r, n, d, GMP_DIV_TRUNC);
2858 +mpz_mod (mpz_t r, const mpz_t n, const mpz_t d)
2860 + mpz_div_qr (NULL, r, n, d, d->_mp_size >= 0 ? GMP_DIV_FLOOR : GMP_DIV_CEIL);
2864 +mpz_div_q_2exp (mpz_t q, const mpz_t u, mp_bitcnt_t bit_index,
2865 + enum mpz_div_round_mode mode)
2868 + mp_size_t limb_cnt;
2878 + limb_cnt = bit_index / GMP_LIMB_BITS;
2879 + qn = GMP_ABS (un) - limb_cnt;
2880 + bit_index %= GMP_LIMB_BITS;
2882 + if (mode == ((un > 0) ? GMP_DIV_CEIL : GMP_DIV_FLOOR)) /* un != 0 here. */
2883 + /* Note: Below, the final indexing at limb_cnt is valid because at
2884 + that point we have qn > 0. */
2886 + || !mpn_zero_p (u->_mp_d, limb_cnt)
2887 + || (u->_mp_d[limb_cnt]
2888 + & (((mp_limb_t) 1 << bit_index) - 1)));
2897 + qp = MPZ_REALLOC (q, qn);
2899 + if (bit_index != 0)
2901 + mpn_rshift (qp, u->_mp_d + limb_cnt, qn, bit_index);
2902 + qn -= qp[qn - 1] == 0;
2906 + mpn_copyi (qp, u->_mp_d + limb_cnt, qn);
2913 + mpz_add_ui (q, q, 1);
2919 +mpz_div_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t bit_index,
2920 + enum mpz_div_round_mode mode)
2922 + mp_size_t us, un, rn;
2927 + if (us == 0 || bit_index == 0)
2932 + rn = (bit_index + GMP_LIMB_BITS - 1) / GMP_LIMB_BITS;
2935 + rp = MPZ_REALLOC (r, rn);
2936 + un = GMP_ABS (us);
2938 + mask = GMP_LIMB_MAX >> (rn * GMP_LIMB_BITS - bit_index);
2942 + /* Quotient (with truncation) is zero, and remainder is
2944 + if (mode == ((us > 0) ? GMP_DIV_CEIL : GMP_DIV_FLOOR)) /* us != 0 here. */
2946 + /* Have to negate and sign extend. */
2950 + for (cy = 1, i = 0; i < un; i++)
2952 + mp_limb_t s = ~u->_mp_d[i] + cy;
2957 + for (; i < rn - 1; i++)
2958 + rp[i] = GMP_LIMB_MAX;
2967 + mpn_copyi (rp, u->_mp_d, un);
2975 + mpn_copyi (rp, u->_mp_d, rn - 1);
2977 + rp[rn-1] = u->_mp_d[rn-1] & mask;
2979 + if (mode == ((us > 0) ? GMP_DIV_CEIL : GMP_DIV_FLOOR)) /* us != 0 here. */
2981 + /* If r != 0, compute 2^{bit_count} - r. */
2984 + for (i = 0; i < rn && rp[i] == 0; i++)
2988 + /* r > 0, need to flip sign. */
2989 + rp[i] = ~rp[i] + 1;
2995 + /* us is not used for anything else, so we can modify it
2996 + here to indicate flipped sign. */
3001 + rn = mpn_normalized_size (rp, rn);
3002 + r->_mp_size = us < 0 ? -rn : rn;
3006 +mpz_cdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
3008 + mpz_div_q_2exp (r, u, cnt, GMP_DIV_CEIL);
3012 +mpz_fdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
3014 + mpz_div_q_2exp (r, u, cnt, GMP_DIV_FLOOR);
3018 +mpz_tdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
3020 + mpz_div_q_2exp (r, u, cnt, GMP_DIV_TRUNC);
3024 +mpz_cdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
3026 + mpz_div_r_2exp (r, u, cnt, GMP_DIV_CEIL);
3030 +mpz_fdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
3032 + mpz_div_r_2exp (r, u, cnt, GMP_DIV_FLOOR);
3036 +mpz_tdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
3038 + mpz_div_r_2exp (r, u, cnt, GMP_DIV_TRUNC);
3042 +mpz_divexact (mpz_t q, const mpz_t n, const mpz_t d)
3044 + gmp_assert_nocarry (mpz_div_qr (q, NULL, n, d, GMP_DIV_TRUNC));
3048 +mpz_divisible_p (const mpz_t n, const mpz_t d)
3050 + return mpz_div_qr (NULL, NULL, n, d, GMP_DIV_TRUNC) == 0;
3054 +mpz_congruent_p (const mpz_t a, const mpz_t b, const mpz_t m)
3059 + /* a == b (mod 0) iff a == b */
3060 + if (mpz_sgn (m) == 0)
3061 + return (mpz_cmp (a, b) == 0);
3064 + mpz_sub (t, a, b);
3065 + res = mpz_divisible_p (t, m);
3071 +static unsigned long
3072 +mpz_div_qr_ui (mpz_t q, mpz_t r,
3073 + const mpz_t n, unsigned long d, enum mpz_div_round_mode mode)
3090 + qn = GMP_ABS (ns);
3092 + qp = MPZ_REALLOC (q, qn);
3096 + rl = mpn_div_qr_1 (qp, n->_mp_d, qn, d);
3100 + rs = (ns < 0) ? -rs : rs;
3102 + if (rl > 0 && ( (mode == GMP_DIV_FLOOR && ns < 0)
3103 + || (mode == GMP_DIV_CEIL && ns >= 0)))
3106 + gmp_assert_nocarry (mpn_add_1 (qp, qp, qn, 1));
3118 + qn -= (qp[qn-1] == 0);
3119 + assert (qn == 0 || qp[qn-1] > 0);
3121 + q->_mp_size = (ns < 0) ? - qn : qn;
3128 +mpz_cdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d)
3130 + return mpz_div_qr_ui (q, r, n, d, GMP_DIV_CEIL);
3134 +mpz_fdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d)
3136 + return mpz_div_qr_ui (q, r, n, d, GMP_DIV_FLOOR);
3140 +mpz_tdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d)
3142 + return mpz_div_qr_ui (q, r, n, d, GMP_DIV_TRUNC);
3146 +mpz_cdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d)
3148 + return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_CEIL);
3152 +mpz_fdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d)
3154 + return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_FLOOR);
3158 +mpz_tdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d)
3160 + return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_TRUNC);
3164 +mpz_cdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d)
3166 + return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_CEIL);
3169 +mpz_fdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d)
3171 + return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_FLOOR);
3174 +mpz_tdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d)
3176 + return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_TRUNC);
3180 +mpz_cdiv_ui (const mpz_t n, unsigned long d)
3182 + return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_CEIL);
3186 +mpz_fdiv_ui (const mpz_t n, unsigned long d)
3188 + return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_FLOOR);
3192 +mpz_tdiv_ui (const mpz_t n, unsigned long d)
3194 + return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_TRUNC);
3198 +mpz_mod_ui (mpz_t r, const mpz_t n, unsigned long d)
3200 + return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_FLOOR);
3204 +mpz_divexact_ui (mpz_t q, const mpz_t n, unsigned long d)
3206 + gmp_assert_nocarry (mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_TRUNC));
3210 +mpz_divisible_ui_p (const mpz_t n, unsigned long d)
3212 + return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_TRUNC) == 0;
3218 +mpn_gcd_11 (mp_limb_t u, mp_limb_t v)
3222 + assert ( (u | v) > 0);
3229 + gmp_ctz (shift, u | v);
3234 + if ( (u & 1) == 0)
3235 + MP_LIMB_T_SWAP (u, v);
3237 + while ( (v & 1) == 0)
3247 + while ( (u & 1) == 0);
3254 + while ( (v & 1) == 0);
3257 + return u << shift;
3261 +mpz_gcd_ui (mpz_t g, const mpz_t u, unsigned long v)
3272 + un = GMP_ABS (u->_mp_size);
3274 + v = mpn_gcd_11 (mpn_div_qr_1 (NULL, u->_mp_d, un, v), v);
3277 + mpz_set_ui (g, v);
3284 +mpz_make_odd (mpz_t r)
3286 + mp_bitcnt_t shift;
3288 + assert (r->_mp_size > 0);
3289 + /* Count trailing zeros, equivalent to mpn_scan1, because we know that there is a 1 */
3290 + shift = mpn_common_scan (r->_mp_d[0], 0, r->_mp_d, 0, 0);
3291 + mpz_tdiv_q_2exp (r, r, shift);
3297 +mpz_gcd (mpz_t g, const mpz_t u, const mpz_t v)
3300 + mp_bitcnt_t uz, vz, gz;
3302 + if (u->_mp_size == 0)
3307 + if (v->_mp_size == 0)
3317 + uz = mpz_make_odd (tu);
3319 + vz = mpz_make_odd (tv);
3320 + gz = GMP_MIN (uz, vz);
3322 + if (tu->_mp_size < tv->_mp_size)
3323 + mpz_swap (tu, tv);
3325 + mpz_tdiv_r (tu, tu, tv);
3326 + if (tu->_mp_size == 0)
3335 + mpz_make_odd (tu);
3336 + c = mpz_cmp (tu, tv);
3343 + mpz_swap (tu, tv);
3345 + if (tv->_mp_size == 1)
3347 + mp_limb_t vl = tv->_mp_d[0];
3348 + mp_limb_t ul = mpz_tdiv_ui (tu, vl);
3349 + mpz_set_ui (g, mpn_gcd_11 (ul, vl));
3352 + mpz_sub (tu, tu, tv);
3356 + mpz_mul_2exp (g, g, gz);
3360 +mpz_gcdext (mpz_t g, mpz_t s, mpz_t t, const mpz_t u, const mpz_t v)
3362 + mpz_t tu, tv, s0, s1, t0, t1;
3363 + mp_bitcnt_t uz, vz, gz;
3364 + mp_bitcnt_t power;
3366 + if (u->_mp_size == 0)
3368 + /* g = 0 u + sgn(v) v */
3369 + signed long sign = mpz_sgn (v);
3372 + mpz_set_ui (s, 0);
3374 + mpz_set_si (t, sign);
3378 + if (v->_mp_size == 0)
3380 + /* g = sgn(u) u + 0 v */
3381 + signed long sign = mpz_sgn (u);
3384 + mpz_set_si (s, sign);
3386 + mpz_set_ui (t, 0);
3398 + uz = mpz_make_odd (tu);
3400 + vz = mpz_make_odd (tv);
3401 + gz = GMP_MIN (uz, vz);
3406 + /* Cofactors corresponding to odd gcd. gz handled later. */
3407 + if (tu->_mp_size < tv->_mp_size)
3409 + mpz_swap (tu, tv);
3410 + MPZ_SRCPTR_SWAP (u, v);
3411 + MPZ_PTR_SWAP (s, t);
3412 + MP_BITCNT_T_SWAP (uz, vz);
3417 + * u = t0 tu + t1 tv
3418 + * v = s0 tu + s1 tv
3420 + * where u and v denote the inputs with common factors of two
3421 + * eliminated, and det (s0, t0; s1, t1) = 2^p. Then
3423 + * 2^p tu = s1 u - t1 v
3424 + * 2^p tv = -s0 u + t0 v
3427 + /* After initial division, tu = q tv + tu', we have
3429 + * u = 2^uz (tu' + q tv)
3434 + * t0 = 2^uz, t1 = 2^uz q
3435 + * s0 = 0, s1 = 2^vz
3438 + mpz_setbit (t0, uz);
3439 + mpz_tdiv_qr (t1, tu, tu, tv);
3440 + mpz_mul_2exp (t1, t1, uz);
3442 + mpz_setbit (s1, vz);
3445 + if (tu->_mp_size > 0)
3447 + mp_bitcnt_t shift;
3448 + shift = mpz_make_odd (tu);
3449 + mpz_mul_2exp (t0, t0, shift);
3450 + mpz_mul_2exp (s0, s0, shift);
3456 + c = mpz_cmp (tu, tv);
3464 + * u = t0 tu + t1 (tv' + tu) = (t0 + t1) tu + t1 tv'
3465 + * v = s0 tu + s1 (tv' + tu) = (s0 + s1) tu + s1 tv' */
3467 + mpz_sub (tv, tv, tu);
3468 + mpz_add (t0, t0, t1);
3469 + mpz_add (s0, s0, s1);
3471 + shift = mpz_make_odd (tv);
3472 + mpz_mul_2exp (t1, t1, shift);
3473 + mpz_mul_2exp (s1, s1, shift);
3477 + mpz_sub (tu, tu, tv);
3478 + mpz_add (t1, t0, t1);
3479 + mpz_add (s1, s0, s1);
3481 + shift = mpz_make_odd (tu);
3482 + mpz_mul_2exp (t0, t0, shift);
3483 + mpz_mul_2exp (s0, s0, shift);
3489 + /* Now tv = odd part of gcd, and -s0 and t0 are corresponding
3492 + mpz_mul_2exp (tv, tv, gz);
3495 + /* 2^p g = s0 u + t0 v. Eliminate one factor of two at a time. To
3496 + adjust cofactors, we need u / g and v / g */
3498 + mpz_divexact (s1, v, tv);
3500 + mpz_divexact (t1, u, tv);
3503 + while (power-- > 0)
3505 + /* s0 u + t0 v = (s0 - v/g) u - (t0 + u/g) v */
3506 + if (mpz_odd_p (s0) || mpz_odd_p (t0))
3508 + mpz_sub (s0, s0, s1);
3509 + mpz_add (t0, t0, t1);
3511 + mpz_divexact_ui (s0, s0, 2);
3512 + mpz_divexact_ui (t0, t0, 2);
3515 + /* Arrange so that |s| < |u| / 2g */
3516 + mpz_add (s1, s0, s1);
3517 + if (mpz_cmpabs (s0, s1) > 0)
3519 + mpz_swap (s0, s1);
3520 + mpz_sub (t0, t0, t1);
3522 + if (u->_mp_size < 0)
3524 + if (v->_mp_size < 0)
3542 +mpz_lcm (mpz_t r, const mpz_t u, const mpz_t v)
3546 + if (u->_mp_size == 0 || v->_mp_size == 0)
3554 + mpz_gcd (g, u, v);
3555 + mpz_divexact (g, u, g);
3556 + mpz_mul (r, g, v);
3563 +mpz_lcm_ui (mpz_t r, const mpz_t u, unsigned long v)
3565 + if (v == 0 || u->_mp_size == 0)
3571 + v /= mpz_gcd_ui (NULL, u, v);
3572 + mpz_mul_ui (r, u, v);
3578 +mpz_invert (mpz_t r, const mpz_t u, const mpz_t m)
3583 + if (u->_mp_size == 0 || mpz_cmpabs_ui (m, 1) <= 0)
3589 + mpz_gcdext (g, tr, NULL, u, m);
3590 + invertible = (mpz_cmp_ui (g, 1) == 0);
3594 + if (tr->_mp_size < 0)
3596 + if (m->_mp_size >= 0)
3597 + mpz_add (tr, tr, m);
3599 + mpz_sub (tr, tr, m);
3606 + return invertible;
3610 +/* Higher level operations (sqrt, pow and root) */
3613 +mpz_pow_ui (mpz_t r, const mpz_t b, unsigned long e)
3615 + unsigned long bit;
3617 + mpz_init_set_ui (tr, 1);
3619 + bit = GMP_ULONG_HIGHBIT;
3622 + mpz_mul (tr, tr, tr);
3624 + mpz_mul (tr, tr, b);
3634 +mpz_ui_pow_ui (mpz_t r, unsigned long blimb, unsigned long e)
3637 + mpz_init_set_ui (b, blimb);
3638 + mpz_pow_ui (r, b, e);
3643 +mpz_powm (mpz_t r, const mpz_t b, const mpz_t e, const mpz_t m)
3649 + struct gmp_div_inverse minv;
3653 + en = GMP_ABS (e->_mp_size);
3654 + mn = GMP_ABS (m->_mp_size);
3656 + gmp_die ("mpz_powm: Zero modulo.");
3660 + mpz_set_ui (r, 1);
3665 + mpn_div_qr_invert (&minv, mp, mn);
3666 + shift = minv.shift;
3670 + /* To avoid shifts, we do all our reductions, except the final
3671 + one, using a *normalized* m. */
3674 + tp = gmp_xalloc_limbs (mn);
3675 + gmp_assert_nocarry (mpn_lshift (tp, mp, mn, shift));
3681 + if (e->_mp_size < 0)
3683 + if (!mpz_invert (base, b, m))
3684 + gmp_die ("mpz_powm: Negative exponent and non-invertible base.");
3689 + mpz_abs (base, b);
3691 + bn = base->_mp_size;
3694 + mpn_div_qr_preinv (NULL, base->_mp_d, base->_mp_size, mp, mn, &minv);
3698 + /* We have reduced the absolute value. Now take care of the
3699 + sign. Note that we get zero represented non-canonically as
3701 + if (b->_mp_size < 0)
3703 + mp_ptr bp = MPZ_REALLOC (base, mn);
3704 + gmp_assert_nocarry (mpn_sub (bp, mp, mn, bp, bn));
3707 + base->_mp_size = mpn_normalized_size (base->_mp_d, bn);
3709 + mpz_init_set_ui (tr, 1);
3713 + mp_limb_t w = e->_mp_d[en];
3716 + bit = GMP_LIMB_HIGHBIT;
3719 + mpz_mul (tr, tr, tr);
3721 + mpz_mul (tr, tr, base);
3722 + if (tr->_mp_size > mn)
3724 + mpn_div_qr_preinv (NULL, tr->_mp_d, tr->_mp_size, mp, mn, &minv);
3725 + tr->_mp_size = mpn_normalized_size (tr->_mp_d, mn);
3732 + /* Final reduction */
3733 + if (tr->_mp_size >= mn)
3735 + minv.shift = shift;
3736 + mpn_div_qr_preinv (NULL, tr->_mp_d, tr->_mp_size, mp, mn, &minv);
3737 + tr->_mp_size = mpn_normalized_size (tr->_mp_d, mn);
3748 +mpz_powm_ui (mpz_t r, const mpz_t b, unsigned long elimb, const mpz_t m)
3751 + mpz_init_set_ui (e, elimb);
3752 + mpz_powm (r, b, e, m);
3756 +/* x=trunc(y^(1/z)), r=y-x^z */
3758 +mpz_rootrem (mpz_t x, mpz_t r, const mpz_t y, unsigned long z)
3763 + sgn = y->_mp_size < 0;
3764 + if ((~z & sgn) != 0)
3765 + gmp_die ("mpz_rootrem: Negative argument, with even root.");
3767 + gmp_die ("mpz_rootrem: Zeroth root.");
3769 + if (mpz_cmpabs_ui (y, 1) <= 0) {
3780 + tb = mpz_sizeinbase (y, 2) / z + 1;
3781 + mpz_init2 (t, tb);
3782 + mpz_setbit (t, tb);
3785 + if (z == 2) /* simplify sqrt loop: z-1 == 1 */
3787 + mpz_swap (u, t); /* u = x */
3788 + mpz_tdiv_q (t, y, u); /* t = y/x */
3789 + mpz_add (t, t, u); /* t = y/x + x */
3790 + mpz_tdiv_q_2exp (t, t, 1); /* x'= (y/x + x)/2 */
3791 + } while (mpz_cmpabs (t, u) < 0); /* |x'| < |x| */
3792 + else /* z != 2 */ {
3800 + mpz_swap (u, t); /* u = x */
3801 + mpz_pow_ui (t, u, z - 1); /* t = x^(z-1) */
3802 + mpz_tdiv_q (t, y, t); /* t = y/x^(z-1) */
3803 + mpz_mul_ui (v, u, z - 1); /* v = x*(z-1) */
3804 + mpz_add (t, t, v); /* t = y/x^(z-1) + x*(z-1) */
3805 + mpz_tdiv_q_ui (t, t, z); /* x'=(y/x^(z-1) + x*(z-1))/z */
3806 + } while (mpz_cmpabs (t, u) < 0); /* |x'| < |x| */
3812 + mpz_pow_ui (t, u, z);
3813 + mpz_sub (r, y, t);
3822 +mpz_root (mpz_t x, const mpz_t y, unsigned long z)
3828 + mpz_rootrem (x, r, y, z);
3829 + res = r->_mp_size == 0;
3835 +/* Compute s = floor(sqrt(u)) and r = u - s^2. Allows r == NULL */
3837 +mpz_sqrtrem (mpz_t s, mpz_t r, const mpz_t u)
3839 + mpz_rootrem (s, r, u, 2);
3843 +mpz_sqrt (mpz_t s, const mpz_t u)
3845 + mpz_rootrem (s, NULL, u, 2);
3849 +mpz_perfect_square_p (const mpz_t u)
3851 + if (u->_mp_size <= 0)
3852 + return (u->_mp_size == 0);
3854 + return mpz_root (NULL, u, 2);
3858 +mpn_perfect_square_p (mp_srcptr p, mp_size_t n)
3863 + assert (p [n-1] != 0);
3864 + return mpz_root (NULL, mpz_roinit_n (t, p, n), 2);
3868 +mpn_sqrtrem (mp_ptr sp, mp_ptr rp, mp_srcptr p, mp_size_t n)
3874 + assert (p [n-1] != 0);
3878 + mpz_rootrem (s, r, mpz_roinit_n (u, p, n), 2);
3880 + assert (s->_mp_size == (n+1)/2);
3881 + mpn_copyd (sp, s->_mp_d, s->_mp_size);
3883 + res = r->_mp_size;
3885 + mpn_copyd (rp, r->_mp_d, res);
3890 +/* Combinatorics */
3893 +mpz_fac_ui (mpz_t x, unsigned long n)
3895 + mpz_set_ui (x, n + (n == 0));
3897 + mpz_mul_ui (x, x, --n);
3901 +mpz_bin_uiui (mpz_t r, unsigned long n, unsigned long k)
3905 + mpz_set_ui (r, k <= n);
3908 + k = (k <= n) ? n - k : 0;
3911 + mpz_fac_ui (t, k);
3913 + for (; k > 0; k--)
3914 + mpz_mul_ui (r, r, n--);
3916 + mpz_divexact (r, r, t);
3921 +/* Primality testing */
3923 +gmp_millerrabin (const mpz_t n, const mpz_t nm1, mpz_t y,
3924 + const mpz_t q, mp_bitcnt_t k)
3928 + /* Caller must initialize y to the base. */
3929 + mpz_powm (y, y, q, n);
3931 + if (mpz_cmp_ui (y, 1) == 0 || mpz_cmp (y, nm1) == 0)
3936 + mpz_powm_ui (y, y, 2, n);
3937 + if (mpz_cmp (y, nm1) == 0)
3939 + /* y == 1 means that the previous y was a non-trivial square root
3940 + of 1 (mod n). y == 0 means that n is a power of the base.
3941 + In either case, n is not prime. */
3942 + if (mpz_cmp_ui (y, 1) <= 0)
3948 +/* This product is 0xc0cfd797, and fits in 32 bits. */
3949 +#define GMP_PRIME_PRODUCT \
3950 + (3UL*5UL*7UL*11UL*13UL*17UL*19UL*23UL*29UL)
3952 +/* Bit (p+1)/2 is set, for each odd prime <= 61 */
3953 +#define GMP_PRIME_MASK 0xc96996dcUL
3956 +mpz_probab_prime_p (const mpz_t n, int reps)
3965 + /* Note that we use the absolute value of n only, for compatibility
3966 + with the real GMP. */
3967 + if (mpz_even_p (n))
3968 + return (mpz_cmpabs_ui (n, 2) == 0) ? 2 : 0;
3970 + /* Above test excludes n == 0 */
3971 + assert (n->_mp_size != 0);
3973 + if (mpz_cmpabs_ui (n, 64) < 0)
3974 + return (GMP_PRIME_MASK >> (n->_mp_d[0] >> 1)) & 2;
3976 + if (mpz_gcd_ui (NULL, n, GMP_PRIME_PRODUCT) != 1)
3979 + /* All prime factors are >= 31. */
3980 + if (mpz_cmpabs_ui (n, 31*31) < 0)
3983 + /* Use Miller-Rabin, with a deterministic sequence of bases, a[j] =
3984 + j^2 + j + 41 using Euler's polynomial. We potentially stop early,
3985 + if a[j] >= n - 1. Since n >= 31*31, this can happen only if reps >
3986 + 30 (a[30] == 971 > 31*31 == 961). */
3992 + /* Find q and k, where q is odd and n = 1 + 2**k * q. */
3993 + nm1->_mp_size = mpz_abs_sub_ui (nm1, n, 1);
3994 + k = mpz_scan1 (nm1, 0);
3995 + mpz_tdiv_q_2exp (q, nm1, k);
3997 + for (j = 0, is_prime = 1; is_prime & (j < reps); j++)
3999 + mpz_set_ui (y, (unsigned long) j*j+j+41);
4000 + if (mpz_cmp (y, nm1) >= 0)
4002 + /* Don't try any further bases. This "early" break does not affect
4003 + the result for any reasonable reps value (<=5000 was tested) */
4007 + is_prime = gmp_millerrabin (n, nm1, y, q, k);
4017 +/* Logical operations and bit manipulation. */
4019 +/* Numbers are treated as if represented in two's complement (and
4020 + infinitely sign extended). For a negative values we get the two's
4021 + complement from -x = ~x + 1, where ~ is bitwise complement.
4022 + Negation transforms
4030 + where yyyy is the bitwise complement of xxxx. So least significant
4031 + bits, up to and including the first one bit, are unchanged, and
4032 + the more significant bits are all complemented.
4034 + To change a bit from zero to one in a negative number, subtract the
4035 + corresponding power of two from the absolute value. This can never
4036 + underflow. To change a bit from one to zero, add the corresponding
4037 + power of two, and this might overflow. E.g., if x = -001111, the
4038 + two's complement is 110001. Clearing the least significant bit, we
4039 + get two's complement 110000, and -010000. */
4042 +mpz_tstbit (const mpz_t d, mp_bitcnt_t bit_index)
4044 + mp_size_t limb_index;
4052 + dn = GMP_ABS (ds);
4053 + limb_index = bit_index / GMP_LIMB_BITS;
4054 + if (limb_index >= dn)
4057 + shift = bit_index % GMP_LIMB_BITS;
4058 + w = d->_mp_d[limb_index];
4059 + bit = (w >> shift) & 1;
4063 + /* d < 0. Check if any of the bits below is set: If so, our bit
4064 + must be complemented. */
4065 + if (shift > 0 && (w << (GMP_LIMB_BITS - shift)) > 0)
4067 + while (limb_index-- > 0)
4068 + if (d->_mp_d[limb_index] > 0)
4075 +mpz_abs_add_bit (mpz_t d, mp_bitcnt_t bit_index)
4077 + mp_size_t dn, limb_index;
4081 + dn = GMP_ABS (d->_mp_size);
4083 + limb_index = bit_index / GMP_LIMB_BITS;
4084 + bit = (mp_limb_t) 1 << (bit_index % GMP_LIMB_BITS);
4086 + if (limb_index >= dn)
4089 + /* The bit should be set outside of the end of the number.
4090 + We have to increase the size of the number. */
4091 + dp = MPZ_REALLOC (d, limb_index + 1);
4093 + dp[limb_index] = bit;
4094 + for (i = dn; i < limb_index; i++)
4096 + dn = limb_index + 1;
4104 + cy = mpn_add_1 (dp + limb_index, dp + limb_index, dn - limb_index, bit);
4107 + dp = MPZ_REALLOC (d, dn + 1);
4112 + d->_mp_size = (d->_mp_size < 0) ? - dn : dn;
4116 +mpz_abs_sub_bit (mpz_t d, mp_bitcnt_t bit_index)
4118 + mp_size_t dn, limb_index;
4122 + dn = GMP_ABS (d->_mp_size);
4125 + limb_index = bit_index / GMP_LIMB_BITS;
4126 + bit = (mp_limb_t) 1 << (bit_index % GMP_LIMB_BITS);
4128 + assert (limb_index < dn);
4130 + gmp_assert_nocarry (mpn_sub_1 (dp + limb_index, dp + limb_index,
4131 + dn - limb_index, bit));
4132 + dn = mpn_normalized_size (dp, dn);
4133 + d->_mp_size = (d->_mp_size < 0) ? - dn : dn;
4137 +mpz_setbit (mpz_t d, mp_bitcnt_t bit_index)
4139 + if (!mpz_tstbit (d, bit_index))
4141 + if (d->_mp_size >= 0)
4142 + mpz_abs_add_bit (d, bit_index);
4144 + mpz_abs_sub_bit (d, bit_index);
4149 +mpz_clrbit (mpz_t d, mp_bitcnt_t bit_index)
4151 + if (mpz_tstbit (d, bit_index))
4153 + if (d->_mp_size >= 0)
4154 + mpz_abs_sub_bit (d, bit_index);
4156 + mpz_abs_add_bit (d, bit_index);
4161 +mpz_combit (mpz_t d, mp_bitcnt_t bit_index)
4163 + if (mpz_tstbit (d, bit_index) ^ (d->_mp_size < 0))
4164 + mpz_abs_sub_bit (d, bit_index);
4166 + mpz_abs_add_bit (d, bit_index);
4170 +mpz_com (mpz_t r, const mpz_t u)
4173 + mpz_sub_ui (r, r, 1);
4177 +mpz_and (mpz_t r, const mpz_t u, const mpz_t v)
4179 + mp_size_t un, vn, rn, i;
4180 + mp_ptr up, vp, rp;
4182 + mp_limb_t ux, vx, rx;
4183 + mp_limb_t uc, vc, rc;
4184 + mp_limb_t ul, vl, rl;
4186 + un = GMP_ABS (u->_mp_size);
4187 + vn = GMP_ABS (v->_mp_size);
4190 + MPZ_SRCPTR_SWAP (u, v);
4191 + MP_SIZE_T_SWAP (un, vn);
4199 + uc = u->_mp_size < 0;
4200 + vc = v->_mp_size < 0;
4207 + /* If the smaller input is positive, higher limbs don't matter. */
4208 + rn = vx ? un : vn;
4210 + rp = MPZ_REALLOC (r, rn + rc);
4218 + ul = (up[i] ^ ux) + uc;
4221 + vl = (vp[i] ^ vx) + vc;
4224 + rl = ( (ul & vl) ^ rx) + rc;
4231 + for (; i < rn; i++)
4233 + ul = (up[i] ^ ux) + uc;
4236 + rl = ( (ul & vx) ^ rx) + rc;
4243 + rn = mpn_normalized_size (rp, rn);
4245 + r->_mp_size = rx ? -rn : rn;
4249 +mpz_ior (mpz_t r, const mpz_t u, const mpz_t v)
4251 + mp_size_t un, vn, rn, i;
4252 + mp_ptr up, vp, rp;
4254 + mp_limb_t ux, vx, rx;
4255 + mp_limb_t uc, vc, rc;
4256 + mp_limb_t ul, vl, rl;
4258 + un = GMP_ABS (u->_mp_size);
4259 + vn = GMP_ABS (v->_mp_size);
4262 + MPZ_SRCPTR_SWAP (u, v);
4263 + MP_SIZE_T_SWAP (un, vn);
4271 + uc = u->_mp_size < 0;
4272 + vc = v->_mp_size < 0;
4279 + /* If the smaller input is negative, by sign extension higher limbs
4281 + rn = vx ? vn : un;
4283 + rp = MPZ_REALLOC (r, rn + rc);
4291 + ul = (up[i] ^ ux) + uc;
4294 + vl = (vp[i] ^ vx) + vc;
4297 + rl = ( (ul | vl) ^ rx) + rc;
4304 + for (; i < rn; i++)
4306 + ul = (up[i] ^ ux) + uc;
4309 + rl = ( (ul | vx) ^ rx) + rc;
4316 + rn = mpn_normalized_size (rp, rn);
4318 + r->_mp_size = rx ? -rn : rn;
4322 +mpz_xor (mpz_t r, const mpz_t u, const mpz_t v)
4324 + mp_size_t un, vn, i;
4325 + mp_ptr up, vp, rp;
4327 + mp_limb_t ux, vx, rx;
4328 + mp_limb_t uc, vc, rc;
4329 + mp_limb_t ul, vl, rl;
4331 + un = GMP_ABS (u->_mp_size);
4332 + vn = GMP_ABS (v->_mp_size);
4335 + MPZ_SRCPTR_SWAP (u, v);
4336 + MP_SIZE_T_SWAP (un, vn);
4344 + uc = u->_mp_size < 0;
4345 + vc = v->_mp_size < 0;
4352 + rp = MPZ_REALLOC (r, un + rc);
4360 + ul = (up[i] ^ ux) + uc;
4363 + vl = (vp[i] ^ vx) + vc;
4366 + rl = (ul ^ vl ^ rx) + rc;
4373 + for (; i < un; i++)
4375 + ul = (up[i] ^ ux) + uc;
4378 + rl = (ul ^ ux) + rc;
4385 + un = mpn_normalized_size (rp, un);
4387 + r->_mp_size = rx ? -un : un;
4391 +gmp_popcount_limb (mp_limb_t x)
4395 + /* Do 16 bits at a time, to avoid limb-sized constants. */
4396 + for (c = 0; x > 0; x >>= 16)
4398 + unsigned w = ((x >> 1) & 0x5555) + (x & 0x5555);
4399 + w = ((w >> 2) & 0x3333) + (w & 0x3333);
4400 + w = ((w >> 4) & 0x0f0f) + (w & 0x0f0f);
4401 + w = (w >> 8) + (w & 0x00ff);
4408 +mpn_popcount (mp_srcptr p, mp_size_t n)
4413 + for (c = 0, i = 0; i < n; i++)
4414 + c += gmp_popcount_limb (p[i]);
4420 +mpz_popcount (const mpz_t u)
4427 + return ~(mp_bitcnt_t) 0;
4429 + return mpn_popcount (u->_mp_d, un);
4433 +mpz_hamdist (const mpz_t u, const mpz_t v)
4435 + mp_size_t un, vn, i;
4436 + mp_limb_t uc, vc, ul, vl, comp;
4443 + if ( (un ^ vn) < 0)
4444 + return ~(mp_bitcnt_t) 0;
4446 + comp = - (uc = vc = (un < 0));
4458 + MPN_SRCPTR_SWAP (up, un, vp, vn);
4460 + for (i = 0, c = 0; i < vn; i++)
4462 + ul = (up[i] ^ comp) + uc;
4465 + vl = (vp[i] ^ comp) + vc;
4468 + c += gmp_popcount_limb (ul ^ vl);
4472 + for (; i < un; i++)
4474 + ul = (up[i] ^ comp) + uc;
4477 + c += gmp_popcount_limb (ul ^ comp);
4484 +mpz_scan1 (const mpz_t u, mp_bitcnt_t starting_bit)
4487 + mp_size_t us, un, i;
4488 + mp_limb_t limb, ux;
4491 + un = GMP_ABS (us);
4492 + i = starting_bit / GMP_LIMB_BITS;
4494 + /* Past the end there's no 1 bits for u>=0, or an immediate 1 bit
4495 + for u<0. Notice this test picks up any u==0 too. */
4497 + return (us >= 0 ? ~(mp_bitcnt_t) 0 : starting_bit);
4503 + if (starting_bit != 0)
4507 + ux = mpn_zero_p (up, i);
4508 + limb = ~ limb + ux;
4509 + ux = - (mp_limb_t) (limb >= ux);
4512 + /* Mask to 0 all bits before starting_bit, thus ignoring them. */
4513 + limb &= (GMP_LIMB_MAX << (starting_bit % GMP_LIMB_BITS));
4516 + return mpn_common_scan (limb, i, up, un, ux);
4520 +mpz_scan0 (const mpz_t u, mp_bitcnt_t starting_bit)
4523 + mp_size_t us, un, i;
4524 + mp_limb_t limb, ux;
4527 + ux = - (mp_limb_t) (us >= 0);
4528 + un = GMP_ABS (us);
4529 + i = starting_bit / GMP_LIMB_BITS;
4531 + /* When past end, there's an immediate 0 bit for u>=0, or no 0 bits for
4532 + u<0. Notice this test picks up all cases of u==0 too. */
4534 + return (ux ? starting_bit : ~(mp_bitcnt_t) 0);
4537 + limb = up[i] ^ ux;
4540 + limb -= mpn_zero_p (up, i); /* limb = ~(~limb + zero_p) */
4542 + /* Mask all bits before starting_bit, thus ignoring them. */
4543 + limb &= (GMP_LIMB_MAX << (starting_bit % GMP_LIMB_BITS));
4545 + return mpn_common_scan (limb, i, up, un, ux);
4549 +/* MPZ base conversion. */
4552 +mpz_sizeinbase (const mpz_t u, int base)
4558 + struct gmp_div_inverse bi;
4561 + assert (base >= 2);
4562 + assert (base <= 36);
4564 + un = GMP_ABS (u->_mp_size);
4570 + bits = (un - 1) * GMP_LIMB_BITS + mpn_limb_size_in_base_2 (up[un-1]);
4576 + return (bits + 1) / 2;
4578 + return (bits + 2) / 3;
4580 + return (bits + 3) / 4;
4582 + return (bits + 4) / 5;
4583 + /* FIXME: Do something more clever for the common case of base
4587 + tp = gmp_xalloc_limbs (un);
4588 + mpn_copyi (tp, up, un);
4589 + mpn_div_qr_1_invert (&bi, base);
4595 + mpn_div_qr_1_preinv (tp, tp, un, &bi);
4596 + un -= (tp[un-1] == 0);
4605 +mpz_get_str (char *sp, int base, const mpz_t u)
4608 + const char *digits;
4614 + digits = "0123456789abcdefghijklmnopqrstuvwxyz";
4619 + digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
4626 + sn = 1 + mpz_sizeinbase (u, base);
4628 + sp = gmp_xalloc (1 + sn);
4630 + un = GMP_ABS (u->_mp_size);
4641 + if (u->_mp_size < 0)
4644 + bits = mpn_base_power_of_two_p (base);
4647 + /* Not modified in this case. */
4648 + sn = i + mpn_get_str_bits ((unsigned char *) sp + i, bits, u->_mp_d, un);
4651 + struct mpn_base_info info;
4654 + mpn_get_base_info (&info, base);
4655 + tp = gmp_xalloc_limbs (un);
4656 + mpn_copyi (tp, u->_mp_d, un);
4658 + sn = i + mpn_get_str_other ((unsigned char *) sp + i, base, &info, tp, un);
4662 + for (; i < sn; i++)
4663 + sp[i] = digits[(unsigned char) sp[i]];
4670 +mpz_set_str (mpz_t r, const char *sp, int base)
4673 + mp_size_t rn, alloc;
4677 + unsigned char *dp;
4679 + assert (base == 0 || (base >= 2 && base <= 36));
4681 + while (isspace( (unsigned char) *sp))
4684 + sign = (*sp == '-');
4692 + if (*sp == 'x' || *sp == 'X')
4697 + else if (*sp == 'b' || *sp == 'B')
4710 + dp = gmp_xalloc (sn + (sn == 0));
4712 + for (sn = 0; *sp; sp++)
4716 + if (isspace ((unsigned char) *sp))
4718 + if (*sp >= '0' && *sp <= '9')
4719 + digit = *sp - '0';
4720 + else if (*sp >= 'a' && *sp <= 'z')
4721 + digit = *sp - 'a' + 10;
4722 + else if (*sp >= 'A' && *sp <= 'Z')
4723 + digit = *sp - 'A' + 10;
4725 + digit = base; /* fail */
4727 + if (digit >= base)
4737 + bits = mpn_base_power_of_two_p (base);
4741 + alloc = (sn * bits + GMP_LIMB_BITS - 1) / GMP_LIMB_BITS;
4742 + rp = MPZ_REALLOC (r, alloc);
4743 + rn = mpn_set_str_bits (rp, dp, sn, bits);
4747 + struct mpn_base_info info;
4748 + mpn_get_base_info (&info, base);
4749 + alloc = (sn + info.exp - 1) / info.exp;
4750 + rp = MPZ_REALLOC (r, alloc);
4751 + rn = mpn_set_str_other (rp, dp, sn, base, &info);
4753 + assert (rn <= alloc);
4756 + r->_mp_size = sign ? - rn : rn;
4762 +mpz_init_set_str (mpz_t r, const char *sp, int base)
4765 + return mpz_set_str (r, sp, base);
4769 +mpz_out_str (FILE *stream, int base, const mpz_t x)
4774 + str = mpz_get_str (NULL, base, x);
4775 + len = strlen (str);
4776 + len = fwrite (str, 1, len, stream);
4783 +gmp_detect_endian (void)
4785 + static const int i = 2;
4786 + const unsigned char *p = (const unsigned char *) &i;
4790 +/* Import and export. Does not support nails. */
4792 +mpz_import (mpz_t r, size_t count, int order, size_t size, int endian,
4793 + size_t nails, const void *src)
4795 + const unsigned char *p;
4796 + ptrdiff_t word_step;
4800 + /* The current (partial) limb. */
4802 + /* The number of bytes already copied to this limb (starting from
4805 + /* The index where the limb should be stored, when completed. */
4809 + gmp_die ("mpz_import: Nails not supported.");
4811 + assert (order == 1 || order == -1);
4812 + assert (endian >= -1 && endian <= 1);
4815 + endian = gmp_detect_endian ();
4817 + p = (unsigned char *) src;
4819 + word_step = (order != endian) ? 2 * size : 0;
4821 + /* Process bytes from the least significant end, so point p at the
4822 + least significant word. */
4825 + p += size * (count - 1);
4826 + word_step = - word_step;
4829 + /* And at least significant byte of that word. */
4833 + rn = (size * count + sizeof(mp_limb_t) - 1) / sizeof(mp_limb_t);
4834 + rp = MPZ_REALLOC (r, rn);
4836 + for (limb = 0, bytes = 0, i = 0; count > 0; count--, p += word_step)
4839 + for (j = 0; j < size; j++, p -= (ptrdiff_t) endian)
4841 + limb |= (mp_limb_t) *p << (bytes++ * CHAR_BIT);
4842 + if (bytes == sizeof(mp_limb_t))
4850 + assert (i + (bytes > 0) == rn);
4854 + i = mpn_normalized_size (rp, i);
4860 +mpz_export (void *r, size_t *countp, int order, size_t size, int endian,
4861 + size_t nails, const mpz_t u)
4867 + gmp_die ("mpz_import: Nails not supported.");
4869 + assert (order == 1 || order == -1);
4870 + assert (endian >= -1 && endian <= 1);
4871 + assert (size > 0 || u->_mp_size == 0);
4879 + ptrdiff_t word_step;
4880 + /* The current (partial) limb. */
4882 + /* The number of bytes left to to in this limb. */
4884 + /* The index where the limb was read. */
4887 + un = GMP_ABS (un);
4889 + /* Count bytes in top limb. */
4890 + limb = u->_mp_d[un-1];
4891 + assert (limb != 0);
4895 + k++; limb >>= CHAR_BIT;
4896 + } while (limb != 0);
4898 + count = (k + (un-1) * sizeof (mp_limb_t) + size - 1) / size;
4901 + r = gmp_xalloc (count * size);
4904 + endian = gmp_detect_endian ();
4906 + p = (unsigned char *) r;
4908 + word_step = (order != endian) ? 2 * size : 0;
4910 + /* Process bytes from the least significant end, so point p at the
4911 + least significant word. */
4914 + p += size * (count - 1);
4915 + word_step = - word_step;
4918 + /* And at least significant byte of that word. */
4922 + for (bytes = 0, i = 0, k = 0; k < count; k++, p += word_step)
4925 + for (j = 0; j < size; j++, p -= (ptrdiff_t) endian)
4930 + limb = u->_mp_d[i++];
4931 + bytes = sizeof (mp_limb_t);
4934 + limb >>= CHAR_BIT;
4939 + assert (k == count);