1 From b1417739f91682442a254cbd732aed6e9a5c5b69 Mon Sep 17 00:00:00 2001
2 From: Steven Barth <steven@midlink.org>
3 Date: Mon, 15 Dec 2014 10:36:04 +0100
4 Subject: [PATCH 3/3] build: add mini-gmp from gmplib 6.0
6 Signed-off-by: Steven Barth <cyrus@openwrt.org>
8 include/mini-gmp.h | 294 ++++
9 src/mini-gmp.c | 4386 ++++++++++++++++++++++++++++++++++++++++++++++++++++
10 2 files changed, 4680 insertions(+)
11 create mode 100644 include/mini-gmp.h
12 create mode 100644 src/mini-gmp.c
14 diff --git a/include/mini-gmp.h b/include/mini-gmp.h
16 index 0000000..c043ca7
18 +++ b/include/mini-gmp.h
20 +/* mini-gmp, a minimalistic implementation of a GNU GMP subset.
22 +Copyright 2011-2014 Free Software Foundation, Inc.
24 +This file is part of the GNU MP Library.
26 +The GNU MP Library is free software; you can redistribute it and/or modify
27 +it under the terms of either:
29 + * the GNU Lesser General Public License as published by the Free
30 + Software Foundation; either version 3 of the License, or (at your
31 + option) any later version.
35 + * the GNU General Public License as published by the Free Software
36 + Foundation; either version 2 of the License, or (at your option) any
39 +or both in parallel, as here.
41 +The GNU MP Library is distributed in the hope that it will be useful, but
42 +WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
43 +or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
46 +You should have received copies of the GNU General Public License and the
47 +GNU Lesser General Public License along with the GNU MP Library. If not,
48 +see https://www.gnu.org/licenses/. */
50 +/* About mini-gmp: This is a minimal implementation of a subset of the
51 + GMP interface. It is intended for inclusion into applications which
52 + have modest bignums needs, as a fallback when the real GMP library
55 + This file defines the public interface. */
57 +#ifndef __MINI_GMP_H__
58 +#define __MINI_GMP_H__
63 +#if defined (__cplusplus)
67 +void mp_set_memory_functions (void *(*) (size_t),
68 + void *(*) (void *, size_t, size_t),
69 + void (*) (void *, size_t));
71 +void mp_get_memory_functions (void *(**) (size_t),
72 + void *(**) (void *, size_t, size_t),
73 + void (**) (void *, size_t));
75 +typedef unsigned long mp_limb_t;
76 +typedef long mp_size_t;
77 +typedef unsigned long mp_bitcnt_t;
79 +typedef mp_limb_t *mp_ptr;
80 +typedef const mp_limb_t *mp_srcptr;
84 + int _mp_alloc; /* Number of *limbs* allocated and pointed
85 + to by the _mp_d field. */
86 + int _mp_size; /* abs(_mp_size) is the number of limbs the
87 + last field points to. If _mp_size is
88 + negative this is a negative number. */
89 + mp_limb_t *_mp_d; /* Pointer to the limbs. */
92 +typedef __mpz_struct mpz_t[1];
94 +typedef __mpz_struct *mpz_ptr;
95 +typedef const __mpz_struct *mpz_srcptr;
97 +extern const int mp_bits_per_limb;
99 +void mpn_copyi (mp_ptr, mp_srcptr, mp_size_t);
100 +void mpn_copyd (mp_ptr, mp_srcptr, mp_size_t);
101 +void mpn_zero (mp_ptr, mp_size_t);
103 +int mpn_cmp (mp_srcptr, mp_srcptr, mp_size_t);
105 +mp_limb_t mpn_add_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t);
106 +mp_limb_t mpn_add_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
107 +mp_limb_t mpn_add (mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t);
109 +mp_limb_t mpn_sub_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t);
110 +mp_limb_t mpn_sub_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
111 +mp_limb_t mpn_sub (mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t);
113 +mp_limb_t mpn_mul_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t);
114 +mp_limb_t mpn_addmul_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t);
115 +mp_limb_t mpn_submul_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t);
117 +mp_limb_t mpn_mul (mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t);
118 +void mpn_mul_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
119 +void mpn_sqr (mp_ptr, mp_srcptr, mp_size_t);
120 +int mpn_perfect_square_p (mp_srcptr, mp_size_t);
121 +mp_size_t mpn_sqrtrem (mp_ptr, mp_ptr, mp_srcptr, mp_size_t);
123 +mp_limb_t mpn_lshift (mp_ptr, mp_srcptr, mp_size_t, unsigned int);
124 +mp_limb_t mpn_rshift (mp_ptr, mp_srcptr, mp_size_t, unsigned int);
126 +mp_bitcnt_t mpn_scan0 (mp_srcptr, mp_bitcnt_t);
127 +mp_bitcnt_t mpn_scan1 (mp_srcptr, mp_bitcnt_t);
129 +mp_bitcnt_t mpn_popcount (mp_srcptr, mp_size_t);
131 +mp_limb_t mpn_invert_3by2 (mp_limb_t, mp_limb_t);
132 +#define mpn_invert_limb(x) mpn_invert_3by2 ((x), 0)
134 +size_t mpn_get_str (unsigned char *, int, mp_ptr, mp_size_t);
135 +mp_size_t mpn_set_str (mp_ptr, const unsigned char *, size_t, int);
137 +void mpz_init (mpz_t);
138 +void mpz_init2 (mpz_t, mp_bitcnt_t);
139 +void mpz_clear (mpz_t);
141 +#define mpz_odd_p(z) (((z)->_mp_size != 0) & (int) (z)->_mp_d[0])
142 +#define mpz_even_p(z) (! mpz_odd_p (z))
144 +int mpz_sgn (const mpz_t);
145 +int mpz_cmp_si (const mpz_t, long);
146 +int mpz_cmp_ui (const mpz_t, unsigned long);
147 +int mpz_cmp (const mpz_t, const mpz_t);
148 +int mpz_cmpabs_ui (const mpz_t, unsigned long);
149 +int mpz_cmpabs (const mpz_t, const mpz_t);
150 +int mpz_cmp_d (const mpz_t, double);
151 +int mpz_cmpabs_d (const mpz_t, double);
153 +void mpz_abs (mpz_t, const mpz_t);
154 +void mpz_neg (mpz_t, const mpz_t);
155 +void mpz_swap (mpz_t, mpz_t);
157 +void mpz_add_ui (mpz_t, const mpz_t, unsigned long);
158 +void mpz_add (mpz_t, const mpz_t, const mpz_t);
159 +void mpz_sub_ui (mpz_t, const mpz_t, unsigned long);
160 +void mpz_ui_sub (mpz_t, unsigned long, const mpz_t);
161 +void mpz_sub (mpz_t, const mpz_t, const mpz_t);
163 +void mpz_mul_si (mpz_t, const mpz_t, long int);
164 +void mpz_mul_ui (mpz_t, const mpz_t, unsigned long int);
165 +void mpz_mul (mpz_t, const mpz_t, const mpz_t);
166 +void mpz_mul_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
167 +void mpz_addmul_ui (mpz_t, const mpz_t, unsigned long int);
168 +void mpz_addmul (mpz_t, const mpz_t, const mpz_t);
169 +void mpz_submul_ui (mpz_t, const mpz_t, unsigned long int);
170 +void mpz_submul (mpz_t, const mpz_t, const mpz_t);
172 +void mpz_cdiv_qr (mpz_t, mpz_t, const mpz_t, const mpz_t);
173 +void mpz_fdiv_qr (mpz_t, mpz_t, const mpz_t, const mpz_t);
174 +void mpz_tdiv_qr (mpz_t, mpz_t, const mpz_t, const mpz_t);
175 +void mpz_cdiv_q (mpz_t, const mpz_t, const mpz_t);
176 +void mpz_fdiv_q (mpz_t, const mpz_t, const mpz_t);
177 +void mpz_tdiv_q (mpz_t, const mpz_t, const mpz_t);
178 +void mpz_cdiv_r (mpz_t, const mpz_t, const mpz_t);
179 +void mpz_fdiv_r (mpz_t, const mpz_t, const mpz_t);
180 +void mpz_tdiv_r (mpz_t, const mpz_t, const mpz_t);
182 +void mpz_cdiv_q_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
183 +void mpz_fdiv_q_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
184 +void mpz_tdiv_q_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
185 +void mpz_cdiv_r_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
186 +void mpz_fdiv_r_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
187 +void mpz_tdiv_r_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
189 +void mpz_mod (mpz_t, const mpz_t, const mpz_t);
191 +void mpz_divexact (mpz_t, const mpz_t, const mpz_t);
193 +int mpz_divisible_p (const mpz_t, const mpz_t);
194 +int mpz_congruent_p (const mpz_t, const mpz_t, const mpz_t);
196 +unsigned long mpz_cdiv_qr_ui (mpz_t, mpz_t, const mpz_t, unsigned long);
197 +unsigned long mpz_fdiv_qr_ui (mpz_t, mpz_t, const mpz_t, unsigned long);
198 +unsigned long mpz_tdiv_qr_ui (mpz_t, mpz_t, const mpz_t, unsigned long);
199 +unsigned long mpz_cdiv_q_ui (mpz_t, const mpz_t, unsigned long);
200 +unsigned long mpz_fdiv_q_ui (mpz_t, const mpz_t, unsigned long);
201 +unsigned long mpz_tdiv_q_ui (mpz_t, const mpz_t, unsigned long);
202 +unsigned long mpz_cdiv_r_ui (mpz_t, const mpz_t, unsigned long);
203 +unsigned long mpz_fdiv_r_ui (mpz_t, const mpz_t, unsigned long);
204 +unsigned long mpz_tdiv_r_ui (mpz_t, const mpz_t, unsigned long);
205 +unsigned long mpz_cdiv_ui (const mpz_t, unsigned long);
206 +unsigned long mpz_fdiv_ui (const mpz_t, unsigned long);
207 +unsigned long mpz_tdiv_ui (const mpz_t, unsigned long);
209 +unsigned long mpz_mod_ui (mpz_t, const mpz_t, unsigned long);
211 +void mpz_divexact_ui (mpz_t, const mpz_t, unsigned long);
213 +int mpz_divisible_ui_p (const mpz_t, unsigned long);
215 +unsigned long mpz_gcd_ui (mpz_t, const mpz_t, unsigned long);
216 +void mpz_gcd (mpz_t, const mpz_t, const mpz_t);
217 +void mpz_gcdext (mpz_t, mpz_t, mpz_t, const mpz_t, const mpz_t);
218 +void mpz_lcm_ui (mpz_t, const mpz_t, unsigned long);
219 +void mpz_lcm (mpz_t, const mpz_t, const mpz_t);
220 +int mpz_invert (mpz_t, const mpz_t, const mpz_t);
222 +void mpz_sqrtrem (mpz_t, mpz_t, const mpz_t);
223 +void mpz_sqrt (mpz_t, const mpz_t);
224 +int mpz_perfect_square_p (const mpz_t);
226 +void mpz_pow_ui (mpz_t, const mpz_t, unsigned long);
227 +void mpz_ui_pow_ui (mpz_t, unsigned long, unsigned long);
228 +void mpz_powm (mpz_t, const mpz_t, const mpz_t, const mpz_t);
229 +void mpz_powm_ui (mpz_t, const mpz_t, unsigned long, const mpz_t);
231 +void mpz_rootrem (mpz_t, mpz_t, const mpz_t, unsigned long);
232 +int mpz_root (mpz_t, const mpz_t, unsigned long);
234 +void mpz_fac_ui (mpz_t, unsigned long);
235 +void mpz_bin_uiui (mpz_t, unsigned long, unsigned long);
237 +int mpz_probab_prime_p (const mpz_t, int);
239 +int mpz_tstbit (const mpz_t, mp_bitcnt_t);
240 +void mpz_setbit (mpz_t, mp_bitcnt_t);
241 +void mpz_clrbit (mpz_t, mp_bitcnt_t);
242 +void mpz_combit (mpz_t, mp_bitcnt_t);
244 +void mpz_com (mpz_t, const mpz_t);
245 +void mpz_and (mpz_t, const mpz_t, const mpz_t);
246 +void mpz_ior (mpz_t, const mpz_t, const mpz_t);
247 +void mpz_xor (mpz_t, const mpz_t, const mpz_t);
249 +mp_bitcnt_t mpz_popcount (const mpz_t);
250 +mp_bitcnt_t mpz_hamdist (const mpz_t, const mpz_t);
251 +mp_bitcnt_t mpz_scan0 (const mpz_t, mp_bitcnt_t);
252 +mp_bitcnt_t mpz_scan1 (const mpz_t, mp_bitcnt_t);
254 +int mpz_fits_slong_p (const mpz_t);
255 +int mpz_fits_ulong_p (const mpz_t);
256 +long int mpz_get_si (const mpz_t);
257 +unsigned long int mpz_get_ui (const mpz_t);
258 +double mpz_get_d (const mpz_t);
259 +size_t mpz_size (const mpz_t);
260 +mp_limb_t mpz_getlimbn (const mpz_t, mp_size_t);
262 +void mpz_realloc2 (mpz_t, mp_bitcnt_t);
263 +mp_srcptr mpz_limbs_read (mpz_srcptr);
264 +mp_ptr mpz_limbs_modify (mpz_t, mp_size_t);
265 +mp_ptr mpz_limbs_write (mpz_t, mp_size_t);
266 +void mpz_limbs_finish (mpz_t, mp_size_t);
267 +mpz_srcptr mpz_roinit_n (mpz_t, mp_srcptr, mp_size_t);
269 +#define MPZ_ROINIT_N(xp, xs) {{0, (xs),(xp) }}
271 +void mpz_set_si (mpz_t, signed long int);
272 +void mpz_set_ui (mpz_t, unsigned long int);
273 +void mpz_set (mpz_t, const mpz_t);
274 +void mpz_set_d (mpz_t, double);
276 +void mpz_init_set_si (mpz_t, signed long int);
277 +void mpz_init_set_ui (mpz_t, unsigned long int);
278 +void mpz_init_set (mpz_t, const mpz_t);
279 +void mpz_init_set_d (mpz_t, double);
281 +size_t mpz_sizeinbase (const mpz_t, int);
282 +char *mpz_get_str (char *, int, const mpz_t);
283 +int mpz_set_str (mpz_t, const char *, int);
284 +int mpz_init_set_str (mpz_t, const char *, int);
286 +/* This long list taken from gmp.h. */
287 +/* For reference, "defined(EOF)" cannot be used here. In g++ 2.95.4,
288 + <iostream> defines EOF but not FILE. */
289 +#if defined (FILE) \
290 + || defined (H_STDIO) \
291 + || defined (_H_STDIO) /* AIX */ \
292 + || defined (_STDIO_H) /* glibc, Sun, SCO */ \
293 + || defined (_STDIO_H_) /* BSD, OSF */ \
294 + || defined (__STDIO_H) /* Borland */ \
295 + || defined (__STDIO_H__) /* IRIX */ \
296 + || defined (_STDIO_INCLUDED) /* HPUX */ \
297 + || defined (__dj_include_stdio_h_) /* DJGPP */ \
298 + || defined (_FILE_DEFINED) /* Microsoft */ \
299 + || defined (__STDIO__) /* Apple MPW MrC */ \
300 + || defined (_MSL_STDIO_H) /* Metrowerks */ \
301 + || defined (_STDIO_H_INCLUDED) /* QNX4 */ \
302 + || defined (_ISO_STDIO_ISO_H) /* Sun C++ */ \
303 + || defined (__STDIO_LOADED) /* VMS */
304 +size_t mpz_out_str (FILE *, int, const mpz_t);
307 +void mpz_import (mpz_t, size_t, int, size_t, int, size_t, const void *);
308 +void *mpz_export (void *, size_t *, int, size_t, int, size_t, const mpz_t);
310 +#if defined (__cplusplus)
313 +#endif /* __MINI_GMP_H__ */
314 diff --git a/src/mini-gmp.c b/src/mini-gmp.c
316 index 0000000..acbe1be
320 +/* mini-gmp, a minimalistic implementation of a GNU GMP subset.
322 + Contributed to the GNU project by Niels Möller
324 +Copyright 1991-1997, 1999-2014 Free Software Foundation, Inc.
326 +This file is part of the GNU MP Library.
328 +The GNU MP Library is free software; you can redistribute it and/or modify
329 +it under the terms of either:
331 + * the GNU Lesser General Public License as published by the Free
332 + Software Foundation; either version 3 of the License, or (at your
333 + option) any later version.
337 + * the GNU General Public License as published by the Free Software
338 + Foundation; either version 2 of the License, or (at your option) any
341 +or both in parallel, as here.
343 +The GNU MP Library is distributed in the hope that it will be useful, but
344 +WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
345 +or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
348 +You should have received copies of the GNU General Public License and the
349 +GNU Lesser General Public License along with the GNU MP Library. If not,
350 +see https://www.gnu.org/licenses/. */
352 +/* NOTE: All functions in this file which are not declared in
353 + mini-gmp.h are internal, and are not intended to be compatible
354 + neither with GMP nor with future versions of mini-gmp. */
356 +/* Much of the material copied from GMP files, including: gmp-impl.h,
357 + longlong.h, mpn/generic/add_n.c, mpn/generic/addmul_1.c,
358 + mpn/generic/lshift.c, mpn/generic/mul_1.c,
359 + mpn/generic/mul_basecase.c, mpn/generic/rshift.c,
360 + mpn/generic/sbpi1_div_qr.c, mpn/generic/sub_n.c,
361 + mpn/generic/submul_1.c. */
370 +#include "mini-gmp.h"
374 +#define GMP_LIMB_BITS (sizeof(mp_limb_t) * CHAR_BIT)
376 +#define GMP_LIMB_MAX (~ (mp_limb_t) 0)
377 +#define GMP_LIMB_HIGHBIT ((mp_limb_t) 1 << (GMP_LIMB_BITS - 1))
379 +#define GMP_HLIMB_BIT ((mp_limb_t) 1 << (GMP_LIMB_BITS / 2))
380 +#define GMP_LLIMB_MASK (GMP_HLIMB_BIT - 1)
382 +#define GMP_ULONG_BITS (sizeof(unsigned long) * CHAR_BIT)
383 +#define GMP_ULONG_HIGHBIT ((unsigned long) 1 << (GMP_ULONG_BITS - 1))
385 +#define GMP_ABS(x) ((x) >= 0 ? (x) : -(x))
386 +#define GMP_NEG_CAST(T,x) (-((T)((x) + 1) - 1))
388 +#define GMP_MIN(a, b) ((a) < (b) ? (a) : (b))
389 +#define GMP_MAX(a, b) ((a) > (b) ? (a) : (b))
391 +#define gmp_assert_nocarry(x) do { \
392 + mp_limb_t __cy = x; \
393 + assert (__cy == 0); \
396 +#define gmp_clz(count, x) do { \
397 + mp_limb_t __clz_x = (x); \
398 + unsigned __clz_c; \
399 + for (__clz_c = 0; \
400 + (__clz_x & ((mp_limb_t) 0xff << (GMP_LIMB_BITS - 8))) == 0; \
403 + for (; (__clz_x & GMP_LIMB_HIGHBIT) == 0; __clz_c++) \
405 + (count) = __clz_c; \
408 +#define gmp_ctz(count, x) do { \
409 + mp_limb_t __ctz_x = (x); \
410 + unsigned __ctz_c = 0; \
411 + gmp_clz (__ctz_c, __ctz_x & - __ctz_x); \
412 + (count) = GMP_LIMB_BITS - 1 - __ctz_c; \
415 +#define gmp_add_ssaaaa(sh, sl, ah, al, bh, bl) \
418 + __x = (al) + (bl); \
419 + (sh) = (ah) + (bh) + (__x < (al)); \
423 +#define gmp_sub_ddmmss(sh, sl, ah, al, bh, bl) \
426 + __x = (al) - (bl); \
427 + (sh) = (ah) - (bh) - ((al) < (bl)); \
431 +#define gmp_umul_ppmm(w1, w0, u, v) \
433 + mp_limb_t __x0, __x1, __x2, __x3; \
434 + unsigned __ul, __vl, __uh, __vh; \
435 + mp_limb_t __u = (u), __v = (v); \
437 + __ul = __u & GMP_LLIMB_MASK; \
438 + __uh = __u >> (GMP_LIMB_BITS / 2); \
439 + __vl = __v & GMP_LLIMB_MASK; \
440 + __vh = __v >> (GMP_LIMB_BITS / 2); \
442 + __x0 = (mp_limb_t) __ul * __vl; \
443 + __x1 = (mp_limb_t) __ul * __vh; \
444 + __x2 = (mp_limb_t) __uh * __vl; \
445 + __x3 = (mp_limb_t) __uh * __vh; \
447 + __x1 += __x0 >> (GMP_LIMB_BITS / 2);/* this can't give carry */ \
448 + __x1 += __x2; /* but this indeed can */ \
449 + if (__x1 < __x2) /* did we get it? */ \
450 + __x3 += GMP_HLIMB_BIT; /* yes, add it in the proper pos. */ \
452 + (w1) = __x3 + (__x1 >> (GMP_LIMB_BITS / 2)); \
453 + (w0) = (__x1 << (GMP_LIMB_BITS / 2)) + (__x0 & GMP_LLIMB_MASK); \
456 +#define gmp_udiv_qrnnd_preinv(q, r, nh, nl, d, di) \
458 + mp_limb_t _qh, _ql, _r, _mask; \
459 + gmp_umul_ppmm (_qh, _ql, (nh), (di)); \
460 + gmp_add_ssaaaa (_qh, _ql, _qh, _ql, (nh) + 1, (nl)); \
461 + _r = (nl) - _qh * (d); \
462 + _mask = -(mp_limb_t) (_r > _ql); /* both > and >= are OK */ \
464 + _r += _mask & (d); \
475 +#define gmp_udiv_qr_3by2(q, r1, r0, n2, n1, n0, d1, d0, dinv) \
477 + mp_limb_t _q0, _t1, _t0, _mask; \
478 + gmp_umul_ppmm ((q), _q0, (n2), (dinv)); \
479 + gmp_add_ssaaaa ((q), _q0, (q), _q0, (n2), (n1)); \
481 + /* Compute the two most significant limbs of n - q'd */ \
482 + (r1) = (n1) - (d1) * (q); \
483 + gmp_sub_ddmmss ((r1), (r0), (r1), (n0), (d1), (d0)); \
484 + gmp_umul_ppmm (_t1, _t0, (d0), (q)); \
485 + gmp_sub_ddmmss ((r1), (r0), (r1), (r0), _t1, _t0); \
488 + /* Conditionally adjust q and the remainders */ \
489 + _mask = - (mp_limb_t) ((r1) >= _q0); \
491 + gmp_add_ssaaaa ((r1), (r0), (r1), (r0), _mask & (d1), _mask & (d0)); \
492 + if ((r1) >= (d1)) \
494 + if ((r1) > (d1) || (r0) >= (d0)) \
497 + gmp_sub_ddmmss ((r1), (r0), (r1), (r0), (d1), (d0)); \
503 +#define MP_LIMB_T_SWAP(x, y) \
505 + mp_limb_t __mp_limb_t_swap__tmp = (x); \
507 + (y) = __mp_limb_t_swap__tmp; \
509 +#define MP_SIZE_T_SWAP(x, y) \
511 + mp_size_t __mp_size_t_swap__tmp = (x); \
513 + (y) = __mp_size_t_swap__tmp; \
515 +#define MP_BITCNT_T_SWAP(x,y) \
517 + mp_bitcnt_t __mp_bitcnt_t_swap__tmp = (x); \
519 + (y) = __mp_bitcnt_t_swap__tmp; \
521 +#define MP_PTR_SWAP(x, y) \
523 + mp_ptr __mp_ptr_swap__tmp = (x); \
525 + (y) = __mp_ptr_swap__tmp; \
527 +#define MP_SRCPTR_SWAP(x, y) \
529 + mp_srcptr __mp_srcptr_swap__tmp = (x); \
531 + (y) = __mp_srcptr_swap__tmp; \
534 +#define MPN_PTR_SWAP(xp,xs, yp,ys) \
536 + MP_PTR_SWAP (xp, yp); \
537 + MP_SIZE_T_SWAP (xs, ys); \
539 +#define MPN_SRCPTR_SWAP(xp,xs, yp,ys) \
541 + MP_SRCPTR_SWAP (xp, yp); \
542 + MP_SIZE_T_SWAP (xs, ys); \
545 +#define MPZ_PTR_SWAP(x, y) \
547 + mpz_ptr __mpz_ptr_swap__tmp = (x); \
549 + (y) = __mpz_ptr_swap__tmp; \
551 +#define MPZ_SRCPTR_SWAP(x, y) \
553 + mpz_srcptr __mpz_srcptr_swap__tmp = (x); \
555 + (y) = __mpz_srcptr_swap__tmp; \
558 +const int mp_bits_per_limb = GMP_LIMB_BITS;
561 +/* Memory allocation and other helper functions. */
563 +gmp_die (const char *msg)
565 + fprintf (stderr, "%s\n", msg);
570 +gmp_default_alloc (size_t size)
578 + gmp_die("gmp_default_alloc: Virtual memory exhausted.");
584 +gmp_default_realloc (void *old, size_t old_size, size_t new_size)
588 + p = realloc (old, new_size);
591 + gmp_die("gmp_default_realoc: Virtual memory exhausted.");
597 +gmp_default_free (void *p, size_t size)
602 +static void * (*gmp_allocate_func) (size_t) = gmp_default_alloc;
603 +static void * (*gmp_reallocate_func) (void *, size_t, size_t) = gmp_default_realloc;
604 +static void (*gmp_free_func) (void *, size_t) = gmp_default_free;
607 +mp_get_memory_functions (void *(**alloc_func) (size_t),
608 + void *(**realloc_func) (void *, size_t, size_t),
609 + void (**free_func) (void *, size_t))
612 + *alloc_func = gmp_allocate_func;
615 + *realloc_func = gmp_reallocate_func;
618 + *free_func = gmp_free_func;
622 +mp_set_memory_functions (void *(*alloc_func) (size_t),
623 + void *(*realloc_func) (void *, size_t, size_t),
624 + void (*free_func) (void *, size_t))
627 + alloc_func = gmp_default_alloc;
629 + realloc_func = gmp_default_realloc;
631 + free_func = gmp_default_free;
633 + gmp_allocate_func = alloc_func;
634 + gmp_reallocate_func = realloc_func;
635 + gmp_free_func = free_func;
638 +#define gmp_xalloc(size) ((*gmp_allocate_func)((size)))
639 +#define gmp_free(p) ((*gmp_free_func) ((p), 0))
642 +gmp_xalloc_limbs (mp_size_t size)
644 + return gmp_xalloc (size * sizeof (mp_limb_t));
648 +gmp_xrealloc_limbs (mp_ptr old, mp_size_t size)
651 + return (*gmp_reallocate_func) (old, 0, size * sizeof (mp_limb_t));
658 +mpn_copyi (mp_ptr d, mp_srcptr s, mp_size_t n)
661 + for (i = 0; i < n; i++)
666 +mpn_copyd (mp_ptr d, mp_srcptr s, mp_size_t n)
673 +mpn_cmp (mp_srcptr ap, mp_srcptr bp, mp_size_t n)
677 + if (ap[n] != bp[n])
678 + return ap[n] > bp[n] ? 1 : -1;
684 +mpn_cmp4 (mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
687 + return an < bn ? -1 : 1;
689 + return mpn_cmp (ap, bp, an);
693 +mpn_normalized_size (mp_srcptr xp, mp_size_t n)
695 + for (; n > 0 && xp[n-1] == 0; n--)
700 +#define mpn_zero_p(xp, n) (mpn_normalized_size ((xp), (n)) == 0)
703 +mpn_zero (mp_ptr rp, mp_size_t n)
707 + for (i = 0; i < n; i++)
712 +mpn_add_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b)
720 + mp_limb_t r = ap[i] + b;
731 +mpn_add_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
736 + for (i = 0, cy = 0; i < n; i++)
739 + a = ap[i]; b = bp[i];
750 +mpn_add (mp_ptr rp, mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
756 + cy = mpn_add_n (rp, ap, bp, bn);
758 + cy = mpn_add_1 (rp + bn, ap + bn, an - bn, cy);
763 +mpn_sub_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b)
772 + mp_limb_t a = ap[i];
774 + mp_limb_t cy = a < b;;
784 +mpn_sub_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
789 + for (i = 0, cy = 0; i < n; i++)
792 + a = ap[i]; b = bp[i];
802 +mpn_sub (mp_ptr rp, mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
808 + cy = mpn_sub_n (rp, ap, bp, bn);
810 + cy = mpn_sub_1 (rp + bn, ap + bn, an - bn, cy);
815 +mpn_mul_1 (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_limb_t vl)
817 + mp_limb_t ul, cl, hpl, lpl;
825 + gmp_umul_ppmm (hpl, lpl, ul, vl);
828 + cl = (lpl < cl) + hpl;
838 +mpn_addmul_1 (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_limb_t vl)
840 + mp_limb_t ul, cl, hpl, lpl, rl;
848 + gmp_umul_ppmm (hpl, lpl, ul, vl);
851 + cl = (lpl < cl) + hpl;
864 +mpn_submul_1 (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_limb_t vl)
866 + mp_limb_t ul, cl, hpl, lpl, rl;
874 + gmp_umul_ppmm (hpl, lpl, ul, vl);
877 + cl = (lpl < cl) + hpl;
890 +mpn_mul (mp_ptr rp, mp_srcptr up, mp_size_t un, mp_srcptr vp, mp_size_t vn)
895 + /* We first multiply by the low order limb. This result can be
896 + stored, not added, to rp. We also avoid a loop for zeroing this
899 + rp[un] = mpn_mul_1 (rp, up, un, vp[0]);
900 + rp += 1, vp += 1, vn -= 1;
902 + /* Now accumulate the product of up[] and the next higher limb from
907 + rp[un] = mpn_addmul_1 (rp, up, un, vp[0]);
908 + rp += 1, vp += 1, vn -= 1;
914 +mpn_mul_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
916 + mpn_mul (rp, ap, n, bp, n);
920 +mpn_sqr (mp_ptr rp, mp_srcptr ap, mp_size_t n)
922 + mpn_mul (rp, ap, n, ap, n);
926 +mpn_lshift (mp_ptr rp, mp_srcptr up, mp_size_t n, unsigned int cnt)
928 + mp_limb_t high_limb, low_limb;
935 + assert (cnt < GMP_LIMB_BITS);
940 + tnc = GMP_LIMB_BITS - cnt;
942 + retval = low_limb >> tnc;
943 + high_limb = (low_limb << cnt);
945 + for (i = n; --i != 0;)
948 + *--rp = high_limb | (low_limb >> tnc);
949 + high_limb = (low_limb << cnt);
957 +mpn_rshift (mp_ptr rp, mp_srcptr up, mp_size_t n, unsigned int cnt)
959 + mp_limb_t high_limb, low_limb;
966 + assert (cnt < GMP_LIMB_BITS);
968 + tnc = GMP_LIMB_BITS - cnt;
970 + retval = (high_limb << tnc);
971 + low_limb = high_limb >> cnt;
973 + for (i = n; --i != 0;)
976 + *rp++ = low_limb | (high_limb << tnc);
977 + low_limb = high_limb >> cnt;
985 +mpn_common_scan (mp_limb_t limb, mp_size_t i, mp_srcptr up, mp_size_t un,
990 + assert (ux == 0 || ux == GMP_LIMB_MAX);
991 + assert (0 <= i && i <= un );
997 + return (ux == 0 ? ~(mp_bitcnt_t) 0 : un * GMP_LIMB_BITS);
1000 + gmp_ctz (cnt, limb);
1001 + return (mp_bitcnt_t) i * GMP_LIMB_BITS + cnt;
1005 +mpn_scan1 (mp_srcptr ptr, mp_bitcnt_t bit)
1008 + i = bit / GMP_LIMB_BITS;
1010 + return mpn_common_scan ( ptr[i] & (GMP_LIMB_MAX << (bit % GMP_LIMB_BITS)),
1015 +mpn_scan0 (mp_srcptr ptr, mp_bitcnt_t bit)
1018 + i = bit / GMP_LIMB_BITS;
1020 + return mpn_common_scan (~ptr[i] & (GMP_LIMB_MAX << (bit % GMP_LIMB_BITS)),
1021 + i, ptr, i, GMP_LIMB_MAX);
1025 +/* MPN division interface. */
1027 +mpn_invert_3by2 (mp_limb_t u1, mp_limb_t u0)
1029 + mp_limb_t r, p, m;
1033 + /* First, do a 2/1 inverse. */
1034 + /* The inverse m is defined as floor( (B^2 - 1 - u1)/u1 ), so that 0 <
1035 + * B^2 - (B + m) u1 <= u1 */
1036 + assert (u1 >= GMP_LIMB_HIGHBIT);
1038 + ul = u1 & GMP_LLIMB_MASK;
1039 + uh = u1 >> (GMP_LIMB_BITS / 2);
1042 + r = ((~u1 - (mp_limb_t) qh * uh) << (GMP_LIMB_BITS / 2)) | GMP_LLIMB_MASK;
1044 + p = (mp_limb_t) qh * ul;
1045 + /* Adjustment steps taken from udiv_qrnnd_c */
1050 + if (r >= u1) /* i.e. we didn't get carry when adding to r */
1059 + /* Do a 3/2 division (with half limb size) */
1060 + p = (r >> (GMP_LIMB_BITS / 2)) * qh + r;
1061 + ql = (p >> (GMP_LIMB_BITS / 2)) + 1;
1063 + /* By the 3/2 method, we don't need the high half limb. */
1064 + r = (r << (GMP_LIMB_BITS / 2)) + GMP_LLIMB_MASK - ql * u1;
1066 + if (r >= (p << (GMP_LIMB_BITS / 2)))
1071 + m = ((mp_limb_t) qh << (GMP_LIMB_BITS / 2)) + ql;
1093 + gmp_umul_ppmm (th, tl, u0, m);
1098 + m -= ((r > u1) | ((r == u1) & (tl > u0)));
1105 +struct gmp_div_inverse
1107 + /* Normalization shift count. */
1109 + /* Normalized divisor (d0 unused for mpn_div_qr_1) */
1111 + /* Inverse, for 2/1 or 3/2. */
1116 +mpn_div_qr_1_invert (struct gmp_div_inverse *inv, mp_limb_t d)
1121 + gmp_clz (shift, d);
1122 + inv->shift = shift;
1123 + inv->d1 = d << shift;
1124 + inv->di = mpn_invert_limb (inv->d1);
1128 +mpn_div_qr_2_invert (struct gmp_div_inverse *inv,
1129 + mp_limb_t d1, mp_limb_t d0)
1134 + gmp_clz (shift, d1);
1135 + inv->shift = shift;
1138 + d1 = (d1 << shift) | (d0 >> (GMP_LIMB_BITS - shift));
1143 + inv->di = mpn_invert_3by2 (d1, d0);
1147 +mpn_div_qr_invert (struct gmp_div_inverse *inv,
1148 + mp_srcptr dp, mp_size_t dn)
1153 + mpn_div_qr_1_invert (inv, dp[0]);
1155 + mpn_div_qr_2_invert (inv, dp[1], dp[0]);
1164 + gmp_clz (shift, d1);
1165 + inv->shift = shift;
1168 + d1 = (d1 << shift) | (d0 >> (GMP_LIMB_BITS - shift));
1169 + d0 = (d0 << shift) | (dp[dn-3] >> (GMP_LIMB_BITS - shift));
1173 + inv->di = mpn_invert_3by2 (d1, d0);
1177 +/* Not matching current public gmp interface, rather corresponding to
1178 + the sbpi1_div_* functions. */
1180 +mpn_div_qr_1_preinv (mp_ptr qp, mp_srcptr np, mp_size_t nn,
1181 + const struct gmp_div_inverse *inv)
1187 + if (inv->shift > 0)
1189 + tp = gmp_xalloc_limbs (nn);
1190 + r = mpn_lshift (tp, np, nn, inv->shift);
1202 + gmp_udiv_qrnnd_preinv (q, r, r, np[nn], d, di);
1206 + if (inv->shift > 0)
1209 + return r >> inv->shift;
1213 +mpn_div_qr_1 (mp_ptr qp, mp_srcptr np, mp_size_t nn, mp_limb_t d)
1217 + /* Special case for powers of two. */
1218 + if ((d & (d-1)) == 0)
1220 + mp_limb_t r = np[0] & (d-1);
1224 + mpn_copyi (qp, np, nn);
1228 + gmp_ctz (shift, d);
1229 + mpn_rshift (qp, np, nn, shift);
1236 + struct gmp_div_inverse inv;
1237 + mpn_div_qr_1_invert (&inv, d);
1238 + return mpn_div_qr_1_preinv (qp, np, nn, &inv);
1243 +mpn_div_qr_2_preinv (mp_ptr qp, mp_ptr rp, mp_srcptr np, mp_size_t nn,
1244 + const struct gmp_div_inverse *inv)
1248 + mp_limb_t d1, d0, di, r1, r0;
1252 + shift = inv->shift;
1259 + tp = gmp_xalloc_limbs (nn);
1260 + r1 = mpn_lshift (tp, np, nn, shift);
1273 + gmp_udiv_qr_3by2 (q, r1, r0, r1, r0, n0, d1, d0, di);
1282 + assert ((r0 << (GMP_LIMB_BITS - shift)) == 0);
1283 + r0 = (r0 >> shift) | (r1 << (GMP_LIMB_BITS - shift));
1295 +mpn_div_qr_2 (mp_ptr qp, mp_ptr rp, mp_srcptr np, mp_size_t nn,
1296 + mp_limb_t d1, mp_limb_t d0)
1298 + struct gmp_div_inverse inv;
1301 + mpn_div_qr_2_invert (&inv, d1, d0);
1302 + mpn_div_qr_2_preinv (qp, rp, np, nn, &inv);
1307 +mpn_div_qr_pi1 (mp_ptr qp,
1308 + mp_ptr np, mp_size_t nn, mp_limb_t n1,
1309 + mp_srcptr dp, mp_size_t dn,
1315 + mp_limb_t cy, cy1;
1319 + assert (nn >= dn);
1324 + assert ((d1 & GMP_LIMB_HIGHBIT) != 0);
1325 + /* Iteration variable is the index of the q limb.
1327 + * We divide <n1, np[dn-1+i], np[dn-2+i], np[dn-3+i],..., np[i]>
1328 + * by <d1, d0, dp[dn-3], ..., dp[0] >
1334 + mp_limb_t n0 = np[dn-1+i];
1336 + if (n1 == d1 && n0 == d0)
1339 + mpn_submul_1 (np+i, dp, dn, q);
1340 + n1 = np[dn-1+i]; /* update n1, last loop's value will now be invalid */
1344 + gmp_udiv_qr_3by2 (q, n1, n0, n1, n0, np[dn-2+i], d1, d0, dinv);
1346 + cy = mpn_submul_1 (np + i, dp, dn-2, q);
1356 + n1 += d1 + mpn_add_n (np + i, np + i, dp, dn - 1);
1370 +mpn_div_qr_preinv (mp_ptr qp, mp_ptr np, mp_size_t nn,
1371 + mp_srcptr dp, mp_size_t dn,
1372 + const struct gmp_div_inverse *inv)
1375 + assert (nn >= dn);
1378 + np[0] = mpn_div_qr_1_preinv (qp, np, nn, inv);
1380 + mpn_div_qr_2_preinv (qp, np, np, nn, inv);
1386 + assert (inv->d1 == dp[dn-1]);
1387 + assert (inv->d0 == dp[dn-2]);
1388 + assert ((inv->d1 & GMP_LIMB_HIGHBIT) != 0);
1390 + shift = inv->shift;
1392 + nh = mpn_lshift (np, np, nn, shift);
1396 + mpn_div_qr_pi1 (qp, np, nn, nh, dp, dn, inv->di);
1399 + gmp_assert_nocarry (mpn_rshift (np, np, dn, shift));
1404 +mpn_div_qr (mp_ptr qp, mp_ptr np, mp_size_t nn, mp_srcptr dp, mp_size_t dn)
1406 + struct gmp_div_inverse inv;
1410 + assert (nn >= dn);
1412 + mpn_div_qr_invert (&inv, dp, dn);
1413 + if (dn > 2 && inv.shift > 0)
1415 + tp = gmp_xalloc_limbs (dn);
1416 + gmp_assert_nocarry (mpn_lshift (tp, dp, dn, inv.shift));
1419 + mpn_div_qr_preinv (qp, np, nn, dp, dn, &inv);
1425 +/* MPN base conversion. */
1427 +mpn_base_power_of_two_p (unsigned b)
1434 + case 16: return 4;
1435 + case 32: return 5;
1436 + case 64: return 6;
1437 + case 128: return 7;
1438 + case 256: return 8;
1439 + default: return 0;
1443 +struct mpn_base_info
1445 + /* bb is the largest power of the base which fits in one limb, and
1446 + exp is the corresponding exponent. */
1452 +mpn_get_base_info (struct mpn_base_info *info, mp_limb_t b)
1458 + m = GMP_LIMB_MAX / b;
1459 + for (exp = 1, p = b; p <= m; exp++)
1467 +mpn_limb_size_in_base_2 (mp_limb_t u)
1472 + gmp_clz (shift, u);
1473 + return GMP_LIMB_BITS - shift;
1477 +mpn_get_str_bits (unsigned char *sp, unsigned bits, mp_srcptr up, mp_size_t un)
1479 + unsigned char mask;
1484 + sn = ((un - 1) * GMP_LIMB_BITS + mpn_limb_size_in_base_2 (up[un-1])
1485 + + bits - 1) / bits;
1487 + mask = (1U << bits) - 1;
1489 + for (i = 0, j = sn, shift = 0; j-- > 0;)
1491 + unsigned char digit = up[i] >> shift;
1495 + if (shift >= GMP_LIMB_BITS && ++i < un)
1497 + shift -= GMP_LIMB_BITS;
1498 + digit |= up[i] << (bits - shift);
1500 + sp[j] = digit & mask;
1505 +/* We generate digits from the least significant end, and reverse at
1508 +mpn_limb_get_str (unsigned char *sp, mp_limb_t w,
1509 + const struct gmp_div_inverse *binv)
1512 + for (i = 0; w > 0; i++)
1514 + mp_limb_t h, l, r;
1516 + h = w >> (GMP_LIMB_BITS - binv->shift);
1517 + l = w << binv->shift;
1519 + gmp_udiv_qrnnd_preinv (w, r, h, l, binv->d1, binv->di);
1520 + assert ( (r << (GMP_LIMB_BITS - binv->shift)) == 0);
1521 + r >>= binv->shift;
1529 +mpn_get_str_other (unsigned char *sp,
1530 + int base, const struct mpn_base_info *info,
1531 + mp_ptr up, mp_size_t un)
1533 + struct gmp_div_inverse binv;
1537 + mpn_div_qr_1_invert (&binv, base);
1543 + struct gmp_div_inverse bbinv;
1544 + mpn_div_qr_1_invert (&bbinv, info->bb);
1550 + w = mpn_div_qr_1_preinv (up, up, un, &bbinv);
1551 + un -= (up[un-1] == 0);
1552 + done = mpn_limb_get_str (sp + sn, w, &binv);
1554 + for (sn += done; done < info->exp; done++)
1559 + sn += mpn_limb_get_str (sp + sn, up[0], &binv);
1561 + /* Reverse order */
1562 + for (i = 0; 2*i + 1 < sn; i++)
1564 + unsigned char t = sp[i];
1565 + sp[i] = sp[sn - i - 1];
1566 + sp[sn - i - 1] = t;
1573 +mpn_get_str (unsigned char *sp, int base, mp_ptr up, mp_size_t un)
1578 + assert (up[un-1] > 0);
1580 + bits = mpn_base_power_of_two_p (base);
1582 + return mpn_get_str_bits (sp, bits, up, un);
1585 + struct mpn_base_info info;
1587 + mpn_get_base_info (&info, base);
1588 + return mpn_get_str_other (sp, base, &info, up, un);
1593 +mpn_set_str_bits (mp_ptr rp, const unsigned char *sp, size_t sn,
1600 + for (j = sn, rn = 0, shift = 0; j-- > 0; )
1609 + rp[rn-1] |= (mp_limb_t) sp[j] << shift;
1611 + if (shift >= GMP_LIMB_BITS)
1613 + shift -= GMP_LIMB_BITS;
1615 + rp[rn++] = (mp_limb_t) sp[j] >> (bits - shift);
1619 + rn = mpn_normalized_size (rp, rn);
1624 +mpn_set_str_other (mp_ptr rp, const unsigned char *sp, size_t sn,
1625 + mp_limb_t b, const struct mpn_base_info *info)
1632 + k = 1 + (sn - 1) % info->exp;
1637 + w = w * b + sp[j++];
1641 + for (rn = (w > 0); j < sn;)
1646 + for (k = 1; k < info->exp; k++)
1647 + w = w * b + sp[j++];
1649 + cy = mpn_mul_1 (rp, rp, rn, info->bb);
1650 + cy += mpn_add_1 (rp, rp, rn, w);
1660 +mpn_set_str (mp_ptr rp, const unsigned char *sp, size_t sn, int base)
1667 + bits = mpn_base_power_of_two_p (base);
1669 + return mpn_set_str_bits (rp, sp, sn, bits);
1672 + struct mpn_base_info info;
1674 + mpn_get_base_info (&info, base);
1675 + return mpn_set_str_other (rp, sp, sn, base, &info);
1680 +/* MPZ interface */
1686 + r->_mp_d = gmp_xalloc_limbs (1);
1689 +/* The utility of this function is a bit limited, since many functions
1690 + assigns the result variable using mpz_swap. */
1692 +mpz_init2 (mpz_t r, mp_bitcnt_t bits)
1696 + bits -= (bits != 0); /* Round down, except if 0 */
1697 + rn = 1 + bits / GMP_LIMB_BITS;
1699 + r->_mp_alloc = rn;
1701 + r->_mp_d = gmp_xalloc_limbs (rn);
1705 +mpz_clear (mpz_t r)
1707 + gmp_free (r->_mp_d);
1711 +mpz_realloc (mpz_t r, mp_size_t size)
1713 + size = GMP_MAX (size, 1);
1715 + r->_mp_d = gmp_xrealloc_limbs (r->_mp_d, size);
1716 + r->_mp_alloc = size;
1718 + if (GMP_ABS (r->_mp_size) > size)
1724 +/* Realloc for an mpz_t WHAT if it has less than NEEDED limbs. */
1725 +#define MPZ_REALLOC(z,n) ((n) > (z)->_mp_alloc \
1726 + ? mpz_realloc(z,n) \
1729 +/* MPZ assignment and basic conversions. */
1731 +mpz_set_si (mpz_t r, signed long int x)
1734 + mpz_set_ui (r, x);
1735 + else /* (x < 0) */
1738 + r->_mp_d[0] = GMP_NEG_CAST (unsigned long int, x);
1743 +mpz_set_ui (mpz_t r, unsigned long int x)
1755 +mpz_set (mpz_t r, const mpz_t x)
1757 + /* Allow the NOP r == x */
1763 + n = GMP_ABS (x->_mp_size);
1764 + rp = MPZ_REALLOC (r, n);
1766 + mpn_copyi (rp, x->_mp_d, n);
1767 + r->_mp_size = x->_mp_size;
1772 +mpz_init_set_si (mpz_t r, signed long int x)
1775 + mpz_set_si (r, x);
1779 +mpz_init_set_ui (mpz_t r, unsigned long int x)
1782 + mpz_set_ui (r, x);
1786 +mpz_init_set (mpz_t r, const mpz_t x)
1793 +mpz_fits_slong_p (const mpz_t u)
1795 + mp_size_t us = u->_mp_size;
1800 + return u->_mp_d[0] < GMP_LIMB_HIGHBIT;
1801 + else if (us == -1)
1802 + return u->_mp_d[0] <= GMP_LIMB_HIGHBIT;
1808 +mpz_fits_ulong_p (const mpz_t u)
1810 + mp_size_t us = u->_mp_size;
1812 + return (us == (us > 0));
1816 +mpz_get_si (const mpz_t u)
1818 + mp_size_t us = u->_mp_size;
1821 + return (long) (u->_mp_d[0] & ~GMP_LIMB_HIGHBIT);
1823 + return (long) (- u->_mp_d[0] | GMP_LIMB_HIGHBIT);
1829 +mpz_get_ui (const mpz_t u)
1831 + return u->_mp_size == 0 ? 0 : u->_mp_d[0];
1835 +mpz_size (const mpz_t u)
1837 + return GMP_ABS (u->_mp_size);
1841 +mpz_getlimbn (const mpz_t u, mp_size_t n)
1843 + if (n >= 0 && n < GMP_ABS (u->_mp_size))
1844 + return u->_mp_d[n];
1850 +mpz_realloc2 (mpz_t x, mp_bitcnt_t n)
1852 + mpz_realloc (x, 1 + (n - (n != 0)) / GMP_LIMB_BITS);
1856 +mpz_limbs_read (mpz_srcptr x)
1862 +mpz_limbs_modify (mpz_t x, mp_size_t n)
1865 + return MPZ_REALLOC (x, n);
1869 +mpz_limbs_write (mpz_t x, mp_size_t n)
1871 + return mpz_limbs_modify (x, n);
1875 +mpz_limbs_finish (mpz_t x, mp_size_t xs)
1878 + xn = mpn_normalized_size (x->_mp_d, GMP_ABS (xs));
1879 + x->_mp_size = xs < 0 ? -xn : xn;
1883 +mpz_roinit_n (mpz_t x, mp_srcptr xp, mp_size_t xs)
1886 + x->_mp_d = (mp_ptr) xp;
1887 + mpz_limbs_finish (x, xs);
1892 +/* Conversions and comparison to double. */
1894 +mpz_set_d (mpz_t r, double x)
1903 + /* x != x is true when x is a NaN, and x == x * 0.5 is true when x is
1904 + zero or infinity. */
1905 + if (x != x || x == x * 0.5)
1920 + B = 2.0 * (double) GMP_LIMB_HIGHBIT;
1922 + for (rn = 1; x >= B; rn++)
1925 + rp = MPZ_REALLOC (r, rn);
1927 + f = (mp_limb_t) x;
1935 + f = (mp_limb_t) x;
1941 + r->_mp_size = sign ? - rn : rn;
1945 +mpz_init_set_d (mpz_t r, double x)
1952 +mpz_get_d (const mpz_t u)
1956 + double B = 2.0 * (double) GMP_LIMB_HIGHBIT;
1958 + un = GMP_ABS (u->_mp_size);
1963 + x = u->_mp_d[--un];
1965 + x = B*x + u->_mp_d[--un];
1967 + if (u->_mp_size < 0)
1974 +mpz_cmpabs_d (const mpz_t x, double d)
1985 + xn = GMP_ABS (xn);
1987 + B = 2.0 * (double) GMP_LIMB_HIGHBIT;
1990 + /* Scale d so it can be compared with the top limb. */
1991 + for (i = 1; i < xn; i++)
1997 + /* Compare floor(d) to top limb, subtract and cancel when equal. */
1998 + for (i = xn; i-- > 0;)
2002 + f = (mp_limb_t) d;
2011 + return - (d > 0.0);
2015 +mpz_cmp_d (const mpz_t x, double d)
2017 + if (x->_mp_size < 0)
2022 + return -mpz_cmpabs_d (x, d);
2029 + return mpz_cmpabs_d (x, d);
2034 +/* MPZ comparisons and the like. */
2036 +mpz_sgn (const mpz_t u)
2038 + mp_size_t usize = u->_mp_size;
2040 + return (usize > 0) - (usize < 0);
2044 +mpz_cmp_si (const mpz_t u, long v)
2046 + mp_size_t usize = u->_mp_size;
2051 + return mpz_cmp_ui (u, v);
2052 + else if (usize >= 0)
2054 + else /* usize == -1 */
2056 + mp_limb_t ul = u->_mp_d[0];
2057 + if ((mp_limb_t)GMP_NEG_CAST (unsigned long int, v) < ul)
2060 + return (mp_limb_t)GMP_NEG_CAST (unsigned long int, v) > ul;
2065 +mpz_cmp_ui (const mpz_t u, unsigned long v)
2067 + mp_size_t usize = u->_mp_size;
2071 + else if (usize < 0)
2075 + mp_limb_t ul = (usize > 0) ? u->_mp_d[0] : 0;
2076 + return (ul > v) - (ul < v);
2081 +mpz_cmp (const mpz_t a, const mpz_t b)
2083 + mp_size_t asize = a->_mp_size;
2084 + mp_size_t bsize = b->_mp_size;
2086 + if (asize != bsize)
2087 + return (asize < bsize) ? -1 : 1;
2088 + else if (asize >= 0)
2089 + return mpn_cmp (a->_mp_d, b->_mp_d, asize);
2091 + return mpn_cmp (b->_mp_d, a->_mp_d, -asize);
2095 +mpz_cmpabs_ui (const mpz_t u, unsigned long v)
2097 + mp_size_t un = GMP_ABS (u->_mp_size);
2103 + ul = (un == 1) ? u->_mp_d[0] : 0;
2105 + return (ul > v) - (ul < v);
2109 +mpz_cmpabs (const mpz_t u, const mpz_t v)
2111 + return mpn_cmp4 (u->_mp_d, GMP_ABS (u->_mp_size),
2112 + v->_mp_d, GMP_ABS (v->_mp_size));
2116 +mpz_abs (mpz_t r, const mpz_t u)
2121 + r->_mp_size = GMP_ABS (r->_mp_size);
2125 +mpz_neg (mpz_t r, const mpz_t u)
2130 + r->_mp_size = -r->_mp_size;
2134 +mpz_swap (mpz_t u, mpz_t v)
2136 + MP_SIZE_T_SWAP (u->_mp_size, v->_mp_size);
2137 + MP_SIZE_T_SWAP (u->_mp_alloc, v->_mp_alloc);
2138 + MP_PTR_SWAP (u->_mp_d, v->_mp_d);
2142 +/* MPZ addition and subtraction */
2144 +/* Adds to the absolute value. Returns new size, but doesn't store it. */
2146 +mpz_abs_add_ui (mpz_t r, const mpz_t a, unsigned long b)
2152 + an = GMP_ABS (a->_mp_size);
2159 + rp = MPZ_REALLOC (r, an + 1);
2161 + cy = mpn_add_1 (rp, a->_mp_d, an, b);
2168 +/* Subtract from the absolute value. Returns new size, (or -1 on underflow),
2169 + but doesn't store it. */
2171 +mpz_abs_sub_ui (mpz_t r, const mpz_t a, unsigned long b)
2173 + mp_size_t an = GMP_ABS (a->_mp_size);
2174 + mp_ptr rp = MPZ_REALLOC (r, an);
2181 + else if (an == 1 && a->_mp_d[0] < b)
2183 + rp[0] = b - a->_mp_d[0];
2188 + gmp_assert_nocarry (mpn_sub_1 (rp, a->_mp_d, an, b));
2189 + return mpn_normalized_size (rp, an);
2194 +mpz_add_ui (mpz_t r, const mpz_t a, unsigned long b)
2196 + if (a->_mp_size >= 0)
2197 + r->_mp_size = mpz_abs_add_ui (r, a, b);
2199 + r->_mp_size = -mpz_abs_sub_ui (r, a, b);
2203 +mpz_sub_ui (mpz_t r, const mpz_t a, unsigned long b)
2205 + if (a->_mp_size < 0)
2206 + r->_mp_size = -mpz_abs_add_ui (r, a, b);
2208 + r->_mp_size = mpz_abs_sub_ui (r, a, b);
2212 +mpz_ui_sub (mpz_t r, unsigned long a, const mpz_t b)
2214 + if (b->_mp_size < 0)
2215 + r->_mp_size = mpz_abs_add_ui (r, b, a);
2217 + r->_mp_size = -mpz_abs_sub_ui (r, b, a);
2221 +mpz_abs_add (mpz_t r, const mpz_t a, const mpz_t b)
2223 + mp_size_t an = GMP_ABS (a->_mp_size);
2224 + mp_size_t bn = GMP_ABS (b->_mp_size);
2230 + MPZ_SRCPTR_SWAP (a, b);
2231 + MP_SIZE_T_SWAP (an, bn);
2234 + rp = MPZ_REALLOC (r, an + 1);
2235 + cy = mpn_add (rp, a->_mp_d, an, b->_mp_d, bn);
2243 +mpz_abs_sub (mpz_t r, const mpz_t a, const mpz_t b)
2245 + mp_size_t an = GMP_ABS (a->_mp_size);
2246 + mp_size_t bn = GMP_ABS (b->_mp_size);
2250 + cmp = mpn_cmp4 (a->_mp_d, an, b->_mp_d, bn);
2253 + rp = MPZ_REALLOC (r, an);
2254 + gmp_assert_nocarry (mpn_sub (rp, a->_mp_d, an, b->_mp_d, bn));
2255 + return mpn_normalized_size (rp, an);
2259 + rp = MPZ_REALLOC (r, bn);
2260 + gmp_assert_nocarry (mpn_sub (rp, b->_mp_d, bn, a->_mp_d, an));
2261 + return -mpn_normalized_size (rp, bn);
2268 +mpz_add (mpz_t r, const mpz_t a, const mpz_t b)
2272 + if ( (a->_mp_size ^ b->_mp_size) >= 0)
2273 + rn = mpz_abs_add (r, a, b);
2275 + rn = mpz_abs_sub (r, a, b);
2277 + r->_mp_size = a->_mp_size >= 0 ? rn : - rn;
2281 +mpz_sub (mpz_t r, const mpz_t a, const mpz_t b)
2285 + if ( (a->_mp_size ^ b->_mp_size) >= 0)
2286 + rn = mpz_abs_sub (r, a, b);
2288 + rn = mpz_abs_add (r, a, b);
2290 + r->_mp_size = a->_mp_size >= 0 ? rn : - rn;
2294 +/* MPZ multiplication */
2296 +mpz_mul_si (mpz_t r, const mpz_t u, long int v)
2300 + mpz_mul_ui (r, u, GMP_NEG_CAST (unsigned long int, v));
2304 + mpz_mul_ui (r, u, (unsigned long int) v);
2308 +mpz_mul_ui (mpz_t r, const mpz_t u, unsigned long int v)
2316 + if (us == 0 || v == 0)
2322 + un = GMP_ABS (us);
2324 + tp = MPZ_REALLOC (r, un + 1);
2325 + cy = mpn_mul_1 (tp, u->_mp_d, un, v);
2329 + r->_mp_size = (us < 0) ? - un : un;
2333 +mpz_mul (mpz_t r, const mpz_t u, const mpz_t v)
2336 + mp_size_t un, vn, rn;
2343 + if (un == 0 || vn == 0)
2349 + sign = (un ^ vn) < 0;
2351 + un = GMP_ABS (un);
2352 + vn = GMP_ABS (vn);
2354 + mpz_init2 (t, (un + vn) * GMP_LIMB_BITS);
2358 + mpn_mul (tp, u->_mp_d, un, v->_mp_d, vn);
2360 + mpn_mul (tp, v->_mp_d, vn, u->_mp_d, un);
2363 + rn -= tp[rn-1] == 0;
2365 + t->_mp_size = sign ? - rn : rn;
2371 +mpz_mul_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t bits)
2378 + un = GMP_ABS (u->_mp_size);
2385 + limbs = bits / GMP_LIMB_BITS;
2386 + shift = bits % GMP_LIMB_BITS;
2388 + rn = un + limbs + (shift > 0);
2389 + rp = MPZ_REALLOC (r, rn);
2392 + mp_limb_t cy = mpn_lshift (rp + limbs, u->_mp_d, un, shift);
2397 + mpn_copyd (rp + limbs, u->_mp_d, un);
2402 + r->_mp_size = (u->_mp_size < 0) ? - rn : rn;
2406 +mpz_addmul_ui (mpz_t r, const mpz_t u, unsigned long int v)
2410 + mpz_mul_ui (t, u, v);
2411 + mpz_add (r, r, t);
2416 +mpz_submul_ui (mpz_t r, const mpz_t u, unsigned long int v)
2420 + mpz_mul_ui (t, u, v);
2421 + mpz_sub (r, r, t);
2426 +mpz_addmul (mpz_t r, const mpz_t u, const mpz_t v)
2430 + mpz_mul (t, u, v);
2431 + mpz_add (r, r, t);
2436 +mpz_submul (mpz_t r, const mpz_t u, const mpz_t v)
2440 + mpz_mul (t, u, v);
2441 + mpz_sub (r, r, t);
2447 +enum mpz_div_round_mode { GMP_DIV_FLOOR, GMP_DIV_CEIL, GMP_DIV_TRUNC };
2449 +/* Allows q or r to be zero. Returns 1 iff remainder is non-zero. */
2451 +mpz_div_qr (mpz_t q, mpz_t r,
2452 + const mpz_t n, const mpz_t d, enum mpz_div_round_mode mode)
2454 + mp_size_t ns, ds, nn, dn, qs;
2459 + gmp_die("mpz_div_qr: Divide by zero.");
2470 + nn = GMP_ABS (ns);
2471 + dn = GMP_ABS (ds);
2477 + if (mode == GMP_DIV_CEIL && qs >= 0)
2479 + /* q = 1, r = n - d */
2481 + mpz_sub (r, n, d);
2483 + mpz_set_ui (q, 1);
2485 + else if (mode == GMP_DIV_FLOOR && qs < 0)
2487 + /* q = -1, r = n + d */
2489 + mpz_add (r, n, d);
2491 + mpz_set_si (q, -1);
2495 + /* q = 0, r = d */
2509 + mpz_init_set (tr, n);
2516 + mpz_init2 (tq, qn * GMP_LIMB_BITS);
2522 + mpn_div_qr (qp, np, nn, d->_mp_d, dn);
2526 + qn -= (qp[qn-1] == 0);
2528 + tq->_mp_size = qs < 0 ? -qn : qn;
2530 + rn = mpn_normalized_size (np, dn);
2531 + tr->_mp_size = ns < 0 ? - rn : rn;
2533 + if (mode == GMP_DIV_FLOOR && qs < 0 && rn != 0)
2536 + mpz_sub_ui (tq, tq, 1);
2538 + mpz_add (tr, tr, d);
2540 + else if (mode == GMP_DIV_CEIL && qs >= 0 && rn != 0)
2543 + mpz_add_ui (tq, tq, 1);
2545 + mpz_sub (tr, tr, d);
2563 +mpz_cdiv_qr (mpz_t q, mpz_t r, const mpz_t n, const mpz_t d)
2565 + mpz_div_qr (q, r, n, d, GMP_DIV_CEIL);
2569 +mpz_fdiv_qr (mpz_t q, mpz_t r, const mpz_t n, const mpz_t d)
2571 + mpz_div_qr (q, r, n, d, GMP_DIV_FLOOR);
2575 +mpz_tdiv_qr (mpz_t q, mpz_t r, const mpz_t n, const mpz_t d)
2577 + mpz_div_qr (q, r, n, d, GMP_DIV_TRUNC);
2581 +mpz_cdiv_q (mpz_t q, const mpz_t n, const mpz_t d)
2583 + mpz_div_qr (q, NULL, n, d, GMP_DIV_CEIL);
2587 +mpz_fdiv_q (mpz_t q, const mpz_t n, const mpz_t d)
2589 + mpz_div_qr (q, NULL, n, d, GMP_DIV_FLOOR);
2593 +mpz_tdiv_q (mpz_t q, const mpz_t n, const mpz_t d)
2595 + mpz_div_qr (q, NULL, n, d, GMP_DIV_TRUNC);
2599 +mpz_cdiv_r (mpz_t r, const mpz_t n, const mpz_t d)
2601 + mpz_div_qr (NULL, r, n, d, GMP_DIV_CEIL);
2605 +mpz_fdiv_r (mpz_t r, const mpz_t n, const mpz_t d)
2607 + mpz_div_qr (NULL, r, n, d, GMP_DIV_FLOOR);
2611 +mpz_tdiv_r (mpz_t r, const mpz_t n, const mpz_t d)
2613 + mpz_div_qr (NULL, r, n, d, GMP_DIV_TRUNC);
2617 +mpz_mod (mpz_t r, const mpz_t n, const mpz_t d)
2619 + mpz_div_qr (NULL, r, n, d, d->_mp_size >= 0 ? GMP_DIV_FLOOR : GMP_DIV_CEIL);
2623 +mpz_div_q_2exp (mpz_t q, const mpz_t u, mp_bitcnt_t bit_index,
2624 + enum mpz_div_round_mode mode)
2627 + mp_size_t limb_cnt;
2637 + limb_cnt = bit_index / GMP_LIMB_BITS;
2638 + qn = GMP_ABS (un) - limb_cnt;
2639 + bit_index %= GMP_LIMB_BITS;
2641 + if (mode == ((un > 0) ? GMP_DIV_CEIL : GMP_DIV_FLOOR)) /* un != 0 here. */
2642 + /* Note: Below, the final indexing at limb_cnt is valid because at
2643 + that point we have qn > 0. */
2645 + || !mpn_zero_p (u->_mp_d, limb_cnt)
2646 + || (u->_mp_d[limb_cnt]
2647 + & (((mp_limb_t) 1 << bit_index) - 1)));
2656 + qp = MPZ_REALLOC (q, qn);
2658 + if (bit_index != 0)
2660 + mpn_rshift (qp, u->_mp_d + limb_cnt, qn, bit_index);
2661 + qn -= qp[qn - 1] == 0;
2665 + mpn_copyi (qp, u->_mp_d + limb_cnt, qn);
2672 + mpz_add_ui (q, q, 1);
2678 +mpz_div_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t bit_index,
2679 + enum mpz_div_round_mode mode)
2681 + mp_size_t us, un, rn;
2686 + if (us == 0 || bit_index == 0)
2691 + rn = (bit_index + GMP_LIMB_BITS - 1) / GMP_LIMB_BITS;
2694 + rp = MPZ_REALLOC (r, rn);
2695 + un = GMP_ABS (us);
2697 + mask = GMP_LIMB_MAX >> (rn * GMP_LIMB_BITS - bit_index);
2701 + /* Quotient (with truncation) is zero, and remainder is
2703 + if (mode == ((us > 0) ? GMP_DIV_CEIL : GMP_DIV_FLOOR)) /* us != 0 here. */
2705 + /* Have to negate and sign extend. */
2709 + for (cy = 1, i = 0; i < un; i++)
2711 + mp_limb_t s = ~u->_mp_d[i] + cy;
2716 + for (; i < rn - 1; i++)
2717 + rp[i] = GMP_LIMB_MAX;
2726 + mpn_copyi (rp, u->_mp_d, un);
2734 + mpn_copyi (rp, u->_mp_d, rn - 1);
2736 + rp[rn-1] = u->_mp_d[rn-1] & mask;
2738 + if (mode == ((us > 0) ? GMP_DIV_CEIL : GMP_DIV_FLOOR)) /* us != 0 here. */
2740 + /* If r != 0, compute 2^{bit_count} - r. */
2743 + for (i = 0; i < rn && rp[i] == 0; i++)
2747 + /* r > 0, need to flip sign. */
2748 + rp[i] = ~rp[i] + 1;
2754 + /* us is not used for anything else, so we can modify it
2755 + here to indicate flipped sign. */
2760 + rn = mpn_normalized_size (rp, rn);
2761 + r->_mp_size = us < 0 ? -rn : rn;
2765 +mpz_cdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
2767 + mpz_div_q_2exp (r, u, cnt, GMP_DIV_CEIL);
2771 +mpz_fdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
2773 + mpz_div_q_2exp (r, u, cnt, GMP_DIV_FLOOR);
2777 +mpz_tdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
2779 + mpz_div_q_2exp (r, u, cnt, GMP_DIV_TRUNC);
2783 +mpz_cdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
2785 + mpz_div_r_2exp (r, u, cnt, GMP_DIV_CEIL);
2789 +mpz_fdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
2791 + mpz_div_r_2exp (r, u, cnt, GMP_DIV_FLOOR);
2795 +mpz_tdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
2797 + mpz_div_r_2exp (r, u, cnt, GMP_DIV_TRUNC);
2801 +mpz_divexact (mpz_t q, const mpz_t n, const mpz_t d)
2803 + gmp_assert_nocarry (mpz_div_qr (q, NULL, n, d, GMP_DIV_TRUNC));
2807 +mpz_divisible_p (const mpz_t n, const mpz_t d)
2809 + return mpz_div_qr (NULL, NULL, n, d, GMP_DIV_TRUNC) == 0;
2813 +mpz_congruent_p (const mpz_t a, const mpz_t b, const mpz_t m)
2818 + /* a == b (mod 0) iff a == b */
2819 + if (mpz_sgn (m) == 0)
2820 + return (mpz_cmp (a, b) == 0);
2823 + mpz_sub (t, a, b);
2824 + res = mpz_divisible_p (t, m);
2830 +static unsigned long
2831 +mpz_div_qr_ui (mpz_t q, mpz_t r,
2832 + const mpz_t n, unsigned long d, enum mpz_div_round_mode mode)
2849 + qn = GMP_ABS (ns);
2851 + qp = MPZ_REALLOC (q, qn);
2855 + rl = mpn_div_qr_1 (qp, n->_mp_d, qn, d);
2859 + rs = (ns < 0) ? -rs : rs;
2861 + if (rl > 0 && ( (mode == GMP_DIV_FLOOR && ns < 0)
2862 + || (mode == GMP_DIV_CEIL && ns >= 0)))
2865 + gmp_assert_nocarry (mpn_add_1 (qp, qp, qn, 1));
2877 + qn -= (qp[qn-1] == 0);
2878 + assert (qn == 0 || qp[qn-1] > 0);
2880 + q->_mp_size = (ns < 0) ? - qn : qn;
2887 +mpz_cdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d)
2889 + return mpz_div_qr_ui (q, r, n, d, GMP_DIV_CEIL);
2893 +mpz_fdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d)
2895 + return mpz_div_qr_ui (q, r, n, d, GMP_DIV_FLOOR);
2899 +mpz_tdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d)
2901 + return mpz_div_qr_ui (q, r, n, d, GMP_DIV_TRUNC);
2905 +mpz_cdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d)
2907 + return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_CEIL);
2911 +mpz_fdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d)
2913 + return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_FLOOR);
2917 +mpz_tdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d)
2919 + return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_TRUNC);
2923 +mpz_cdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d)
2925 + return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_CEIL);
2928 +mpz_fdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d)
2930 + return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_FLOOR);
2933 +mpz_tdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d)
2935 + return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_TRUNC);
2939 +mpz_cdiv_ui (const mpz_t n, unsigned long d)
2941 + return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_CEIL);
2945 +mpz_fdiv_ui (const mpz_t n, unsigned long d)
2947 + return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_FLOOR);
2951 +mpz_tdiv_ui (const mpz_t n, unsigned long d)
2953 + return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_TRUNC);
2957 +mpz_mod_ui (mpz_t r, const mpz_t n, unsigned long d)
2959 + return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_FLOOR);
2963 +mpz_divexact_ui (mpz_t q, const mpz_t n, unsigned long d)
2965 + gmp_assert_nocarry (mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_TRUNC));
2969 +mpz_divisible_ui_p (const mpz_t n, unsigned long d)
2971 + return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_TRUNC) == 0;
2977 +mpn_gcd_11 (mp_limb_t u, mp_limb_t v)
2981 + assert ( (u | v) > 0);
2988 + gmp_ctz (shift, u | v);
2993 + if ( (u & 1) == 0)
2994 + MP_LIMB_T_SWAP (u, v);
2996 + while ( (v & 1) == 0)
3006 + while ( (u & 1) == 0);
3013 + while ( (v & 1) == 0);
3016 + return u << shift;
3020 +mpz_gcd_ui (mpz_t g, const mpz_t u, unsigned long v)
3031 + un = GMP_ABS (u->_mp_size);
3033 + v = mpn_gcd_11 (mpn_div_qr_1 (NULL, u->_mp_d, un, v), v);
3036 + mpz_set_ui (g, v);
3043 +mpz_make_odd (mpz_t r)
3045 + mp_bitcnt_t shift;
3047 + assert (r->_mp_size > 0);
3048 + /* Count trailing zeros, equivalent to mpn_scan1, because we know that there is a 1 */
3049 + shift = mpn_common_scan (r->_mp_d[0], 0, r->_mp_d, 0, 0);
3050 + mpz_tdiv_q_2exp (r, r, shift);
3056 +mpz_gcd (mpz_t g, const mpz_t u, const mpz_t v)
3059 + mp_bitcnt_t uz, vz, gz;
3061 + if (u->_mp_size == 0)
3066 + if (v->_mp_size == 0)
3076 + uz = mpz_make_odd (tu);
3078 + vz = mpz_make_odd (tv);
3079 + gz = GMP_MIN (uz, vz);
3081 + if (tu->_mp_size < tv->_mp_size)
3082 + mpz_swap (tu, tv);
3084 + mpz_tdiv_r (tu, tu, tv);
3085 + if (tu->_mp_size == 0)
3094 + mpz_make_odd (tu);
3095 + c = mpz_cmp (tu, tv);
3102 + mpz_swap (tu, tv);
3104 + if (tv->_mp_size == 1)
3106 + mp_limb_t vl = tv->_mp_d[0];
3107 + mp_limb_t ul = mpz_tdiv_ui (tu, vl);
3108 + mpz_set_ui (g, mpn_gcd_11 (ul, vl));
3111 + mpz_sub (tu, tu, tv);
3115 + mpz_mul_2exp (g, g, gz);
3119 +mpz_gcdext (mpz_t g, mpz_t s, mpz_t t, const mpz_t u, const mpz_t v)
3121 + mpz_t tu, tv, s0, s1, t0, t1;
3122 + mp_bitcnt_t uz, vz, gz;
3123 + mp_bitcnt_t power;
3125 + if (u->_mp_size == 0)
3127 + /* g = 0 u + sgn(v) v */
3128 + signed long sign = mpz_sgn (v);
3131 + mpz_set_ui (s, 0);
3133 + mpz_set_si (t, sign);
3137 + if (v->_mp_size == 0)
3139 + /* g = sgn(u) u + 0 v */
3140 + signed long sign = mpz_sgn (u);
3143 + mpz_set_si (s, sign);
3145 + mpz_set_ui (t, 0);
3157 + uz = mpz_make_odd (tu);
3159 + vz = mpz_make_odd (tv);
3160 + gz = GMP_MIN (uz, vz);
3165 + /* Cofactors corresponding to odd gcd. gz handled later. */
3166 + if (tu->_mp_size < tv->_mp_size)
3168 + mpz_swap (tu, tv);
3169 + MPZ_SRCPTR_SWAP (u, v);
3170 + MPZ_PTR_SWAP (s, t);
3171 + MP_BITCNT_T_SWAP (uz, vz);
3176 + * u = t0 tu + t1 tv
3177 + * v = s0 tu + s1 tv
3179 + * where u and v denote the inputs with common factors of two
3180 + * eliminated, and det (s0, t0; s1, t1) = 2^p. Then
3182 + * 2^p tu = s1 u - t1 v
3183 + * 2^p tv = -s0 u + t0 v
3186 + /* After initial division, tu = q tv + tu', we have
3188 + * u = 2^uz (tu' + q tv)
3193 + * t0 = 2^uz, t1 = 2^uz q
3194 + * s0 = 0, s1 = 2^vz
3197 + mpz_setbit (t0, uz);
3198 + mpz_tdiv_qr (t1, tu, tu, tv);
3199 + mpz_mul_2exp (t1, t1, uz);
3201 + mpz_setbit (s1, vz);
3204 + if (tu->_mp_size > 0)
3206 + mp_bitcnt_t shift;
3207 + shift = mpz_make_odd (tu);
3208 + mpz_mul_2exp (t0, t0, shift);
3209 + mpz_mul_2exp (s0, s0, shift);
3215 + c = mpz_cmp (tu, tv);
3223 + * u = t0 tu + t1 (tv' + tu) = (t0 + t1) tu + t1 tv'
3224 + * v = s0 tu + s1 (tv' + tu) = (s0 + s1) tu + s1 tv' */
3226 + mpz_sub (tv, tv, tu);
3227 + mpz_add (t0, t0, t1);
3228 + mpz_add (s0, s0, s1);
3230 + shift = mpz_make_odd (tv);
3231 + mpz_mul_2exp (t1, t1, shift);
3232 + mpz_mul_2exp (s1, s1, shift);
3236 + mpz_sub (tu, tu, tv);
3237 + mpz_add (t1, t0, t1);
3238 + mpz_add (s1, s0, s1);
3240 + shift = mpz_make_odd (tu);
3241 + mpz_mul_2exp (t0, t0, shift);
3242 + mpz_mul_2exp (s0, s0, shift);
3248 + /* Now tv = odd part of gcd, and -s0 and t0 are corresponding
3251 + mpz_mul_2exp (tv, tv, gz);
3254 + /* 2^p g = s0 u + t0 v. Eliminate one factor of two at a time. To
3255 + adjust cofactors, we need u / g and v / g */
3257 + mpz_divexact (s1, v, tv);
3259 + mpz_divexact (t1, u, tv);
3262 + while (power-- > 0)
3264 + /* s0 u + t0 v = (s0 - v/g) u - (t0 + u/g) v */
3265 + if (mpz_odd_p (s0) || mpz_odd_p (t0))
3267 + mpz_sub (s0, s0, s1);
3268 + mpz_add (t0, t0, t1);
3270 + mpz_divexact_ui (s0, s0, 2);
3271 + mpz_divexact_ui (t0, t0, 2);
3274 + /* Arrange so that |s| < |u| / 2g */
3275 + mpz_add (s1, s0, s1);
3276 + if (mpz_cmpabs (s0, s1) > 0)
3278 + mpz_swap (s0, s1);
3279 + mpz_sub (t0, t0, t1);
3281 + if (u->_mp_size < 0)
3283 + if (v->_mp_size < 0)
3301 +mpz_lcm (mpz_t r, const mpz_t u, const mpz_t v)
3305 + if (u->_mp_size == 0 || v->_mp_size == 0)
3313 + mpz_gcd (g, u, v);
3314 + mpz_divexact (g, u, g);
3315 + mpz_mul (r, g, v);
3322 +mpz_lcm_ui (mpz_t r, const mpz_t u, unsigned long v)
3324 + if (v == 0 || u->_mp_size == 0)
3330 + v /= mpz_gcd_ui (NULL, u, v);
3331 + mpz_mul_ui (r, u, v);
3337 +mpz_invert (mpz_t r, const mpz_t u, const mpz_t m)
3342 + if (u->_mp_size == 0 || mpz_cmpabs_ui (m, 1) <= 0)
3348 + mpz_gcdext (g, tr, NULL, u, m);
3349 + invertible = (mpz_cmp_ui (g, 1) == 0);
3353 + if (tr->_mp_size < 0)
3355 + if (m->_mp_size >= 0)
3356 + mpz_add (tr, tr, m);
3358 + mpz_sub (tr, tr, m);
3365 + return invertible;
3369 +/* Higher level operations (sqrt, pow and root) */
3372 +mpz_pow_ui (mpz_t r, const mpz_t b, unsigned long e)
3374 + unsigned long bit;
3376 + mpz_init_set_ui (tr, 1);
3378 + bit = GMP_ULONG_HIGHBIT;
3381 + mpz_mul (tr, tr, tr);
3383 + mpz_mul (tr, tr, b);
3393 +mpz_ui_pow_ui (mpz_t r, unsigned long blimb, unsigned long e)
3396 + mpz_init_set_ui (b, blimb);
3397 + mpz_pow_ui (r, b, e);
3402 +mpz_powm (mpz_t r, const mpz_t b, const mpz_t e, const mpz_t m)
3408 + struct gmp_div_inverse minv;
3412 + en = GMP_ABS (e->_mp_size);
3413 + mn = GMP_ABS (m->_mp_size);
3415 + gmp_die ("mpz_powm: Zero modulo.");
3419 + mpz_set_ui (r, 1);
3424 + mpn_div_qr_invert (&minv, mp, mn);
3425 + shift = minv.shift;
3429 + /* To avoid shifts, we do all our reductions, except the final
3430 + one, using a *normalized* m. */
3433 + tp = gmp_xalloc_limbs (mn);
3434 + gmp_assert_nocarry (mpn_lshift (tp, mp, mn, shift));
3440 + if (e->_mp_size < 0)
3442 + if (!mpz_invert (base, b, m))
3443 + gmp_die ("mpz_powm: Negative exponent and non-invertible base.");
3448 + mpz_abs (base, b);
3450 + bn = base->_mp_size;
3453 + mpn_div_qr_preinv (NULL, base->_mp_d, base->_mp_size, mp, mn, &minv);
3457 + /* We have reduced the absolute value. Now take care of the
3458 + sign. Note that we get zero represented non-canonically as
3460 + if (b->_mp_size < 0)
3462 + mp_ptr bp = MPZ_REALLOC (base, mn);
3463 + gmp_assert_nocarry (mpn_sub (bp, mp, mn, bp, bn));
3466 + base->_mp_size = mpn_normalized_size (base->_mp_d, bn);
3468 + mpz_init_set_ui (tr, 1);
3472 + mp_limb_t w = e->_mp_d[en];
3475 + bit = GMP_LIMB_HIGHBIT;
3478 + mpz_mul (tr, tr, tr);
3480 + mpz_mul (tr, tr, base);
3481 + if (tr->_mp_size > mn)
3483 + mpn_div_qr_preinv (NULL, tr->_mp_d, tr->_mp_size, mp, mn, &minv);
3484 + tr->_mp_size = mpn_normalized_size (tr->_mp_d, mn);
3491 + /* Final reduction */
3492 + if (tr->_mp_size >= mn)
3494 + minv.shift = shift;
3495 + mpn_div_qr_preinv (NULL, tr->_mp_d, tr->_mp_size, mp, mn, &minv);
3496 + tr->_mp_size = mpn_normalized_size (tr->_mp_d, mn);
3507 +mpz_powm_ui (mpz_t r, const mpz_t b, unsigned long elimb, const mpz_t m)
3510 + mpz_init_set_ui (e, elimb);
3511 + mpz_powm (r, b, e, m);
3515 +/* x=trunc(y^(1/z)), r=y-x^z */
3517 +mpz_rootrem (mpz_t x, mpz_t r, const mpz_t y, unsigned long z)
3522 + sgn = y->_mp_size < 0;
3523 + if ((~z & sgn) != 0)
3524 + gmp_die ("mpz_rootrem: Negative argument, with even root.");
3526 + gmp_die ("mpz_rootrem: Zeroth root.");
3528 + if (mpz_cmpabs_ui (y, 1) <= 0) {
3539 + tb = mpz_sizeinbase (y, 2) / z + 1;
3540 + mpz_init2 (t, tb);
3541 + mpz_setbit (t, tb);
3544 + if (z == 2) /* simplify sqrt loop: z-1 == 1 */
3546 + mpz_swap (u, t); /* u = x */
3547 + mpz_tdiv_q (t, y, u); /* t = y/x */
3548 + mpz_add (t, t, u); /* t = y/x + x */
3549 + mpz_tdiv_q_2exp (t, t, 1); /* x'= (y/x + x)/2 */
3550 + } while (mpz_cmpabs (t, u) < 0); /* |x'| < |x| */
3551 + else /* z != 2 */ {
3559 + mpz_swap (u, t); /* u = x */
3560 + mpz_pow_ui (t, u, z - 1); /* t = x^(z-1) */
3561 + mpz_tdiv_q (t, y, t); /* t = y/x^(z-1) */
3562 + mpz_mul_ui (v, u, z - 1); /* v = x*(z-1) */
3563 + mpz_add (t, t, v); /* t = y/x^(z-1) + x*(z-1) */
3564 + mpz_tdiv_q_ui (t, t, z); /* x'=(y/x^(z-1) + x*(z-1))/z */
3565 + } while (mpz_cmpabs (t, u) < 0); /* |x'| < |x| */
3571 + mpz_pow_ui (t, u, z);
3572 + mpz_sub (r, y, t);
3581 +mpz_root (mpz_t x, const mpz_t y, unsigned long z)
3587 + mpz_rootrem (x, r, y, z);
3588 + res = r->_mp_size == 0;
3594 +/* Compute s = floor(sqrt(u)) and r = u - s^2. Allows r == NULL */
3596 +mpz_sqrtrem (mpz_t s, mpz_t r, const mpz_t u)
3598 + mpz_rootrem (s, r, u, 2);
3602 +mpz_sqrt (mpz_t s, const mpz_t u)
3604 + mpz_rootrem (s, NULL, u, 2);
3608 +mpz_perfect_square_p (const mpz_t u)
3610 + if (u->_mp_size <= 0)
3611 + return (u->_mp_size == 0);
3613 + return mpz_root (NULL, u, 2);
3617 +mpn_perfect_square_p (mp_srcptr p, mp_size_t n)
3622 + assert (p [n-1] != 0);
3623 + return mpz_root (NULL, mpz_roinit_n (t, p, n), 2);
3627 +mpn_sqrtrem (mp_ptr sp, mp_ptr rp, mp_srcptr p, mp_size_t n)
3633 + assert (p [n-1] != 0);
3637 + mpz_rootrem (s, r, mpz_roinit_n (u, p, n), 2);
3639 + assert (s->_mp_size == (n+1)/2);
3640 + mpn_copyd (sp, s->_mp_d, s->_mp_size);
3642 + res = r->_mp_size;
3644 + mpn_copyd (rp, r->_mp_d, res);
3649 +/* Combinatorics */
3652 +mpz_fac_ui (mpz_t x, unsigned long n)
3654 + mpz_set_ui (x, n + (n == 0));
3656 + mpz_mul_ui (x, x, --n);
3660 +mpz_bin_uiui (mpz_t r, unsigned long n, unsigned long k)
3664 + mpz_set_ui (r, k <= n);
3667 + k = (k <= n) ? n - k : 0;
3670 + mpz_fac_ui (t, k);
3672 + for (; k > 0; k--)
3673 + mpz_mul_ui (r, r, n--);
3675 + mpz_divexact (r, r, t);
3680 +/* Primality testing */
3682 +gmp_millerrabin (const mpz_t n, const mpz_t nm1, mpz_t y,
3683 + const mpz_t q, mp_bitcnt_t k)
3687 + /* Caller must initialize y to the base. */
3688 + mpz_powm (y, y, q, n);
3690 + if (mpz_cmp_ui (y, 1) == 0 || mpz_cmp (y, nm1) == 0)
3695 + mpz_powm_ui (y, y, 2, n);
3696 + if (mpz_cmp (y, nm1) == 0)
3698 + /* y == 1 means that the previous y was a non-trivial square root
3699 + of 1 (mod n). y == 0 means that n is a power of the base.
3700 + In either case, n is not prime. */
3701 + if (mpz_cmp_ui (y, 1) <= 0)
3707 +/* This product is 0xc0cfd797, and fits in 32 bits. */
3708 +#define GMP_PRIME_PRODUCT \
3709 + (3UL*5UL*7UL*11UL*13UL*17UL*19UL*23UL*29UL)
3711 +/* Bit (p+1)/2 is set, for each odd prime <= 61 */
3712 +#define GMP_PRIME_MASK 0xc96996dcUL
3715 +mpz_probab_prime_p (const mpz_t n, int reps)
3724 + /* Note that we use the absolute value of n only, for compatibility
3725 + with the real GMP. */
3726 + if (mpz_even_p (n))
3727 + return (mpz_cmpabs_ui (n, 2) == 0) ? 2 : 0;
3729 + /* Above test excludes n == 0 */
3730 + assert (n->_mp_size != 0);
3732 + if (mpz_cmpabs_ui (n, 64) < 0)
3733 + return (GMP_PRIME_MASK >> (n->_mp_d[0] >> 1)) & 2;
3735 + if (mpz_gcd_ui (NULL, n, GMP_PRIME_PRODUCT) != 1)
3738 + /* All prime factors are >= 31. */
3739 + if (mpz_cmpabs_ui (n, 31*31) < 0)
3742 + /* Use Miller-Rabin, with a deterministic sequence of bases, a[j] =
3743 + j^2 + j + 41 using Euler's polynomial. We potentially stop early,
3744 + if a[j] >= n - 1. Since n >= 31*31, this can happen only if reps >
3745 + 30 (a[30] == 971 > 31*31 == 961). */
3751 + /* Find q and k, where q is odd and n = 1 + 2**k * q. */
3752 + nm1->_mp_size = mpz_abs_sub_ui (nm1, n, 1);
3753 + k = mpz_scan1 (nm1, 0);
3754 + mpz_tdiv_q_2exp (q, nm1, k);
3756 + for (j = 0, is_prime = 1; is_prime & (j < reps); j++)
3758 + mpz_set_ui (y, (unsigned long) j*j+j+41);
3759 + if (mpz_cmp (y, nm1) >= 0)
3761 + /* Don't try any further bases. This "early" break does not affect
3762 + the result for any reasonable reps value (<=5000 was tested) */
3766 + is_prime = gmp_millerrabin (n, nm1, y, q, k);
3776 +/* Logical operations and bit manipulation. */
3778 +/* Numbers are treated as if represented in two's complement (and
3779 + infinitely sign extended). For a negative values we get the two's
3780 + complement from -x = ~x + 1, where ~ is bitwise complement.
3781 + Negation transforms
3789 + where yyyy is the bitwise complement of xxxx. So least significant
3790 + bits, up to and including the first one bit, are unchanged, and
3791 + the more significant bits are all complemented.
3793 + To change a bit from zero to one in a negative number, subtract the
3794 + corresponding power of two from the absolute value. This can never
3795 + underflow. To change a bit from one to zero, add the corresponding
3796 + power of two, and this might overflow. E.g., if x = -001111, the
3797 + two's complement is 110001. Clearing the least significant bit, we
3798 + get two's complement 110000, and -010000. */
3801 +mpz_tstbit (const mpz_t d, mp_bitcnt_t bit_index)
3803 + mp_size_t limb_index;
3811 + dn = GMP_ABS (ds);
3812 + limb_index = bit_index / GMP_LIMB_BITS;
3813 + if (limb_index >= dn)
3816 + shift = bit_index % GMP_LIMB_BITS;
3817 + w = d->_mp_d[limb_index];
3818 + bit = (w >> shift) & 1;
3822 + /* d < 0. Check if any of the bits below is set: If so, our bit
3823 + must be complemented. */
3824 + if (shift > 0 && (w << (GMP_LIMB_BITS - shift)) > 0)
3826 + while (limb_index-- > 0)
3827 + if (d->_mp_d[limb_index] > 0)
3834 +mpz_abs_add_bit (mpz_t d, mp_bitcnt_t bit_index)
3836 + mp_size_t dn, limb_index;
3840 + dn = GMP_ABS (d->_mp_size);
3842 + limb_index = bit_index / GMP_LIMB_BITS;
3843 + bit = (mp_limb_t) 1 << (bit_index % GMP_LIMB_BITS);
3845 + if (limb_index >= dn)
3848 + /* The bit should be set outside of the end of the number.
3849 + We have to increase the size of the number. */
3850 + dp = MPZ_REALLOC (d, limb_index + 1);
3852 + dp[limb_index] = bit;
3853 + for (i = dn; i < limb_index; i++)
3855 + dn = limb_index + 1;
3863 + cy = mpn_add_1 (dp + limb_index, dp + limb_index, dn - limb_index, bit);
3866 + dp = MPZ_REALLOC (d, dn + 1);
3871 + d->_mp_size = (d->_mp_size < 0) ? - dn : dn;
3875 +mpz_abs_sub_bit (mpz_t d, mp_bitcnt_t bit_index)
3877 + mp_size_t dn, limb_index;
3881 + dn = GMP_ABS (d->_mp_size);
3884 + limb_index = bit_index / GMP_LIMB_BITS;
3885 + bit = (mp_limb_t) 1 << (bit_index % GMP_LIMB_BITS);
3887 + assert (limb_index < dn);
3889 + gmp_assert_nocarry (mpn_sub_1 (dp + limb_index, dp + limb_index,
3890 + dn - limb_index, bit));
3891 + dn = mpn_normalized_size (dp, dn);
3892 + d->_mp_size = (d->_mp_size < 0) ? - dn : dn;
3896 +mpz_setbit (mpz_t d, mp_bitcnt_t bit_index)
3898 + if (!mpz_tstbit (d, bit_index))
3900 + if (d->_mp_size >= 0)
3901 + mpz_abs_add_bit (d, bit_index);
3903 + mpz_abs_sub_bit (d, bit_index);
3908 +mpz_clrbit (mpz_t d, mp_bitcnt_t bit_index)
3910 + if (mpz_tstbit (d, bit_index))
3912 + if (d->_mp_size >= 0)
3913 + mpz_abs_sub_bit (d, bit_index);
3915 + mpz_abs_add_bit (d, bit_index);
3920 +mpz_combit (mpz_t d, mp_bitcnt_t bit_index)
3922 + if (mpz_tstbit (d, bit_index) ^ (d->_mp_size < 0))
3923 + mpz_abs_sub_bit (d, bit_index);
3925 + mpz_abs_add_bit (d, bit_index);
3929 +mpz_com (mpz_t r, const mpz_t u)
3932 + mpz_sub_ui (r, r, 1);
3936 +mpz_and (mpz_t r, const mpz_t u, const mpz_t v)
3938 + mp_size_t un, vn, rn, i;
3939 + mp_ptr up, vp, rp;
3941 + mp_limb_t ux, vx, rx;
3942 + mp_limb_t uc, vc, rc;
3943 + mp_limb_t ul, vl, rl;
3945 + un = GMP_ABS (u->_mp_size);
3946 + vn = GMP_ABS (v->_mp_size);
3949 + MPZ_SRCPTR_SWAP (u, v);
3950 + MP_SIZE_T_SWAP (un, vn);
3958 + uc = u->_mp_size < 0;
3959 + vc = v->_mp_size < 0;
3966 + /* If the smaller input is positive, higher limbs don't matter. */
3967 + rn = vx ? un : vn;
3969 + rp = MPZ_REALLOC (r, rn + rc);
3977 + ul = (up[i] ^ ux) + uc;
3980 + vl = (vp[i] ^ vx) + vc;
3983 + rl = ( (ul & vl) ^ rx) + rc;
3990 + for (; i < rn; i++)
3992 + ul = (up[i] ^ ux) + uc;
3995 + rl = ( (ul & vx) ^ rx) + rc;
4002 + rn = mpn_normalized_size (rp, rn);
4004 + r->_mp_size = rx ? -rn : rn;
4008 +mpz_ior (mpz_t r, const mpz_t u, const mpz_t v)
4010 + mp_size_t un, vn, rn, i;
4011 + mp_ptr up, vp, rp;
4013 + mp_limb_t ux, vx, rx;
4014 + mp_limb_t uc, vc, rc;
4015 + mp_limb_t ul, vl, rl;
4017 + un = GMP_ABS (u->_mp_size);
4018 + vn = GMP_ABS (v->_mp_size);
4021 + MPZ_SRCPTR_SWAP (u, v);
4022 + MP_SIZE_T_SWAP (un, vn);
4030 + uc = u->_mp_size < 0;
4031 + vc = v->_mp_size < 0;
4038 + /* If the smaller input is negative, by sign extension higher limbs
4040 + rn = vx ? vn : un;
4042 + rp = MPZ_REALLOC (r, rn + rc);
4050 + ul = (up[i] ^ ux) + uc;
4053 + vl = (vp[i] ^ vx) + vc;
4056 + rl = ( (ul | vl) ^ rx) + rc;
4063 + for (; i < rn; i++)
4065 + ul = (up[i] ^ ux) + uc;
4068 + rl = ( (ul | vx) ^ rx) + rc;
4075 + rn = mpn_normalized_size (rp, rn);
4077 + r->_mp_size = rx ? -rn : rn;
4081 +mpz_xor (mpz_t r, const mpz_t u, const mpz_t v)
4083 + mp_size_t un, vn, i;
4084 + mp_ptr up, vp, rp;
4086 + mp_limb_t ux, vx, rx;
4087 + mp_limb_t uc, vc, rc;
4088 + mp_limb_t ul, vl, rl;
4090 + un = GMP_ABS (u->_mp_size);
4091 + vn = GMP_ABS (v->_mp_size);
4094 + MPZ_SRCPTR_SWAP (u, v);
4095 + MP_SIZE_T_SWAP (un, vn);
4103 + uc = u->_mp_size < 0;
4104 + vc = v->_mp_size < 0;
4111 + rp = MPZ_REALLOC (r, un + rc);
4119 + ul = (up[i] ^ ux) + uc;
4122 + vl = (vp[i] ^ vx) + vc;
4125 + rl = (ul ^ vl ^ rx) + rc;
4132 + for (; i < un; i++)
4134 + ul = (up[i] ^ ux) + uc;
4137 + rl = (ul ^ ux) + rc;
4144 + un = mpn_normalized_size (rp, un);
4146 + r->_mp_size = rx ? -un : un;
4150 +gmp_popcount_limb (mp_limb_t x)
4154 + /* Do 16 bits at a time, to avoid limb-sized constants. */
4155 + for (c = 0; x > 0; x >>= 16)
4157 + unsigned w = ((x >> 1) & 0x5555) + (x & 0x5555);
4158 + w = ((w >> 2) & 0x3333) + (w & 0x3333);
4159 + w = ((w >> 4) & 0x0f0f) + (w & 0x0f0f);
4160 + w = (w >> 8) + (w & 0x00ff);
4167 +mpn_popcount (mp_srcptr p, mp_size_t n)
4172 + for (c = 0, i = 0; i < n; i++)
4173 + c += gmp_popcount_limb (p[i]);
4179 +mpz_popcount (const mpz_t u)
4186 + return ~(mp_bitcnt_t) 0;
4188 + return mpn_popcount (u->_mp_d, un);
4192 +mpz_hamdist (const mpz_t u, const mpz_t v)
4194 + mp_size_t un, vn, i;
4195 + mp_limb_t uc, vc, ul, vl, comp;
4202 + if ( (un ^ vn) < 0)
4203 + return ~(mp_bitcnt_t) 0;
4205 + comp = - (uc = vc = (un < 0));
4217 + MPN_SRCPTR_SWAP (up, un, vp, vn);
4219 + for (i = 0, c = 0; i < vn; i++)
4221 + ul = (up[i] ^ comp) + uc;
4224 + vl = (vp[i] ^ comp) + vc;
4227 + c += gmp_popcount_limb (ul ^ vl);
4231 + for (; i < un; i++)
4233 + ul = (up[i] ^ comp) + uc;
4236 + c += gmp_popcount_limb (ul ^ comp);
4243 +mpz_scan1 (const mpz_t u, mp_bitcnt_t starting_bit)
4246 + mp_size_t us, un, i;
4247 + mp_limb_t limb, ux;
4250 + un = GMP_ABS (us);
4251 + i = starting_bit / GMP_LIMB_BITS;
4253 + /* Past the end there's no 1 bits for u>=0, or an immediate 1 bit
4254 + for u<0. Notice this test picks up any u==0 too. */
4256 + return (us >= 0 ? ~(mp_bitcnt_t) 0 : starting_bit);
4262 + if (starting_bit != 0)
4266 + ux = mpn_zero_p (up, i);
4267 + limb = ~ limb + ux;
4268 + ux = - (mp_limb_t) (limb >= ux);
4271 + /* Mask to 0 all bits before starting_bit, thus ignoring them. */
4272 + limb &= (GMP_LIMB_MAX << (starting_bit % GMP_LIMB_BITS));
4275 + return mpn_common_scan (limb, i, up, un, ux);
4279 +mpz_scan0 (const mpz_t u, mp_bitcnt_t starting_bit)
4282 + mp_size_t us, un, i;
4283 + mp_limb_t limb, ux;
4286 + ux = - (mp_limb_t) (us >= 0);
4287 + un = GMP_ABS (us);
4288 + i = starting_bit / GMP_LIMB_BITS;
4290 + /* When past end, there's an immediate 0 bit for u>=0, or no 0 bits for
4291 + u<0. Notice this test picks up all cases of u==0 too. */
4293 + return (ux ? starting_bit : ~(mp_bitcnt_t) 0);
4296 + limb = up[i] ^ ux;
4299 + limb -= mpn_zero_p (up, i); /* limb = ~(~limb + zero_p) */
4301 + /* Mask all bits before starting_bit, thus ignoring them. */
4302 + limb &= (GMP_LIMB_MAX << (starting_bit % GMP_LIMB_BITS));
4304 + return mpn_common_scan (limb, i, up, un, ux);
4308 +/* MPZ base conversion. */
4311 +mpz_sizeinbase (const mpz_t u, int base)
4317 + struct gmp_div_inverse bi;
4320 + assert (base >= 2);
4321 + assert (base <= 36);
4323 + un = GMP_ABS (u->_mp_size);
4329 + bits = (un - 1) * GMP_LIMB_BITS + mpn_limb_size_in_base_2 (up[un-1]);
4335 + return (bits + 1) / 2;
4337 + return (bits + 2) / 3;
4339 + return (bits + 3) / 4;
4341 + return (bits + 4) / 5;
4342 + /* FIXME: Do something more clever for the common case of base
4346 + tp = gmp_xalloc_limbs (un);
4347 + mpn_copyi (tp, up, un);
4348 + mpn_div_qr_1_invert (&bi, base);
4354 + mpn_div_qr_1_preinv (tp, tp, un, &bi);
4355 + un -= (tp[un-1] == 0);
4364 +mpz_get_str (char *sp, int base, const mpz_t u)
4367 + const char *digits;
4373 + digits = "0123456789abcdefghijklmnopqrstuvwxyz";
4378 + digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
4385 + sn = 1 + mpz_sizeinbase (u, base);
4387 + sp = gmp_xalloc (1 + sn);
4389 + un = GMP_ABS (u->_mp_size);
4400 + if (u->_mp_size < 0)
4403 + bits = mpn_base_power_of_two_p (base);
4406 + /* Not modified in this case. */
4407 + sn = i + mpn_get_str_bits ((unsigned char *) sp + i, bits, u->_mp_d, un);
4410 + struct mpn_base_info info;
4413 + mpn_get_base_info (&info, base);
4414 + tp = gmp_xalloc_limbs (un);
4415 + mpn_copyi (tp, u->_mp_d, un);
4417 + sn = i + mpn_get_str_other ((unsigned char *) sp + i, base, &info, tp, un);
4421 + for (; i < sn; i++)
4422 + sp[i] = digits[(unsigned char) sp[i]];
4429 +mpz_set_str (mpz_t r, const char *sp, int base)
4432 + mp_size_t rn, alloc;
4436 + unsigned char *dp;
4438 + assert (base == 0 || (base >= 2 && base <= 36));
4440 + while (isspace( (unsigned char) *sp))
4443 + sign = (*sp == '-');
4451 + if (*sp == 'x' || *sp == 'X')
4456 + else if (*sp == 'b' || *sp == 'B')
4469 + dp = gmp_xalloc (sn + (sn == 0));
4471 + for (sn = 0; *sp; sp++)
4475 + if (isspace ((unsigned char) *sp))
4477 + if (*sp >= '0' && *sp <= '9')
4478 + digit = *sp - '0';
4479 + else if (*sp >= 'a' && *sp <= 'z')
4480 + digit = *sp - 'a' + 10;
4481 + else if (*sp >= 'A' && *sp <= 'Z')
4482 + digit = *sp - 'A' + 10;
4484 + digit = base; /* fail */
4486 + if (digit >= base)
4496 + bits = mpn_base_power_of_two_p (base);
4500 + alloc = (sn * bits + GMP_LIMB_BITS - 1) / GMP_LIMB_BITS;
4501 + rp = MPZ_REALLOC (r, alloc);
4502 + rn = mpn_set_str_bits (rp, dp, sn, bits);
4506 + struct mpn_base_info info;
4507 + mpn_get_base_info (&info, base);
4508 + alloc = (sn + info.exp - 1) / info.exp;
4509 + rp = MPZ_REALLOC (r, alloc);
4510 + rn = mpn_set_str_other (rp, dp, sn, base, &info);
4512 + assert (rn <= alloc);
4515 + r->_mp_size = sign ? - rn : rn;
4521 +mpz_init_set_str (mpz_t r, const char *sp, int base)
4524 + return mpz_set_str (r, sp, base);
4528 +mpz_out_str (FILE *stream, int base, const mpz_t x)
4533 + str = mpz_get_str (NULL, base, x);
4534 + len = strlen (str);
4535 + len = fwrite (str, 1, len, stream);
4542 +gmp_detect_endian (void)
4544 + static const int i = 2;
4545 + const unsigned char *p = (const unsigned char *) &i;
4549 +/* Import and export. Does not support nails. */
4551 +mpz_import (mpz_t r, size_t count, int order, size_t size, int endian,
4552 + size_t nails, const void *src)
4554 + const unsigned char *p;
4555 + ptrdiff_t word_step;
4559 + /* The current (partial) limb. */
4561 + /* The number of bytes already copied to this limb (starting from
4564 + /* The index where the limb should be stored, when completed. */
4568 + gmp_die ("mpz_import: Nails not supported.");
4570 + assert (order == 1 || order == -1);
4571 + assert (endian >= -1 && endian <= 1);
4574 + endian = gmp_detect_endian ();
4576 + p = (unsigned char *) src;
4578 + word_step = (order != endian) ? 2 * size : 0;
4580 + /* Process bytes from the least significant end, so point p at the
4581 + least significant word. */
4584 + p += size * (count - 1);
4585 + word_step = - word_step;
4588 + /* And at least significant byte of that word. */
4592 + rn = (size * count + sizeof(mp_limb_t) - 1) / sizeof(mp_limb_t);
4593 + rp = MPZ_REALLOC (r, rn);
4595 + for (limb = 0, bytes = 0, i = 0; count > 0; count--, p += word_step)
4598 + for (j = 0; j < size; j++, p -= (ptrdiff_t) endian)
4600 + limb |= (mp_limb_t) *p << (bytes++ * CHAR_BIT);
4601 + if (bytes == sizeof(mp_limb_t))
4609 + assert (i + (bytes > 0) == rn);
4613 + i = mpn_normalized_size (rp, i);
4619 +mpz_export (void *r, size_t *countp, int order, size_t size, int endian,
4620 + size_t nails, const mpz_t u)
4626 + gmp_die ("mpz_import: Nails not supported.");
4628 + assert (order == 1 || order == -1);
4629 + assert (endian >= -1 && endian <= 1);
4630 + assert (size > 0 || u->_mp_size == 0);
4638 + ptrdiff_t word_step;
4639 + /* The current (partial) limb. */
4641 + /* The number of bytes left to to in this limb. */
4643 + /* The index where the limb was read. */
4646 + un = GMP_ABS (un);
4648 + /* Count bytes in top limb. */
4649 + limb = u->_mp_d[un-1];
4650 + assert (limb != 0);
4654 + k++; limb >>= CHAR_BIT;
4655 + } while (limb != 0);
4657 + count = (k + (un-1) * sizeof (mp_limb_t) + size - 1) / size;
4660 + r = gmp_xalloc (count * size);
4663 + endian = gmp_detect_endian ();
4665 + p = (unsigned char *) r;
4667 + word_step = (order != endian) ? 2 * size : 0;
4669 + /* Process bytes from the least significant end, so point p at the
4670 + least significant word. */
4673 + p += size * (count - 1);
4674 + word_step = - word_step;
4677 + /* And at least significant byte of that word. */
4681 + for (bytes = 0, i = 0, k = 0; k < count; k++, p += word_step)
4684 + for (j = 0; j < size; j++, p -= (ptrdiff_t) endian)
4689 + limb = u->_mp_d[i++];
4690 + bytes = sizeof (mp_limb_t);
4693 + limb >>= CHAR_BIT;
4698 + assert (k == count);