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-rw-r--r--src/gmp/mini-gmp.c4130
1 files changed, 0 insertions, 4130 deletions
diff --git a/src/gmp/mini-gmp.c b/src/gmp/mini-gmp.c
deleted file mode 100644
index f3b43fbe8..000000000
--- a/src/gmp/mini-gmp.c
+++ /dev/null
@@ -1,4130 +0,0 @@
-/* mini-gmp, a minimalistic implementation of a GNU GMP subset.
-
- Contributed to the GNU project by Niels Möller
-
-Copyright 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1999, 2000, 2001,
-2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013
-Free Software Foundation, Inc.
-
-This file is part of the GNU MP Library.
-
-The GNU MP Library is free software; you can redistribute it and/or modify
-it under the terms of the GNU Lesser General Public License as published by
-the Free Software Foundation; either version 3 of the License, or (at your
-option) any later version.
-
-The GNU MP Library is distributed in the hope that it will be useful, but
-WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
-License for more details.
-
-You should have received a copy of the GNU Lesser General Public License
-along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
-
-/* NOTE: All functions in this file which are not declared in
- mini-gmp.h are internal, and are not intended to be compatible
- neither with GMP nor with future versions of mini-gmp. */
-
-/* Much of the material copied from GMP files, including: gmp-impl.h,
- longlong.h, mpn/generic/add_n.c, mpn/generic/addmul_1.c,
- mpn/generic/lshift.c, mpn/generic/mul_1.c,
- mpn/generic/mul_basecase.c, mpn/generic/rshift.c,
- mpn/generic/sbpi1_div_qr.c, mpn/generic/sub_n.c,
- mpn/generic/submul_1.c. */
-
-#include <assert.h>
-#include <ctype.h>
-#include <limits.h>
-#include <stdio.h>
-#include <stdlib.h>
-#include <string.h>
-
-#include "mini-gmp.h"
-
-
-/* Macros */
-#define GMP_LIMB_BITS (sizeof(mp_limb_t) * CHAR_BIT)
-
-#define GMP_LIMB_MAX (~ (mp_limb_t) 0)
-#define GMP_LIMB_HIGHBIT ((mp_limb_t) 1 << (GMP_LIMB_BITS - 1))
-
-#define GMP_HLIMB_BIT ((mp_limb_t) 1 << (GMP_LIMB_BITS / 2))
-#define GMP_LLIMB_MASK (GMP_HLIMB_BIT - 1)
-
-#define GMP_ULONG_BITS (sizeof(unsigned long) * CHAR_BIT)
-#define GMP_ULONG_HIGHBIT ((unsigned long) 1 << (GMP_ULONG_BITS - 1))
-
-#define GMP_ABS(x) ((x) >= 0 ? (x) : -(x))
-#define GMP_NEG_CAST(T,x) (-((T)((x) + 1) - 1))
-
-#define GMP_MIN(a, b) ((a) < (b) ? (a) : (b))
-#define GMP_MAX(a, b) ((a) > (b) ? (a) : (b))
-
-#define gmp_assert_nocarry(x) do { \
- mp_limb_t __cy = x; \
- assert (__cy == 0); \
- } while (0)
-
-#define gmp_clz(count, x) do { \
- mp_limb_t __clz_x = (x); \
- unsigned __clz_c; \
- for (__clz_c = 0; \
- (__clz_x & ((mp_limb_t) 0xff << (GMP_LIMB_BITS - 8))) == 0; \
- __clz_c += 8) \
- __clz_x <<= 8; \
- for (; (__clz_x & GMP_LIMB_HIGHBIT) == 0; __clz_c++) \
- __clz_x <<= 1; \
- (count) = __clz_c; \
- } while (0)
-
-#define gmp_ctz(count, x) do { \
- mp_limb_t __ctz_x = (x); \
- unsigned __ctz_c = 0; \
- gmp_clz (__ctz_c, __ctz_x & - __ctz_x); \
- (count) = GMP_LIMB_BITS - 1 - __ctz_c; \
- } while (0)
-
-#define gmp_add_ssaaaa(sh, sl, ah, al, bh, bl) \
- do { \
- mp_limb_t __x; \
- __x = (al) + (bl); \
- (sh) = (ah) + (bh) + (__x < (al)); \
- (sl) = __x; \
- } while (0)
-
-#define gmp_sub_ddmmss(sh, sl, ah, al, bh, bl) \
- do { \
- mp_limb_t __x; \
- __x = (al) - (bl); \
- (sh) = (ah) - (bh) - ((al) < (bl)); \
- (sl) = __x; \
- } while (0)
-
-#define gmp_umul_ppmm(w1, w0, u, v) \
- do { \
- mp_limb_t __x0, __x1, __x2, __x3; \
- unsigned __ul, __vl, __uh, __vh; \
- mp_limb_t __u = (u), __v = (v); \
- \
- __ul = __u & GMP_LLIMB_MASK; \
- __uh = __u >> (GMP_LIMB_BITS / 2); \
- __vl = __v & GMP_LLIMB_MASK; \
- __vh = __v >> (GMP_LIMB_BITS / 2); \
- \
- __x0 = (mp_limb_t) __ul * __vl; \
- __x1 = (mp_limb_t) __ul * __vh; \
- __x2 = (mp_limb_t) __uh * __vl; \
- __x3 = (mp_limb_t) __uh * __vh; \
- \
- __x1 += __x0 >> (GMP_LIMB_BITS / 2);/* this can't give carry */ \
- __x1 += __x2; /* but this indeed can */ \
- if (__x1 < __x2) /* did we get it? */ \
- __x3 += GMP_HLIMB_BIT; /* yes, add it in the proper pos. */ \
- \
- (w1) = __x3 + (__x1 >> (GMP_LIMB_BITS / 2)); \
- (w0) = (__x1 << (GMP_LIMB_BITS / 2)) + (__x0 & GMP_LLIMB_MASK); \
- } while (0)
-
-#define gmp_udiv_qrnnd_preinv(q, r, nh, nl, d, di) \
- do { \
- mp_limb_t _qh, _ql, _r, _mask; \
- gmp_umul_ppmm (_qh, _ql, (nh), (di)); \
- gmp_add_ssaaaa (_qh, _ql, _qh, _ql, (nh) + 1, (nl)); \
- _r = (nl) - _qh * (d); \
- _mask = -(mp_limb_t) (_r > _ql); /* both > and >= are OK */ \
- _qh += _mask; \
- _r += _mask & (d); \
- if (_r >= (d)) \
- { \
- _r -= (d); \
- _qh++; \
- } \
- \
- (r) = _r; \
- (q) = _qh; \
- } while (0)
-
-#define gmp_udiv_qr_3by2(q, r1, r0, n2, n1, n0, d1, d0, dinv) \
- do { \
- mp_limb_t _q0, _t1, _t0, _mask; \
- gmp_umul_ppmm ((q), _q0, (n2), (dinv)); \
- gmp_add_ssaaaa ((q), _q0, (q), _q0, (n2), (n1)); \
- \
- /* Compute the two most significant limbs of n - q'd */ \
- (r1) = (n1) - (d1) * (q); \
- gmp_sub_ddmmss ((r1), (r0), (r1), (n0), (d1), (d0)); \
- gmp_umul_ppmm (_t1, _t0, (d0), (q)); \
- gmp_sub_ddmmss ((r1), (r0), (r1), (r0), _t1, _t0); \
- (q)++; \
- \
- /* Conditionally adjust q and the remainders */ \
- _mask = - (mp_limb_t) ((r1) >= _q0); \
- (q) += _mask; \
- gmp_add_ssaaaa ((r1), (r0), (r1), (r0), _mask & (d1), _mask & (d0)); \
- if ((r1) >= (d1)) \
- { \
- if ((r1) > (d1) || (r0) >= (d0)) \
- { \
- (q)++; \
- gmp_sub_ddmmss ((r1), (r0), (r1), (r0), (d1), (d0)); \
- } \
- } \
- } while (0)
-
-/* Swap macros. */
-#define MP_LIMB_T_SWAP(x, y) \
- do { \
- mp_limb_t __mp_limb_t_swap__tmp = (x); \
- (x) = (y); \
- (y) = __mp_limb_t_swap__tmp; \
- } while (0)
-#define MP_SIZE_T_SWAP(x, y) \
- do { \
- mp_size_t __mp_size_t_swap__tmp = (x); \
- (x) = (y); \
- (y) = __mp_size_t_swap__tmp; \
- } while (0)
-#define MP_BITCNT_T_SWAP(x,y) \
- do { \
- mp_bitcnt_t __mp_bitcnt_t_swap__tmp = (x); \
- (x) = (y); \
- (y) = __mp_bitcnt_t_swap__tmp; \
- } while (0)
-#define MP_PTR_SWAP(x, y) \
- do { \
- mp_ptr __mp_ptr_swap__tmp = (x); \
- (x) = (y); \
- (y) = __mp_ptr_swap__tmp; \
- } while (0)
-#define MP_SRCPTR_SWAP(x, y) \
- do { \
- mp_srcptr __mp_srcptr_swap__tmp = (x); \
- (x) = (y); \
- (y) = __mp_srcptr_swap__tmp; \
- } while (0)
-
-#define MPN_PTR_SWAP(xp,xs, yp,ys) \
- do { \
- MP_PTR_SWAP (xp, yp); \
- MP_SIZE_T_SWAP (xs, ys); \
- } while(0)
-#define MPN_SRCPTR_SWAP(xp,xs, yp,ys) \
- do { \
- MP_SRCPTR_SWAP (xp, yp); \
- MP_SIZE_T_SWAP (xs, ys); \
- } while(0)
-
-#define MPZ_PTR_SWAP(x, y) \
- do { \
- mpz_ptr __mpz_ptr_swap__tmp = (x); \
- (x) = (y); \
- (y) = __mpz_ptr_swap__tmp; \
- } while (0)
-#define MPZ_SRCPTR_SWAP(x, y) \
- do { \
- mpz_srcptr __mpz_srcptr_swap__tmp = (x); \
- (x) = (y); \
- (y) = __mpz_srcptr_swap__tmp; \
- } while (0)
-
-
-/* Memory allocation and other helper functions. */
-static void
-gmp_die (const char *msg)
-{
- fprintf (stderr, "%s\n", msg);
- abort();
-}
-
-static void *
-gmp_default_alloc (size_t size)
-{
- void *p;
-
- assert (size > 0);
-
- p = malloc (size);
- if (!p)
- gmp_die("gmp_default_alloc: Virtual memory exhausted.");
-
- return p;
-}
-
-static void *
-gmp_default_realloc (void *old, size_t old_size, size_t new_size)
-{
- mp_ptr p;
-
- p = realloc (old, new_size);
-
- if (!p)
- gmp_die("gmp_default_realoc: Virtual memory exhausted.");
-
- return p;
-}
-
-static void
-gmp_default_free (void *p, size_t size)
-{
- free (p);
-}
-
-static void * (*gmp_allocate_func) (size_t) = gmp_default_alloc;
-static void * (*gmp_reallocate_func) (void *, size_t, size_t) = gmp_default_realloc;
-static void (*gmp_free_func) (void *, size_t) = gmp_default_free;
-
-void
-mp_get_memory_functions (void *(**alloc_func) (size_t),
- void *(**realloc_func) (void *, size_t, size_t),
- void (**free_func) (void *, size_t))
-{
- if (alloc_func)
- *alloc_func = gmp_allocate_func;
-
- if (realloc_func)
- *realloc_func = gmp_reallocate_func;
-
- if (free_func)
- *free_func = gmp_free_func;
-}
-
-void
-mp_set_memory_functions (void *(*alloc_func) (size_t),
- void *(*realloc_func) (void *, size_t, size_t),
- void (*free_func) (void *, size_t))
-{
- if (!alloc_func)
- alloc_func = gmp_default_alloc;
- if (!realloc_func)
- realloc_func = gmp_default_realloc;
- if (!free_func)
- free_func = gmp_default_free;
-
- gmp_allocate_func = alloc_func;
- gmp_reallocate_func = realloc_func;
- gmp_free_func = free_func;
-}
-
-#define gmp_xalloc(size) ((*gmp_allocate_func)((size)))
-#define gmp_free(p) ((*gmp_free_func) ((p), 0))
-
-static mp_ptr
-gmp_xalloc_limbs (mp_size_t size)
-{
- return gmp_xalloc (size * sizeof (mp_limb_t));
-}
-
-static mp_ptr
-gmp_xrealloc_limbs (mp_ptr old, mp_size_t size)
-{
- assert (size > 0);
- return (*gmp_reallocate_func) (old, 0, size * sizeof (mp_limb_t));
-}
-
-
-/* MPN interface */
-
-void
-mpn_copyi (mp_ptr d, mp_srcptr s, mp_size_t n)
-{
- mp_size_t i;
- for (i = 0; i < n; i++)
- d[i] = s[i];
-}
-
-void
-mpn_copyd (mp_ptr d, mp_srcptr s, mp_size_t n)
-{
- while (n-- > 0)
- d[n] = s[n];
-}
-
-int
-mpn_cmp (mp_srcptr ap, mp_srcptr bp, mp_size_t n)
-{
- for (; n > 0; n--)
- {
- if (ap[n-1] < bp[n-1])
- return -1;
- else if (ap[n-1] > bp[n-1])
- return 1;
- }
- return 0;
-}
-
-static int
-mpn_cmp4 (mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
-{
- if (an > bn)
- return 1;
- else if (an < bn)
- return -1;
- else
- return mpn_cmp (ap, bp, an);
-}
-
-static mp_size_t
-mpn_normalized_size (mp_srcptr xp, mp_size_t n)
-{
- for (; n > 0 && xp[n-1] == 0; n--)
- ;
- return n;
-}
-
-#define mpn_zero_p(xp, n) (mpn_normalized_size ((xp), (n)) == 0)
-
-mp_limb_t
-mpn_add_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b)
-{
- mp_size_t i;
-
- assert (n > 0);
-
- for (i = 0; i < n; i++)
- {
- mp_limb_t r = ap[i] + b;
- /* Carry out */
- b = (r < b);
- rp[i] = r;
- }
- return b;
-}
-
-mp_limb_t
-mpn_add_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
-{
- mp_size_t i;
- mp_limb_t cy;
-
- for (i = 0, cy = 0; i < n; i++)
- {
- mp_limb_t a, b, r;
- a = ap[i]; b = bp[i];
- r = a + cy;
- cy = (r < cy);
- r += b;
- cy += (r < b);
- rp[i] = r;
- }
- return cy;
-}
-
-mp_limb_t
-mpn_add (mp_ptr rp, mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
-{
- mp_limb_t cy;
-
- assert (an >= bn);
-
- cy = mpn_add_n (rp, ap, bp, bn);
- if (an > bn)
- cy = mpn_add_1 (rp + bn, ap + bn, an - bn, cy);
- return cy;
-}
-
-mp_limb_t
-mpn_sub_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b)
-{
- mp_size_t i;
-
- assert (n > 0);
-
- for (i = 0; i < n; i++)
- {
- mp_limb_t a = ap[i];
- /* Carry out */
- mp_limb_t cy = a < b;;
- rp[i] = a - b;
- b = cy;
- }
- return b;
-}
-
-mp_limb_t
-mpn_sub_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
-{
- mp_size_t i;
- mp_limb_t cy;
-
- for (i = 0, cy = 0; i < n; i++)
- {
- mp_limb_t a, b;
- a = ap[i]; b = bp[i];
- b += cy;
- cy = (b < cy);
- cy += (a < b);
- rp[i] = a - b;
- }
- return cy;
-}
-
-mp_limb_t
-mpn_sub (mp_ptr rp, mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
-{
- mp_limb_t cy;
-
- assert (an >= bn);
-
- cy = mpn_sub_n (rp, ap, bp, bn);
- if (an > bn)
- cy = mpn_sub_1 (rp + bn, ap + bn, an - bn, cy);
- return cy;
-}
-
-mp_limb_t
-mpn_mul_1 (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_limb_t vl)
-{
- mp_limb_t ul, cl, hpl, lpl;
-
- assert (n >= 1);
-
- cl = 0;
- do
- {
- ul = *up++;
- gmp_umul_ppmm (hpl, lpl, ul, vl);
-
- lpl += cl;
- cl = (lpl < cl) + hpl;
-
- *rp++ = lpl;
- }
- while (--n != 0);
-
- return cl;
-}
-
-mp_limb_t
-mpn_addmul_1 (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_limb_t vl)
-{
- mp_limb_t ul, cl, hpl, lpl, rl;
-
- assert (n >= 1);
-
- cl = 0;
- do
- {
- ul = *up++;
- gmp_umul_ppmm (hpl, lpl, ul, vl);
-
- lpl += cl;
- cl = (lpl < cl) + hpl;
-
- rl = *rp;
- lpl = rl + lpl;
- cl += lpl < rl;
- *rp++ = lpl;
- }
- while (--n != 0);
-
- return cl;
-}
-
-mp_limb_t
-mpn_submul_1 (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_limb_t vl)
-{
- mp_limb_t ul, cl, hpl, lpl, rl;
-
- assert (n >= 1);
-
- cl = 0;
- do
- {
- ul = *up++;
- gmp_umul_ppmm (hpl, lpl, ul, vl);
-
- lpl += cl;
- cl = (lpl < cl) + hpl;
-
- rl = *rp;
- lpl = rl - lpl;
- cl += lpl > rl;
- *rp++ = lpl;
- }
- while (--n != 0);
-
- return cl;
-}
-
-mp_limb_t
-mpn_mul (mp_ptr rp, mp_srcptr up, mp_size_t un, mp_srcptr vp, mp_size_t vn)
-{
- assert (un >= vn);
- assert (vn >= 1);
-
- /* We first multiply by the low order limb. This result can be
- stored, not added, to rp. We also avoid a loop for zeroing this
- way. */
-
- rp[un] = mpn_mul_1 (rp, up, un, vp[0]);
- rp += 1, vp += 1, vn -= 1;
-
- /* Now accumulate the product of up[] and the next higher limb from
- vp[]. */
-
- while (vn >= 1)
- {
- rp[un] = mpn_addmul_1 (rp, up, un, vp[0]);
- rp += 1, vp += 1, vn -= 1;
- }
- return rp[un - 1];
-}
-
-void
-mpn_mul_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
-{
- mpn_mul (rp, ap, n, bp, n);
-}
-
-void
-mpn_sqr (mp_ptr rp, mp_srcptr ap, mp_size_t n)
-{
- mpn_mul (rp, ap, n, ap, n);
-}
-
-mp_limb_t
-mpn_lshift (mp_ptr rp, mp_srcptr up, mp_size_t n, unsigned int cnt)
-{
- mp_limb_t high_limb, low_limb;
- unsigned int tnc;
- mp_size_t i;
- mp_limb_t retval;
-
- assert (n >= 1);
- assert (cnt >= 1);
- assert (cnt < GMP_LIMB_BITS);
-
- up += n;
- rp += n;
-
- tnc = GMP_LIMB_BITS - cnt;
- low_limb = *--up;
- retval = low_limb >> tnc;
- high_limb = (low_limb << cnt);
-
- for (i = n - 1; i != 0; i--)
- {
- low_limb = *--up;
- *--rp = high_limb | (low_limb >> tnc);
- high_limb = (low_limb << cnt);
- }
- *--rp = high_limb;
-
- return retval;
-}
-
-mp_limb_t
-mpn_rshift (mp_ptr rp, mp_srcptr up, mp_size_t n, unsigned int cnt)
-{
- mp_limb_t high_limb, low_limb;
- unsigned int tnc;
- mp_size_t i;
- mp_limb_t retval;
-
- assert (n >= 1);
- assert (cnt >= 1);
- assert (cnt < GMP_LIMB_BITS);
-
- tnc = GMP_LIMB_BITS - cnt;
- high_limb = *up++;
- retval = (high_limb << tnc);
- low_limb = high_limb >> cnt;
-
- for (i = n - 1; i != 0; i--)
- {
- high_limb = *up++;
- *rp++ = low_limb | (high_limb << tnc);
- low_limb = high_limb >> cnt;
- }
- *rp = low_limb;
-
- return retval;
-}
-
-
-/* MPN division interface. */
-mp_limb_t
-mpn_invert_3by2 (mp_limb_t u1, mp_limb_t u0)
-{
- mp_limb_t r, p, m;
- unsigned ul, uh;
- unsigned ql, qh;
-
- /* First, do a 2/1 inverse. */
- /* The inverse m is defined as floor( (B^2 - 1 - u1)/u1 ), so that 0 <
- * B^2 - (B + m) u1 <= u1 */
- assert (u1 >= GMP_LIMB_HIGHBIT);
-
- ul = u1 & GMP_LLIMB_MASK;
- uh = u1 >> (GMP_LIMB_BITS / 2);
-
- qh = ~u1 / uh;
- r = ((~u1 - (mp_limb_t) qh * uh) << (GMP_LIMB_BITS / 2)) | GMP_LLIMB_MASK;
-
- p = (mp_limb_t) qh * ul;
- /* Adjustment steps taken from udiv_qrnnd_c */
- if (r < p)
- {
- qh--;
- r += u1;
- if (r >= u1) /* i.e. we didn't get carry when adding to r */
- if (r < p)
- {
- qh--;
- r += u1;
- }
- }
- r -= p;
-
- /* Do a 3/2 division (with half limb size) */
- p = (r >> (GMP_LIMB_BITS / 2)) * qh + r;
- ql = (p >> (GMP_LIMB_BITS / 2)) + 1;
-
- /* By the 3/2 method, we don't need the high half limb. */
- r = (r << (GMP_LIMB_BITS / 2)) + GMP_LLIMB_MASK - ql * u1;
-
- if (r >= (p << (GMP_LIMB_BITS / 2)))
- {
- ql--;
- r += u1;
- }
- m = ((mp_limb_t) qh << (GMP_LIMB_BITS / 2)) + ql;
- if (r >= u1)
- {
- m++;
- r -= u1;
- }
-
- if (u0 > 0)
- {
- mp_limb_t th, tl;
- r = ~r;
- r += u0;
- if (r < u0)
- {
- m--;
- if (r >= u1)
- {
- m--;
- r -= u1;
- }
- r -= u1;
- }
- gmp_umul_ppmm (th, tl, u0, m);
- r += th;
- if (r < th)
- {
- m--;
- if (r > u1 || (r == u1 && tl > u0))
- m--;
- }
- }
-
- return m;
-}
-
-struct gmp_div_inverse
-{
- /* Normalization shift count. */
- unsigned shift;
- /* Normalized divisor (d0 unused for mpn_div_qr_1) */
- mp_limb_t d1, d0;
- /* Inverse, for 2/1 or 3/2. */
- mp_limb_t di;
-};
-
-static void
-mpn_div_qr_1_invert (struct gmp_div_inverse *inv, mp_limb_t d)
-{
- unsigned shift;
-
- assert (d > 0);
- gmp_clz (shift, d);
- inv->shift = shift;
- inv->d1 = d << shift;
- inv->di = mpn_invert_limb (inv->d1);
-}
-
-static void
-mpn_div_qr_2_invert (struct gmp_div_inverse *inv,
- mp_limb_t d1, mp_limb_t d0)
-{
- unsigned shift;
-
- assert (d1 > 0);
- gmp_clz (shift, d1);
- inv->shift = shift;
- if (shift > 0)
- {
- d1 = (d1 << shift) | (d0 >> (GMP_LIMB_BITS - shift));
- d0 <<= shift;
- }
- inv->d1 = d1;
- inv->d0 = d0;
- inv->di = mpn_invert_3by2 (d1, d0);
-}
-
-static void
-mpn_div_qr_invert (struct gmp_div_inverse *inv,
- mp_srcptr dp, mp_size_t dn)
-{
- assert (dn > 0);
-
- if (dn == 1)
- mpn_div_qr_1_invert (inv, dp[0]);
- else if (dn == 2)
- mpn_div_qr_2_invert (inv, dp[1], dp[0]);
- else
- {
- unsigned shift;
- mp_limb_t d1, d0;
-
- d1 = dp[dn-1];
- d0 = dp[dn-2];
- assert (d1 > 0);
- gmp_clz (shift, d1);
- inv->shift = shift;
- if (shift > 0)
- {
- d1 = (d1 << shift) | (d0 >> (GMP_LIMB_BITS - shift));
- d0 = (d0 << shift) | (dp[dn-3] >> (GMP_LIMB_BITS - shift));
- }
- inv->d1 = d1;
- inv->d0 = d0;
- inv->di = mpn_invert_3by2 (d1, d0);
- }
-}
-
-/* Not matching current public gmp interface, rather corresponding to
- the sbpi1_div_* functions. */
-static mp_limb_t
-mpn_div_qr_1_preinv (mp_ptr qp, mp_srcptr np, mp_size_t nn,
- const struct gmp_div_inverse *inv)
-{
- mp_limb_t d, di;
- mp_limb_t r;
- mp_ptr tp = NULL;
-
- if (inv->shift > 0)
- {
- tp = gmp_xalloc_limbs (nn);
- r = mpn_lshift (tp, np, nn, inv->shift);
- np = tp;
- }
- else
- r = 0;
-
- d = inv->d1;
- di = inv->di;
- while (nn-- > 0)
- {
- mp_limb_t q;
-
- gmp_udiv_qrnnd_preinv (q, r, r, np[nn], d, di);
- if (qp)
- qp[nn] = q;
- }
- if (inv->shift > 0)
- gmp_free (tp);
-
- return r >> inv->shift;
-}
-
-static mp_limb_t
-mpn_div_qr_1 (mp_ptr qp, mp_srcptr np, mp_size_t nn, mp_limb_t d)
-{
- assert (d > 0);
-
- /* Special case for powers of two. */
- if (d > 1 && (d & (d-1)) == 0)
- {
- unsigned shift;
- mp_limb_t r = np[0] & (d-1);
- gmp_ctz (shift, d);
- if (qp)
- mpn_rshift (qp, np, nn, shift);
-
- return r;
- }
- else
- {
- struct gmp_div_inverse inv;
- mpn_div_qr_1_invert (&inv, d);
- return mpn_div_qr_1_preinv (qp, np, nn, &inv);
- }
-}
-
-static void
-mpn_div_qr_2_preinv (mp_ptr qp, mp_ptr rp, mp_srcptr np, mp_size_t nn,
- const struct gmp_div_inverse *inv)
-{
- unsigned shift;
- mp_size_t i;
- mp_limb_t d1, d0, di, r1, r0;
- mp_ptr tp;
-
- assert (nn >= 2);
- shift = inv->shift;
- d1 = inv->d1;
- d0 = inv->d0;
- di = inv->di;
-
- if (shift > 0)
- {
- tp = gmp_xalloc_limbs (nn);
- r1 = mpn_lshift (tp, np, nn, shift);
- np = tp;
- }
- else
- r1 = 0;
-
- r0 = np[nn - 1];
-
- for (i = nn - 2; i >= 0; i--)
- {
- mp_limb_t n0, q;
- n0 = np[i];
- gmp_udiv_qr_3by2 (q, r1, r0, r1, r0, n0, d1, d0, di);
-
- if (qp)
- qp[i] = q;
- }
-
- if (shift > 0)
- {
- assert ((r0 << (GMP_LIMB_BITS - shift)) == 0);
- r0 = (r0 >> shift) | (r1 << (GMP_LIMB_BITS - shift));
- r1 >>= shift;
-
- gmp_free (tp);
- }
-
- rp[1] = r1;
- rp[0] = r0;
-}
-
-#if 0
-static void
-mpn_div_qr_2 (mp_ptr qp, mp_ptr rp, mp_srcptr np, mp_size_t nn,
- mp_limb_t d1, mp_limb_t d0)
-{
- struct gmp_div_inverse inv;
- assert (nn >= 2);
-
- mpn_div_qr_2_invert (&inv, d1, d0);
- mpn_div_qr_2_preinv (qp, rp, np, nn, &inv);
-}
-#endif
-
-static void
-mpn_div_qr_pi1 (mp_ptr qp,
- mp_ptr np, mp_size_t nn, mp_limb_t n1,
- mp_srcptr dp, mp_size_t dn,
- mp_limb_t dinv)
-{
- mp_size_t i;
-
- mp_limb_t d1, d0;
- mp_limb_t cy, cy1;
- mp_limb_t q;
-
- assert (dn > 2);
- assert (nn >= dn);
-
- d1 = dp[dn - 1];
- d0 = dp[dn - 2];
-
- assert ((d1 & GMP_LIMB_HIGHBIT) != 0);
- /* Iteration variable is the index of the q limb.
- *
- * We divide <n1, np[dn-1+i], np[dn-2+i], np[dn-3+i],..., np[i]>
- * by <d1, d0, dp[dn-3], ..., dp[0] >
- */
-
- for (i = nn - dn; i >= 0; i--)
- {
- mp_limb_t n0 = np[dn-1+i];
-
- if (n1 == d1 && n0 == d0)
- {
- q = GMP_LIMB_MAX;
- mpn_submul_1 (np+i, dp, dn, q);
- n1 = np[dn-1+i]; /* update n1, last loop's value will now be invalid */
- }
- else
- {
- gmp_udiv_qr_3by2 (q, n1, n0, n1, n0, np[dn-2+i], d1, d0, dinv);
-
- cy = mpn_submul_1 (np + i, dp, dn-2, q);
-
- cy1 = n0 < cy;
- n0 = n0 - cy;
- cy = n1 < cy1;
- n1 = n1 - cy1;
- np[dn-2+i] = n0;
-
- if (cy != 0)
- {
- n1 += d1 + mpn_add_n (np + i, np + i, dp, dn - 1);
- q--;
- }
- }
-
- if (qp)
- qp[i] = q;
- }
-
- np[dn - 1] = n1;
-}
-
-static void
-mpn_div_qr_preinv (mp_ptr qp, mp_ptr np, mp_size_t nn,
- mp_srcptr dp, mp_size_t dn,
- const struct gmp_div_inverse *inv)
-{
- assert (dn > 0);
- assert (nn >= dn);
-
- if (dn == 1)
- np[0] = mpn_div_qr_1_preinv (qp, np, nn, inv);
- else if (dn == 2)
- mpn_div_qr_2_preinv (qp, np, np, nn, inv);
- else
- {
- mp_limb_t nh;
- unsigned shift;
-
- assert (inv->d1 == dp[dn-1]);
- assert (inv->d0 == dp[dn-2]);
- assert ((inv->d1 & GMP_LIMB_HIGHBIT) != 0);
-
- shift = inv->shift;
- if (shift > 0)
- nh = mpn_lshift (np, np, nn, shift);
- else
- nh = 0;
-
- mpn_div_qr_pi1 (qp, np, nn, nh, dp, dn, inv->di);
-
- if (shift > 0)
- gmp_assert_nocarry (mpn_rshift (np, np, dn, shift));
- }
-}
-
-static void
-mpn_div_qr (mp_ptr qp, mp_ptr np, mp_size_t nn, mp_srcptr dp, mp_size_t dn)
-{
- struct gmp_div_inverse inv;
- mp_ptr tp = NULL;
-
- assert (dn > 0);
- assert (nn >= dn);
-
- mpn_div_qr_invert (&inv, dp, dn);
- if (dn > 2 && inv.shift > 0)
- {
- tp = gmp_xalloc_limbs (dn);
- gmp_assert_nocarry (mpn_lshift (tp, dp, dn, inv.shift));
- dp = tp;
- }
- mpn_div_qr_preinv (qp, np, nn, dp, dn, &inv);
- if (tp)
- gmp_free (tp);
-}
-
-
-/* MPN base conversion. */
-static unsigned
-mpn_base_power_of_two_p (unsigned b)
-{
- switch (b)
- {
- case 2: return 1;
- case 4: return 2;
- case 8: return 3;
- case 16: return 4;
- case 32: return 5;
- case 64: return 6;
- case 128: return 7;
- case 256: return 8;
- default: return 0;
- }
-}
-
-struct mpn_base_info
-{
- /* bb is the largest power of the base which fits in one limb, and
- exp is the corresponding exponent. */
- unsigned exp;
- mp_limb_t bb;
-};
-
-static void
-mpn_get_base_info (struct mpn_base_info *info, mp_limb_t b)
-{
- mp_limb_t m;
- mp_limb_t p;
- unsigned exp;
-
- m = GMP_LIMB_MAX / b;
- for (exp = 1, p = b; p <= m; exp++)
- p *= b;
-
- info->exp = exp;
- info->bb = p;
-}
-
-static mp_bitcnt_t
-mpn_limb_size_in_base_2 (mp_limb_t u)
-{
- unsigned shift;
-
- assert (u > 0);
- gmp_clz (shift, u);
- return GMP_LIMB_BITS - shift;
-}
-
-static size_t
-mpn_get_str_bits (unsigned char *sp, unsigned bits, mp_srcptr up, mp_size_t un)
-{
- unsigned char mask;
- size_t sn, j;
- mp_size_t i;
- int shift;
-
- sn = ((un - 1) * GMP_LIMB_BITS + mpn_limb_size_in_base_2 (up[un-1])
- + bits - 1) / bits;
-
- mask = (1U << bits) - 1;
-
- for (i = 0, j = sn, shift = 0; j-- > 0;)
- {
- unsigned char digit = up[i] >> shift;
-
- shift += bits;
-
- if (shift >= GMP_LIMB_BITS && ++i < un)
- {
- shift -= GMP_LIMB_BITS;
- digit |= up[i] << (bits - shift);
- }
- sp[j] = digit & mask;
- }
- return sn;
-}
-
-/* We generate digits from the least significant end, and reverse at
- the end. */
-static size_t
-mpn_limb_get_str (unsigned char *sp, mp_limb_t w,
- const struct gmp_div_inverse *binv)
-{
- mp_size_t i;
- for (i = 0; w > 0; i++)
- {
- mp_limb_t h, l, r;
-
- h = w >> (GMP_LIMB_BITS - binv->shift);
- l = w << binv->shift;
-
- gmp_udiv_qrnnd_preinv (w, r, h, l, binv->d1, binv->di);
- assert ( (r << (GMP_LIMB_BITS - binv->shift)) == 0);
- r >>= binv->shift;
-
- sp[i] = r;
- }
- return i;
-}
-
-static size_t
-mpn_get_str_other (unsigned char *sp,
- int base, const struct mpn_base_info *info,
- mp_ptr up, mp_size_t un)
-{
- struct gmp_div_inverse binv;
- size_t sn;
- size_t i;
-
- mpn_div_qr_1_invert (&binv, base);
-
- sn = 0;
-
- if (un > 1)
- {
- struct gmp_div_inverse bbinv;
- mpn_div_qr_1_invert (&bbinv, info->bb);
-
- do
- {
- mp_limb_t w;
- size_t done;
- w = mpn_div_qr_1_preinv (up, up, un, &bbinv);
- un -= (up[un-1] == 0);
- done = mpn_limb_get_str (sp + sn, w, &binv);
-
- for (sn += done; done < info->exp; done++)
- sp[sn++] = 0;
- }
- while (un > 1);
- }
- sn += mpn_limb_get_str (sp + sn, up[0], &binv);
-
- /* Reverse order */
- for (i = 0; 2*i + 1 < sn; i++)
- {
- unsigned char t = sp[i];
- sp[i] = sp[sn - i - 1];
- sp[sn - i - 1] = t;
- }
-
- return sn;
-}
-
-size_t
-mpn_get_str (unsigned char *sp, int base, mp_ptr up, mp_size_t un)
-{
- unsigned bits;
-
- assert (un > 0);
- assert (up[un-1] > 0);
-
- bits = mpn_base_power_of_two_p (base);
- if (bits)
- return mpn_get_str_bits (sp, bits, up, un);
- else
- {
- struct mpn_base_info info;
-
- mpn_get_base_info (&info, base);
- return mpn_get_str_other (sp, base, &info, up, un);
- }
-}
-
-static mp_size_t
-mpn_set_str_bits (mp_ptr rp, const unsigned char *sp, size_t sn,
- unsigned bits)
-{
- mp_size_t rn;
- size_t j;
- unsigned shift;
-
- for (j = sn, rn = 0, shift = 0; j-- > 0; )
- {
- if (shift == 0)
- {
- rp[rn++] = sp[j];
- shift += bits;
- }
- else
- {
- rp[rn-1] |= (mp_limb_t) sp[j] << shift;
- shift += bits;
- if (shift >= GMP_LIMB_BITS)
- {
- shift -= GMP_LIMB_BITS;
- if (shift > 0)
- rp[rn++] = (mp_limb_t) sp[j] >> (bits - shift);
- }
- }
- }
- rn = mpn_normalized_size (rp, rn);
- return rn;
-}
-
-static mp_size_t
-mpn_set_str_other (mp_ptr rp, const unsigned char *sp, size_t sn,
- mp_limb_t b, const struct mpn_base_info *info)
-{
- mp_size_t rn;
- mp_limb_t w;
- unsigned first;
- unsigned k;
- size_t j;
-
- first = 1 + (sn - 1) % info->exp;
-
- j = 0;
- w = sp[j++];
- for (k = 1; k < first; k++)
- w = w * b + sp[j++];
-
- rp[0] = w;
-
- for (rn = (w > 0); j < sn;)
- {
- mp_limb_t cy;
-
- w = sp[j++];
- for (k = 1; k < info->exp; k++)
- w = w * b + sp[j++];
-
- cy = mpn_mul_1 (rp, rp, rn, info->bb);
- cy += mpn_add_1 (rp, rp, rn, w);
- if (cy > 0)
- rp[rn++] = cy;
- }
- assert (j == sn);
-
- return rn;
-}
-
-mp_size_t
-mpn_set_str (mp_ptr rp, const unsigned char *sp, size_t sn, int base)
-{
- unsigned bits;
-
- if (sn == 0)
- return 0;
-
- bits = mpn_base_power_of_two_p (base);
- if (bits)
- return mpn_set_str_bits (rp, sp, sn, bits);
- else
- {
- struct mpn_base_info info;
-
- mpn_get_base_info (&info, base);
- return mpn_set_str_other (rp, sp, sn, base, &info);
- }
-}
-
-
-/* MPZ interface */
-void
-mpz_init (mpz_t r)
-{
- r->_mp_alloc = 1;
- r->_mp_size = 0;
- r->_mp_d = gmp_xalloc_limbs (1);
-}
-
-/* The utility of this function is a bit limited, since many functions
- assings the result variable using mpz_swap. */
-void
-mpz_init2 (mpz_t r, mp_bitcnt_t bits)
-{
- mp_size_t rn;
-
- bits -= (bits != 0); /* Round down, except if 0 */
- rn = 1 + bits / GMP_LIMB_BITS;
-
- r->_mp_alloc = rn;
- r->_mp_size = 0;
- r->_mp_d = gmp_xalloc_limbs (rn);
-}
-
-void
-mpz_clear (mpz_t r)
-{
- gmp_free (r->_mp_d);
-}
-
-static void *
-mpz_realloc (mpz_t r, mp_size_t size)
-{
- size = GMP_MAX (size, 1);
-
- r->_mp_d = gmp_xrealloc_limbs (r->_mp_d, size);
- r->_mp_alloc = size;
-
- if (GMP_ABS (r->_mp_size) > size)
- r->_mp_size = 0;
-
- return r->_mp_d;
-}
-
-/* Realloc for an mpz_t WHAT if it has less than NEEDED limbs. */
-#define MPZ_REALLOC(z,n) ((n) > (z)->_mp_alloc \
- ? mpz_realloc(z,n) \
- : (z)->_mp_d)
-
-/* MPZ assignment and basic conversions. */
-void
-mpz_set_si (mpz_t r, signed long int x)
-{
- if (x >= 0)
- mpz_set_ui (r, x);
- else /* (x < 0) */
- {
- r->_mp_size = -1;
- r->_mp_d[0] = GMP_NEG_CAST (unsigned long int, x);
- }
-}
-
-void
-mpz_set_ui (mpz_t r, unsigned long int x)
-{
- if (x > 0)
- {
- r->_mp_size = 1;
- r->_mp_d[0] = x;
- }
- else
- r->_mp_size = 0;
-}
-
-void
-mpz_set (mpz_t r, const mpz_t x)
-{
- /* Allow the NOP r == x */
- if (r != x)
- {
- mp_size_t n;
- mp_ptr rp;
-
- n = GMP_ABS (x->_mp_size);
- rp = MPZ_REALLOC (r, n);
-
- mpn_copyi (rp, x->_mp_d, n);
- r->_mp_size = x->_mp_size;
- }
-}
-
-void
-mpz_init_set_si (mpz_t r, signed long int x)
-{
- mpz_init (r);
- mpz_set_si (r, x);
-}
-
-void
-mpz_init_set_ui (mpz_t r, unsigned long int x)
-{
- mpz_init (r);
- mpz_set_ui (r, x);
-}
-
-void
-mpz_init_set (mpz_t r, const mpz_t x)
-{
- mpz_init (r);
- mpz_set (r, x);
-}
-
-int
-mpz_fits_slong_p (const mpz_t u)
-{
- mp_size_t us = u->_mp_size;
-
- if (us == 0)
- return 1;
- else if (us == 1)
- return u->_mp_d[0] < GMP_LIMB_HIGHBIT;
- else if (us == -1)
- return u->_mp_d[0] <= GMP_LIMB_HIGHBIT;
- else
- return 0;
-}
-
-int
-mpz_fits_ulong_p (const mpz_t u)
-{
- mp_size_t us = u->_mp_size;
-
- return us == 0 || us == 1;
-}
-
-long int
-mpz_get_si (const mpz_t u)
-{
- mp_size_t us = u->_mp_size;
-
- if (us > 0)
- return (long) (u->_mp_d[0] & ~GMP_LIMB_HIGHBIT);
- else if (us < 0)
- return (long) (- u->_mp_d[0] | GMP_LIMB_HIGHBIT);
- else
- return 0;
-}
-
-unsigned long int
-mpz_get_ui (const mpz_t u)
-{
- return u->_mp_size == 0 ? 0 : u->_mp_d[0];
-}
-
-size_t
-mpz_size (const mpz_t u)
-{
- return GMP_ABS (u->_mp_size);
-}
-
-mp_limb_t
-mpz_getlimbn (const mpz_t u, mp_size_t n)
-{
- if (n >= 0 && n < GMP_ABS (u->_mp_size))
- return u->_mp_d[n];
- else
- return 0;
-}
-
-
-/* Conversions and comparison to double. */
-void
-mpz_set_d (mpz_t r, double x)
-{
- int sign;
- mp_ptr rp;
- mp_size_t rn, i;
- double B;
- double Bi;
- mp_limb_t f;
-
- /* x != x is true when x is a NaN, and x == x * 0.5 is true when x is
- zero or infinity. */
- if (x == 0.0 || x != x || x == x * 0.5)
- {
- r->_mp_size = 0;
- return;
- }
-
- if (x < 0.0)
- {
- x = - x;
- sign = 1;
- }
- else
- sign = 0;
-
- if (x < 1.0)
- {
- r->_mp_size = 0;
- return;
- }
- B = 2.0 * (double) GMP_LIMB_HIGHBIT;
- Bi = 1.0 / B;
- for (rn = 1; x >= B; rn++)
- x *= Bi;
-
- rp = MPZ_REALLOC (r, rn);
-
- f = (mp_limb_t) x;
- x -= f;
- assert (x < 1.0);
- rp[rn-1] = f;
- for (i = rn-1; i-- > 0; )
- {
- x = B * x;
- f = (mp_limb_t) x;
- x -= f;
- assert (x < 1.0);
- rp[i] = f;
- }
-
- r->_mp_size = sign ? - rn : rn;
-}
-
-void
-mpz_init_set_d (mpz_t r, double x)
-{
- mpz_init (r);
- mpz_set_d (r, x);
-}
-
-double
-mpz_get_d (const mpz_t u)
-{
- mp_size_t un;
- double x;
- double B = 2.0 * (double) GMP_LIMB_HIGHBIT;
-
- un = GMP_ABS (u->_mp_size);
-
- if (un == 0)
- return 0.0;
-
- x = u->_mp_d[--un];
- while (un > 0)
- x = B*x + u->_mp_d[--un];
-
- if (u->_mp_size < 0)
- x = -x;
-
- return x;
-}
-
-int
-mpz_cmpabs_d (const mpz_t x, double d)
-{
- mp_size_t xn;
- double B, Bi;
- mp_size_t i;
-
- xn = x->_mp_size;
- d = GMP_ABS (d);
-
- if (xn != 0)
- {
- xn = GMP_ABS (xn);
-
- B = 2.0 * (double) GMP_LIMB_HIGHBIT;
- Bi = 1.0 / B;
-
- /* Scale d so it can be compared with the top limb. */
- for (i = 1; i < xn; i++)
- d *= Bi;
-
- if (d >= B)
- return -1;
-
- /* Compare floor(d) to top limb, subtract and cancel when equal. */
- for (i = xn; i-- > 0;)
- {
- mp_limb_t f, xl;
-
- f = (mp_limb_t) d;
- xl = x->_mp_d[i];
- if (xl > f)
- return 1;
- else if (xl < f)
- return -1;
- d = B * (d - f);
- }
- }
- return - (d > 0.0);
-}
-
-int
-mpz_cmp_d (const mpz_t x, double d)
-{
- if (x->_mp_size < 0)
- {
- if (d >= 0.0)
- return -1;
- else
- return -mpz_cmpabs_d (x, d);
- }
- else
- {
- if (d < 0.0)
- return 1;
- else
- return mpz_cmpabs_d (x, d);
- }
-}
-
-
-/* MPZ comparisons and the like. */
-int
-mpz_sgn (const mpz_t u)
-{
- mp_size_t usize = u->_mp_size;
-
- if (usize > 0)
- return 1;
- else if (usize < 0)
- return -1;
- else
- return 0;
-}
-
-int
-mpz_cmp_si (const mpz_t u, long v)
-{
- mp_size_t usize = u->_mp_size;
-
- if (usize < -1)
- return -1;
- else if (v >= 0)
- return mpz_cmp_ui (u, v);
- else if (usize >= 0)
- return 1;
- else /* usize == -1 */
- {
- mp_limb_t ul = u->_mp_d[0];
- if ((mp_limb_t)GMP_NEG_CAST (unsigned long int, v) < ul)
- return -1;
- else if ( (mp_limb_t)GMP_NEG_CAST (unsigned long int, v) > ul)
- return 1;
- }
- return 0;
-}
-
-int
-mpz_cmp_ui (const mpz_t u, unsigned long v)
-{
- mp_size_t usize = u->_mp_size;
-
- if (usize > 1)
- return 1;
- else if (usize < 0)
- return -1;
- else
- {
- mp_limb_t ul = (usize > 0) ? u->_mp_d[0] : 0;
- if (ul > v)
- return 1;
- else if (ul < v)
- return -1;
- }
- return 0;
-}
-
-int
-mpz_cmp (const mpz_t a, const mpz_t b)
-{
- mp_size_t asize = a->_mp_size;
- mp_size_t bsize = b->_mp_size;
-
- if (asize > bsize)
- return 1;
- else if (asize < bsize)
- return -1;
- else if (asize > 0)
- return mpn_cmp (a->_mp_d, b->_mp_d, asize);
- else if (asize < 0)
- return -mpn_cmp (a->_mp_d, b->_mp_d, -asize);
- else
- return 0;
-}
-
-int
-mpz_cmpabs_ui (const mpz_t u, unsigned long v)
-{
- mp_size_t un = GMP_ABS (u->_mp_size);
- mp_limb_t ul;
-
- if (un > 1)
- return 1;
-
- ul = (un == 1) ? u->_mp_d[0] : 0;
-
- if (ul > v)
- return 1;
- else if (ul < v)
- return -1;
- else
- return 0;
-}
-
-int
-mpz_cmpabs (const mpz_t u, const mpz_t v)
-{
- return mpn_cmp4 (u->_mp_d, GMP_ABS (u->_mp_size),
- v->_mp_d, GMP_ABS (v->_mp_size));
-}
-
-void
-mpz_abs (mpz_t r, const mpz_t u)
-{
- if (r != u)
- mpz_set (r, u);
-
- r->_mp_size = GMP_ABS (r->_mp_size);
-}
-
-void
-mpz_neg (mpz_t r, const mpz_t u)
-{
- if (r != u)
- mpz_set (r, u);
-
- r->_mp_size = -r->_mp_size;
-}
-
-void
-mpz_swap (mpz_t u, mpz_t v)
-{
- MP_SIZE_T_SWAP (u->_mp_size, v->_mp_size);
- MP_SIZE_T_SWAP (u->_mp_alloc, v->_mp_alloc);
- MP_PTR_SWAP (u->_mp_d, v->_mp_d);
-}
-
-
-/* MPZ addition and subtraction */
-
-/* Adds to the absolute value. Returns new size, but doesn't store it. */
-static mp_size_t
-mpz_abs_add_ui (mpz_t r, const mpz_t a, unsigned long b)
-{
- mp_size_t an;
- mp_ptr rp;
- mp_limb_t cy;
-
- an = GMP_ABS (a->_mp_size);
- if (an == 0)
- {
- r->_mp_d[0] = b;
- return b > 0;
- }
-
- rp = MPZ_REALLOC (r, an + 1);
-
- cy = mpn_add_1 (rp, a->_mp_d, an, b);
- rp[an] = cy;
- an += (cy > 0);
-
- return an;
-}
-
-/* Subtract from the absolute value. Returns new size, (or -1 on underflow),
- but doesn't store it. */
-static mp_size_t
-mpz_abs_sub_ui (mpz_t r, const mpz_t a, unsigned long b)
-{
- mp_size_t an = GMP_ABS (a->_mp_size);
- mp_ptr rp = MPZ_REALLOC (r, an);
-
- if (an == 0)
- {
- rp[0] = b;
- return -(b > 0);
- }
- else if (an == 1 && a->_mp_d[0] < b)
- {
- rp[0] = b - a->_mp_d[0];
- return -1;
- }
- else
- {
- gmp_assert_nocarry (mpn_sub_1 (rp, a->_mp_d, an, b));
- return mpn_normalized_size (rp, an);
- }
-}
-
-void
-mpz_add_ui (mpz_t r, const mpz_t a, unsigned long b)
-{
- if (a->_mp_size >= 0)
- r->_mp_size = mpz_abs_add_ui (r, a, b);
- else
- r->_mp_size = -mpz_abs_sub_ui (r, a, b);
-}
-
-void
-mpz_sub_ui (mpz_t r, const mpz_t a, unsigned long b)
-{
- if (a->_mp_size < 0)
- r->_mp_size = -mpz_abs_add_ui (r, a, b);
- else
- r->_mp_size = mpz_abs_sub_ui (r, a, b);
-}
-
-void
-mpz_ui_sub (mpz_t r, unsigned long a, const mpz_t b)
-{
- if (b->_mp_size < 0)
- r->_mp_size = mpz_abs_add_ui (r, b, a);
- else
- r->_mp_size = -mpz_abs_sub_ui (r, b, a);
-}
-
-static mp_size_t
-mpz_abs_add (mpz_t r, const mpz_t a, const mpz_t b)
-{
- mp_size_t an = GMP_ABS (a->_mp_size);
- mp_size_t bn = GMP_ABS (b->_mp_size);
- mp_size_t rn;
- mp_ptr rp;
- mp_limb_t cy;
-
- rn = GMP_MAX (an, bn);
- rp = MPZ_REALLOC (r, rn + 1);
- if (an >= bn)
- cy = mpn_add (rp, a->_mp_d, an, b->_mp_d, bn);
- else
- cy = mpn_add (rp, b->_mp_d, bn, a->_mp_d, an);
-
- rp[rn] = cy;
-
- return rn + (cy > 0);
-}
-
-static mp_size_t
-mpz_abs_sub (mpz_t r, const mpz_t a, const mpz_t b)
-{
- mp_size_t an = GMP_ABS (a->_mp_size);
- mp_size_t bn = GMP_ABS (b->_mp_size);
- int cmp;
- mp_ptr rp;
-
- cmp = mpn_cmp4 (a->_mp_d, an, b->_mp_d, bn);
- if (cmp > 0)
- {
- rp = MPZ_REALLOC (r, an);
- gmp_assert_nocarry (mpn_sub (rp, a->_mp_d, an, b->_mp_d, bn));
- return mpn_normalized_size (rp, an);
- }
- else if (cmp < 0)
- {
- rp = MPZ_REALLOC (r, bn);
- gmp_assert_nocarry (mpn_sub (rp, b->_mp_d, bn, a->_mp_d, an));
- return -mpn_normalized_size (rp, bn);
- }
- else
- return 0;
-}
-
-void
-mpz_add (mpz_t r, const mpz_t a, const mpz_t b)
-{
- mp_size_t rn;
-
- if ( (a->_mp_size ^ b->_mp_size) >= 0)
- rn = mpz_abs_add (r, a, b);
- else
- rn = mpz_abs_sub (r, a, b);
-
- r->_mp_size = a->_mp_size >= 0 ? rn : - rn;
-}
-
-void
-mpz_sub (mpz_t r, const mpz_t a, const mpz_t b)
-{
- mp_size_t rn;
-
- if ( (a->_mp_size ^ b->_mp_size) >= 0)
- rn = mpz_abs_sub (r, a, b);
- else
- rn = mpz_abs_add (r, a, b);
-
- r->_mp_size = a->_mp_size >= 0 ? rn : - rn;
-}
-
-
-/* MPZ multiplication */
-void
-mpz_mul_si (mpz_t r, const mpz_t u, long int v)
-{
- if (v < 0)
- {
- mpz_mul_ui (r, u, GMP_NEG_CAST (unsigned long int, v));
- mpz_neg (r, r);
- }
- else
- mpz_mul_ui (r, u, (unsigned long int) v);
-}
-
-void
-mpz_mul_ui (mpz_t r, const mpz_t u, unsigned long int v)
-{
- mp_size_t un;
- mpz_t t;
- mp_ptr tp;
- mp_limb_t cy;
-
- un = GMP_ABS (u->_mp_size);
-
- if (un == 0 || v == 0)
- {
- r->_mp_size = 0;
- return;
- }
-
- mpz_init2 (t, (un + 1) * GMP_LIMB_BITS);
-
- tp = t->_mp_d;
- cy = mpn_mul_1 (tp, u->_mp_d, un, v);
- tp[un] = cy;
-
- t->_mp_size = un + (cy > 0);
- if (u->_mp_size < 0)
- t->_mp_size = - t->_mp_size;
-
- mpz_swap (r, t);
- mpz_clear (t);
-}
-
-void
-mpz_mul (mpz_t r, const mpz_t u, const mpz_t v)
-{
- int sign;
- mp_size_t un, vn, rn;
- mpz_t t;
- mp_ptr tp;
-
- un = GMP_ABS (u->_mp_size);
- vn = GMP_ABS (v->_mp_size);
-
- if (un == 0 || vn == 0)
- {
- r->_mp_size = 0;
- return;
- }
-
- sign = (u->_mp_size ^ v->_mp_size) < 0;
-
- mpz_init2 (t, (un + vn) * GMP_LIMB_BITS);
-
- tp = t->_mp_d;
- if (un >= vn)
- mpn_mul (tp, u->_mp_d, un, v->_mp_d, vn);
- else
- mpn_mul (tp, v->_mp_d, vn, u->_mp_d, un);
-
- rn = un + vn;
- rn -= tp[rn-1] == 0;
-
- t->_mp_size = sign ? - rn : rn;
- mpz_swap (r, t);
- mpz_clear (t);
-}
-
-void
-mpz_mul_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t bits)
-{
- mp_size_t un, rn;
- mp_size_t limbs;
- unsigned shift;
- mp_ptr rp;
-
- un = GMP_ABS (u->_mp_size);
- if (un == 0)
- {
- r->_mp_size = 0;
- return;
- }
-
- limbs = bits / GMP_LIMB_BITS;
- shift = bits % GMP_LIMB_BITS;
-
- rn = un + limbs + (shift > 0);
- rp = MPZ_REALLOC (r, rn);
- if (shift > 0)
- {
- mp_limb_t cy = mpn_lshift (rp + limbs, u->_mp_d, un, shift);
- rp[rn-1] = cy;
- rn -= (cy == 0);
- }
- else
- mpn_copyd (rp + limbs, u->_mp_d, un);
-
- while (limbs > 0)
- rp[--limbs] = 0;
-
- r->_mp_size = (u->_mp_size < 0) ? - rn : rn;
-}
-
-
-/* MPZ division */
-enum mpz_div_round_mode { GMP_DIV_FLOOR, GMP_DIV_CEIL, GMP_DIV_TRUNC };
-
-/* Allows q or r to be zero. Returns 1 iff remainder is non-zero. */
-static int
-mpz_div_qr (mpz_t q, mpz_t r,
- const mpz_t n, const mpz_t d, enum mpz_div_round_mode mode)
-{
- mp_size_t ns, ds, nn, dn, qs;
- ns = n->_mp_size;
- ds = d->_mp_size;
-
- if (ds == 0)
- gmp_die("mpz_div_qr: Divide by zero.");
-
- if (ns == 0)
- {
- if (q)
- q->_mp_size = 0;
- if (r)
- r->_mp_size = 0;
- return 0;
- }
-
- nn = GMP_ABS (ns);
- dn = GMP_ABS (ds);
-
- qs = ds ^ ns;
-
- if (nn < dn)
- {
- if (mode == GMP_DIV_CEIL && qs >= 0)
- {
- /* q = 1, r = n - d */
- if (r)
- mpz_sub (r, n, d);
- if (q)
- mpz_set_ui (q, 1);
- }
- else if (mode == GMP_DIV_FLOOR && qs < 0)
- {
- /* q = -1, r = n + d */
- if (r)
- mpz_add (r, n, d);
- if (q)
- mpz_set_si (q, -1);
- }
- else
- {
- /* q = 0, r = d */
- if (r)
- mpz_set (r, n);
- if (q)
- q->_mp_size = 0;
- }
- return 1;
- }
- else
- {
- mp_ptr np, qp;
- mp_size_t qn, rn;
- mpz_t tq, tr;
-
- mpz_init (tr);
- mpz_set (tr, n);
- np = tr->_mp_d;
-
- qn = nn - dn + 1;
-
- if (q)
- {
- mpz_init2 (tq, qn * GMP_LIMB_BITS);
- qp = tq->_mp_d;
- }
- else
- qp = NULL;
-
- mpn_div_qr (qp, np, nn, d->_mp_d, dn);
-
- if (qp)
- {
- qn -= (qp[qn-1] == 0);
-
- tq->_mp_size = qs < 0 ? -qn : qn;
- }
- rn = mpn_normalized_size (np, dn);
- tr->_mp_size = ns < 0 ? - rn : rn;
-
- if (mode == GMP_DIV_FLOOR && qs < 0 && rn != 0)
- {
- if (q)
- mpz_sub_ui (tq, tq, 1);
- if (r)
- mpz_add (tr, tr, d);
- }
- else if (mode == GMP_DIV_CEIL && qs >= 0 && rn != 0)
- {
- if (q)
- mpz_add_ui (tq, tq, 1);
- if (r)
- mpz_sub (tr, tr, d);
- }
-
- if (q)
- {
- mpz_swap (tq, q);
- mpz_clear (tq);
- }
- if (r)
- mpz_swap (tr, r);
-
- mpz_clear (tr);
-
- return rn != 0;
- }
-}
-
-void
-mpz_cdiv_qr (mpz_t q, mpz_t r, const mpz_t n, const mpz_t d)
-{
- mpz_div_qr (q, r, n, d, GMP_DIV_CEIL);
-}
-
-void
-mpz_fdiv_qr (mpz_t q, mpz_t r, const mpz_t n, const mpz_t d)
-{
- mpz_div_qr (q, r, n, d, GMP_DIV_FLOOR);
-}
-
-void
-mpz_tdiv_qr (mpz_t q, mpz_t r, const mpz_t n, const mpz_t d)
-{
- mpz_div_qr (q, r, n, d, GMP_DIV_TRUNC);
-}
-
-void
-mpz_cdiv_q (mpz_t q, const mpz_t n, const mpz_t d)
-{
- mpz_div_qr (q, NULL, n, d, GMP_DIV_CEIL);
-}
-
-void
-mpz_fdiv_q (mpz_t q, const mpz_t n, const mpz_t d)
-{
- mpz_div_qr (q, NULL, n, d, GMP_DIV_FLOOR);
-}
-
-void
-mpz_tdiv_q (mpz_t q, const mpz_t n, const mpz_t d)
-{
- mpz_div_qr (q, NULL, n, d, GMP_DIV_TRUNC);
-}
-
-void
-mpz_cdiv_r (mpz_t r, const mpz_t n, const mpz_t d)
-{
- mpz_div_qr (NULL, r, n, d, GMP_DIV_CEIL);
-}
-
-void
-mpz_fdiv_r (mpz_t r, const mpz_t n, const mpz_t d)
-{
- mpz_div_qr (NULL, r, n, d, GMP_DIV_FLOOR);
-}
-
-void
-mpz_tdiv_r (mpz_t r, const mpz_t n, const mpz_t d)
-{
- mpz_div_qr (NULL, r, n, d, GMP_DIV_TRUNC);
-}
-
-void
-mpz_mod (mpz_t r, const mpz_t n, const mpz_t d)
-{
- if (d->_mp_size >= 0)
- mpz_div_qr (NULL, r, n, d, GMP_DIV_FLOOR);
- else
- mpz_div_qr (NULL, r, n, d, GMP_DIV_CEIL);
-}
-
-static void
-mpz_div_q_2exp (mpz_t q, const mpz_t u, mp_bitcnt_t bit_index,
- enum mpz_div_round_mode mode)
-{
- mp_size_t un, qn;
- mp_size_t limb_cnt;
- mp_ptr qp;
- mp_limb_t adjust;
-
- un = u->_mp_size;
- if (un == 0)
- {
- q->_mp_size = 0;
- return;
- }
- limb_cnt = bit_index / GMP_LIMB_BITS;
- qn = GMP_ABS (un) - limb_cnt;
- bit_index %= GMP_LIMB_BITS;
-
- if (mode == ((un > 0) ? GMP_DIV_CEIL : GMP_DIV_FLOOR)) /* un != 0 here. */
- /* Note: Below, the final indexing at limb_cnt is valid because at
- that point we have qn > 0. */
- adjust = (qn <= 0
- || !mpn_zero_p (u->_mp_d, limb_cnt)
- || (u->_mp_d[limb_cnt]
- & (((mp_limb_t) 1 << bit_index) - 1)));
- else
- adjust = 0;
-
- if (qn <= 0)
- qn = 0;
-
- else
- {
- qp = MPZ_REALLOC (q, qn);
-
- if (bit_index != 0)
- {
- mpn_rshift (qp, u->_mp_d + limb_cnt, qn, bit_index);
- qn -= qp[qn - 1] == 0;
- }
- else
- {
- mpn_copyi (qp, u->_mp_d + limb_cnt, qn);
- }
- }
-
- q->_mp_size = qn;
-
- mpz_add_ui (q, q, adjust);
- if (un < 0)
- mpz_neg (q, q);
-}
-
-static void
-mpz_div_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t bit_index,
- enum mpz_div_round_mode mode)
-{
- mp_size_t us, un, rn;
- mp_ptr rp;
- mp_limb_t mask;
-
- us = u->_mp_size;
- if (us == 0 || bit_index == 0)
- {
- r->_mp_size = 0;
- return;
- }
- rn = (bit_index + GMP_LIMB_BITS - 1) / GMP_LIMB_BITS;
- assert (rn > 0);
-
- rp = MPZ_REALLOC (r, rn);
- un = GMP_ABS (us);
-
- mask = GMP_LIMB_MAX >> (rn * GMP_LIMB_BITS - bit_index);
-
- if (rn > un)
- {
- /* Quotient (with truncation) is zero, and remainder is
- non-zero */
- if (mode == ((us > 0) ? GMP_DIV_CEIL : GMP_DIV_FLOOR)) /* us != 0 here. */
- {
- /* Have to negate and sign extend. */
- mp_size_t i;
- mp_limb_t cy;
-
- for (cy = 1, i = 0; i < un; i++)
- {
- mp_limb_t s = ~u->_mp_d[i] + cy;
- cy = s < cy;
- rp[i] = s;
- }
- assert (cy == 0);
- for (; i < rn - 1; i++)
- rp[i] = GMP_LIMB_MAX;
-
- rp[rn-1] = mask;
- us = -us;
- }
- else
- {
- /* Just copy */
- if (r != u)
- mpn_copyi (rp, u->_mp_d, un);
-
- rn = un;
- }
- }
- else
- {
- if (r != u)
- mpn_copyi (rp, u->_mp_d, rn - 1);
-
- rp[rn-1] = u->_mp_d[rn-1] & mask;
-
- if (mode == ((us > 0) ? GMP_DIV_CEIL : GMP_DIV_FLOOR)) /* us != 0 here. */
- {
- /* If r != 0, compute 2^{bit_count} - r. */
- mp_size_t i;
-
- for (i = 0; i < rn && rp[i] == 0; i++)
- ;
- if (i < rn)
- {
- /* r > 0, need to flip sign. */
- rp[i] = ~rp[i] + 1;
- for (i++; i < rn; i++)
- rp[i] = ~rp[i];
-
- rp[rn-1] &= mask;
-
- /* us is not used for anything else, so we can modify it
- here to indicate flipped sign. */
- us = -us;
- }
- }
- }
- rn = mpn_normalized_size (rp, rn);
- r->_mp_size = us < 0 ? -rn : rn;
-}
-
-void
-mpz_cdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
-{
- mpz_div_q_2exp (r, u, cnt, GMP_DIV_CEIL);
-}
-
-void
-mpz_fdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
-{
- mpz_div_q_2exp (r, u, cnt, GMP_DIV_FLOOR);
-}
-
-void
-mpz_tdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
-{
- mpz_div_q_2exp (r, u, cnt, GMP_DIV_TRUNC);
-}
-
-void
-mpz_cdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
-{
- mpz_div_r_2exp (r, u, cnt, GMP_DIV_CEIL);
-}
-
-void
-mpz_fdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
-{
- mpz_div_r_2exp (r, u, cnt, GMP_DIV_FLOOR);
-}
-
-void
-mpz_tdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
-{
- mpz_div_r_2exp (r, u, cnt, GMP_DIV_TRUNC);
-}
-
-void
-mpz_divexact (mpz_t q, const mpz_t n, const mpz_t d)
-{
- gmp_assert_nocarry (mpz_div_qr (q, NULL, n, d, GMP_DIV_TRUNC));
-}
-
-int
-mpz_divisible_p (const mpz_t n, const mpz_t d)
-{
- return mpz_div_qr (NULL, NULL, n, d, GMP_DIV_TRUNC) == 0;
-}
-
-static unsigned long
-mpz_div_qr_ui (mpz_t q, mpz_t r,
- const mpz_t n, unsigned long d, enum mpz_div_round_mode mode)
-{
- mp_size_t ns, qn;
- mp_ptr qp;
- mp_limb_t rl;
- mp_size_t rs;
-
- ns = n->_mp_size;
- if (ns == 0)
- {
- if (q)
- q->_mp_size = 0;
- if (r)
- r->_mp_size = 0;
- return 0;
- }
-
- qn = GMP_ABS (ns);
- if (q)
- qp = MPZ_REALLOC (q, qn);
- else
- qp = NULL;
-
- rl = mpn_div_qr_1 (qp, n->_mp_d, qn, d);
- assert (rl < d);
-
- rs = rl > 0;
- rs = (ns < 0) ? -rs : rs;
-
- if (rl > 0 && ( (mode == GMP_DIV_FLOOR && ns < 0)
- || (mode == GMP_DIV_CEIL && ns >= 0)))
- {
- if (q)
- gmp_assert_nocarry (mpn_add_1 (qp, qp, qn, 1));
- rl = d - rl;
- rs = -rs;
- }
-
- if (r)
- {
- r->_mp_d[0] = rl;
- r->_mp_size = rs;
- }
- if (q)
- {
- qn -= (qp[qn-1] == 0);
- assert (qn == 0 || qp[qn-1] > 0);
-
- q->_mp_size = (ns < 0) ? - qn : qn;
- }
-
- return rl;
-}
-
-unsigned long
-mpz_cdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d)
-{
- return mpz_div_qr_ui (q, r, n, d, GMP_DIV_CEIL);
-}
-
-unsigned long
-mpz_fdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d)
-{
- return mpz_div_qr_ui (q, r, n, d, GMP_DIV_FLOOR);
-}
-
-unsigned long
-mpz_tdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d)
-{
- return mpz_div_qr_ui (q, r, n, d, GMP_DIV_TRUNC);
-}
-
-unsigned long
-mpz_cdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d)
-{
- return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_CEIL);
-}
-
-unsigned long
-mpz_fdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d)
-{
- return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_FLOOR);
-}
-
-unsigned long
-mpz_tdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d)
-{
- return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_TRUNC);
-}
-
-unsigned long
-mpz_cdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d)
-{
- return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_CEIL);
-}
-unsigned long
-mpz_fdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d)
-{
- return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_FLOOR);
-}
-unsigned long
-mpz_tdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d)
-{
- return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_TRUNC);
-}
-
-unsigned long
-mpz_cdiv_ui (const mpz_t n, unsigned long d)
-{
- return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_CEIL);
-}
-
-unsigned long
-mpz_fdiv_ui (const mpz_t n, unsigned long d)
-{
- return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_FLOOR);
-}
-
-unsigned long
-mpz_tdiv_ui (const mpz_t n, unsigned long d)
-{
- return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_TRUNC);
-}
-
-unsigned long
-mpz_mod_ui (mpz_t r, const mpz_t n, unsigned long d)
-{
- return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_FLOOR);
-}
-
-void
-mpz_divexact_ui (mpz_t q, const mpz_t n, unsigned long d)
-{
- gmp_assert_nocarry (mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_TRUNC));
-}
-
-int
-mpz_divisible_ui_p (const mpz_t n, unsigned long d)
-{
- return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_TRUNC) == 0;
-}
-
-
-/* GCD */
-static mp_limb_t
-mpn_gcd_11 (mp_limb_t u, mp_limb_t v)
-{
- unsigned shift;
-
- assert ( (u | v) > 0);
-
- if (u == 0)
- return v;
- else if (v == 0)
- return u;
-
- gmp_ctz (shift, u | v);
-
- u >>= shift;
- v >>= shift;
-
- if ( (u & 1) == 0)
- MP_LIMB_T_SWAP (u, v);
-
- while ( (v & 1) == 0)
- v >>= 1;
-
- while (u != v)
- {
- if (u > v)
- {
- u -= v;
- do
- u >>= 1;
- while ( (u & 1) == 0);
- }
- else
- {
- v -= u;
- do
- v >>= 1;
- while ( (v & 1) == 0);
- }
- }
- return u << shift;
-}
-
-unsigned long
-mpz_gcd_ui (mpz_t g, const mpz_t u, unsigned long v)
-{
- mp_size_t un;
-
- if (v == 0)
- {
- if (g)
- mpz_abs (g, u);
- }
- else
- {
- un = GMP_ABS (u->_mp_size);
- if (un != 0)
- v = mpn_gcd_11 (mpn_div_qr_1 (NULL, u->_mp_d, un, v), v);
-
- if (g)
- mpz_set_ui (g, v);
- }
-
- return v;
-}
-
-static mp_bitcnt_t
-mpz_make_odd (mpz_t r, const mpz_t u)
-{
- mp_size_t un, rn, i;
- mp_ptr rp;
- unsigned shift;
-
- un = GMP_ABS (u->_mp_size);
- assert (un > 0);
-
- for (i = 0; u->_mp_d[i] == 0; i++)
- ;
-
- gmp_ctz (shift, u->_mp_d[i]);
-
- rn = un - i;
- rp = MPZ_REALLOC (r, rn);
- if (shift > 0)
- {
- mpn_rshift (rp, u->_mp_d + i, rn, shift);
- rn -= (rp[rn-1] == 0);
- }
- else
- mpn_copyi (rp, u->_mp_d + i, rn);
-
- r->_mp_size = rn;
- return i * GMP_LIMB_BITS + shift;
-}
-
-void
-mpz_gcd (mpz_t g, const mpz_t u, const mpz_t v)
-{
- mpz_t tu, tv;
- mp_bitcnt_t uz, vz, gz;
-
- if (u->_mp_size == 0)
- {
- mpz_abs (g, v);
- return;
- }
- if (v->_mp_size == 0)
- {
- mpz_abs (g, u);
- return;
- }
-
- mpz_init (tu);
- mpz_init (tv);
-
- uz = mpz_make_odd (tu, u);
- vz = mpz_make_odd (tv, v);
- gz = GMP_MIN (uz, vz);
-
- if (tu->_mp_size < tv->_mp_size)
- mpz_swap (tu, tv);
-
- mpz_tdiv_r (tu, tu, tv);
- if (tu->_mp_size == 0)
- {
- mpz_swap (g, tv);
- }
- else
- for (;;)
- {
- int c;
-
- mpz_make_odd (tu, tu);
- c = mpz_cmp (tu, tv);
- if (c == 0)
- {
- mpz_swap (g, tu);
- break;
- }
- if (c < 0)
- mpz_swap (tu, tv);
-
- if (tv->_mp_size == 1)
- {
- mp_limb_t vl = tv->_mp_d[0];
- mp_limb_t ul = mpz_tdiv_ui (tu, vl);
- mpz_set_ui (g, mpn_gcd_11 (ul, vl));
- break;
- }
- mpz_sub (tu, tu, tv);
- }
- mpz_clear (tu);
- mpz_clear (tv);
- mpz_mul_2exp (g, g, gz);
-}
-
-void
-mpz_gcdext (mpz_t g, mpz_t s, mpz_t t, const mpz_t u, const mpz_t v)
-{
- mpz_t tu, tv, s0, s1, t0, t1;
- mp_bitcnt_t uz, vz, gz;
- mp_bitcnt_t power;
-
- if (u->_mp_size == 0)
- {
- /* g = 0 u + sgn(v) v */
- signed long sign = mpz_sgn (v);
- mpz_abs (g, v);
- if (s)
- mpz_set_ui (s, 0);
- if (t)
- mpz_set_si (t, sign);
- return;
- }
-
- if (v->_mp_size == 0)
- {
- /* g = sgn(u) u + 0 v */
- signed long sign = mpz_sgn (u);
- mpz_abs (g, u);
- if (s)
- mpz_set_si (s, sign);
- if (t)
- mpz_set_ui (t, 0);
- return;
- }
-
- mpz_init (tu);
- mpz_init (tv);
- mpz_init (s0);
- mpz_init (s1);
- mpz_init (t0);
- mpz_init (t1);
-
- uz = mpz_make_odd (tu, u);
- vz = mpz_make_odd (tv, v);
- gz = GMP_MIN (uz, vz);
-
- uz -= gz;
- vz -= gz;
-
- /* Cofactors corresponding to odd gcd. gz handled later. */
- if (tu->_mp_size < tv->_mp_size)
- {
- mpz_swap (tu, tv);
- MPZ_SRCPTR_SWAP (u, v);
- MPZ_PTR_SWAP (s, t);
- MP_BITCNT_T_SWAP (uz, vz);
- }
-
- /* Maintain
- *
- * u = t0 tu + t1 tv
- * v = s0 tu + s1 tv
- *
- * where u and v denote the inputs with common factors of two
- * eliminated, and det (s0, t0; s1, t1) = 2^p. Then
- *
- * 2^p tu = s1 u - t1 v
- * 2^p tv = -s0 u + t0 v
- */
-
- /* After initial division, tu = q tv + tu', we have
- *
- * u = 2^uz (tu' + q tv)
- * v = 2^vz tv
- *
- * or
- *
- * t0 = 2^uz, t1 = 2^uz q
- * s0 = 0, s1 = 2^vz
- */
-
- mpz_setbit (t0, uz);
- mpz_tdiv_qr (t1, tu, tu, tv);
- mpz_mul_2exp (t1, t1, uz);
-
- mpz_setbit (s1, vz);
- power = uz + vz;
-
- if (tu->_mp_size > 0)
- {
- mp_bitcnt_t shift;
- shift = mpz_make_odd (tu, tu);
- mpz_mul_2exp (t0, t0, shift);
- mpz_mul_2exp (s0, s0, shift);
- power += shift;
-
- for (;;)
- {
- int c;
- c = mpz_cmp (tu, tv);
- if (c == 0)
- break;
-
- if (c < 0)
- {
- /* tv = tv' + tu
- *
- * u = t0 tu + t1 (tv' + tu) = (t0 + t1) tu + t1 tv'
- * v = s0 tu + s1 (tv' + tu) = (s0 + s1) tu + s1 tv' */
-
- mpz_sub (tv, tv, tu);
- mpz_add (t0, t0, t1);
- mpz_add (s0, s0, s1);
-
- shift = mpz_make_odd (tv, tv);
- mpz_mul_2exp (t1, t1, shift);
- mpz_mul_2exp (s1, s1, shift);
- }
- else
- {
- mpz_sub (tu, tu, tv);
- mpz_add (t1, t0, t1);
- mpz_add (s1, s0, s1);
-
- shift = mpz_make_odd (tu, tu);
- mpz_mul_2exp (t0, t0, shift);
- mpz_mul_2exp (s0, s0, shift);
- }
- power += shift;
- }
- }
-
- /* Now tv = odd part of gcd, and -s0 and t0 are corresponding
- cofactors. */
-
- mpz_mul_2exp (tv, tv, gz);
- mpz_neg (s0, s0);
-
- /* 2^p g = s0 u + t0 v. Eliminate one factor of two at a time. To
- adjust cofactors, we need u / g and v / g */
-
- mpz_divexact (s1, v, tv);
- mpz_abs (s1, s1);
- mpz_divexact (t1, u, tv);
- mpz_abs (t1, t1);
-
- while (power-- > 0)
- {
- /* s0 u + t0 v = (s0 - v/g) u - (t0 + u/g) v */
- if (mpz_odd_p (s0) || mpz_odd_p (t0))
- {
- mpz_sub (s0, s0, s1);
- mpz_add (t0, t0, t1);
- }
- mpz_divexact_ui (s0, s0, 2);
- mpz_divexact_ui (t0, t0, 2);
- }
-
- /* Arrange so that |s| < |u| / 2g */
- mpz_add (s1, s0, s1);
- if (mpz_cmpabs (s0, s1) > 0)
- {
- mpz_swap (s0, s1);
- mpz_sub (t0, t0, t1);
- }
- if (u->_mp_size < 0)
- mpz_neg (s0, s0);
- if (v->_mp_size < 0)
- mpz_neg (t0, t0);
-
- mpz_swap (g, tv);
- if (s)
- mpz_swap (s, s0);
- if (t)
- mpz_swap (t, t0);
-
- mpz_clear (tu);
- mpz_clear (tv);
- mpz_clear (s0);
- mpz_clear (s1);
- mpz_clear (t0);
- mpz_clear (t1);
-}
-
-void
-mpz_lcm (mpz_t r, const mpz_t u, const mpz_t v)
-{
- mpz_t g;
-
- if (u->_mp_size == 0 || v->_mp_size == 0)
- {
- r->_mp_size = 0;
- return;
- }
-
- mpz_init (g);
-
- mpz_gcd (g, u, v);
- mpz_divexact (g, u, g);
- mpz_mul (r, g, v);
-
- mpz_clear (g);
- mpz_abs (r, r);
-}
-
-void
-mpz_lcm_ui (mpz_t r, const mpz_t u, unsigned long v)
-{
- if (v == 0 || u->_mp_size == 0)
- {
- r->_mp_size = 0;
- return;
- }
-
- v /= mpz_gcd_ui (NULL, u, v);
- mpz_mul_ui (r, u, v);
-
- mpz_abs (r, r);
-}
-
-int
-mpz_invert (mpz_t r, const mpz_t u, const mpz_t m)
-{
- mpz_t g, tr;
- int invertible;
-
- if (u->_mp_size == 0 || mpz_cmpabs_ui (m, 1) <= 0)
- return 0;
-
- mpz_init (g);
- mpz_init (tr);
-
- mpz_gcdext (g, tr, NULL, u, m);
- invertible = (mpz_cmp_ui (g, 1) == 0);
-
- if (invertible)
- {
- if (tr->_mp_size < 0)
- {
- if (m->_mp_size >= 0)
- mpz_add (tr, tr, m);
- else
- mpz_sub (tr, tr, m);
- }
- mpz_swap (r, tr);
- }
-
- mpz_clear (g);
- mpz_clear (tr);
- return invertible;
-}
-
-
-/* Higher level operations (sqrt, pow and root) */
-
-void
-mpz_pow_ui (mpz_t r, const mpz_t b, unsigned long e)
-{
- unsigned long bit;
- mpz_t tr;
- mpz_init_set_ui (tr, 1);
-
- for (bit = GMP_ULONG_HIGHBIT; bit > 0; bit >>= 1)
- {
- mpz_mul (tr, tr, tr);
- if (e & bit)
- mpz_mul (tr, tr, b);
- }
- mpz_swap (r, tr);
- mpz_clear (tr);
-}
-
-void
-mpz_ui_pow_ui (mpz_t r, unsigned long blimb, unsigned long e)
-{
- mpz_t b;
- mpz_init_set_ui (b, blimb);
- mpz_pow_ui (r, b, e);
- mpz_clear (b);
-}
-
-void
-mpz_powm (mpz_t r, const mpz_t b, const mpz_t e, const mpz_t m)
-{
- mpz_t tr;
- mpz_t base;
- mp_size_t en, mn;
- mp_srcptr mp;
- struct gmp_div_inverse minv;
- unsigned shift;
- mp_ptr tp = NULL;
-
- en = GMP_ABS (e->_mp_size);
- mn = GMP_ABS (m->_mp_size);
- if (mn == 0)
- gmp_die ("mpz_powm: Zero modulo.");
-
- if (en == 0)
- {
- mpz_set_ui (r, 1);
- return;
- }
-
- mp = m->_mp_d;
- mpn_div_qr_invert (&minv, mp, mn);
- shift = minv.shift;
-
- if (shift > 0)
- {
- /* To avoid shifts, we do all our reductions, except the final
- one, using a *normalized* m. */
- minv.shift = 0;
-
- tp = gmp_xalloc_limbs (mn);
- gmp_assert_nocarry (mpn_lshift (tp, mp, mn, shift));
- mp = tp;
- }
-
- mpz_init (base);
-
- if (e->_mp_size < 0)
- {
- if (!mpz_invert (base, b, m))
- gmp_die ("mpz_powm: Negative exponent and non-invertibe base.");
- }
- else
- {
- mp_size_t bn;
- mpz_abs (base, b);
-
- bn = base->_mp_size;
- if (bn >= mn)
- {
- mpn_div_qr_preinv (NULL, base->_mp_d, base->_mp_size, mp, mn, &minv);
- bn = mn;
- }
-
- /* We have reduced the absolute value. Now take care of the
- sign. Note that we get zero represented non-canonically as
- m. */
- if (b->_mp_size < 0)
- {
- mp_ptr bp = MPZ_REALLOC (base, mn);
- gmp_assert_nocarry (mpn_sub (bp, mp, mn, bp, bn));
- bn = mn;
- }
- base->_mp_size = mpn_normalized_size (base->_mp_d, bn);
- }
- mpz_init_set_ui (tr, 1);
-
- while (en-- > 0)
- {
- mp_limb_t w = e->_mp_d[en];
- mp_limb_t bit;
-
- for (bit = GMP_LIMB_HIGHBIT; bit > 0; bit >>= 1)
- {
- mpz_mul (tr, tr, tr);
- if (w & bit)
- mpz_mul (tr, tr, base);
- if (tr->_mp_size > mn)
- {
- mpn_div_qr_preinv (NULL, tr->_mp_d, tr->_mp_size, mp, mn, &minv);
- tr->_mp_size = mpn_normalized_size (tr->_mp_d, mn);
- }
- }
- }
-
- /* Final reduction */
- if (tr->_mp_size >= mn)
- {
- minv.shift = shift;
- mpn_div_qr_preinv (NULL, tr->_mp_d, tr->_mp_size, mp, mn, &minv);
- tr->_mp_size = mpn_normalized_size (tr->_mp_d, mn);
- }
- if (tp)
- gmp_free (tp);
-
- mpz_swap (r, tr);
- mpz_clear (tr);
- mpz_clear (base);
-}
-
-void
-mpz_powm_ui (mpz_t r, const mpz_t b, unsigned long elimb, const mpz_t m)
-{
- mpz_t e;
- mpz_init_set_ui (e, elimb);
- mpz_powm (r, b, e, m);
- mpz_clear (e);
-}
-
-/* x=trunc(y^(1/z)), r=y-x^z */
-void
-mpz_rootrem (mpz_t x, mpz_t r, const mpz_t y, unsigned long z)
-{
- int sgn;
- mpz_t t, u;
-
- sgn = y->_mp_size < 0;
- if (sgn && (z & 1) == 0)
- gmp_die ("mpz_rootrem: Negative argument, with even root.");
- if (z == 0)
- gmp_die ("mpz_rootrem: Zeroth root.");
-
- if (mpz_cmpabs_ui (y, 1) <= 0) {
- mpz_set (x, y);
- if (r)
- r->_mp_size = 0;
- return;
- }
-
- mpz_init (t);
- mpz_init (u);
- mpz_setbit (t, mpz_sizeinbase (y, 2) / z + 1);
-
- if (z == 2) /* simplify sqrt loop: z-1 == 1 */
- do {
- mpz_swap (u, t); /* u = x */
- mpz_tdiv_q (t, y, u); /* t = y/x */
- mpz_add (t, t, u); /* t = y/x + x */
- mpz_tdiv_q_2exp (t, t, 1); /* x'= (y/x + x)/2 */
- } while (mpz_cmpabs (t, u) < 0); /* |x'| < |x| */
- else /* z != 2 */ {
- mpz_t v;
-
- mpz_init (v);
- if (sgn)
- mpz_neg (t, t);
-
- do {
- mpz_swap (u, t); /* u = x */
- mpz_pow_ui (t, u, z - 1); /* t = x^(z-1) */
- mpz_tdiv_q (t, y, t); /* t = y/x^(z-1) */
- mpz_mul_ui (v, u, z - 1); /* v = x*(z-1) */
- mpz_add (t, t, v); /* t = y/x^(z-1) + x*(z-1) */
- mpz_tdiv_q_ui (t, t, z); /* x'=(y/x^(z-1) + x*(z-1))/z */
- } while (mpz_cmpabs (t, u) < 0); /* |x'| < |x| */
-
- mpz_clear (v);
- }
-
- if (r) {
- mpz_pow_ui (t, u, z);
- mpz_sub (r, y, t);
- }
- mpz_swap (x, u);
- mpz_clear (u);
- mpz_clear (t);
-}
-
-int
-mpz_root (mpz_t x, const mpz_t y, unsigned long z)
-{
- int res;
- mpz_t r;
-
- mpz_init (r);
- mpz_rootrem (x, r, y, z);
- res = r->_mp_size == 0;
- mpz_clear (r);
-
- return res;
-}
-
-/* Compute s = floor(sqrt(u)) and r = u - s^2. Allows r == NULL */
-void
-mpz_sqrtrem (mpz_t s, mpz_t r, const mpz_t u)
-{
- mpz_rootrem (s, r, u, 2);
-}
-
-void
-mpz_sqrt (mpz_t s, const mpz_t u)
-{
- mpz_rootrem (s, NULL, u, 2);
-}
-
-
-/* Combinatorics */
-
-void
-mpz_fac_ui (mpz_t x, unsigned long n)
-{
- if (n < 2) {
- mpz_set_ui (x, 1);
- return;
- }
- mpz_set_ui (x, n);
- for (;--n > 1;)
- mpz_mul_ui (x, x, n);
-}
-
-void
-mpz_bin_uiui (mpz_t r, unsigned long n, unsigned long k)
-{
- mpz_t t;
-
- if (k > n) {
- r->_mp_size = 0;
- return;
- }
- mpz_fac_ui (r, n);
- mpz_init (t);
- mpz_fac_ui (t, k);
- mpz_divexact (r, r, t);
- mpz_fac_ui (t, n - k);
- mpz_divexact (r, r, t);
- mpz_clear (t);
-}
-
-
-/* Logical operations and bit manipulation. */
-
-/* Numbers are treated as if represented in two's complement (and
- infinitely sign extended). For a negative values we get the two's
- complement from -x = ~x + 1, where ~ is bitwise complementt.
- Negation transforms
-
- xxxx10...0
-
- into
-
- yyyy10...0
-
- where yyyy is the bitwise complement of xxxx. So least significant
- bits, up to and including the first one bit, are unchanged, and
- the more significant bits are all complemented.
-
- To change a bit from zero to one in a negative number, subtract the
- corresponding power of two from the absolute value. This can never
- underflow. To change a bit from one to zero, add the corresponding
- power of two, and this might overflow. E.g., if x = -001111, the
- two's complement is 110001. Clearing the least significant bit, we
- get two's complement 110000, and -010000. */
-
-int
-mpz_tstbit (const mpz_t d, mp_bitcnt_t bit_index)
-{
- mp_size_t limb_index;
- unsigned shift;
- mp_size_t ds;
- mp_size_t dn;
- mp_limb_t w;
- int bit;
-
- ds = d->_mp_size;
- dn = GMP_ABS (ds);
- limb_index = bit_index / GMP_LIMB_BITS;
- if (limb_index >= dn)
- return ds < 0;
-
- shift = bit_index % GMP_LIMB_BITS;
- w = d->_mp_d[limb_index];
- bit = (w >> shift) & 1;
-
- if (ds < 0)
- {
- /* d < 0. Check if any of the bits below is set: If so, our bit
- must be complemented. */
- if (shift > 0 && (w << (GMP_LIMB_BITS - shift)) > 0)
- return bit ^ 1;
- while (limb_index-- > 0)
- if (d->_mp_d[limb_index] > 0)
- return bit ^ 1;
- }
- return bit;
-}
-
-static void
-mpz_abs_add_bit (mpz_t d, mp_bitcnt_t bit_index)
-{
- mp_size_t dn, limb_index;
- mp_limb_t bit;
- mp_ptr dp;
-
- dn = GMP_ABS (d->_mp_size);
-
- limb_index = bit_index / GMP_LIMB_BITS;
- bit = (mp_limb_t) 1 << (bit_index % GMP_LIMB_BITS);
-
- if (limb_index >= dn)
- {
- mp_size_t i;
- /* The bit should be set outside of the end of the number.
- We have to increase the size of the number. */
- dp = MPZ_REALLOC (d, limb_index + 1);
-
- dp[limb_index] = bit;
- for (i = dn; i < limb_index; i++)
- dp[i] = 0;
- dn = limb_index + 1;
- }
- else
- {
- mp_limb_t cy;
-
- dp = d->_mp_d;
-
- cy = mpn_add_1 (dp + limb_index, dp + limb_index, dn - limb_index, bit);
- if (cy > 0)
- {
- dp = MPZ_REALLOC (d, dn + 1);
- dp[dn++] = cy;
- }
- }
-
- d->_mp_size = (d->_mp_size < 0) ? - dn : dn;
-}
-
-static void
-mpz_abs_sub_bit (mpz_t d, mp_bitcnt_t bit_index)
-{
- mp_size_t dn, limb_index;
- mp_ptr dp;
- mp_limb_t bit;
-
- dn = GMP_ABS (d->_mp_size);
- dp = d->_mp_d;
-
- limb_index = bit_index / GMP_LIMB_BITS;
- bit = (mp_limb_t) 1 << (bit_index % GMP_LIMB_BITS);
-
- assert (limb_index < dn);
-
- gmp_assert_nocarry (mpn_sub_1 (dp + limb_index, dp + limb_index,
- dn - limb_index, bit));
- dn -= (dp[dn-1] == 0);
- d->_mp_size = (d->_mp_size < 0) ? - dn : dn;
-}
-
-void
-mpz_setbit (mpz_t d, mp_bitcnt_t bit_index)
-{
- if (!mpz_tstbit (d, bit_index))
- {
- if (d->_mp_size >= 0)
- mpz_abs_add_bit (d, bit_index);
- else
- mpz_abs_sub_bit (d, bit_index);
- }
-}
-
-void
-mpz_clrbit (mpz_t d, mp_bitcnt_t bit_index)
-{
- if (mpz_tstbit (d, bit_index))
- {
- if (d->_mp_size >= 0)
- mpz_abs_sub_bit (d, bit_index);
- else
- mpz_abs_add_bit (d, bit_index);
- }
-}
-
-void
-mpz_combit (mpz_t d, mp_bitcnt_t bit_index)
-{
- if (mpz_tstbit (d, bit_index) ^ (d->_mp_size < 0))
- mpz_abs_sub_bit (d, bit_index);
- else
- mpz_abs_add_bit (d, bit_index);
-}
-
-void
-mpz_com (mpz_t r, const mpz_t u)
-{
- mpz_neg (r, u);
- mpz_sub_ui (r, r, 1);
-}
-
-void
-mpz_and (mpz_t r, const mpz_t u, const mpz_t v)
-{
- mp_size_t un, vn, rn, i;
- mp_ptr up, vp, rp;
-
- mp_limb_t ux, vx, rx;
- mp_limb_t uc, vc, rc;
- mp_limb_t ul, vl, rl;
-
- un = GMP_ABS (u->_mp_size);
- vn = GMP_ABS (v->_mp_size);
- if (un < vn)
- {
- MPZ_SRCPTR_SWAP (u, v);
- MP_SIZE_T_SWAP (un, vn);
- }
- if (vn == 0)
- {
- r->_mp_size = 0;
- return;
- }
-
- uc = u->_mp_size < 0;
- vc = v->_mp_size < 0;
- rc = uc & vc;
-
- ux = -uc;
- vx = -vc;
- rx = -rc;
-
- /* If the smaller input is positive, higher limbs don't matter. */
- rn = vx ? un : vn;
-
- rp = MPZ_REALLOC (r, rn + rc);
-
- up = u->_mp_d;
- vp = v->_mp_d;
-
- for (i = 0; i < vn; i++)
- {
- ul = (up[i] ^ ux) + uc;
- uc = ul < uc;
-
- vl = (vp[i] ^ vx) + vc;
- vc = vl < vc;
-
- rl = ( (ul & vl) ^ rx) + rc;
- rc = rl < rc;
- rp[i] = rl;
- }
- assert (vc == 0);
-
- for (; i < rn; i++)
- {
- ul = (up[i] ^ ux) + uc;
- uc = ul < uc;
-
- rl = ( (ul & vx) ^ rx) + rc;
- rc = rl < rc;
- rp[i] = rl;
- }
- if (rc)
- rp[rn++] = rc;
- else
- rn = mpn_normalized_size (rp, rn);
-
- r->_mp_size = rx ? -rn : rn;
-}
-
-void
-mpz_ior (mpz_t r, const mpz_t u, const mpz_t v)
-{
- mp_size_t un, vn, rn, i;
- mp_ptr up, vp, rp;
-
- mp_limb_t ux, vx, rx;
- mp_limb_t uc, vc, rc;
- mp_limb_t ul, vl, rl;
-
- un = GMP_ABS (u->_mp_size);
- vn = GMP_ABS (v->_mp_size);
- if (un < vn)
- {
- MPZ_SRCPTR_SWAP (u, v);
- MP_SIZE_T_SWAP (un, vn);
- }
- if (vn == 0)
- {
- mpz_set (r, u);
- return;
- }
-
- uc = u->_mp_size < 0;
- vc = v->_mp_size < 0;
- rc = uc | vc;
-
- ux = -uc;
- vx = -vc;
- rx = -rc;
-
- /* If the smaller input is negative, by sign extension higher limbs
- don't matter. */
- rn = vx ? vn : un;
-
- rp = MPZ_REALLOC (r, rn + rc);
-
- up = u->_mp_d;
- vp = v->_mp_d;
-
- for (i = 0; i < vn; i++)
- {
- ul = (up[i] ^ ux) + uc;
- uc = ul < uc;
-
- vl = (vp[i] ^ vx) + vc;
- vc = vl < vc;
-
- rl = ( (ul | vl) ^ rx) + rc;
- rc = rl < rc;
- rp[i] = rl;
- }
- assert (vc == 0);
-
- for (; i < rn; i++)
- {
- ul = (up[i] ^ ux) + uc;
- uc = ul < uc;
-
- rl = ( (ul | vx) ^ rx) + rc;
- rc = rl < rc;
- rp[i] = rl;
- }
- if (rc)
- rp[rn++] = rc;
- else
- rn = mpn_normalized_size (rp, rn);
-
- r->_mp_size = rx ? -rn : rn;
-}
-
-void
-mpz_xor (mpz_t r, const mpz_t u, const mpz_t v)
-{
- mp_size_t un, vn, i;
- mp_ptr up, vp, rp;
-
- mp_limb_t ux, vx, rx;
- mp_limb_t uc, vc, rc;
- mp_limb_t ul, vl, rl;
-
- un = GMP_ABS (u->_mp_size);
- vn = GMP_ABS (v->_mp_size);
- if (un < vn)
- {
- MPZ_SRCPTR_SWAP (u, v);
- MP_SIZE_T_SWAP (un, vn);
- }
- if (vn == 0)
- {
- mpz_set (r, u);
- return;
- }
-
- uc = u->_mp_size < 0;
- vc = v->_mp_size < 0;
- rc = uc ^ vc;
-
- ux = -uc;
- vx = -vc;
- rx = -rc;
-
- rp = MPZ_REALLOC (r, un + rc);
-
- up = u->_mp_d;
- vp = v->_mp_d;
-
- for (i = 0; i < vn; i++)
- {
- ul = (up[i] ^ ux) + uc;
- uc = ul < uc;
-
- vl = (vp[i] ^ vx) + vc;
- vc = vl < vc;
-
- rl = (ul ^ vl ^ rx) + rc;
- rc = rl < rc;
- rp[i] = rl;
- }
- assert (vc == 0);
-
- for (; i < un; i++)
- {
- ul = (up[i] ^ ux) + uc;
- uc = ul < uc;
-
- rl = (ul ^ ux) + rc;
- rc = rl < rc;
- rp[i] = rl;
- }
- if (rc)
- rp[un++] = rc;
- else
- un = mpn_normalized_size (rp, un);
-
- r->_mp_size = rx ? -un : un;
-}
-
-static unsigned
-gmp_popcount_limb (mp_limb_t x)
-{
- unsigned c;
-
- /* Do 16 bits at a time, to avoid limb-sized constants. */
- for (c = 0; x > 0; x >>= 16)
- {
- unsigned w = ((x >> 1) & 0x5555) + (x & 0x5555);
- w = ((w >> 2) & 0x3333) + (w & 0x3333);
- w = ((w >> 4) & 0x0f0f) + (w & 0x0f0f);
- w = (w >> 8) + (w & 0x00ff);
- c += w;
- }
- return c;
-}
-
-mp_bitcnt_t
-mpz_popcount (const mpz_t u)
-{
- mp_size_t un, i;
- mp_bitcnt_t c;
-
- un = u->_mp_size;
-
- if (un < 0)
- return ~(mp_bitcnt_t) 0;
-
- for (c = 0, i = 0; i < un; i++)
- c += gmp_popcount_limb (u->_mp_d[i]);
-
- return c;
-}
-
-mp_bitcnt_t
-mpz_hamdist (const mpz_t u, const mpz_t v)
-{
- mp_size_t un, vn, i;
- mp_limb_t uc, vc, ul, vl, comp;
- mp_srcptr up, vp;
- mp_bitcnt_t c;
-
- un = u->_mp_size;
- vn = v->_mp_size;
-
- if ( (un ^ vn) < 0)
- return ~(mp_bitcnt_t) 0;
-
- if (un < 0)
- {
- assert (vn < 0);
- un = -un;
- vn = -vn;
- uc = vc = 1;
- comp = - (mp_limb_t) 1;
- }
- else
- uc = vc = comp = 0;
-
- up = u->_mp_d;
- vp = v->_mp_d;
-
- if (un < vn)
- MPN_SRCPTR_SWAP (up, un, vp, vn);
-
- for (i = 0, c = 0; i < vn; i++)
- {
- ul = (up[i] ^ comp) + uc;
- uc = ul < uc;
-
- vl = (vp[i] ^ comp) + vc;
- vc = vl < vc;
-
- c += gmp_popcount_limb (ul ^ vl);
- }
- assert (vc == 0);
-
- for (; i < un; i++)
- {
- ul = (up[i] ^ comp) + uc;
- uc = ul < uc;
-
- c += gmp_popcount_limb (ul ^ comp);
- }
-
- return c;
-}
-
-mp_bitcnt_t
-mpz_scan1 (const mpz_t u, mp_bitcnt_t starting_bit)
-{
- mp_ptr up;
- mp_size_t us, un, i;
- mp_limb_t limb, ux, uc;
- unsigned cnt;
-
- up = u->_mp_d;
- us = u->_mp_size;
- un = GMP_ABS (us);
- i = starting_bit / GMP_LIMB_BITS;
-
- /* Past the end there's no 1 bits for u>=0, or an immediate 1 bit
- for u<0. Notice this test picks up any u==0 too. */
- if (i >= un)
- return (us >= 0 ? ~(mp_bitcnt_t) 0 : starting_bit);
-
- if (us < 0)
- {
- ux = GMP_LIMB_MAX;
- uc = mpn_zero_p (up, i);
- }
- else
- ux = uc = 0;
-
- limb = (ux ^ up[i]) + uc;
- uc = limb < uc;
-
- /* Mask to 0 all bits before starting_bit, thus ignoring them. */
- limb &= (GMP_LIMB_MAX << (starting_bit % GMP_LIMB_BITS));
-
- while (limb == 0)
- {
- i++;
- if (i == un)
- {
- assert (uc == 0);
- /* For the u > 0 case, this can happen only for the first
- masked limb. For the u < 0 case, it happens when the
- highest limbs of the absolute value are all ones. */
- return (us >= 0 ? ~(mp_bitcnt_t) 0 : un * GMP_LIMB_BITS);
- }
- limb = (ux ^ up[i]) + uc;
- uc = limb < uc;
- }
- gmp_ctz (cnt, limb);
- return (mp_bitcnt_t) i * GMP_LIMB_BITS + cnt;
-}
-
-mp_bitcnt_t
-mpz_scan0 (const mpz_t u, mp_bitcnt_t starting_bit)
-{
- mp_ptr up;
- mp_size_t us, un, i;
- mp_limb_t limb, ux, uc;
- unsigned cnt;
-
- up = u->_mp_d;
- us = u->_mp_size;
- un = GMP_ABS (us);
- i = starting_bit / GMP_LIMB_BITS;
-
- /* When past end, there's an immediate 0 bit for u>=0, or no 0 bits for
- u<0. Notice this test picks up all cases of u==0 too. */
- if (i >= un)
- return (us >= 0 ? starting_bit : ~(mp_bitcnt_t) 0);
-
- if (us < 0)
- {
- ux = GMP_LIMB_MAX;
- uc = mpn_zero_p (up, i);
- }
- else
- ux = uc = 0;
-
- limb = (ux ^ up[i]) + uc;
- uc = limb < uc;
-
- /* Mask to 1 all bits before starting_bit, thus ignoring them. */
- limb |= ((mp_limb_t) 1 << (starting_bit % GMP_LIMB_BITS)) - 1;
-
- while (limb == GMP_LIMB_MAX)
- {
- i++;
- if (i == un)
- {
- assert (uc == 0);
- return (us >= 0 ? un * GMP_LIMB_BITS : ~(mp_bitcnt_t) 0);
- }
- limb = (ux ^ up[i]) + uc;
- uc = limb < uc;
- }
- gmp_ctz (cnt, ~limb);
- return (mp_bitcnt_t) i * GMP_LIMB_BITS + cnt;
-}
-
-
-/* MPZ base conversion. */
-
-size_t
-mpz_sizeinbase (const mpz_t u, int base)
-{
- mp_size_t un;
- mp_srcptr up;
- mp_ptr tp;
- mp_bitcnt_t bits;
- struct gmp_div_inverse bi;
- size_t ndigits;
-
- assert (base >= 2);
- assert (base <= 36);
-
- un = GMP_ABS (u->_mp_size);
- if (un == 0)
- return 1;
-
- up = u->_mp_d;
-
- bits = (un - 1) * GMP_LIMB_BITS + mpn_limb_size_in_base_2 (up[un-1]);
- switch (base)
- {
- case 2:
- return bits;
- case 4:
- return (bits + 1) / 2;
- case 8:
- return (bits + 2) / 3;
- case 16:
- return (bits + 3) / 4;
- case 32:
- return (bits + 4) / 5;
- /* FIXME: Do something more clever for the common case of base
- 10. */
- }
-
- tp = gmp_xalloc_limbs (un);
- mpn_copyi (tp, up, un);
- mpn_div_qr_1_invert (&bi, base);
-
- for (ndigits = 0; un > 0; ndigits++)
- {
- mpn_div_qr_1_preinv (tp, tp, un, &bi);
- un -= (tp[un-1] == 0);
- }
- gmp_free (tp);
- return ndigits;
-}
-
-char *
-mpz_get_str (char *sp, int base, const mpz_t u)
-{
- unsigned bits;
- const char *digits;
- mp_size_t un;
- size_t i, sn;
-
- if (base >= 0)
- {
- digits = "0123456789abcdefghijklmnopqrstuvwxyz";
- }
- else
- {
- base = -base;
- digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
- }
- if (base <= 1)
- base = 10;
- if (base > 36)
- return NULL;
-
- sn = 1 + mpz_sizeinbase (u, base);
- if (!sp)
- sp = gmp_xalloc (1 + sn);
-
- un = GMP_ABS (u->_mp_size);
-
- if (un == 0)
- {
- sp[0] = '0';
- sp[1] = '\0';
- return sp;
- }
-
- i = 0;
-
- if (u->_mp_size < 0)
- sp[i++] = '-';
-
- bits = mpn_base_power_of_two_p (base);
-
- if (bits)
- /* Not modified in this case. */
- sn = i + mpn_get_str_bits ((unsigned char *) sp + i, bits, u->_mp_d, un);
- else
- {
- struct mpn_base_info info;
- mp_ptr tp;
-
- mpn_get_base_info (&info, base);
- tp = gmp_xalloc_limbs (un);
- mpn_copyi (tp, u->_mp_d, un);
-
- sn = i + mpn_get_str_other ((unsigned char *) sp + i, base, &info, tp, un);
- gmp_free (tp);
- }
-
- for (; i < sn; i++)
- sp[i] = digits[(unsigned char) sp[i]];
-
- sp[sn] = '\0';
- return sp;
-}
-
-int
-mpz_set_str (mpz_t r, const char *sp, int base)
-{
- unsigned bits;
- mp_size_t rn, alloc;
- mp_ptr rp;
- size_t sn;
- size_t dn;
- int sign;
- unsigned char *dp;
-
- assert (base == 0 || (base >= 2 && base <= 36));
-
- while (isspace( (unsigned char) *sp))
- sp++;
-
- if (*sp == '-')
- {
- sign = 1;
- sp++;
- }
- else
- sign = 0;
-
- if (base == 0)
- {
- if (*sp == '0')
- {
- sp++;
- if (*sp == 'x' || *sp == 'X')
- {
- base = 16;
- sp++;
- }
- else if (*sp == 'b' || *sp == 'B')
- {
- base = 2;
- sp++;
- }
- else
- base = 8;
- }
- else
- base = 10;
- }
-
- sn = strlen (sp);
- dp = gmp_xalloc (sn + (sn == 0));
-
- for (dn = 0; *sp; sp++)
- {
- unsigned digit;
-
- if (isspace ((unsigned char) *sp))
- continue;
- if (*sp >= '0' && *sp <= '9')
- digit = *sp - '0';
- else if (*sp >= 'a' && *sp <= 'z')
- digit = *sp - 'a' + 10;
- else if (*sp >= 'A' && *sp <= 'Z')
- digit = *sp - 'A' + 10;
- else
- digit = base; /* fail */
-
- if (digit >= base)
- {
- gmp_free (dp);
- r->_mp_size = 0;
- return -1;
- }
-
- dp[dn++] = digit;
- }
-
- bits = mpn_base_power_of_two_p (base);
-
- if (bits > 0)
- {
- alloc = (sn * bits + GMP_LIMB_BITS - 1) / GMP_LIMB_BITS;
- rp = MPZ_REALLOC (r, alloc);
- rn = mpn_set_str_bits (rp, dp, dn, bits);
- }
- else
- {
- struct mpn_base_info info;
- mpn_get_base_info (&info, base);
- alloc = (sn + info.exp - 1) / info.exp;
- rp = MPZ_REALLOC (r, alloc);
- rn = mpn_set_str_other (rp, dp, dn, base, &info);
- }
- assert (rn <= alloc);
- gmp_free (dp);
-
- r->_mp_size = sign ? - rn : rn;
-
- return 0;
-}
-
-int
-mpz_init_set_str (mpz_t r, const char *sp, int base)
-{
- mpz_init (r);
- return mpz_set_str (r, sp, base);
-}
-
-size_t
-mpz_out_str (FILE *stream, int base, const mpz_t x)
-{
- char *str;
- size_t len;
-
- str = mpz_get_str (NULL, base, x);
- len = strlen (str);
- len = fwrite (str, 1, len, stream);
- gmp_free (str);
- return len;
-}
-
-
-static int
-gmp_detect_endian (void)
-{
- static const int i = 1;
- const unsigned char *p = (const unsigned char *) &i;
- if (*p == 1)
- /* Little endian */
- return -1;
- else
- /* Big endian */
- return 1;
-}
-
-/* Import and export. Does not support nails. */
-void
-mpz_import (mpz_t r, size_t count, int order, size_t size, int endian,
- size_t nails, const void *src)
-{
- const unsigned char *p;
- ptrdiff_t word_step;
- mp_ptr rp;
- mp_size_t rn;
-
- /* The current (partial) limb. */
- mp_limb_t limb;
- /* The number of bytes already copied to this limb (starting from
- the low end). */
- size_t bytes;
- /* The index where the limb should be stored, when completed. */
- mp_size_t i;
-
- if (nails != 0)
- gmp_die ("mpz_import: Nails not supported.");
-
- assert (order == 1 || order == -1);
- assert (endian >= -1 && endian <= 1);
-
- if (endian == 0)
- endian = gmp_detect_endian ();
-
- p = (unsigned char *) src;
-
- word_step = (order != endian) ? 2 * size : 0;
-
- /* Process bytes from the least significant end, so point p at the
- least significant word. */
- if (order == 1)
- {
- p += size * (count - 1);
- word_step = - word_step;
- }
-
- /* And at least significant byte of that word. */
- if (endian == 1)
- p += (size - 1);
-
- rn = (size * count + sizeof(mp_limb_t) - 1) / sizeof(mp_limb_t);
- rp = MPZ_REALLOC (r, rn);
-
- for (limb = 0, bytes = 0, i = 0; count > 0; count--, p += word_step)
- {
- size_t j;
- for (j = 0; j < size; j++, p -= (ptrdiff_t) endian)
- {
- limb |= (mp_limb_t) *p << (bytes++ * CHAR_BIT);
- if (bytes == sizeof(mp_limb_t))
- {
- rp[i++] = limb;
- bytes = 0;
- limb = 0;
- }
- }
- }
- if (bytes > 0)
- rp[i++] = limb;
- assert (i == rn);
-
- r->_mp_size = mpn_normalized_size (rp, i);
-}
-
-void *
-mpz_export (void *r, size_t *countp, int order, size_t size, int endian,
- size_t nails, const mpz_t u)
-{
- unsigned char *p;
- ptrdiff_t word_step;
- size_t count, k;
- mp_size_t un;
-
- /* The current (partial) limb. */
- mp_limb_t limb;
- /* The number of bytes left to to in this limb. */
- size_t bytes;
- /* The index where the limb was read. */
- mp_size_t i;
-
- if (nails != 0)
- gmp_die ("mpz_import: Nails not supported.");
-
- assert (order == 1 || order == -1);
- assert (endian >= -1 && endian <= 1);
- assert (size > 0 || u->_mp_size == 0);
-
- un = GMP_ABS (u->_mp_size);
- if (un == 0)
- {
- if (countp)
- *countp = 0;
- return r;
- }
-
- /* Count bytes in top limb. */
- for (limb = u->_mp_d[un-1], k = 0; limb > 0; k++, limb >>= CHAR_BIT)
- ;
-
- assert (k > 0);
-
- count = (k + (un-1) * sizeof (mp_limb_t) + size - 1) / size;
-
- if (!r)
- r = gmp_xalloc (count * size);
-
- if (endian == 0)
- endian = gmp_detect_endian ();
-
- p = (unsigned char *) r;
-
- word_step = (order != endian) ? 2 * size : 0;
-
- /* Process bytes from the least significant end, so point p at the
- least significant word. */
- if (order == 1)
- {
- p += size * (count - 1);
- word_step = - word_step;
- }
-
- /* And at least significant byte of that word. */
- if (endian == 1)
- p += (size - 1);
-
- for (bytes = 0, i = 0, k = 0; k < count; k++, p += word_step)
- {
- size_t j;
- for (j = 0; j < size; j++, p -= (ptrdiff_t) endian)
- {
- if (bytes == 0)
- {
- if (i < un)
- limb = u->_mp_d[i++];
- bytes = sizeof (mp_limb_t);
- }
- *p = limb;
- limb >>= CHAR_BIT;
- bytes--;
- }
- }
- assert (i == un);
- assert (k == count);
-
- if (countp)
- *countp = count;
-
- return r;
-}
generated by cgit v1.2.3 (git 2.25.1) at 2024-11-03 22:11:24 +0000