--- /dev/null
+/* 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"
+
+\f
+/* 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)
+
+\f
+/* 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));
+}
+
+\f
+/* 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;
+}
+
+\f
+/* 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);
+}
+
+\f
+/* 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);
+ }
+}
+
+\f
+/* 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)
+\f
+/* 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;
+}
+
+\f
+/* 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);
+ }
+}
+
+\f
+/* 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);
+}
+
+\f
+/* 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;
+}
+
+\f
+/* 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;
+}
+
+\f
+/* 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;
+}
+
+\f
+/* 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;
+}
+
+\f
+/* 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);
+}
+
+\f
+/* 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);
+}
+
+\f
+/* 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;
+}
+
+\f
+/* 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;
+}
+
+\f
+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;
+}
projects / oweals / minetest.git / commitdiff