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4621 lines
89 KiB
C
4621 lines
89 KiB
C
/* mini-gmp, a minimalistic implementation of a GNU GMP subset.
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Contributed to the GNU project by Niels Möller
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Additional functionalities and improvements by Marco Bodrato.
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Copyright 1991-1997, 1999-2022 Free Software Foundation, Inc.
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This file is part of the GNU MP Library.
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The GNU MP Library is free software; you can redistribute it and/or modify
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it under the terms of either:
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* the GNU Lesser General Public License as published by the Free
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Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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or
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* the GNU General Public License as published by the Free Software
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Foundation; either version 2 of the License, or (at your option) any
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later version.
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or both in parallel, as here.
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The GNU MP Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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You should have received copies of the GNU General Public License and the
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GNU Lesser General Public License along with the GNU MP Library. If not,
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see https://www.gnu.org/licenses/. */
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/* NOTE: All functions in this file which are not declared in
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mini-gmp.h are internal, and are not intended to be compatible
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with GMP or with future versions of mini-gmp. */
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/* Much of the material copied from GMP files, including: gmp-impl.h,
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longlong.h, mpn/generic/add_n.c, mpn/generic/addmul_1.c,
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mpn/generic/lshift.c, mpn/generic/mul_1.c,
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mpn/generic/mul_basecase.c, mpn/generic/rshift.c,
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mpn/generic/sbpi1_div_qr.c, mpn/generic/sub_n.c,
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mpn/generic/submul_1.c. */
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#include <assert.h>
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#include <ctype.h>
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#include <limits.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#include "mini-gmp.h"
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#if !defined(MINI_GMP_DONT_USE_FLOAT_H)
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#include <float.h>
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#endif
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/* Macros */
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#define GMP_LIMB_BITS (sizeof(mp_limb_t) * CHAR_BIT)
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#define GMP_LIMB_MAX ((mp_limb_t) ~ (mp_limb_t) 0)
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#define GMP_LIMB_HIGHBIT ((mp_limb_t) 1 << (GMP_LIMB_BITS - 1))
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#define GMP_HLIMB_BIT ((mp_limb_t) 1 << (GMP_LIMB_BITS / 2))
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#define GMP_LLIMB_MASK (GMP_HLIMB_BIT - 1)
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#define GMP_ULONG_BITS (sizeof(unsigned long) * CHAR_BIT)
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#define GMP_ULONG_HIGHBIT ((unsigned long) 1 << (GMP_ULONG_BITS - 1))
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#define GMP_ABS(x) ((x) >= 0 ? (x) : -(x))
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#define GMP_NEG_CAST(T,x) (-((T)((x) + 1) - 1))
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#define GMP_MIN(a, b) ((a) < (b) ? (a) : (b))
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#define GMP_MAX(a, b) ((a) > (b) ? (a) : (b))
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#define GMP_CMP(a,b) (((a) > (b)) - ((a) < (b)))
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#if defined(DBL_MANT_DIG) && FLT_RADIX == 2
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#define GMP_DBL_MANT_BITS DBL_MANT_DIG
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#else
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#define GMP_DBL_MANT_BITS (53)
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#endif
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/* Return non-zero if xp,xsize and yp,ysize overlap.
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If xp+xsize<=yp there's no overlap, or if yp+ysize<=xp there's no
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overlap. If both these are false, there's an overlap. */
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#define GMP_MPN_OVERLAP_P(xp, xsize, yp, ysize) \
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((xp) + (xsize) > (yp) && (yp) + (ysize) > (xp))
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#define gmp_assert_nocarry(x) do { \
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mp_limb_t __cy = (x); \
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assert (__cy == 0); \
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(void) (__cy); \
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} while (0)
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#define gmp_clz(count, x) do { \
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mp_limb_t __clz_x = (x); \
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unsigned __clz_c = 0; \
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int LOCAL_SHIFT_BITS = 8; \
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if (GMP_LIMB_BITS > LOCAL_SHIFT_BITS) \
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for (; \
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(__clz_x & ((mp_limb_t) 0xff << (GMP_LIMB_BITS - 8))) == 0; \
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__clz_c += 8) \
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{ __clz_x <<= LOCAL_SHIFT_BITS; } \
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for (; (__clz_x & GMP_LIMB_HIGHBIT) == 0; __clz_c++) \
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__clz_x <<= 1; \
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(count) = __clz_c; \
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} while (0)
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#define gmp_ctz(count, x) do { \
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mp_limb_t __ctz_x = (x); \
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unsigned __ctz_c = 0; \
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gmp_clz (__ctz_c, __ctz_x & - __ctz_x); \
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(count) = GMP_LIMB_BITS - 1 - __ctz_c; \
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} while (0)
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#define gmp_add_ssaaaa(sh, sl, ah, al, bh, bl) \
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do { \
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mp_limb_t __x; \
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__x = (al) + (bl); \
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(sh) = (ah) + (bh) + (__x < (al)); \
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(sl) = __x; \
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} while (0)
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#define gmp_sub_ddmmss(sh, sl, ah, al, bh, bl) \
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do { \
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mp_limb_t __x; \
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__x = (al) - (bl); \
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(sh) = (ah) - (bh) - ((al) < (bl)); \
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(sl) = __x; \
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} while (0)
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#define gmp_umul_ppmm(w1, w0, u, v) \
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do { \
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int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS; \
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if (sizeof(unsigned int) * CHAR_BIT >= 2 * GMP_LIMB_BITS) \
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{ \
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unsigned int __ww = (unsigned int) (u) * (v); \
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w0 = (mp_limb_t) __ww; \
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w1 = (mp_limb_t) (__ww >> LOCAL_GMP_LIMB_BITS); \
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} \
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else if (GMP_ULONG_BITS >= 2 * GMP_LIMB_BITS) \
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{ \
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unsigned long int __ww = (unsigned long int) (u) * (v); \
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w0 = (mp_limb_t) __ww; \
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w1 = (mp_limb_t) (__ww >> LOCAL_GMP_LIMB_BITS); \
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} \
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else { \
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mp_limb_t __x0, __x1, __x2, __x3; \
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unsigned __ul, __vl, __uh, __vh; \
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mp_limb_t __u = (u), __v = (v); \
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assert (sizeof (unsigned) * 2 >= sizeof (mp_limb_t)); \
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\
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__ul = __u & GMP_LLIMB_MASK; \
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__uh = __u >> (GMP_LIMB_BITS / 2); \
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__vl = __v & GMP_LLIMB_MASK; \
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__vh = __v >> (GMP_LIMB_BITS / 2); \
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\
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__x0 = (mp_limb_t) __ul * __vl; \
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__x1 = (mp_limb_t) __ul * __vh; \
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__x2 = (mp_limb_t) __uh * __vl; \
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__x3 = (mp_limb_t) __uh * __vh; \
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\
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__x1 += __x0 >> (GMP_LIMB_BITS / 2);/* this can't give carry */ \
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__x1 += __x2; /* but this indeed can */ \
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if (__x1 < __x2) /* did we get it? */ \
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__x3 += GMP_HLIMB_BIT; /* yes, add it in the proper pos. */ \
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\
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(w1) = __x3 + (__x1 >> (GMP_LIMB_BITS / 2)); \
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(w0) = (__x1 << (GMP_LIMB_BITS / 2)) + (__x0 & GMP_LLIMB_MASK); \
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} \
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} while (0)
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#define gmp_udiv_qrnnd_preinv(q, r, nh, nl, d, di) \
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do { \
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mp_limb_t _qh, _ql, _r, _mask; \
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gmp_umul_ppmm (_qh, _ql, (nh), (di)); \
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gmp_add_ssaaaa (_qh, _ql, _qh, _ql, (nh) + 1, (nl)); \
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_r = (nl) - _qh * (d); \
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_mask = -(mp_limb_t) (_r > _ql); /* both > and >= are OK */ \
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_qh += _mask; \
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_r += _mask & (d); \
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if (_r >= (d)) \
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{ \
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_r -= (d); \
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_qh++; \
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} \
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\
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(r) = _r; \
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(q) = _qh; \
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} while (0)
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#define gmp_udiv_qr_3by2(q, r1, r0, n2, n1, n0, d1, d0, dinv) \
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do { \
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mp_limb_t _q0, _t1, _t0, _mask; \
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gmp_umul_ppmm ((q), _q0, (n2), (dinv)); \
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gmp_add_ssaaaa ((q), _q0, (q), _q0, (n2), (n1)); \
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\
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/* Compute the two most significant limbs of n - q'd */ \
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(r1) = (n1) - (d1) * (q); \
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gmp_sub_ddmmss ((r1), (r0), (r1), (n0), (d1), (d0)); \
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gmp_umul_ppmm (_t1, _t0, (d0), (q)); \
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gmp_sub_ddmmss ((r1), (r0), (r1), (r0), _t1, _t0); \
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(q)++; \
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\
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/* Conditionally adjust q and the remainders */ \
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_mask = - (mp_limb_t) ((r1) >= _q0); \
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(q) += _mask; \
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gmp_add_ssaaaa ((r1), (r0), (r1), (r0), _mask & (d1), _mask & (d0)); \
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if ((r1) >= (d1)) \
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{ \
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if ((r1) > (d1) || (r0) >= (d0)) \
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{ \
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(q)++; \
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gmp_sub_ddmmss ((r1), (r0), (r1), (r0), (d1), (d0)); \
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} \
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} \
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} while (0)
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/* Swap macros. */
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#define MP_LIMB_T_SWAP(x, y) \
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do { \
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mp_limb_t __mp_limb_t_swap__tmp = (x); \
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(x) = (y); \
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(y) = __mp_limb_t_swap__tmp; \
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} while (0)
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#define MP_SIZE_T_SWAP(x, y) \
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do { \
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mp_size_t __mp_size_t_swap__tmp = (x); \
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(x) = (y); \
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(y) = __mp_size_t_swap__tmp; \
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} while (0)
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#define MP_BITCNT_T_SWAP(x,y) \
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do { \
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mp_bitcnt_t __mp_bitcnt_t_swap__tmp = (x); \
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(x) = (y); \
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(y) = __mp_bitcnt_t_swap__tmp; \
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} while (0)
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#define MP_PTR_SWAP(x, y) \
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do { \
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mp_ptr __mp_ptr_swap__tmp = (x); \
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(x) = (y); \
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(y) = __mp_ptr_swap__tmp; \
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} while (0)
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#define MP_SRCPTR_SWAP(x, y) \
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do { \
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mp_srcptr __mp_srcptr_swap__tmp = (x); \
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(x) = (y); \
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(y) = __mp_srcptr_swap__tmp; \
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} while (0)
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#define MPN_PTR_SWAP(xp,xs, yp,ys) \
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do { \
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MP_PTR_SWAP (xp, yp); \
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MP_SIZE_T_SWAP (xs, ys); \
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} while(0)
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#define MPN_SRCPTR_SWAP(xp,xs, yp,ys) \
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do { \
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MP_SRCPTR_SWAP (xp, yp); \
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MP_SIZE_T_SWAP (xs, ys); \
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} while(0)
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#define MPZ_PTR_SWAP(x, y) \
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do { \
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mpz_ptr __mpz_ptr_swap__tmp = (x); \
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(x) = (y); \
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(y) = __mpz_ptr_swap__tmp; \
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} while (0)
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#define MPZ_SRCPTR_SWAP(x, y) \
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do { \
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mpz_srcptr __mpz_srcptr_swap__tmp = (x); \
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(x) = (y); \
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(y) = __mpz_srcptr_swap__tmp; \
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} while (0)
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const int mp_bits_per_limb = GMP_LIMB_BITS;
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/* Memory allocation and other helper functions. */
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static void
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gmp_die (const char *msg)
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{
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fprintf (stderr, "%s\n", msg);
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abort();
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}
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static void *
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gmp_default_alloc (size_t size)
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{
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void *p;
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assert (size > 0);
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p = malloc (size);
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if (!p)
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gmp_die("gmp_default_alloc: Virtual memory exhausted.");
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return p;
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}
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static void *
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gmp_default_realloc (void *old, size_t unused_old_size, size_t new_size)
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{
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void * p;
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p = realloc (old, new_size);
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if (!p)
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gmp_die("gmp_default_realloc: Virtual memory exhausted.");
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return p;
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}
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static void
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gmp_default_free (void *p, size_t unused_size)
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{
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free (p);
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}
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static void * (*gmp_allocate_func) (size_t) = gmp_default_alloc;
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static void * (*gmp_reallocate_func) (void *, size_t, size_t) = gmp_default_realloc;
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static void (*gmp_free_func) (void *, size_t) = gmp_default_free;
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void
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mp_get_memory_functions (void *(**alloc_func) (size_t),
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void *(**realloc_func) (void *, size_t, size_t),
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void (**free_func) (void *, size_t))
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{
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if (alloc_func)
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*alloc_func = gmp_allocate_func;
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if (realloc_func)
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*realloc_func = gmp_reallocate_func;
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if (free_func)
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*free_func = gmp_free_func;
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}
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void
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mp_set_memory_functions (void *(*alloc_func) (size_t),
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void *(*realloc_func) (void *, size_t, size_t),
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void (*free_func) (void *, size_t))
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{
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if (!alloc_func)
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alloc_func = gmp_default_alloc;
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if (!realloc_func)
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realloc_func = gmp_default_realloc;
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if (!free_func)
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free_func = gmp_default_free;
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gmp_allocate_func = alloc_func;
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gmp_reallocate_func = realloc_func;
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gmp_free_func = free_func;
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}
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#define gmp_alloc(size) ((*gmp_allocate_func)((size)))
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#define gmp_free(p, size) ((*gmp_free_func) ((p), (size)))
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#define gmp_realloc(ptr, old_size, size) ((*gmp_reallocate_func)(ptr, old_size, size))
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static mp_ptr
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gmp_alloc_limbs (mp_size_t size)
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{
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return (mp_ptr) gmp_alloc (size * sizeof (mp_limb_t));
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}
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static mp_ptr
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gmp_realloc_limbs (mp_ptr old, mp_size_t old_size, mp_size_t size)
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{
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assert (size > 0);
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return (mp_ptr) gmp_realloc (old, old_size * sizeof (mp_limb_t), size * sizeof (mp_limb_t));
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}
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static void
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gmp_free_limbs (mp_ptr old, mp_size_t size)
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{
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gmp_free (old, size * sizeof (mp_limb_t));
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}
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/* MPN interface */
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||
|
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void
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mpn_copyi (mp_ptr d, mp_srcptr s, mp_size_t n)
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{
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mp_size_t i;
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for (i = 0; i < n; i++)
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d[i] = s[i];
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}
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void
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mpn_copyd (mp_ptr d, mp_srcptr s, mp_size_t n)
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{
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||
while (--n >= 0)
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d[n] = s[n];
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||
}
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||
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||
int
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||
mpn_cmp (mp_srcptr ap, mp_srcptr bp, mp_size_t n)
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{
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||
while (--n >= 0)
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||
{
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||
if (ap[n] != bp[n])
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return ap[n] > bp[n] ? 1 : -1;
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}
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return 0;
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||
}
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||
static int
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mpn_cmp4 (mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
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{
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||
if (an != bn)
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return an < bn ? -1 : 1;
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else
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return mpn_cmp (ap, bp, an);
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||
}
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||
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||
static mp_size_t
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||
mpn_normalized_size (mp_srcptr xp, mp_size_t n)
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{
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||
while (n > 0 && xp[n-1] == 0)
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||
--n;
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||
return n;
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||
}
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int
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mpn_zero_p(mp_srcptr rp, mp_size_t n)
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{
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return mpn_normalized_size (rp, n) == 0;
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||
}
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||
|
||
void
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mpn_zero (mp_ptr rp, mp_size_t n)
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||
{
|
||
while (--n >= 0)
|
||
rp[n] = 0;
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||
}
|
||
|
||
mp_limb_t
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||
mpn_add_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b)
|
||
{
|
||
mp_size_t i;
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||
|
||
assert (n > 0);
|
||
i = 0;
|
||
do
|
||
{
|
||
mp_limb_t r = ap[i] + b;
|
||
/* Carry out */
|
||
b = (r < b);
|
||
rp[i] = r;
|
||
}
|
||
while (++i < n);
|
||
|
||
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);
|
||
|
||
i = 0;
|
||
do
|
||
{
|
||
mp_limb_t a = ap[i];
|
||
/* Carry out */
|
||
mp_limb_t cy = a < b;
|
||
rp[i] = a - b;
|
||
b = cy;
|
||
}
|
||
while (++i < n);
|
||
|
||
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);
|
||
assert (!GMP_MPN_OVERLAP_P(rp, un + vn, up, un));
|
||
assert (!GMP_MPN_OVERLAP_P(rp, un + vn, vp, vn));
|
||
|
||
/* 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]);
|
||
|
||
/* Now accumulate the product of up[] and the next higher limb from
|
||
vp[]. */
|
||
|
||
while (--vn >= 1)
|
||
{
|
||
rp += 1, vp += 1;
|
||
rp[un] = mpn_addmul_1 (rp, up, un, vp[0]);
|
||
}
|
||
return rp[un];
|
||
}
|
||
|
||
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_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);
|
||
|
||
while (--n != 0)
|
||
{
|
||
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_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;
|
||
|
||
while (--n != 0)
|
||
{
|
||
high_limb = *up++;
|
||
*rp++ = low_limb | (high_limb << tnc);
|
||
low_limb = high_limb >> cnt;
|
||
}
|
||
*rp = low_limb;
|
||
|
||
return retval;
|
||
}
|
||
|
||
static mp_bitcnt_t
|
||
mpn_common_scan (mp_limb_t limb, mp_size_t i, mp_srcptr up, mp_size_t un,
|
||
mp_limb_t ux)
|
||
{
|
||
unsigned cnt;
|
||
|
||
assert (ux == 0 || ux == GMP_LIMB_MAX);
|
||
assert (0 <= i && i <= un );
|
||
|
||
while (limb == 0)
|
||
{
|
||
i++;
|
||
if (i == un)
|
||
return (ux == 0 ? ~(mp_bitcnt_t) 0 : un * GMP_LIMB_BITS);
|
||
limb = ux ^ up[i];
|
||
}
|
||
gmp_ctz (cnt, limb);
|
||
return (mp_bitcnt_t) i * GMP_LIMB_BITS + cnt;
|
||
}
|
||
|
||
mp_bitcnt_t
|
||
mpn_scan1 (mp_srcptr ptr, mp_bitcnt_t bit)
|
||
{
|
||
mp_size_t i;
|
||
i = bit / GMP_LIMB_BITS;
|
||
|
||
return mpn_common_scan ( ptr[i] & (GMP_LIMB_MAX << (bit % GMP_LIMB_BITS)),
|
||
i, ptr, i, 0);
|
||
}
|
||
|
||
mp_bitcnt_t
|
||
mpn_scan0 (mp_srcptr ptr, mp_bitcnt_t bit)
|
||
{
|
||
mp_size_t i;
|
||
i = bit / GMP_LIMB_BITS;
|
||
|
||
return mpn_common_scan (~ptr[i] & (GMP_LIMB_MAX << (bit % GMP_LIMB_BITS)),
|
||
i, ptr, i, GMP_LIMB_MAX);
|
||
}
|
||
|
||
void
|
||
mpn_com (mp_ptr rp, mp_srcptr up, mp_size_t n)
|
||
{
|
||
while (--n >= 0)
|
||
*rp++ = ~ *up++;
|
||
}
|
||
|
||
mp_limb_t
|
||
mpn_neg (mp_ptr rp, mp_srcptr up, mp_size_t n)
|
||
{
|
||
while (*up == 0)
|
||
{
|
||
*rp = 0;
|
||
if (!--n)
|
||
return 0;
|
||
++up; ++rp;
|
||
}
|
||
*rp = - *up;
|
||
mpn_com (++rp, ++up, --n);
|
||
return 1;
|
||
}
|
||
|
||
|
||
/* MPN division interface. */
|
||
|
||
/* The 3/2 inverse is defined as
|
||
|
||
m = floor( (B^3-1) / (B u1 + u0)) - B
|
||
*/
|
||
mp_limb_t
|
||
mpn_invert_3by2 (mp_limb_t u1, mp_limb_t u0)
|
||
{
|
||
mp_limb_t r, m;
|
||
|
||
{
|
||
mp_limb_t p, ql;
|
||
unsigned ul, uh, qh;
|
||
|
||
assert (sizeof (unsigned) * 2 >= sizeof (mp_limb_t));
|
||
/* For notation, let b denote the half-limb base, so that B = b^2.
|
||
Split u1 = b uh + ul. */
|
||
ul = u1 & GMP_LLIMB_MASK;
|
||
uh = u1 >> (GMP_LIMB_BITS / 2);
|
||
|
||
/* Approximation of the high half of quotient. Differs from the 2/1
|
||
inverse of the half limb uh, since we have already subtracted
|
||
u0. */
|
||
qh = (u1 ^ GMP_LIMB_MAX) / uh;
|
||
|
||
/* Adjust to get a half-limb 3/2 inverse, i.e., we want
|
||
|
||
qh' = floor( (b^3 - 1) / u) - b = floor ((b^3 - b u - 1) / u
|
||
= floor( (b (~u) + b-1) / u),
|
||
|
||
and the remainder
|
||
|
||
r = b (~u) + b-1 - qh (b uh + ul)
|
||
= b (~u - qh uh) + b-1 - qh ul
|
||
|
||
Subtraction of qh ul may underflow, which implies adjustments.
|
||
But by normalization, 2 u >= B > qh ul, so we need to adjust by
|
||
at most 2.
|
||
*/
|
||
|
||
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;
|
||
|
||
/* Low half of the quotient is
|
||
|
||
ql = floor ( (b r + b-1) / u1).
|
||
|
||
This is a 3/2 division (on half-limbs), for which qh is a
|
||
suitable inverse. */
|
||
|
||
p = (r >> (GMP_LIMB_BITS / 2)) * qh + r;
|
||
/* Unlike full-limb 3/2, we can add 1 without overflow. For this to
|
||
work, it is essential that ql is a full mp_limb_t. */
|
||
ql = (p >> (GMP_LIMB_BITS / 2)) + 1;
|
||
|
||
/* By the 3/2 trick, we don't need the high half limb. */
|
||
r = (r << (GMP_LIMB_BITS / 2)) + GMP_LLIMB_MASK - ql * u1;
|
||
|
||
if (r >= (GMP_LIMB_MAX & (p << (GMP_LIMB_BITS / 2))))
|
||
{
|
||
ql--;
|
||
r += u1;
|
||
}
|
||
m = ((mp_limb_t) qh << (GMP_LIMB_BITS / 2)) + ql;
|
||
if (r >= u1)
|
||
{
|
||
m++;
|
||
r -= u1;
|
||
}
|
||
}
|
||
|
||
/* Now m is the 2/1 inverse of u1. If u0 > 0, adjust it to become a
|
||
3/2 inverse. */
|
||
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--;
|
||
m -= ((r > u1) | ((r == u1) & (tl > u0)));
|
||
}
|
||
}
|
||
|
||
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;
|
||
mp_size_t tn = 0;
|
||
|
||
if (inv->shift > 0)
|
||
{
|
||
/* Shift, reusing qp area if possible. In-place shift if qp == np. */
|
||
tp = qp;
|
||
if (!tp)
|
||
{
|
||
tn = nn;
|
||
tp = gmp_alloc_limbs (tn);
|
||
}
|
||
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 (tn)
|
||
gmp_free_limbs (tp, tn);
|
||
|
||
return r >> inv->shift;
|
||
}
|
||
|
||
static void
|
||
mpn_div_qr_2_preinv (mp_ptr qp, mp_ptr 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;
|
||
|
||
assert (nn >= 2);
|
||
shift = inv->shift;
|
||
d1 = inv->d1;
|
||
d0 = inv->d0;
|
||
di = inv->di;
|
||
|
||
if (shift > 0)
|
||
r1 = mpn_lshift (np, np, nn, shift);
|
||
else
|
||
r1 = 0;
|
||
|
||
r0 = np[nn - 1];
|
||
|
||
i = nn - 2;
|
||
do
|
||
{
|
||
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;
|
||
}
|
||
while (--i >= 0);
|
||
|
||
if (shift > 0)
|
||
{
|
||
assert ((r0 & (GMP_LIMB_MAX >> (GMP_LIMB_BITS - shift))) == 0);
|
||
r0 = (r0 >> shift) | (r1 << (GMP_LIMB_BITS - shift));
|
||
r1 >>= shift;
|
||
}
|
||
|
||
np[1] = r1;
|
||
np[0] = r0;
|
||
}
|
||
|
||
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] >
|
||
*/
|
||
|
||
i = nn - dn;
|
||
do
|
||
{
|
||
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;
|
||
}
|
||
while (--i >= 0);
|
||
|
||
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, 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_alloc_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_limbs (tp, dn);
|
||
}
|
||
|
||
|
||
/* 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;
|
||
unsigned 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_MAX >> (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;
|
||
mp_limb_t limb;
|
||
unsigned shift;
|
||
|
||
for (limb = 0, rn = 0, shift = 0; sn-- > 0; )
|
||
{
|
||
limb |= (mp_limb_t) sp[sn] << shift;
|
||
shift += bits;
|
||
if (shift >= GMP_LIMB_BITS)
|
||
{
|
||
shift -= GMP_LIMB_BITS;
|
||
rp[rn++] = limb;
|
||
/* Next line is correct also if shift == 0,
|
||
bits == 8, and mp_limb_t == unsigned char. */
|
||
limb = (unsigned int) sp[sn] >> (bits - shift);
|
||
}
|
||
}
|
||
if (limb != 0)
|
||
rp[rn++] = limb;
|
||
else
|
||
rn = mpn_normalized_size (rp, rn);
|
||
return rn;
|
||
}
|
||
|
||
/* Result is usually normalized, except for all-zero input, in which
|
||
case a single zero limb is written at *RP, and 1 is returned. */
|
||
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 k;
|
||
size_t j;
|
||
|
||
assert (sn > 0);
|
||
|
||
k = 1 + (sn - 1) % info->exp;
|
||
|
||
j = 0;
|
||
w = sp[j++];
|
||
while (--k != 0)
|
||
w = w * b + sp[j++];
|
||
|
||
rp[0] = w;
|
||
|
||
for (rn = 1; 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)
|
||
{
|
||
static const mp_limb_t dummy_limb = GMP_LIMB_MAX & 0xc1a0;
|
||
|
||
r->_mp_alloc = 0;
|
||
r->_mp_size = 0;
|
||
r->_mp_d = (mp_ptr) &dummy_limb;
|
||
}
|
||
|
||
/* The utility of this function is a bit limited, since many functions
|
||
assigns 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_alloc_limbs (rn);
|
||
}
|
||
|
||
void
|
||
mpz_clear (mpz_t r)
|
||
{
|
||
if (r->_mp_alloc)
|
||
gmp_free_limbs (r->_mp_d, r->_mp_alloc);
|
||
}
|
||
|
||
static mp_ptr
|
||
mpz_realloc (mpz_t r, mp_size_t size)
|
||
{
|
||
size = GMP_MAX (size, 1);
|
||
|
||
if (r->_mp_alloc)
|
||
r->_mp_d = gmp_realloc_limbs (r->_mp_d, r->_mp_alloc, size);
|
||
else
|
||
r->_mp_d = gmp_alloc_limbs (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) */
|
||
if (GMP_LIMB_BITS < GMP_ULONG_BITS)
|
||
{
|
||
mpz_set_ui (r, GMP_NEG_CAST (unsigned long int, x));
|
||
mpz_neg (r, r);
|
||
}
|
||
else
|
||
{
|
||
r->_mp_size = -1;
|
||
MPZ_REALLOC (r, 1)[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;
|
||
MPZ_REALLOC (r, 1)[0] = x;
|
||
if (GMP_LIMB_BITS < GMP_ULONG_BITS)
|
||
{
|
||
int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS;
|
||
while (x >>= LOCAL_GMP_LIMB_BITS)
|
||
{
|
||
++ r->_mp_size;
|
||
MPZ_REALLOC (r, r->_mp_size)[r->_mp_size - 1] = 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)
|
||
{
|
||
return mpz_cmp_si (u, LONG_MAX) <= 0 && mpz_cmp_si (u, LONG_MIN) >= 0;
|
||
}
|
||
|
||
static int
|
||
mpn_absfits_ulong_p (mp_srcptr up, mp_size_t un)
|
||
{
|
||
int ulongsize = GMP_ULONG_BITS / GMP_LIMB_BITS;
|
||
mp_limb_t ulongrem = 0;
|
||
|
||
if (GMP_ULONG_BITS % GMP_LIMB_BITS != 0)
|
||
ulongrem = (mp_limb_t) (ULONG_MAX >> GMP_LIMB_BITS * ulongsize) + 1;
|
||
|
||
return un <= ulongsize || (up[ulongsize] < ulongrem && un == ulongsize + 1);
|
||
}
|
||
|
||
int
|
||
mpz_fits_ulong_p (const mpz_t u)
|
||
{
|
||
mp_size_t us = u->_mp_size;
|
||
|
||
return us >= 0 && mpn_absfits_ulong_p (u->_mp_d, us);
|
||
}
|
||
|
||
int
|
||
mpz_fits_sint_p (const mpz_t u)
|
||
{
|
||
return mpz_cmp_si (u, INT_MAX) <= 0 && mpz_cmp_si (u, INT_MIN) >= 0;
|
||
}
|
||
|
||
int
|
||
mpz_fits_uint_p (const mpz_t u)
|
||
{
|
||
return u->_mp_size >= 0 && mpz_cmpabs_ui (u, UINT_MAX) <= 0;
|
||
}
|
||
|
||
int
|
||
mpz_fits_sshort_p (const mpz_t u)
|
||
{
|
||
return mpz_cmp_si (u, SHRT_MAX) <= 0 && mpz_cmp_si (u, SHRT_MIN) >= 0;
|
||
}
|
||
|
||
int
|
||
mpz_fits_ushort_p (const mpz_t u)
|
||
{
|
||
return u->_mp_size >= 0 && mpz_cmpabs_ui (u, USHRT_MAX) <= 0;
|
||
}
|
||
|
||
long int
|
||
mpz_get_si (const mpz_t u)
|
||
{
|
||
unsigned long r = mpz_get_ui (u);
|
||
unsigned long c = -LONG_MAX - LONG_MIN;
|
||
|
||
if (u->_mp_size < 0)
|
||
/* This expression is necessary to properly handle -LONG_MIN */
|
||
return -(long) c - (long) ((r - c) & LONG_MAX);
|
||
else
|
||
return (long) (r & LONG_MAX);
|
||
}
|
||
|
||
unsigned long int
|
||
mpz_get_ui (const mpz_t u)
|
||
{
|
||
if (GMP_LIMB_BITS < GMP_ULONG_BITS)
|
||
{
|
||
int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS;
|
||
unsigned long r = 0;
|
||
mp_size_t n = GMP_ABS (u->_mp_size);
|
||
n = GMP_MIN (n, 1 + (mp_size_t) (GMP_ULONG_BITS - 1) / GMP_LIMB_BITS);
|
||
while (--n >= 0)
|
||
r = (r << LOCAL_GMP_LIMB_BITS) + u->_mp_d[n];
|
||
return r;
|
||
}
|
||
|
||
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;
|
||
}
|
||
|
||
void
|
||
mpz_realloc2 (mpz_t x, mp_bitcnt_t n)
|
||
{
|
||
mpz_realloc (x, 1 + (n - (n != 0)) / GMP_LIMB_BITS);
|
||
}
|
||
|
||
mp_srcptr
|
||
mpz_limbs_read (mpz_srcptr x)
|
||
{
|
||
return x->_mp_d;
|
||
}
|
||
|
||
mp_ptr
|
||
mpz_limbs_modify (mpz_t x, mp_size_t n)
|
||
{
|
||
assert (n > 0);
|
||
return MPZ_REALLOC (x, n);
|
||
}
|
||
|
||
mp_ptr
|
||
mpz_limbs_write (mpz_t x, mp_size_t n)
|
||
{
|
||
return mpz_limbs_modify (x, n);
|
||
}
|
||
|
||
void
|
||
mpz_limbs_finish (mpz_t x, mp_size_t xs)
|
||
{
|
||
mp_size_t xn;
|
||
xn = mpn_normalized_size (x->_mp_d, GMP_ABS (xs));
|
||
x->_mp_size = xs < 0 ? -xn : xn;
|
||
}
|
||
|
||
static mpz_srcptr
|
||
mpz_roinit_normal_n (mpz_t x, mp_srcptr xp, mp_size_t xs)
|
||
{
|
||
x->_mp_alloc = 0;
|
||
x->_mp_d = (mp_ptr) xp;
|
||
x->_mp_size = xs;
|
||
return x;
|
||
}
|
||
|
||
mpz_srcptr
|
||
mpz_roinit_n (mpz_t x, mp_srcptr xp, mp_size_t xs)
|
||
{
|
||
mpz_roinit_normal_n (x, xp, xs);
|
||
mpz_limbs_finish (x, xs);
|
||
return x;
|
||
}
|
||
|
||
|
||
/* 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 != x || x == x * 0.5)
|
||
{
|
||
r->_mp_size = 0;
|
||
return;
|
||
}
|
||
|
||
sign = x < 0.0 ;
|
||
if (sign)
|
||
x = - x;
|
||
|
||
if (x < 1.0)
|
||
{
|
||
r->_mp_size = 0;
|
||
return;
|
||
}
|
||
B = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1);
|
||
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);
|
||
i = rn-1;
|
||
rp[i] = f;
|
||
while (--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)
|
||
{
|
||
int m;
|
||
mp_limb_t l;
|
||
mp_size_t un;
|
||
double x;
|
||
double B = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1);
|
||
|
||
un = GMP_ABS (u->_mp_size);
|
||
|
||
if (un == 0)
|
||
return 0.0;
|
||
|
||
l = u->_mp_d[--un];
|
||
gmp_clz (m, l);
|
||
m = m + GMP_DBL_MANT_BITS - GMP_LIMB_BITS;
|
||
if (m < 0)
|
||
l &= GMP_LIMB_MAX << -m;
|
||
|
||
for (x = l; --un >= 0;)
|
||
{
|
||
x = B*x;
|
||
if (m > 0) {
|
||
l = u->_mp_d[un];
|
||
m -= GMP_LIMB_BITS;
|
||
if (m < 0)
|
||
l &= GMP_LIMB_MAX << -m;
|
||
x += l;
|
||
}
|
||
}
|
||
|
||
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 = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1);
|
||
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)
|
||
{
|
||
return GMP_CMP (u->_mp_size, 0);
|
||
}
|
||
|
||
int
|
||
mpz_cmp_si (const mpz_t u, long v)
|
||
{
|
||
mp_size_t usize = u->_mp_size;
|
||
|
||
if (v >= 0)
|
||
return mpz_cmp_ui (u, v);
|
||
else if (usize >= 0)
|
||
return 1;
|
||
else
|
||
return - mpz_cmpabs_ui (u, GMP_NEG_CAST (unsigned long int, v));
|
||
}
|
||
|
||
int
|
||
mpz_cmp_ui (const mpz_t u, unsigned long v)
|
||
{
|
||
mp_size_t usize = u->_mp_size;
|
||
|
||
if (usize < 0)
|
||
return -1;
|
||
else
|
||
return mpz_cmpabs_ui (u, v);
|
||
}
|
||
|
||
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 (asize < bsize) ? -1 : 1;
|
||
else if (asize >= 0)
|
||
return mpn_cmp (a->_mp_d, b->_mp_d, asize);
|
||
else
|
||
return mpn_cmp (b->_mp_d, a->_mp_d, -asize);
|
||
}
|
||
|
||
int
|
||
mpz_cmpabs_ui (const mpz_t u, unsigned long v)
|
||
{
|
||
mp_size_t un = GMP_ABS (u->_mp_size);
|
||
|
||
if (! mpn_absfits_ulong_p (u->_mp_d, un))
|
||
return 1;
|
||
else
|
||
{
|
||
unsigned long uu = mpz_get_ui (u);
|
||
return GMP_CMP(uu, v);
|
||
}
|
||
}
|
||
|
||
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)
|
||
{
|
||
mpz_set (r, u);
|
||
r->_mp_size = GMP_ABS (r->_mp_size);
|
||
}
|
||
|
||
void
|
||
mpz_neg (mpz_t r, const mpz_t 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_alloc, v->_mp_alloc);
|
||
MPN_PTR_SWAP (u->_mp_d, u->_mp_size, v->_mp_d, v->_mp_size);
|
||
}
|
||
|
||
|
||
/* MPZ addition and subtraction */
|
||
|
||
|
||
void
|
||
mpz_add_ui (mpz_t r, const mpz_t a, unsigned long b)
|
||
{
|
||
mpz_t bb;
|
||
mpz_init_set_ui (bb, b);
|
||
mpz_add (r, a, bb);
|
||
mpz_clear (bb);
|
||
}
|
||
|
||
void
|
||
mpz_sub_ui (mpz_t r, const mpz_t a, unsigned long b)
|
||
{
|
||
mpz_ui_sub (r, b, a);
|
||
mpz_neg (r, r);
|
||
}
|
||
|
||
void
|
||
mpz_ui_sub (mpz_t r, unsigned long a, const mpz_t b)
|
||
{
|
||
mpz_neg (r, b);
|
||
mpz_add_ui (r, r, 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_ptr rp;
|
||
mp_limb_t cy;
|
||
|
||
if (an < bn)
|
||
{
|
||
MPZ_SRCPTR_SWAP (a, b);
|
||
MP_SIZE_T_SWAP (an, bn);
|
||
}
|
||
|
||
rp = MPZ_REALLOC (r, an + 1);
|
||
cy = mpn_add (rp, a->_mp_d, an, b->_mp_d, bn);
|
||
|
||
rp[an] = cy;
|
||
|
||
return an + cy;
|
||
}
|
||
|
||
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, v);
|
||
}
|
||
|
||
void
|
||
mpz_mul_ui (mpz_t r, const mpz_t u, unsigned long int v)
|
||
{
|
||
mpz_t vv;
|
||
mpz_init_set_ui (vv, v);
|
||
mpz_mul (r, u, vv);
|
||
mpz_clear (vv);
|
||
return;
|
||
}
|
||
|
||
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 = u->_mp_size;
|
||
vn = v->_mp_size;
|
||
|
||
if (un == 0 || vn == 0)
|
||
{
|
||
r->_mp_size = 0;
|
||
return;
|
||
}
|
||
|
||
sign = (un ^ vn) < 0;
|
||
|
||
un = GMP_ABS (un);
|
||
vn = GMP_ABS (vn);
|
||
|
||
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);
|
||
|
||
mpn_zero (rp, limbs);
|
||
|
||
r->_mp_size = (u->_mp_size < 0) ? - rn : rn;
|
||
}
|
||
|
||
void
|
||
mpz_addmul_ui (mpz_t r, const mpz_t u, unsigned long int v)
|
||
{
|
||
mpz_t t;
|
||
mpz_init_set_ui (t, v);
|
||
mpz_mul (t, u, t);
|
||
mpz_add (r, r, t);
|
||
mpz_clear (t);
|
||
}
|
||
|
||
void
|
||
mpz_submul_ui (mpz_t r, const mpz_t u, unsigned long int v)
|
||
{
|
||
mpz_t t;
|
||
mpz_init_set_ui (t, v);
|
||
mpz_mul (t, u, t);
|
||
mpz_sub (r, r, t);
|
||
mpz_clear (t);
|
||
}
|
||
|
||
void
|
||
mpz_addmul (mpz_t r, const mpz_t u, const mpz_t v)
|
||
{
|
||
mpz_t t;
|
||
mpz_init (t);
|
||
mpz_mul (t, u, v);
|
||
mpz_add (r, r, t);
|
||
mpz_clear (t);
|
||
}
|
||
|
||
void
|
||
mpz_submul (mpz_t r, const mpz_t u, const mpz_t v)
|
||
{
|
||
mpz_t t;
|
||
mpz_init (t);
|
||
mpz_mul (t, u, v);
|
||
mpz_sub (r, r, t);
|
||
mpz_clear (t);
|
||
}
|
||
|
||
|
||
/* 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_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)
|
||
{
|
||
mpz_div_qr (NULL, r, n, d, d->_mp_size >= 0 ? GMP_DIV_FLOOR : 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;
|
||
int 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;
|
||
|
||
if (adjust)
|
||
mpz_add_ui (q, q, 1);
|
||
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;
|
||
|
||
gmp_assert_nocarry (! mpn_neg (rp, u->_mp_d, un));
|
||
for (i = un; 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. */
|
||
mpn_neg (rp, rp, rn);
|
||
|
||
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;
|
||
}
|
||
|
||
int
|
||
mpz_congruent_p (const mpz_t a, const mpz_t b, const mpz_t m)
|
||
{
|
||
mpz_t t;
|
||
int res;
|
||
|
||
/* a == b (mod 0) iff a == b */
|
||
if (mpz_sgn (m) == 0)
|
||
return (mpz_cmp (a, b) == 0);
|
||
|
||
mpz_init (t);
|
||
mpz_sub (t, a, b);
|
||
res = mpz_divisible_p (t, m);
|
||
mpz_clear (t);
|
||
|
||
return res;
|
||
}
|
||
|
||
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)
|
||
{
|
||
unsigned long ret;
|
||
mpz_t rr, dd;
|
||
|
||
mpz_init (rr);
|
||
mpz_init_set_ui (dd, d);
|
||
mpz_div_qr (q, rr, n, dd, mode);
|
||
mpz_clear (dd);
|
||
ret = mpz_get_ui (rr);
|
||
|
||
if (r)
|
||
mpz_swap (r, rr);
|
||
mpz_clear (rr);
|
||
|
||
return ret;
|
||
}
|
||
|
||
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)
|
||
{
|
||
mpz_t t;
|
||
mpz_init_set_ui(t, v);
|
||
mpz_gcd (t, u, t);
|
||
if (v > 0)
|
||
v = mpz_get_ui (t);
|
||
|
||
if (g)
|
||
mpz_swap (t, g);
|
||
|
||
mpz_clear (t);
|
||
|
||
return v;
|
||
}
|
||
|
||
static mp_bitcnt_t
|
||
mpz_make_odd (mpz_t r)
|
||
{
|
||
mp_bitcnt_t shift;
|
||
|
||
assert (r->_mp_size > 0);
|
||
/* Count trailing zeros, equivalent to mpn_scan1, because we know that there is a 1 */
|
||
shift = mpn_scan1 (r->_mp_d, 0);
|
||
mpz_tdiv_q_2exp (r, r, shift);
|
||
|
||
return 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);
|
||
|
||
mpz_abs (tu, u);
|
||
uz = mpz_make_odd (tu);
|
||
mpz_abs (tv, v);
|
||
vz = mpz_make_odd (tv);
|
||
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);
|
||
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 *gp;
|
||
|
||
mpz_tdiv_r (tu, tu, tv);
|
||
gp = MPZ_REALLOC (g, 1); /* gp = mpz_limbs_modify (g, 1); */
|
||
*gp = mpn_gcd_11 (tu->_mp_d[0], tv->_mp_d[0]);
|
||
|
||
g->_mp_size = *gp != 0; /* mpz_limbs_finish (g, 1); */
|
||
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)
|
||
s->_mp_size = 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)
|
||
t->_mp_size = 0;
|
||
return;
|
||
}
|
||
|
||
mpz_init (tu);
|
||
mpz_init (tv);
|
||
mpz_init (s0);
|
||
mpz_init (s1);
|
||
mpz_init (t0);
|
||
mpz_init (t1);
|
||
|
||
mpz_abs (tu, u);
|
||
uz = mpz_make_odd (tu);
|
||
mpz_abs (tv, v);
|
||
vz = mpz_make_odd (tv);
|
||
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_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);
|
||
mpz_setbit (t0, uz + 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);
|
||
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);
|
||
mpz_mul_2exp (t0, t0, shift);
|
||
mpz_mul_2exp (s0, s0, shift);
|
||
}
|
||
power += shift;
|
||
}
|
||
}
|
||
else
|
||
mpz_setbit (t0, uz);
|
||
|
||
/* 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);
|
||
}
|
||
assert (mpz_even_p (t0) && mpz_even_p (s0));
|
||
mpz_tdiv_q_2exp (s0, s0, 1);
|
||
mpz_tdiv_q_2exp (t0, t0, 1);
|
||
}
|
||
|
||
/* 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);
|
||
|
||
bit = GMP_ULONG_HIGHBIT;
|
||
do
|
||
{
|
||
mpz_mul (tr, tr, tr);
|
||
if (e & bit)
|
||
mpz_mul (tr, tr, b);
|
||
bit >>= 1;
|
||
}
|
||
while (bit > 0);
|
||
|
||
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, mpz_cmpabs_ui (m, 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_alloc_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-invertible 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;
|
||
|
||
bit = GMP_LIMB_HIGHBIT;
|
||
do
|
||
{
|
||
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);
|
||
}
|
||
bit >>= 1;
|
||
}
|
||
while (bit > 0);
|
||
}
|
||
|
||
/* 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_limbs (tp, mn);
|
||
|
||
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;
|
||
mp_bitcnt_t bc;
|
||
mpz_t t, u;
|
||
|
||
sgn = y->_mp_size < 0;
|
||
if ((~z & sgn) != 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) {
|
||
if (x)
|
||
mpz_set (x, y);
|
||
if (r)
|
||
r->_mp_size = 0;
|
||
return;
|
||
}
|
||
|
||
mpz_init (u);
|
||
mpz_init (t);
|
||
bc = (mpz_sizeinbase (y, 2) - 1) / z + 1;
|
||
mpz_setbit (t, bc);
|
||
|
||
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);
|
||
}
|
||
if (x)
|
||
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);
|
||
}
|
||
|
||
int
|
||
mpz_perfect_square_p (const mpz_t u)
|
||
{
|
||
if (u->_mp_size <= 0)
|
||
return (u->_mp_size == 0);
|
||
else
|
||
return mpz_root (NULL, u, 2);
|
||
}
|
||
|
||
int
|
||
mpn_perfect_square_p (mp_srcptr p, mp_size_t n)
|
||
{
|
||
mpz_t t;
|
||
|
||
assert (n > 0);
|
||
assert (p [n-1] != 0);
|
||
return mpz_root (NULL, mpz_roinit_normal_n (t, p, n), 2);
|
||
}
|
||
|
||
mp_size_t
|
||
mpn_sqrtrem (mp_ptr sp, mp_ptr rp, mp_srcptr p, mp_size_t n)
|
||
{
|
||
mpz_t s, r, u;
|
||
mp_size_t res;
|
||
|
||
assert (n > 0);
|
||
assert (p [n-1] != 0);
|
||
|
||
mpz_init (r);
|
||
mpz_init (s);
|
||
mpz_rootrem (s, r, mpz_roinit_normal_n (u, p, n), 2);
|
||
|
||
assert (s->_mp_size == (n+1)/2);
|
||
mpn_copyd (sp, s->_mp_d, s->_mp_size);
|
||
mpz_clear (s);
|
||
res = r->_mp_size;
|
||
if (rp)
|
||
mpn_copyd (rp, r->_mp_d, res);
|
||
mpz_clear (r);
|
||
return res;
|
||
}
|
||
|
||
/* Combinatorics */
|
||
|
||
void
|
||
mpz_mfac_uiui (mpz_t x, unsigned long n, unsigned long m)
|
||
{
|
||
mpz_set_ui (x, n + (n == 0));
|
||
if (m + 1 < 2) return;
|
||
while (n > m + 1)
|
||
mpz_mul_ui (x, x, n -= m);
|
||
}
|
||
|
||
void
|
||
mpz_2fac_ui (mpz_t x, unsigned long n)
|
||
{
|
||
mpz_mfac_uiui (x, n, 2);
|
||
}
|
||
|
||
void
|
||
mpz_fac_ui (mpz_t x, unsigned long n)
|
||
{
|
||
mpz_mfac_uiui (x, n, 1);
|
||
}
|
||
|
||
void
|
||
mpz_bin_uiui (mpz_t r, unsigned long n, unsigned long k)
|
||
{
|
||
mpz_t t;
|
||
|
||
mpz_set_ui (r, k <= n);
|
||
|
||
if (k > (n >> 1))
|
||
k = (k <= n) ? n - k : 0;
|
||
|
||
mpz_init (t);
|
||
mpz_fac_ui (t, k);
|
||
|
||
for (; k > 0; --k)
|
||
mpz_mul_ui (r, r, n--);
|
||
|
||
mpz_divexact (r, r, t);
|
||
mpz_clear (t);
|
||
}
|
||
|
||
|
||
/* Primality testing */
|
||
|
||
/* Computes Kronecker (a/b) with odd b, a!=0 and GCD(a,b) = 1 */
|
||
/* Adapted from JACOBI_BASE_METHOD==4 in mpn/generic/jacbase.c */
|
||
static int
|
||
gmp_jacobi_coprime (mp_limb_t a, mp_limb_t b)
|
||
{
|
||
int c, bit = 0;
|
||
|
||
assert (b & 1);
|
||
assert (a != 0);
|
||
/* assert (mpn_gcd_11 (a, b) == 1); */
|
||
|
||
/* Below, we represent a and b shifted right so that the least
|
||
significant one bit is implicit. */
|
||
b >>= 1;
|
||
|
||
gmp_ctz(c, a);
|
||
a >>= 1;
|
||
|
||
for (;;)
|
||
{
|
||
a >>= c;
|
||
/* (2/b) = -1 if b = 3 or 5 mod 8 */
|
||
bit ^= c & (b ^ (b >> 1));
|
||
if (a < b)
|
||
{
|
||
if (a == 0)
|
||
return bit & 1 ? -1 : 1;
|
||
bit ^= a & b;
|
||
a = b - a;
|
||
b -= a;
|
||
}
|
||
else
|
||
{
|
||
a -= b;
|
||
assert (a != 0);
|
||
}
|
||
|
||
gmp_ctz(c, a);
|
||
++c;
|
||
}
|
||
}
|
||
|
||
static void
|
||
gmp_lucas_step_k_2k (mpz_t V, mpz_t Qk, const mpz_t n)
|
||
{
|
||
mpz_mod (Qk, Qk, n);
|
||
/* V_{2k} <- V_k ^ 2 - 2Q^k */
|
||
mpz_mul (V, V, V);
|
||
mpz_submul_ui (V, Qk, 2);
|
||
mpz_tdiv_r (V, V, n);
|
||
/* Q^{2k} = (Q^k)^2 */
|
||
mpz_mul (Qk, Qk, Qk);
|
||
}
|
||
|
||
/* Computes V_k, Q^k (mod n) for the Lucas' sequence */
|
||
/* with P=1, Q=Q; k = (n>>b0)|1. */
|
||
/* Requires an odd n > 4; b0 > 0; -2*Q must not overflow a long */
|
||
/* Returns (U_k == 0) and sets V=V_k and Qk=Q^k. */
|
||
static int
|
||
gmp_lucas_mod (mpz_t V, mpz_t Qk, long Q,
|
||
mp_bitcnt_t b0, const mpz_t n)
|
||
{
|
||
mp_bitcnt_t bs;
|
||
mpz_t U;
|
||
int res;
|
||
|
||
assert (b0 > 0);
|
||
assert (Q <= - (LONG_MIN / 2));
|
||
assert (Q >= - (LONG_MAX / 2));
|
||
assert (mpz_cmp_ui (n, 4) > 0);
|
||
assert (mpz_odd_p (n));
|
||
|
||
mpz_init_set_ui (U, 1); /* U1 = 1 */
|
||
mpz_set_ui (V, 1); /* V1 = 1 */
|
||
mpz_set_si (Qk, Q);
|
||
|
||
for (bs = mpz_sizeinbase (n, 2) - 1; --bs >= b0;)
|
||
{
|
||
/* U_{2k} <- U_k * V_k */
|
||
mpz_mul (U, U, V);
|
||
/* V_{2k} <- V_k ^ 2 - 2Q^k */
|
||
/* Q^{2k} = (Q^k)^2 */
|
||
gmp_lucas_step_k_2k (V, Qk, n);
|
||
|
||
/* A step k->k+1 is performed if the bit in $n$ is 1 */
|
||
/* mpz_tstbit(n,bs) or the bit is 0 in $n$ but */
|
||
/* should be 1 in $n+1$ (bs == b0) */
|
||
if (b0 == bs || mpz_tstbit (n, bs))
|
||
{
|
||
/* Q^{k+1} <- Q^k * Q */
|
||
mpz_mul_si (Qk, Qk, Q);
|
||
/* U_{k+1} <- (U_k + V_k) / 2 */
|
||
mpz_swap (U, V); /* Keep in V the old value of U_k */
|
||
mpz_add (U, U, V);
|
||
/* We have to compute U/2, so we need an even value, */
|
||
/* equivalent (mod n) */
|
||
if (mpz_odd_p (U))
|
||
mpz_add (U, U, n);
|
||
mpz_tdiv_q_2exp (U, U, 1);
|
||
/* V_{k+1} <-(D*U_k + V_k) / 2 =
|
||
U_{k+1} + (D-1)/2*U_k = U_{k+1} - 2Q*U_k */
|
||
mpz_mul_si (V, V, -2*Q);
|
||
mpz_add (V, U, V);
|
||
mpz_tdiv_r (V, V, n);
|
||
}
|
||
mpz_tdiv_r (U, U, n);
|
||
}
|
||
|
||
res = U->_mp_size == 0;
|
||
mpz_clear (U);
|
||
return res;
|
||
}
|
||
|
||
/* Performs strong Lucas' test on x, with parameters suggested */
|
||
/* for the BPSW test. Qk is only passed to recycle a variable. */
|
||
/* Requires GCD (x,6) = 1.*/
|
||
static int
|
||
gmp_stronglucas (const mpz_t x, mpz_t Qk)
|
||
{
|
||
mp_bitcnt_t b0;
|
||
mpz_t V, n;
|
||
mp_limb_t maxD, D; /* The absolute value is stored. */
|
||
long Q;
|
||
mp_limb_t tl;
|
||
|
||
/* Test on the absolute value. */
|
||
mpz_roinit_normal_n (n, x->_mp_d, GMP_ABS (x->_mp_size));
|
||
|
||
assert (mpz_odd_p (n));
|
||
/* assert (mpz_gcd_ui (NULL, n, 6) == 1); */
|
||
if (mpz_root (Qk, n, 2))
|
||
return 0; /* A square is composite. */
|
||
|
||
/* Check Ds up to square root (in case, n is prime)
|
||
or avoid overflows */
|
||
maxD = (Qk->_mp_size == 1) ? Qk->_mp_d [0] - 1 : GMP_LIMB_MAX;
|
||
|
||
D = 3;
|
||
/* Search a D such that (D/n) = -1 in the sequence 5,-7,9,-11,.. */
|
||
/* For those Ds we have (D/n) = (n/|D|) */
|
||
do
|
||
{
|
||
if (D >= maxD)
|
||
return 1 + (D != GMP_LIMB_MAX); /* (1 + ! ~ D) */
|
||
D += 2;
|
||
tl = mpz_tdiv_ui (n, D);
|
||
if (tl == 0)
|
||
return 0;
|
||
}
|
||
while (gmp_jacobi_coprime (tl, D) == 1);
|
||
|
||
mpz_init (V);
|
||
|
||
/* n-(D/n) = n+1 = d*2^{b0}, with d = (n>>b0) | 1 */
|
||
b0 = mpn_common_scan (~ n->_mp_d[0], 0, n->_mp_d, n->_mp_size, GMP_LIMB_MAX);
|
||
/* b0 = mpz_scan0 (n, 0); */
|
||
|
||
/* D= P^2 - 4Q; P = 1; Q = (1-D)/4 */
|
||
Q = (D & 2) ? (long) (D >> 2) + 1 : -(long) (D >> 2);
|
||
|
||
if (! gmp_lucas_mod (V, Qk, Q, b0, n)) /* If Ud != 0 */
|
||
while (V->_mp_size != 0 && --b0 != 0) /* while Vk != 0 */
|
||
/* V <- V ^ 2 - 2Q^k */
|
||
/* Q^{2k} = (Q^k)^2 */
|
||
gmp_lucas_step_k_2k (V, Qk, n);
|
||
|
||
mpz_clear (V);
|
||
return (b0 != 0);
|
||
}
|
||
|
||
static int
|
||
gmp_millerrabin (const mpz_t n, const mpz_t nm1, mpz_t y,
|
||
const mpz_t q, mp_bitcnt_t k)
|
||
{
|
||
assert (k > 0);
|
||
|
||
/* Caller must initialize y to the base. */
|
||
mpz_powm (y, y, q, n);
|
||
|
||
if (mpz_cmp_ui (y, 1) == 0 || mpz_cmp (y, nm1) == 0)
|
||
return 1;
|
||
|
||
while (--k > 0)
|
||
{
|
||
mpz_powm_ui (y, y, 2, n);
|
||
if (mpz_cmp (y, nm1) == 0)
|
||
return 1;
|
||
}
|
||
return 0;
|
||
}
|
||
|
||
/* This product is 0xc0cfd797, and fits in 32 bits. */
|
||
#define GMP_PRIME_PRODUCT \
|
||
(3UL*5UL*7UL*11UL*13UL*17UL*19UL*23UL*29UL)
|
||
|
||
/* Bit (p+1)/2 is set, for each odd prime <= 61 */
|
||
#define GMP_PRIME_MASK 0xc96996dcUL
|
||
|
||
int
|
||
mpz_probab_prime_p (const mpz_t n, int reps)
|
||
{
|
||
mpz_t nm1;
|
||
mpz_t q;
|
||
mpz_t y;
|
||
mp_bitcnt_t k;
|
||
int is_prime;
|
||
int j;
|
||
|
||
/* Note that we use the absolute value of n only, for compatibility
|
||
with the real GMP. */
|
||
if (mpz_even_p (n))
|
||
return (mpz_cmpabs_ui (n, 2) == 0) ? 2 : 0;
|
||
|
||
/* Above test excludes n == 0 */
|
||
assert (n->_mp_size != 0);
|
||
|
||
if (mpz_cmpabs_ui (n, 64) < 0)
|
||
return (GMP_PRIME_MASK >> (n->_mp_d[0] >> 1)) & 2;
|
||
|
||
if (mpz_gcd_ui (NULL, n, GMP_PRIME_PRODUCT) != 1)
|
||
return 0;
|
||
|
||
/* All prime factors are >= 31. */
|
||
if (mpz_cmpabs_ui (n, 31*31) < 0)
|
||
return 2;
|
||
|
||
mpz_init (nm1);
|
||
mpz_init (q);
|
||
|
||
/* Find q and k, where q is odd and n = 1 + 2**k * q. */
|
||
mpz_abs (nm1, n);
|
||
nm1->_mp_d[0] -= 1;
|
||
/* Count trailing zeros, equivalent to mpn_scan1, because we know that there is a 1 */
|
||
k = mpn_scan1 (nm1->_mp_d, 0);
|
||
mpz_tdiv_q_2exp (q, nm1, k);
|
||
|
||
/* BPSW test */
|
||
mpz_init_set_ui (y, 2);
|
||
is_prime = gmp_millerrabin (n, nm1, y, q, k) && gmp_stronglucas (n, y);
|
||
reps -= 24; /* skip the first 24 repetitions */
|
||
|
||
/* Use Miller-Rabin, with a deterministic sequence of bases, a[j] =
|
||
j^2 + j + 41 using Euler's polynomial. We potentially stop early,
|
||
if a[j] >= n - 1. Since n >= 31*31, this can happen only if reps >
|
||
30 (a[30] == 971 > 31*31 == 961). */
|
||
|
||
for (j = 0; is_prime & (j < reps); j++)
|
||
{
|
||
mpz_set_ui (y, (unsigned long) j*j+j+41);
|
||
if (mpz_cmp (y, nm1) >= 0)
|
||
{
|
||
/* Don't try any further bases. This "early" break does not affect
|
||
the result for any reasonable reps value (<=5000 was tested) */
|
||
assert (j >= 30);
|
||
break;
|
||
}
|
||
is_prime = gmp_millerrabin (n, nm1, y, q, k);
|
||
}
|
||
mpz_clear (nm1);
|
||
mpz_clear (q);
|
||
mpz_clear (y);
|
||
|
||
return is_prime;
|
||
}
|
||
|
||
|
||
/* 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 complement.
|
||
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 && (mp_limb_t) (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 = mpn_normalized_size (dp, dn);
|
||
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_add_ui (r, u, 1);
|
||
mpz_neg (r, r);
|
||
}
|
||
|
||
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 + (mp_size_t) rc);
|
||
|
||
up = u->_mp_d;
|
||
vp = v->_mp_d;
|
||
|
||
i = 0;
|
||
do
|
||
{
|
||
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;
|
||
}
|
||
while (++i < vn);
|
||
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 + (mp_size_t) rc);
|
||
|
||
up = u->_mp_d;
|
||
vp = v->_mp_d;
|
||
|
||
i = 0;
|
||
do
|
||
{
|
||
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;
|
||
}
|
||
while (++i < vn);
|
||
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 + (mp_size_t) rc);
|
||
|
||
up = u->_mp_d;
|
||
vp = v->_mp_d;
|
||
|
||
i = 0;
|
||
do
|
||
{
|
||
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;
|
||
}
|
||
while (++i < vn);
|
||
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. */
|
||
int LOCAL_SHIFT_BITS = 16;
|
||
for (c = 0; x > 0;)
|
||
{
|
||
unsigned w = x - ((x >> 1) & 0x5555);
|
||
w = ((w >> 2) & 0x3333) + (w & 0x3333);
|
||
w = (w >> 4) + w;
|
||
w = ((w >> 8) & 0x000f) + (w & 0x000f);
|
||
c += w;
|
||
if (GMP_LIMB_BITS > LOCAL_SHIFT_BITS)
|
||
x >>= LOCAL_SHIFT_BITS;
|
||
else
|
||
x = 0;
|
||
}
|
||
return c;
|
||
}
|
||
|
||
mp_bitcnt_t
|
||
mpn_popcount (mp_srcptr p, mp_size_t n)
|
||
{
|
||
mp_size_t i;
|
||
mp_bitcnt_t c;
|
||
|
||
for (c = 0, i = 0; i < n; i++)
|
||
c += gmp_popcount_limb (p[i]);
|
||
|
||
return c;
|
||
}
|
||
|
||
mp_bitcnt_t
|
||
mpz_popcount (const mpz_t u)
|
||
{
|
||
mp_size_t un;
|
||
|
||
un = u->_mp_size;
|
||
|
||
if (un < 0)
|
||
return ~(mp_bitcnt_t) 0;
|
||
|
||
return mpn_popcount (u->_mp_d, un);
|
||
}
|
||
|
||
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;
|
||
|
||
comp = - (uc = vc = (un < 0));
|
||
if (uc)
|
||
{
|
||
assert (vn < 0);
|
||
un = -un;
|
||
vn = -vn;
|
||
}
|
||
|
||
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;
|
||
|
||
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);
|
||
|
||
up = u->_mp_d;
|
||
ux = 0;
|
||
limb = up[i];
|
||
|
||
if (starting_bit != 0)
|
||
{
|
||
if (us < 0)
|
||
{
|
||
ux = mpn_zero_p (up, i);
|
||
limb = ~ limb + ux;
|
||
ux = - (mp_limb_t) (limb >= ux);
|
||
}
|
||
|
||
/* Mask to 0 all bits before starting_bit, thus ignoring them. */
|
||
limb &= GMP_LIMB_MAX << (starting_bit % GMP_LIMB_BITS);
|
||
}
|
||
|
||
return mpn_common_scan (limb, i, up, un, ux);
|
||
}
|
||
|
||
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;
|
||
|
||
us = u->_mp_size;
|
||
ux = - (mp_limb_t) (us >= 0);
|
||
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 (ux ? starting_bit : ~(mp_bitcnt_t) 0);
|
||
|
||
up = u->_mp_d;
|
||
limb = up[i] ^ ux;
|
||
|
||
if (ux == 0)
|
||
limb -= mpn_zero_p (up, i); /* limb = ~(~limb + zero_p) */
|
||
|
||
/* Mask all bits before starting_bit, thus ignoring them. */
|
||
limb &= GMP_LIMB_MAX << (starting_bit % GMP_LIMB_BITS);
|
||
|
||
return mpn_common_scan (limb, i, up, un, ux);
|
||
}
|
||
|
||
|
||
/* MPZ base conversion. */
|
||
|
||
size_t
|
||
mpz_sizeinbase (const mpz_t u, int base)
|
||
{
|
||
mp_size_t un, tn;
|
||
mp_srcptr up;
|
||
mp_ptr tp;
|
||
mp_bitcnt_t bits;
|
||
struct gmp_div_inverse bi;
|
||
size_t ndigits;
|
||
|
||
assert (base >= 2);
|
||
assert (base <= 62);
|
||
|
||
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_alloc_limbs (un);
|
||
mpn_copyi (tp, up, un);
|
||
mpn_div_qr_1_invert (&bi, base);
|
||
|
||
tn = un;
|
||
ndigits = 0;
|
||
do
|
||
{
|
||
ndigits++;
|
||
mpn_div_qr_1_preinv (tp, tp, tn, &bi);
|
||
tn -= (tp[tn-1] == 0);
|
||
}
|
||
while (tn > 0);
|
||
|
||
gmp_free_limbs (tp, un);
|
||
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, osn;
|
||
|
||
digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz";
|
||
if (base > 1)
|
||
{
|
||
if (base <= 36)
|
||
digits = "0123456789abcdefghijklmnopqrstuvwxyz";
|
||
else if (base > 62)
|
||
return NULL;
|
||
}
|
||
else if (base >= -1)
|
||
base = 10;
|
||
else
|
||
{
|
||
base = -base;
|
||
if (base > 36)
|
||
return NULL;
|
||
}
|
||
|
||
sn = 1 + mpz_sizeinbase (u, base);
|
||
if (!sp)
|
||
{
|
||
osn = 1 + sn;
|
||
sp = (char *) gmp_alloc (osn);
|
||
}
|
||
else
|
||
osn = 0;
|
||
un = GMP_ABS (u->_mp_size);
|
||
|
||
if (un == 0)
|
||
{
|
||
sp[0] = '0';
|
||
sn = 1;
|
||
goto ret;
|
||
}
|
||
|
||
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_alloc_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_limbs (tp, un);
|
||
}
|
||
|
||
for (; i < sn; i++)
|
||
sp[i] = digits[(unsigned char) sp[i]];
|
||
|
||
ret:
|
||
sp[sn] = '\0';
|
||
if (osn && osn != sn + 1)
|
||
sp = (char*) gmp_realloc (sp, osn, sn + 1);
|
||
return sp;
|
||
}
|
||
|
||
int
|
||
mpz_set_str (mpz_t r, const char *sp, int base)
|
||
{
|
||
unsigned bits, value_of_a;
|
||
mp_size_t rn, alloc;
|
||
mp_ptr rp;
|
||
size_t dn, sn;
|
||
int sign;
|
||
unsigned char *dp;
|
||
|
||
assert (base == 0 || (base >= 2 && base <= 62));
|
||
|
||
while (isspace( (unsigned char) *sp))
|
||
sp++;
|
||
|
||
sign = (*sp == '-');
|
||
sp += sign;
|
||
|
||
if (base == 0)
|
||
{
|
||
if (sp[0] == '0')
|
||
{
|
||
if (sp[1] == 'x' || sp[1] == 'X')
|
||
{
|
||
base = 16;
|
||
sp += 2;
|
||
}
|
||
else if (sp[1] == 'b' || sp[1] == 'B')
|
||
{
|
||
base = 2;
|
||
sp += 2;
|
||
}
|
||
else
|
||
base = 8;
|
||
}
|
||
else
|
||
base = 10;
|
||
}
|
||
|
||
if (!*sp)
|
||
{
|
||
r->_mp_size = 0;
|
||
return -1;
|
||
}
|
||
sn = strlen(sp);
|
||
dp = (unsigned char *) gmp_alloc (sn);
|
||
|
||
value_of_a = (base > 36) ? 36 : 10;
|
||
for (dn = 0; *sp; sp++)
|
||
{
|
||
unsigned digit;
|
||
|
||
if (isspace ((unsigned char) *sp))
|
||
continue;
|
||
else if (*sp >= '0' && *sp <= '9')
|
||
digit = *sp - '0';
|
||
else if (*sp >= 'a' && *sp <= 'z')
|
||
digit = *sp - 'a' + value_of_a;
|
||
else if (*sp >= 'A' && *sp <= 'Z')
|
||
digit = *sp - 'A' + 10;
|
||
else
|
||
digit = base; /* fail */
|
||
|
||
if (digit >= (unsigned) base)
|
||
{
|
||
gmp_free (dp, sn);
|
||
r->_mp_size = 0;
|
||
return -1;
|
||
}
|
||
|
||
dp[dn++] = digit;
|
||
}
|
||
|
||
if (!dn)
|
||
{
|
||
gmp_free (dp, sn);
|
||
r->_mp_size = 0;
|
||
return -1;
|
||
}
|
||
bits = mpn_base_power_of_two_p (base);
|
||
|
||
if (bits > 0)
|
||
{
|
||
alloc = (dn * 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 = (dn + info.exp - 1) / info.exp;
|
||
rp = MPZ_REALLOC (r, alloc);
|
||
rn = mpn_set_str_other (rp, dp, dn, base, &info);
|
||
/* Normalization, needed for all-zero input. */
|
||
assert (rn > 0);
|
||
rn -= rp[rn-1] == 0;
|
||
}
|
||
assert (rn <= alloc);
|
||
gmp_free (dp, sn);
|
||
|
||
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, n;
|
||
|
||
str = mpz_get_str (NULL, base, x);
|
||
if (!str)
|
||
return 0;
|
||
len = strlen (str);
|
||
n = fwrite (str, 1, len, stream);
|
||
gmp_free (str, len + 1);
|
||
return n;
|
||
}
|
||
|
||
|
||
static int
|
||
gmp_detect_endian (void)
|
||
{
|
||
static const int i = 2;
|
||
const unsigned char *p = (const unsigned char *) &i;
|
||
return 1 - *p;
|
||
}
|
||
|
||
/* 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;
|
||
}
|
||
}
|
||
}
|
||
assert (i + (bytes > 0) == rn);
|
||
if (limb != 0)
|
||
rp[i++] = limb;
|
||
else
|
||
i = mpn_normalized_size (rp, i);
|
||
|
||
r->_mp_size = i;
|
||
}
|
||
|
||
void *
|
||
mpz_export (void *r, size_t *countp, int order, size_t size, int endian,
|
||
size_t nails, const mpz_t u)
|
||
{
|
||
size_t count;
|
||
mp_size_t un;
|
||
|
||
if (nails != 0)
|
||
gmp_die ("mpz_export: Nails not supported.");
|
||
|
||
assert (order == 1 || order == -1);
|
||
assert (endian >= -1 && endian <= 1);
|
||
assert (size > 0 || u->_mp_size == 0);
|
||
|
||
un = u->_mp_size;
|
||
count = 0;
|
||
if (un != 0)
|
||
{
|
||
size_t k;
|
||
unsigned char *p;
|
||
ptrdiff_t word_step;
|
||
/* The current (partial) limb. */
|
||
mp_limb_t limb;
|
||
/* The number of bytes left to do in this limb. */
|
||
size_t bytes;
|
||
/* The index where the limb was read. */
|
||
mp_size_t i;
|
||
|
||
un = GMP_ABS (un);
|
||
|
||
/* Count bytes in top limb. */
|
||
limb = u->_mp_d[un-1];
|
||
assert (limb != 0);
|
||
|
||
k = (GMP_LIMB_BITS <= CHAR_BIT);
|
||
if (!k)
|
||
{
|
||
do {
|
||
int LOCAL_CHAR_BIT = CHAR_BIT;
|
||
k++; limb >>= LOCAL_CHAR_BIT;
|
||
} while (limb != 0);
|
||
}
|
||
/* else limb = 0; */
|
||
|
||
count = (k + (un-1) * sizeof (mp_limb_t) + size - 1) / size;
|
||
|
||
if (!r)
|
||
r = gmp_alloc (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 (sizeof (mp_limb_t) == 1)
|
||
{
|
||
if (i < un)
|
||
*p = u->_mp_d[i++];
|
||
else
|
||
*p = 0;
|
||
}
|
||
else
|
||
{
|
||
int LOCAL_CHAR_BIT = CHAR_BIT;
|
||
if (bytes == 0)
|
||
{
|
||
if (i < un)
|
||
limb = u->_mp_d[i++];
|
||
bytes = sizeof (mp_limb_t);
|
||
}
|
||
*p = limb;
|
||
limb >>= LOCAL_CHAR_BIT;
|
||
bytes--;
|
||
}
|
||
}
|
||
}
|
||
assert (i == un);
|
||
assert (k == count);
|
||
}
|
||
|
||
if (countp)
|
||
*countp = count;
|
||
|
||
return r;
|
||
}
|