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4466 lines
90 KiB
4466 lines
90 KiB
/* 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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Copyright 1991-1997, 1999-2015 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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neither with GMP nor 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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/* 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) 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(uint64_t) * CHAR_BIT)
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#define GMP_ULONG_HIGHBIT ((uint64_t) 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) (-(int64_t)((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_assert_nocarry(x) do { \
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mp_limb_t __cy = x; if ( __cy != 0 ) \
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; \
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assert (__cy == 0); \
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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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uint32_t __clz_c; \
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for (__clz_c = 0; \
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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 <<= 8; \
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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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uint32_t __ctz_c = 0; \
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gmp_clz (__ctz_c, __ctz_x & - (int64_t)__ctz_x); \
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(count) = GMP_LIMB_BITS - 1 - (int64_t)__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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mp_limb_t __x0, __x1, __x2, __x3; \
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uint32_t __ul, __vl, __uh, __vh; \
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mp_limb_t __u = (u), __v = (v); \
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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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} 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 = -(_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 = -((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_SIZE_sT_SWAP(x, y) \
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do { \
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uint32_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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/* Realloc for an mpz_t WHAT if it has less than NEEDED limbs. */
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#define MPZ_REALLOC(z,n) ((n) > (z)->_mp_alloc \
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? mpz_realloc(z,n) \
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: (z)->_mp_d)
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struct gmp_div_inverse
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{
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/* Normalization shift count. */
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uint32_t shift;
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/* Normalized divisor (d0 unused for mpn_div_qr_1) */
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mp_limb_t d1, d0;
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/* Inverse, for 2/1 or 3/2. */
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mp_limb_t di;
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};
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/* MPZ division */
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enum mpz_div_round_mode { GMP_DIV_FLOOR, GMP_DIV_CEIL, GMP_DIV_TRUNC };
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const int mp_bits_per_limb = GMP_LIMB_BITS;
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struct mpn_base_info
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{
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/* bb is the largest power of the base which fits in one limb, and
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exp is the corresponding exponent. */
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uint32_t exp;
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mp_limb_t bb;
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};
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#ifdef nonessential
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/* Memory allocation and other helper functions. */
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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 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 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_xalloc(size) ((*gmp_allocate_func)((size)))
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#define gmp_free(p) ((*gmp_free_func) ((p), 0))
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/* MPN interface */
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int 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_mul_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
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{
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mpn_mul (rp, ap, n, bp, n);
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}
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void
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mpn_sqr (mp_ptr rp, mp_srcptr ap, mp_size_t n)
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{
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mpn_mul (rp, ap, n, ap, n);
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}
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static mp_bitcnt_t
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mpn_common_scan (mp_limb_t limb, mp_size_t i, mp_srcptr up, mp_size_t un,
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mp_limb_t ux)
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{
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uint32_t cnt;
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assert (ux == 0 || ux == GMP_LIMB_MAX);
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assert (0 <= i && i <= un );
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while (limb == 0)
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{
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i++;
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if (i == un)
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return (ux == 0 ? ~(mp_bitcnt_t) 0 : un * GMP_LIMB_BITS);
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limb = ux ^ up[i];
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}
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gmp_ctz (cnt, limb);
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return (mp_bitcnt_t) i * GMP_LIMB_BITS + cnt;
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}
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mp_bitcnt_t
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mpn_scan1 (mp_srcptr ptr, mp_bitcnt_t bit)
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{
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mp_size_t i;
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i = bit / GMP_LIMB_BITS;
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return mpn_common_scan ( ptr[i] & (GMP_LIMB_MAX << (bit % GMP_LIMB_BITS)),
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i, ptr, i, 0);
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}
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mp_bitcnt_t
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mpn_scan0 (mp_srcptr ptr, mp_bitcnt_t bit)
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{
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mp_size_t i;
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i = bit / GMP_LIMB_BITS;
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return mpn_common_scan (~ptr[i] & (GMP_LIMB_MAX << (bit % GMP_LIMB_BITS)),
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i, ptr, i, GMP_LIMB_MAX);
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}
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#if 0
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static void
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mpn_div_qr_2 (mp_ptr qp, mp_ptr rp, mp_srcptr np, mp_size_t nn,
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mp_limb_t d1, mp_limb_t d0)
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{
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struct gmp_div_inverse inv;
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assert (nn >= 2);
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mpn_div_qr_2_invert (&inv, d1, d0);
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mpn_div_qr_2_preinv (qp, rp, np, nn, &inv);
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}
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#endif
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/* MPN base conversion. */
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static mp_bitcnt_t
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mpn_limb_size_in_base_2 (mp_limb_t u)
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{
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uint32_t shift;
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assert (u > 0);
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gmp_clz (shift, u);
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return GMP_LIMB_BITS - shift;
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}
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static size_t
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mpn_get_str_bits (uint8_t *sp, uint32_t bits, mp_srcptr up, mp_size_t un)
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{
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uint8_t mask;
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size_t sn, j;
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mp_size_t i;
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int shift;
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sn = ((un - 1) * GMP_LIMB_BITS + mpn_limb_size_in_base_2 (up[un-1])
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+ bits - 1) / bits;
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mask = (1U << bits) - 1;
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for (i = 0, j = sn, shift = 0; j-- > 0;)
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{
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uint8_t digit = up[i] >> shift;
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shift += bits;
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if (shift >= GMP_LIMB_BITS && ++i < un)
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{
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|
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 (uint8_t *sp, mp_limb_t w,
|
|
const struct gmp_div_inverse *binv)
|
|
{
|
|
mp_size_t i;
|
|
for (i = 0; w > 0; i++)
|
|
{
|
|
mp_limb_t h, l, r;
|
|
|
|
h = w >> (GMP_LIMB_BITS - binv->shift);
|
|
l = w << binv->shift;
|
|
|
|
gmp_udiv_qrnnd_preinv (w, r, h, l, binv->d1, binv->di);
|
|
assert ( (r << (GMP_LIMB_BITS - binv->shift)) == 0);
|
|
r >>= binv->shift;
|
|
|
|
sp[i] = r;
|
|
}
|
|
return i;
|
|
}
|
|
|
|
static size_t
|
|
mpn_get_str_other (uint8_t *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++)
|
|
{
|
|
uint8_t t = sp[i];
|
|
sp[i] = sp[sn - i - 1];
|
|
sp[sn - i - 1] = t;
|
|
}
|
|
|
|
return sn;
|
|
}
|
|
|
|
size_t
|
|
mpn_get_str (uint8_t *sp, int base, mp_ptr up, mp_size_t un)
|
|
{
|
|
uint32_t 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);
|
|
}
|
|
}
|
|
|
|
mp_size_t
|
|
mpn_set_str (mp_ptr rp, const uint8_t *sp, size_t sn, int base)
|
|
{
|
|
uint32_t 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 */
|
|
|
|
|
|
|
|
|
|
/* MPZ assignment and basic conversions. */
|
|
|
|
void
|
|
mpz_init_set_si (mpz_t r, int64_t x)
|
|
{
|
|
mpz_init (r);
|
|
mpz_set_si (r, x);
|
|
}
|
|
|
|
|
|
|
|
|
|
int
|
|
mpz_fits_slong_p (const mpz_t u)
|
|
{
|
|
mp_size_t us = u->_mp_size;
|
|
|
|
if (us == 1)
|
|
return u->_mp_d[0] < GMP_LIMB_HIGHBIT;
|
|
else if (us == -1)
|
|
return u->_mp_d[0] <= GMP_LIMB_HIGHBIT;
|
|
else
|
|
return (us == 0);
|
|
}
|
|
|
|
int
|
|
mpz_fits_ulong_p (const mpz_t u)
|
|
{
|
|
mp_size_t us = u->_mp_size;
|
|
|
|
return (us == (us > 0));
|
|
}
|
|
|
|
long int
|
|
mpz_get_si (const mpz_t u)
|
|
{
|
|
mp_size_t us = u->_mp_size;
|
|
|
|
if (us > 0)
|
|
return (long) (u->_mp_d[0] & ~GMP_LIMB_HIGHBIT);
|
|
else if (us < 0)
|
|
return (long) (- u->_mp_d[0] | GMP_LIMB_HIGHBIT);
|
|
else
|
|
return 0;
|
|
}
|
|
|
|
|
|
|
|
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;
|
|
}
|
|
|
|
mpz_srcptr
|
|
mpz_roinit_n (mpz_t x, mp_srcptr xp, mp_size_t xs)
|
|
{
|
|
x->_mp_alloc = 0;
|
|
x->_mp_d = (mp_ptr) xp;
|
|
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 = 2.0 * (double) GMP_LIMB_HIGHBIT;
|
|
Bi = 1.0 / B;
|
|
for (rn = 1; x >= B; rn++)
|
|
x *= Bi;
|
|
|
|
rp = MPZ_REALLOC (r, rn);
|
|
|
|
f = (mp_limb_t) x;
|
|
x -= f;
|
|
assert (x < 1.0);
|
|
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)
|
|
{
|
|
mp_size_t un;
|
|
double x;
|
|
double B = 2.0 * (double) GMP_LIMB_HIGHBIT;
|
|
|
|
un = GMP_ABS (u->_mp_size);
|
|
|
|
if (un == 0)
|
|
return 0.0;
|
|
|
|
x = u->_mp_d[--un];
|
|
while (un > 0)
|
|
x = B*x + u->_mp_d[--un];
|
|
|
|
if (u->_mp_size < 0)
|
|
x = -x;
|
|
|
|
return x;
|
|
}
|
|
|
|
int
|
|
mpz_cmpabs_d (const mpz_t x, double d)
|
|
{
|
|
mp_size_t xn;
|
|
double B, Bi;
|
|
mp_size_t i;
|
|
|
|
xn = x->_mp_size;
|
|
d = GMP_ABS (d);
|
|
|
|
if (xn != 0)
|
|
{
|
|
xn = GMP_ABS (xn);
|
|
|
|
B = 2.0 * (double) GMP_LIMB_HIGHBIT;
|
|
Bi = 1.0 / B;
|
|
|
|
/* Scale d so it can be compared with the top limb. */
|
|
for (i = 1; i < xn; i++)
|
|
d *= Bi;
|
|
|
|
if (d >= B)
|
|
return -1;
|
|
|
|
/* Compare floor(d) to top limb, subtract and cancel when equal. */
|
|
for (i = xn; i-- > 0;)
|
|
{
|
|
mp_limb_t f, xl;
|
|
|
|
f = (mp_limb_t) d;
|
|
xl = x->_mp_d[i];
|
|
if (xl > f)
|
|
return 1;
|
|
else if (xl < f)
|
|
return -1;
|
|
d = B * (d - f);
|
|
}
|
|
}
|
|
return - (d > 0.0);
|
|
}
|
|
|
|
int
|
|
mpz_cmp_d (const mpz_t x, double d)
|
|
{
|
|
if (x->_mp_size < 0)
|
|
{
|
|
if (d >= 0.0)
|
|
return -1;
|
|
else
|
|
return -mpz_cmpabs_d (x, d);
|
|
}
|
|
else
|
|
{
|
|
if (d < 0.0)
|
|
return 1;
|
|
else
|
|
return mpz_cmpabs_d (x, d);
|
|
}
|
|
}
|
|
|
|
|
|
/* MPZ comparisons and the like. */
|
|
int
|
|
mpz_sgn (const mpz_t u)
|
|
{
|
|
mp_size_t usize = u->_mp_size;
|
|
|
|
return (usize > 0) - (usize < 0);
|
|
}
|
|
|
|
int
|
|
mpz_cmp_si (const mpz_t u, long v)
|
|
{
|
|
mp_size_t usize = u->_mp_size;
|
|
|
|
if (usize < -1)
|
|
return -1;
|
|
else if (v >= 0)
|
|
return mpz_cmp_ui (u, v);
|
|
else if (usize >= 0)
|
|
return 1;
|
|
else /* usize == -1 */
|
|
{
|
|
mp_limb_t ul = u->_mp_d[0];
|
|
if ((mp_limb_t)GMP_NEG_CAST (uint64_t, v) < ul)
|
|
return -1;
|
|
else
|
|
return (mp_limb_t)GMP_NEG_CAST (uint64_t, v) > ul;
|
|
}
|
|
}
|
|
|
|
int
|
|
mpz_cmp_ui (const mpz_t u, uint64_t v)
|
|
{
|
|
mp_size_t usize = u->_mp_size;
|
|
|
|
if (usize > 1)
|
|
return 1;
|
|
else if (usize < 0)
|
|
return -1;
|
|
else
|
|
{
|
|
mp_limb_t ul = (usize > 0) ? u->_mp_d[0] : 0;
|
|
return (ul > v) - (ul < v);
|
|
}
|
|
}
|
|
|
|
int
|
|
mpz_cmpabs_ui (const mpz_t u, uint64_t v)
|
|
{
|
|
mp_size_t un = GMP_ABS (u->_mp_size);
|
|
mp_limb_t ul;
|
|
|
|
if (un > 1)
|
|
return 1;
|
|
|
|
ul = (un == 1) ? u->_mp_d[0] : 0;
|
|
|
|
return (ul > v) - (ul < 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;
|
|
}
|
|
|
|
|
|
|
|
/* MPZ addition and subtraction */
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
void
|
|
mpz_ui_sub (mpz_t r, uint64_t a, const mpz_t b)
|
|
{
|
|
if (b->_mp_size < 0)
|
|
r->_mp_size = mpz_abs_add_ui (r, b, a);
|
|
else
|
|
r->_mp_size = -mpz_abs_sub_ui (r, b, a);
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
/* 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 (uint64_t, v));
|
|
mpz_neg (r, r);
|
|
}
|
|
else
|
|
mpz_mul_ui (r, u, (uint64_t) v);
|
|
}
|
|
|
|
|
|
|
|
|
|
void
|
|
mpz_addmul_ui (mpz_t r, const mpz_t u, uint64_t v)
|
|
{
|
|
mpz_t t;
|
|
mpz_init (t);
|
|
mpz_mul_ui (t, u, v);
|
|
mpz_add (r, r, t);
|
|
mpz_clear (t);
|
|
}
|
|
|
|
void
|
|
mpz_submul_ui (mpz_t r, const mpz_t u, uint64_t v)
|
|
{
|
|
mpz_t t;
|
|
mpz_init (t);
|
|
mpz_mul_ui (t, u, v);
|
|
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);
|
|
}
|
|
|
|
|
|
|
|
|
|
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_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;
|
|
mp_limb_t cy;
|
|
|
|
for (cy = 1, i = 0; i < un; i++)
|
|
{
|
|
mp_limb_t s = ~u->_mp_d[i] + cy;
|
|
cy = s < cy;
|
|
rp[i] = s;
|
|
}
|
|
assert (cy == 0);
|
|
for (; i < rn - 1; i++)
|
|
rp[i] = GMP_LIMB_MAX;
|
|
|
|
rp[rn-1] = mask;
|
|
us = -us;
|
|
}
|
|
else
|
|
{
|
|
/* Just copy */
|
|
if (r != u)
|
|
mpn_copyi (rp, u->_mp_d, un);
|
|
|
|
rn = un;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
if (r != u)
|
|
mpn_copyi (rp, u->_mp_d, rn - 1);
|
|
|
|
rp[rn-1] = u->_mp_d[rn-1] & mask;
|
|
|
|
if (mode == ((us > 0) ? GMP_DIV_CEIL : GMP_DIV_FLOOR)) /* us != 0 here. */
|
|
{
|
|
/* If r != 0, compute 2^{bit_count} - r. */
|
|
mp_size_t i;
|
|
|
|
for (i = 0; i < rn && rp[i] == 0; i++)
|
|
;
|
|
if (i < rn)
|
|
{
|
|
/* r > 0, need to flip sign. */
|
|
rp[i] = ~rp[i] + 1;
|
|
while (++i < rn)
|
|
rp[i] = ~rp[i];
|
|
|
|
rp[rn-1] &= mask;
|
|
|
|
/* us is not used for anything else, so we can modify it
|
|
here to indicate flipped sign. */
|
|
us = -us;
|
|
}
|
|
}
|
|
}
|
|
rn = mpn_normalized_size (rp, rn);
|
|
r->_mp_size = us < 0 ? -rn : rn;
|
|
}
|
|
|
|
void
|
|
mpz_cdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
|
|
{
|
|
mpz_div_q_2exp (r, u, cnt, GMP_DIV_CEIL);
|
|
}
|
|
|
|
void
|
|
mpz_fdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
|
|
{
|
|
mpz_div_q_2exp (r, u, cnt, GMP_DIV_FLOOR);
|
|
}
|
|
|
|
void
|
|
mpz_tdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
|
|
{
|
|
mpz_div_q_2exp (r, u, cnt, GMP_DIV_TRUNC);
|
|
}
|
|
|
|
void
|
|
mpz_cdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
|
|
{
|
|
mpz_div_r_2exp (r, u, cnt, GMP_DIV_CEIL);
|
|
}
|
|
|
|
void
|
|
mpz_fdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
|
|
{
|
|
mpz_div_r_2exp (r, u, cnt, GMP_DIV_FLOOR);
|
|
}
|
|
|
|
void
|
|
mpz_tdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
|
|
{
|
|
mpz_div_r_2exp (r, u, cnt, GMP_DIV_TRUNC);
|
|
}
|
|
|
|
void
|
|
mpz_divexact (mpz_t q, const mpz_t n, const mpz_t d)
|
|
{
|
|
gmp_assert_nocarry (mpz_div_qr (q, NULL, n, d, GMP_DIV_TRUNC));
|
|
}
|
|
|
|
int
|
|
mpz_divisible_p (const mpz_t n, const mpz_t d)
|
|
{
|
|
return mpz_div_qr (NULL, NULL, n, d, GMP_DIV_TRUNC) == 0;
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
|
|
uint64_t
|
|
mpz_cdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, uint64_t d)
|
|
{
|
|
return mpz_div_qr_ui (q, r, n, d, GMP_DIV_CEIL);
|
|
}
|
|
|
|
uint64_t
|
|
mpz_fdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, uint64_t d)
|
|
{
|
|
return mpz_div_qr_ui (q, r, n, d, GMP_DIV_FLOOR);
|
|
}
|
|
|
|
uint64_t
|
|
mpz_tdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, uint64_t d)
|
|
{
|
|
return mpz_div_qr_ui (q, r, n, d, GMP_DIV_TRUNC);
|
|
}
|
|
|
|
uint64_t
|
|
mpz_cdiv_q_ui (mpz_t q, const mpz_t n, uint64_t d)
|
|
{
|
|
return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_CEIL);
|
|
}
|
|
|
|
uint64_t
|
|
mpz_fdiv_q_ui (mpz_t q, const mpz_t n, uint64_t d)
|
|
{
|
|
return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_FLOOR);
|
|
}
|
|
|
|
uint64_t
|
|
mpz_tdiv_q_ui (mpz_t q, const mpz_t n, uint64_t d)
|
|
{
|
|
return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_TRUNC);
|
|
}
|
|
|
|
uint64_t
|
|
mpz_cdiv_r_ui (mpz_t r, const mpz_t n, uint64_t d)
|
|
{
|
|
return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_CEIL);
|
|
}
|
|
uint64_t
|
|
mpz_fdiv_r_ui (mpz_t r, const mpz_t n, uint64_t d)
|
|
{
|
|
return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_FLOOR);
|
|
}
|
|
uint64_t
|
|
mpz_tdiv_r_ui (mpz_t r, const mpz_t n, uint64_t d)
|
|
{
|
|
return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_TRUNC);
|
|
}
|
|
|
|
uint64_t
|
|
mpz_cdiv_ui (const mpz_t n, uint64_t d)
|
|
{
|
|
return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_CEIL);
|
|
}
|
|
|
|
uint64_t
|
|
mpz_fdiv_ui (const mpz_t n, uint64_t d)
|
|
{
|
|
return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_FLOOR);
|
|
}
|
|
|
|
uint64_t
|
|
mpz_tdiv_ui (const mpz_t n, uint64_t d)
|
|
{
|
|
return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_TRUNC);
|
|
}
|
|
|
|
uint64_t
|
|
mpz_mod_ui (mpz_t r, const mpz_t n, uint64_t d)
|
|
{
|
|
return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_FLOOR);
|
|
}
|
|
|
|
void
|
|
mpz_divexact_ui (mpz_t q, const mpz_t n, uint64_t d)
|
|
{
|
|
gmp_assert_nocarry (mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_TRUNC));
|
|
}
|
|
|
|
int
|
|
mpz_divisible_ui_p (const mpz_t n, uint64_t 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)
|
|
{
|
|
uint32_t 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;
|
|
}
|
|
|
|
uint64_t
|
|
mpz_gcd_ui (mpz_t g, const mpz_t u, uint64_t v)
|
|
{
|
|
mp_size_t un;
|
|
|
|
if (v == 0)
|
|
{
|
|
if (g)
|
|
mpz_abs (g, u);
|
|
}
|
|
else
|
|
{
|
|
un = GMP_ABS (u->_mp_size);
|
|
if (un != 0)
|
|
v = mpn_gcd_11 (mpn_div_qr_1 (NULL, u->_mp_d, un, v), v);
|
|
|
|
if (g)
|
|
mpz_set_ui (g, v);
|
|
}
|
|
|
|
return v;
|
|
}
|
|
|
|
static mp_bitcnt_t
|
|
mpz_make_odd (mpz_t r)
|
|
{
|
|
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_common_scan (r->_mp_d[0], 0, r->_mp_d, 0, 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 vl = tv->_mp_d[0];
|
|
mp_limb_t ul = mpz_tdiv_ui (tu, vl);
|
|
mpz_set_ui (g, mpn_gcd_11 (ul, vl));
|
|
break;
|
|
}
|
|
mpz_sub (tu, tu, tv);
|
|
}
|
|
mpz_clear (tu);
|
|
mpz_clear (tv);
|
|
mpz_mul_2exp (g, g, gz);
|
|
}
|
|
|
|
void
|
|
mpz_gcdext (mpz_t g, mpz_t s, mpz_t t, const mpz_t u, const mpz_t v)
|
|
{
|
|
mpz_t tu, tv, s0, s1, t0, t1;
|
|
mp_bitcnt_t uz, vz, gz;
|
|
mp_bitcnt_t power;
|
|
|
|
if (u->_mp_size == 0)
|
|
{
|
|
/* g = 0 u + sgn(v) v */
|
|
int64_t sign = mpz_sgn (v);
|
|
mpz_abs (g, v);
|
|
if (s)
|
|
mpz_set_ui (s, 0);
|
|
if (t)
|
|
mpz_set_si (t, sign);
|
|
return;
|
|
}
|
|
|
|
if (v->_mp_size == 0)
|
|
{
|
|
/* g = sgn(u) u + 0 v */
|
|
int64_t sign = mpz_sgn (u);
|
|
mpz_abs (g, u);
|
|
if (s)
|
|
mpz_set_si (s, sign);
|
|
if (t)
|
|
mpz_set_ui (t, 0);
|
|
return;
|
|
}
|
|
|
|
mpz_init (tu);
|
|
mpz_init (tv);
|
|
mpz_init (s0);
|
|
mpz_init (s1);
|
|
mpz_init (t0);
|
|
mpz_init (t1);
|
|
|
|
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_setbit (t0, uz);
|
|
mpz_tdiv_qr (t1, tu, tu, tv);
|
|
mpz_mul_2exp (t1, t1, uz);
|
|
|
|
mpz_setbit (s1, vz);
|
|
power = uz + vz;
|
|
|
|
if (tu->_mp_size > 0)
|
|
{
|
|
mp_bitcnt_t shift;
|
|
shift = mpz_make_odd (tu);
|
|
mpz_mul_2exp (t0, t0, shift);
|
|
mpz_mul_2exp (s0, s0, shift);
|
|
power += shift;
|
|
|
|
for (;;)
|
|
{
|
|
int c;
|
|
c = mpz_cmp (tu, tv);
|
|
if (c == 0)
|
|
break;
|
|
|
|
if (c < 0)
|
|
{
|
|
/* tv = tv' + tu
|
|
*
|
|
* u = t0 tu + t1 (tv' + tu) = (t0 + t1) tu + t1 tv'
|
|
* v = s0 tu + s1 (tv' + tu) = (s0 + s1) tu + s1 tv' */
|
|
|
|
mpz_sub (tv, tv, tu);
|
|
mpz_add (t0, t0, t1);
|
|
mpz_add (s0, s0, s1);
|
|
|
|
shift = mpz_make_odd (tv);
|
|
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;
|
|
}
|
|
}
|
|
|
|
/* Now tv = odd part of gcd, and -s0 and t0 are corresponding
|
|
cofactors. */
|
|
|
|
mpz_mul_2exp (tv, tv, gz);
|
|
mpz_neg (s0, s0);
|
|
|
|
/* 2^p g = s0 u + t0 v. Eliminate one factor of two at a time. To
|
|
adjust cofactors, we need u / g and v / g */
|
|
|
|
mpz_divexact (s1, v, tv);
|
|
mpz_abs (s1, s1);
|
|
mpz_divexact (t1, u, tv);
|
|
mpz_abs (t1, t1);
|
|
|
|
while (power-- > 0)
|
|
{
|
|
/* s0 u + t0 v = (s0 - v/g) u - (t0 + u/g) v */
|
|
if (mpz_odd_p (s0) || mpz_odd_p (t0))
|
|
{
|
|
mpz_sub (s0, s0, s1);
|
|
mpz_add (t0, t0, t1);
|
|
}
|
|
mpz_divexact_ui (s0, s0, 2);
|
|
mpz_divexact_ui (t0, t0, 2);
|
|
}
|
|
|
|
/* Arrange so that |s| < |u| / 2g */
|
|
mpz_add (s1, s0, s1);
|
|
if (mpz_cmpabs (s0, s1) > 0)
|
|
{
|
|
mpz_swap (s0, s1);
|
|
mpz_sub (t0, t0, t1);
|
|
}
|
|
if (u->_mp_size < 0)
|
|
mpz_neg (s0, s0);
|
|
if (v->_mp_size < 0)
|
|
mpz_neg (t0, t0);
|
|
|
|
mpz_swap (g, tv);
|
|
if (s)
|
|
mpz_swap (s, s0);
|
|
if (t)
|
|
mpz_swap (t, t0);
|
|
|
|
mpz_clear (tu);
|
|
mpz_clear (tv);
|
|
mpz_clear (s0);
|
|
mpz_clear (s1);
|
|
mpz_clear (t0);
|
|
mpz_clear (t1);
|
|
}
|
|
|
|
void
|
|
mpz_lcm (mpz_t r, const mpz_t u, const mpz_t v)
|
|
{
|
|
mpz_t g;
|
|
|
|
if (u->_mp_size == 0 || v->_mp_size == 0)
|
|
{
|
|
r->_mp_size = 0;
|
|
return;
|
|
}
|
|
|
|
mpz_init (g);
|
|
|
|
mpz_gcd (g, u, v);
|
|
mpz_divexact (g, u, g);
|
|
mpz_mul (r, g, v);
|
|
|
|
mpz_clear (g);
|
|
mpz_abs (r, r);
|
|
}
|
|
|
|
void
|
|
mpz_lcm_ui (mpz_t r, const mpz_t u, uint64_t 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, uint64_t e)
|
|
{
|
|
uint64_t 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, uint64_t blimb, uint64_t e)
|
|
{
|
|
mpz_t b;
|
|
mpz_pow_ui (r, mpz_roinit_n (b, &blimb, 1), e);
|
|
}
|
|
|
|
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;
|
|
uint32_t shift;
|
|
mp_ptr tp = NULL;
|
|
|
|
en = GMP_ABS (e->_mp_size);
|
|
mn = GMP_ABS (m->_mp_size);
|
|
if (mn == 0)
|
|
gmp_die ("mpz_powm: Zero modulo.");
|
|
|
|
if (en == 0)
|
|
{
|
|
mpz_set_ui (r, 1);
|
|
return;
|
|
}
|
|
|
|
mp = m->_mp_d;
|
|
mpn_div_qr_invert (&minv, mp, mn);
|
|
shift = minv.shift;
|
|
|
|
if (shift > 0)
|
|
{
|
|
/* To avoid shifts, we do all our reductions, except the final
|
|
one, using a *normalized* m. */
|
|
minv.shift = 0;
|
|
|
|
tp = gmp_xalloc_limbs (mn);
|
|
gmp_assert_nocarry (mpn_lshift (tp, mp, mn, shift));
|
|
mp = tp;
|
|
}
|
|
|
|
mpz_init (base);
|
|
|
|
if (e->_mp_size < 0)
|
|
{
|
|
if (!mpz_invert (base, b, m))
|
|
gmp_die ("mpz_powm: Negative exponent and non-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 (tp);
|
|
|
|
mpz_swap (r, tr);
|
|
mpz_clear (tr);
|
|
mpz_clear (base);
|
|
}
|
|
|
|
void
|
|
mpz_powm_ui (mpz_t r, const mpz_t b, uint64_t elimb, const mpz_t m)
|
|
{
|
|
mpz_t e;
|
|
mpz_powm (r, b, mpz_roinit_n (e, &elimb, 1), m);
|
|
}
|
|
|
|
/* x=trunc(y^(1/z)), r=y-x^z */
|
|
void
|
|
mpz_rootrem (mpz_t x, mpz_t r, const mpz_t y, uint64_t z)
|
|
{
|
|
int sgn;
|
|
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);
|
|
{
|
|
mp_bitcnt_t tb;
|
|
tb = mpz_sizeinbase (y, 2) / z + 1;
|
|
mpz_init2 (t, tb + 1);
|
|
mpz_setbit (t, tb);
|
|
}
|
|
|
|
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, uint64_t 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_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_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_fac_ui (mpz_t x, uint64_t n)
|
|
{
|
|
mpz_set_ui (x, n + (n == 0));
|
|
while (n > 2)
|
|
mpz_mul_ui (x, x, --n);
|
|
}
|
|
|
|
void
|
|
mpz_bin_uiui (mpz_t r, uint64_t n, uint64_t 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 */
|
|
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;
|
|
/* y == 1 means that the previous y was a non-trivial square root
|
|
of 1 (mod n). y == 0 means that n is a power of the base.
|
|
In either case, n is not prime. */
|
|
if (mpz_cmp_ui (y, 1) <= 0)
|
|
return 0;
|
|
}
|
|
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;
|
|
|
|
/* 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). */
|
|
|
|
mpz_init (nm1);
|
|
mpz_init (q);
|
|
mpz_init (y);
|
|
|
|
/* Find q and k, where q is odd and n = 1 + 2**k * q. */
|
|
nm1->_mp_size = mpz_abs_sub_ui (nm1, n, 1);
|
|
k = mpz_scan1 (nm1, 0);
|
|
mpz_tdiv_q_2exp (q, nm1, k);
|
|
|
|
for (j = 0, is_prime = 1; is_prime & (j < reps); j++)
|
|
{
|
|
mpz_set_ui (y, (uint64_t) 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;
|
|
uint32_t shift;
|
|
mp_size_t ds;
|
|
mp_size_t dn;
|
|
mp_limb_t w;
|
|
int bit;
|
|
|
|
ds = d->_mp_size;
|
|
dn = GMP_ABS (ds);
|
|
limb_index = bit_index / GMP_LIMB_BITS;
|
|
if (limb_index >= dn)
|
|
return ds < 0;
|
|
|
|
shift = bit_index % GMP_LIMB_BITS;
|
|
w = d->_mp_d[limb_index];
|
|
bit = (w >> shift) & 1;
|
|
|
|
if (ds < 0)
|
|
{
|
|
/* d < 0. Check if any of the bits below is set: If so, our bit
|
|
must be complemented. */
|
|
if (shift > 0 && (w << (GMP_LIMB_BITS - shift)) > 0)
|
|
return bit ^ 1;
|
|
while (--limb_index >= 0)
|
|
if (d->_mp_d[limb_index] > 0)
|
|
return bit ^ 1;
|
|
}
|
|
return bit;
|
|
}
|
|
|
|
static void
|
|
mpz_abs_add_bit (mpz_t d, mp_bitcnt_t bit_index)
|
|
{
|
|
mp_size_t dn, limb_index;
|
|
mp_limb_t bit;
|
|
mp_ptr dp;
|
|
|
|
dn = GMP_ABS (d->_mp_size);
|
|
|
|
limb_index = bit_index / GMP_LIMB_BITS;
|
|
bit = (mp_limb_t) 1 << (bit_index % GMP_LIMB_BITS);
|
|
|
|
if (limb_index >= dn)
|
|
{
|
|
mp_size_t i;
|
|
/* The bit should be set outside of the end of the number.
|
|
We have to increase the size of the number. */
|
|
dp = MPZ_REALLOC (d, limb_index + 1);
|
|
|
|
dp[limb_index] = bit;
|
|
for (i = dn; i < limb_index; i++)
|
|
dp[i] = 0;
|
|
dn = limb_index + 1;
|
|
}
|
|
else
|
|
{
|
|
mp_limb_t cy;
|
|
|
|
dp = d->_mp_d;
|
|
|
|
cy = mpn_add_1 (dp + limb_index, dp + limb_index, dn - limb_index, bit);
|
|
if (cy > 0)
|
|
{
|
|
dp = MPZ_REALLOC (d, dn + 1);
|
|
dp[dn++] = cy;
|
|
}
|
|
}
|
|
|
|
d->_mp_size = (d->_mp_size < 0) ? - dn : dn;
|
|
}
|
|
|
|
static void
|
|
mpz_abs_sub_bit (mpz_t d, mp_bitcnt_t bit_index)
|
|
{
|
|
mp_size_t dn, limb_index;
|
|
mp_ptr dp;
|
|
mp_limb_t bit;
|
|
|
|
dn = GMP_ABS (d->_mp_size);
|
|
dp = d->_mp_d;
|
|
|
|
limb_index = bit_index / GMP_LIMB_BITS;
|
|
bit = (mp_limb_t) 1 << (bit_index % GMP_LIMB_BITS);
|
|
|
|
assert (limb_index < dn);
|
|
|
|
gmp_assert_nocarry (mpn_sub_1 (dp + limb_index, dp + limb_index,
|
|
dn - limb_index, bit));
|
|
dn = 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_neg (r, u);
|
|
mpz_sub_ui (r, r, 1);
|
|
}
|
|
|
|
void
|
|
mpz_and (mpz_t r, const mpz_t u, const mpz_t v)
|
|
{
|
|
mp_size_t un, vn, rn, i;
|
|
mp_ptr up, vp, rp;
|
|
|
|
mp_limb_t ux, vx, rx;
|
|
mp_limb_t uc, vc, rc;
|
|
mp_limb_t ul, vl, rl;
|
|
|
|
un = GMP_ABS (u->_mp_size);
|
|
vn = GMP_ABS (v->_mp_size);
|
|
if (un < vn)
|
|
{
|
|
MPZ_SRCPTR_SWAP (u, v);
|
|
MP_SIZE_T_SWAP (un, vn);
|
|
}
|
|
if (vn == 0)
|
|
{
|
|
r->_mp_size = 0;
|
|
return;
|
|
}
|
|
|
|
uc = u->_mp_size < 0;
|
|
vc = v->_mp_size < 0;
|
|
rc = uc & vc;
|
|
|
|
ux = -uc;
|
|
vx = -vc;
|
|
rx = -rc;
|
|
|
|
/* If the smaller input is positive, higher limbs don't matter. */
|
|
rn = vx ? un : vn;
|
|
|
|
rp = MPZ_REALLOC (r, rn + rc);
|
|
|
|
up = u->_mp_d;
|
|
vp = v->_mp_d;
|
|
|
|
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 + 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 + 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 uint32_t
|
|
gmp_popcount_limb (mp_limb_t x)
|
|
{
|
|
uint32_t c;
|
|
|
|
/* Do 16 bits at a time, to avoid limb-sized constants. */
|
|
for (c = 0; x > 0; x >>= 16)
|
|
{
|
|
uint32_t w = ((x >> 1) & 0x5555) + (x & 0x5555);
|
|
w = ((w >> 2) & 0x3333) + (w & 0x3333);
|
|
w = ((w >> 4) & 0x0f0f) + (w & 0x0f0f);
|
|
w = (w >> 8) + (w & 0x00ff);
|
|
c += w;
|
|
}
|
|
return c;
|
|
}
|
|
|
|
mp_bitcnt_t
|
|
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;
|
|
mp_srcptr up;
|
|
mp_ptr tp;
|
|
mp_bitcnt_t bits;
|
|
struct gmp_div_inverse bi;
|
|
size_t ndigits;
|
|
|
|
assert (base >= 2);
|
|
assert (base <= 36);
|
|
|
|
un = GMP_ABS (u->_mp_size);
|
|
if (un == 0)
|
|
return 1;
|
|
|
|
up = u->_mp_d;
|
|
|
|
bits = (un - 1) * GMP_LIMB_BITS + mpn_limb_size_in_base_2 (up[un-1]);
|
|
switch (base)
|
|
{
|
|
case 2:
|
|
return bits;
|
|
case 4:
|
|
return (bits + 1) / 2;
|
|
case 8:
|
|
return (bits + 2) / 3;
|
|
case 16:
|
|
return (bits + 3) / 4;
|
|
case 32:
|
|
return (bits + 4) / 5;
|
|
/* FIXME: Do something more clever for the common case of base
|
|
10. */
|
|
}
|
|
|
|
tp = gmp_xalloc_limbs (un);
|
|
mpn_copyi (tp, up, un);
|
|
mpn_div_qr_1_invert (&bi, base);
|
|
|
|
ndigits = 0;
|
|
do
|
|
{
|
|
ndigits++;
|
|
mpn_div_qr_1_preinv (tp, tp, un, &bi);
|
|
un -= (tp[un-1] == 0);
|
|
}
|
|
while (un > 0);
|
|
|
|
gmp_free (tp);
|
|
return ndigits;
|
|
}
|
|
|
|
char *
|
|
mpz_get_str (char *sp, int base, const mpz_t u)
|
|
{
|
|
uint32_t bits;
|
|
const char *digits;
|
|
mp_size_t un;
|
|
size_t i, sn;
|
|
|
|
if (base >= 0)
|
|
{
|
|
digits = "0123456789abcdefghijklmnopqrstuvwxyz";
|
|
}
|
|
else
|
|
{
|
|
base = -base;
|
|
digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
|
|
}
|
|
if (base <= 1)
|
|
base = 10;
|
|
if (base > 36)
|
|
return NULL;
|
|
|
|
sn = 1 + mpz_sizeinbase (u, base);
|
|
if (!sp)
|
|
sp = (char *) gmp_xalloc (1 + sn);
|
|
|
|
un = GMP_ABS (u->_mp_size);
|
|
|
|
if (un == 0)
|
|
{
|
|
sp[0] = '0';
|
|
sp[1] = '\0';
|
|
return sp;
|
|
}
|
|
|
|
i = 0;
|
|
|
|
if (u->_mp_size < 0)
|
|
sp[i++] = '-';
|
|
|
|
bits = mpn_base_power_of_two_p (base);
|
|
|
|
if (bits)
|
|
/* Not modified in this case. */
|
|
sn = i + mpn_get_str_bits ((uint8_t *) sp + i, bits, u->_mp_d, un);
|
|
else
|
|
{
|
|
struct mpn_base_info info;
|
|
mp_ptr tp;
|
|
|
|
mpn_get_base_info (&info, base);
|
|
tp = gmp_xalloc_limbs (un);
|
|
mpn_copyi (tp, u->_mp_d, un);
|
|
|
|
sn = i + mpn_get_str_other ((uint8_t *) sp + i, base, &info, tp, un);
|
|
gmp_free (tp);
|
|
}
|
|
|
|
for (; i < sn; i++)
|
|
sp[i] = digits[(uint8_t) sp[i]];
|
|
|
|
sp[sn] = '\0';
|
|
return sp;
|
|
}
|
|
|
|
size_t
|
|
mpz_out_str (FILE *stream, int base, const mpz_t x)
|
|
{
|
|
char *str;
|
|
size_t len;
|
|
|
|
str = mpz_get_str (NULL, base, x);
|
|
len = strlen (str);
|
|
len = fwrite (str, 1, len, stream);
|
|
gmp_free (str);
|
|
return len;
|
|
}
|
|
#endif
|
|
|
|
|
|
static void gmp_die (const char *msg)
|
|
{
|
|
fprintf (stderr, "%s\n", msg);
|
|
abort();
|
|
}
|
|
|
|
static mp_ptr gmp_xalloc_limbs (mp_size_t size)
|
|
{
|
|
return (mp_ptr) malloc(size * sizeof(mp_limb_t));
|
|
}
|
|
|
|
static int gmp_detect_endian (void)
|
|
{
|
|
static const int i = 2;
|
|
const uint8_t *p = (const uint8_t *) &i;
|
|
return 1 - *p;
|
|
}
|
|
|
|
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_import: 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;
|
|
uint8_t *p;
|
|
ptrdiff_t word_step;
|
|
/* The current (partial) limb. */
|
|
mp_limb_t limb;
|
|
/* The number of bytes left to to in this limb. */
|
|
size_t bytes;
|
|
/* The index where the limb was read. */
|
|
mp_size_t i;
|
|
|
|
un = GMP_ABS (un);
|
|
|
|
/* Count bytes in top limb. */
|
|
limb = u->_mp_d[un-1];
|
|
assert (limb != 0);
|
|
|
|
k = 0;
|
|
do {
|
|
k++; limb >>= CHAR_BIT;
|
|
} while (limb != 0);
|
|
|
|
count = (k + (un-1) * sizeof (mp_limb_t) + size - 1) / size;
|
|
|
|
if (!r)
|
|
r = malloc (count * size);
|
|
|
|
if (endian == 0)
|
|
endian = gmp_detect_endian ();
|
|
|
|
p = (uint8_t *) r;
|
|
|
|
word_step = (order != endian) ? 2 * size : 0;
|
|
|
|
/* Process bytes from the least significant end, so point p at the
|
|
least significant word. */
|
|
if (order == 1)
|
|
{
|
|
p += size * (count - 1);
|
|
word_step = - word_step;
|
|
}
|
|
|
|
/* And at least significant byte of that word. */
|
|
if (endian == 1)
|
|
p += (size - 1);
|
|
|
|
for (bytes = 0, i = 0, k = 0; k < count; k++, p += word_step)
|
|
{
|
|
size_t j;
|
|
for (j = 0; j < size; j++, p -= (ptrdiff_t) endian)
|
|
{
|
|
if (bytes == 0)
|
|
{
|
|
if (i < un)
|
|
limb = u->_mp_d[i++];
|
|
bytes = sizeof (mp_limb_t);
|
|
}
|
|
*p = limb;
|
|
//printf("{%02x} ",*p);
|
|
limb >>= CHAR_BIT;
|
|
bytes--;
|
|
}
|
|
}
|
|
assert (i == un);
|
|
assert (k == count);
|
|
}
|
|
|
|
if (countp)
|
|
*countp = count;
|
|
//printf("mpz_export.%d\n",(int32_t)count);
|
|
return r;
|
|
}
|
|
|
|
/////////////////////////////////
|
|
|
|
|
|
static mp_size_t mpn_normalized_size (mp_srcptr xp, mp_size_t n)
|
|
{
|
|
while (n > 0 && xp[n-1] == 0)
|
|
--n;
|
|
return n;
|
|
}
|
|
|
|
|
|
static mp_ptr gmp_xrealloc_limbs (mp_ptr old, mp_size_t size)
|
|
{
|
|
assert (size > 0);
|
|
return (mp_ptr) realloc(old, size * sizeof (mp_limb_t));
|
|
}
|
|
|
|
|
|
static mp_ptr
|
|
mpz_realloc (mpz_t r, mp_size_t size)
|
|
{
|
|
size = GMP_MAX (size, 1);
|
|
|
|
r->_mp_d = gmp_xrealloc_limbs (r->_mp_d, size);
|
|
r->_mp_alloc = (int32_t)size;
|
|
|
|
if (GMP_ABS (r->_mp_size) > size)
|
|
r->_mp_size = 0;
|
|
|
|
return r->_mp_d;
|
|
}
|
|
|
|
/* 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 uint8_t *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 = (uint8_t *) 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 = (int32_t)i;
|
|
}
|
|
|
|
void mpz_init (mpz_t r)
|
|
{
|
|
r->_mp_alloc = 1;
|
|
r->_mp_size = 0;
|
|
r->_mp_d = gmp_xalloc_limbs (1);
|
|
}
|
|
|
|
void
|
|
mpz_clear (mpz_t r)
|
|
{
|
|
free (r->_mp_d);
|
|
}
|
|
|
|
static void
|
|
mpn_get_base_info (struct mpn_base_info *info, mp_limb_t b)
|
|
{
|
|
mp_limb_t m;
|
|
mp_limb_t p;
|
|
uint32_t exp;
|
|
|
|
m = GMP_LIMB_MAX / b;
|
|
for (exp = 1, p = b; p <= m; exp++)
|
|
p *= b;
|
|
|
|
info->exp = exp;
|
|
info->bb = p;
|
|
}
|
|
|
|
static uint32_t mpn_base_power_of_two_p (uint32_t 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;
|
|
}
|
|
}
|
|
|
|
|
|
static mp_size_t mpn_set_str_bits (mp_ptr rp, const uint8_t *sp, size_t sn, uint32_t bits)
|
|
{
|
|
mp_size_t rn;
|
|
size_t j;
|
|
uint32_t shift;
|
|
|
|
for (j = sn, rn = 0, shift = 0; j-- > 0; )
|
|
{
|
|
if (shift == 0)
|
|
{
|
|
rp[rn++] = sp[j];
|
|
shift += bits;
|
|
}
|
|
else
|
|
{
|
|
rp[rn-1] |= (mp_limb_t) sp[j] << shift;
|
|
shift += bits;
|
|
if (shift >= GMP_LIMB_BITS)
|
|
{
|
|
shift -= GMP_LIMB_BITS;
|
|
if (shift > 0)
|
|
rp[rn++] = (mp_limb_t) sp[j] >> (bits - shift);
|
|
}
|
|
}
|
|
}
|
|
rn = mpn_normalized_size (rp, rn);
|
|
return rn;
|
|
}
|
|
|
|
mp_limb_t
|
|
mpn_add_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b)
|
|
{
|
|
mp_size_t i;
|
|
|
|
assert (n > 0);
|
|
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_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;
|
|
}
|
|
|
|
static mp_size_t
|
|
mpn_set_str_other (mp_ptr rp, const uint8_t *sp, size_t sn,
|
|
mp_limb_t b, const struct mpn_base_info *info)
|
|
{
|
|
mp_size_t rn;
|
|
mp_limb_t w;
|
|
uint32_t k;
|
|
size_t j;
|
|
|
|
k = 1 + (sn - 1) % info->exp;
|
|
|
|
j = 0;
|
|
w = sp[j++];
|
|
while (--k != 0)
|
|
w = w * b + sp[j++];
|
|
|
|
rp[0] = w;
|
|
|
|
for (rn = (w > 0); j < sn;)
|
|
{
|
|
mp_limb_t cy;
|
|
|
|
w = sp[j++];
|
|
for (k = 1; k < info->exp; k++)
|
|
w = w * b + sp[j++];
|
|
|
|
cy = mpn_mul_1 (rp, rp, rn, info->bb);
|
|
cy += mpn_add_1 (rp, rp, rn, w);
|
|
if (cy > 0)
|
|
rp[rn++] = cy;
|
|
}
|
|
assert (j == sn);
|
|
|
|
return rn;
|
|
}
|
|
|
|
void mpn_copyi (mp_ptr d, mp_srcptr s, mp_size_t n)
|
|
{
|
|
mp_size_t i;
|
|
for (i = 0; i < n; i++)
|
|
d[i] = s[i];
|
|
}
|
|
|
|
void 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;
|
|
}
|
|
}
|
|
|
|
int mpz_set_str (mpz_t r, const char *sp, int base)
|
|
{
|
|
uint32_t bits;
|
|
mp_size_t rn, alloc;
|
|
mp_ptr rp;
|
|
size_t sn;
|
|
int sign;
|
|
uint8_t *dp;
|
|
|
|
assert (base == 0 || (base >= 2 && base <= 36));
|
|
|
|
while (isspace( (uint8_t) *sp))
|
|
sp++;
|
|
|
|
sign = (*sp == '-');
|
|
sp += sign;
|
|
|
|
if (base == 0)
|
|
{
|
|
if (*sp == '0')
|
|
{
|
|
sp++;
|
|
if (*sp == 'x' || *sp == 'X')
|
|
{
|
|
base = 16;
|
|
sp++;
|
|
}
|
|
else if (*sp == 'b' || *sp == 'B')
|
|
{
|
|
base = 2;
|
|
sp++;
|
|
}
|
|
else
|
|
base = 8;
|
|
}
|
|
else
|
|
base = 10;
|
|
}
|
|
|
|
sn = strlen (sp);
|
|
dp = (uint8_t *) malloc (sn + (sn == 0));
|
|
|
|
for (sn = 0; *sp; sp++)
|
|
{
|
|
uint32_t digit;
|
|
|
|
if (isspace ((uint8_t) *sp))
|
|
continue;
|
|
if (*sp >= '0' && *sp <= '9')
|
|
digit = *sp - '0';
|
|
else if (*sp >= 'a' && *sp <= 'z')
|
|
digit = *sp - 'a' + 10;
|
|
else if (*sp >= 'A' && *sp <= 'Z')
|
|
digit = *sp - 'A' + 10;
|
|
else
|
|
digit = base; /* fail */
|
|
|
|
if (digit >= base)
|
|
{
|
|
free (dp);
|
|
r->_mp_size = 0;
|
|
return -1;
|
|
}
|
|
|
|
dp[sn++] = digit;
|
|
}
|
|
|
|
bits = mpn_base_power_of_two_p (base);
|
|
|
|
if (bits > 0)
|
|
{
|
|
alloc = (sn * bits + GMP_LIMB_BITS - 1) / GMP_LIMB_BITS;
|
|
rp = MPZ_REALLOC (r, alloc);
|
|
rn = mpn_set_str_bits (rp, dp, sn, bits);
|
|
}
|
|
else
|
|
{
|
|
struct mpn_base_info info;
|
|
mpn_get_base_info (&info, base);
|
|
alloc = (sn + info.exp - 1) / info.exp;
|
|
rp = MPZ_REALLOC (r, alloc);
|
|
rn = mpn_set_str_other (rp, dp, sn, base, &info);
|
|
}
|
|
assert (rn <= alloc);
|
|
free (dp);
|
|
|
|
r->_mp_size = (int32_t)(sign ? - rn : rn);
|
|
|
|
return 0;
|
|
}
|
|
|
|
void mpz_init_set (mpz_t r, const mpz_t x)
|
|
{
|
|
mpz_init (r);
|
|
mpz_set (r, x);
|
|
}
|
|
|
|
int mpz_init_set_str (mpz_t r, const char *sp, int base)
|
|
{
|
|
mpz_init (r);
|
|
return mpz_set_str (r, sp, base);
|
|
}
|
|
|
|
int mpn_cmp (mp_srcptr ap, mp_srcptr bp, mp_size_t n)
|
|
{
|
|
while (--n >= 0)
|
|
{
|
|
if (ap[n] != bp[n])
|
|
return ap[n] > bp[n] ? 1 : -1;
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
int mpz_cmp (const mpz_t a, const mpz_t b)
|
|
{
|
|
mp_size_t asize = a->_mp_size;
|
|
mp_size_t bsize = b->_mp_size;
|
|
|
|
if (asize != bsize)
|
|
return (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);
|
|
}
|
|
|
|
static void mpn_div_qr_1_invert (struct gmp_div_inverse *inv, mp_limb_t d)
|
|
{
|
|
uint32_t shift;
|
|
|
|
assert (d > 0);
|
|
gmp_clz (shift, d);
|
|
inv->shift = shift;
|
|
inv->d1 = d << shift;
|
|
inv->di = mpn_invert_limb (inv->d1);
|
|
}
|
|
|
|
/* MPN division interface. */
|
|
mp_limb_t
|
|
mpn_invert_3by2 (mp_limb_t u1, mp_limb_t u0)
|
|
{
|
|
mp_limb_t r, p, m;
|
|
uint32_t ul, uh;
|
|
uint32_t ql, qh;
|
|
|
|
/* First, do a 2/1 inverse. */
|
|
/* The inverse m is defined as floor( (B^2 - 1 - u1)/u1 ), so that 0 <
|
|
* B^2 - (B + m) u1 <= u1 */
|
|
assert (u1 >= GMP_LIMB_HIGHBIT);
|
|
|
|
ul = u1 & GMP_LLIMB_MASK;
|
|
uh = u1 >> (GMP_LIMB_BITS / 2);
|
|
|
|
qh = (uint32_t)(~u1 / uh);
|
|
r = ((~u1 - (mp_limb_t) qh * uh) << (GMP_LIMB_BITS / 2)) | GMP_LLIMB_MASK;
|
|
|
|
p = (mp_limb_t) qh * ul;
|
|
/* Adjustment steps taken from udiv_qrnnd_c */
|
|
if (r < p)
|
|
{
|
|
qh--;
|
|
r += u1;
|
|
if (r >= u1) /* i.e. we didn't get carry when adding to r */
|
|
if (r < p)
|
|
{
|
|
qh--;
|
|
r += u1;
|
|
}
|
|
}
|
|
r -= p;
|
|
|
|
/* Do a 3/2 division (with half limb size) */
|
|
p = (r >> (GMP_LIMB_BITS / 2)) * qh + r;
|
|
ql = (p >> (GMP_LIMB_BITS / 2)) + 1;
|
|
|
|
/* By the 3/2 method, we don't need the high half limb. */
|
|
r = (r << (GMP_LIMB_BITS / 2)) + GMP_LLIMB_MASK - ql * u1;
|
|
|
|
if (r >= (p << (GMP_LIMB_BITS / 2)))
|
|
{
|
|
ql--;
|
|
r += u1;
|
|
}
|
|
m = ((mp_limb_t) qh << (GMP_LIMB_BITS / 2)) + ql;
|
|
if (r >= u1)
|
|
{
|
|
m++;
|
|
r -= u1;
|
|
}
|
|
|
|
if (u0 > 0)
|
|
{
|
|
mp_limb_t th, tl;
|
|
r = ~r;
|
|
r += u0;
|
|
if (r < u0)
|
|
{
|
|
m--;
|
|
if (r >= u1)
|
|
{
|
|
m--;
|
|
r -= u1;
|
|
}
|
|
r -= u1;
|
|
}
|
|
gmp_umul_ppmm (th, tl, u0, m);
|
|
r += th;
|
|
if (r < th)
|
|
{
|
|
m--;
|
|
m -= ((r > u1) | ((r == u1) & (tl > u0)));
|
|
}
|
|
}
|
|
|
|
return m;
|
|
}
|
|
|
|
static void mpn_div_qr_2_invert (struct gmp_div_inverse *inv,mp_limb_t d1, mp_limb_t d0)
|
|
{
|
|
uint32_t 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
|
|
{
|
|
uint32_t 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);
|
|
}
|
|
}
|
|
|
|
mp_limb_t mpn_lshift(mp_ptr rp, mp_srcptr up, mp_size_t n, uint32_t cnt)
|
|
{
|
|
mp_limb_t high_limb, low_limb;
|
|
uint32_t 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;
|
|
}
|
|
|
|
// Not matching current public gmp interface, rather corresponding to the sbpi1_div_* functions.
|
|
static mp_limb_t mpn_div_qr_1_preinv (mp_ptr qp, mp_srcptr np, mp_size_t nn,const struct gmp_div_inverse *inv)
|
|
{
|
|
mp_limb_t d, di;
|
|
mp_limb_t r;
|
|
mp_ptr tp = NULL;
|
|
|
|
if (inv->shift > 0)
|
|
{
|
|
tp = gmp_xalloc_limbs (nn);
|
|
r = mpn_lshift (tp, np, nn, inv->shift);
|
|
np = tp;
|
|
}
|
|
else
|
|
r = 0;
|
|
|
|
d = inv->d1;
|
|
di = inv->di;
|
|
while (--nn >= 0)
|
|
{
|
|
mp_limb_t q;
|
|
|
|
gmp_udiv_qrnnd_preinv (q, r, r, np[nn], d, di);
|
|
if (qp)
|
|
qp[nn] = q;
|
|
}
|
|
if (inv->shift > 0)
|
|
free (tp);
|
|
|
|
return r >> inv->shift;
|
|
}
|
|
static void mpn_div_qr_2_preinv (mp_ptr qp, mp_ptr rp, mp_srcptr np, mp_size_t nn, const struct gmp_div_inverse *inv)
|
|
{
|
|
uint32_t shift;
|
|
mp_size_t i;
|
|
mp_limb_t d1, d0, di, r1, r0;
|
|
mp_ptr tp=0;
|
|
|
|
assert (nn >= 2);
|
|
shift = inv->shift;
|
|
d1 = inv->d1;
|
|
d0 = inv->d0;
|
|
di = inv->di;
|
|
|
|
if (shift > 0)
|
|
{
|
|
tp = gmp_xalloc_limbs (nn);
|
|
r1 = mpn_lshift (tp, np, nn, shift);
|
|
np = tp;
|
|
}
|
|
else
|
|
r1 = 0;
|
|
|
|
r0 = np[nn - 1];
|
|
|
|
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_BITS - shift)) == 0);
|
|
r0 = (r0 >> shift) | (r1 << (GMP_LIMB_BITS - shift));
|
|
r1 >>= shift;
|
|
if ( tp != 0 )
|
|
free (tp);
|
|
}
|
|
|
|
rp[1] = r1;
|
|
rp[0] = r0;
|
|
}
|
|
|
|
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_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;
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
mp_limb_t mpn_rshift (mp_ptr rp, mp_srcptr up, mp_size_t n, uint32_t cnt)
|
|
{
|
|
mp_limb_t high_limb, low_limb;
|
|
uint32_t 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 void mpn_div_qr_preinv (mp_ptr qp, mp_ptr np, mp_size_t nn,mp_srcptr dp, mp_size_t dn,const struct gmp_div_inverse *inv)
|
|
{
|
|
assert (dn > 0);
|
|
assert (nn >= dn);
|
|
|
|
if (dn == 1)
|
|
np[0] = mpn_div_qr_1_preinv (qp, np, nn, inv);
|
|
else if (dn == 2)
|
|
mpn_div_qr_2_preinv (qp, np, np, nn, inv);
|
|
else
|
|
{
|
|
mp_limb_t nh;
|
|
uint32_t shift;
|
|
|
|
assert (inv->d1 == dp[dn-1]);
|
|
assert (inv->d0 == dp[dn-2]);
|
|
assert ((inv->d1 & GMP_LIMB_HIGHBIT) != 0);
|
|
|
|
shift = inv->shift;
|
|
if (shift > 0)
|
|
nh = mpn_lshift (np, np, nn, shift);
|
|
else
|
|
nh = 0;
|
|
|
|
mpn_div_qr_pi1 (qp, np, nn, nh, dp, dn, inv->di);
|
|
|
|
if (shift > 0)
|
|
gmp_assert_nocarry (mpn_rshift (np, np, dn, shift));
|
|
}
|
|
}
|
|
|
|
static void mpn_div_qr (mp_ptr qp, mp_ptr np, mp_size_t nn, mp_srcptr dp, mp_size_t dn)
|
|
{
|
|
struct gmp_div_inverse inv;
|
|
mp_ptr tp = NULL;
|
|
|
|
assert (dn > 0);
|
|
assert (nn >= dn);
|
|
|
|
mpn_div_qr_invert (&inv, dp, dn);
|
|
if (dn > 2 && inv.shift > 0)
|
|
{
|
|
tp = gmp_xalloc_limbs (dn);
|
|
gmp_assert_nocarry (mpn_lshift (tp, dp, dn, inv.shift));
|
|
dp = tp;
|
|
}
|
|
mpn_div_qr_preinv (qp, np, nn, dp, dn, &inv);
|
|
if (tp)
|
|
free (tp);
|
|
}
|
|
|
|
static int
|
|
mpn_cmp4 (mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
|
|
{
|
|
if (an != bn)
|
|
return an < bn ? -1 : 1;
|
|
else
|
|
return mpn_cmp (ap, bp, an);
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
|
|
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 = (int)(a->_mp_size >= 0 ? rn : - rn);
|
|
}
|
|
|
|
/* Adds to the absolute value. Returns new size, but doesn't store it. */
|
|
static mp_size_t mpz_abs_add_ui (mpz_t r, const mpz_t a, uint64_t b)
|
|
{
|
|
mp_size_t an;
|
|
mp_ptr rp;
|
|
mp_limb_t cy;
|
|
|
|
an = GMP_ABS (a->_mp_size);
|
|
if (an == 0)
|
|
{
|
|
r->_mp_d[0] = b;
|
|
return b > 0;
|
|
}
|
|
|
|
rp = MPZ_REALLOC (r, an + 1);
|
|
|
|
cy = mpn_add_1 (rp, a->_mp_d, an, b);
|
|
rp[an] = cy;
|
|
an += cy;
|
|
|
|
return an;
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
// Subtract from the absolute value. Returns new size, (or -1 on underflow), but doesn't store it.
|
|
static mp_size_t mpz_abs_sub_ui (mpz_t r, const mpz_t a, uint64_t b)
|
|
{
|
|
mp_size_t an = GMP_ABS (a->_mp_size);
|
|
mp_ptr rp = MPZ_REALLOC (r, an);
|
|
|
|
if (an == 0)
|
|
{
|
|
rp[0] = b;
|
|
return -(b > 0);
|
|
}
|
|
else if (an == 1 && a->_mp_d[0] < b)
|
|
{
|
|
rp[0] = b - a->_mp_d[0];
|
|
return -1;
|
|
}
|
|
else
|
|
{
|
|
gmp_assert_nocarry (mpn_sub_1 (rp, a->_mp_d, an, b));
|
|
return mpn_normalized_size (rp, an);
|
|
}
|
|
}
|
|
|
|
void mpz_sub_ui (mpz_t r, const mpz_t a, uint64_t b)
|
|
{
|
|
if (a->_mp_size < 0)
|
|
r->_mp_size = (int)-mpz_abs_add_ui (r, a, b);
|
|
else
|
|
r->_mp_size = (int)mpz_abs_sub_ui (r, a, b);
|
|
}
|
|
|
|
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 = (int32_t)(a->_mp_size >= 0 ? rn : - rn);
|
|
}
|
|
|
|
void mpz_add_ui (mpz_t r, const mpz_t a, uint64_t b)
|
|
{
|
|
if (a->_mp_size >= 0)
|
|
r->_mp_size = (int32_t)mpz_abs_add_ui (r, a, b);
|
|
else
|
|
r->_mp_size = (int32_t)-mpz_abs_sub_ui (r, a, b);
|
|
}
|
|
|
|
/* 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 = (int32_t)rn;
|
|
r->_mp_size = 0;
|
|
r->_mp_d = gmp_xalloc_limbs (rn);
|
|
}
|
|
|
|
void mpz_set_ui (mpz_t r, uint64_t x)
|
|
{
|
|
if (x > 0)
|
|
{
|
|
r->_mp_size = 1;
|
|
r->_mp_d[0] = x;
|
|
}
|
|
else
|
|
r->_mp_size = 0;
|
|
}
|
|
|
|
void mpz_set_si (mpz_t r, int64_t x)
|
|
{
|
|
if (x >= 0)
|
|
mpz_set_ui (r, x);
|
|
else /* (x < 0) */
|
|
{
|
|
r->_mp_size = -1;
|
|
r->_mp_d[0] = GMP_NEG_CAST (uint64_t, x);
|
|
}
|
|
}
|
|
|
|
void mpz_swap (mpz_t u, mpz_t v)
|
|
{
|
|
MP_SIZE_sT_SWAP (u->_mp_size, v->_mp_size);
|
|
MP_SIZE_sT_SWAP (u->_mp_alloc, v->_mp_alloc);
|
|
MP_PTR_SWAP (u->_mp_d, v->_mp_d);
|
|
}
|
|
|
|
// 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 = (uint32_t)(qs < 0 ? -qn : qn);
|
|
}
|
|
rn = mpn_normalized_size (np, dn);
|
|
tr->_mp_size = (uint32_t)(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);
|
|
}
|
|
|
|
uint64_t mpz_get_ui (const mpz_t u)
|
|
{
|
|
return u->_mp_size == 0 ? 0 : u->_mp_d[0];
|
|
}
|
|
|
|
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_init_set_ui (mpz_t r, uint64_t x)
|
|
{
|
|
mpz_init (r);
|
|
mpz_set_ui (r, x);
|
|
}
|
|
|
|
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_mul (mp_ptr rp, mp_srcptr up, mp_size_t un, mp_srcptr vp, mp_size_t vn)
|
|
{
|
|
assert (un >= vn);
|
|
assert (vn >= 1);
|
|
|
|
/* We first multiply by the low order limb. This result can be
|
|
stored, not added, to rp. We also avoid a loop for zeroing this
|
|
way. */
|
|
|
|
rp[un] = mpn_mul_1 (rp, up, un, vp[0]);
|
|
|
|
/* 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 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 = (int32_t)(sign ? - rn : rn);
|
|
mpz_swap (r, t);
|
|
mpz_clear (t);
|
|
}
|
|
void mpz_mul_ui (mpz_t r, const mpz_t u, uint64_t v)
|
|
{
|
|
mp_size_t un, us; mp_ptr tp; mp_limb_t cy;
|
|
|
|
us = u->_mp_size;
|
|
if (us == 0 || v == 0)
|
|
{
|
|
r->_mp_size = 0;
|
|
return;
|
|
}
|
|
un = GMP_ABS (us);
|
|
tp = MPZ_REALLOC (r, un + 1);
|
|
cy = mpn_mul_1 (tp, u->_mp_d, un, v);
|
|
tp[un] = cy;
|
|
un += (cy > 0);
|
|
r->_mp_size = (int32_t)((us < 0) ? -un : un);
|
|
}
|
|
|
|
static mp_limb_t mpn_div_qr_1 (mp_ptr qp, mp_srcptr np, mp_size_t nn, mp_limb_t d)
|
|
{
|
|
assert (d > 0);
|
|
// Special case for powers of two.
|
|
if ((d & (d-1)) == 0)
|
|
{
|
|
mp_limb_t r = np[0] & (d-1);
|
|
if (qp)
|
|
{
|
|
if (d <= 1)
|
|
mpn_copyi (qp, np, nn);
|
|
else
|
|
{
|
|
uint64_t shift;
|
|
gmp_ctz (shift, d);
|
|
mpn_rshift (qp, np, nn, (uint32_t)shift);
|
|
}
|
|
}
|
|
return r;
|
|
}
|
|
else
|
|
{
|
|
struct gmp_div_inverse inv;
|
|
mpn_div_qr_1_invert (&inv, d);
|
|
return mpn_div_qr_1_preinv (qp, np, nn, &inv);
|
|
}
|
|
}
|
|
|
|
static uint64_t mpz_div_qr_ui (mpz_t q, mpz_t r,const mpz_t n, uint64_t d, enum mpz_div_round_mode mode)
|
|
{
|
|
mp_size_t ns,qn; mp_ptr qp; mp_limb_t rl; mp_size_t rs;
|
|
ns = n->_mp_size;
|
|
if (ns == 0)
|
|
{
|
|
if (q)
|
|
q->_mp_size = 0;
|
|
if (r)
|
|
r->_mp_size = 0;
|
|
return 0;
|
|
}
|
|
qn = GMP_ABS (ns);
|
|
if (q)
|
|
qp = MPZ_REALLOC (q, qn);
|
|
else qp = NULL;
|
|
rl = mpn_div_qr_1 (qp, n->_mp_d, qn, d);
|
|
assert (rl < d);
|
|
rs = rl > 0;
|
|
rs = (ns < 0) ? -rs : rs;
|
|
if (rl > 0 && ( (mode == GMP_DIV_FLOOR && ns < 0) || (mode == GMP_DIV_CEIL && ns >= 0)))
|
|
{
|
|
if (q)
|
|
gmp_assert_nocarry (mpn_add_1 (qp, qp, qn, 1));
|
|
rl = d - rl;
|
|
rs = -rs;
|
|
}
|
|
if (r)
|
|
{
|
|
r->_mp_d[0] = rl;
|
|
r->_mp_size = (int32_t)rs;
|
|
}
|
|
if (q)
|
|
{
|
|
qn -= (qp[qn-1] == 0);
|
|
assert (qn == 0 || qp[qn-1] > 0);
|
|
q->_mp_size = (int32_t)((ns < 0) ? -qn : qn);
|
|
}
|
|
return rl;
|
|
}
|
|
|
|
uint64_t mpz_tdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, uint64_t d)
|
|
{
|
|
return mpz_div_qr_ui (q, r, n, d, GMP_DIV_TRUNC);
|
|
}
|
|
|
|
void mpn_copyd (mp_ptr d, mp_srcptr s, mp_size_t n)
|
|
{
|
|
while (--n >= 0)
|
|
d[n] = s[n];
|
|
}
|
|
|
|
void mpn_zero(mp_ptr rp, mp_size_t n)
|
|
{
|
|
while (--n >= 0)
|
|
rp[n] = 0;
|
|
}
|
|
|
|
void mpz_mul_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t bits)
|
|
{
|
|
mp_size_t un,rn,limbs; uint32_t 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 = (int32_t)((u->_mp_size < 0) ? - rn : rn);
|
|
}
|
|
|
|
#include <stdint.h>
|
|
|
|
static const char base58_chars[] = "123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz";
|
|
|
|
char *bitcoin_base58encode(char *coinaddr,uint8_t *data,int32_t datalen)
|
|
{
|
|
mpz_t bn0,bn58,dv,rem,bn; char rs[128]; int32_t i,n=0;
|
|
//mpz_init_set_str(bn58,"58",10);
|
|
//mpz_init_set_str(bn0,"0",10);
|
|
mpz_init_set_ui(bn58,58);
|
|
mpz_init_set_ui(bn0,0);
|
|
mpz_init(dv), mpz_init(rem), mpz_init(bn);
|
|
mpz_import(bn,datalen,1,sizeof(data[0]),0,0,data);
|
|
while ( mpz_cmp(bn,bn0) > 0 )
|
|
{
|
|
mpz_tdiv_qr(bn,rem,bn,bn58);
|
|
rs[n++] = base58_chars[mpz_get_ui(rem)];
|
|
}
|
|
for (i=0; i<datalen; i++)
|
|
{
|
|
if ( data[i] == 0 )
|
|
rs[n++] = base58_chars[0];
|
|
else break;
|
|
}
|
|
for (i=0; i<n; i++)
|
|
coinaddr[n - i - 1] = rs[i];
|
|
coinaddr[n] = 0;
|
|
mpz_clear(bn0), mpz_clear(bn58), mpz_clear(dv), mpz_clear(rem), mpz_clear(bn);
|
|
return(coinaddr);
|
|
}
|
|
|
|
|
|
#include "../includes/curve25519.h"
|
|
|
|
void mpz_from_bits256(mpz_t bn,bits256 x)
|
|
{
|
|
int32_t i;
|
|
mpz_init_set_ui(bn,x.ulongs[3]);
|
|
for (i=2; i>=0; i--)
|
|
{
|
|
mpz_mul_2exp(bn,bn,64);
|
|
if ( x.ulongs[i] != 0 )
|
|
mpz_add_ui(bn,bn,x.ulongs[i]);
|
|
}
|
|
}
|
|
|
|
bits256 mpz_to_bits256(mpz_t bn)
|
|
{
|
|
bits256 x,rev; size_t count; int32_t i;
|
|
memset(x.bytes,0,sizeof(x));
|
|
mpz_export(rev.bytes,&count,1,sizeof(uint64_t),1,0,bn);
|
|
for (i=0; i<32; i++)
|
|
x.bytes[i] = rev.bytes[31-i];
|
|
return(x);
|
|
}
|
|
|
|
int32_t bitcoin_base58decode(uint8_t *data,char *coinaddr)
|
|
{
|
|
uint32_t zeroes,be_sz=0; size_t count; const char *p,*p1; mpz_t bn58,bn; int32_t nonz=0;
|
|
mpz_init_set_ui(bn58,58);
|
|
mpz_init_set_ui(bn,0);
|
|
while ( isspace((uint32_t)(*coinaddr & 0xff)) )
|
|
coinaddr++;
|
|
for (p=coinaddr; *p; p++)
|
|
{
|
|
p1 = strchr(base58_chars,*p);
|
|
if ( p1 == 0 )
|
|
{
|
|
while (isspace((uint32_t)*p))
|
|
p++;
|
|
if ( *p != '\0' )
|
|
{
|
|
printf("bitcoin_base58decode error: p %02x != 0x00\n",*p);
|
|
mpz_clear(bn), mpz_clear(bn58);
|
|
return(-1);
|
|
}
|
|
break;
|
|
}
|
|
mpz_mul(bn,bn,bn58);
|
|
mpz_add_ui(bn,bn,(int32_t)(p1 - base58_chars));
|
|
//printf("%d ",(int32_t)(p1 - base58_chars));
|
|
nonz++;
|
|
}
|
|
//printf("nonz.%d\n",nonz);
|
|
zeroes = 0;
|
|
for (p=coinaddr; *p==base58_chars[0]; p++)
|
|
data[zeroes++] = 0;
|
|
mpz_export(data+zeroes,&count,1,sizeof(data[0]),-1,0,bn);
|
|
/*if ( 0 )
|
|
{
|
|
bits256 privkey; char *bits256_str(char *str,bits256 privkey);
|
|
privkey = mpz_to_bits256(bn);
|
|
char str[65]; printf("bn -> %s\n",bits256_str(str,privkey));
|
|
}*/
|
|
if ( count >= 2 && data[count - 1] == 0 && data[count - 2] >= 0x80 )
|
|
count--;
|
|
be_sz = (uint32_t)count + (uint32_t)zeroes;
|
|
//memset(data,0,be_sz);
|
|
//for (i=0; i<count; i++)
|
|
// data[i+zeroes] = revdata[count - 1 - i];
|
|
//printf(" count.%d len.%d be_sz.%d zeroes.%d data[0] %02x %02x\n",(int32_t)count,be_sz+zeroes,be_sz,zeroes,data[0],data[1]);
|
|
mpz_clear(bn), mpz_clear(bn58);
|
|
return(be_sz);
|
|
}
|
|
|
|
bits256 mpz_muldivcmp(bits256 oldval,int32_t mulval,int32_t divval,bits256 targetval)
|
|
{
|
|
mpz_t bn,target; bits256 newval;
|
|
//printf("mulval.%d divval.%d]\n",mulval,divval);
|
|
mpz_init(bn), mpz_init(target);
|
|
mpz_from_bits256(bn,oldval);
|
|
mpz_mul_ui(bn,bn,mulval);
|
|
mpz_tdiv_qr_ui(bn,NULL,bn,divval);
|
|
if ( bn->_mp_size <= 0 || mpz_cmp(bn,target) > 0 )
|
|
newval = targetval;
|
|
newval = mpz_to_bits256(bn);
|
|
//char *bits256_str(char *,bits256);
|
|
//char str[65],str2[65]; printf("%s mul.%d div.%d -> %s size.%d\n",bits256_str(str,oldval),mulval,divval,bits256_str(str2,newval),bn->_mp_size);
|
|
mpz_clear(bn), mpz_clear(target);
|
|
return(newval);
|
|
}
|
|
|
|
bits256 mpz_div64(bits256 hash,uint64_t divval)
|
|
{
|
|
mpz_t bn; bits256 newval;
|
|
mpz_init(bn);
|
|
mpz_from_bits256(bn,hash);
|
|
mpz_tdiv_qr_ui(bn,NULL,bn,divval);
|
|
newval = mpz_to_bits256(bn);
|
|
//char *bits256_str(char *,bits256);
|
|
//char str[65],str2[65]; printf("%s div.%lld -> %s size.%d\n",bits256_str(str,hash),(long long)divval,bits256_str(str2,newval),bn->_mp_size);
|
|
mpz_clear(bn);
|
|
return(newval);
|
|
}
|
|
|