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Diffstat (limited to 'src/mini-gmp.c')
| -rw-r--r-- | src/mini-gmp.c | 4559 |
1 files changed, 0 insertions, 4559 deletions
diff --git a/src/mini-gmp.c b/src/mini-gmp.c deleted file mode 100644 index bf8a6164981..00000000000 --- a/src/mini-gmp.c +++ /dev/null @@ -1,4559 +0,0 @@ -/* mini-gmp, a minimalistic implementation of a GNU GMP subset. - - Contributed to the GNU project by Niels Möller - -Copyright 1991-1997, 1999-2019 Free Software Foundation, Inc. - -This file is part of the GNU MP Library. - -The GNU MP Library is free software; you can redistribute it and/or modify -it under the terms of either: - - * the GNU Lesser General Public License as published by the Free - Software Foundation; either version 3 of the License, or (at your - option) any later version. - -or - - * the GNU General Public License as published by the Free Software - Foundation; either version 2 of the License, or (at your option) any - later version. - -or both in parallel, as here. - -The GNU MP Library is distributed in the hope that it will be useful, but -WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY -or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License -for more details. - -You should have received copies of the GNU General Public License and the -GNU Lesser General Public License along with the GNU MP Library. If not, -see https://www.gnu.org/licenses/. */ - -/* NOTE: All functions in this file which are not declared in - mini-gmp.h are internal, and are not intended to be compatible - neither with GMP nor with future versions of mini-gmp. */ - -/* Much of the material copied from GMP files, including: gmp-impl.h, - longlong.h, mpn/generic/add_n.c, mpn/generic/addmul_1.c, - mpn/generic/lshift.c, mpn/generic/mul_1.c, - mpn/generic/mul_basecase.c, mpn/generic/rshift.c, - mpn/generic/sbpi1_div_qr.c, mpn/generic/sub_n.c, - mpn/generic/submul_1.c. */ - -#include <assert.h> -#include <ctype.h> -#include <limits.h> -#include <stdio.h> -#include <stdlib.h> -#include <string.h> - -#include "mini-gmp.h" - -#if !defined(MINI_GMP_DONT_USE_FLOAT_H) -#include <float.h> -#endif - - -/* Macros */ -#define GMP_LIMB_BITS (sizeof(mp_limb_t) * CHAR_BIT) - -#define GMP_LIMB_MAX ((mp_limb_t) ~ (mp_limb_t) 0) -#define GMP_LIMB_HIGHBIT ((mp_limb_t) 1 << (GMP_LIMB_BITS - 1)) - -#define GMP_HLIMB_BIT ((mp_limb_t) 1 << (GMP_LIMB_BITS / 2)) -#define GMP_LLIMB_MASK (GMP_HLIMB_BIT - 1) - -#define GMP_ULONG_BITS (sizeof(unsigned long) * CHAR_BIT) -#define GMP_ULONG_HIGHBIT ((unsigned long) 1 << (GMP_ULONG_BITS - 1)) - -#define GMP_ABS(x) ((x) >= 0 ? (x) : -(x)) -#define GMP_NEG_CAST(T,x) (-((T)((x) + 1) - 1)) - -#define GMP_MIN(a, b) ((a) < (b) ? (a) : (b)) -#define GMP_MAX(a, b) ((a) > (b) ? (a) : (b)) - -#define GMP_CMP(a,b) (((a) > (b)) - ((a) < (b))) - -#if defined(DBL_MANT_DIG) && FLT_RADIX == 2 -#define GMP_DBL_MANT_BITS DBL_MANT_DIG -#else -#define GMP_DBL_MANT_BITS (53) -#endif - -/* Return non-zero if xp,xsize and yp,ysize overlap. - If xp+xsize<=yp there's no overlap, or if yp+ysize<=xp there's no - overlap. If both these are false, there's an overlap. */ -#define GMP_MPN_OVERLAP_P(xp, xsize, yp, ysize) \ - ((xp) + (xsize) > (yp) && (yp) + (ysize) > (xp)) - -#define gmp_assert_nocarry(x) do { \ - mp_limb_t __cy = (x); \ - assert (__cy == 0); \ - } while (0) - -#define gmp_clz(count, x) do { \ - mp_limb_t __clz_x = (x); \ - unsigned __clz_c; \ - for (__clz_c = 0; \ - (__clz_x & ((mp_limb_t) 0xff << (GMP_LIMB_BITS - 8))) == 0; \ - __clz_c += 8) \ - __clz_x <<= 8; \ - for (; (__clz_x & GMP_LIMB_HIGHBIT) == 0; __clz_c++) \ - __clz_x <<= 1; \ - (count) = __clz_c; \ - } while (0) - -#define gmp_ctz(count, x) do { \ - mp_limb_t __ctz_x = (x); \ - unsigned __ctz_c = 0; \ - gmp_clz (__ctz_c, __ctz_x & - __ctz_x); \ - (count) = GMP_LIMB_BITS - 1 - __ctz_c; \ - } while (0) - -#define gmp_add_ssaaaa(sh, sl, ah, al, bh, bl) \ - do { \ - mp_limb_t __x; \ - __x = (al) + (bl); \ - (sh) = (ah) + (bh) + (__x < (al)); \ - (sl) = __x; \ - } while (0) - -#define gmp_sub_ddmmss(sh, sl, ah, al, bh, bl) \ - do { \ - mp_limb_t __x; \ - __x = (al) - (bl); \ - (sh) = (ah) - (bh) - ((al) < (bl)); \ - (sl) = __x; \ - } while (0) - -#define gmp_umul_ppmm(w1, w0, u, v) \ - do { \ - int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS; \ - if (sizeof(unsigned int) * CHAR_BIT >= 2 * GMP_LIMB_BITS) \ - { \ - unsigned int __ww = (unsigned int) (u) * (v); \ - w0 = (mp_limb_t) __ww; \ - w1 = (mp_limb_t) (__ww >> LOCAL_GMP_LIMB_BITS); \ - } \ - else if (GMP_ULONG_BITS >= 2 * GMP_LIMB_BITS) \ - { \ - unsigned long int __ww = (unsigned long int) (u) * (v); \ - w0 = (mp_limb_t) __ww; \ - w1 = (mp_limb_t) (__ww >> LOCAL_GMP_LIMB_BITS); \ - } \ - else { \ - mp_limb_t __x0, __x1, __x2, __x3; \ - unsigned __ul, __vl, __uh, __vh; \ - mp_limb_t __u = (u), __v = (v); \ - \ - __ul = __u & GMP_LLIMB_MASK; \ - __uh = __u >> (GMP_LIMB_BITS / 2); \ - __vl = __v & GMP_LLIMB_MASK; \ - __vh = __v >> (GMP_LIMB_BITS / 2); \ - \ - __x0 = (mp_limb_t) __ul * __vl; \ - __x1 = (mp_limb_t) __ul * __vh; \ - __x2 = (mp_limb_t) __uh * __vl; \ - __x3 = (mp_limb_t) __uh * __vh; \ - \ - __x1 += __x0 >> (GMP_LIMB_BITS / 2);/* this can't give carry */ \ - __x1 += __x2; /* but this indeed can */ \ - if (__x1 < __x2) /* did we get it? */ \ - __x3 += GMP_HLIMB_BIT; /* yes, add it in the proper pos. */ \ - \ - (w1) = __x3 + (__x1 >> (GMP_LIMB_BITS / 2)); \ - (w0) = (__x1 << (GMP_LIMB_BITS / 2)) + (__x0 & GMP_LLIMB_MASK); \ - } \ - } while (0) - -#define gmp_udiv_qrnnd_preinv(q, r, nh, nl, d, di) \ - do { \ - mp_limb_t _qh, _ql, _r, _mask; \ - gmp_umul_ppmm (_qh, _ql, (nh), (di)); \ - gmp_add_ssaaaa (_qh, _ql, _qh, _ql, (nh) + 1, (nl)); \ - _r = (nl) - _qh * (d); \ - _mask = -(mp_limb_t) (_r > _ql); /* both > and >= are OK */ \ - _qh += _mask; \ - _r += _mask & (d); \ - if (_r >= (d)) \ - { \ - _r -= (d); \ - _qh++; \ - } \ - \ - (r) = _r; \ - (q) = _qh; \ - } while (0) - -#define gmp_udiv_qr_3by2(q, r1, r0, n2, n1, n0, d1, d0, dinv) \ - do { \ - mp_limb_t _q0, _t1, _t0, _mask; \ - gmp_umul_ppmm ((q), _q0, (n2), (dinv)); \ - gmp_add_ssaaaa ((q), _q0, (q), _q0, (n2), (n1)); \ - \ - /* Compute the two most significant limbs of n - q'd */ \ - (r1) = (n1) - (d1) * (q); \ - gmp_sub_ddmmss ((r1), (r0), (r1), (n0), (d1), (d0)); \ - gmp_umul_ppmm (_t1, _t0, (d0), (q)); \ - gmp_sub_ddmmss ((r1), (r0), (r1), (r0), _t1, _t0); \ - (q)++; \ - \ - /* Conditionally adjust q and the remainders */ \ - _mask = - (mp_limb_t) ((r1) >= _q0); \ - (q) += _mask; \ - gmp_add_ssaaaa ((r1), (r0), (r1), (r0), _mask & (d1), _mask & (d0)); \ - if ((r1) >= (d1)) \ - { \ - if ((r1) > (d1) || (r0) >= (d0)) \ - { \ - (q)++; \ - gmp_sub_ddmmss ((r1), (r0), (r1), (r0), (d1), (d0)); \ - } \ - } \ - } while (0) - -/* Swap macros. */ -#define MP_LIMB_T_SWAP(x, y) \ - do { \ - mp_limb_t __mp_limb_t_swap__tmp = (x); \ - (x) = (y); \ - (y) = __mp_limb_t_swap__tmp; \ - } while (0) -#define MP_SIZE_T_SWAP(x, y) \ - do { \ - mp_size_t __mp_size_t_swap__tmp = (x); \ - (x) = (y); \ - (y) = __mp_size_t_swap__tmp; \ - } while (0) -#define MP_BITCNT_T_SWAP(x,y) \ - do { \ - mp_bitcnt_t __mp_bitcnt_t_swap__tmp = (x); \ - (x) = (y); \ - (y) = __mp_bitcnt_t_swap__tmp; \ - } while (0) -#define MP_PTR_SWAP(x, y) \ - do { \ - mp_ptr __mp_ptr_swap__tmp = (x); \ - (x) = (y); \ - (y) = __mp_ptr_swap__tmp; \ - } while (0) -#define MP_SRCPTR_SWAP(x, y) \ - do { \ - mp_srcptr __mp_srcptr_swap__tmp = (x); \ - (x) = (y); \ - (y) = __mp_srcptr_swap__tmp; \ - } while (0) - -#define MPN_PTR_SWAP(xp,xs, yp,ys) \ - do { \ - MP_PTR_SWAP (xp, yp); \ - MP_SIZE_T_SWAP (xs, ys); \ - } while(0) -#define MPN_SRCPTR_SWAP(xp,xs, yp,ys) \ - do { \ - MP_SRCPTR_SWAP (xp, yp); \ - MP_SIZE_T_SWAP (xs, ys); \ - } while(0) - -#define MPZ_PTR_SWAP(x, y) \ - do { \ - mpz_ptr __mpz_ptr_swap__tmp = (x); \ - (x) = (y); \ - (y) = __mpz_ptr_swap__tmp; \ - } while (0) -#define MPZ_SRCPTR_SWAP(x, y) \ - do { \ - mpz_srcptr __mpz_srcptr_swap__tmp = (x); \ - (x) = (y); \ - (y) = __mpz_srcptr_swap__tmp; \ - } while (0) - -const int mp_bits_per_limb = GMP_LIMB_BITS; - - -/* Memory allocation and other helper functions. */ -static void -gmp_die (const char *msg) -{ - fprintf (stderr, "%s\n", msg); - abort(); -} - -static void * -gmp_default_alloc (size_t size) -{ - void *p; - - assert (size > 0); - - p = malloc (size); - if (!p) - gmp_die("gmp_default_alloc: Virtual memory exhausted."); - - return p; -} - -static void * -gmp_default_realloc (void *old, size_t unused_old_size, size_t new_size) -{ - void * p; - - p = realloc (old, new_size); - - if (!p) - gmp_die("gmp_default_realloc: Virtual memory exhausted."); - - return p; -} - -static void -gmp_default_free (void *p, size_t unused_size) -{ - free (p); -} - -static void * (*gmp_allocate_func) (size_t) = gmp_default_alloc; -static void * (*gmp_reallocate_func) (void *, size_t, size_t) = gmp_default_realloc; -static void (*gmp_free_func) (void *, size_t) = gmp_default_free; - -void -mp_get_memory_functions (void *(**alloc_func) (size_t), - void *(**realloc_func) (void *, size_t, size_t), - void (**free_func) (void *, size_t)) -{ - if (alloc_func) - *alloc_func = gmp_allocate_func; - - if (realloc_func) - *realloc_func = gmp_reallocate_func; - - if (free_func) - *free_func = gmp_free_func; -} - -void -mp_set_memory_functions (void *(*alloc_func) (size_t), - void *(*realloc_func) (void *, size_t, size_t), - void (*free_func) (void *, size_t)) -{ - if (!alloc_func) - alloc_func = gmp_default_alloc; - if (!realloc_func) - realloc_func = gmp_default_realloc; - if (!free_func) - free_func = gmp_default_free; - - gmp_allocate_func = alloc_func; - gmp_reallocate_func = realloc_func; - gmp_free_func = free_func; -} - -#define gmp_xalloc(size) ((*gmp_allocate_func)((size))) -#define gmp_free(p) ((*gmp_free_func) ((p), 0)) - -static mp_ptr -gmp_xalloc_limbs (mp_size_t size) -{ - return (mp_ptr) gmp_xalloc (size * sizeof (mp_limb_t)); -} - -static mp_ptr -gmp_xrealloc_limbs (mp_ptr old, mp_size_t size) -{ - assert (size > 0); - return (mp_ptr) (*gmp_reallocate_func) (old, 0, size * sizeof (mp_limb_t)); -} - - -/* MPN interface */ - -void -mpn_copyi (mp_ptr d, mp_srcptr s, mp_size_t n) -{ - mp_size_t i; - for (i = 0; i < n; i++) - d[i] = s[i]; -} - -void -mpn_copyd (mp_ptr d, mp_srcptr s, mp_size_t n) -{ - while (--n >= 0) - d[n] = s[n]; -} - -int -mpn_cmp (mp_srcptr ap, mp_srcptr bp, mp_size_t n) -{ - while (--n >= 0) - { - if (ap[n] != bp[n]) - return ap[n] > bp[n] ? 1 : -1; - } - return 0; -} - -static int -mpn_cmp4 (mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn) -{ - if (an != bn) - return an < bn ? -1 : 1; - else - return mpn_cmp (ap, bp, an); -} - -static mp_size_t -mpn_normalized_size (mp_srcptr xp, mp_size_t n) -{ - while (n > 0 && xp[n-1] == 0) - --n; - return n; -} - -int -mpn_zero_p(mp_srcptr rp, mp_size_t n) -{ - return mpn_normalized_size (rp, n) == 0; -} - -void -mpn_zero (mp_ptr rp, mp_size_t n) -{ - while (--n >= 0) - rp[n] = 0; -} - -mp_limb_t -mpn_add_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b) -{ - mp_size_t i; - - assert (n > 0); - i = 0; - do - { - mp_limb_t r = ap[i] + b; - /* Carry out */ - b = (r < b); - rp[i] = r; - } - while (++i < n); - - return b; -} - -mp_limb_t -mpn_add_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n) -{ - mp_size_t i; - mp_limb_t cy; - - for (i = 0, cy = 0; i < n; i++) - { - mp_limb_t a, b, r; - a = ap[i]; b = bp[i]; - r = a + cy; - cy = (r < cy); - r += b; - cy += (r < b); - rp[i] = r; - } - return cy; -} - -mp_limb_t -mpn_add (mp_ptr rp, mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn) -{ - mp_limb_t cy; - - assert (an >= bn); - - cy = mpn_add_n (rp, ap, bp, bn); - if (an > bn) - cy = mpn_add_1 (rp + bn, ap + bn, an - bn, cy); - return cy; -} - -mp_limb_t -mpn_sub_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b) -{ - mp_size_t i; - - assert (n > 0); - - i = 0; - do - { - mp_limb_t a = ap[i]; - /* Carry out */ - mp_limb_t cy = a < b; - rp[i] = a - b; - b = cy; - } - while (++i < n); - - return b; -} - -mp_limb_t -mpn_sub_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n) -{ - mp_size_t i; - mp_limb_t cy; - - for (i = 0, cy = 0; i < n; i++) - { - mp_limb_t a, b; - a = ap[i]; b = bp[i]; - b += cy; - cy = (b < cy); - cy += (a < b); - rp[i] = a - b; - } - return cy; -} - -mp_limb_t -mpn_sub (mp_ptr rp, mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn) -{ - mp_limb_t cy; - - assert (an >= bn); - - cy = mpn_sub_n (rp, ap, bp, bn); - if (an > bn) - cy = mpn_sub_1 (rp + bn, ap + bn, an - bn, cy); - return cy; -} - -mp_limb_t -mpn_mul_1 (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_limb_t vl) -{ - mp_limb_t ul, cl, hpl, lpl; - - assert (n >= 1); - - cl = 0; - do - { - ul = *up++; - gmp_umul_ppmm (hpl, lpl, ul, vl); - - lpl += cl; - cl = (lpl < cl) + hpl; - - *rp++ = lpl; - } - while (--n != 0); - - return cl; -} - -mp_limb_t -mpn_addmul_1 (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_limb_t vl) -{ - mp_limb_t ul, cl, hpl, lpl, rl; - - assert (n >= 1); - - cl = 0; - do - { - ul = *up++; - gmp_umul_ppmm (hpl, lpl, ul, vl); - - lpl += cl; - cl = (lpl < cl) + hpl; - - rl = *rp; - lpl = rl + lpl; - cl += lpl < rl; - *rp++ = lpl; - } - while (--n != 0); - - return cl; -} - -mp_limb_t -mpn_submul_1 (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_limb_t vl) -{ - mp_limb_t ul, cl, hpl, lpl, rl; - - assert (n >= 1); - - cl = 0; - do - { - ul = *up++; - gmp_umul_ppmm (hpl, lpl, ul, vl); - - lpl += cl; - cl = (lpl < cl) + hpl; - - rl = *rp; - lpl = rl - lpl; - cl += lpl > rl; - *rp++ = lpl; - } - while (--n != 0); - - return cl; -} - -mp_limb_t -mpn_mul (mp_ptr rp, mp_srcptr up, mp_size_t un, mp_srcptr vp, mp_size_t vn) -{ - assert (un >= vn); - assert (vn >= 1); - assert (!GMP_MPN_OVERLAP_P(rp, un + vn, up, un)); - assert (!GMP_MPN_OVERLAP_P(rp, un + vn, vp, vn)); - - /* We first multiply by the low order limb. This result can be - stored, not added, to rp. We also avoid a loop for zeroing this - way. */ - - rp[un] = mpn_mul_1 (rp, up, un, vp[0]); - - /* Now accumulate the product of up[] and the next higher limb from - vp[]. */ - - while (--vn >= 1) - { - rp += 1, vp += 1; - rp[un] = mpn_addmul_1 (rp, up, un, vp[0]); - } - return rp[un]; -} - -void -mpn_mul_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n) -{ - mpn_mul (rp, ap, n, bp, n); -} - -void -mpn_sqr (mp_ptr rp, mp_srcptr ap, mp_size_t n) -{ - mpn_mul (rp, ap, n, ap, n); -} - -mp_limb_t -mpn_lshift (mp_ptr rp, mp_srcptr up, mp_size_t n, unsigned int cnt) -{ - mp_limb_t high_limb, low_limb; - unsigned int tnc; - mp_limb_t retval; - - assert (n >= 1); - assert (cnt >= 1); - assert (cnt < GMP_LIMB_BITS); - - up += n; - rp += n; - - tnc = GMP_LIMB_BITS - cnt; - low_limb = *--up; - retval = low_limb >> tnc; - high_limb = (low_limb << cnt); - - while (--n != 0) - { - low_limb = *--up; - *--rp = high_limb | (low_limb >> tnc); - high_limb = (low_limb << cnt); - } - *--rp = high_limb; - - return retval; -} - -mp_limb_t -mpn_rshift (mp_ptr rp, mp_srcptr up, mp_size_t n, unsigned int cnt) -{ - mp_limb_t high_limb, low_limb; - unsigned int tnc; - mp_limb_t retval; - - assert (n >= 1); - assert (cnt >= 1); - assert (cnt < GMP_LIMB_BITS); - - tnc = GMP_LIMB_BITS - cnt; - high_limb = *up++; - retval = (high_limb << tnc); - low_limb = high_limb >> cnt; - - while (--n != 0) - { - high_limb = *up++; - *rp++ = low_limb | (high_limb << tnc); - low_limb = high_limb >> cnt; - } - *rp = low_limb; - - return retval; -} - -static mp_bitcnt_t -mpn_common_scan (mp_limb_t limb, mp_size_t i, mp_srcptr up, mp_size_t un, - mp_limb_t ux) -{ - unsigned cnt; - - assert (ux == 0 || ux == GMP_LIMB_MAX); - assert (0 <= i && i <= un ); - - while (limb == 0) - { - i++; - if (i == un) - return (ux == 0 ? ~(mp_bitcnt_t) 0 : un * GMP_LIMB_BITS); - limb = ux ^ up[i]; - } - gmp_ctz (cnt, limb); - return (mp_bitcnt_t) i * GMP_LIMB_BITS + cnt; -} - -mp_bitcnt_t -mpn_scan1 (mp_srcptr ptr, mp_bitcnt_t bit) -{ - mp_size_t i; - i = bit / GMP_LIMB_BITS; - - return mpn_common_scan ( ptr[i] & (GMP_LIMB_MAX << (bit % GMP_LIMB_BITS)), - i, ptr, i, 0); -} - -mp_bitcnt_t -mpn_scan0 (mp_srcptr ptr, mp_bitcnt_t bit) -{ - mp_size_t i; - i = bit / GMP_LIMB_BITS; - - return mpn_common_scan (~ptr[i] & (GMP_LIMB_MAX << (bit % GMP_LIMB_BITS)), - i, ptr, i, GMP_LIMB_MAX); -} - -void -mpn_com (mp_ptr rp, mp_srcptr up, mp_size_t n) -{ - while (--n >= 0) - *rp++ = ~ *up++; -} - -mp_limb_t -mpn_neg (mp_ptr rp, mp_srcptr up, mp_size_t n) -{ - while (*up == 0) - { - *rp = 0; - if (!--n) - return 0; - ++up; ++rp; - } - *rp = - *up; - mpn_com (++rp, ++up, --n); - return 1; -} - - -/* MPN division interface. */ - -/* The 3/2 inverse is defined as - - m = floor( (B^3-1) / (B u1 + u0)) - B -*/ -mp_limb_t -mpn_invert_3by2 (mp_limb_t u1, mp_limb_t u0) -{ - int GMP_LIMB_BITS_MUL_3 = GMP_LIMB_BITS * 3; - if (sizeof (unsigned) * CHAR_BIT > GMP_LIMB_BITS * 3) - { - return (((unsigned) 1 << GMP_LIMB_BITS_MUL_3) - 1) / - (((unsigned) u1 << GMP_LIMB_BITS_MUL_3 / 3) + u0); - } - else if (GMP_ULONG_BITS > GMP_LIMB_BITS * 3) - { - return (((unsigned long) 1 << GMP_LIMB_BITS_MUL_3) - 1) / - (((unsigned long) u1 << GMP_LIMB_BITS_MUL_3 / 3) + u0); - } - else { - mp_limb_t r, p, m, ql; - unsigned ul, uh, qh; - - assert (u1 >= GMP_LIMB_HIGHBIT); - - /* For notation, let b denote the half-limb base, so that B = b^2. - Split u1 = b uh + ul. */ - ul = u1 & GMP_LLIMB_MASK; - uh = u1 >> (GMP_LIMB_BITS / 2); - - /* Approximation of the high half of quotient. Differs from the 2/1 - inverse of the half limb uh, since we have already subtracted - u0. */ - qh = ~u1 / uh; - - /* Adjust to get a half-limb 3/2 inverse, i.e., we want - - qh' = floor( (b^3 - 1) / u) - b = floor ((b^3 - b u - 1) / u - = floor( (b (~u) + b-1) / u), - - and the remainder - - r = b (~u) + b-1 - qh (b uh + ul) - = b (~u - qh uh) + b-1 - qh ul - - Subtraction of qh ul may underflow, which implies adjustments. - But by normalization, 2 u >= B > qh ul, so we need to adjust by - at most 2. - */ - - r = ((~u1 - (mp_limb_t) qh * uh) << (GMP_LIMB_BITS / 2)) | GMP_LLIMB_MASK; - - p = (mp_limb_t) qh * ul; - /* Adjustment steps taken from udiv_qrnnd_c */ - if (r < p) - { - qh--; - r += u1; - if (r >= u1) /* i.e. we didn't get carry when adding to r */ - if (r < p) - { - qh--; - r += u1; - } - } - r -= p; - - /* Low half of the quotient is - - ql = floor ( (b r + b-1) / u1). - - This is a 3/2 division (on half-limbs), for which qh is a - suitable inverse. */ - - p = (r >> (GMP_LIMB_BITS / 2)) * qh + r; - /* Unlike full-limb 3/2, we can add 1 without overflow. For this to - work, it is essential that ql is a full mp_limb_t. */ - ql = (p >> (GMP_LIMB_BITS / 2)) + 1; - - /* By the 3/2 trick, we don't need the high half limb. */ - r = (r << (GMP_LIMB_BITS / 2)) + GMP_LLIMB_MASK - ql * u1; - - if (r >= (p << (GMP_LIMB_BITS / 2))) - { - ql--; - r += u1; - } - m = ((mp_limb_t) qh << (GMP_LIMB_BITS / 2)) + ql; - if (r >= u1) - { - m++; - r -= u1; - } - - /* Now m is the 2/1 inverse of u1. If u0 > 0, adjust it to become a - 3/2 inverse. */ - if (u0 > 0) - { - mp_limb_t th, tl; - r = ~r; - r += u0; - if (r < u0) - { - m--; - if (r >= u1) - { - m--; - r -= u1; - } - r -= u1; - } - gmp_umul_ppmm (th, tl, u0, m); - r += th; - if (r < th) - { - m--; - m -= ((r > u1) | ((r == u1) & (tl > u0))); - } - } - - return m; - } -} - -struct gmp_div_inverse -{ - /* Normalization shift count. */ - unsigned shift; - /* Normalized divisor (d0 unused for mpn_div_qr_1) */ - mp_limb_t d1, d0; - /* Inverse, for 2/1 or 3/2. */ - mp_limb_t di; -}; - -static void -mpn_div_qr_1_invert (struct gmp_div_inverse *inv, mp_limb_t d) -{ - unsigned shift; - - assert (d > 0); - gmp_clz (shift, d); - inv->shift = shift; - inv->d1 = d << shift; - inv->di = mpn_invert_limb (inv->d1); -} - -static void -mpn_div_qr_2_invert (struct gmp_div_inverse *inv, - mp_limb_t d1, mp_limb_t d0) -{ - unsigned shift; - - assert (d1 > 0); - gmp_clz (shift, d1); - inv->shift = shift; - if (shift > 0) - { - d1 = (d1 << shift) | (d0 >> (GMP_LIMB_BITS - shift)); - d0 <<= shift; - } - inv->d1 = d1; - inv->d0 = d0; - inv->di = mpn_invert_3by2 (d1, d0); -} - -static void -mpn_div_qr_invert (struct gmp_div_inverse *inv, - mp_srcptr dp, mp_size_t dn) -{ - assert (dn > 0); - - if (dn == 1) - mpn_div_qr_1_invert (inv, dp[0]); - else if (dn == 2) - mpn_div_qr_2_invert (inv, dp[1], dp[0]); - else - { - unsigned shift; - mp_limb_t d1, d0; - - d1 = dp[dn-1]; - d0 = dp[dn-2]; - assert (d1 > 0); - gmp_clz (shift, d1); - inv->shift = shift; - if (shift > 0) - { - d1 = (d1 << shift) | (d0 >> (GMP_LIMB_BITS - shift)); - d0 = (d0 << shift) | (dp[dn-3] >> (GMP_LIMB_BITS - shift)); - } - inv->d1 = d1; - inv->d0 = d0; - inv->di = mpn_invert_3by2 (d1, d0); - } -} - -/* Not matching current public gmp interface, rather corresponding to - the sbpi1_div_* functions. */ -static mp_limb_t -mpn_div_qr_1_preinv (mp_ptr qp, mp_srcptr np, mp_size_t nn, - const struct gmp_div_inverse *inv) -{ - mp_limb_t d, di; - mp_limb_t r; - mp_ptr tp = NULL; - - if (inv->shift > 0) - { - /* Shift, reusing qp area if possible. In-place shift if qp == np. */ - tp = qp ? qp : 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) && (tp != qp)) - gmp_free (tp); - - return r >> inv->shift; -} - -static void -mpn_div_qr_2_preinv (mp_ptr qp, mp_ptr np, mp_size_t nn, - const struct gmp_div_inverse *inv) -{ - unsigned shift; - mp_size_t i; - mp_limb_t d1, d0, di, r1, r0; - - assert (nn >= 2); - shift = inv->shift; - d1 = inv->d1; - d0 = inv->d0; - di = inv->di; - - if (shift > 0) - r1 = mpn_lshift (np, np, nn, shift); - else - r1 = 0; - - r0 = np[nn - 1]; - - i = nn - 2; - do - { - mp_limb_t n0, q; - n0 = np[i]; - gmp_udiv_qr_3by2 (q, r1, r0, r1, r0, n0, d1, d0, di); - - if (qp) - qp[i] = q; - } - while (--i >= 0); - - if (shift > 0) - { - assert ((r0 & (GMP_LIMB_MAX >> (GMP_LIMB_BITS - shift))) == 0); - r0 = (r0 >> shift) | (r1 << (GMP_LIMB_BITS - shift)); - r1 >>= shift; - } - - np[1] = r1; - np[0] = r0; -} - -static void -mpn_div_qr_pi1 (mp_ptr qp, - mp_ptr np, mp_size_t nn, mp_limb_t n1, - mp_srcptr dp, mp_size_t dn, - mp_limb_t dinv) -{ - mp_size_t i; - - mp_limb_t d1, d0; - mp_limb_t cy, cy1; - mp_limb_t q; - - assert (dn > 2); - assert (nn >= dn); - - d1 = dp[dn - 1]; - d0 = dp[dn - 2]; - - assert ((d1 & GMP_LIMB_HIGHBIT) != 0); - /* Iteration variable is the index of the q limb. - * - * We divide <n1, np[dn-1+i], np[dn-2+i], np[dn-3+i],..., np[i]> - * by <d1, d0, dp[dn-3], ..., dp[0] > - */ - - i = nn - dn; - do - { - mp_limb_t n0 = np[dn-1+i]; - - if (n1 == d1 && n0 == d0) - { - q = GMP_LIMB_MAX; - mpn_submul_1 (np+i, dp, dn, q); - n1 = np[dn-1+i]; /* update n1, last loop's value will now be invalid */ - } - else - { - gmp_udiv_qr_3by2 (q, n1, n0, n1, n0, np[dn-2+i], d1, d0, dinv); - - cy = mpn_submul_1 (np + i, dp, dn-2, q); - - cy1 = n0 < cy; - n0 = n0 - cy; - cy = n1 < cy1; - n1 = n1 - cy1; - np[dn-2+i] = n0; - - if (cy != 0) - { - n1 += d1 + mpn_add_n (np + i, np + i, dp, dn - 1); - q--; - } - } - - if (qp) - qp[i] = q; - } - while (--i >= 0); - - np[dn - 1] = n1; -} - -static void -mpn_div_qr_preinv (mp_ptr qp, mp_ptr np, mp_size_t nn, - mp_srcptr dp, mp_size_t dn, - const struct gmp_div_inverse *inv) -{ - assert (dn > 0); - assert (nn >= dn); - - if (dn == 1) - np[0] = mpn_div_qr_1_preinv (qp, np, nn, inv); - else if (dn == 2) - mpn_div_qr_2_preinv (qp, np, nn, inv); - else - { - mp_limb_t nh; - unsigned shift; - - assert (inv->d1 == dp[dn-1]); - assert (inv->d0 == dp[dn-2]); - assert ((inv->d1 & GMP_LIMB_HIGHBIT) != 0); - - shift = inv->shift; - if (shift > 0) - nh = mpn_lshift (np, np, nn, shift); - else - nh = 0; - - mpn_div_qr_pi1 (qp, np, nn, nh, dp, dn, inv->di); - - if (shift > 0) - gmp_assert_nocarry (mpn_rshift (np, np, dn, shift)); - } -} - -static void -mpn_div_qr (mp_ptr qp, mp_ptr np, mp_size_t nn, mp_srcptr dp, mp_size_t dn) -{ - struct gmp_div_inverse inv; - mp_ptr tp = NULL; - - assert (dn > 0); - assert (nn >= dn); - - mpn_div_qr_invert (&inv, dp, dn); - if (dn > 2 && inv.shift > 0) - { - tp = gmp_xalloc_limbs (dn); - gmp_assert_nocarry (mpn_lshift (tp, dp, dn, inv.shift)); - dp = tp; - } - mpn_div_qr_preinv (qp, np, nn, dp, dn, &inv); - if (tp) - gmp_free (tp); -} - - -/* MPN base conversion. */ -static unsigned -mpn_base_power_of_two_p (unsigned b) -{ - switch (b) - { - case 2: return 1; - case 4: return 2; - case 8: return 3; - case 16: return 4; - case 32: return 5; - case 64: return 6; - case 128: return 7; - case 256: return 8; - default: return 0; - } -} - -struct mpn_base_info -{ - /* bb is the largest power of the base which fits in one limb, and - exp is the corresponding exponent. */ - unsigned exp; - mp_limb_t bb; -}; - -static void -mpn_get_base_info (struct mpn_base_info *info, mp_limb_t b) -{ - mp_limb_t m; - mp_limb_t p; - unsigned exp; - - m = GMP_LIMB_MAX / b; - for (exp = 1, p = b; p <= m; exp++) - p *= b; - - info->exp = exp; - info->bb = p; -} - -static mp_bitcnt_t -mpn_limb_size_in_base_2 (mp_limb_t u) -{ - unsigned shift; - - assert (u > 0); - gmp_clz (shift, u); - return GMP_LIMB_BITS - shift; -} - -static size_t -mpn_get_str_bits (unsigned char *sp, unsigned bits, mp_srcptr up, mp_size_t un) -{ - unsigned char mask; - size_t sn, j; - mp_size_t i; - unsigned shift; - - sn = ((un - 1) * GMP_LIMB_BITS + mpn_limb_size_in_base_2 (up[un-1]) - + bits - 1) / bits; - - mask = (1U << bits) - 1; - - for (i = 0, j = sn, shift = 0; j-- > 0;) - { - unsigned char digit = up[i] >> shift; - - shift += bits; - - if (shift >= GMP_LIMB_BITS && ++i < un) - { - shift -= GMP_LIMB_BITS; - digit |= up[i] << (bits - shift); - } - sp[j] = digit & mask; - } - return sn; -} - -/* We generate digits from the least significant end, and reverse at - the end. */ -static size_t -mpn_limb_get_str (unsigned char *sp, mp_limb_t w, - const struct gmp_div_inverse *binv) -{ - mp_size_t i; - for (i = 0; w > 0; i++) - { - mp_limb_t h, l, r; - - h = w >> (GMP_LIMB_BITS - binv->shift); - l = w << binv->shift; - - gmp_udiv_qrnnd_preinv (w, r, h, l, binv->d1, binv->di); - assert ((r & (GMP_LIMB_MAX >> (GMP_LIMB_BITS - binv->shift))) == 0); - r >>= binv->shift; - - sp[i] = r; - } - return i; -} - -static size_t -mpn_get_str_other (unsigned char *sp, - int base, const struct mpn_base_info *info, - mp_ptr up, mp_size_t un) -{ - struct gmp_div_inverse binv; - size_t sn; - size_t i; - - mpn_div_qr_1_invert (&binv, base); - - sn = 0; - - if (un > 1) - { - struct gmp_div_inverse bbinv; - mpn_div_qr_1_invert (&bbinv, info->bb); - - do - { - mp_limb_t w; - size_t done; - w = mpn_div_qr_1_preinv (up, up, un, &bbinv); - un -= (up[un-1] == 0); - done = mpn_limb_get_str (sp + sn, w, &binv); - - for (sn += done; done < info->exp; done++) - sp[sn++] = 0; - } - while (un > 1); - } - sn += mpn_limb_get_str (sp + sn, up[0], &binv); - - /* Reverse order */ - for (i = 0; 2*i + 1 < sn; i++) - { - unsigned char t = sp[i]; - sp[i] = sp[sn - i - 1]; - sp[sn - i - 1] = t; - } - - return sn; -} - -size_t -mpn_get_str (unsigned char *sp, int base, mp_ptr up, mp_size_t un) -{ - unsigned bits; - - assert (un > 0); - assert (up[un-1] > 0); - - bits = mpn_base_power_of_two_p (base); - if (bits) - return mpn_get_str_bits (sp, bits, up, un); - else - { - struct mpn_base_info info; - - mpn_get_base_info (&info, base); - return mpn_get_str_other (sp, base, &info, up, un); - } -} - -static mp_size_t -mpn_set_str_bits (mp_ptr rp, const unsigned char *sp, size_t sn, - unsigned bits) -{ - mp_size_t rn; - size_t j; - unsigned shift; - - for (j = sn, rn = 0, shift = 0; j-- > 0; ) - { - if (shift == 0) - { - rp[rn++] = sp[j]; - shift += bits; - } - else - { - rp[rn-1] |= (mp_limb_t) sp[j] << shift; - shift += bits; - if (shift >= GMP_LIMB_BITS) - { - shift -= GMP_LIMB_BITS; - if (shift > 0) - rp[rn++] = (mp_limb_t) sp[j] >> (bits - shift); - } - } - } - rn = mpn_normalized_size (rp, rn); - return rn; -} - -/* Result is usually normalized, except for all-zero input, in which - case a single zero limb is written at *RP, and 1 is returned. */ -static mp_size_t -mpn_set_str_other (mp_ptr rp, const unsigned char *sp, size_t sn, - mp_limb_t b, const struct mpn_base_info *info) -{ - mp_size_t rn; - mp_limb_t w; - unsigned k; - size_t j; - - assert (sn > 0); - - k = 1 + (sn - 1) % info->exp; - - j = 0; - w = sp[j++]; - while (--k != 0) - w = w * b + sp[j++]; - - rp[0] = w; - - for (rn = 1; j < sn;) - { - mp_limb_t cy; - - w = sp[j++]; - for (k = 1; k < info->exp; k++) - w = w * b + sp[j++]; - - cy = mpn_mul_1 (rp, rp, rn, info->bb); - cy += mpn_add_1 (rp, rp, rn, w); - if (cy > 0) - rp[rn++] = cy; - } - assert (j == sn); - - return rn; -} - -mp_size_t -mpn_set_str (mp_ptr rp, const unsigned char *sp, size_t sn, int base) -{ - unsigned bits; - - if (sn == 0) - return 0; - - bits = mpn_base_power_of_two_p (base); - if (bits) - return mpn_set_str_bits (rp, sp, sn, bits); - else - { - struct mpn_base_info info; - - mpn_get_base_info (&info, base); - return mpn_set_str_other (rp, sp, sn, base, &info); - } -} - - -/* MPZ interface */ -void -mpz_init (mpz_t r) -{ - static const mp_limb_t dummy_limb = GMP_LIMB_MAX & 0xc1a0; - - r->_mp_alloc = 0; - r->_mp_size = 0; - r->_mp_d = (mp_ptr) &dummy_limb; -} - -/* The utility of this function is a bit limited, since many functions - assigns the result variable using mpz_swap. */ -void -mpz_init2 (mpz_t r, mp_bitcnt_t bits) -{ - mp_size_t rn; - - bits -= (bits != 0); /* Round down, except if 0 */ - rn = 1 + bits / GMP_LIMB_BITS; - - r->_mp_alloc = rn; - r->_mp_size = 0; - r->_mp_d = gmp_xalloc_limbs (rn); -} - -void -mpz_clear (mpz_t r) -{ - if (r->_mp_alloc) - gmp_free (r->_mp_d); -} - -static mp_ptr -mpz_realloc (mpz_t r, mp_size_t size) -{ - size = GMP_MAX (size, 1); - - if (r->_mp_alloc) - r->_mp_d = gmp_xrealloc_limbs (r->_mp_d, size); - else - r->_mp_d = gmp_xalloc_limbs (size); - r->_mp_alloc = size; - - if (GMP_ABS (r->_mp_size) > size) - r->_mp_size = 0; - - return r->_mp_d; -} - -/* Realloc for an mpz_t WHAT if it has less than NEEDED limbs. */ -#define MPZ_REALLOC(z,n) ((n) > (z)->_mp_alloc \ - ? mpz_realloc(z,n) \ - : (z)->_mp_d) - -/* MPZ assignment and basic conversions. */ -void -mpz_set_si (mpz_t r, signed long int x) -{ - if (x >= 0) - mpz_set_ui (r, x); - else /* (x < 0) */ - if (GMP_LIMB_BITS < GMP_ULONG_BITS) - { - mpz_set_ui (r, GMP_NEG_CAST (unsigned long int, x)); - mpz_neg (r, r); - } - else - { - r->_mp_size = -1; - MPZ_REALLOC (r, 1)[0] = GMP_NEG_CAST (unsigned long int, x); - } -} - -void -mpz_set_ui (mpz_t r, unsigned long int x) -{ - if (x > 0) - { - r->_mp_size = 1; - MPZ_REALLOC (r, 1)[0] = x; - if (GMP_LIMB_BITS < GMP_ULONG_BITS) - { - int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS; - while (x >>= LOCAL_GMP_LIMB_BITS) - { - ++ r->_mp_size; - MPZ_REALLOC (r, r->_mp_size)[r->_mp_size - 1] = x; - } - } - } - else - r->_mp_size = 0; -} - -void -mpz_set (mpz_t r, const mpz_t x) -{ - /* Allow the NOP r == x */ - if (r != x) - { - mp_size_t n; - mp_ptr rp; - - n = GMP_ABS (x->_mp_size); - rp = MPZ_REALLOC (r, n); - - mpn_copyi (rp, x->_mp_d, n); - r->_mp_size = x->_mp_size; - } -} - -void -mpz_init_set_si (mpz_t r, signed long int x) -{ - mpz_init (r); - mpz_set_si (r, x); -} - -void -mpz_init_set_ui (mpz_t r, unsigned long int x) -{ - mpz_init (r); - mpz_set_ui (r, x); -} - -void -mpz_init_set (mpz_t r, const mpz_t x) -{ - mpz_init (r); - mpz_set (r, x); -} - -int -mpz_fits_slong_p (const mpz_t u) -{ - return (LONG_MAX + LONG_MIN == 0 || mpz_cmp_ui (u, LONG_MAX) <= 0) && - mpz_cmpabs_ui (u, GMP_NEG_CAST (unsigned long int, LONG_MIN)) <= 0; -} - -static int -mpn_absfits_ulong_p (mp_srcptr up, mp_size_t un) -{ - int ulongsize = GMP_ULONG_BITS / GMP_LIMB_BITS; - mp_limb_t ulongrem = 0; - - if (GMP_ULONG_BITS % GMP_LIMB_BITS != 0) - ulongrem = (mp_limb_t) (ULONG_MAX >> GMP_LIMB_BITS * ulongsize) + 1; - - return un <= ulongsize || (up[ulongsize] < ulongrem && un == ulongsize + 1); -} - -int -mpz_fits_ulong_p (const mpz_t u) -{ - mp_size_t us = u->_mp_size; - - return us >= 0 && mpn_absfits_ulong_p (u->_mp_d, us); -} - -long int -mpz_get_si (const mpz_t u) -{ - unsigned long r = mpz_get_ui (u); - unsigned long c = -LONG_MAX - LONG_MIN; - - if (u->_mp_size < 0) - /* This expression is necessary to properly handle -LONG_MIN */ - return -(long) c - (long) ((r - c) & LONG_MAX); - else - return (long) (r & LONG_MAX); -} - -unsigned long int -mpz_get_ui (const mpz_t u) -{ - if (GMP_LIMB_BITS < GMP_ULONG_BITS) - { - int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS; - unsigned long r = 0; - mp_size_t n = GMP_ABS (u->_mp_size); - n = GMP_MIN (n, 1 + (mp_size_t) (GMP_ULONG_BITS - 1) / GMP_LIMB_BITS); - while (--n >= 0) - r = (r << LOCAL_GMP_LIMB_BITS) + u->_mp_d[n]; - return r; - } - - return u->_mp_size == 0 ? 0 : u->_mp_d[0]; -} - -size_t -mpz_size (const mpz_t u) -{ - return GMP_ABS (u->_mp_size); -} - -mp_limb_t -mpz_getlimbn (const mpz_t u, mp_size_t n) -{ - if (n >= 0 && n < GMP_ABS (u->_mp_size)) - return u->_mp_d[n]; - else - return 0; -} - -void -mpz_realloc2 (mpz_t x, mp_bitcnt_t n) -{ - mpz_realloc (x, 1 + (n - (n != 0)) / GMP_LIMB_BITS); -} - -mp_srcptr -mpz_limbs_read (mpz_srcptr x) -{ - return x->_mp_d; -} - -mp_ptr -mpz_limbs_modify (mpz_t x, mp_size_t n) -{ - assert (n > 0); - return MPZ_REALLOC (x, n); -} - -mp_ptr -mpz_limbs_write (mpz_t x, mp_size_t n) -{ - return mpz_limbs_modify (x, n); -} - -void -mpz_limbs_finish (mpz_t x, mp_size_t xs) -{ - mp_size_t xn; - xn = mpn_normalized_size (x->_mp_d, GMP_ABS (xs)); - x->_mp_size = xs < 0 ? -xn : xn; -} - -static mpz_srcptr -mpz_roinit_normal_n (mpz_t x, mp_srcptr xp, mp_size_t xs) -{ - x->_mp_alloc = 0; - x->_mp_d = (mp_ptr) xp; - x->_mp_size = xs; - return x; -} - -mpz_srcptr -mpz_roinit_n (mpz_t x, mp_srcptr xp, mp_size_t xs) -{ - mpz_roinit_normal_n (x, xp, xs); - mpz_limbs_finish (x, xs); - return x; -} - - -/* Conversions and comparison to double. */ -void -mpz_set_d (mpz_t r, double x) -{ - int sign; - mp_ptr rp; - mp_size_t rn, i; - double B; - double Bi; - mp_limb_t f; - - /* x != x is true when x is a NaN, and x == x * 0.5 is true when x is - zero or infinity. */ - if (x != x || x == x * 0.5) - { - r->_mp_size = 0; - return; - } - - sign = x < 0.0 ; - if (sign) - x = - x; - - if (x < 1.0) - { - r->_mp_size = 0; - return; - } - B = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1); - Bi = 1.0 / B; - for (rn = 1; x >= B; rn++) - x *= Bi; - - rp = MPZ_REALLOC (r, rn); - - f = (mp_limb_t) x; - x -= f; - assert (x < 1.0); - i = rn-1; - rp[i] = f; - while (--i >= 0) - { - x = B * x; - f = (mp_limb_t) x; - x -= f; - assert (x < 1.0); - rp[i] = f; - } - - r->_mp_size = sign ? - rn : rn; -} - -void -mpz_init_set_d (mpz_t r, double x) -{ - mpz_init (r); - mpz_set_d (r, x); -} - -double -mpz_get_d (const mpz_t u) -{ - int m; - mp_limb_t l; - mp_size_t un; - double x; - double B = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1); - - un = GMP_ABS (u->_mp_size); - - if (un == 0) - return 0.0; - - l = u->_mp_d[--un]; - gmp_clz (m, l); - m = m + GMP_DBL_MANT_BITS - GMP_LIMB_BITS; - if (m < 0) - l &= GMP_LIMB_MAX << -m; - - for (x = l; --un >= 0;) - { - x = B*x; - if (m > 0) { - l = u->_mp_d[un]; - m -= GMP_LIMB_BITS; - if (m < 0) - l &= GMP_LIMB_MAX << -m; - x += l; - } - } - - if (u->_mp_size < 0) - x = -x; - - return x; -} - -int -mpz_cmpabs_d (const mpz_t x, double d) -{ - mp_size_t xn; - double B, Bi; - mp_size_t i; - - xn = x->_mp_size; - d = GMP_ABS (d); - - if (xn != 0) - { - xn = GMP_ABS (xn); - - B = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1); - Bi = 1.0 / B; - - /* Scale d so it can be compared with the top limb. */ - for (i = 1; i < xn; i++) - d *= Bi; - - if (d >= B) - return -1; - - /* Compare floor(d) to top limb, subtract and cancel when equal. */ - for (i = xn; i-- > 0;) - { - mp_limb_t f, xl; - - f = (mp_limb_t) d; - xl = x->_mp_d[i]; - if (xl > f) - return 1; - else if (xl < f) - return -1; - d = B * (d - f); - } - } - return - (d > 0.0); -} - -int -mpz_cmp_d (const mpz_t x, double d) -{ - if (x->_mp_size < 0) - { - if (d >= 0.0) - return -1; - else - return -mpz_cmpabs_d (x, d); - } - else - { - if (d < 0.0) - return 1; - else - return mpz_cmpabs_d (x, d); - } -} - - -/* MPZ comparisons and the like. */ -int -mpz_sgn (const mpz_t u) -{ - return GMP_CMP (u->_mp_size, 0); -} - -int -mpz_cmp_si (const mpz_t u, long v) -{ - mp_size_t usize = u->_mp_size; - - if (v >= 0) - return mpz_cmp_ui (u, v); - else if (usize >= 0) - return 1; - else - return - mpz_cmpabs_ui (u, GMP_NEG_CAST (unsigned long int, v)); -} - -int -mpz_cmp_ui (const mpz_t u, unsigned long v) -{ - mp_size_t usize = u->_mp_size; - - if (usize < 0) - return -1; - else - return mpz_cmpabs_ui (u, v); -} - -int -mpz_cmp (const mpz_t a, const mpz_t b) -{ - mp_size_t asize = a->_mp_size; - mp_size_t bsize = b->_mp_size; - - if (asize != bsize) - return (asize < bsize) ? -1 : 1; - else if (asize >= 0) - return mpn_cmp (a->_mp_d, b->_mp_d, asize); - else - return mpn_cmp (b->_mp_d, a->_mp_d, -asize); -} - -int -mpz_cmpabs_ui (const mpz_t u, unsigned long v) -{ - mp_size_t un = GMP_ABS (u->_mp_size); - - if (! mpn_absfits_ulong_p (u->_mp_d, un)) - return 1; - else - { - unsigned long uu = mpz_get_ui (u); - return GMP_CMP(uu, v); - } -} - -int -mpz_cmpabs (const mpz_t u, const mpz_t v) -{ - return mpn_cmp4 (u->_mp_d, GMP_ABS (u->_mp_size), - v->_mp_d, GMP_ABS (v->_mp_size)); -} - -void -mpz_abs (mpz_t r, const mpz_t u) -{ - mpz_set (r, u); - r->_mp_size = GMP_ABS (r->_mp_size); -} - -void -mpz_neg (mpz_t r, const mpz_t u) -{ - mpz_set (r, u); - r->_mp_size = -r->_mp_size; -} - -void -mpz_swap (mpz_t u, mpz_t v) -{ - MP_SIZE_T_SWAP (u->_mp_size, v->_mp_size); - MP_SIZE_T_SWAP (u->_mp_alloc, v->_mp_alloc); - MP_PTR_SWAP (u->_mp_d, v->_mp_d); -} - - -/* MPZ addition and subtraction */ - - -void -mpz_add_ui (mpz_t r, const mpz_t a, unsigned long b) -{ - mpz_t bb; - mpz_init_set_ui (bb, b); - mpz_add (r, a, bb); - mpz_clear (bb); -} - -void -mpz_sub_ui (mpz_t r, const mpz_t a, unsigned long b) -{ - mpz_ui_sub (r, b, a); - mpz_neg (r, r); -} - -void -mpz_ui_sub (mpz_t r, unsigned long a, const mpz_t b) -{ - mpz_neg (r, b); - mpz_add_ui (r, r, a); -} - -static mp_size_t -mpz_abs_add (mpz_t r, const mpz_t a, const mpz_t b) -{ - mp_size_t an = GMP_ABS (a->_mp_size); - mp_size_t bn = GMP_ABS (b->_mp_size); - mp_ptr rp; - mp_limb_t cy; - - if (an < bn) - { - MPZ_SRCPTR_SWAP (a, b); - MP_SIZE_T_SWAP (an, bn); - } - - rp = MPZ_REALLOC (r, an + 1); - cy = mpn_add (rp, a->_mp_d, an, b->_mp_d, bn); - - rp[an] = cy; - - return an + cy; -} - -static mp_size_t -mpz_abs_sub (mpz_t r, const mpz_t a, const mpz_t b) -{ - mp_size_t an = GMP_ABS (a->_mp_size); - mp_size_t bn = GMP_ABS (b->_mp_size); - int cmp; - mp_ptr rp; - - cmp = mpn_cmp4 (a->_mp_d, an, b->_mp_d, bn); - if (cmp > 0) - { - rp = MPZ_REALLOC (r, an); - gmp_assert_nocarry (mpn_sub (rp, a->_mp_d, an, b->_mp_d, bn)); - return mpn_normalized_size (rp, an); - } - else if (cmp < 0) - { - rp = MPZ_REALLOC (r, bn); - gmp_assert_nocarry (mpn_sub (rp, b->_mp_d, bn, a->_mp_d, an)); - return -mpn_normalized_size (rp, bn); - } - else - return 0; -} - -void -mpz_add (mpz_t r, const mpz_t a, const mpz_t b) -{ - mp_size_t rn; - - if ( (a->_mp_size ^ b->_mp_size) >= 0) - rn = mpz_abs_add (r, a, b); - else - rn = mpz_abs_sub (r, a, b); - - r->_mp_size = a->_mp_size >= 0 ? rn : - rn; -} - -void -mpz_sub (mpz_t r, const mpz_t a, const mpz_t b) -{ - mp_size_t rn; - - if ( (a->_mp_size ^ b->_mp_size) >= 0) - rn = mpz_abs_sub (r, a, b); - else - rn = mpz_abs_add (r, a, b); - - r->_mp_size = a->_mp_size >= 0 ? rn : - rn; -} - - -/* MPZ multiplication */ -void -mpz_mul_si (mpz_t r, const mpz_t u, long int v) -{ - if (v < 0) - { - mpz_mul_ui (r, u, GMP_NEG_CAST (unsigned long int, v)); - mpz_neg (r, r); - } - else - mpz_mul_ui (r, u, v); -} - -void -mpz_mul_ui (mpz_t r, const mpz_t u, unsigned long int v) -{ - mpz_t vv; - mpz_init_set_ui (vv, v); - mpz_mul (r, u, vv); - mpz_clear (vv); - return; -} - -void -mpz_mul (mpz_t r, const mpz_t u, const mpz_t v) -{ - int sign; - mp_size_t un, vn, rn; - mpz_t t; - mp_ptr tp; - - un = u->_mp_size; - vn = v->_mp_size; - - if (un == 0 || vn == 0) - { - r->_mp_size = 0; - return; - } - - sign = (un ^ vn) < 0; - - un = GMP_ABS (un); - vn = GMP_ABS (vn); - - mpz_init2 (t, (un + vn) * GMP_LIMB_BITS); - - tp = t->_mp_d; - if (un >= vn) - mpn_mul (tp, u->_mp_d, un, v->_mp_d, vn); - else - mpn_mul (tp, v->_mp_d, vn, u->_mp_d, un); - - rn = un + vn; - rn -= tp[rn-1] == 0; - - t->_mp_size = sign ? - rn : rn; - mpz_swap (r, t); - mpz_clear (t); -} - -void -mpz_mul_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t bits) -{ - mp_size_t un, rn; - mp_size_t limbs; - unsigned shift; - mp_ptr rp; - - un = GMP_ABS (u->_mp_size); - if (un == 0) - { - r->_mp_size = 0; - return; - } - - limbs = bits / GMP_LIMB_BITS; - shift = bits % GMP_LIMB_BITS; - - rn = un + limbs + (shift > 0); - rp = MPZ_REALLOC (r, rn); - if (shift > 0) - { - mp_limb_t cy = mpn_lshift (rp + limbs, u->_mp_d, un, shift); - rp[rn-1] = cy; - rn -= (cy == 0); - } - else - mpn_copyd (rp + limbs, u->_mp_d, un); - - mpn_zero (rp, limbs); - - r->_mp_size = (u->_mp_size < 0) ? - rn : rn; -} - -void -mpz_addmul_ui (mpz_t r, const mpz_t u, unsigned long int v) -{ - mpz_t t; - mpz_init_set_ui (t, v); - mpz_mul (t, u, t); - mpz_add (r, r, t); - mpz_clear (t); -} - -void -mpz_submul_ui (mpz_t r, const mpz_t u, unsigned long int v) -{ - mpz_t t; - mpz_init_set_ui (t, v); - mpz_mul (t, u, t); - mpz_sub (r, r, t); - mpz_clear (t); -} - -void -mpz_addmul (mpz_t r, const mpz_t u, const mpz_t v) -{ - mpz_t t; - mpz_init (t); - mpz_mul (t, u, v); - mpz_add (r, r, t); - mpz_clear (t); -} - -void -mpz_submul (mpz_t r, const mpz_t u, const mpz_t v) -{ - mpz_t t; - mpz_init (t); - mpz_mul (t, u, v); - mpz_sub (r, r, t); - mpz_clear (t); -} - - -/* MPZ division */ -enum mpz_div_round_mode { GMP_DIV_FLOOR, GMP_DIV_CEIL, GMP_DIV_TRUNC }; - -/* Allows q or r to be zero. Returns 1 iff remainder is non-zero. */ -static int -mpz_div_qr (mpz_t q, mpz_t r, - const mpz_t n, const mpz_t d, enum mpz_div_round_mode mode) -{ - mp_size_t ns, ds, nn, dn, qs; - ns = n->_mp_size; - ds = d->_mp_size; - - if (ds == 0) - gmp_die("mpz_div_qr: Divide by zero."); - - if (ns == 0) - { - if (q) - q->_mp_size = 0; - if (r) - r->_mp_size = 0; - return 0; - } - - nn = GMP_ABS (ns); - dn = GMP_ABS (ds); - - qs = ds ^ ns; - - if (nn < dn) - { - if (mode == GMP_DIV_CEIL && qs >= 0) - { - /* q = 1, r = n - d */ - if (r) - mpz_sub (r, n, d); - if (q) - mpz_set_ui (q, 1); - } - else if (mode == GMP_DIV_FLOOR && qs < 0) - { - /* q = -1, r = n + d */ - if (r) - mpz_add (r, n, d); - if (q) - mpz_set_si (q, -1); - } - else - { - /* q = 0, r = d */ - if (r) - mpz_set (r, n); - if (q) - q->_mp_size = 0; - } - return 1; - } - else - { - mp_ptr np, qp; - mp_size_t qn, rn; - mpz_t tq, tr; - - mpz_init_set (tr, n); - np = tr->_mp_d; - - qn = nn - dn + 1; - - if (q) - { - mpz_init2 (tq, qn * GMP_LIMB_BITS); - qp = tq->_mp_d; - } - else - qp = NULL; - - mpn_div_qr (qp, np, nn, d->_mp_d, dn); - - if (qp) - { - qn -= (qp[qn-1] == 0); - - tq->_mp_size = qs < 0 ? -qn : qn; - } - rn = mpn_normalized_size (np, dn); - tr->_mp_size = ns < 0 ? - rn : rn; - - if (mode == GMP_DIV_FLOOR && qs < 0 && rn != 0) - { - if (q) - mpz_sub_ui (tq, tq, 1); - if (r) - mpz_add (tr, tr, d); - } - else if (mode == GMP_DIV_CEIL && qs >= 0 && rn != 0) - { - if (q) - mpz_add_ui (tq, tq, 1); - if (r) - mpz_sub (tr, tr, d); - } - - if (q) - { - mpz_swap (tq, q); - mpz_clear (tq); - } - if (r) - mpz_swap (tr, r); - - mpz_clear (tr); - - return rn != 0; - } -} - -void -mpz_cdiv_qr (mpz_t q, mpz_t r, const mpz_t n, const mpz_t d) -{ - mpz_div_qr (q, r, n, d, GMP_DIV_CEIL); -} - -void -mpz_fdiv_qr (mpz_t q, mpz_t r, const mpz_t n, const mpz_t d) -{ - mpz_div_qr (q, r, n, d, GMP_DIV_FLOOR); -} - -void -mpz_tdiv_qr (mpz_t q, mpz_t r, const mpz_t n, const mpz_t d) -{ - mpz_div_qr (q, r, n, d, GMP_DIV_TRUNC); -} - -void -mpz_cdiv_q (mpz_t q, const mpz_t n, const mpz_t d) -{ - mpz_div_qr (q, NULL, n, d, GMP_DIV_CEIL); -} - -void -mpz_fdiv_q (mpz_t q, const mpz_t n, const mpz_t d) -{ - mpz_div_qr (q, NULL, n, d, GMP_DIV_FLOOR); -} - -void -mpz_tdiv_q (mpz_t q, const mpz_t n, const mpz_t d) -{ - mpz_div_qr (q, NULL, n, d, GMP_DIV_TRUNC); -} - -void -mpz_cdiv_r (mpz_t r, const mpz_t n, const mpz_t d) -{ - mpz_div_qr (NULL, r, n, d, GMP_DIV_CEIL); -} - -void -mpz_fdiv_r (mpz_t r, const mpz_t n, const mpz_t d) -{ - mpz_div_qr (NULL, r, n, d, GMP_DIV_FLOOR); -} - -void -mpz_tdiv_r (mpz_t r, const mpz_t n, const mpz_t d) -{ - mpz_div_qr (NULL, r, n, d, GMP_DIV_TRUNC); -} - -void -mpz_mod (mpz_t r, const mpz_t n, const mpz_t d) -{ - mpz_div_qr (NULL, r, n, d, d->_mp_size >= 0 ? GMP_DIV_FLOOR : GMP_DIV_CEIL); -} - -static void -mpz_div_q_2exp (mpz_t q, const mpz_t u, mp_bitcnt_t bit_index, - enum mpz_div_round_mode mode) -{ - mp_size_t un, qn; - mp_size_t limb_cnt; - mp_ptr qp; - int adjust; - - un = u->_mp_size; - if (un == 0) - { - q->_mp_size = 0; - return; - } - limb_cnt = bit_index / GMP_LIMB_BITS; - qn = GMP_ABS (un) - limb_cnt; - bit_index %= GMP_LIMB_BITS; - - if (mode == ((un > 0) ? GMP_DIV_CEIL : GMP_DIV_FLOOR)) /* un != 0 here. */ - /* Note: Below, the final indexing at limb_cnt is valid because at - that point we have qn > 0. */ - adjust = (qn <= 0 - || !mpn_zero_p (u->_mp_d, limb_cnt) - || (u->_mp_d[limb_cnt] - & (((mp_limb_t) 1 << bit_index) - 1))); - else - adjust = 0; - - if (qn <= 0) - qn = 0; - else - { - qp = MPZ_REALLOC (q, qn); - - if (bit_index != 0) - { - mpn_rshift (qp, u->_mp_d + limb_cnt, qn, bit_index); - qn -= qp[qn - 1] == 0; - } - else - { - mpn_copyi (qp, u->_mp_d + limb_cnt, qn); - } - } - - q->_mp_size = qn; - - if (adjust) - mpz_add_ui (q, q, 1); - if (un < 0) - mpz_neg (q, q); -} - -static void -mpz_div_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t bit_index, - enum mpz_div_round_mode mode) -{ - mp_size_t us, un, rn; - mp_ptr rp; - mp_limb_t mask; - - us = u->_mp_size; - if (us == 0 || bit_index == 0) - { - r->_mp_size = 0; - return; - } - rn = (bit_index + GMP_LIMB_BITS - 1) / GMP_LIMB_BITS; - assert (rn > 0); - - rp = MPZ_REALLOC (r, rn); - un = GMP_ABS (us); - - mask = GMP_LIMB_MAX >> (rn * GMP_LIMB_BITS - bit_index); - - if (rn > un) - { - /* Quotient (with truncation) is zero, and remainder is - non-zero */ - if (mode == ((us > 0) ? GMP_DIV_CEIL : GMP_DIV_FLOOR)) /* us != 0 here. */ - { - /* Have to negate and sign extend. */ - mp_size_t i; - - gmp_assert_nocarry (! mpn_neg (rp, u->_mp_d, un)); - for (i = un; i < rn - 1; i++) - rp[i] = GMP_LIMB_MAX; - - rp[rn-1] = mask; - us = -us; - } - else - { - /* Just copy */ - if (r != u) - mpn_copyi (rp, u->_mp_d, un); - - rn = un; - } - } - else - { - if (r != u) - mpn_copyi (rp, u->_mp_d, rn - 1); - - rp[rn-1] = u->_mp_d[rn-1] & mask; - - if (mode == ((us > 0) ? GMP_DIV_CEIL : GMP_DIV_FLOOR)) /* us != 0 here. */ - { - /* If r != 0, compute 2^{bit_count} - r. */ - mpn_neg (rp, rp, rn); - - rp[rn-1] &= mask; - - /* us is not used for anything else, so we can modify it - here to indicate flipped sign. */ - us = -us; - } - } - rn = mpn_normalized_size (rp, rn); - r->_mp_size = us < 0 ? -rn : rn; -} - -void -mpz_cdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt) -{ - mpz_div_q_2exp (r, u, cnt, GMP_DIV_CEIL); -} - -void -mpz_fdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt) -{ - mpz_div_q_2exp (r, u, cnt, GMP_DIV_FLOOR); -} - -void -mpz_tdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt) -{ - mpz_div_q_2exp (r, u, cnt, GMP_DIV_TRUNC); -} - -void -mpz_cdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt) -{ - mpz_div_r_2exp (r, u, cnt, GMP_DIV_CEIL); -} - -void -mpz_fdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt) -{ - mpz_div_r_2exp (r, u, cnt, GMP_DIV_FLOOR); -} - -void -mpz_tdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt) -{ - mpz_div_r_2exp (r, u, cnt, GMP_DIV_TRUNC); -} - -void -mpz_divexact (mpz_t q, const mpz_t n, const mpz_t d) -{ - gmp_assert_nocarry (mpz_div_qr (q, NULL, n, d, GMP_DIV_TRUNC)); -} - -int -mpz_divisible_p (const mpz_t n, const mpz_t d) -{ - return mpz_div_qr (NULL, NULL, n, d, GMP_DIV_TRUNC) == 0; -} - -int -mpz_congruent_p (const mpz_t a, const mpz_t b, const mpz_t m) -{ - mpz_t t; - int res; - - /* a == b (mod 0) iff a == b */ - if (mpz_sgn (m) == 0) - return (mpz_cmp (a, b) == 0); - - mpz_init (t); - mpz_sub (t, a, b); - res = mpz_divisible_p (t, m); - mpz_clear (t); - - return res; -} - -static unsigned long -mpz_div_qr_ui (mpz_t q, mpz_t r, - const mpz_t n, unsigned long d, enum mpz_div_round_mode mode) -{ - unsigned long ret; - mpz_t rr, dd; - - mpz_init (rr); - mpz_init_set_ui (dd, d); - mpz_div_qr (q, rr, n, dd, mode); - mpz_clear (dd); - ret = mpz_get_ui (rr); - - if (r) - mpz_swap (r, rr); - mpz_clear (rr); - - return ret; -} - -unsigned long -mpz_cdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (q, r, n, d, GMP_DIV_CEIL); -} - -unsigned long -mpz_fdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (q, r, n, d, GMP_DIV_FLOOR); -} - -unsigned long -mpz_tdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (q, r, n, d, GMP_DIV_TRUNC); -} - -unsigned long -mpz_cdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_CEIL); -} - -unsigned long -mpz_fdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_FLOOR); -} - -unsigned long -mpz_tdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_TRUNC); -} - -unsigned long -mpz_cdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_CEIL); -} -unsigned long -mpz_fdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_FLOOR); -} -unsigned long -mpz_tdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_TRUNC); -} - -unsigned long -mpz_cdiv_ui (const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_CEIL); -} - -unsigned long -mpz_fdiv_ui (const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_FLOOR); -} - -unsigned long -mpz_tdiv_ui (const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_TRUNC); -} - -unsigned long -mpz_mod_ui (mpz_t r, const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_FLOOR); -} - -void -mpz_divexact_ui (mpz_t q, const mpz_t n, unsigned long d) -{ - gmp_assert_nocarry (mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_TRUNC)); -} - -int -mpz_divisible_ui_p (const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_TRUNC) == 0; -} - - -/* GCD */ -static mp_limb_t -mpn_gcd_11 (mp_limb_t u, mp_limb_t v) -{ - unsigned shift; - - assert ( (u | v) > 0); - - if (u == 0) - return v; - else if (v == 0) - return u; - - gmp_ctz (shift, u | v); - - u >>= shift; - v >>= shift; - - if ( (u & 1) == 0) - MP_LIMB_T_SWAP (u, v); - - while ( (v & 1) == 0) - v >>= 1; - - while (u != v) - { - if (u > v) - { - u -= v; - do - u >>= 1; - while ( (u & 1) == 0); - } - else - { - v -= u; - do - v >>= 1; - while ( (v & 1) == 0); - } - } - return u << shift; -} - -unsigned long -mpz_gcd_ui (mpz_t g, const mpz_t u, unsigned long v) -{ - mpz_t t; - mpz_init_set_ui(t, v); - mpz_gcd (t, u, t); - if (v > 0) - v = mpz_get_ui (t); - - if (g) - mpz_swap (t, g); - - mpz_clear (t); - - return v; -} - -static mp_bitcnt_t -mpz_make_odd (mpz_t r) -{ - mp_bitcnt_t shift; - - assert (r->_mp_size > 0); - /* Count trailing zeros, equivalent to mpn_scan1, because we know that there is a 1 */ - shift = mpn_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 */ - signed long sign = mpz_sgn (v); - mpz_abs (g, v); - if (s) - s->_mp_size = 0; - if (t) - mpz_set_si (t, sign); - return; - } - - if (v->_mp_size == 0) - { - /* g = sgn(u) u + 0 v */ - signed long sign = mpz_sgn (u); - mpz_abs (g, u); - if (s) - mpz_set_si (s, sign); - if (t) - t->_mp_size = 0; - return; - } - - mpz_init (tu); - mpz_init (tv); - mpz_init (s0); - mpz_init (s1); - mpz_init (t0); - mpz_init (t1); - - mpz_abs (tu, u); - uz = mpz_make_odd (tu); - mpz_abs (tv, v); - vz = mpz_make_odd (tv); - gz = GMP_MIN (uz, vz); - - uz -= gz; - vz -= gz; - - /* Cofactors corresponding to odd gcd. gz handled later. */ - if (tu->_mp_size < tv->_mp_size) - { - mpz_swap (tu, tv); - MPZ_SRCPTR_SWAP (u, v); - MPZ_PTR_SWAP (s, t); - MP_BITCNT_T_SWAP (uz, vz); - } - - /* Maintain - * - * u = t0 tu + t1 tv - * v = s0 tu + s1 tv - * - * where u and v denote the inputs with common factors of two - * eliminated, and det (s0, t0; s1, t1) = 2^p. Then - * - * 2^p tu = s1 u - t1 v - * 2^p tv = -s0 u + t0 v - */ - - /* After initial division, tu = q tv + tu', we have - * - * u = 2^uz (tu' + q tv) - * v = 2^vz tv - * - * or - * - * t0 = 2^uz, t1 = 2^uz q - * s0 = 0, s1 = 2^vz - */ - - mpz_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); - } - assert (mpz_even_p (t0) && mpz_even_p (s0)); - mpz_tdiv_q_2exp (s0, s0, 1); - mpz_tdiv_q_2exp (t0, t0, 1); - } - - /* Arrange so that |s| < |u| / 2g */ - mpz_add (s1, s0, s1); - if (mpz_cmpabs (s0, s1) > 0) - { - mpz_swap (s0, s1); - mpz_sub (t0, t0, t1); - } - if (u->_mp_size < 0) - mpz_neg (s0, s0); - if (v->_mp_size < 0) - mpz_neg (t0, t0); - - mpz_swap (g, tv); - if (s) - mpz_swap (s, s0); - if (t) - mpz_swap (t, t0); - - mpz_clear (tu); - mpz_clear (tv); - mpz_clear (s0); - mpz_clear (s1); - mpz_clear (t0); - mpz_clear (t1); -} - -void -mpz_lcm (mpz_t r, const mpz_t u, const mpz_t v) -{ - mpz_t g; - - if (u->_mp_size == 0 || v->_mp_size == 0) - { - r->_mp_size = 0; - return; - } - - mpz_init (g); - - mpz_gcd (g, u, v); - mpz_divexact (g, u, g); - mpz_mul (r, g, v); - - mpz_clear (g); - mpz_abs (r, r); -} - -void -mpz_lcm_ui (mpz_t r, const mpz_t u, unsigned long v) -{ - if (v == 0 || u->_mp_size == 0) - { - r->_mp_size = 0; - return; - } - - v /= mpz_gcd_ui (NULL, u, v); - mpz_mul_ui (r, u, v); - - mpz_abs (r, r); -} - -int -mpz_invert (mpz_t r, const mpz_t u, const mpz_t m) -{ - mpz_t g, tr; - int invertible; - - if (u->_mp_size == 0 || mpz_cmpabs_ui (m, 1) <= 0) - return 0; - - mpz_init (g); - mpz_init (tr); - - mpz_gcdext (g, tr, NULL, u, m); - invertible = (mpz_cmp_ui (g, 1) == 0); - - if (invertible) - { - if (tr->_mp_size < 0) - { - if (m->_mp_size >= 0) - mpz_add (tr, tr, m); - else - mpz_sub (tr, tr, m); - } - mpz_swap (r, tr); - } - - mpz_clear (g); - mpz_clear (tr); - return invertible; -} - - -/* Higher level operations (sqrt, pow and root) */ - -void -mpz_pow_ui (mpz_t r, const mpz_t b, unsigned long e) -{ - unsigned long bit; - mpz_t tr; - mpz_init_set_ui (tr, 1); - - bit = GMP_ULONG_HIGHBIT; - do - { - mpz_mul (tr, tr, tr); - if (e & bit) - mpz_mul (tr, tr, b); - bit >>= 1; - } - while (bit > 0); - - mpz_swap (r, tr); - mpz_clear (tr); -} - -void -mpz_ui_pow_ui (mpz_t r, unsigned long blimb, unsigned long e) -{ - mpz_t b; - - mpz_init_set_ui (b, blimb); - mpz_pow_ui (r, b, e); - mpz_clear (b); -} - -void -mpz_powm (mpz_t r, const mpz_t b, const mpz_t e, const mpz_t m) -{ - mpz_t tr; - mpz_t base; - mp_size_t en, mn; - mp_srcptr mp; - struct gmp_div_inverse minv; - unsigned shift; - mp_ptr tp = NULL; - - en = GMP_ABS (e->_mp_size); - mn = GMP_ABS (m->_mp_size); - if (mn == 0) - gmp_die ("mpz_powm: Zero modulo."); - - if (en == 0) - { - mpz_set_ui (r, 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, unsigned long elimb, const mpz_t m) -{ - mpz_t e; - - mpz_init_set_ui (e, elimb); - mpz_powm (r, b, e, m); - mpz_clear (e); -} - -/* x=trunc(y^(1/z)), r=y-x^z */ -void -mpz_rootrem (mpz_t x, mpz_t r, const mpz_t y, unsigned long z) -{ - int sgn; - mpz_t t, u; - - sgn = y->_mp_size < 0; - if ((~z & sgn) != 0) - gmp_die ("mpz_rootrem: Negative argument, with even root."); - if (z == 0) - gmp_die ("mpz_rootrem: Zeroth root."); - - if (mpz_cmpabs_ui (y, 1) <= 0) { - if (x) - mpz_set (x, y); - if (r) - r->_mp_size = 0; - return; - } - - mpz_init (u); - mpz_init (t); - mpz_setbit (t, mpz_sizeinbase (y, 2) / z + 1); - - if (z == 2) /* simplify sqrt loop: z-1 == 1 */ - do { - mpz_swap (u, t); /* u = x */ - mpz_tdiv_q (t, y, u); /* t = y/x */ - mpz_add (t, t, u); /* t = y/x + x */ - mpz_tdiv_q_2exp (t, t, 1); /* x'= (y/x + x)/2 */ - } while (mpz_cmpabs (t, u) < 0); /* |x'| < |x| */ - else /* z != 2 */ { - mpz_t v; - - mpz_init (v); - if (sgn) - mpz_neg (t, t); - - do { - mpz_swap (u, t); /* u = x */ - mpz_pow_ui (t, u, z - 1); /* t = x^(z-1) */ - mpz_tdiv_q (t, y, t); /* t = y/x^(z-1) */ - mpz_mul_ui (v, u, z - 1); /* v = x*(z-1) */ - mpz_add (t, t, v); /* t = y/x^(z-1) + x*(z-1) */ - mpz_tdiv_q_ui (t, t, z); /* x'=(y/x^(z-1) + x*(z-1))/z */ - } while (mpz_cmpabs (t, u) < 0); /* |x'| < |x| */ - - mpz_clear (v); - } - - if (r) { - mpz_pow_ui (t, u, z); - mpz_sub (r, y, t); - } - if (x) - mpz_swap (x, u); - mpz_clear (u); - mpz_clear (t); -} - -int -mpz_root (mpz_t x, const mpz_t y, unsigned long z) -{ - int res; - mpz_t r; - - mpz_init (r); - mpz_rootrem (x, r, y, z); - res = r->_mp_size == 0; - mpz_clear (r); - - return res; -} - -/* Compute s = floor(sqrt(u)) and r = u - s^2. Allows r == NULL */ -void -mpz_sqrtrem (mpz_t s, mpz_t r, const mpz_t u) -{ - mpz_rootrem (s, r, u, 2); -} - -void -mpz_sqrt (mpz_t s, const mpz_t u) -{ - mpz_rootrem (s, NULL, u, 2); -} - -int -mpz_perfect_square_p (const mpz_t u) -{ - if (u->_mp_size <= 0) - return (u->_mp_size == 0); - else - return mpz_root (NULL, u, 2); -} - -int -mpn_perfect_square_p (mp_srcptr p, mp_size_t n) -{ - mpz_t t; - - assert (n > 0); - assert (p [n-1] != 0); - return mpz_root (NULL, mpz_roinit_normal_n (t, p, n), 2); -} - -mp_size_t -mpn_sqrtrem (mp_ptr sp, mp_ptr rp, mp_srcptr p, mp_size_t n) -{ - mpz_t s, r, u; - mp_size_t res; - - assert (n > 0); - assert (p [n-1] != 0); - - mpz_init (r); - mpz_init (s); - mpz_rootrem (s, r, mpz_roinit_normal_n (u, p, n), 2); - - assert (s->_mp_size == (n+1)/2); - mpn_copyd (sp, s->_mp_d, s->_mp_size); - mpz_clear (s); - res = r->_mp_size; - if (rp) - mpn_copyd (rp, r->_mp_d, res); - mpz_clear (r); - return res; -} - -/* Combinatorics */ - -void -mpz_mfac_uiui (mpz_t x, unsigned long n, unsigned long m) -{ - mpz_set_ui (x, n + (n == 0)); - if (m + 1 < 2) return; - while (n > m + 1) - mpz_mul_ui (x, x, n -= m); -} - -void -mpz_2fac_ui (mpz_t x, unsigned long n) -{ - mpz_mfac_uiui (x, n, 2); -} - -void -mpz_fac_ui (mpz_t x, unsigned long n) -{ - mpz_mfac_uiui (x, n, 1); -} - -void -mpz_bin_uiui (mpz_t r, unsigned long n, unsigned long k) -{ - mpz_t t; - - mpz_set_ui (r, k <= n); - - if (k > (n >> 1)) - k = (k <= n) ? n - k : 0; - - mpz_init (t); - mpz_fac_ui (t, k); - - for (; k > 0; --k) - mpz_mul_ui (r, r, n--); - - mpz_divexact (r, r, t); - mpz_clear (t); -} - - -/* Primality testing */ - -/* Computes Kronecker (a/b) with odd b, a!=0 and GCD(a,b) = 1 */ -/* Adapted from JACOBI_BASE_METHOD==4 in mpn/generic/jacbase.c */ -static int -gmp_jacobi_coprime (mp_limb_t a, mp_limb_t b) -{ - int c, bit = 0; - - assert (b & 1); - assert (a != 0); - /* assert (mpn_gcd_11 (a, b) == 1); */ - - /* Below, we represent a and b shifted right so that the least - significant one bit is implicit. */ - b >>= 1; - - gmp_ctz(c, a); - a >>= 1; - - do - { - a >>= c; - /* (2/b) = -1 if b = 3 or 5 mod 8 */ - bit ^= c & (b ^ (b >> 1)); - if (a < b) - { - bit ^= a & b; - a = b - a; - b -= a; - } - else - { - a -= b; - assert (a != 0); - } - - gmp_ctz(c, a); - ++c; - } - while (b > 0); - - return bit & 1 ? -1 : 1; -} - -static void -gmp_lucas_step_k_2k (mpz_t V, mpz_t Qk, const mpz_t n) -{ - mpz_mod (Qk, Qk, n); - /* V_{2k} <- V_k ^ 2 - 2Q^k */ - mpz_mul (V, V, V); - mpz_submul_ui (V, Qk, 2); - mpz_tdiv_r (V, V, n); - /* Q^{2k} = (Q^k)^2 */ - mpz_mul (Qk, Qk, Qk); -} - -/* Computes V_k, Q^k (mod n) for the Lucas' sequence */ -/* with P=1, Q=Q; k = (n>>b0)|1. */ -/* Requires an odd n > 4; b0 > 0; -2*Q must not overflow a long */ -/* Returns (U_k == 0) and sets V=V_k and Qk=Q^k. */ -static int -gmp_lucas_mod (mpz_t V, mpz_t Qk, long Q, - mp_bitcnt_t b0, const mpz_t n) -{ - mp_bitcnt_t bs; - mpz_t U; - int res; - - assert (b0 > 0); - assert (Q <= - (LONG_MIN / 2)); - assert (Q >= - (LONG_MAX / 2)); - assert (mpz_cmp_ui (n, 4) > 0); - assert (mpz_odd_p (n)); - - mpz_init_set_ui (U, 1); /* U1 = 1 */ - mpz_set_ui (V, 1); /* V1 = 1 */ - mpz_set_si (Qk, Q); - - for (bs = mpz_sizeinbase (n, 2) - 1; --bs >= b0;) - { - /* U_{2k} <- U_k * V_k */ - mpz_mul (U, U, V); - /* V_{2k} <- V_k ^ 2 - 2Q^k */ - /* Q^{2k} = (Q^k)^2 */ - gmp_lucas_step_k_2k (V, Qk, n); - - /* A step k->k+1 is performed if the bit in $n$ is 1 */ - /* mpz_tstbit(n,bs) or the bit is 0 in $n$ but */ - /* should be 1 in $n+1$ (bs == b0) */ - if (b0 == bs || mpz_tstbit (n, bs)) - { - /* Q^{k+1} <- Q^k * Q */ - mpz_mul_si (Qk, Qk, Q); - /* U_{k+1} <- (U_k + V_k) / 2 */ - mpz_swap (U, V); /* Keep in V the old value of U_k */ - mpz_add (U, U, V); - /* We have to compute U/2, so we need an even value, */ - /* equivalent (mod n) */ - if (mpz_odd_p (U)) - mpz_add (U, U, n); - mpz_tdiv_q_2exp (U, U, 1); - /* V_{k+1} <-(D*U_k + V_k) / 2 = - U_{k+1} + (D-1)/2*U_k = U_{k+1} - 2Q*U_k */ - mpz_mul_si (V, V, -2*Q); - mpz_add (V, U, V); - mpz_tdiv_r (V, V, n); - } - mpz_tdiv_r (U, U, n); - } - - res = U->_mp_size == 0; - mpz_clear (U); - return res; -} - -/* Performs strong Lucas' test on x, with parameters suggested */ -/* for the BPSW test. Qk is only passed to recycle a variable. */ -/* Requires GCD (x,6) = 1.*/ -static int -gmp_stronglucas (const mpz_t x, mpz_t Qk) -{ - mp_bitcnt_t b0; - mpz_t V, n; - mp_limb_t maxD, D; /* The absolute value is stored. */ - long Q; - mp_limb_t tl; - - /* Test on the absolute value. */ - mpz_roinit_normal_n (n, x->_mp_d, GMP_ABS (x->_mp_size)); - - assert (mpz_odd_p (n)); - /* assert (mpz_gcd_ui (NULL, n, 6) == 1); */ - if (mpz_root (Qk, n, 2)) - return 0; /* A square is composite. */ - - /* Check Ds up to square root (in case, n is prime) - or avoid overflows */ - maxD = (Qk->_mp_size == 1) ? Qk->_mp_d [0] - 1 : GMP_LIMB_MAX; - - D = 3; - /* Search a D such that (D/n) = -1 in the sequence 5,-7,9,-11,.. */ - /* For those Ds we have (D/n) = (n/|D|) */ - do - { - if (D >= maxD) - return 1 + (D != GMP_LIMB_MAX); /* (1 + ! ~ D) */ - D += 2; - tl = mpz_tdiv_ui (n, D); - if (tl == 0) - return 0; - } - while (gmp_jacobi_coprime (tl, D) == 1); - - mpz_init (V); - - /* n-(D/n) = n+1 = d*2^{b0}, with d = (n>>b0) | 1 */ - b0 = mpz_scan0 (n, 0); - - /* D= P^2 - 4Q; P = 1; Q = (1-D)/4 */ - Q = (D & 2) ? (long) (D >> 2) + 1 : -(long) (D >> 2); - - if (! gmp_lucas_mod (V, Qk, Q, b0, n)) /* If Ud != 0 */ - while (V->_mp_size != 0 && --b0 != 0) /* while Vk != 0 */ - /* V <- V ^ 2 - 2Q^k */ - /* Q^{2k} = (Q^k)^2 */ - gmp_lucas_step_k_2k (V, Qk, n); - - mpz_clear (V); - return (b0 != 0); -} - -static int -gmp_millerrabin (const mpz_t n, const mpz_t nm1, mpz_t y, - const mpz_t q, mp_bitcnt_t k) -{ - assert (k > 0); - - /* Caller must initialize y to the base. */ - mpz_powm (y, y, q, n); - - if (mpz_cmp_ui (y, 1) == 0 || mpz_cmp (y, nm1) == 0) - return 1; - - while (--k > 0) - { - mpz_powm_ui (y, y, 2, n); - if (mpz_cmp (y, nm1) == 0) - return 1; - /* 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; - - mpz_init (nm1); - mpz_init (q); - - /* Find q and k, where q is odd and n = 1 + 2**k * q. */ - mpz_abs (nm1, n); - nm1->_mp_d[0] -= 1; - k = mpz_scan1 (nm1, 0); - mpz_tdiv_q_2exp (q, nm1, k); - - /* BPSW test */ - mpz_init_set_ui (y, 2); - is_prime = gmp_millerrabin (n, nm1, y, q, k) && gmp_stronglucas (n, y); - reps -= 24; /* skip the first 24 repetitions */ - - /* Use Miller-Rabin, with a deterministic sequence of bases, a[j] = - j^2 + j + 41 using Euler's polynomial. We potentially stop early, - if a[j] >= n - 1. Since n >= 31*31, this can happen only if reps > - 30 (a[30] == 971 > 31*31 == 961). */ - - for (j = 0; is_prime & (j < reps); j++) - { - mpz_set_ui (y, (unsigned long) j*j+j+41); - if (mpz_cmp (y, nm1) >= 0) - { - /* Don't try any further bases. This "early" break does not affect - the result for any reasonable reps value (<=5000 was tested) */ - assert (j >= 30); - break; - } - is_prime = gmp_millerrabin (n, nm1, y, q, k); - } - mpz_clear (nm1); - mpz_clear (q); - mpz_clear (y); - - return is_prime; -} - - -/* Logical operations and bit manipulation. */ - -/* Numbers are treated as if represented in two's complement (and - infinitely sign extended). For a negative values we get the two's - complement from -x = ~x + 1, where ~ is bitwise complement. - Negation transforms - - xxxx10...0 - - into - - yyyy10...0 - - where yyyy is the bitwise complement of xxxx. So least significant - bits, up to and including the first one bit, are unchanged, and - the more significant bits are all complemented. - - To change a bit from zero to one in a negative number, subtract the - corresponding power of two from the absolute value. This can never - underflow. To change a bit from one to zero, add the corresponding - power of two, and this might overflow. E.g., if x = -001111, the - two's complement is 110001. Clearing the least significant bit, we - get two's complement 110000, and -010000. */ - -int -mpz_tstbit (const mpz_t d, mp_bitcnt_t bit_index) -{ - mp_size_t limb_index; - unsigned shift; - mp_size_t ds; - mp_size_t dn; - mp_limb_t w; - int bit; - - ds = d->_mp_size; - dn = GMP_ABS (ds); - limb_index = bit_index / GMP_LIMB_BITS; - if (limb_index >= dn) - return ds < 0; - - shift = bit_index % GMP_LIMB_BITS; - w = d->_mp_d[limb_index]; - bit = (w >> shift) & 1; - - if (ds < 0) - { - /* d < 0. Check if any of the bits below is set: If so, our bit - must be complemented. */ - if (shift > 0 && (mp_limb_t) (w << (GMP_LIMB_BITS - shift)) > 0) - return bit ^ 1; - while (--limb_index >= 0) - if (d->_mp_d[limb_index] > 0) - return bit ^ 1; - } - return bit; -} - -static void -mpz_abs_add_bit (mpz_t d, mp_bitcnt_t bit_index) -{ - mp_size_t dn, limb_index; - mp_limb_t bit; - mp_ptr dp; - - dn = GMP_ABS (d->_mp_size); - - limb_index = bit_index / GMP_LIMB_BITS; - bit = (mp_limb_t) 1 << (bit_index % GMP_LIMB_BITS); - - if (limb_index >= dn) - { - mp_size_t i; - /* The bit should be set outside of the end of the number. - We have to increase the size of the number. */ - dp = MPZ_REALLOC (d, limb_index + 1); - - dp[limb_index] = bit; - for (i = dn; i < limb_index; i++) - dp[i] = 0; - dn = limb_index + 1; - } - else - { - mp_limb_t cy; - - dp = d->_mp_d; - - cy = mpn_add_1 (dp + limb_index, dp + limb_index, dn - limb_index, bit); - if (cy > 0) - { - dp = MPZ_REALLOC (d, dn + 1); - dp[dn++] = cy; - } - } - - d->_mp_size = (d->_mp_size < 0) ? - dn : dn; -} - -static void -mpz_abs_sub_bit (mpz_t d, mp_bitcnt_t bit_index) -{ - mp_size_t dn, limb_index; - mp_ptr dp; - mp_limb_t bit; - - dn = GMP_ABS (d->_mp_size); - dp = d->_mp_d; - - limb_index = bit_index / GMP_LIMB_BITS; - bit = (mp_limb_t) 1 << (bit_index % GMP_LIMB_BITS); - - assert (limb_index < dn); - - gmp_assert_nocarry (mpn_sub_1 (dp + limb_index, dp + limb_index, - dn - limb_index, bit)); - dn = mpn_normalized_size (dp, dn); - d->_mp_size = (d->_mp_size < 0) ? - dn : dn; -} - -void -mpz_setbit (mpz_t d, mp_bitcnt_t bit_index) -{ - if (!mpz_tstbit (d, bit_index)) - { - if (d->_mp_size >= 0) - mpz_abs_add_bit (d, bit_index); - else - mpz_abs_sub_bit (d, bit_index); - } -} - -void -mpz_clrbit (mpz_t d, mp_bitcnt_t bit_index) -{ - if (mpz_tstbit (d, bit_index)) - { - if (d->_mp_size >= 0) - mpz_abs_sub_bit (d, bit_index); - else - mpz_abs_add_bit (d, bit_index); - } -} - -void -mpz_combit (mpz_t d, mp_bitcnt_t bit_index) -{ - if (mpz_tstbit (d, bit_index) ^ (d->_mp_size < 0)) - mpz_abs_sub_bit (d, bit_index); - else - mpz_abs_add_bit (d, bit_index); -} - -void -mpz_com (mpz_t r, const mpz_t u) -{ - mpz_add_ui (r, u, 1); - mpz_neg (r, r); -} - -void -mpz_and (mpz_t r, const mpz_t u, const mpz_t v) -{ - mp_size_t un, vn, rn, i; - mp_ptr up, vp, rp; - - mp_limb_t ux, vx, rx; - mp_limb_t uc, vc, rc; - mp_limb_t ul, vl, rl; - - un = GMP_ABS (u->_mp_size); - vn = GMP_ABS (v->_mp_size); - if (un < vn) - { - MPZ_SRCPTR_SWAP (u, v); - MP_SIZE_T_SWAP (un, vn); - } - if (vn == 0) - { - r->_mp_size = 0; - return; - } - - uc = u->_mp_size < 0; - vc = v->_mp_size < 0; - rc = uc & vc; - - ux = -uc; - vx = -vc; - rx = -rc; - - /* If the smaller input is positive, higher limbs don't matter. */ - rn = vx ? un : vn; - - rp = MPZ_REALLOC (r, rn + (mp_size_t) rc); - - up = u->_mp_d; - vp = v->_mp_d; - - i = 0; - do - { - ul = (up[i] ^ ux) + uc; - uc = ul < uc; - - vl = (vp[i] ^ vx) + vc; - vc = vl < vc; - - rl = ( (ul & vl) ^ rx) + rc; - rc = rl < rc; - rp[i] = rl; - } - while (++i < vn); - assert (vc == 0); - - for (; i < rn; i++) - { - ul = (up[i] ^ ux) + uc; - uc = ul < uc; - - rl = ( (ul & vx) ^ rx) + rc; - rc = rl < rc; - rp[i] = rl; - } - if (rc) - rp[rn++] = rc; - else - rn = mpn_normalized_size (rp, rn); - - r->_mp_size = rx ? -rn : rn; -} - -void -mpz_ior (mpz_t r, const mpz_t u, const mpz_t v) -{ - mp_size_t un, vn, rn, i; - mp_ptr up, vp, rp; - - mp_limb_t ux, vx, rx; - mp_limb_t uc, vc, rc; - mp_limb_t ul, vl, rl; - - un = GMP_ABS (u->_mp_size); - vn = GMP_ABS (v->_mp_size); - if (un < vn) - { - MPZ_SRCPTR_SWAP (u, v); - MP_SIZE_T_SWAP (un, vn); - } - if (vn == 0) - { - mpz_set (r, u); - return; - } - - uc = u->_mp_size < 0; - vc = v->_mp_size < 0; - rc = uc | vc; - - ux = -uc; - vx = -vc; - rx = -rc; - - /* If the smaller input is negative, by sign extension higher limbs - don't matter. */ - rn = vx ? vn : un; - - rp = MPZ_REALLOC (r, rn + (mp_size_t) rc); - - up = u->_mp_d; - vp = v->_mp_d; - - i = 0; - do - { - ul = (up[i] ^ ux) + uc; - uc = ul < uc; - - vl = (vp[i] ^ vx) + vc; - vc = vl < vc; - - rl = ( (ul | vl) ^ rx) + rc; - rc = rl < rc; - rp[i] = rl; - } - while (++i < vn); - assert (vc == 0); - - for (; i < rn; i++) - { - ul = (up[i] ^ ux) + uc; - uc = ul < uc; - - rl = ( (ul | vx) ^ rx) + rc; - rc = rl < rc; - rp[i] = rl; - } - if (rc) - rp[rn++] = rc; - else - rn = mpn_normalized_size (rp, rn); - - r->_mp_size = rx ? -rn : rn; -} - -void -mpz_xor (mpz_t r, const mpz_t u, const mpz_t v) -{ - mp_size_t un, vn, i; - mp_ptr up, vp, rp; - - mp_limb_t ux, vx, rx; - mp_limb_t uc, vc, rc; - mp_limb_t ul, vl, rl; - - un = GMP_ABS (u->_mp_size); - vn = GMP_ABS (v->_mp_size); - if (un < vn) - { - MPZ_SRCPTR_SWAP (u, v); - MP_SIZE_T_SWAP (un, vn); - } - if (vn == 0) - { - mpz_set (r, u); - return; - } - - uc = u->_mp_size < 0; - vc = v->_mp_size < 0; - rc = uc ^ vc; - - ux = -uc; - vx = -vc; - rx = -rc; - - rp = MPZ_REALLOC (r, un + (mp_size_t) rc); - - up = u->_mp_d; - vp = v->_mp_d; - - i = 0; - do - { - ul = (up[i] ^ ux) + uc; - uc = ul < uc; - - vl = (vp[i] ^ vx) + vc; - vc = vl < vc; - - rl = (ul ^ vl ^ rx) + rc; - rc = rl < rc; - rp[i] = rl; - } - while (++i < vn); - assert (vc == 0); - - for (; i < un; i++) - { - ul = (up[i] ^ ux) + uc; - uc = ul < uc; - - rl = (ul ^ ux) + rc; - rc = rl < rc; - rp[i] = rl; - } - if (rc) - rp[un++] = rc; - else - un = mpn_normalized_size (rp, un); - - r->_mp_size = rx ? -un : un; -} - -static unsigned -gmp_popcount_limb (mp_limb_t x) -{ - unsigned c; - - /* Do 16 bits at a time, to avoid limb-sized constants. */ - for (c = 0; x > 0; x >>= 16) - { - unsigned w = x - ((x >> 1) & 0x5555); - w = ((w >> 2) & 0x3333) + (w & 0x3333); - w = (w >> 4) + w; - w = ((w >> 8) & 0x000f) + (w & 0x000f); - 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 <= 62); - - un = GMP_ABS (u->_mp_size); - if (un == 0) - return 1; - - up = u->_mp_d; - - bits = (un - 1) * GMP_LIMB_BITS + mpn_limb_size_in_base_2 (up[un-1]); - switch (base) - { - case 2: - return bits; - case 4: - return (bits + 1) / 2; - case 8: - return (bits + 2) / 3; - case 16: - return (bits + 3) / 4; - case 32: - return (bits + 4) / 5; - /* FIXME: Do something more clever for the common case of base - 10. */ - } - - tp = gmp_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) -{ - unsigned bits; - const char *digits; - mp_size_t un; - size_t i, sn; - - digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"; - if (base > 1) - { - if (base <= 36) - digits = "0123456789abcdefghijklmnopqrstuvwxyz"; - else if (base > 62) - return NULL; - } - else if (base >= -1) - base = 10; - else - { - base = -base; - if (base > 36) - return NULL; - } - - sn = 1 + mpz_sizeinbase (u, base); - if (!sp) - 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 ((unsigned char *) sp + i, bits, u->_mp_d, un); - else - { - struct mpn_base_info info; - mp_ptr tp; - - mpn_get_base_info (&info, base); - tp = gmp_xalloc_limbs (un); - mpn_copyi (tp, u->_mp_d, un); - - sn = i + mpn_get_str_other ((unsigned char *) sp + i, base, &info, tp, un); - gmp_free (tp); - } - - for (; i < sn; i++) - sp[i] = digits[(unsigned char) sp[i]]; - - sp[sn] = '\0'; - return sp; -} - -int -mpz_set_str (mpz_t r, const char *sp, int base) -{ - unsigned bits, value_of_a; - mp_size_t rn, alloc; - mp_ptr rp; - size_t dn; - int sign; - unsigned char *dp; - - assert (base == 0 || (base >= 2 && base <= 62)); - - while (isspace( (unsigned char) *sp)) - sp++; - - sign = (*sp == '-'); - sp += sign; - - if (base == 0) - { - if (sp[0] == '0') - { - if (sp[1] == 'x' || sp[1] == 'X') - { - base = 16; - sp += 2; - } - else if (sp[1] == 'b' || sp[1] == 'B') - { - base = 2; - sp += 2; - } - else - base = 8; - } - else - base = 10; - } - - if (!*sp) - { - r->_mp_size = 0; - return -1; - } - dp = (unsigned char *) gmp_xalloc (strlen (sp)); - - value_of_a = (base > 36) ? 36 : 10; - for (dn = 0; *sp; sp++) - { - unsigned digit; - - if (isspace ((unsigned char) *sp)) - continue; - else if (*sp >= '0' && *sp <= '9') - digit = *sp - '0'; - else if (*sp >= 'a' && *sp <= 'z') - digit = *sp - 'a' + value_of_a; - else if (*sp >= 'A' && *sp <= 'Z') - digit = *sp - 'A' + 10; - else - digit = base; /* fail */ - - if (digit >= (unsigned) base) - { - gmp_free (dp); - r->_mp_size = 0; - return -1; - } - - dp[dn++] = digit; - } - - if (!dn) - { - gmp_free (dp); - r->_mp_size = 0; - return -1; - } - bits = mpn_base_power_of_two_p (base); - - if (bits > 0) - { - alloc = (dn * bits + GMP_LIMB_BITS - 1) / GMP_LIMB_BITS; - rp = MPZ_REALLOC (r, alloc); - rn = mpn_set_str_bits (rp, dp, dn, bits); - } - else - { - struct mpn_base_info info; - mpn_get_base_info (&info, base); - alloc = (dn + info.exp - 1) / info.exp; - rp = MPZ_REALLOC (r, alloc); - rn = mpn_set_str_other (rp, dp, dn, base, &info); - /* Normalization, needed for all-zero input. */ - assert (rn > 0); - rn -= rp[rn-1] == 0; - } - assert (rn <= alloc); - gmp_free (dp); - - r->_mp_size = sign ? - rn : rn; - - return 0; -} - -int -mpz_init_set_str (mpz_t r, const char *sp, int base) -{ - mpz_init (r); - return mpz_set_str (r, sp, base); -} - -size_t -mpz_out_str (FILE *stream, int base, const mpz_t x) -{ - char *str; - size_t len; - - str = mpz_get_str (NULL, base, x); - len = strlen (str); - len = fwrite (str, 1, len, stream); - gmp_free (str); - return len; -} - - -static int -gmp_detect_endian (void) -{ - static const int i = 2; - const unsigned char *p = (const unsigned char *) &i; - return 1 - *p; -} - -/* Import and export. Does not support nails. */ -void -mpz_import (mpz_t r, size_t count, int order, size_t size, int endian, - size_t nails, const void *src) -{ - const unsigned char *p; - ptrdiff_t word_step; - mp_ptr rp; - mp_size_t rn; - - /* The current (partial) limb. */ - mp_limb_t limb; - /* The number of bytes already copied to this limb (starting from - the low end). */ - size_t bytes; - /* The index where the limb should be stored, when completed. */ - mp_size_t i; - - if (nails != 0) - gmp_die ("mpz_import: Nails not supported."); - - assert (order == 1 || order == -1); - assert (endian >= -1 && endian <= 1); - - if (endian == 0) - endian = gmp_detect_endian (); - - p = (unsigned char *) src; - - word_step = (order != endian) ? 2 * size : 0; - - /* Process bytes from the least significant end, so point p at the - least significant word. */ - if (order == 1) - { - p += size * (count - 1); - word_step = - word_step; - } - - /* And at least significant byte of that word. */ - if (endian == 1) - p += (size - 1); - - rn = (size * count + sizeof(mp_limb_t) - 1) / sizeof(mp_limb_t); - rp = MPZ_REALLOC (r, rn); - - for (limb = 0, bytes = 0, i = 0; count > 0; count--, p += word_step) - { - size_t j; - for (j = 0; j < size; j++, p -= (ptrdiff_t) endian) - { - limb |= (mp_limb_t) *p << (bytes++ * CHAR_BIT); - if (bytes == sizeof(mp_limb_t)) - { - rp[i++] = limb; - bytes = 0; - limb = 0; - } - } - } - assert (i + (bytes > 0) == rn); - if (limb != 0) - rp[i++] = limb; - else - i = mpn_normalized_size (rp, i); - - r->_mp_size = i; -} - -void * -mpz_export (void *r, size_t *countp, int order, size_t size, int endian, - size_t nails, const mpz_t u) -{ - size_t count; - mp_size_t un; - - if (nails != 0) - gmp_die ("mpz_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; - unsigned char *p; - ptrdiff_t word_step; - /* The current (partial) limb. */ - mp_limb_t limb; - /* The number of bytes left to do in this limb. */ - size_t bytes; - /* The index where the limb was read. */ - mp_size_t i; - - un = GMP_ABS (un); - - /* Count bytes in top limb. */ - limb = u->_mp_d[un-1]; - assert (limb != 0); - - k = 0; - do { - k++; limb >>= CHAR_BIT; - } while (limb != 0); - - count = (k + (un-1) * sizeof (mp_limb_t) + size - 1) / size; - - if (!r) - r = gmp_xalloc (count * size); - - if (endian == 0) - endian = gmp_detect_endian (); - - p = (unsigned char *) r; - - word_step = (order != endian) ? 2 * size : 0; - - /* Process bytes from the least significant end, so point p at the - least significant word. */ - if (order == 1) - { - p += size * (count - 1); - word_step = - word_step; - } - - /* And at least significant byte of that word. */ - if (endian == 1) - p += (size - 1); - - for (bytes = 0, i = 0, k = 0; k < count; k++, p += word_step) - { - size_t j; - for (j = 0; j < size; j++, p -= (ptrdiff_t) endian) - { - if (bytes == 0) - { - if (i < un) - limb = u->_mp_d[i++]; - bytes = sizeof (mp_limb_t); - } - *p = limb; - limb >>= CHAR_BIT; - bytes--; - } - } - assert (i == un); - assert (k == count); - } - - if (countp) - *countp = count; - - return r; -} |