+++ /dev/null
-/* mpn_gcdext -- Extended Greatest Common Divisor.
-
-Copyright (C) 1996, 1998, 2000 Free Software Foundation, Inc.
-
-This file is part of the GNU MP Library.
-
-The GNU MP Library is free software; you can redistribute it and/or modify
-it under the terms of the GNU Lesser General Public License as published by
-the Free Software Foundation; either version 2.1 of the License, or (at your
-option) any later version.
-
-The GNU MP Library is distributed in the hope that it will be useful, but
-WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
-License for more details.
-
-You should have received a copy of the GNU Lesser General Public License
-along with the GNU MP Library; see the file COPYING.LIB. If not, write to
-the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
-MA 02111-1307, USA. */
-
-#include "gmp.h"
-#include "gmp-impl.h"
-#include "longlong.h"
-
-#ifndef GCDEXT_THRESHOLD
-#define GCDEXT_THRESHOLD 17
-#endif
-
-#ifndef EXTEND
-#define EXTEND 1
-#endif
-
-#if STAT
-int arr[BITS_PER_MP_LIMB];
-#endif
-
-
-/* mpn_gcdext (GP, SP, SSIZE, UP, USIZE, VP, VSIZE)
-
- Compute the extended GCD of {UP,USIZE} and {VP,VSIZE} and store the
- greatest common divisor at GP (unless it is 0), and the first cofactor at
- SP. Write the size of the cofactor through the pointer SSIZE. Return the
- size of the value at GP. Note that SP might be a negative number; this is
- denoted by storing the negative of the size through SSIZE.
-
- {UP,USIZE} and {VP,VSIZE} are both clobbered.
-
- The space allocation for all four areas needs to be USIZE+1.
-
- Preconditions: 1) U >= V.
- 2) V > 0. */
-
-/* We use Lehmer's algorithm. The idea is to extract the most significant
- bits of the operands, and compute the continued fraction for them. We then
- apply the gathered cofactors to the full operands.
-
- Idea 1: After we have performed a full division, don't shift operands back,
- but instead account for the extra factors-of-2 thus introduced.
- Idea 2: Simple generalization to use divide-and-conquer would give us an
- algorithm that runs faster than O(n^2).
- Idea 3: The input numbers need less space as the computation progresses,
- while the s0 and s1 variables need more space. To save memory, we
- could make them share space, and have the latter variables grow
- into the former.
- Idea 4: We should not do double-limb arithmetic from the start. Instead,
- do things in single-limb arithmetic until the quotients differ,
- and then switch to double-limb arithmetic. */
-
-
-/* Division optimized for small quotients. If the quotient is more than one limb,
- store 1 in *qh and return 0. */
-static mp_limb_t
-#if __STDC__
-div2 (mp_limb_t *qh, mp_limb_t n1, mp_limb_t n0, mp_limb_t d1, mp_limb_t d0)
-#else
-div2 (qh, n1, n0, d1, d0)
- mp_limb_t *qh;
- mp_limb_t n1;
- mp_limb_t n0;
- mp_limb_t d1;
- mp_limb_t d0;
-#endif
-{
- if (d1 == 0)
- {
- *qh = 1;
- return 0;
- }
-
- if ((mp_limb_signed_t) n1 < 0)
- {
- mp_limb_t q;
- int cnt;
- for (cnt = 1; (mp_limb_signed_t) d1 >= 0; cnt++)
- {
- d1 = (d1 << 1) | (d0 >> (BITS_PER_MP_LIMB - 1));
- d0 = d0 << 1;
- }
-
- q = 0;
- while (cnt)
- {
- q <<= 1;
- if (n1 > d1 || (n1 == d1 && n0 >= d0))
- {
- sub_ddmmss (n1, n0, n1, n0, d1, d0);
- q |= 1;
- }
- d0 = (d1 << (BITS_PER_MP_LIMB - 1)) | (d0 >> 1);
- d1 = d1 >> 1;
- cnt--;
- }
-
- *qh = 0;
- return q;
- }
- else
- {
- mp_limb_t q;
- int cnt;
- for (cnt = 0; n1 > d1 || (n1 == d1 && n0 >= d0); cnt++)
- {
- d1 = (d1 << 1) | (d0 >> (BITS_PER_MP_LIMB - 1));
- d0 = d0 << 1;
- }
-
- q = 0;
- while (cnt)
- {
- d0 = (d1 << (BITS_PER_MP_LIMB - 1)) | (d0 >> 1);
- d1 = d1 >> 1;
- q <<= 1;
- if (n1 > d1 || (n1 == d1 && n0 >= d0))
- {
- sub_ddmmss (n1, n0, n1, n0, d1, d0);
- q |= 1;
- }
- cnt--;
- }
-
- *qh = 0;
- return q;
- }
-}
-
-mp_size_t
-#if EXTEND
-#if __STDC__
-mpn_gcdext (mp_ptr gp, mp_ptr s0p, mp_size_t *s0size,
- mp_ptr up, mp_size_t size, mp_ptr vp, mp_size_t vsize)
-#else
-mpn_gcdext (gp, s0p, s0size, up, size, vp, vsize)
- mp_ptr gp;
- mp_ptr s0p;
- mp_size_t *s0size;
- mp_ptr up;
- mp_size_t size;
- mp_ptr vp;
- mp_size_t vsize;
-#endif
-#else
-#if __STDC__
-mpn_gcd (mp_ptr gp,
- mp_ptr up, mp_size_t size, mp_ptr vp, mp_size_t vsize)
-#else
-mpn_gcd (gp, up, size, vp, vsize)
- mp_ptr gp;
- mp_ptr up;
- mp_size_t size;
- mp_ptr vp;
- mp_size_t vsize;
-#endif
-#endif
-{
- mp_limb_t A, B, C, D;
- int cnt;
- mp_ptr tp, wp;
-#if RECORD
- mp_limb_t max = 0;
-#endif
-#if EXTEND
- mp_ptr s1p;
- mp_ptr orig_s0p = s0p;
- mp_size_t ssize;
- int sign = 1;
-#endif
- int use_double_flag;
- TMP_DECL (mark);
-
- TMP_MARK (mark);
-
- use_double_flag = (size >= GCDEXT_THRESHOLD);
-
- tp = (mp_ptr) TMP_ALLOC ((size + 1) * BYTES_PER_MP_LIMB);
- wp = (mp_ptr) TMP_ALLOC ((size + 1) * BYTES_PER_MP_LIMB);
-#if EXTEND
- s1p = (mp_ptr) TMP_ALLOC ((size + 1) * BYTES_PER_MP_LIMB);
-
- MPN_ZERO (s0p, size);
- MPN_ZERO (s1p, size);
-
- s0p[0] = 1;
- s1p[0] = 0;
- ssize = 1;
-#endif
-
- if (size > vsize)
- {
- /* Normalize V (and shift up U the same amount). */
- count_leading_zeros (cnt, vp[vsize - 1]);
- if (cnt != 0)
- {
- mp_limb_t cy;
- mpn_lshift (vp, vp, vsize, cnt);
- cy = mpn_lshift (up, up, size, cnt);
- up[size] = cy;
- size += cy != 0;
- }
-
- mpn_divmod (up + vsize, up, size, vp, vsize);
-#if EXTEND
- /* This is really what it boils down to in this case... */
- s0p[0] = 0;
- s1p[0] = 1;
- sign = -sign;
-#endif
- size = vsize;
- if (cnt != 0)
- {
- mpn_rshift (up, up, size, cnt);
- mpn_rshift (vp, vp, size, cnt);
- }
- MP_PTR_SWAP (up, vp);
- }
-
- for (;;)
- {
- mp_limb_t asign;
- /* Figure out exact size of V. */
- vsize = size;
- MPN_NORMALIZE (vp, vsize);
- if (vsize <= 1)
- break;
-
- if (use_double_flag)
- {
- mp_limb_t uh, vh, ul, vl;
- /* Let UH,UL be the most significant limbs of U, and let VH,VL be
- the corresponding bits from V. */
- uh = up[size - 1];
- vh = vp[size - 1];
- ul = up[size - 2];
- vl = vp[size - 2];
- count_leading_zeros (cnt, uh);
- if (cnt != 0)
- {
- uh = (uh << cnt) | (ul >> (BITS_PER_MP_LIMB - cnt));
- vh = (vh << cnt) | (vl >> (BITS_PER_MP_LIMB - cnt));
- vl <<= cnt;
- ul <<= cnt;
- if (size >= 3)
- {
- ul |= (up[size - 3] >> (BITS_PER_MP_LIMB - cnt));
- vl |= (vp[size - 3] >> (BITS_PER_MP_LIMB - cnt));
- }
- }
-
- A = 1;
- B = 0;
- C = 0;
- D = 1;
-
- asign = 0;
- for (;;)
- {
- mp_limb_t T;
- mp_limb_t qh, q1, q2;
- mp_limb_t nh, nl, dh, dl;
- mp_limb_t t1, t0;
- mp_limb_t Th, Tl;
-
- sub_ddmmss (dh, dl, vh, vl, 0, C);
- if ((dl | dh) == 0)
- break;
- add_ssaaaa (nh, nl, uh, ul, 0, A);
- q1 = div2 (&qh, nh, nl, dh, dl);
- if (qh != 0)
- break; /* could handle this */
-
- add_ssaaaa (dh, dl, vh, vl, 0, D);
- if ((dl | dh) == 0)
- break;
- sub_ddmmss (nh, nl, uh, ul, 0, B);
- q2 = div2 (&qh, nh, nl, dh, dl);
- if (qh != 0)
- break; /* could handle this */
-
- if (q1 != q2)
- break;
-
- asign = ~asign;
-
- T = A + q1 * C;
- A = C;
- C = T;
- T = B + q1 * D;
- B = D;
- D = T;
- umul_ppmm (t1, t0, q1, vl);
- t1 += q1 * vh;
- sub_ddmmss (Th, Tl, uh, ul, t1, t0);
- uh = vh, ul = vl;
- vh = Th, vl = Tl;
-
- add_ssaaaa (dh, dl, vh, vl, 0, C);
- sub_ddmmss (nh, nl, uh, ul, 0, A);
- q1 = div2 (&qh, nh, nl, dh, dl);
- if (qh != 0)
- break; /* could handle this */
-
- sub_ddmmss (dh, dl, vh, vl, 0, D);
- if ((dl | dh) == 0)
- break;
- add_ssaaaa (nh, nl, uh, ul, 0, B);
- q2 = div2 (&qh, nh, nl, dh, dl);
- if (qh != 0)
- break; /* could handle this */
-
- if (q1 != q2)
- break;
-
- asign = ~asign;
-
- T = A + q1 * C;
- A = C;
- C = T;
- T = B + q1 * D;
- B = D;
- D = T;
- umul_ppmm (t1, t0, q1, vl);
- t1 += q1 * vh;
- sub_ddmmss (Th, Tl, uh, ul, t1, t0);
- uh = vh, ul = vl;
- vh = Th, vl = Tl;
- }
-#if EXTEND
- if (asign)
- sign = -sign;
-#endif
- }
- else /* Same, but using single-limb calculations. */
- {
- mp_limb_t uh, vh;
- /* Make UH be the most significant limb of U, and make VH be
- corresponding bits from V. */
- uh = up[size - 1];
- vh = vp[size - 1];
- count_leading_zeros (cnt, uh);
- if (cnt != 0)
- {
- uh = (uh << cnt) | (up[size - 2] >> (BITS_PER_MP_LIMB - cnt));
- vh = (vh << cnt) | (vp[size - 2] >> (BITS_PER_MP_LIMB - cnt));
- }
-
- A = 1;
- B = 0;
- C = 0;
- D = 1;
-
- asign = 0;
- for (;;)
- {
- mp_limb_t q, T;
- if (vh - C == 0 || vh + D == 0)
- break;
-
- q = (uh + A) / (vh - C);
- if (q != (uh - B) / (vh + D))
- break;
-
- asign = ~asign;
-
- T = A + q * C;
- A = C;
- C = T;
- T = B + q * D;
- B = D;
- D = T;
- T = uh - q * vh;
- uh = vh;
- vh = T;
-
- if (vh - D == 0)
- break;
-
- q = (uh - A) / (vh + C);
- if (q != (uh + B) / (vh - D))
- break;
-
- asign = ~asign;
-
- T = A + q * C;
- A = C;
- C = T;
- T = B + q * D;
- B = D;
- D = T;
- T = uh - q * vh;
- uh = vh;
- vh = T;
- }
-#if EXTEND
- if (asign)
- sign = -sign;
-#endif
- }
-
-#if RECORD
- max = MAX (A, max); max = MAX (B, max);
- max = MAX (C, max); max = MAX (D, max);
-#endif
-
- if (B == 0)
- {
- mp_limb_t qh;
- mp_size_t i;
- /* This is quite rare. I.e., optimize something else! */
-
- /* Normalize V (and shift up U the same amount). */
- count_leading_zeros (cnt, vp[vsize - 1]);
- if (cnt != 0)
- {
- mp_limb_t cy;
- mpn_lshift (vp, vp, vsize, cnt);
- cy = mpn_lshift (up, up, size, cnt);
- up[size] = cy;
- size += cy != 0;
- }
-
- qh = mpn_divmod (up + vsize, up, size, vp, vsize);
-#if EXTEND
- MPN_COPY (tp, s0p, ssize);
- {
- mp_size_t qsize;
-
- qsize = size - vsize; /* size of stored quotient from division */
- if (ssize < qsize)
- {
- MPN_ZERO (tp + ssize, qsize - ssize);
- MPN_ZERO (s1p + ssize, qsize); /* zero s1 too */
- for (i = 0; i < ssize; i++)
- {
- mp_limb_t cy;
- cy = mpn_addmul_1 (tp + i, up + vsize, qsize, s1p[i]);
- tp[qsize + i] = cy;
- }
- if (qh != 0)
- {
- mp_limb_t cy;
- cy = mpn_add_n (tp + qsize, tp + qsize, s1p, ssize);
- if (cy != 0)
- abort ();
- }
- }
- else
- {
- MPN_ZERO (s1p + ssize, qsize); /* zero s1 too */
- for (i = 0; i < qsize; i++)
- {
- mp_limb_t cy;
- cy = mpn_addmul_1 (tp + i, s1p, ssize, up[vsize + i]);
- tp[ssize + i] = cy;
- }
- if (qh != 0)
- {
- mp_limb_t cy;
- cy = mpn_add_n (tp + qsize, tp + qsize, s1p, ssize);
- if (cy != 0)
- {
- tp[qsize + ssize] = cy;
- s1p[qsize + ssize] = 0;
- ssize++;
- }
- }
- }
- ssize += qsize;
- ssize -= tp[ssize - 1] == 0;
- }
-
- sign = -sign;
- MP_PTR_SWAP (s0p, s1p);
- MP_PTR_SWAP (s1p, tp);
-#endif
- size = vsize;
- if (cnt != 0)
- {
- mpn_rshift (up, up, size, cnt);
- mpn_rshift (vp, vp, size, cnt);
- }
- MP_PTR_SWAP (up, vp);
- }
- else
- {
-#if EXTEND
- mp_size_t tsize, wsize;
-#endif
- /* T = U*A + V*B
- W = U*C + V*D
- U = T
- V = W */
-
-#if STAT
- { mp_limb_t x; x = A | B | C | D; count_leading_zeros (cnt, x);
- arr[BITS_PER_MP_LIMB - cnt]++; }
-#endif
- if (A == 0)
- {
- /* B == 1 and C == 1 (D is arbitrary) */
- mp_limb_t cy;
- MPN_COPY (tp, vp, size);
- MPN_COPY (wp, up, size);
- mpn_submul_1 (wp, vp, size, D);
- MP_PTR_SWAP (tp, up);
- MP_PTR_SWAP (wp, vp);
-#if EXTEND
- MPN_COPY (tp, s1p, ssize);
- tsize = ssize;
- tp[ssize] = 0; /* must zero since wp might spill below */
- MPN_COPY (wp, s0p, ssize);
- cy = mpn_addmul_1 (wp, s1p, ssize, D);
- wp[ssize] = cy;
- wsize = ssize + (cy != 0);
- MP_PTR_SWAP (tp, s0p);
- MP_PTR_SWAP (wp, s1p);
- ssize = MAX (wsize, tsize);
-#endif
- }
- else
- {
- if (asign)
- {
- mp_limb_t cy;
- mpn_mul_1 (tp, vp, size, B);
- mpn_submul_1 (tp, up, size, A);
- mpn_mul_1 (wp, up, size, C);
- mpn_submul_1 (wp, vp, size, D);
- MP_PTR_SWAP (tp, up);
- MP_PTR_SWAP (wp, vp);
-#if EXTEND
- cy = mpn_mul_1 (tp, s1p, ssize, B);
- cy += mpn_addmul_1 (tp, s0p, ssize, A);
- tp[ssize] = cy;
- tsize = ssize + (cy != 0);
- cy = mpn_mul_1 (wp, s0p, ssize, C);
- cy += mpn_addmul_1 (wp, s1p, ssize, D);
- wp[ssize] = cy;
- wsize = ssize + (cy != 0);
- MP_PTR_SWAP (tp, s0p);
- MP_PTR_SWAP (wp, s1p);
- ssize = MAX (wsize, tsize);
-#endif
- }
- else
- {
- mp_limb_t cy;
- mpn_mul_1 (tp, up, size, A);
- mpn_submul_1 (tp, vp, size, B);
- mpn_mul_1 (wp, vp, size, D);
- mpn_submul_1 (wp, up, size, C);
- MP_PTR_SWAP (tp, up);
- MP_PTR_SWAP (wp, vp);
-#if EXTEND
- cy = mpn_mul_1 (tp, s0p, ssize, A);
- cy += mpn_addmul_1 (tp, s1p, ssize, B);
- tp[ssize] = cy;
- tsize = ssize + (cy != 0);
- cy = mpn_mul_1 (wp, s1p, ssize, D);
- cy += mpn_addmul_1 (wp, s0p, ssize, C);
- wp[ssize] = cy;
- wsize = ssize + (cy != 0);
- MP_PTR_SWAP (tp, s0p);
- MP_PTR_SWAP (wp, s1p);
- ssize = MAX (wsize, tsize);
-#endif
- }
- }
-
- size -= up[size - 1] == 0;
- }
- }
-
-#if RECORD
- printf ("max: %lx\n", max);
-#endif
-
-#if STAT
- {int i; for (i = 0; i < BITS_PER_MP_LIMB; i++) printf ("%d:%d\n", i, arr[i]);}
-#endif
-
- if (vsize == 0)
- {
- if (gp != up && gp != 0)
- MPN_COPY (gp, up, size);
-#if EXTEND
- MPN_NORMALIZE (s0p, ssize);
- if (orig_s0p != s0p)
- MPN_COPY (orig_s0p, s0p, ssize);
- *s0size = sign >= 0 ? ssize : -ssize;
-#endif
- TMP_FREE (mark);
- return size;
- }
- else
- {
- mp_limb_t vl, ul, t;
-#if EXTEND
- mp_size_t qsize, i;
-#endif
- vl = vp[0];
-#if EXTEND
- t = mpn_divmod_1 (wp, up, size, vl);
-
- MPN_COPY (tp, s0p, ssize);
-
- qsize = size - (wp[size - 1] == 0); /* size of quotient from division */
- if (ssize < qsize)
- {
- MPN_ZERO (tp + ssize, qsize - ssize);
- MPN_ZERO (s1p + ssize, qsize); /* zero s1 too */
- for (i = 0; i < ssize; i++)
- {
- mp_limb_t cy;
- cy = mpn_addmul_1 (tp + i, wp, qsize, s1p[i]);
- tp[qsize + i] = cy;
- }
- }
- else
- {
- MPN_ZERO (s1p + ssize, qsize); /* zero s1 too */
- for (i = 0; i < qsize; i++)
- {
- mp_limb_t cy;
- cy = mpn_addmul_1 (tp + i, s1p, ssize, wp[i]);
- tp[ssize + i] = cy;
- }
- }
- ssize += qsize;
- ssize -= tp[ssize - 1] == 0;
-
- sign = -sign;
- MP_PTR_SWAP (s0p, s1p);
- MP_PTR_SWAP (s1p, tp);
-#else
- t = mpn_mod_1 (up, size, vl);
-#endif
- ul = vl;
- vl = t;
- while (vl != 0)
- {
- mp_limb_t t;
-#if EXTEND
- mp_limb_t q;
- q = ul / vl;
- t = ul - q * vl;
-
- MPN_COPY (tp, s0p, ssize);
-
- MPN_ZERO (s1p + ssize, 1); /* zero s1 too */
-
- {
- mp_limb_t cy;
- cy = mpn_addmul_1 (tp, s1p, ssize, q);
- tp[ssize] = cy;
- }
-
- ssize += 1;
- ssize -= tp[ssize - 1] == 0;
-
- sign = -sign;
- MP_PTR_SWAP (s0p, s1p);
- MP_PTR_SWAP (s1p, tp);
-#else
- t = ul % vl;
-#endif
- ul = vl;
- vl = t;
- }
- if (gp != 0)
- gp[0] = ul;
-#if EXTEND
- MPN_NORMALIZE (s0p, ssize);
- if (orig_s0p != s0p)
- MPN_COPY (orig_s0p, s0p, ssize);
- *s0size = sign >= 0 ? ssize : -ssize;
-#endif
- TMP_FREE (mark);
- return 1;
- }
-}
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