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./.libs/libspeed.a(gcd_bin.o): In function `__gmpn_ngcd_matrix_init': gcd_bin.c:(.text+0x0): multiple definition of `__gmpn_ngcd_matrix_init' gcd.o:gcd.c:(.text+0x0): first defined here ./.libs/libspeed.a(gcd_bin.o): In function `__gmpn_nhgcd_itch': gcd_bin.c:(.text+0x80): multiple definition of `__gmpn_nhgcd_itch' gcd.o:gcd.c:(.text+0x80): first defined here ./.libs/libspeed.a(gcd_bin.o): In function `__gmpn_nhgcd': gcd_bin.c:(.text+0xc4): multiple definition of `__gmpn_nhgcd' gcd.o:gcd.c:(.text+0xc4): first defined here ./.libs/libspeed.a(gcd_bin.o): In function `mpn_basic_gcd': gcd_bin.c:(.text+0x2ed): multiple definition of `mpn_basic_gcd' gcd.o:gcd.c:(.text+0x2ed): first defined here Bill. 2008/12/23 Jason Martin <jason.worth.mar...@gmail.com>: > Attached are some edited versions of > > mpn/generic/gcd.c > > and > > mpn/generic/ngcd.c > > Drop them in, test them for correctness and speed. Let me know what > breaks. When everyone is happy, I'll check them in to svn > > --jason > > Jason Worth Martin > Asst. Professor of Mathematics > http://www.math.jmu.edu/~martin > > > > > /* Schönhage's 1987 algorithm, reorganized into hgcd form */ > > #include <stdio.h> /* for NULL */ > > #include "gmp.h" > #include "gmp-impl.h" > #include "longlong.h" > > > /* ****************************************************************** > * Here we are including the original GMP version of mpn_gcd > * but we rename it as mpn_basic_gcd. It needs to be available > * for the ngcd algorithm to call in the base case. > * > * Preconditions [U = (up, usize) and V = (vp, vsize)]: > * > * 1. V is odd. > * 2. numbits(U) >= numbits(V). > * > * Both U and V are destroyed by the operation. The result is left at vp, > * and its size is returned. > * > * Ken Weber (kwe...@mat.ufrgs.br, kwe...@mcs.kent.edu) > * > * Funding for this work has been partially provided by Conselho > * Nacional de Desenvolvimento Cienti'fico e Tecnolo'gico (CNPq) do > * Brazil, Grant 301314194-2, and was done while I was a visiting > * reseacher in the Instituto de Matema'tica at Universidade Federal > * do Rio Grande do Sul (UFRGS). > * > * Refer to K. Weber, The accelerated integer GCD algorithm, ACM > * Transactions on Mathematical Software, v. 21 (March), 1995, > * pp. 111-122. > * > * *****************************************************************/ > > > > /* If MIN (usize, vsize) >= GCD_ACCEL_THRESHOLD, then the accelerated > algorithm is used, otherwise the binary algorithm is used. This may be > adjusted for different architectures. */ > #ifndef GCD_ACCEL_THRESHOLD > #define GCD_ACCEL_THRESHOLD 5 > #endif > > /* When U and V differ in size by more than BMOD_THRESHOLD, the accelerated > algorithm reduces using the bmod operation. Otherwise, the k-ary reduction > is used. 0 <= BMOD_THRESHOLD < GMP_NUMB_BITS. */ > enum > { > BMOD_THRESHOLD = GMP_NUMB_BITS/2 > }; > > > /* Use binary algorithm to compute V <-- GCD (V, U) for usize, vsize == 2. > Both U and V must be odd. */ > static inline mp_size_t > gcd_2 (mp_ptr vp, mp_srcptr up) > { > mp_limb_t u0, u1, v0, v1; > mp_size_t vsize; > > u0 = up[0]; > u1 = up[1]; > v0 = vp[0]; > v1 = vp[1]; > > while (u1 != v1 && u0 != v0) > { > unsigned long int r; > if (u1 > v1) > { > u1 -= v1 + (u0 < v0); > u0 = (u0 - v0) & GMP_NUMB_MASK; > count_trailing_zeros (r, u0); > u0 = ((u1 << (GMP_NUMB_BITS - r)) & GMP_NUMB_MASK) | (u0 >> r); > u1 >>= r; > } > else /* u1 < v1. */ > { > v1 -= u1 + (v0 < u0); > v0 = (v0 - u0) & GMP_NUMB_MASK; > count_trailing_zeros (r, v0); > v0 = ((v1 << (GMP_NUMB_BITS - r)) & GMP_NUMB_MASK) | (v0 >> r); > v1 >>= r; > } > } > > vp[0] = v0, vp[1] = v1, vsize = 1 + (v1 != 0); > > /* If U == V == GCD, done. Otherwise, compute GCD (V, |U - V|). */ > if (u1 == v1 && u0 == v0) > return vsize; > > v0 = (u0 == v0) ? (u1 > v1) ? u1-v1 : v1-u1 : (u0 > v0) ? u0-v0 : v0-u0; > vp[0] = mpn_gcd_1 (vp, vsize, v0); > > return 1; > } > > /* The function find_a finds 0 < N < 2^GMP_NUMB_BITS such that there exists > 0 < |D| < 2^GMP_NUMB_BITS, and N == D * C mod 2^(2*GMP_NUMB_BITS). > In the reference article, D was computed along with N, but it is better to > compute D separately as D <-- N / C mod 2^(GMP_NUMB_BITS + 1), treating > the result as a twos' complement signed integer. > > Initialize N1 to C mod 2^(2*GMP_NUMB_BITS). According to the reference > article, N2 should be initialized to 2^(2*GMP_NUMB_BITS), but we use > 2^(2*GMP_NUMB_BITS) - N1 to start the calculations within double > precision. If N2 > N1 initially, the first iteration of the while loop > will swap them. In all other situations, N1 >= N2 is maintained. */ > > #if HAVE_NATIVE_mpn_gcd_finda > #define find_a(cp) mpn_gcd_finda (cp) > > #else > static > #if ! defined (__i386__) > inline /* don't inline this for the x86 */ > #endif > mp_limb_t > find_a (mp_srcptr cp) > { > unsigned long int leading_zero_bits = 0; > > mp_limb_t n1_l = cp[0]; /* N1 == n1_h * 2^GMP_NUMB_BITS + n1_l. */ > mp_limb_t n1_h = cp[1]; > > mp_limb_t n2_l = (-n1_l & GMP_NUMB_MASK); /* N2 == n2_h * > 2^GMP_NUMB_BITS + n2_l. */ > mp_limb_t n2_h = (~n1_h & GMP_NUMB_MASK); > > /* Main loop. */ > while (n2_h != 0) /* While N2 >= 2^GMP_NUMB_BITS. */ > { > /* N1 <-- N1 % N2. */ > if (((GMP_NUMB_HIGHBIT >> leading_zero_bits) & n2_h) == 0) > { > unsigned long int i; > count_leading_zeros (i, n2_h); > i -= GMP_NAIL_BITS; > i -= leading_zero_bits; > leading_zero_bits += i; > n2_h = ((n2_h << i) & GMP_NUMB_MASK) | (n2_l >> (GMP_NUMB_BITS - i)); > n2_l = (n2_l << i) & GMP_NUMB_MASK; > do > { > if (n1_h > n2_h || (n1_h == n2_h && n1_l >= n2_l)) > { > n1_h -= n2_h + (n1_l < n2_l); > n1_l = (n1_l - n2_l) & GMP_NUMB_MASK; > } > n2_l = (n2_l >> 1) | ((n2_h << (GMP_NUMB_BITS - 1)) & > GMP_NUMB_MASK); > n2_h >>= 1; > i -= 1; > } > while (i != 0); > } > if (n1_h > n2_h || (n1_h == n2_h && n1_l >= n2_l)) > { > n1_h -= n2_h + (n1_l < n2_l); > n1_l = (n1_l - n2_l) & GMP_NUMB_MASK; > } > > MP_LIMB_T_SWAP (n1_h, n2_h); > MP_LIMB_T_SWAP (n1_l, n2_l); > } > > return n2_l; > } > #endif > > > mp_size_t > mpn_basic_gcd (mp_ptr gp, mp_ptr up, mp_size_t usize, mp_ptr vp, mp_size_t > vsize) > { > mp_ptr orig_vp = vp; > mp_size_t orig_vsize = vsize; > int binary_gcd_ctr; /* Number of times binary gcd will execute. */ > mp_size_t scratch; > mp_ptr tp; > TMP_DECL; > > ASSERT (usize >= 1); > ASSERT (vsize >= 1); > ASSERT (usize >= vsize); > ASSERT (vp[0] & 1); > ASSERT (up[usize - 1] != 0); > ASSERT (vp[vsize - 1] != 0); > #if WANT_ASSERT > if (usize == vsize) > { > int uzeros, vzeros; > count_leading_zeros (uzeros, up[usize - 1]); > count_leading_zeros (vzeros, vp[vsize - 1]); > ASSERT (uzeros <= vzeros); > } > #endif > ASSERT (! MPN_OVERLAP_P (up, usize, vp, vsize)); > ASSERT (MPN_SAME_OR_SEPARATE2_P (gp, vsize, up, usize)); > ASSERT (MPN_SAME_OR_SEPARATE2_P (gp, vsize, vp, vsize)); > > TMP_MARK; > > /* Use accelerated algorithm if vsize is over GCD_ACCEL_THRESHOLD. > Two EXTRA limbs for U and V are required for kary reduction. */ > if (vsize >= GCD_ACCEL_THRESHOLD) > { > unsigned long int vbitsize, d; > mp_ptr orig_up = up; > mp_size_t orig_usize = usize; > mp_ptr anchor_up = (mp_ptr) TMP_ALLOC ((usize + 2) * BYTES_PER_MP_LIMB); > > MPN_COPY (anchor_up, orig_up, usize); > up = anchor_up; > > count_leading_zeros (d, up[usize - 1]); > d -= GMP_NAIL_BITS; > d = usize * GMP_NUMB_BITS - d; > count_leading_zeros (vbitsize, vp[vsize - 1]); > vbitsize -= GMP_NAIL_BITS; > vbitsize = vsize * GMP_NUMB_BITS - vbitsize; > ASSERT (d >= vbitsize); > d = d - vbitsize + 1; > > /* Use bmod reduction to quickly discover whether V divides U. */ > up[usize++] = 0; /* Insert leading zero. */ > mpn_bdivmod (up, up, usize, vp, vsize, d); > > /* Now skip U/V mod 2^d and any low zero limbs. */ > d /= GMP_NUMB_BITS, up += d, usize -= d; > while (usize != 0 && up[0] == 0) > up++, usize--; > > if (usize == 0) /* GCD == ORIG_V. */ > goto done; > > vp = (mp_ptr) TMP_ALLOC ((vsize + 2) * BYTES_PER_MP_LIMB); > MPN_COPY (vp, orig_vp, vsize); > > do /* Main loop. */ > { > /* mpn_com_n can't be used here because anchor_up and up may > partially overlap */ > if ((up[usize - 1] & GMP_NUMB_HIGHBIT) != 0) /* U < 0; take twos' > compl. */ > { > mp_size_t i; > anchor_up[0] = -up[0] & GMP_NUMB_MASK; > for (i = 1; i < usize; i++) > anchor_up[i] = (~up[i] & GMP_NUMB_MASK); > up = anchor_up; > } > > MPN_NORMALIZE_NOT_ZERO (up, usize); > > if ((up[0] & 1) == 0) /* Result even; remove twos. */ > { > unsigned int r; > count_trailing_zeros (r, up[0]); > mpn_rshift (anchor_up, up, usize, r); > usize -= (anchor_up[usize - 1] == 0); > } > else if (anchor_up != up) > MPN_COPY_INCR (anchor_up, up, usize); > > MPN_PTR_SWAP (anchor_up,usize, vp,vsize); > up = anchor_up; > > if (vsize <= 2) /* Kary can't handle < 2 limbs and */ > break; /* isn't efficient for == 2 limbs. */ > > d = vbitsize; > count_leading_zeros (vbitsize, vp[vsize - 1]); > vbitsize -= GMP_NAIL_BITS; > vbitsize = vsize * GMP_NUMB_BITS - vbitsize; > d = d - vbitsize + 1; > > if (d > BMOD_THRESHOLD) /* Bmod reduction. */ > { > up[usize++] = 0; > mpn_bdivmod (up, up, usize, vp, vsize, d); > d /= GMP_NUMB_BITS, up += d, usize -= d; > } > else /* Kary reduction. */ > { > mp_limb_t bp[2], cp[2]; > > /* C <-- V/U mod 2^(2*GMP_NUMB_BITS). */ > { > mp_limb_t u_inv, hi, lo; > modlimb_invert (u_inv, up[0]); > cp[0] = (vp[0] * u_inv) & GMP_NUMB_MASK; > umul_ppmm (hi, lo, cp[0], up[0] << GMP_NAIL_BITS); > lo >>= GMP_NAIL_BITS; > cp[1] = (vp[1] - hi - cp[0] * up[1]) * u_inv & GMP_NUMB_MASK; > } > > /* U <-- find_a (C) * U. */ > up[usize] = mpn_mul_1 (up, up, usize, find_a (cp)); > usize++; > > /* B <-- A/C == U/V mod 2^(GMP_NUMB_BITS + 1). > bp[0] <-- U/V mod 2^GMP_NUMB_BITS and > bp[1] <-- ( (U - bp[0] * V)/2^GMP_NUMB_BITS ) / V mod 2 > > Like V/U above, but simplified because only the low bit of > bp[1] is wanted. */ > { > mp_limb_t v_inv, hi, lo; > modlimb_invert (v_inv, vp[0]); > bp[0] = (up[0] * v_inv) & GMP_NUMB_MASK; > umul_ppmm (hi, lo, bp[0], vp[0] << GMP_NAIL_BITS); > lo >>= GMP_NAIL_BITS; > bp[1] = (up[1] + hi + (bp[0] & vp[1])) & 1; > } > > up[usize++] = 0; > if (bp[1] != 0) /* B < 0: U <-- U + (-B) * V. */ > { > mp_limb_t c = mpn_addmul_1 (up, vp, vsize, -bp[0] & > GMP_NUMB_MASK); > mpn_add_1 (up + vsize, up + vsize, usize - vsize, c); > } > else /* B >= 0: U <-- U - B * V. */ > { > mp_limb_t b = mpn_submul_1 (up, vp, vsize, bp[0]); > mpn_sub_1 (up + vsize, up + vsize, usize - vsize, b); > } > > up += 2, usize -= 2; /* At least two low limbs are zero. */ > } > > /* Must remove low zero limbs before complementing. */ > while (usize != 0 && up[0] == 0) > up++, usize--; > } > while (usize != 0); > > /* Compute GCD (ORIG_V, GCD (ORIG_U, V)). Binary will execute twice. */ > up = orig_up, usize = orig_usize; > binary_gcd_ctr = 2; > } > else > binary_gcd_ctr = 1; > > scratch = MPN_NGCD_LEHMER_ITCH (vsize); > if (usize + 1 > scratch) > scratch = usize + 1; > > tp = TMP_ALLOC_LIMBS (scratch); > > /* Finish up with the binary algorithm. Executes once or twice. */ > for ( ; binary_gcd_ctr--; up = orig_vp, usize = orig_vsize) > { > #if 1 > if (usize > vsize) > { > /* FIXME: Could use mpn_bdivmod. */ > mp_size_t rsize; > > mpn_tdiv_qr (tp + vsize, tp, 0, up, usize, vp, vsize); > rsize = vsize; > MPN_NORMALIZE (tp, rsize); > if (rsize == 0) > continue; > > MPN_COPY (up, tp, vsize); > } > vsize = mpn_ngcd_lehmer (vp, up, vp, vsize, tp); > #else > if (usize > 2) /* First make U close to V in size. */ > { > unsigned long int vbitsize, d; > count_leading_zeros (d, up[usize - 1]); > d -= GMP_NAIL_BITS; > d = usize * GMP_NUMB_BITS - d; > count_leading_zeros (vbitsize, vp[vsize - 1]); > vbitsize -= GMP_NAIL_BITS; > vbitsize = vsize * GMP_NUMB_BITS - vbitsize; > d = d - vbitsize - 1; > if (d != -(unsigned long int)1 && d > 2) > { > mpn_bdivmod (up, up, usize, vp, vsize, d); /* Result > 0. */ > d /= (unsigned long int)GMP_NUMB_BITS, up += d, usize -= d; > } > } > > /* Start binary GCD. */ > do > { > mp_size_t zeros; > > /* Make sure U is odd. */ > MPN_NORMALIZE (up, usize); > while (up[0] == 0) > up += 1, usize -= 1; > if ((up[0] & 1) == 0) > { > unsigned int r; > count_trailing_zeros (r, up[0]); > mpn_rshift (up, up, usize, r); > usize -= (up[usize - 1] == 0); > } > > /* Keep usize >= vsize. */ > if (usize < vsize) > MPN_PTR_SWAP (up, usize, vp, vsize); > > if (usize <= 2) /* Double precision. */ > { > if (vsize == 1) > vp[0] = mpn_gcd_1 (up, usize, vp[0]); > else > vsize = gcd_2 (vp, up); > break; /* Binary GCD done. */ > } > > /* Count number of low zero limbs of U - V. */ > for (zeros = 0; up[zeros] == vp[zeros] && ++zeros != vsize; ) > continue; > > /* If U < V, swap U and V; in any case, subtract V from U. */ > if (zeros == vsize) /* Subtract done. */ > up += zeros, usize -= zeros; > else if (usize == vsize) > { > mp_size_t size = vsize; > do > size--; > while (up[size] == vp[size]); > if (up[size] < vp[size]) /* usize == vsize. */ > MP_PTR_SWAP (up, vp); > up += zeros, usize = size + 1 - zeros; > mpn_sub_n (up, up, vp + zeros, usize); > } > else > { > mp_size_t size = vsize - zeros; > up += zeros, usize -= zeros; > if (mpn_sub_n (up, up, vp + zeros, size)) > { > while (up[size] == 0) /* Propagate borrow. */ > up[size++] = -(mp_limb_t)1; > up[size] -= 1; > } > } > } > while (usize); /* End binary GCD. */ > #endif > } > > done: > if (vp != gp) > MPN_COPY_INCR (gp, vp, vsize); > TMP_FREE; > return vsize; > } > > > > /* ****************************************************************** > * END of original GMP mpn_gcd > * *****************************************************************/ > > > > > > /* For input of size n, matrix elements are of size at most ceil(n/2) > - 1, but we need one limb extra. */ > > void > mpn_ngcd_matrix_init (struct ngcd_matrix *M, mp_size_t n, mp_ptr p) > { > mp_size_t s = (n+1)/2; > M->alloc = s; > M->n = 1; > MPN_ZERO (p, 4 * s); > M->p[0][0] = p; > M->p[0][1] = p + s; > M->p[1][0] = p + 2 * s; > M->p[1][1] = p + 3 * s; > M->tp = p + 4*s; > > M->p[0][0][0] = M->p[1][1][0] = 1; > } > > #define NHGCD_BASE_ITCH MPN_NGCD_STEP_ITCH > > /* Reduces a,b until |a-b| fits in n/2 + 1 limbs. Constructs matrix M > with elements of size at most (n+1)/2 - 1. Returns new size of a, > b, or zero if no reduction is possible. */ > static mp_size_t > nhgcd_base (mp_ptr ap, mp_ptr bp, mp_size_t n, > struct ngcd_matrix *M, mp_ptr tp) > { > mp_size_t s = n/2 + 1; > mp_size_t nn; > > ASSERT (n > s); > ASSERT (ap[n-1] > 0 || bp[n-1] > 0); > > nn = mpn_ngcd_step (n, ap, bp, s, M, tp); > if (!nn) > return 0; > > for (;;) > { > n = nn; > ASSERT (n > s); > nn = mpn_ngcd_step (n, ap, bp, s, M, tp); > if (!nn ) > return n; > } > } > > /* Size analysis for nhgcd: > > For the recursive calls, we have n1 <= ceil(n / 2). Then the > storage need is determined by the storage for the recursive call > computing M1, and ngcd_matrix_adjust and ngcd_matrix_mul calls that use M1 > (after this, the storage needed for M1 can be recycled). > > Let S(r) denote the required storage. For M1 we need 5 * ceil(n1/2) > = 5 * ceil(n/4), and for the ngcd_matrix_adjust call, we need n + 2. In > total, 5 * ceil(n/4) + n + 2 <= 9 ceil(n/4) + 2. > > For the recursive call, we need S(n1) = S(ceil(n/2)). > > S(n) <= 9*ceil(n/4) + 2 + S(ceil(n/2)) > <= 9*(ceil(n/4) + ... + ceil(n/2^(1+k))) + 2k + S(ceil(n/2^k)) > <= 9*(2 ceil(n/4) + k) + 2k + S(n/2^k) > <= 18 ceil(n/4) + 11k + S(n/2^k) > > */ > > mp_size_t > mpn_nhgcd_itch (mp_size_t n) > { > unsigned k; > mp_size_t nn; > > /* Inefficient way to almost compute > log_2(n/NHGCD_BASE_THRESHOLD) */ > for (k = 0, nn = n; > ABOVE_THRESHOLD (nn, NHGCD_THRESHOLD); > nn = (nn + 1) / 2) > k++; > > if (k == 0) > return NHGCD_BASE_ITCH (n); > > return 18 * ((n+3) / 4) + 11 * k > + NHGCD_BASE_ITCH (NHGCD_THRESHOLD); > } > > /* Reduces a,b until |a-b| fits in n/2 + 1 limbs. Constructs matrix M > with elements of size at most (n+1)/2 - 1. Returns new size of a, > b, or zero if no reduction is possible. */ > > mp_size_t > mpn_nhgcd (mp_ptr ap, mp_ptr bp, mp_size_t n, > struct ngcd_matrix *M, mp_ptr tp) > { > mp_size_t s = n/2 + 1; > mp_size_t n2 = (3*n)/4 + 1; > > mp_size_t p, nn; > unsigned count; > int success = 0; > > ASSERT (n > s); > ASSERT ((ap[n-1] | bp[n-1]) > 0); > > ASSERT ((n+1)/2 - 1 < M->alloc); > > if (BELOW_THRESHOLD (n, NHGCD_THRESHOLD)) > return nhgcd_base (ap, bp, n, M, tp); > > p = n/2; > nn = mpn_nhgcd (ap + p, bp + p, n - p, M, tp); > if (nn > 0) > { > /* Needs 2*(p + M->n) <= 2*(floor(n/2) + ceil(n/2) - 1) > = 2 (n - 1) */ > n = mpn_ngcd_matrix_adjust (M, p + nn, ap, bp, p, tp); > success = 1; > } > count = 0; > while (n > n2) > { > count++; > /* Needs n + 1 storage */ > nn = mpn_ngcd_step (n, ap, bp, s, M, tp); > if (!nn) > return success ? n : 0; > n = nn; > success = 1; > } > > if (n > s + 2) > { > struct ngcd_matrix M1; > mp_size_t scratch; > > p = 2*s - n + 1; > scratch = MPN_NGCD_MATRIX_INIT_ITCH (n-p); > > mpn_ngcd_matrix_init(&M1, n - p, tp); > nn = mpn_nhgcd (ap + p, bp + p, n - p, &M1, tp + scratch); > if (nn > 0) > { > /* Needs 2 (p + M->n) <= 2 (2*s - n2 + 1 + n2 - s - 1) > = 2*s <= 2*(floor(n/2) + 1) <= n + 2. */ > n = mpn_ngcd_matrix_adjust (&M1, p + nn, ap, bp, p, tp + scratch); > /* Needs M->n <= n2 - s - 1 < n/4 */ > mpn_ngcd_matrix_mul (M, &M1, tp + scratch); > success = 1; > } > } > > /* FIXME: This really is the base case */ > for (count = 0;; count++) > { > /* Needs s+3 < n */ > nn = mpn_ngcd_step (n, ap, bp, s, M, tp); > if (!nn) > return success ? n : 0; > > n = nn; > success = 1; > } > } > > #define EVEN_P(x) (((x) & 1) == 0) > > mp_size_t > mpn_gcd (mp_ptr gp, mp_ptr ap, mp_size_t an, mp_ptr bp, mp_size_t n) > { > mp_size_t init_scratch; > mp_size_t scratch; > mp_ptr tp; > TMP_DECL; > > ASSERT (an >= n); > > if (BELOW_THRESHOLD (n, NGCD_THRESHOLD)) > return mpn_basic_gcd (gp, ap, an, bp, n); > > init_scratch = MPN_NGCD_MATRIX_INIT_ITCH ((n+1)/2); > scratch = mpn_nhgcd_itch ((n+1)/2); > > /* Space needed for mpn_ngcd_matrix_adjust */ > if (scratch < 2*n) > scratch = 2*n; > > TMP_MARK; > > if (an + 1 > init_scratch + scratch) > tp = TMP_ALLOC_LIMBS (an + 1); > else > tp = TMP_ALLOC_LIMBS (init_scratch + scratch); > > if (an > n) > { > mp_ptr rp = tp; > mp_ptr qp = rp + n; > > mpn_tdiv_qr (qp, rp, 0, ap, an, bp, n); > MPN_COPY (ap, rp, n); > an = n; > MPN_NORMALIZE (ap, an); > if (an == 0) > { > MPN_COPY (gp, bp, n); > TMP_FREE; > return n; > } > } > > while (ABOVE_THRESHOLD (n, NGCD_THRESHOLD)) > { > struct ngcd_matrix M; > mp_size_t p = n/2; > mp_size_t nn; > > mpn_ngcd_matrix_init (&M, n - p, tp); > nn = mpn_nhgcd (ap + p, bp + p, n - p, &M, tp + init_scratch); > if (nn > 0) > /* Needs 2*(p + M->n) <= 2*(floor(n/2) + ceil(n/2) - 1) > = 2(n-1) */ > n = mpn_ngcd_matrix_adjust (&M, p + nn, ap, bp, p, tp + init_scratch); > > else > { > mp_size_t gn; > n = mpn_ngcd_subdiv_step (gp, &gn, ap, bp, n, tp); > if (n == 0) > { > TMP_FREE; > return gn; > } > } > } > > ASSERT (ap[n-1] > 0 || bp[n-1] > 0); > #if 0 > /* FIXME: We may want to use lehmer on some systems. */ > n = mpn_ngcd_lehmer (gp, ap, bp, n, tp); > > TMP_FREE; > return n; > #endif > > if (ap[n-1] < bp[n-1]) > MP_PTR_SWAP (ap, bp); > > an = n; > MPN_NORMALIZE (bp, n); > > if (n == 0) > { > MPN_COPY (gp, ap, an); > TMP_FREE; > return an; > } > > if (EVEN_P (bp[0])) > { > /* Then a must be odd (since the calling convention implies that > there's no common factor of 2) */ > ASSERT (!EVEN_P (ap[0])); > > while (bp[0] == 0) > { > bp++; > n--; > } > > if (EVEN_P(bp[0])) > { > int count; > count_trailing_zeros (count, bp[0]); > ASSERT_NOCARRY (mpn_rshift (bp, bp, n, count)); > n -= (bp[n-1] == 0); > } > } > > TMP_FREE; > return mpn_basic_gcd (gp, ap, an, bp, n); > } > > /* Schönhage's 1987 algorithm, reorganized into hgcd form */ > > #include <stdio.h> /* for NULL */ > > #include "gmp.h" > #include "gmp-impl.h" > #include "longlong.h" > > > > > > > /* For input of size n, matrix elements are of size at most ceil(n/2) > - 1, but we need one limb extra. */ > > void > mpn_ngcd_matrix_init (struct ngcd_matrix *M, mp_size_t n, mp_ptr p); > > #define NHGCD_BASE_ITCH MPN_NGCD_STEP_ITCH > > /* Reduces a,b until |a-b| fits in n/2 + 1 limbs. Constructs matrix M > with elements of size at most (n+1)/2 - 1. Returns new size of a, > b, or zero if no reduction is possible. */ > static mp_size_t > nhgcd_base (mp_ptr ap, mp_ptr bp, mp_size_t n, > struct ngcd_matrix *M, mp_ptr tp); > > /* Size analysis for nhgcd: > > For the recursive calls, we have n1 <= ceil(n / 2). Then the > storage need is determined by the storage for the recursive call > computing M1, and ngcd_matrix_adjust and ngcd_matrix_mul calls that use M1 > (after this, the storage needed for M1 can be recycled). > > Let S(r) denote the required storage. For M1 we need 5 * ceil(n1/2) > = 5 * ceil(n/4), and for the ngcd_matrix_adjust call, we need n + 2. In > total, 5 * ceil(n/4) + n + 2 <= 9 ceil(n/4) + 2. > > For the recursive call, we need S(n1) = S(ceil(n/2)). > > S(n) <= 9*ceil(n/4) + 2 + S(ceil(n/2)) > <= 9*(ceil(n/4) + ... + ceil(n/2^(1+k))) + 2k + S(ceil(n/2^k)) > <= 9*(2 ceil(n/4) + k) + 2k + S(n/2^k) > <= 18 ceil(n/4) + 11k + S(n/2^k) > > */ > > mp_size_t > mpn_nhgcd_itch (mp_size_t n); > > > /* Reduces a,b until |a-b| fits in n/2 + 1 limbs. Constructs matrix M > with elements of size at most (n+1)/2 - 1. Returns new size of a, > b, or zero if no reduction is possible. */ > > mp_size_t > mpn_nhgcd (mp_ptr ap, mp_ptr bp, mp_size_t n, > struct ngcd_matrix *M, mp_ptr tp); > > > #define EVEN_P(x) (((x) & 1) == 0) > > mp_size_t > mpn_ngcd (mp_ptr gp, mp_ptr ap, mp_size_t an, mp_ptr bp, mp_size_t n) > { > mp_size_t init_scratch; > mp_size_t scratch; > mp_ptr tp; > TMP_DECL; > > ASSERT (an >= n); > > if (BELOW_THRESHOLD (n, NGCD_THRESHOLD)) > return mpn_basic_gcd (gp, ap, an, bp, n); > > init_scratch = MPN_NGCD_MATRIX_INIT_ITCH ((n+1)/2); > scratch = mpn_nhgcd_itch ((n+1)/2); > > /* Space needed for mpn_ngcd_matrix_adjust */ > if (scratch < 2*n) > scratch = 2*n; > > TMP_MARK; > > if (an + 1 > init_scratch + scratch) > tp = TMP_ALLOC_LIMBS (an + 1); > else > tp = TMP_ALLOC_LIMBS (init_scratch + scratch); > > if (an > n) > { > mp_ptr rp = tp; > mp_ptr qp = rp + n; > > mpn_tdiv_qr (qp, rp, 0, ap, an, bp, n); > MPN_COPY (ap, rp, n); > an = n; > MPN_NORMALIZE (ap, an); > if (an == 0) > { > MPN_COPY (gp, bp, n); > TMP_FREE; > return n; > } > } > > while (ABOVE_THRESHOLD (n, NGCD_THRESHOLD)) > { > struct ngcd_matrix M; > mp_size_t p = n/2; > mp_size_t nn; > > mpn_ngcd_matrix_init (&M, n - p, tp); > nn = mpn_nhgcd (ap + p, bp + p, n - p, &M, tp + init_scratch); > if (nn > 0) > /* Needs 2*(p + M->n) <= 2*(floor(n/2) + ceil(n/2) - 1) > = 2(n-1) */ > n = mpn_ngcd_matrix_adjust (&M, p + nn, ap, bp, p, tp + init_scratch); > > else > { > mp_size_t gn; > n = mpn_ngcd_subdiv_step (gp, &gn, ap, bp, n, tp); > if (n == 0) > { > TMP_FREE; > return gn; > } > } > } > > ASSERT (ap[n-1] > 0 || bp[n-1] > 0); > #if 0 > /* FIXME: We may want to use lehmer on some systems. */ > n = mpn_ngcd_lehmer (gp, ap, bp, n, tp); > > TMP_FREE; > return n; > #endif > > if (ap[n-1] < bp[n-1]) > MP_PTR_SWAP (ap, bp); > > an = n; > MPN_NORMALIZE (bp, n); > > if (n == 0) > { > MPN_COPY (gp, ap, an); > TMP_FREE; > return an; > } > > if (EVEN_P (bp[0])) > { > /* Then a must be odd (since the calling convention implies that > there's no common factor of 2) */ > ASSERT (!EVEN_P (ap[0])); > > while (bp[0] == 0) > { > bp++; > n--; > } > > if (EVEN_P(bp[0])) > { > int count; > count_trailing_zeros (count, bp[0]); > ASSERT_NOCARRY (mpn_rshift (bp, bp, n, count)); > n -= (bp[n-1] == 0); > } > } > > TMP_FREE; > return mpn_basic_gcd (gp, ap, an, bp, n); > } > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "mpir-devel" group. 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