On Wednesday 24 December 2008 00:44:22 Bill Hart wrote: > Times seem great for GCD. Just some build issues to fix and we're done! > > Oh and I need to fix the perfect power bug. >
I've got a fix , but I would like to check it some more tomorrow. Jason > Bill. > > 2008/12/24 Bill Hart <goodwillh...@googlemail.com>: > > On sage.math: > > > > cd tune > > make tune > > > > ./.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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