Great! Torbjorn's patch is clearly licensed v3+, so we cannot use it as eMPIRe is LGPL v2+.
Bill. 2008/12/24 <ja...@njkfrudils.plus.com>: > > 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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