Likewise for me make try is running fine. I will leave it running overnight.
Bill. 2008/12/24 <ja...@njkfrudils.plus.com>: > > On Wednesday 24 December 2008 00:31:50 Bill Hart wrote: >> 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 > > On my K8-linux same problem with make speed and tune > > ./configure && make && make check passes OK , and I got bored running ./try > mpn_gcd :) > > get this warning from the build though > > ngcd.c: In function 'mpn_ngcd': > ngcd.c:75: warning: implicit declaration of function 'mpn_basic_gcd' > > > gcc -std=gnu99 -DHAVE_CONFIG_H -I. -I.. -D__GMP_WITHIN_GMP -I.. -O2 -m64 > -march=k8 -mtune=k8 -c > gcd.c -fPIC -DPIC -o .libs/gcd.o > gcd.c: In function 'mpz_rgcd': > gcd.c:167: warning: implicit declaration of function 'mpn_rgcd' > gcd.c: In function 'mpz_bgcd': > gcd.c:171: warning: implicit declaration of function 'mpn_bgcd' > gcd.c: In function 'mpz_sgcd': > gcd.c:175: warning: implicit declaration of function 'mpn_sgcd' > gcd.c: In function 'mpz_ngcd': > gcd.c:179: warning: implicit declaration of function 'mpn_ngcd' > > > ./configure --enable-alloca=debug --enable-assert && make && make check > passes OK > > but > > ./configure --enable-alloca=debug --enable-assert --enable-nails=2 && make && > make check > > PASS: t-mul_i > PASS: t-tdiv > PASS: t-tdiv_ui > PASS: t-fdiv > PASS: t-fdiv_ui > PASS: t-cdiv_ui > nhgcd2.c:206: GNU MP assertion failed: h0 == h1 > /bin/sh: line 4: 31599 Aborted ${dir}$tst > FAIL: t-gcd > PASS: t-gcd_ui > nhgcd2.c:206: GNU MP assertion failed: h0 == h1 > /bin/sh: line 4: 31647 Aborted ${dir}$tst > FAIL: t-lcm > PASS: dive > PASS: dive_ui > PASS: t-sqrtrem > PASS: convert > PASS: io > > >> >> 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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