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Diffstat (limited to 'rts/gmp/mpn/generic/gcd.c')
| -rw-r--r-- | rts/gmp/mpn/generic/gcd.c | 414 |
1 files changed, 414 insertions, 0 deletions
diff --git a/rts/gmp/mpn/generic/gcd.c b/rts/gmp/mpn/generic/gcd.c new file mode 100644 index 0000000000..059e219a06 --- /dev/null +++ b/rts/gmp/mpn/generic/gcd.c @@ -0,0 +1,414 @@ +/* mpn/gcd.c: mpn_gcd for gcd of two odd integers. + +Copyright (C) 1991, 1993, 1994, 1995, 1996, 1997, 1998, 2000 Free Software +Foundation, Inc. + +This file is part of the GNU MP Library. + +The GNU MP Library is free software; you can redistribute it and/or modify +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation; either version 2.1 of the License, or (at your +option) any later version. + +The GNU MP Library is distributed in the hope that it will be useful, but +WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY +or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public +License for more details. + +You should have received a copy of the GNU Lesser General Public License +along with the GNU MP Library; see the file COPYING.LIB. If not, write to +the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, +MA 02111-1307, USA. */ + +/* Integer greatest common divisor of two unsigned integers, using + the accelerated algorithm (see reference below). + + mp_size_t mpn_gcd (up, usize, vp, vsize). + + 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 (kweber@mat.ufrgs.br, kweber@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. */ + +#include "gmp.h" +#include "gmp-impl.h" +#include "longlong.h" + +/* 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 < BITS_PER_MP_LIMB. */ +enum + { + BMOD_THRESHOLD = BITS_PER_MP_LIMB/2 + }; + + +/* Use binary algorithm to compute V <-- GCD (V, U) for usize, vsize == 2. + Both U and V must be odd. */ +static __gmp_inline mp_size_t +#if __STDC__ +gcd_2 (mp_ptr vp, mp_srcptr up) +#else +gcd_2 (vp, up) + mp_ptr vp; + mp_srcptr up; +#endif +{ + 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 -= v0; + count_trailing_zeros (r, u0); + u0 = u1 << (BITS_PER_MP_LIMB - r) | u0 >> r; + u1 >>= r; + } + else /* u1 < v1. */ + { + v1 -= u1 + (v0 < u0), v0 -= u0; + count_trailing_zeros (r, v0); + v0 = v1 << (BITS_PER_MP_LIMB - r) | 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^BITS_PER_MP_LIMB such that there exists + 0 < |D| < 2^BITS_PER_MP_LIMB, and N == D * C mod 2^(2*BITS_PER_MP_LIMB). + In the reference article, D was computed along with N, but it is better to + compute D separately as D <-- N / C mod 2^(BITS_PER_MP_LIMB + 1), treating + the result as a twos' complement signed integer. + + Initialize N1 to C mod 2^(2*BITS_PER_MP_LIMB). According to the reference + article, N2 should be initialized to 2^(2*BITS_PER_MP_LIMB), but we use + 2^(2*BITS_PER_MP_LIMB) - 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. */ + +static +#if ! defined (__i386__) +__gmp_inline /* don't inline this for the x86 */ +#endif +mp_limb_t +#if __STDC__ +find_a (mp_srcptr cp) +#else +find_a (cp) + mp_srcptr cp; +#endif +{ + unsigned long int leading_zero_bits = 0; + + mp_limb_t n1_l = cp[0]; /* N1 == n1_h * 2^BITS_PER_MP_LIMB + n1_l. */ + mp_limb_t n1_h = cp[1]; + + mp_limb_t n2_l = -n1_l; /* N2 == n2_h * 2^BITS_PER_MP_LIMB + n2_l. */ + mp_limb_t n2_h = ~n1_h; + + /* Main loop. */ + while (n2_h) /* While N2 >= 2^BITS_PER_MP_LIMB. */ + { + /* N1 <-- N1 % N2. */ + if ((MP_LIMB_T_HIGHBIT >> leading_zero_bits & n2_h) == 0) + { + unsigned long int i; + count_leading_zeros (i, n2_h); + i -= leading_zero_bits, leading_zero_bits += i; + n2_h = n2_h<<i | n2_l>>(BITS_PER_MP_LIMB - i), n2_l <<= i; + do + { + if (n1_h > n2_h || (n1_h == n2_h && n1_l >= n2_l)) + n1_h -= n2_h + (n1_l < n2_l), n1_l -= n2_l; + n2_l = n2_l>>1 | n2_h<<(BITS_PER_MP_LIMB - 1), n2_h >>= 1; + i -= 1; + } + while (i); + } + if (n1_h > n2_h || (n1_h == n2_h && n1_l >= n2_l)) + n1_h -= n2_h + (n1_l < n2_l), n1_l -= n2_l; + + MP_LIMB_T_SWAP (n1_h, n2_h); + MP_LIMB_T_SWAP (n1_l, n2_l); + } + + return n2_l; +} + +mp_size_t +#if __STDC__ +mpn_gcd (mp_ptr gp, mp_ptr up, mp_size_t usize, mp_ptr vp, mp_size_t vsize) +#else +mpn_gcd (gp, up, usize, vp, vsize) + mp_ptr gp; + mp_ptr up; + mp_size_t usize; + mp_ptr vp; + mp_size_t vsize; +#endif +{ + mp_ptr orig_vp = vp; + mp_size_t orig_vsize = vsize; + int binary_gcd_ctr; /* Number of times binary gcd will execute. */ + TMP_DECL (marker); + + TMP_MARK (marker); + + /* 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 = usize * BITS_PER_MP_LIMB - d; + count_leading_zeros (vbitsize, vp[vsize-1]); + vbitsize = vsize * BITS_PER_MP_LIMB - 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 /= BITS_PER_MP_LIMB, 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] & MP_LIMB_T_HIGHBIT) /* U < 0; take twos' compl. */ + { + mp_size_t i; + anchor_up[0] = -up[0]; + for (i = 1; i < usize; i++) + anchor_up[i] = ~up[i]; + 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 = vsize * BITS_PER_MP_LIMB - vbitsize; + d = d - vbitsize + 1; + + if (d > BMOD_THRESHOLD) /* Bmod reduction. */ + { + up[usize++] = 0; + mpn_bdivmod (up, up, usize, vp, vsize, d); + d /= BITS_PER_MP_LIMB, up += d, usize -= d; + } + else /* Kary reduction. */ + { + mp_limb_t bp[2], cp[2]; + + /* C <-- V/U mod 2^(2*BITS_PER_MP_LIMB). */ + { + mp_limb_t u_inv, hi, lo; + modlimb_invert (u_inv, up[0]); + cp[0] = vp[0] * u_inv; + umul_ppmm (hi, lo, cp[0], up[0]); + cp[1] = (vp[1] - hi - cp[0] * up[1]) * u_inv; + } + + /* U <-- find_a (C) * U. */ + up[usize] = mpn_mul_1 (up, up, usize, find_a (cp)); + usize++; + + /* B <-- A/C == U/V mod 2^(BITS_PER_MP_LIMB + 1). + bp[0] <-- U/V mod 2^BITS_PER_MP_LIMB and + bp[1] <-- ( (U - bp[0] * V)/2^BITS_PER_MP_LIMB ) / 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; + umul_ppmm (hi, lo, bp[0], vp[0]); + bp[1] = (up[1] + hi + (bp[0]&vp[1])) & 1; + } + + up[usize++] = 0; + if (bp[1]) /* B < 0: U <-- U + (-B) * V. */ + { + mp_limb_t c = mpn_addmul_1 (up, vp, vsize, -bp[0]); + 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); + + /* 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; + + /* Finish up with the binary algorithm. Executes once or twice. */ + for ( ; binary_gcd_ctr--; up = orig_vp, usize = orig_vsize) + { + if (usize > 2) /* First make U close to V in size. */ + { + unsigned long int vbitsize, d; + count_leading_zeros (d, up[usize-1]); + d = usize * BITS_PER_MP_LIMB - d; + count_leading_zeros (vbitsize, vp[vsize-1]); + vbitsize = vsize * BITS_PER_MP_LIMB - 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)BITS_PER_MP_LIMB, 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. */ + } + +done: + if (vp != gp) + MPN_COPY (gp, vp, vsize); + TMP_FREE (marker); + return vsize; +} |