139 lines
3.7 KiB
C
139 lines
3.7 KiB
C
/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2010 Fredrik Johansson
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******************************************************************************/
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#include "arith.h"
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static void
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_rising_factorial(fmpz * res, slong a, slong b, slong trunc)
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{
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const slong span = b - a;
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switch (span)
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{
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case 0:
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fmpz_one(res);
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break;
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case 1:
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fmpz_set_ui(res, a);
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if (trunc > 1) fmpz_one(res+1);
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break;
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case 2:
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fmpz_set_ui(res, a);
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fmpz_mul_ui(res, res, a + UWORD(1));
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if (trunc > 1)
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{
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fmpz_set_ui(res+1, 2*a + UWORD(1));
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if (trunc > 2) fmpz_one(res+2);
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}
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break;
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case 3:
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fmpz_set_ui(res, a);
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fmpz_mul_ui(res, res, a + UWORD(1));
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fmpz_mul_ui(res, res, a + UWORD(2));
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if (trunc > 1)
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{
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fmpz_set_ui(res+1, 3*a);
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fmpz_mul_ui(res+1, res+1, a + UWORD(2));
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fmpz_add_ui(res+1, res+1, 2);
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if (trunc > 2)
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{
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fmpz_set_ui(res+2, 3*(a+1));
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if (trunc > 3)
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fmpz_one(res+3);
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}
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}
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break;
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default:
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{
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const slong mid = (a + b) / 2;
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const int chk = (b - a + 1 < trunc); /* i.e. nprod < trunc */
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const slong nleft = chk ? mid - a + 1 : trunc;
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const slong nright = chk ? b - mid + 1 : trunc;
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fmpz *left = _fmpz_vec_init(nleft);
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fmpz *right = _fmpz_vec_init(nright);
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_rising_factorial(left, a, mid, trunc);
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_rising_factorial(right, mid, b, trunc);
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if (chk)
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_fmpz_poly_mul(res, right, nright, left, nleft);
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else
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_fmpz_poly_mullow(res, left, nleft, right, nright, trunc);
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_fmpz_vec_clear(left, nleft);
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_fmpz_vec_clear(right, nright);
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}
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}
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}
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void
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arith_stirling_number_1u(fmpz_t s, slong n, slong k)
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{
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/* Various special cases
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TODO: factorials, binomial coefficients, harmonic numbers ... */
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if (k < 1)
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{
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fmpz_set_ui(s, (n == 0) & (k == 0));
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}
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if (k >= n)
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{
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fmpz_set_ui(s, n == k);
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}
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else
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{
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fmpz *tmp = _fmpz_vec_init(k+1);
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_rising_factorial(tmp, 0, n, k+1);
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fmpz_set(s, tmp+k);
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_fmpz_vec_clear(tmp, k+1);
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}
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}
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void
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arith_stirling_number_1(fmpz_t s, slong n, slong k)
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{
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arith_stirling_number_1u(s, n, k);
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if ((n + k) % 2)
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fmpz_neg(s, s);
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}
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void
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arith_stirling_number_1u_vec(fmpz * row, slong n, slong klen)
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{
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if (klen > 0)
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_rising_factorial(row, 0, n, klen);
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}
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void
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arith_stirling_number_1_vec(fmpz * row, slong n, slong klen)
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{
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slong k;
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arith_stirling_number_1u_vec(row, n, klen);
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for (k = (n + 1) % 2; k < klen; k += 2)
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fmpz_neg(row + k, row + k);
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}
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