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/*
Copyright (C) 2011 Fredrik Johansson
Copyright (C) 2020-2021 William Hart
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "ulong_extras.h"
#include "fmpz.h"
#include "fmpz_vec.h"
#include "fmpz_mat.h"
#define XX(ii,jj) fmpz_mat_entry(X,(ii),(jj))
#define XXx(ii,jj) fmpz_mat_entry(Xx,(ii),(jj))
#define BB(ii,jj) fmpz_mat_entry(B,(ii),(jj))
#define LU(ii,jj) fmpz_mat_entry(FFLU,(ii),(jj))
#define r_shift(in, c) (((c) == FLINT_BITS) ? WORD(0) : ((in) >> (c)))
static void
fmpz_mat_set_perm(fmpz_mat_t X, const slong * perm, const fmpz_mat_t B)
{
if (X == B)
{
/* Not implemented */
flint_throw(FLINT_ERROR, "(%s): Not implemented\n", __func__);
}
else
{
slong i, j;
if (perm == NULL)
flint_throw(FLINT_ERROR, "(%s): perm == NULL\n", __func__);
for (i = 0; i < fmpz_mat_nrows(B); i++)
for (j = 0; j < fmpz_mat_ncols(B); j++)
fmpz_set(fmpz_mat_entry(X, i, j),
fmpz_mat_entry(B, perm[i], j));
}
}
int
fmpz_mat_solve_fflu_precomp(fmpz_mat_t X,
const slong * perm,
const fmpz_mat_t FFLU, const fmpz_mat_t B)
{
fmpz_t T;
slong c, i, j, k, l, m, n, rnk, norm = 0;
ulong p1h, p1m, p1l, p2h, p2m, p2l, uden = 0, dinv = 0, quo;
ulong FLINT_SET_BUT_UNUSED(rem);
slong fbits = fmpz_mat_max_bits(FFLU);
slong bbits = fmpz_mat_max_bits(B);
int small = FLINT_ABS(fbits) <= SMALL_FMPZ_BITCOUNT_MAX
&& FLINT_ABS(bbits) <= SMALL_FMPZ_BITCOUNT_MAX;
int sgn, dsgn = 0, den1 = 0, work_to_do, flag = 1;
fmpz_mat_t Xx;
fmpz * diag;
slong * piv;
n = B->r;
m = B->c;
c = FFLU->c;
fmpz_init(T);
fmpz_mat_init(Xx, B->r, B->c);
fmpz_mat_set_perm(Xx, perm, B);
diag = _fmpz_vec_init(n);
piv = (slong *) flint_malloc(n*sizeof(slong));
rnk = 0;
for (i = 0, l = 0; i < n; i++, l++)
{
while (l < c && fmpz_is_zero(LU(i, l)))
l++;
piv[i] = l;
if (l < c)
{
fmpz_set(diag + i, LU(i, l));
rnk += 1;
}
}
for (k = 0; k < m; k++)
{
/* Fraction-free forward substitution */
for (i = 0; i < n - 1; i++)
{
if (small)
{
den1 = 0;
if (i > 0)
{
uden = FLINT_ABS((slong)(diag[i - 1]));
dsgn = 0 > (slong)(diag[i - 1]);
if (uden != 0) /* see #1029 */
{
norm = flint_clz(uden);
dinv = n_preinvert_limb_prenorm(uden << norm);
} else
dinv = 0;
den1 = fmpz_is_one(diag + i - 1);
}
work_to_do = (!den1 || !fmpz_is_zero(XXx(i, k)) ||
!fmpz_is_one(diag + i));
if (work_to_do)
{
for (j = i + 1; j < n; j++)
{
if (i < c && piv[i] < c)
{
smul_ppmm(p1h, p1l, *XXx(j, k), diag[i]);
smul_ppmm(p2h, p2l, *LU(j, piv[i]), *XXx(i, k));
sub_ddmmss(p1h, p1l, p1h, p1l, p2h, p2l);
sgn = 0 > (slong) p1h;
if (sgn) /* take absolute value */
sub_ddmmss(p1h, p1l, UWORD(0), UWORD(0), p1h, p1l);
if (i > 0 && !den1 && i < c && piv[i - 1] < c)
{
if (p1h >= uden)
{
fmpz_set_uiui(XXx(j, k), p1h, p1l);
if (sgn)
fmpz_neg(XXx(j, k), XXx(j, k));
if (i < c && piv[i - 1] < c)
{
flag = fmpz_divides(XXx(j, k), XXx(j, k), diag + i - 1);
if (!flag)
goto cleanup;
}
small = 0;
} else
{
udiv_qrnnd_preinv(quo, rem,
(p1h << norm) + r_shift(p1l, (FLINT_BITS - norm)),
p1l << norm, uden << norm, dinv);
flag = rem == 0;
if (!flag)
goto cleanup;
if (sgn ^ dsgn)
fmpz_neg_ui(XXx(j, k), quo);
else
fmpz_set_ui(XXx(j, k), quo);
if (quo > COEFF_MAX)
small = 0;
}
} else
{
if (p1h > 0)
{
fmpz_set_uiui(XXx(j, k), p1h, p1l);
small = 0;
} else
{
fmpz_set_ui(XXx(j, k), p1l);
if (p1l > COEFF_MAX)
small = 0;
}
if (sgn)
fmpz_neg(XXx(j, k), XXx(j, k));
}
} else if (i > 0)
{
if (i < c && piv[i - 1] < c)
{
flag = fmpz_divides(XXx(j, k), XXx(j, k), diag + i - 1);
if (!flag)
goto cleanup;
}
}
}
}
} else
{
for (j = i + 1; j < n; j++)
{
if (i < c && piv[i] < c)
{
fmpz_mul(XXx(j, k), XXx(j, k), diag + i);
fmpz_mul(T, LU(j, piv[i]), XXx(i, k));
fmpz_sub(XXx(j, k), XXx(j, k), T);
}
if (i > 0)
{
if (i < c && piv[i - 1] < c)
{
flag = fmpz_divides(XXx(j, k), XXx(j, k), diag + i - 1);
if (!flag)
goto cleanup;
}
}
}
}
}
l = rnk - 1;
/* Fraction-free back substitution */
for (i = c - 1; i >= 0; i--)
{
if (l > -1 && i == piv[l])
{
if (small)
{
if (rnk != 0)
smul_ppmm(p1m, p1l, *XXx(l, k), diag[rnk - 1]);
else
{
p1l = *XXx(l, k);
p1m = FLINT_SIGN_EXT(p1l);
}
p1h = FLINT_SIGN_EXT(p1m);
uden = FLINT_ABS((slong)(diag[l]));
dsgn = 0 > (slong)(diag[l]);
if (uden != 0) /* see #1029 */
{
norm = flint_clz(uden);
dinv = n_preinvert_limb_prenorm(uden << norm);
} else
dinv = 0;
for (j = piv[l] + 1; j < c; j++)
{
if (!fmpz_is_zero(LU(l, j)))
{
smul_ppmm(p2m, p2l, *XX(j, k), *LU(l, j));
p2h = FLINT_SIGN_EXT(p2m);
sub_dddmmmsss(p1h, p1m, p1l, p1h, p1m, p1l, p2h, p2m, p2l);
}
}
sgn = 0 > (slong) p1h;
if (sgn) /* take absolute value */
sub_dddmmmsss(p1h, p1m, p1l, UWORD(0), UWORD(0), UWORD(0), p1h, p1m, p1l);
if (p1h != 0 || p1m >= uden)
{
fmpz_set_signed_uiuiui(XX(i, k), p1h, p1m, p1l);
flag = fmpz_divides(XX(i, k), XX(i, k), diag + l);
if (!flag)
goto cleanup;
if (sgn)
fmpz_neg(XX(i, k), XX(i, k));
small = 0;
} else
{
udiv_qrnnd_preinv(quo, rem,
(p1m << norm) + r_shift(p1l, (FLINT_BITS - norm)),
p1l << norm, uden << norm, dinv);
flag = rem == 0;
if (!flag)
goto cleanup;
if (sgn ^ dsgn)
fmpz_neg_ui(XX(i, k), quo);
else
fmpz_set_ui(XX(i, k), quo);
if (quo > COEFF_MAX)
small = 0;
}
} else
{
if (rnk != 0)
fmpz_mul(XX(i, k), XXx(l, k), diag + rnk - 1);
else
fmpz_set(XX(i, k), XXx(l, k));
for (j = piv[l] + 1; j < c; j++)
{
fmpz_mul(T, XX(j, k), LU(l, j));
fmpz_sub(XX(i, k), XX(i, k), T);
}
flag = fmpz_divides(XX(i, k), XX(i, k), diag + l);
if (!flag)
goto cleanup;
}
l--;
} else
fmpz_zero(XX(i, k));
}
}
cleanup:
_fmpz_vec_clear(diag, n);
flint_free(piv);
fmpz_mat_clear(Xx);
fmpz_clear(T);
return flag;
}