X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_polynomial.c;h=050f666cebc2496b1a3e2cba52bfe3a1b277ac22;hb=e87d6a05c8cc412abd7c1061cf9cb577f62d6ad6;hp=1bfff5ce551b3747cdd601fafc3500023e548c03;hpb=01bf1a9d67e594d91d8fdf8eaff78218d01d189b;p=platform%2Fupstream%2Fisl.git diff --git a/isl_polynomial.c b/isl_polynomial.c index 1bfff5c..050f666 100644 --- a/isl_polynomial.c +++ b/isl_polynomial.c @@ -9,12 +9,15 @@ */ #include +#include +#include #include #include #include #include #include #include +#include static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type) { @@ -238,6 +241,20 @@ __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx) return &cst->up; } +__isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx) +{ + struct isl_upoly_cst *cst; + + cst = isl_upoly_cst_alloc(ctx); + if (!cst) + return NULL; + + isl_int_set_si(cst->n, 1); + isl_int_set_si(cst->d, 1); + + return &cst->up; +} + __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx) { struct isl_upoly_cst *cst; @@ -322,6 +339,7 @@ __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx, __isl_give isl_qpolynomial *isl_qpolynomial_reset_dim( __isl_take isl_qpolynomial *qp, __isl_take isl_dim *dim) { + qp = isl_qpolynomial_cow(qp); if (!qp || !dim) goto error; @@ -941,6 +959,67 @@ void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp) free(qp); } +__isl_give struct isl_upoly *isl_upoly_pow(isl_ctx *ctx, int pos, int power) +{ + int i; + struct isl_upoly *up; + struct isl_upoly_rec *rec; + struct isl_upoly_cst *cst; + + rec = isl_upoly_alloc_rec(ctx, pos, 1 + power); + if (!rec) + return NULL; + for (i = 0; i < 1 + power; ++i) { + rec->p[i] = isl_upoly_zero(ctx); + if (!rec->p[i]) + goto error; + rec->n++; + } + cst = isl_upoly_as_cst(rec->p[power]); + isl_int_set_si(cst->n, 1); + + return &rec->up; +error: + isl_upoly_free(&rec->up); + return NULL; +} + +/* r array maps original positions to new positions. + */ +static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up, + int *r) +{ + int i; + struct isl_upoly_rec *rec; + struct isl_upoly *base; + struct isl_upoly *res; + + if (isl_upoly_is_cst(up)) + return up; + + rec = isl_upoly_as_rec(up); + if (!rec) + goto error; + + isl_assert(up->ctx, rec->n >= 1, goto error); + + base = isl_upoly_pow(up->ctx, r[up->var], 1); + res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r); + + for (i = rec->n - 2; i >= 0; --i) { + res = isl_upoly_mul(res, isl_upoly_copy(base)); + res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r)); + } + + isl_upoly_free(base); + isl_upoly_free(up); + + return res; +error: + isl_upoly_free(up); + return NULL; +} + static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2) { int n_row, n_col; @@ -1005,49 +1084,87 @@ static int div_sort_cmp(const void *p1, const void *p2) return cmp_row(i1->div, i1->row, i2->row); } -static __isl_give isl_mat *sort_divs(__isl_take isl_mat *div) +/* Sort divs and remove duplicates. + */ +static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp) { int i; + int skip; + int len; struct isl_div_sort_info *array = NULL; - int *pos = NULL; + int *pos = NULL, *at = NULL; + int *reordering = NULL; + unsigned div_pos; - if (!div) + if (!qp) return NULL; - if (div->n_row <= 1) - return div; + if (qp->div->n_row <= 1) + return qp; - array = isl_alloc_array(div->ctx, struct isl_div_sort_info, div->n_row); - pos = isl_alloc_array(div->ctx, int, div->n_row); - if (!array || !pos) + div_pos = isl_dim_total(qp->dim); + + array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info, + qp->div->n_row); + pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row); + at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row); + len = qp->div->n_col - 2; + reordering = isl_alloc_array(qp->div->ctx, int, len); + if (!array || !pos || !at || !reordering) goto error; - for (i = 0; i < div->n_row; ++i) { - array[i].div = div; + for (i = 0; i < qp->div->n_row; ++i) { + array[i].div = qp->div; array[i].row = i; pos[i] = i; + at[i] = i; } - qsort(array, div->n_row, sizeof(struct isl_div_sort_info), + qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info), div_sort_cmp); - for (i = 0; i < div->n_row; ++i) { - int t; + for (i = 0; i < div_pos; ++i) + reordering[i] = i; + + for (i = 0; i < qp->div->n_row; ++i) { if (pos[array[i].row] == i) continue; - div = isl_mat_cow(div); - div = isl_mat_swap_rows(div, i, pos[array[i].row]); - t = pos[array[i].row]; - pos[array[i].row] = pos[i]; - pos[i] = t; + qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]); + pos[at[i]] = pos[array[i].row]; + at[pos[array[i].row]] = at[i]; + at[i] = array[i].row; + pos[array[i].row] = i; + } + + skip = 0; + for (i = 0; i < len - div_pos; ++i) { + if (i > 0 && + isl_seq_eq(qp->div->row[i - skip - 1], + qp->div->row[i - skip], qp->div->n_col)) { + qp->div = isl_mat_drop_rows(qp->div, i - skip, 1); + qp->div = isl_mat_drop_cols(qp->div, + 2 + div_pos + i - skip, 1); + skip++; + } + reordering[div_pos + array[i].row] = div_pos + i - skip; } + qp->upoly = reorder(qp->upoly, reordering); + + if (!qp->upoly || !qp->div) + goto error; + + free(at); + free(pos); free(array); + free(reordering); - return div; + return qp; error: + free(at); free(pos); free(array); - isl_mat_free(div); + free(reordering); + isl_qpolynomial_free(qp); return NULL; } @@ -1212,6 +1329,14 @@ error: return NULL; } +__isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain( + __isl_keep isl_set *dom, + __isl_take isl_qpolynomial *qp1, + __isl_take isl_qpolynomial *qp2) +{ + return isl_qpolynomial_add(qp1, qp2); +} + __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2) { @@ -1268,6 +1393,11 @@ __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim) return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx)); } +__isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim) +{ + return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx)); +} + __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim) { return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx)); @@ -1480,31 +1610,6 @@ void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d) upoly_update_den(qp->upoly, d); } -__isl_give struct isl_upoly *isl_upoly_pow(isl_ctx *ctx, int pos, int power) -{ - int i; - struct isl_upoly *up; - struct isl_upoly_rec *rec; - struct isl_upoly_cst *cst; - - rec = isl_upoly_alloc_rec(ctx, pos, 1 + power); - if (!rec) - return NULL; - for (i = 0; i < 1 + power; ++i) { - rec->p[i] = isl_upoly_zero(ctx); - if (!rec->p[i]) - goto error; - rec->n++; - } - cst = isl_upoly_as_cst(rec->p[power]); - isl_int_set_si(cst->n, 1); - - return &rec->up; -error: - isl_upoly_free(&rec->up); - return NULL; -} - __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_dim *dim, int pos, int power) { @@ -1536,28 +1641,52 @@ error: return NULL; } +/* Remove common factor of non-constant terms and denominator. + */ +static void normalize_div(__isl_keep isl_qpolynomial *qp, int div) +{ + isl_ctx *ctx = qp->div->ctx; + unsigned total = qp->div->n_col - 2; + + isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd); + isl_int_gcd(ctx->normalize_gcd, + ctx->normalize_gcd, qp->div->row[div][0]); + if (isl_int_is_one(ctx->normalize_gcd)) + return; + + isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2, + ctx->normalize_gcd, total); + isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0], + ctx->normalize_gcd); + isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1], + ctx->normalize_gcd); +} + __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div, int power) { struct isl_qpolynomial *qp = NULL; struct isl_upoly_rec *rec; struct isl_upoly_cst *cst; - int i; + int i, d; int pos; if (!div) return NULL; - isl_assert(div->ctx, div->bmap->n_div == 1, goto error); - pos = isl_dim_total(div->bmap->dim); + d = div->line - div->bmap->div; + + pos = isl_dim_total(div->bmap->dim) + d; rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power); - qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap), 1, - &rec->up); + qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap), + div->bmap->n_div, &rec->up); if (!qp) goto error; - isl_seq_cpy(qp->div->row[0], div->line[0], qp->div->n_col - 1); - isl_int_set_si(qp->div->row[0][qp->div->n_col - 1], 0); + for (i = 0; i < div->bmap->n_div; ++i) { + isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col); + normalize_div(qp, i); + } for (i = 0; i < 1 + power; ++i) { rec->p[i] = isl_upoly_zero(div->ctx); @@ -1711,6 +1840,22 @@ error: return NULL; } +__isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name( + __isl_take isl_qpolynomial *qp, + enum isl_dim_type type, unsigned pos, const char *s) +{ + qp = isl_qpolynomial_cow(qp); + if (!qp) + return NULL; + qp->dim = isl_dim_set_name(qp->dim, type, pos, s); + if (!qp->dim) + goto error; + return qp; +error: + isl_qpolynomial_free(qp); + return NULL; +} + __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims( __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned first, unsigned n) @@ -1750,78 +1895,350 @@ error: return NULL; } -#undef PW -#define PW isl_pw_qpolynomial -#undef EL -#define EL isl_qpolynomial -#undef IS_ZERO -#define IS_ZERO is_zero -#undef FIELD -#define FIELD qp -#undef ADD -#define ADD(d,e1,e2) isl_qpolynomial_add(e1,e2) +__isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up, + unsigned first, unsigned n, __isl_keep struct isl_upoly **subs) +{ + int i; + struct isl_upoly_rec *rec; + struct isl_upoly *base, *res; -#include + if (!up) + return NULL; -#undef UNION -#define UNION isl_union_pw_qpolynomial -#undef PART -#define PART isl_pw_qpolynomial -#undef PARTS -#define PARTS pw_qpolynomial + if (isl_upoly_is_cst(up)) + return up; -#include + if (up->var < first) + return up; -int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp) -{ - if (!pwqp) - return -1; + rec = isl_upoly_as_rec(up); + if (!rec) + goto error; - if (pwqp->n != -1) - return 0; + isl_assert(up->ctx, rec->n >= 1, goto error); - if (!isl_set_fast_is_universe(pwqp->p[0].set)) - return 0; + if (up->var >= first + n) + base = isl_upoly_pow(up->ctx, up->var, 1); + else + base = isl_upoly_copy(subs[up->var - first]); - return isl_qpolynomial_is_one(pwqp->p[0].qp); -} + res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs); + for (i = rec->n - 2; i >= 0; --i) { + struct isl_upoly *t; + t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs); + res = isl_upoly_mul(res, isl_upoly_copy(base)); + res = isl_upoly_sum(res, t); + } -__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul( - __isl_take isl_pw_qpolynomial *pwqp1, - __isl_take isl_pw_qpolynomial *pwqp2) -{ - int i, j, n; - struct isl_pw_qpolynomial *res; - isl_set *set; + isl_upoly_free(base); + isl_upoly_free(up); + + return res; +error: + isl_upoly_free(up); + return NULL; +} - if (!pwqp1 || !pwqp2) - goto error; +__isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f, + isl_int denom, unsigned len) +{ + int i; + struct isl_upoly *up; - isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim), - goto error); + isl_assert(ctx, len >= 1, return NULL); - if (isl_pw_qpolynomial_is_zero(pwqp1)) { - isl_pw_qpolynomial_free(pwqp2); - return pwqp1; - } + up = isl_upoly_rat_cst(ctx, f[0], denom); + for (i = 0; i < len - 1; ++i) { + struct isl_upoly *t; + struct isl_upoly *c; - if (isl_pw_qpolynomial_is_zero(pwqp2)) { - isl_pw_qpolynomial_free(pwqp1); - return pwqp2; - } + if (isl_int_is_zero(f[1 + i])) + continue; - if (isl_pw_qpolynomial_is_one(pwqp1)) { - isl_pw_qpolynomial_free(pwqp1); - return pwqp2; + c = isl_upoly_rat_cst(ctx, f[1 + i], denom); + t = isl_upoly_pow(ctx, i, 1); + t = isl_upoly_mul(c, t); + up = isl_upoly_sum(up, t); } - if (isl_pw_qpolynomial_is_one(pwqp2)) { - isl_pw_qpolynomial_free(pwqp2); - return pwqp1; - } + return up; +} - n = pwqp1->n * pwqp2->n; - res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n); +/* Replace the integer division identified by "div" by the polynomial "s". + * The integer division is assumed not to appear in the definition + * of any other integer divisions. + */ +static __isl_give isl_qpolynomial *substitute_div( + __isl_take isl_qpolynomial *qp, + int div, __isl_take struct isl_upoly *s) +{ + int i; + int total; + int *reordering; + + if (!qp || !s) + goto error; + + qp = isl_qpolynomial_cow(qp); + if (!qp) + goto error; + + total = isl_dim_total(qp->dim); + qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s); + if (!qp->upoly) + goto error; + + reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row); + if (!reordering) + goto error; + for (i = 0; i < total + div; ++i) + reordering[i] = i; + for (i = total + div + 1; i < total + qp->div->n_row; ++i) + reordering[i] = i - 1; + qp->div = isl_mat_drop_rows(qp->div, div, 1); + qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1); + qp->upoly = reorder(qp->upoly, reordering); + free(reordering); + + if (!qp->upoly || !qp->div) + goto error; + + isl_upoly_free(s); + return qp; +error: + isl_qpolynomial_free(qp); + isl_upoly_free(s); + return NULL; +} + +/* Replace all integer divisions [e/d] that turn out to not actually be integer + * divisions because d is equal to 1 by their definition, i.e., e. + */ +static __isl_give isl_qpolynomial *substitute_non_divs( + __isl_take isl_qpolynomial *qp) +{ + int i, j; + int total; + struct isl_upoly *s; + + if (!qp) + return NULL; + + total = isl_dim_total(qp->dim); + for (i = 0; qp && i < qp->div->n_row; ++i) { + if (!isl_int_is_one(qp->div->row[i][0])) + continue; + for (j = i + 1; j < qp->div->n_row; ++j) { + if (isl_int_is_zero(qp->div->row[j][2 + total + i])) + continue; + isl_seq_combine(qp->div->row[j] + 1, + qp->div->ctx->one, qp->div->row[j] + 1, + qp->div->row[j][2 + total + i], + qp->div->row[i] + 1, 1 + total + i); + isl_int_set_si(qp->div->row[j][2 + total + i], 0); + normalize_div(qp, j); + } + s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1, + qp->div->row[i][0], qp->div->n_col - 1); + qp = substitute_div(qp, i, s); + --i; + } + + return qp; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities( + __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq) +{ + int i, j, k; + isl_int denom; + unsigned total; + unsigned n_div; + struct isl_upoly *up; + + if (!eq) + goto error; + if (eq->n_eq == 0) { + isl_basic_set_free(eq); + return qp; + } + + qp = isl_qpolynomial_cow(qp); + if (!qp) + goto error; + qp->div = isl_mat_cow(qp->div); + if (!qp->div) + goto error; + + total = 1 + isl_dim_total(eq->dim); + n_div = eq->n_div; + isl_int_init(denom); + for (i = 0; i < eq->n_eq; ++i) { + j = isl_seq_last_non_zero(eq->eq[i], total + n_div); + if (j < 0 || j == 0 || j >= total) + continue; + + for (k = 0; k < qp->div->n_row; ++k) { + if (isl_int_is_zero(qp->div->row[k][1 + j])) + continue; + isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total, + &qp->div->row[k][0]); + normalize_div(qp, k); + } + + if (isl_int_is_pos(eq->eq[i][j])) + isl_seq_neg(eq->eq[i], eq->eq[i], total); + isl_int_abs(denom, eq->eq[i][j]); + isl_int_set_si(eq->eq[i][j], 0); + + up = isl_upoly_from_affine(qp->dim->ctx, + eq->eq[i], denom, total); + qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up); + isl_upoly_free(up); + } + isl_int_clear(denom); + + if (!qp->upoly) + goto error; + + isl_basic_set_free(eq); + + qp = substitute_non_divs(qp); + qp = sort_divs(qp); + + return qp; +error: + isl_basic_set_free(eq); + isl_qpolynomial_free(qp); + return NULL; +} + +static __isl_give isl_basic_set *add_div_constraints( + __isl_take isl_basic_set *bset, __isl_take isl_mat *div) +{ + int i; + unsigned total; + + if (!bset || !div) + goto error; + + bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row); + if (!bset) + goto error; + total = isl_basic_set_total_dim(bset); + for (i = 0; i < div->n_row; ++i) + if (isl_basic_set_add_div_constraints_var(bset, + total - div->n_row + i, div->row[i]) < 0) + goto error; + + isl_mat_free(div); + return bset; +error: + isl_mat_free(div); + isl_basic_set_free(bset); + return NULL; +} + +/* Look for equalities among the variables shared by context and qp + * and the integer divisions of qp, if any. + * The equalities are then used to eliminate variables and/or integer + * divisions from qp. + */ +__isl_give isl_qpolynomial *isl_qpolynomial_gist( + __isl_take isl_qpolynomial *qp, __isl_take isl_set *context) +{ + isl_basic_set *aff; + + if (!qp) + goto error; + if (qp->div->n_row > 0) { + isl_basic_set *bset; + context = isl_set_add_dims(context, isl_dim_set, + qp->div->n_row); + bset = isl_basic_set_universe(isl_set_get_dim(context)); + bset = add_div_constraints(bset, isl_mat_copy(qp->div)); + context = isl_set_intersect(context, + isl_set_from_basic_set(bset)); + } + + aff = isl_set_affine_hull(context); + return isl_qpolynomial_substitute_equalities(qp, aff); +error: + isl_qpolynomial_free(qp); + isl_set_free(context); + return NULL; +} + +#undef PW +#define PW isl_pw_qpolynomial +#undef EL +#define EL isl_qpolynomial +#undef IS_ZERO +#define IS_ZERO is_zero +#undef FIELD +#define FIELD qp + +#include + +#undef UNION +#define UNION isl_union_pw_qpolynomial +#undef PART +#define PART isl_pw_qpolynomial +#undef PARTS +#define PARTS pw_qpolynomial + +#include + +int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp) +{ + if (!pwqp) + return -1; + + if (pwqp->n != -1) + return 0; + + if (!isl_set_fast_is_universe(pwqp->p[0].set)) + return 0; + + return isl_qpolynomial_is_one(pwqp->p[0].qp); +} + +__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul( + __isl_take isl_pw_qpolynomial *pwqp1, + __isl_take isl_pw_qpolynomial *pwqp2) +{ + int i, j, n; + struct isl_pw_qpolynomial *res; + isl_set *set; + + if (!pwqp1 || !pwqp2) + goto error; + + isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim), + goto error); + + if (isl_pw_qpolynomial_is_zero(pwqp1)) { + isl_pw_qpolynomial_free(pwqp2); + return pwqp1; + } + + if (isl_pw_qpolynomial_is_zero(pwqp2)) { + isl_pw_qpolynomial_free(pwqp1); + return pwqp2; + } + + if (isl_pw_qpolynomial_is_one(pwqp1)) { + isl_pw_qpolynomial_free(pwqp1); + return pwqp2; + } + + if (isl_pw_qpolynomial_is_one(pwqp2)) { + isl_pw_qpolynomial_free(pwqp2); + return pwqp1; + } + + n = pwqp1->n * pwqp2->n; + res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n); for (i = 0; i < pwqp1->n; ++i) { for (j = 0; j < pwqp2->n; ++j) { @@ -1855,9 +2272,7 @@ error: __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg( __isl_take isl_pw_qpolynomial *pwqp) { - int i, j, n; - struct isl_pw_qpolynomial *res; - isl_set *set; + int i; if (!pwqp) return NULL; @@ -1866,6 +2281,8 @@ __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg( return pwqp; pwqp = isl_pw_qpolynomial_cow(pwqp); + if (!pwqp) + return NULL; for (i = 0; i < pwqp->n; ++i) { pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp); @@ -2119,32 +2536,11 @@ __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims( __isl_take isl_pw_qpolynomial *pwqp, enum isl_dim_type type, unsigned n) { - int i; - - if (n == 0) - return pwqp; - - pwqp = isl_pw_qpolynomial_cow(pwqp); - if (!pwqp) - return NULL; - - pwqp->dim = isl_dim_add(pwqp->dim, type, n); - if (!pwqp->dim) - goto error; + unsigned pos; - for (i = 0; i < pwqp->n; ++i) { - pwqp->p[i].set = isl_set_add(pwqp->p[i].set, type, n); - if (!pwqp->p[i].set) - goto error; - pwqp->p[i].qp = isl_qpolynomial_add_dims(pwqp->p[i].qp, type, n); - if (!pwqp->p[i].qp) - goto error; - } + pos = isl_pw_qpolynomial_dim(pwqp, type); - return pwqp; -error: - isl_pw_qpolynomial_free(pwqp); - return NULL; + return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n); } static int *reordering_move(isl_ctx *ctx, @@ -2180,40 +2576,6 @@ static int *reordering_move(isl_ctx *ctx, return reordering; } -static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up, - int *r) -{ - int i; - struct isl_upoly_rec *rec; - struct isl_upoly *base; - struct isl_upoly *res; - - if (isl_upoly_is_cst(up)) - return up; - - rec = isl_upoly_as_rec(up); - if (!rec) - goto error; - - isl_assert(up->ctx, rec->n >= 1, goto error); - - base = isl_upoly_pow(up->ctx, r[up->var], 1); - res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r); - - for (i = rec->n - 2; i >= 0; --i) { - res = isl_upoly_mul(res, isl_upoly_copy(base)); - res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r)); - } - - isl_upoly_free(base); - isl_upoly_free(up); - - return res; -error: - isl_upoly_free(up); - return NULL; -} - __isl_give isl_qpolynomial *isl_qpolynomial_move_dims( __isl_take isl_qpolynomial *qp, enum isl_dim_type dst_type, unsigned dst_pos, @@ -2236,9 +2598,11 @@ __isl_give isl_qpolynomial *isl_qpolynomial_move_dims( g_dst_pos -= n; qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n); - qp->div = sort_divs(qp->div); if (!qp->div) goto error; + qp = sort_divs(qp); + if (!qp) + goto error; reordering = reordering_move(qp->dim->ctx, qp->div->n_col - 2, g_dst_pos, g_src_pos, n); @@ -2260,31 +2624,6 @@ error: return NULL; } -__isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f, - isl_int denom, unsigned len) -{ - int i; - struct isl_upoly *up; - - isl_assert(ctx, len >= 1, return NULL); - - up = isl_upoly_rat_cst(ctx, f[0], denom); - for (i = 0; i < len - 1; ++i) { - struct isl_upoly *t; - struct isl_upoly *c; - - if (isl_int_is_zero(f[1 + i])) - continue; - - c = isl_upoly_rat_cst(ctx, f[1 + i], denom); - t = isl_upoly_pow(ctx, i, 1); - t = isl_upoly_mul(c, t); - up = isl_upoly_sum(up, t); - } - - return up; -} - __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim, isl_int *f, isl_int denom) { @@ -2320,62 +2659,18 @@ __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint( 1 + isl_constraint_dim(c, isl_dim_all)); if (sgn < 0) isl_int_neg(denom, denom); - isl_constraint_set_coefficient(c, type, pos, denom); - - dim = isl_dim_copy(c->bmap->dim); - - isl_int_clear(denom); - isl_constraint_free(c); - - qp = isl_qpolynomial_alloc(dim, 0, up); - if (sgn > 0) - qp = isl_qpolynomial_neg(qp); - return qp; -} - -__isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up, - unsigned first, unsigned n, __isl_keep struct isl_upoly **subs) -{ - int i; - struct isl_upoly_rec *rec; - struct isl_upoly *base, *res; - - if (!up) - return NULL; - - if (isl_upoly_is_cst(up)) - return up; - - if (up->var < first) - return up; - - rec = isl_upoly_as_rec(up); - if (!rec) - goto error; - - isl_assert(up->ctx, rec->n >= 1, goto error); - - if (up->var >= first + n) - base = isl_upoly_pow(up->ctx, up->var, 1); - else - base = isl_upoly_copy(subs[up->var - first]); - - res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs); - for (i = rec->n - 2; i >= 0; --i) { - struct isl_upoly *t; - t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs); - res = isl_upoly_mul(res, isl_upoly_copy(base)); - res = isl_upoly_sum(res, t); - } + isl_constraint_set_coefficient(c, type, pos, denom); - isl_upoly_free(base); - isl_upoly_free(up); - - return res; -error: - isl_upoly_free(up); - return NULL; -} + dim = isl_dim_copy(c->bmap->dim); + + isl_int_clear(denom); + isl_constraint_free(c); + + qp = isl_qpolynomial_alloc(dim, 0, up); + if (sgn > 0) + qp = isl_qpolynomial_neg(qp); + return qp; +} /* For each 0 <= i < "n", replace variable "first" + i of type "type" * in "qp" by subs[i]. @@ -2430,32 +2725,6 @@ error: return NULL; } -__isl_give isl_basic_set *add_div_constraints(__isl_take isl_basic_set *bset, - __isl_take isl_mat *div) -{ - int i; - unsigned total; - - if (!bset || !div) - goto error; - - bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row); - if (!bset) - goto error; - total = isl_basic_set_total_dim(bset); - for (i = 0; i < div->n_row; ++i) - if (isl_basic_set_add_div_constraints_var(bset, - total - div->n_row + i, div->row[i]) < 0) - goto error; - - isl_mat_free(div); - return bset; -error: - isl_mat_free(div); - isl_basic_set_free(bset); - return NULL; -} - /* Extend "bset" with extra set dimensions for each integer division * in "qp" and then call "fn" with the extended bset and the polynomial * that results from replacing each of the integer divisions by the @@ -3140,6 +3409,7 @@ __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp __isl_take isl_morph *morph) { int i; + int n_sub; isl_ctx *ctx; struct isl_upoly *up; unsigned n_div; @@ -3153,17 +3423,24 @@ __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp ctx = qp->dim->ctx; isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error); - subs = isl_calloc_array(ctx, struct isl_upoly *, morph->inv->n_row - 1); + n_sub = morph->inv->n_row - 1; + if (morph->inv->n_row != morph->inv->n_col) + n_sub += qp->div->n_row; + subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub); if (!subs) goto error; for (i = 0; 1 + i < morph->inv->n_row; ++i) subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i], morph->inv->row[0][0], morph->inv->n_col); + if (morph->inv->n_row != morph->inv->n_col) + for (i = 0; i < qp->div->n_row; ++i) + subs[morph->inv->n_row - 1 + i] = + isl_upoly_pow(ctx, morph->inv->n_col - 1 + i, 1); - qp->upoly = isl_upoly_subs(qp->upoly, 0, morph->inv->n_row - 1, subs); + qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs); - for (i = 0; 1 + i < morph->inv->n_row; ++i) + for (i = 0; i < n_sub; ++i) isl_upoly_free(subs[i]); free(subs); @@ -3228,8 +3505,7 @@ static int mul_entry(void **entry, void *user) int empty; hash = isl_dim_get_hash(pwpq->dim); - entry2 = isl_hash_table_find(data->upwqp2->dim->ctx, - &data->upwqp2->table, + entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table, hash, &has_dim, pwpq->dim, 0); if (!entry2) return 0; @@ -3259,3 +3535,437 @@ __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul( { return match_bin_op(upwqp1, upwqp2, &mul_entry); } + +/* Reorder the columns of the given div definitions according to the + * given reordering. + */ +static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div, + __isl_take isl_reordering *r) +{ + int i, j; + isl_mat *mat; + int extra; + + if (!div || !r) + goto error; + + extra = isl_dim_total(r->dim) + div->n_row - r->len; + mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra); + if (!mat) + goto error; + + for (i = 0; i < div->n_row; ++i) { + isl_seq_cpy(mat->row[i], div->row[i], 2); + isl_seq_clr(mat->row[i] + 2, mat->n_col - 2); + for (j = 0; j < r->len; ++j) + isl_int_set(mat->row[i][2 + r->pos[j]], + div->row[i][2 + j]); + } + + isl_reordering_free(r); + isl_mat_free(div); + return mat; +error: + isl_reordering_free(r); + isl_mat_free(div); + return NULL; +} + +/* Reorder the dimension of "qp" according to the given reordering. + */ +__isl_give isl_qpolynomial *isl_qpolynomial_realign( + __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r) +{ + qp = isl_qpolynomial_cow(qp); + if (!qp) + goto error; + + r = isl_reordering_extend(r, qp->div->n_row); + if (!r) + goto error; + + qp->div = reorder_divs(qp->div, isl_reordering_copy(r)); + if (!qp->div) + goto error; + + qp->upoly = reorder(qp->upoly, r->pos); + if (!qp->upoly) + goto error; + + qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim)); + + isl_reordering_free(r); + return qp; +error: + isl_qpolynomial_free(qp); + isl_reordering_free(r); + return NULL; +} + +struct isl_split_periods_data { + int max_periods; + isl_pw_qpolynomial *res; +}; + +/* Create a slice where the integer division "div" has the fixed value "v". + * In particular, if "div" refers to floor(f/m), then create a slice + * + * m v <= f <= m v + (m - 1) + * + * or + * + * f - m v >= 0 + * -f + m v + (m - 1) >= 0 + */ +static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim, + __isl_keep isl_qpolynomial *qp, int div, isl_int v) +{ + int total; + isl_basic_set *bset = NULL; + int k; + + if (!dim || !qp) + goto error; + + total = isl_dim_total(dim); + bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2); + + k = isl_basic_set_alloc_inequality(bset); + if (k < 0) + goto error; + isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total); + isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]); + + k = isl_basic_set_alloc_inequality(bset); + if (k < 0) + goto error; + isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total); + isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]); + isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]); + isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1); + + isl_dim_free(dim); + return isl_set_from_basic_set(bset); +error: + isl_basic_set_free(bset); + isl_dim_free(dim); + return NULL; +} + +static int split_periods(__isl_take isl_set *set, + __isl_take isl_qpolynomial *qp, void *user); + +/* Create a slice of the domain "set" such that integer division "div" + * has the fixed value "v" and add the results to data->res, + * replacing the integer division by "v" in "qp". + */ +static int set_div(__isl_take isl_set *set, + __isl_take isl_qpolynomial *qp, int div, isl_int v, + struct isl_split_periods_data *data) +{ + int i; + int total; + isl_set *slice; + struct isl_upoly *cst; + + slice = set_div_slice(isl_set_get_dim(set), qp, div, v); + set = isl_set_intersect(set, slice); + + if (!qp) + goto error; + + total = isl_dim_total(qp->dim); + + for (i = div + 1; i < qp->div->n_row; ++i) { + if (isl_int_is_zero(qp->div->row[i][2 + total + div])) + continue; + isl_int_addmul(qp->div->row[i][1], + qp->div->row[i][2 + total + div], v); + isl_int_set_si(qp->div->row[i][2 + total + div], 0); + } + + cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one); + qp = substitute_div(qp, div, cst); + + return split_periods(set, qp, data); +error: + isl_set_free(set); + isl_qpolynomial_free(qp); + return -1; +} + +/* Split the domain "set" such that integer division "div" + * has a fixed value (ranging from "min" to "max") on each slice + * and add the results to data->res. + */ +static int split_div(__isl_take isl_set *set, + __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max, + struct isl_split_periods_data *data) +{ + for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) { + isl_set *set_i = isl_set_copy(set); + isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp); + + if (set_div(set_i, qp_i, div, min, data) < 0) + goto error; + } + isl_set_free(set); + isl_qpolynomial_free(qp); + return 0; +error: + isl_set_free(set); + isl_qpolynomial_free(qp); + return -1; +} + +/* If "qp" refers to any integer division + * that can only attain "max_periods" distinct values on "set" + * then split the domain along those distinct values. + * Add the results (or the original if no splitting occurs) + * to data->res. + */ +static int split_periods(__isl_take isl_set *set, + __isl_take isl_qpolynomial *qp, void *user) +{ + int i; + isl_pw_qpolynomial *pwqp; + struct isl_split_periods_data *data; + isl_int min, max; + int total; + int r = 0; + + data = (struct isl_split_periods_data *)user; + + if (!set || !qp) + goto error; + + if (qp->div->n_row == 0) { + pwqp = isl_pw_qpolynomial_alloc(set, qp); + data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp); + return 0; + } + + isl_int_init(min); + isl_int_init(max); + total = isl_dim_total(qp->dim); + for (i = 0; i < qp->div->n_row; ++i) { + enum isl_lp_result lp_res; + + if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total, + qp->div->n_row) != -1) + continue; + + lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1, + set->ctx->one, &min, NULL, NULL); + if (lp_res == isl_lp_error) + goto error2; + if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty) + continue; + isl_int_fdiv_q(min, min, qp->div->row[i][0]); + + lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1, + set->ctx->one, &max, NULL, NULL); + if (lp_res == isl_lp_error) + goto error2; + if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty) + continue; + isl_int_fdiv_q(max, max, qp->div->row[i][0]); + + isl_int_sub(max, max, min); + if (isl_int_cmp_si(max, data->max_periods) < 0) { + isl_int_add(max, max, min); + break; + } + } + + if (i < qp->div->n_row) { + r = split_div(set, qp, i, min, max, data); + } else { + pwqp = isl_pw_qpolynomial_alloc(set, qp); + data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp); + } + + isl_int_clear(max); + isl_int_clear(min); + + return r; +error2: + isl_int_clear(max); + isl_int_clear(min); +error: + isl_set_free(set); + isl_qpolynomial_free(qp); + return -1; +} + +/* If any quasi-polynomial in pwqp refers to any integer division + * that can only attain "max_periods" distinct values on its domain + * then split the domain along those distinct values. + */ +__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods( + __isl_take isl_pw_qpolynomial *pwqp, int max_periods) +{ + struct isl_split_periods_data data; + + data.max_periods = max_periods; + data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp)); + + if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0) + goto error; + + isl_pw_qpolynomial_free(pwqp); + + return data.res; +error: + isl_pw_qpolynomial_free(data.res); + isl_pw_qpolynomial_free(pwqp); + return NULL; +} + +/* Construct a piecewise quasipolynomial that is constant on the given + * domain. In particular, it is + * 0 if cst == 0 + * 1 if cst == 1 + * infinity if cst == -1 + */ +static __isl_give isl_pw_qpolynomial *constant_on_domain( + __isl_take isl_basic_set *bset, int cst) +{ + isl_dim *dim; + isl_qpolynomial *qp; + + if (!bset) + return NULL; + + bset = isl_basic_map_domain(isl_basic_map_from_range(bset)); + dim = isl_basic_set_get_dim(bset); + if (cst < 0) + qp = isl_qpolynomial_infty(dim); + else if (cst == 0) + qp = isl_qpolynomial_zero(dim); + else + qp = isl_qpolynomial_one(dim); + return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp); +} + +/* Factor bset, call fn on each of the factors and return the product. + * + * If no factors can be found, simply call fn on the input. + * Otherwise, construct the factors based on the factorizer, + * call fn on each factor and compute the product. + */ +static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call( + __isl_take isl_basic_set *bset, + __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset)) +{ + int i, n; + isl_dim *dim; + isl_set *set; + isl_factorizer *f; + isl_qpolynomial *qp; + isl_pw_qpolynomial *pwqp; + unsigned nparam; + unsigned nvar; + + f = isl_basic_set_factorizer(bset); + if (!f) + goto error; + if (f->n_group == 0) { + isl_factorizer_free(f); + return fn(bset); + } + + nparam = isl_basic_set_dim(bset, isl_dim_param); + nvar = isl_basic_set_dim(bset, isl_dim_set); + + dim = isl_basic_set_get_dim(bset); + dim = isl_dim_domain(dim); + set = isl_set_universe(isl_dim_copy(dim)); + qp = isl_qpolynomial_one(dim); + pwqp = isl_pw_qpolynomial_alloc(set, qp); + + bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset); + + for (i = 0, n = 0; i < f->n_group; ++i) { + isl_basic_set *bset_i; + isl_pw_qpolynomial *pwqp_i; + + bset_i = isl_basic_set_copy(bset); + bset_i = isl_basic_set_drop_constraints_involving(bset_i, + nparam + n + f->len[i], nvar - n - f->len[i]); + bset_i = isl_basic_set_drop_constraints_involving(bset_i, + nparam, n); + bset_i = isl_basic_set_drop(bset_i, isl_dim_set, + n + f->len[i], nvar - n - f->len[i]); + bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n); + + pwqp_i = fn(bset_i); + pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i); + + n += f->len[i]; + } + + isl_basic_set_free(bset); + isl_factorizer_free(f); + + return pwqp; +error: + isl_basic_set_free(bset); + return NULL; +} + +/* Factor bset, call fn on each of the factors and return the product. + * The function is assumed to evaluate to zero on empty domains, + * to one on zero-dimensional domains and to infinity on unbounded domains + * and will not be called explicitly on zero-dimensional or unbounded domains. + * + * We first check for some special cases and remove all equalities. + * Then we hand over control to compressed_multiplicative_call. + */ +__isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call( + __isl_take isl_basic_set *bset, + __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset)) +{ + int bounded; + isl_morph *morph; + isl_pw_qpolynomial *pwqp; + unsigned orig_nvar, final_nvar; + + if (!bset) + return NULL; + + if (isl_basic_set_fast_is_empty(bset)) + return constant_on_domain(bset, 0); + + orig_nvar = isl_basic_set_dim(bset, isl_dim_set); + + if (orig_nvar == 0) + return constant_on_domain(bset, 1); + + bounded = isl_basic_set_is_bounded(bset); + if (bounded < 0) + goto error; + if (!bounded) + return constant_on_domain(bset, -1); + + if (bset->n_eq == 0) + return compressed_multiplicative_call(bset, fn); + + morph = isl_basic_set_full_compression(bset); + bset = isl_morph_basic_set(isl_morph_copy(morph), bset); + + final_nvar = isl_basic_set_dim(bset, isl_dim_set); + + pwqp = compressed_multiplicative_call(bset, fn); + + morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar); + morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar); + morph = isl_morph_inverse(morph); + + pwqp = isl_pw_qpolynomial_morph(pwqp, morph); + + return pwqp; +error: + isl_basic_set_free(bset); + return NULL; +}