X-Git-Url: http://review.tizen.org/git/?a=blobdiff_plain;f=isl_polynomial.c;h=046b63a29235293fbaad1bbb7c05ccd50b00a191;hb=fe8f991cf09ecb1aed45cd2599f23a490ac46501;hp=b9cc6573d15d5da8bfad2da72312165071d89187;hpb=7af8aff2a3ed0aadde3198d1bde456234f855d05;p=platform%2Fupstream%2Fisl.git diff --git a/isl_polynomial.c b/isl_polynomial.c index b9cc657..046b63a 100644 --- a/isl_polynomial.c +++ b/isl_polynomial.c @@ -9,11 +9,20 @@ */ #include -#include +#include +#include +#include +#include +#include +#include #include #include -#include -#include +#include +#include +#include +#include +#include +#include static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type) { @@ -21,6 +30,7 @@ static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type) case isl_dim_param: return 0; case isl_dim_in: return dim->nparam; case isl_dim_out: return dim->nparam + dim->n_in; + default: return 0; } } @@ -236,6 +246,20 @@ __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; @@ -250,6 +274,20 @@ __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx) return &cst->up; } +__isl_give struct isl_upoly *isl_upoly_neginfty(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, 0); + + return &cst->up; +} + __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx) { struct isl_upoly_cst *cst; @@ -286,7 +324,7 @@ __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx, isl_assert(ctx, var >= 0, return NULL); isl_assert(ctx, size >= 0, return NULL); - rec = isl_calloc(dim->ctx, struct isl_upoly_rec, + rec = isl_calloc(ctx, struct isl_upoly_rec, sizeof(struct isl_upoly_rec) + (size - 1) * sizeof(struct isl_upoly *)); if (!rec) @@ -301,8 +339,22 @@ __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx, rec->size = size; return rec; +} + +__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; + + isl_dim_free(qp->dim); + qp->dim = dim; + + return qp; error: - isl_upoly_free(&rec->up); + isl_qpolynomial_free(qp); + isl_dim_free(dim); return NULL; } @@ -311,6 +363,17 @@ isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp) return qp ? qp->dim->ctx : NULL; } +__isl_give isl_dim *isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial *qp) +{ + return qp ? isl_dim_copy(qp->dim) : NULL; +} + +unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp, + enum isl_dim_type type) +{ + return qp ? isl_dim_size(qp->dim, type) : 0; +} + int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp) { return qp ? isl_upoly_is_zero(qp->upoly) : -1; @@ -615,7 +678,50 @@ error: return NULL; } -__isl_give struct isl_upoly *isl_upoly_neg_cst(__isl_take struct isl_upoly *up) +__isl_give struct isl_upoly *isl_upoly_cst_add_isl_int( + __isl_take struct isl_upoly *up, isl_int v) +{ + struct isl_upoly_cst *cst; + + up = isl_upoly_cow(up); + if (!up) + return NULL; + + cst = isl_upoly_as_cst(up); + + isl_int_addmul(cst->n, cst->d, v); + + return up; +} + +__isl_give struct isl_upoly *isl_upoly_add_isl_int( + __isl_take struct isl_upoly *up, isl_int v) +{ + struct isl_upoly_rec *rec; + + if (!up) + return NULL; + + if (isl_upoly_is_cst(up)) + return isl_upoly_cst_add_isl_int(up, v); + + up = isl_upoly_cow(up); + rec = isl_upoly_as_rec(up); + if (!rec) + goto error; + + rec->p[0] = isl_upoly_add_isl_int(rec->p[0], v); + if (!rec->p[0]) + goto error; + + return up; +error: + isl_upoly_free(up); + return NULL; +} + +__isl_give struct isl_upoly *isl_upoly_cst_mul_isl_int( + __isl_take struct isl_upoly *up, isl_int v) { struct isl_upoly_cst *cst; @@ -628,12 +734,13 @@ __isl_give struct isl_upoly *isl_upoly_neg_cst(__isl_take struct isl_upoly *up) cst = isl_upoly_as_cst(up); - isl_int_neg(cst->n, cst->n); + isl_int_mul(cst->n, cst->n, v); return up; } -__isl_give struct isl_upoly *isl_upoly_neg(__isl_take struct isl_upoly *up) +__isl_give struct isl_upoly *isl_upoly_mul_isl_int( + __isl_take struct isl_upoly *up, isl_int v) { int i; struct isl_upoly_rec *rec; @@ -642,7 +749,7 @@ __isl_give struct isl_upoly *isl_upoly_neg(__isl_take struct isl_upoly *up) return NULL; if (isl_upoly_is_cst(up)) - return isl_upoly_neg_cst(up); + return isl_upoly_cst_mul_isl_int(up, v); up = isl_upoly_cow(up); rec = isl_upoly_as_rec(up); @@ -650,7 +757,7 @@ __isl_give struct isl_upoly *isl_upoly_neg(__isl_take struct isl_upoly *up) goto error; for (i = 0; i < rec->n; ++i) { - rec->p[i] = isl_upoly_neg(rec->p[i]); + rec->p[i] = isl_upoly_mul_isl_int(rec->p[i], v); if (!rec->p[i]) goto error; } @@ -813,6 +920,31 @@ error: return NULL; } +__isl_give struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up, + unsigned power) +{ + struct isl_upoly *res; + + if (!up) + return NULL; + if (power == 1) + return up; + + if (power % 2) + res = isl_upoly_copy(up); + else + res = isl_upoly_one(up->ctx); + + while (power >>= 1) { + up = isl_upoly_mul(up, isl_upoly_copy(up)); + if (power % 2) + res = isl_upoly_mul(res, isl_upoly_copy(up)); + } + + isl_upoly_free(up); + return res; +} + __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim, unsigned n_div, __isl_take struct isl_upoly *up) { @@ -901,6 +1033,67 @@ void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp) free(qp); } +__isl_give struct isl_upoly *isl_upoly_var_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_var_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; @@ -925,19 +1118,6 @@ static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2) return equal; } -static void expand_row(__isl_keep isl_mat *dst, int d, - __isl_keep isl_mat *src, int s, int *exp) -{ - int i; - unsigned c = src->n_col - src->n_row; - - isl_seq_cpy(dst->row[d], src->row[s], c); - isl_seq_clr(dst->row[d] + c, dst->n_col - c); - - for (i = 0; i < s; ++i) - isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]); -} - static int cmp_row(__isl_keep isl_mat *div, int i, int j) { int li, lj; @@ -965,96 +1145,92 @@ 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); + isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1, + 2 + div_pos + i - skip); + 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; } -static __isl_give isl_mat *merge_divs(__isl_keep isl_mat *div1, - __isl_keep isl_mat *div2, int *exp1, int *exp2) -{ - int i, j, k; - isl_mat *div = NULL; - unsigned d = div1->n_col - div1->n_row; - - div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row, - d + div1->n_row + div2->n_row); - if (!div) - return NULL; - - for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) { - int cmp; - - expand_row(div, k, div1, i, exp1); - expand_row(div, k + 1, div2, j, exp2); - - cmp = cmp_row(div, k, k + 1); - if (cmp == 0) { - exp1[i++] = k; - exp2[j++] = k; - } else if (cmp < 0) { - exp1[i++] = k; - } else { - exp2[j++] = k; - isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col); - } - } - for (; i < div1->n_row; ++i, ++k) { - expand_row(div, k, div1, i, exp1); - exp1[i] = k; - } - for (; j < div2->n_row; ++j, ++k) { - expand_row(div, k, div2, j, exp2); - exp2[j] = k; - } - - div->n_row = k; - div->n_col = d + k; - - return div; -} - static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up, int *exp, int first) { @@ -1115,7 +1291,7 @@ static __isl_give isl_qpolynomial *with_merged_divs( if (!exp1 || !exp2) goto error; - div = merge_divs(qp1->div, qp2->div, exp1, exp2); + div = isl_merge_divs(qp1->div, qp2->div, exp1, exp2); if (!div) goto error; @@ -1172,20 +1348,69 @@ 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) +{ + qp1 = isl_qpolynomial_add(qp1, qp2); + qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom)); + return qp1; +} + __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2) { return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2)); } -__isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp) +__isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int( + __isl_take isl_qpolynomial *qp, isl_int v) { + if (isl_int_is_zero(v)) + return qp; + qp = isl_qpolynomial_cow(qp); + if (!qp) + return NULL; + + qp->upoly = isl_upoly_add_isl_int(qp->upoly, v); + if (!qp->upoly) + goto error; + + return qp; +error: + isl_qpolynomial_free(qp); + return NULL; + +} + +__isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp) +{ + if (!qp) + return NULL; + + return isl_qpolynomial_mul_isl_int(qp, qp->dim->ctx->negone); +} + +__isl_give isl_qpolynomial *isl_qpolynomial_mul_isl_int( + __isl_take isl_qpolynomial *qp, isl_int v) +{ + if (isl_int_is_one(v)) + return qp; + if (qp && isl_int_is_zero(v)) { + isl_qpolynomial *zero; + zero = isl_qpolynomial_zero(isl_dim_copy(qp->dim)); + isl_qpolynomial_free(qp); + return zero; + } + + qp = isl_qpolynomial_cow(qp); if (!qp) return NULL; - qp->upoly = isl_upoly_neg(qp->upoly); + qp->upoly = isl_upoly_mul_isl_int(qp->upoly, v); if (!qp->upoly) goto error; @@ -1223,33 +1448,17 @@ error: return NULL; } -__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_infty(__isl_take isl_dim *dim) -{ - return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx)); -} - -__isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim) -{ - return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx)); -} - -__isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim, - isl_int v) +__isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp, + unsigned power) { - struct isl_qpolynomial *qp; - struct isl_upoly_cst *cst; + qp = isl_qpolynomial_cow(qp); - qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx)); if (!qp) return NULL; - cst = isl_upoly_as_cst(qp->upoly); - isl_int_set(cst->n, v); + qp->upoly = isl_upoly_pow(qp->upoly, power); + if (!qp->upoly) + goto error; return qp; error: @@ -1257,6 +1466,60 @@ error: return NULL; } +__isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim) +{ + if (!dim) + return NULL; + return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx)); +} + +__isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim) +{ + if (!dim) + return NULL; + return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx)); +} + +__isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim) +{ + if (!dim) + return NULL; + return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx)); +} + +__isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim) +{ + if (!dim) + return NULL; + return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx)); +} + +__isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim) +{ + if (!dim) + return NULL; + return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx)); +} + +__isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim, + isl_int v) +{ + struct isl_qpolynomial *qp; + struct isl_upoly_cst *cst; + + if (!dim) + return NULL; + + qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx)); + if (!qp) + return NULL; + + cst = isl_upoly_as_cst(qp->upoly); + isl_int_set(cst->n, v); + + return qp; +} + int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp, isl_int *n, isl_int *d) { @@ -1381,13 +1644,12 @@ __isl_give isl_vec *isl_qpolynomial_extract_affine( if (!qp) return NULL; - isl_assert(qp->div->ctx, qp->div->n_row == 0, return NULL); d = isl_dim_total(qp->dim); - aff = isl_vec_alloc(qp->div->ctx, 2 + d); + aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row); if (!aff) return NULL; - isl_seq_clr(aff->el + 1, 1 + d); + isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row); isl_int_set_si(aff->el[0], 1); if (isl_upoly_update_affine(qp->upoly, aff) < 0) @@ -1438,32 +1700,7 @@ 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, +__isl_give isl_qpolynomial *isl_qpolynomial_var_pow(__isl_take isl_dim *dim, int pos, int power) { struct isl_ctx *ctx; @@ -1473,7 +1710,7 @@ __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_dim *dim, ctx = dim->ctx; - return isl_qpolynomial_alloc(dim, 0, isl_upoly_pow(ctx, pos, power)); + return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power)); } __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim, @@ -1488,34 +1725,352 @@ __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim, if (type == isl_dim_set) pos += isl_dim_size(dim, isl_dim_param); - return isl_qpolynomial_pow(dim, pos, 1); + return isl_qpolynomial_var_pow(dim, pos, 1); error: isl_dim_free(dim); return NULL; } +__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_var_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_upoly_free(base); + isl_upoly_free(up); + + return res; +error: + isl_upoly_free(up); + 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_var_pow(ctx, i, 1); + t = isl_upoly_mul(c, t); + up = isl_upoly_sum(up, t); + } + + return up; +} + +/* 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); +} + +/* 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; +} + +/* Reduce the coefficients of div "div" to lie in the interval [0, d-1], + * with d the denominator. When replacing the coefficient e of x by + * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x + * inside the division, so we need to add floor(e/d) * x outside. + * That is, we replace q by q' + floor(e/d) * x and we therefore need + * to adjust the coefficient of x in each later div that depends on the + * current div "div" and also in the affine expression "aff" + * (if it too depends on "div"). + */ +static void reduce_div(__isl_keep isl_qpolynomial *qp, int div, + __isl_keep isl_vec *aff) +{ + int i, j; + isl_int v; + unsigned total = qp->div->n_col - qp->div->n_row - 2; + + isl_int_init(v); + for (i = 0; i < 1 + total + div; ++i) { + if (isl_int_is_nonneg(qp->div->row[div][1 + i]) && + isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0])) + continue; + isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]); + isl_int_fdiv_r(qp->div->row[div][1 + i], + qp->div->row[div][1 + i], qp->div->row[div][0]); + if (!isl_int_is_zero(aff->el[1 + total + div])) + isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]); + for (j = div + 1; j < qp->div->n_row; ++j) { + if (isl_int_is_zero(qp->div->row[j][2 + total + div])) + continue; + isl_int_addmul(qp->div->row[j][1 + i], + v, qp->div->row[j][2 + total + div]); + } + } + isl_int_clear(v); +} + +/* Check if the last non-zero coefficient is bigger that half of the + * denominator. If so, we will invert the div to further reduce the number + * of distinct divs that may appear. + * If the last non-zero coefficient is exactly half the denominator, + * then we continue looking for earlier coefficients that are bigger + * than half the denominator. + */ +static int needs_invert(__isl_keep isl_mat *div, int row) +{ + int i; + int cmp; + + for (i = div->n_col - 1; i >= 1; --i) { + if (isl_int_is_zero(div->row[row][i])) + continue; + isl_int_mul_ui(div->row[row][i], div->row[row][i], 2); + cmp = isl_int_cmp(div->row[row][i], div->row[row][0]); + isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2); + if (cmp) + return cmp > 0; + if (i == 1) + return 1; + } + + return 0; +} + +/* Replace div "div" q = [e/d] by -[(-e+(d-1))/d]. + * We only invert the coefficients of e (and the coefficient of q in + * later divs and in "aff"). After calling this function, the + * coefficients of e should be reduced again. + */ +static void invert_div(__isl_keep isl_qpolynomial *qp, int div, + __isl_keep isl_vec *aff) +{ + unsigned total = qp->div->n_col - qp->div->n_row - 2; + + isl_seq_neg(qp->div->row[div] + 1, + qp->div->row[div] + 1, qp->div->n_col - 1); + isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1); + isl_int_add(qp->div->row[div][1], + qp->div->row[div][1], qp->div->row[div][0]); + if (!isl_int_is_zero(aff->el[1 + total + div])) + isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]); + isl_mat_col_mul(qp->div, 2 + total + div, + qp->div->ctx->negone, 2 + total + div); +} + +/* Assuming "qp" is a monomial, reduce all its divs to have coefficients + * in the interval [0, d-1], with d the denominator and such that the + * last non-zero coefficient that is not equal to d/2 is smaller than d/2. + * + * After the reduction, some divs may have become redundant or identical, + * so we call substitute_non_divs and sort_divs. If these functions + * eliminate divs or merge two or more divs into one, the coefficients + * of the enclosing divs may have to be reduced again, so we call + * ourselves recursively if the number of divs decreases. + */ +static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp) +{ + int i, j; + isl_vec *aff = NULL; + struct isl_upoly *s; + unsigned n_div; + + if (!qp) + return NULL; + + aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1); + aff = isl_vec_clr(aff); + if (!aff) + goto error; + + isl_int_set_si(aff->el[1 + qp->upoly->var], 1); + + for (i = 0; i < qp->div->n_row; ++i) { + normalize_div(qp, i); + reduce_div(qp, i, aff); + if (needs_invert(qp->div, i)) { + invert_div(qp, i, aff); + reduce_div(qp, i, aff); + } + } + + s = isl_upoly_from_affine(qp->div->ctx, aff->el, + qp->div->ctx->one, aff->size); + qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s); + isl_upoly_free(s); + if (!qp->upoly) + goto error; + + isl_vec_free(aff); + + n_div = qp->div->n_row; + qp = substitute_non_divs(qp); + qp = sort_divs(qp); + if (qp && qp->div->n_row < n_div) + return reduce_divs(qp); + + return qp; +error: + isl_qpolynomial_free(qp); + isl_vec_free(aff); + return NULL; +} + +/* Assumes each div only depends on earlier divs. + */ __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); for (i = 0; i < 1 + power; ++i) { rec->p[i] = isl_upoly_zero(div->ctx); @@ -1528,6 +2083,8 @@ __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div, isl_div_free(div); + qp = reduce_divs(qp); + return qp; error: isl_qpolynomial_free(qp); @@ -1555,9 +2112,6 @@ __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim, isl_int_set(cst->d, d); return qp; -error: - isl_qpolynomial_free(qp); - return NULL; } static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d) @@ -1618,7 +2172,7 @@ int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp, isl_assert(qp->dim->ctx, type == isl_dim_param || type == isl_dim_set, return -1); - active = isl_calloc_array(set->ctx, int, isl_dim_total(qp->dim)); + active = isl_calloc_array(qp->dim->ctx, int, isl_dim_total(qp->dim)); if (set_active(qp, active) < 0) goto error; @@ -1638,28 +2192,110 @@ error: return -1; } -__isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up, - unsigned first, unsigned n) +/* Remove divs that do not appear in the quasi-polynomial, nor in any + * of the divs that do appear in the quasi-polynomial. + */ +static __isl_give isl_qpolynomial *remove_redundant_divs( + __isl_take isl_qpolynomial *qp) { - int i; - struct isl_upoly_rec *rec; + int i, j; + int d; + int len; + int skip; + int *active = NULL; + int *reordering = NULL; + int redundant = 0; + int n_div; - if (!up) - return NULL; - if (n == 0 || up->var < 0 || up->var < first) - return up; - if (up->var < first + n) { - up = replace_by_constant_term(up); - return isl_upoly_drop(up, first, n); - } - up = isl_upoly_cow(up); - if (!up) + if (!qp) return NULL; - up->var -= n; - rec = isl_upoly_as_rec(up); - if (!rec) - goto error; - + if (qp->div->n_row == 0) + return qp; + + d = isl_dim_total(qp->dim); + len = qp->div->n_col - 2; + active = isl_calloc_array(qp->ctx, int, len); + if (!active) + goto error; + + if (up_set_active(qp->upoly, active, len) < 0) + goto error; + + for (i = qp->div->n_row - 1; i >= 0; --i) { + if (!active[d + i]) { + redundant = 1; + continue; + } + for (j = 0; j < i; ++j) { + if (isl_int_is_zero(qp->div->row[i][2 + d + j])) + continue; + active[d + j] = 1; + break; + } + } + + if (!redundant) { + free(active); + return qp; + } + + reordering = isl_alloc_array(qp->div->ctx, int, len); + if (!reordering) + goto error; + + for (i = 0; i < d; ++i) + reordering[i] = i; + + skip = 0; + n_div = qp->div->n_row; + for (i = 0; i < n_div; ++i) { + if (!active[d + i]) { + qp->div = isl_mat_drop_rows(qp->div, i - skip, 1); + qp->div = isl_mat_drop_cols(qp->div, + 2 + d + i - skip, 1); + skip++; + } + reordering[d + i] = d + i - skip; + } + + qp->upoly = reorder(qp->upoly, reordering); + + if (!qp->upoly || !qp->div) + goto error; + + free(active); + free(reordering); + + return qp; +error: + free(active); + free(reordering); + isl_qpolynomial_free(qp); + return NULL; +} + +__isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up, + unsigned first, unsigned n) +{ + int i; + struct isl_upoly_rec *rec; + + if (!up) + return NULL; + if (n == 0 || up->var < 0 || up->var < first) + return up; + if (up->var < first + n) { + up = replace_by_constant_term(up); + return isl_upoly_drop(up, first, n); + } + up = isl_upoly_cow(up); + if (!up) + return NULL; + up->var -= n; + rec = isl_upoly_as_rec(up); + if (!rec) + goto error; + for (i = 0; i < rec->n; ++i) { rec->p[i] = isl_upoly_drop(rec->p[i], first, n); if (!rec->p[i]) @@ -1672,13 +2308,29 @@ 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) { if (!qp) return NULL; - if (n == 0) + if (n == 0 && !isl_dim_get_tuple_name(qp->dim, type)) return qp; qp = isl_qpolynomial_cow(qp); @@ -1711,6 +2363,128 @@ error: return NULL; } +__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 @@ -1719,11 +2493,18 @@ error: #define IS_ZERO is_zero #undef FIELD #define FIELD qp -#undef ADD -#define ADD(d,e1,e2) isl_qpolynomial_add(e1,e2) #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) @@ -1732,7 +2513,7 @@ int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp) if (pwqp->n != -1) return 0; - if (!isl_set_fast_is_universe(pwqp->p[0].set)) + if (!isl_set_plain_is_universe(pwqp->p[0].set)) return 0; return isl_qpolynomial_is_one(pwqp->p[0].qp); @@ -1781,7 +2562,7 @@ __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul( struct isl_qpolynomial *prod; common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set), isl_set_copy(pwqp2->p[j].set)); - if (isl_set_fast_is_empty(common)) { + if (isl_set_plain_is_empty(common)) { isl_set_free(common); continue; } @@ -1807,9 +2588,7 @@ 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; @@ -1818,6 +2597,8 @@ __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); @@ -1936,6 +2717,25 @@ int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1, return cmp; } +int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1, + __isl_keep isl_qpolynomial *qp2) +{ + struct isl_upoly_cst *cst1, *cst2; + + if (!qp1 || !qp2) + return -1; + isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1); + isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1); + if (isl_qpolynomial_is_nan(qp1)) + return -1; + if (isl_qpolynomial_is_nan(qp2)) + return -1; + cst1 = isl_upoly_as_cst(qp1->upoly); + cst2 = isl_upoly_as_cst(qp2->upoly); + + return isl_upoly_cmp(cst1, cst2) <= 0; +} + __isl_give isl_qpolynomial *isl_qpolynomial_min_cst( __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2) { @@ -1990,8 +2790,9 @@ error: return NULL; } -__isl_give isl_qpolynomial *isl_qpolynomial_add_dims( - __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n) +__isl_give isl_qpolynomial *isl_qpolynomial_insert_dims( + __isl_take isl_qpolynomial *qp, enum isl_dim_type type, + unsigned first, unsigned n) { unsigned total; unsigned g_pos; @@ -2004,7 +2805,10 @@ __isl_give isl_qpolynomial *isl_qpolynomial_add_dims( if (!qp) return NULL; - g_pos = pos(qp->dim, type) + isl_dim_size(qp->dim, type); + isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type), + goto error); + + g_pos = pos(qp->dim, type) + first; qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n); if (!qp->div) @@ -2024,7 +2828,7 @@ __isl_give isl_qpolynomial *isl_qpolynomial_add_dims( goto error; } - qp->dim = isl_dim_add(qp->dim, type, n); + qp->dim = isl_dim_insert(qp->dim, type, first, n); if (!qp->dim) goto error; @@ -2034,36 +2838,25 @@ error: return NULL; } -__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims( - __isl_take isl_pw_qpolynomial *pwqp, - enum isl_dim_type type, unsigned n) +__isl_give isl_qpolynomial *isl_qpolynomial_add_dims( + __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n) { - int i; + unsigned pos; - if (n == 0) - return pwqp; + pos = isl_qpolynomial_dim(qp, type); - pwqp = isl_pw_qpolynomial_cow(pwqp); - if (!pwqp) - return NULL; + return isl_qpolynomial_insert_dims(qp, type, pos, n); +} - pwqp->dim = isl_dim_add(pwqp->dim, type, n); - if (!pwqp->dim) - goto error; +__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims( + __isl_take isl_pw_qpolynomial *pwqp, + enum isl_dim_type type, unsigned n) +{ + 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, @@ -2099,41 +2892,8 @@ 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(__isl_take isl_qpolynomial *qp, +__isl_give isl_qpolynomial *isl_qpolynomial_move_dims( + __isl_take isl_qpolynomial *qp, enum isl_dim_type dst_type, unsigned dst_pos, enum isl_dim_type src_type, unsigned src_pos, unsigned n) { @@ -2154,9 +2914,11 @@ __isl_give isl_qpolynomial *isl_qpolynomial_move(__isl_take isl_qpolynomial *qp, 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); @@ -2178,49 +2940,392 @@ error: return NULL; } -__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_move( - __isl_take isl_pw_qpolynomial *pwqp, - enum isl_dim_type dst_type, unsigned dst_pos, - enum isl_dim_type src_type, unsigned src_pos, unsigned n) +__isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim, + isl_int *f, isl_int denom) { - int i; + struct isl_upoly *up; - pwqp = isl_pw_qpolynomial_cow(pwqp); - if (!pwqp) + if (!dim) return NULL; - pwqp->dim = isl_dim_move(pwqp->dim, - dst_type, dst_pos, src_type, src_pos, n); - if (!pwqp->dim) - goto error; - - for (i = 0; i < pwqp->n; ++i) { - pwqp->p[i].set = isl_set_move(pwqp->p[i].set, dst_type, dst_pos, - src_type, src_pos, n); - if (!pwqp->p[i].set) - goto error; - pwqp->p[i].qp = isl_qpolynomial_move(pwqp->p[i].qp, - dst_type, dst_pos, src_type, src_pos, n); - if (!pwqp->p[i].qp) - goto error; - } + up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim)); - return pwqp; -error: - isl_pw_qpolynomial_free(pwqp); - return NULL; + return isl_qpolynomial_alloc(dim, 0, up); } -__isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim, - __isl_take isl_mat *div) +__isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff) { - isl_term *term; - int n; + isl_ctx *ctx; + struct isl_upoly *up; + isl_qpolynomial *qp; - if (!dim || !div) - goto error; + if (!aff) + return NULL; - n = isl_dim_total(dim) + div->n_row; + ctx = isl_aff_get_ctx(aff); + up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0], + aff->v->size - 1); + + qp = isl_qpolynomial_alloc(isl_aff_get_dim(aff), + aff->ls->div->n_row, up); + if (!qp) + goto error; + + isl_mat_free(qp->div); + qp->div = isl_mat_copy(aff->ls->div); + if (!qp->div) + goto error; + + isl_aff_free(aff); + qp = reduce_divs(qp); + qp = remove_redundant_divs(qp); + return qp; +error: + isl_aff_free(aff); + return NULL; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_from_constraint( + __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos) +{ + isl_int denom; + isl_dim *dim; + struct isl_upoly *up; + isl_qpolynomial *qp; + int sgn; + + if (!c) + return NULL; + + isl_int_init(denom); + + isl_constraint_get_coefficient(c, type, pos, &denom); + isl_constraint_set_coefficient(c, type, pos, c->ctx->zero); + sgn = isl_int_sgn(denom); + isl_int_abs(denom, denom); + up = isl_upoly_from_affine(c->ctx, c->line[0], denom, + 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; +} + +/* For each 0 <= i < "n", replace variable "first" + i of type "type" + * in "qp" by subs[i]. + */ +__isl_give isl_qpolynomial *isl_qpolynomial_substitute( + __isl_take isl_qpolynomial *qp, + enum isl_dim_type type, unsigned first, unsigned n, + __isl_keep isl_qpolynomial **subs) +{ + int i; + struct isl_upoly **ups; + + if (n == 0) + return qp; + + qp = isl_qpolynomial_cow(qp); + if (!qp) + return NULL; + for (i = 0; i < n; ++i) + if (!subs[i]) + goto error; + + isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type), + goto error); + + for (i = 0; i < n; ++i) + isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim), + goto error); + + isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error); + for (i = 0; i < n; ++i) + isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error); + + first += pos(qp->dim, type); + + ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n); + if (!ups) + goto error; + for (i = 0; i < n; ++i) + ups[i] = subs[i]->upoly; + + qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups); + + free(ups); + + if (!qp->upoly) + goto error; + + return qp; +error: + isl_qpolynomial_free(qp); + 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 + * corresponding extra set dimension. + */ +int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp, + __isl_keep isl_basic_set *bset, + int (*fn)(__isl_take isl_basic_set *bset, + __isl_take isl_qpolynomial *poly, void *user), void *user) +{ + isl_dim *dim; + isl_mat *div; + isl_qpolynomial *poly; + + if (!qp || !bset) + goto error; + if (qp->div->n_row == 0) + return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp), + user); + + div = isl_mat_copy(qp->div); + dim = isl_dim_copy(qp->dim); + dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row); + poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly)); + bset = isl_basic_set_copy(bset); + bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row); + bset = add_div_constraints(bset, div); + + return fn(bset, poly, user); +error: + return -1; +} + +/* Return total degree in variables first (inclusive) up to last (exclusive). + */ +int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last) +{ + int deg = -1; + int i; + struct isl_upoly_rec *rec; + + if (!up) + return -2; + if (isl_upoly_is_zero(up)) + return -1; + if (isl_upoly_is_cst(up) || up->var < first) + return 0; + + rec = isl_upoly_as_rec(up); + if (!rec) + return -2; + + for (i = 0; i < rec->n; ++i) { + int d; + + if (isl_upoly_is_zero(rec->p[i])) + continue; + d = isl_upoly_degree(rec->p[i], first, last); + if (up->var < last) + d += i; + if (d > deg) + deg = d; + } + + return deg; +} + +/* Return total degree in set variables. + */ +int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly) +{ + unsigned ovar; + unsigned nvar; + + if (!poly) + return -2; + + ovar = isl_dim_offset(poly->dim, isl_dim_set); + nvar = isl_dim_size(poly->dim, isl_dim_set); + return isl_upoly_degree(poly->upoly, ovar, ovar + nvar); +} + +__isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up, + unsigned pos, int deg) +{ + int i; + struct isl_upoly_rec *rec; + + if (!up) + return NULL; + + if (isl_upoly_is_cst(up) || up->var < pos) { + if (deg == 0) + return isl_upoly_copy(up); + else + return isl_upoly_zero(up->ctx); + } + + rec = isl_upoly_as_rec(up); + if (!rec) + return NULL; + + if (up->var == pos) { + if (deg < rec->n) + return isl_upoly_copy(rec->p[deg]); + else + return isl_upoly_zero(up->ctx); + } + + up = isl_upoly_copy(up); + up = isl_upoly_cow(up); + rec = isl_upoly_as_rec(up); + if (!rec) + goto error; + + for (i = 0; i < rec->n; ++i) { + struct isl_upoly *t; + t = isl_upoly_coeff(rec->p[i], pos, deg); + if (!t) + goto error; + isl_upoly_free(rec->p[i]); + rec->p[i] = t; + } + + return up; +error: + isl_upoly_free(up); + return NULL; +} + +/* Return coefficient of power "deg" of variable "t_pos" of type "type". + */ +__isl_give isl_qpolynomial *isl_qpolynomial_coeff( + __isl_keep isl_qpolynomial *qp, + enum isl_dim_type type, unsigned t_pos, int deg) +{ + unsigned g_pos; + struct isl_upoly *up; + isl_qpolynomial *c; + + if (!qp) + return NULL; + + isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type), + return NULL); + + g_pos = pos(qp->dim, type) + t_pos; + up = isl_upoly_coeff(qp->upoly, g_pos, deg); + + c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up); + if (!c) + return NULL; + isl_mat_free(c->div); + c->div = isl_mat_copy(qp->div); + if (!c->div) + goto error; + return c; +error: + isl_qpolynomial_free(c); + return NULL; +} + +/* Homogenize the polynomial in the variables first (inclusive) up to + * last (exclusive) by inserting powers of variable first. + * Variable first is assumed not to appear in the input. + */ +__isl_give struct isl_upoly *isl_upoly_homogenize( + __isl_take struct isl_upoly *up, int deg, int target, + int first, int last) +{ + int i; + struct isl_upoly_rec *rec; + + if (!up) + return NULL; + if (isl_upoly_is_zero(up)) + return up; + if (deg == target) + return up; + if (isl_upoly_is_cst(up) || up->var < first) { + struct isl_upoly *hom; + + hom = isl_upoly_var_pow(up->ctx, first, target - deg); + if (!hom) + goto error; + rec = isl_upoly_as_rec(hom); + rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up); + + return hom; + } + + up = isl_upoly_cow(up); + rec = isl_upoly_as_rec(up); + if (!rec) + goto error; + + for (i = 0; i < rec->n; ++i) { + if (isl_upoly_is_zero(rec->p[i])) + continue; + rec->p[i] = isl_upoly_homogenize(rec->p[i], + up->var < last ? deg + i : i, target, + first, last); + if (!rec->p[i]) + goto error; + } + + return up; +error: + isl_upoly_free(up); + return NULL; +} + +/* Homogenize the polynomial in the set variables by introducing + * powers of an extra set variable at position 0. + */ +__isl_give isl_qpolynomial *isl_qpolynomial_homogenize( + __isl_take isl_qpolynomial *poly) +{ + unsigned ovar; + unsigned nvar; + int deg = isl_qpolynomial_degree(poly); + + if (deg < -1) + goto error; + + poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1); + poly = isl_qpolynomial_cow(poly); + if (!poly) + goto error; + + ovar = isl_dim_offset(poly->dim, isl_dim_set); + nvar = isl_dim_size(poly->dim, isl_dim_set); + poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg, + ovar, ovar + nvar); + if (!poly->upoly) + goto error; + + return poly; +error: + isl_qpolynomial_free(poly); + return NULL; +} + +__isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim, + __isl_take isl_mat *div) +{ + isl_term *term; + int n; + + if (!dim || !div) + goto error; + + n = isl_dim_total(dim) + div->n_row; term = isl_calloc(dim->ctx, struct isl_term, sizeof(struct isl_term) + (n - 1) * sizeof(int)); @@ -2310,6 +3415,7 @@ unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type) case isl_dim_out: return isl_dim_size(term->dim, type); case isl_dim_div: return term->div->n_row; case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row; + default: return 0; } } @@ -2451,40 +3557,48 @@ int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp, return term ? 0 : -1; } -int isl_pw_qpolynomial_foreach_piece(__isl_keep isl_pw_qpolynomial *pwqp, - int (*fn)(__isl_take isl_set *set, __isl_take isl_qpolynomial *qp, - void *user), void *user) +__isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term) { - int i; - - if (!pwqp) - return -1; - - for (i = 0; i < pwqp->n; ++i) - if (fn(isl_set_copy(pwqp->p[i].set), - isl_qpolynomial_copy(pwqp->p[i].qp), user) < 0) - return -1; + struct isl_upoly *up; + isl_qpolynomial *qp; + int i, n; - return 0; -} + if (!term) + return NULL; -static int any_divs(__isl_keep isl_set *set) -{ - int i; + n = isl_dim_total(term->dim) + term->div->n_row; - if (!set) - return -1; + up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d); + for (i = 0; i < n; ++i) { + if (!term->pow[i]) + continue; + up = isl_upoly_mul(up, + isl_upoly_var_pow(term->dim->ctx, i, term->pow[i])); + } - for (i = 0; i < set->n; ++i) - if (set->p[i]->n_div > 0) - return 1; + qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up); + if (!qp) + goto error; + isl_mat_free(qp->div); + qp->div = isl_mat_copy(term->div); + if (!qp->div) + goto error; - return 0; + isl_term_free(term); + return qp; +error: + isl_qpolynomial_free(qp); + isl_term_free(term); + return NULL; } __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp, __isl_take isl_dim *dim) { + int i; + int extra; + unsigned total; + if (!qp || !dim) goto error; @@ -2497,15 +3611,12 @@ __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp, if (!qp) goto error; + extra = isl_dim_size(dim, isl_dim_set) - + isl_dim_size(qp->dim, isl_dim_set); + total = isl_dim_total(qp->dim); if (qp->div->n_row) { - int i; - int extra; - unsigned total; int *exp; - extra = isl_dim_size(dim, isl_dim_set) - - isl_dim_size(qp->dim, isl_dim_set); - total = isl_dim_total(qp->dim); exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row); if (!exp) goto error; @@ -2515,12 +3626,12 @@ __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp, free(exp); if (!qp->upoly) goto error; - qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra); - if (!qp->div) - goto error; - for (i = 0; i < qp->div->n_row; ++i) - isl_seq_clr(qp->div->row[i] + 2 + total, extra); } + qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra); + if (!qp->div) + goto error; + for (i = 0; i < qp->div->n_row; ++i) + isl_seq_clr(qp->div->row[i] + 2 + total, extra); isl_dim_free(qp->dim); qp->dim = dim; @@ -2532,78 +3643,17 @@ error: return NULL; } -static int foreach_lifted_subset(__isl_take isl_set *set, - __isl_take isl_qpolynomial *qp, - int (*fn)(__isl_take isl_set *set, __isl_take isl_qpolynomial *qp, - void *user), void *user) +/* For each parameter or variable that does not appear in qp, + * first eliminate the variable from all constraints and then set it to zero. + */ +static __isl_give isl_set *fix_inactive(__isl_take isl_set *set, + __isl_keep isl_qpolynomial *qp) { + int *active = NULL; int i; - - if (!set || !qp) - goto error; - - for (i = 0; i < set->n; ++i) { - isl_set *lift; - isl_qpolynomial *copy; - - lift = isl_set_from_basic_set(isl_basic_set_copy(set->p[i])); - lift = isl_set_lift(lift); - - copy = isl_qpolynomial_copy(qp); - copy = isl_qpolynomial_lift(copy, isl_set_get_dim(lift)); - - if (fn(lift, copy, user) < 0) - goto error; - } - - isl_set_free(set); - isl_qpolynomial_free(qp); - - return 0; -error: - isl_set_free(set); - isl_qpolynomial_free(qp); - return -1; -} - -int isl_pw_qpolynomial_foreach_lifted_piece(__isl_keep isl_pw_qpolynomial *pwqp, - int (*fn)(__isl_take isl_set *set, __isl_take isl_qpolynomial *qp, - void *user), void *user) -{ - int i; - - if (!pwqp) - return -1; - - for (i = 0; i < pwqp->n; ++i) { - isl_set *set; - isl_qpolynomial *qp; - - set = isl_set_copy(pwqp->p[i].set); - qp = isl_qpolynomial_copy(pwqp->p[i].qp); - if (!any_divs(set)) { - if (fn(set, qp, user) < 0) - return -1; - continue; - } - if (foreach_lifted_subset(set, qp, fn, user) < 0) - return -1; - } - - return 0; -} - -/* For each parameter or variable that does not appear in qp, - * first eliminate the variable from all constraints and then set it to zero. - */ -static __isl_give isl_set *fix_inactive(__isl_take isl_set *set, - __isl_keep isl_qpolynomial *qp) -{ - int *active = NULL; - int i; - int d; - unsigned nparam; - unsigned nvar; + int d; + unsigned nparam; + unsigned nvar; if (!set || !qp) goto error; @@ -2690,6 +3740,9 @@ __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain( if (isl_set_foreach_point(set, opt_fn, &data) < 0) goto error; + if (data.first) + data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp)); + isl_set_free(set); isl_qpolynomial_free(qp); return data.opt; @@ -2699,3 +3752,913 @@ error: isl_qpolynomial_free(data.opt); return NULL; } + +__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; + struct isl_upoly **subs; + isl_mat *mat; + + qp = isl_qpolynomial_cow(qp); + if (!qp || !morph) + goto error; + + ctx = qp->dim->ctx; + isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error); + + 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_var_pow(ctx, morph->inv->n_col - 1 + i, 1); + + qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs); + + for (i = 0; i < n_sub; ++i) + isl_upoly_free(subs[i]); + free(subs); + + mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv)); + mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row)); + qp->div = isl_mat_product(qp->div, mat); + isl_dim_free(qp->dim); + qp->dim = isl_dim_copy(morph->ran->dim); + + if (!qp->upoly || !qp->div || !qp->dim) + goto error; + + isl_morph_free(morph); + + return qp; +error: + isl_qpolynomial_free(qp); + isl_morph_free(morph); + return NULL; +} + +static int neg_entry(void **entry, void *user) +{ + isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry; + + *pwqp = isl_pw_qpolynomial_neg(*pwqp); + + return *pwqp ? 0 : -1; +} + +__isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg( + __isl_take isl_union_pw_qpolynomial *upwqp) +{ + upwqp = isl_union_pw_qpolynomial_cow(upwqp); + if (!upwqp) + return NULL; + + if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table, + &neg_entry, NULL) < 0) + goto error; + + return upwqp; +error: + isl_union_pw_qpolynomial_free(upwqp); + return NULL; +} + +__isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub( + __isl_take isl_union_pw_qpolynomial *upwqp1, + __isl_take isl_union_pw_qpolynomial *upwqp2) +{ + return isl_union_pw_qpolynomial_add(upwqp1, + isl_union_pw_qpolynomial_neg(upwqp2)); +} + +static int mul_entry(void **entry, void *user) +{ + struct isl_union_pw_qpolynomial_match_bin_data *data = user; + uint32_t hash; + struct isl_hash_table_entry *entry2; + isl_pw_qpolynomial *pwpq = *entry; + int empty; + + hash = isl_dim_get_hash(pwpq->dim); + entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table, + hash, &has_dim, pwpq->dim, 0); + if (!entry2) + return 0; + + pwpq = isl_pw_qpolynomial_copy(pwpq); + pwpq = isl_pw_qpolynomial_mul(pwpq, + isl_pw_qpolynomial_copy(entry2->data)); + + empty = isl_pw_qpolynomial_is_zero(pwpq); + if (empty < 0) { + isl_pw_qpolynomial_free(pwpq); + return -1; + } + if (empty) { + isl_pw_qpolynomial_free(pwpq); + return 0; + } + + data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq); + + return 0; +} + +__isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul( + __isl_take isl_union_pw_qpolynomial *upwqp1, + __isl_take isl_union_pw_qpolynomial *upwqp2) +{ + 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; +} + +__isl_give isl_qpolynomial *isl_qpolynomial_align_params( + __isl_take isl_qpolynomial *qp, __isl_take isl_dim *model) +{ + if (!qp || !model) + goto error; + + if (!isl_dim_match(qp->dim, isl_dim_param, model, isl_dim_param)) { + isl_reordering *exp; + + model = isl_dim_drop(model, isl_dim_in, + 0, isl_dim_size(model, isl_dim_in)); + model = isl_dim_drop(model, isl_dim_out, + 0, isl_dim_size(model, isl_dim_out)); + exp = isl_parameter_alignment_reordering(qp->dim, model); + exp = isl_reordering_extend_dim(exp, + isl_qpolynomial_get_dim(qp)); + qp = isl_qpolynomial_realign(qp, exp); + } + + isl_dim_free(model); + return qp; +error: + isl_dim_free(model); + isl_qpolynomial_free(qp); + 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_plain_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; +} + +/* Drop all floors in "qp", turning each integer division [a/m] into + * a rational division a/m. If "down" is set, then the integer division + * is replaces by (a-(m-1))/m instead. + */ +static __isl_give isl_qpolynomial *qp_drop_floors( + __isl_take isl_qpolynomial *qp, int down) +{ + int i; + struct isl_upoly *s; + + if (!qp) + return NULL; + if (qp->div->n_row == 0) + return qp; + + qp = isl_qpolynomial_cow(qp); + if (!qp) + return NULL; + + for (i = qp->div->n_row - 1; i >= 0; --i) { + if (down) { + isl_int_sub(qp->div->row[i][1], + qp->div->row[i][1], qp->div->row[i][0]); + isl_int_add_ui(qp->div->row[i][1], + qp->div->row[i][1], 1); + } + 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); + if (!qp) + return NULL; + } + + return qp; +} + +/* Drop all floors in "pwqp", turning each integer division [a/m] into + * a rational division a/m. + */ +static __isl_give isl_pw_qpolynomial *pwqp_drop_floors( + __isl_take isl_pw_qpolynomial *pwqp) +{ + int i; + + if (!pwqp) + return NULL; + + if (isl_pw_qpolynomial_is_zero(pwqp)) + return pwqp; + + pwqp = isl_pw_qpolynomial_cow(pwqp); + if (!pwqp) + return NULL; + + for (i = 0; i < pwqp->n; ++i) { + pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0); + if (!pwqp->p[i].qp) + goto error; + } + + return pwqp; +error: + isl_pw_qpolynomial_free(pwqp); + return NULL; +} + +/* Adjust all the integer divisions in "qp" such that they are at least + * one over the given orthant (identified by "signs"). This ensures + * that they will still be non-negative even after subtracting (m-1)/m. + * + * In particular, f is replaced by f' + v, changing f = [a/m] + * to f' = [(a - m v)/m]. + * If the constant term k in a is smaller than m, + * the constant term of v is set to floor(k/m) - 1. + * For any other term, if the coefficient c and the variable x have + * the same sign, then no changes are needed. + * Otherwise, if the variable is positive (and c is negative), + * then the coefficient of x in v is set to floor(c/m). + * If the variable is negative (and c is positive), + * then the coefficient of x in v is set to ceil(c/m). + */ +static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp, + int *signs) +{ + int i, j; + int total; + isl_vec *v = NULL; + struct isl_upoly *s; + + qp = isl_qpolynomial_cow(qp); + if (!qp) + return NULL; + qp->div = isl_mat_cow(qp->div); + if (!qp->div) + goto error; + + total = isl_dim_total(qp->dim); + v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1); + + for (i = 0; i < qp->div->n_row; ++i) { + isl_int *row = qp->div->row[i]; + v = isl_vec_clr(v); + if (!v) + goto error; + if (isl_int_lt(row[1], row[0])) { + isl_int_fdiv_q(v->el[0], row[1], row[0]); + isl_int_sub_ui(v->el[0], v->el[0], 1); + isl_int_submul(row[1], row[0], v->el[0]); + } + for (j = 0; j < total; ++j) { + if (isl_int_sgn(row[2 + j]) * signs[j] >= 0) + continue; + if (signs[j] < 0) + isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]); + else + isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]); + isl_int_submul(row[2 + j], row[0], v->el[1 + j]); + } + for (j = 0; j < i; ++j) { + if (isl_int_sgn(row[2 + total + j]) >= 0) + continue; + isl_int_fdiv_q(v->el[1 + total + j], + row[2 + total + j], row[0]); + isl_int_submul(row[2 + total + j], + row[0], v->el[1 + total + j]); + } + 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], v->el, v->size); + } + isl_int_set_si(v->el[1 + total + i], 1); + s = isl_upoly_from_affine(qp->dim->ctx, v->el, + qp->div->ctx->one, v->size); + qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s); + isl_upoly_free(s); + if (!qp->upoly) + goto error; + } + + isl_vec_free(v); + return qp; +error: + isl_vec_free(v); + isl_qpolynomial_free(qp); + return NULL; +} + +struct isl_to_poly_data { + int sign; + isl_pw_qpolynomial *res; + isl_qpolynomial *qp; +}; + +/* Appoximate data->qp by a polynomial on the orthant identified by "signs". + * We first make all integer divisions positive and then split the + * quasipolynomials into terms with sign data->sign (the direction + * of the requested approximation) and terms with the opposite sign. + * In the first set of terms, each integer division [a/m] is + * overapproximated by a/m, while in the second it is underapproximated + * by (a-(m-1))/m. + */ +static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs, + void *user) +{ + struct isl_to_poly_data *data = user; + isl_pw_qpolynomial *t; + isl_qpolynomial *qp, *up, *down; + + qp = isl_qpolynomial_copy(data->qp); + qp = make_divs_pos(qp, signs); + + up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign); + up = qp_drop_floors(up, 0); + down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign); + down = qp_drop_floors(down, 1); + + isl_qpolynomial_free(qp); + qp = isl_qpolynomial_add(up, down); + + t = isl_pw_qpolynomial_alloc(orthant, qp); + data->res = isl_pw_qpolynomial_add_disjoint(data->res, t); + + return 0; +} + +/* Approximate each quasipolynomial by a polynomial. If "sign" is positive, + * the polynomial will be an overapproximation. If "sign" is negative, + * it will be an underapproximation. If "sign" is zero, the approximation + * will lie somewhere in between. + * + * In particular, is sign == 0, we simply drop the floors, turning + * the integer divisions into rational divisions. + * Otherwise, we split the domains into orthants, make all integer divisions + * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m, + * depending on the requested sign and the sign of the term in which + * the integer division appears. + */ +__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial( + __isl_take isl_pw_qpolynomial *pwqp, int sign) +{ + int i; + struct isl_to_poly_data data; + + if (sign == 0) + return pwqp_drop_floors(pwqp); + + if (!pwqp) + return NULL; + + data.sign = sign; + data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp)); + + for (i = 0; i < pwqp->n; ++i) { + if (pwqp->p[i].qp->div->n_row == 0) { + isl_pw_qpolynomial *t; + t = isl_pw_qpolynomial_alloc( + isl_set_copy(pwqp->p[i].set), + isl_qpolynomial_copy(pwqp->p[i].qp)); + data.res = isl_pw_qpolynomial_add_disjoint(data.res, t); + continue; + } + data.qp = pwqp->p[i].qp; + if (isl_set_foreach_orthant(pwqp->p[i].set, + &to_polynomial_on_orthant, &data) < 0) + goto error; + } + + isl_pw_qpolynomial_free(pwqp); + + return data.res; +error: + isl_pw_qpolynomial_free(pwqp); + isl_pw_qpolynomial_free(data.res); + return NULL; +} + +static int poly_entry(void **entry, void *user) +{ + int *sign = user; + isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry; + + *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign); + + return *pwqp ? 0 : -1; +} + +__isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial( + __isl_take isl_union_pw_qpolynomial *upwqp, int sign) +{ + upwqp = isl_union_pw_qpolynomial_cow(upwqp); + if (!upwqp) + return NULL; + + if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table, + &poly_entry, &sign) < 0) + goto error; + + return upwqp; +error: + isl_union_pw_qpolynomial_free(upwqp); + return NULL; +} + +__isl_give isl_basic_map *isl_basic_map_from_qpolynomial( + __isl_take isl_qpolynomial *qp) +{ + int i, k; + isl_dim *dim; + isl_vec *aff = NULL; + isl_basic_map *bmap = NULL; + unsigned pos; + unsigned n_div; + + if (!qp) + return NULL; + if (!isl_upoly_is_affine(qp->upoly)) + isl_die(qp->dim->ctx, isl_error_invalid, + "input quasi-polynomial not affine", goto error); + aff = isl_qpolynomial_extract_affine(qp); + if (!aff) + goto error; + dim = isl_qpolynomial_get_dim(qp); + dim = isl_dim_from_domain(dim); + pos = 1 + isl_dim_offset(dim, isl_dim_out); + dim = isl_dim_add(dim, isl_dim_out, 1); + n_div = qp->div->n_row; + bmap = isl_basic_map_alloc_dim(dim, n_div, 1, 2 * n_div); + + for (i = 0; i < n_div; ++i) { + k = isl_basic_map_alloc_div(bmap); + if (k < 0) + goto error; + isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col); + isl_int_set_si(bmap->div[k][qp->div->n_col], 0); + if (isl_basic_map_add_div_constraints(bmap, k) < 0) + goto error; + } + k = isl_basic_map_alloc_equality(bmap); + if (k < 0) + goto error; + isl_int_neg(bmap->eq[k][pos], aff->el[0]); + isl_seq_cpy(bmap->eq[k], aff->el + 1, pos); + isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div); + + isl_vec_free(aff); + isl_qpolynomial_free(qp); + bmap = isl_basic_map_finalize(bmap); + return bmap; +error: + isl_vec_free(aff); + isl_qpolynomial_free(qp); + isl_basic_map_free(bmap); + return NULL; +}