/* Set the stride and offset of data->pos to the given
* value and expression.
*
* If we had already found a stride before, then the two strides
* are combined into a single stride.
*
* In particular, if the new stride information is of the form
*
* i = f + s (...)
*
* and the old stride information is of the form
*
* i = f2 + s2 (...)
*
* then we compute the extended gcd of s and s2
*
* a s + b s2 = g,
*
* with g = gcd(s,s2), multiply the first equation with t1 = b s2/g
* and the second with t2 = a s1/g.
* This results in
*
* i = (b s2 + a s1)/g i = t1 f + t2 f2 + (s s2)/g (...)
*
* so that t1 f + t2 f2 is the combined offset and (s s2)/g = lcm(s,s2)
* is the combined stride.
*/
static isl_stat set_stride(struct isl_detect_stride_data *data,
__isl_take isl_val *stride, __isl_take isl_aff *offset)
{
int pos;
if (!stride || !offset)
goto error;
pos = data->pos;
if (data->found) {
isl_val *stride2, *a, *b, *g;
isl_aff *offset2;
stride2 = data->stride;
g = isl_val_gcdext(isl_val_copy(stride), isl_val_copy(stride2),
&a, &b);
a = isl_val_mul(a, isl_val_copy(stride));
a = isl_val_div(a, isl_val_copy(g));
stride2 = isl_val_div(stride2, g);
b = isl_val_mul(b, isl_val_copy(stride2));
stride = isl_val_mul(stride, stride2);
if (!data->want_offset) {
isl_val_free(a);
isl_val_free(b);
} else {
offset2 = data->offset;
offset2 = isl_aff_scale_val(offset2, a);
offset = isl_aff_scale_val(offset, b);
offset = isl_aff_add(offset, offset2);
}
}
data->found = 1;
data->stride = stride;
if (data->want_offset)
data->offset = offset;
else
isl_aff_free(offset);
if (!data->stride || (data->want_offset && !data->offset))
return isl_stat_error;
return isl_stat_ok;
error:
isl_val_free(stride);
isl_aff_free(offset);
return isl_stat_error;
}
/* Check if the constraints in "set" imply any stride on set dimension "pos" and
* store the results in data->stride and data->offset.
*
* In particular, compute the affine hull and then check if
* any of the constraints in the hull impose any stride on the dimension.
* If no such constraint can be found, then the offset is taken
* to be the zero expression and the stride is taken to be one.
*/
static void set_detect_stride(__isl_keep isl_set *set, int pos,
struct isl_detect_stride_data *data)
{
isl_basic_set *hull;
hull = isl_set_affine_hull(isl_set_copy(set));
data->pos = pos;
data->found = 0;
data->stride = NULL;
data->offset = NULL;
if (isl_basic_set_foreach_constraint(hull, &detect_stride, data) < 0)
goto error;
if (!data->found) {
data->stride = isl_val_one(isl_set_get_ctx(set));
if (data->want_offset) {
isl_space *space;
isl_local_space *ls;
space = isl_set_get_space(set);
ls = isl_local_space_from_space(space);
data->offset = isl_aff_zero_on_domain(ls);
}
}
isl_basic_set_free(hull);
return;
error:
isl_basic_set_free(hull);
data->stride = isl_val_free(data->stride);
data->offset = isl_aff_free(data->offset);
}
static struct clast_expr *div_expr(CloogConstraint *constraint, int pos,
CloogNames *names)
{
int i, nb_elts;
unsigned dim = cloog_constraint_total_dimension(constraint);
cloog_int_t c;
struct clast_reduction *r;
struct clast_expr *e = NULL;
isl_aff *div;
div = isl_constraint_get_div(cloog_constraint_to_isl(constraint), pos);
cloog_int_init(c);
for (i = 0, nb_elts = 0; i < dim; ++i) {
struct cloog_isl_dim dim;
dim = constraint_cloog_dim_to_isl_dim(constraint, i);
if (dim.type == isl_dim_set)
dim.type = isl_dim_in;
isl_aff_get_coefficient(div, dim.type, dim.pos, &c);
if (!cloog_int_is_zero(c))
++nb_elts;
}
isl_aff_get_constant(div, &c);
if (!cloog_int_is_zero(c))
++nb_elts;
r = new_clast_reduction(clast_red_sum, nb_elts);
for (i = 0, nb_elts = 0; i < dim; ++i) {
struct clast_expr *v;
struct cloog_isl_dim dim;
dim = constraint_cloog_dim_to_isl_dim(constraint, i);
if (dim.type == isl_dim_set)
dim.type = isl_dim_in;
isl_aff_get_coefficient(div, dim.type, dim.pos, &c);
if (cloog_int_is_zero(c))
continue;
v = cloog_constraint_variable_expr(constraint, 1 + i, names);
r->elts[nb_elts++] = &new_clast_term(c, v)->expr;
}
isl_aff_get_constant(div, &c);
if (!cloog_int_is_zero(c))
r->elts[nb_elts++] = &new_clast_term(c, NULL)->expr;
isl_aff_get_denominator(div, &c);
e = &new_clast_binary(clast_bin_fdiv, &r->expr, c)->expr;
cloog_int_clear(c);
isl_aff_free(div);
return e;
}
/* Free "si" and return NULL.
*/
__isl_null isl_stride_info *isl_stride_info_free(
__isl_take isl_stride_info *si)
{
if (!si)
return NULL;
isl_val_free(si->stride);
isl_aff_free(si->offset);
free(si);
return NULL;
}
enum lp_result isl_constraints_opt(Matrix *C, Value *obj, Value denom,
enum lp_dir dir, Value *opt)
{
int i;
isl_ctx *ctx = isl_ctx_alloc();
isl_space *dim;
isl_local_space *ls;
isl_mat *eq, *ineq;
isl_basic_set *bset;
isl_aff *aff;
isl_val *v;
enum isl_lp_result res;
int max = dir == lp_max;
eq = extract_equalities(ctx, C);
ineq = extract_inequalities(ctx, C);
dim = isl_space_set_alloc(ctx, 0, C->NbColumns - 2);
ls = isl_local_space_from_space(isl_space_copy(dim));
bset = isl_basic_set_from_constraint_matrices(dim, eq, ineq,
isl_dim_set, isl_dim_div, isl_dim_param, isl_dim_cst);
aff = isl_aff_zero_on_domain(ls);
for (i = 0; i < C->NbColumns - 2; ++i) {
v = isl_val_int_from_gmp(ctx, obj[i]);
aff = isl_aff_set_coefficient_val(aff, isl_dim_in, i, v);
}
v = isl_val_int_from_gmp(ctx, obj[C->NbColumns - 2]);
aff = isl_aff_set_constant_val(aff, v);
v = isl_val_int_from_gmp(ctx, denom);
aff = isl_aff_scale_down_val(aff, v);
if (max)
v = isl_val_floor(isl_basic_set_max_lp_val(bset, aff));
else
v = isl_val_ceil(isl_basic_set_min_lp_val(bset, aff));
if (!v)
res = isl_lp_error;
else if (isl_val_is_nan(v))
res = isl_lp_empty;
else if (!isl_val_is_rat(v))
res = isl_lp_unbounded;
else {
res = isl_lp_ok;
isl_val_get_num_gmp(v, *opt);
}
isl_val_free(v);
isl_aff_free(aff);
isl_basic_set_free(bset);
isl_ctx_free(ctx);
return isl_lp_result2lp_result(res);
}
/* If the isl_pw_aff on which isl_pw_aff_foreach_piece is called
* has a constant expression on its only domain, then replace
* the isl_val in *user by this constant.
* The caller is assumed to have checked that this function will
* be called exactly once.
*/
static isl_stat extract_cst(__isl_take isl_set *set, __isl_take isl_aff *aff,
void *user)
{
isl_val **inc = (isl_val **)user;
if (isl_aff_is_cst(aff)) {
isl_val_free(*inc);
*inc = isl_aff_get_constant_val(aff);
}
isl_set_free(set);
isl_aff_free(aff);
return isl_stat_ok;
}
/* Construct an isl_stride_info object with given offset and stride.
*/
__isl_give isl_stride_info *isl_stride_info_alloc(
__isl_take isl_val *stride, __isl_take isl_aff *offset)
{
struct isl_stride_info *si;
if (!stride || !offset)
goto error;
si = isl_alloc_type(isl_val_get_ctx(stride), struct isl_stride_info);
if (!si)
goto error;
si->stride = stride;
si->offset = offset;
return si;
error:
isl_val_free(stride);
isl_aff_free(offset);
return NULL;
}
static isl_constraint *
build_linearized_memory_access (isl_map *map, poly_dr_p pdr)
{
isl_constraint *res;
isl_local_space *ls = isl_local_space_from_space (isl_map_get_space (map));
unsigned offset, nsubs;
int i;
isl_int size, subsize;
res = isl_equality_alloc (ls);
isl_int_init (size);
isl_int_set_ui (size, 1);
isl_int_init (subsize);
isl_int_set_ui (subsize, 1);
nsubs = isl_set_dim (pdr->extent, isl_dim_set);
/* -1 for the already included L dimension. */
offset = isl_map_dim (map, isl_dim_out) - 1 - nsubs;
res = isl_constraint_set_coefficient_si (res, isl_dim_out, offset + nsubs, -1);
/* Go through all subscripts from last to first. First dimension
is the alias set, ignore it. */
for (i = nsubs - 1; i >= 1; i--)
{
isl_space *dc;
isl_aff *aff;
res = isl_constraint_set_coefficient (res, isl_dim_out, offset + i, size);
dc = isl_set_get_space (pdr->extent);
aff = isl_aff_zero_on_domain (isl_local_space_from_space (dc));
aff = isl_aff_set_coefficient_si (aff, isl_dim_in, i, 1);
isl_set_max (pdr->extent, aff, &subsize);
isl_aff_free (aff);
isl_int_mul (size, size, subsize);
}
isl_int_clear (subsize);
isl_int_clear (size);
return res;
}
static void
pdr_stride_in_loop (mpz_t stride, graphite_dim_t depth, poly_dr_p pdr)
{
poly_bb_p pbb = PDR_PBB (pdr);
isl_map *map;
isl_set *set;
isl_aff *aff;
isl_space *dc;
isl_constraint *lma, *c;
isl_int islstride;
graphite_dim_t time_depth;
unsigned offset, nt;
unsigned i;
/* XXX isl rewrite following comments. */
/* Builds a partial difference equations and inserts them
into pointset powerset polyhedron P. Polyhedron is assumed
to have the format: T|I|T'|I'|G|S|S'|l1|l2.
TIME_DEPTH is the time dimension w.r.t. which we are
differentiating.
OFFSET represents the number of dimensions between
columns t_{time_depth} and t'_{time_depth}.
DIM_SCTR is the number of scattering dimensions. It is
essentially the dimensionality of the T vector.
The following equations are inserted into the polyhedron P:
| t_1 = t_1'
| ...
| t_{time_depth-1} = t'_{time_depth-1}
| t_{time_depth} = t'_{time_depth} + 1
| t_{time_depth+1} = t'_{time_depth + 1}
| ...
| t_{dim_sctr} = t'_{dim_sctr}. */
/* Add the equality: t_{time_depth} = t'_{time_depth} + 1.
This is the core part of this alogrithm, since this
constraint asks for the memory access stride (difference)
between two consecutive points in time dimensions. */
/* Add equalities:
| t1 = t1'
| ...
| t_{time_depth-1} = t'_{time_depth-1}
| t_{time_depth+1} = t'_{time_depth+1}
| ...
| t_{dim_sctr} = t'_{dim_sctr}
This means that all the time dimensions are equal except for
time_depth, where the constraint is t_{depth} = t'_{depth} + 1
step. More to this: we should be careful not to add equalities
to the 'coupled' dimensions, which happens when the one dimension
is stripmined dimension, and the other dimension corresponds
to the point loop inside stripmined dimension. */
/* pdr->accesses: [P1..nb_param,I1..nb_domain]->[a,S1..nb_subscript]
??? [P] not used for PDRs?
pdr->extent: [a,S1..nb_subscript]
pbb->domain: [P1..nb_param,I1..nb_domain]
pbb->transformed: [P1..nb_param,I1..nb_domain]->[T1..Tnb_sctr]
[T] includes local vars (currently unused)
First we create [P,I] -> [T,a,S]. */
map = isl_map_flat_range_product (isl_map_copy (pbb->transformed),
isl_map_copy (pdr->accesses));
/* Add a dimension for L: [P,I] -> [T,a,S,L].*/
map = isl_map_add_dims (map, isl_dim_out, 1);
/* Build a constraint for "lma[S] - L == 0", effectively calculating
L in terms of subscripts. */
lma = build_linearized_memory_access (map, pdr);
/* And add it to the map, so we now have:
[P,I] -> [T,a,S,L] : lma([S]) == L. */
map = isl_map_add_constraint (map, lma);
/* Then we create [P,I,P',I'] -> [T,a,S,L,T',a',S',L']. */
map = isl_map_flat_product (map, isl_map_copy (map));
/* Now add the equality T[time_depth] == T'[time_depth]+1. This will
force L' to be the linear address at T[time_depth] + 1. */
time_depth = psct_dynamic_dim (pbb, depth);
/* Length of [a,S] plus [L] ... */
offset = 1 + isl_map_dim (pdr->accesses, isl_dim_out);
/* ... plus [T]. */
offset += isl_map_dim (pbb->transformed, isl_dim_out);
c = isl_equality_alloc (isl_local_space_from_space (isl_map_get_space (map)));
c = isl_constraint_set_coefficient_si (c, isl_dim_out, time_depth, 1);
c = isl_constraint_set_coefficient_si (c, isl_dim_out,
offset + time_depth, -1);
c = isl_constraint_set_constant_si (c, 1);
map = isl_map_add_constraint (map, c);
/* Now we equate most of the T/T' elements (making PITaSL nearly
the same is (PITaSL)', except for one dimension, namely for 'depth'
(an index into [I]), after translating to index into [T]. Take care
to not produce an empty map, which indicates we wanted to equate
two dimensions that are already coupled via the above time_depth
dimension. Happens with strip mining where several scatter dimension
are interdependend. */
/* Length of [T]. */
nt = pbb_nb_scattering_transform (pbb) + pbb_nb_local_vars (pbb);
for (i = 0; i < nt; i++)
if (i != time_depth)
{
isl_map *temp = isl_map_equate (isl_map_copy (map),
isl_dim_out, i,
isl_dim_out, offset + i);
if (isl_map_is_empty (temp))
isl_map_free (temp);
else
{
isl_map_free (map);
map = temp;
}
}
/* Now maximize the expression L' - L. */
set = isl_map_range (map);
dc = isl_set_get_space (set);
aff = isl_aff_zero_on_domain (isl_local_space_from_space (dc));
aff = isl_aff_set_coefficient_si (aff, isl_dim_in, offset - 1, -1);
aff = isl_aff_set_coefficient_si (aff, isl_dim_in, offset + offset - 1, 1);
isl_int_init (islstride);
isl_set_max (set, aff, &islstride);
isl_int_get_gmp (islstride, stride);
isl_int_clear (islstride);
isl_aff_free (aff);
isl_set_free (set);
if (dump_file && (dump_flags & TDF_DETAILS))
{
char *str;
void (*gmp_free) (void *, size_t);
fprintf (dump_file, "\nStride in BB_%d, DR_%d, depth %d:",
pbb_index (pbb), PDR_ID (pdr), (int) depth);
str = mpz_get_str (0, 10, stride);
fprintf (dump_file, " %s ", str);
mp_get_memory_functions (NULL, NULL, &gmp_free);
(*gmp_free) (str, strlen (str) + 1);
}
}
enum order_sign isl_polyhedron_affine_sign(Polyhedron *D, Matrix *T,
struct barvinok_options *options)
{
int i;
isl_ctx *ctx = isl_ctx_alloc();
isl_space *dim;
isl_local_space *ls;
isl_aff *aff;
isl_basic_set *bset;
isl_val *min, *max = NULL;
isl_val *v;
enum order_sign sign = order_undefined;
assert(D->Dimension == T->NbColumns - 1);
dim = isl_space_set_alloc(ctx, 0, D->Dimension);
ls = isl_local_space_from_space(isl_space_copy(dim));
bset = isl_basic_set_new_from_polylib(D, dim);
aff = isl_aff_zero_on_domain(ls);
for (i = 0; i < D->Dimension; ++i) {
v = isl_val_int_from_gmp(ctx, T->p[0][i]);
aff = isl_aff_set_coefficient_val(aff, isl_dim_in, i, v);
}
v = isl_val_int_from_gmp(ctx, T->p[0][D->Dimension]);
aff = isl_aff_set_constant_val(aff, v);
v = isl_val_int_from_gmp(ctx, T->p[1][D->Dimension]);
aff = isl_aff_scale_down_val(aff, v);
min = isl_basic_set_min_lp_val(bset, aff);
min = isl_val_ceil(min);
assert(min);
if (isl_val_is_nan(min))
sign = order_undefined;
else if (isl_val_is_pos(min))
sign = order_gt;
else {
max = isl_basic_set_max_lp_val(bset, aff);
max = isl_val_floor(max);
assert(max);
if (isl_val_is_neg(max))
sign = order_lt;
else if (isl_val_is_zero(min) && isl_val_is_zero(max))
sign = order_eq;
else if (isl_val_is_zero(min))
sign = order_ge;
else if (isl_val_is_zero(max))
sign = order_le;
else
sign = order_unknown;
}
isl_basic_set_free(bset);
isl_aff_free(aff);
isl_val_free(min);
isl_val_free(max);
isl_ctx_free(ctx);
return sign;
}