1/*
2 * Copyright 2012-2013 Ecole Normale Superieure
3 *
4 * Use of this software is governed by the MIT license
5 *
6 * Written by Sven Verdoolaege,
7 * Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
8 */
9
10#include <isl/val.h>
11#include <isl_map_private.h>
12#include <isl_aff_private.h>
13#include <isl/constraint.h>
14#include <isl/set.h>
15
16/* Stride information about a specific set dimension.
17 * The values of the set dimension are equal to
18 * "offset" plus a multiple of "stride".
19 */
20struct isl_stride_info {
21	isl_val *stride;
22	isl_aff *offset;
23};
24
25/* Return the ctx to which "si" belongs.
26 */
27isl_ctx *isl_stride_info_get_ctx(__isl_keep isl_stride_info *si)
28{
29	if (!si)
30		return NULL;
31
32	return isl_val_get_ctx(si->stride);
33}
34
35/* Free "si" and return NULL.
36 */
37__isl_null isl_stride_info *isl_stride_info_free(
38	__isl_take isl_stride_info *si)
39{
40	if (!si)
41		return NULL;
42	isl_val_free(si->stride);
43	isl_aff_free(si->offset);
44	free(si);
45	return NULL;
46}
47
48/* Construct an isl_stride_info object with given offset and stride.
49 */
50__isl_give isl_stride_info *isl_stride_info_alloc(
51	__isl_take isl_val *stride, __isl_take isl_aff *offset)
52{
53	struct isl_stride_info *si;
54
55	if (!stride || !offset)
56		goto error;
57	si = isl_alloc_type(isl_val_get_ctx(stride), struct isl_stride_info);
58	if (!si)
59		goto error;
60	si->stride = stride;
61	si->offset = offset;
62	return si;
63error:
64	isl_val_free(stride);
65	isl_aff_free(offset);
66	return NULL;
67}
68
69/* Make a copy of "si" and return it.
70 */
71__isl_give isl_stride_info *isl_stride_info_copy(
72	__isl_keep isl_stride_info *si)
73{
74	if (!si)
75		return NULL;
76
77	return isl_stride_info_alloc(isl_val_copy(si->stride),
78		isl_aff_copy(si->offset));
79}
80
81/* Return the stride of "si".
82 */
83__isl_give isl_val *isl_stride_info_get_stride(__isl_keep isl_stride_info *si)
84{
85	if (!si)
86		return NULL;
87	return isl_val_copy(si->stride);
88}
89
90/* Return the offset of "si".
91 */
92__isl_give isl_aff *isl_stride_info_get_offset(__isl_keep isl_stride_info *si)
93{
94	if (!si)
95		return NULL;
96	return isl_aff_copy(si->offset);
97}
98
99/* Information used inside detect_stride.
100 *
101 * "pos" is the set dimension at which the stride is being determined.
102 * "want_offset" is set if the offset should be computed.
103 * "found" is set if some stride was found already.
104 * "stride" and "offset" contain the (combined) stride and offset
105 * found so far and are NULL when "found" is not set.
106 * If "want_offset" is not set, then "offset" remains NULL.
107 */
108struct isl_detect_stride_data {
109	int pos;
110	int want_offset;
111	int found;
112	isl_val *stride;
113	isl_aff *offset;
114};
115
116/* Set the stride and offset of data->pos to the given
117 * value and expression.
118 *
119 * If we had already found a stride before, then the two strides
120 * are combined into a single stride.
121 *
122 * In particular, if the new stride information is of the form
123 *
124 *	i = f + s (...)
125 *
126 * and the old stride information is of the form
127 *
128 *	i = f2 + s2 (...)
129 *
130 * then we compute the extended gcd of s and s2
131 *
132 *	a s + b s2 = g,
133 *
134 * with g = gcd(s,s2), multiply the first equation with t1 = b s2/g
135 * and the second with t2 = a s1/g.
136 * This results in
137 *
138 *	i = (b s2 + a s1)/g i = t1 f + t2 f2 + (s s2)/g (...)
139 *
140 * so that t1 f + t2 f2 is the combined offset and (s s2)/g = lcm(s,s2)
141 * is the combined stride.
142 */
143static isl_stat set_stride(struct isl_detect_stride_data *data,
144	__isl_take isl_val *stride, __isl_take isl_aff *offset)
145{
146	if (!stride || !offset)
147		goto error;
148
149	if (data->found) {
150		isl_val *stride2, *a, *b, *g;
151		isl_aff *offset2;
152
153		stride2 = data->stride;
154		g = isl_val_gcdext(isl_val_copy(stride), isl_val_copy(stride2),
155					&a, &b);
156		a = isl_val_mul(a, isl_val_copy(stride));
157		a = isl_val_div(a, isl_val_copy(g));
158		stride2 = isl_val_div(stride2, g);
159		b = isl_val_mul(b, isl_val_copy(stride2));
160		stride = isl_val_mul(stride, stride2);
161
162		if (!data->want_offset) {
163			isl_val_free(a);
164			isl_val_free(b);
165		} else {
166			offset2 = data->offset;
167			offset2 = isl_aff_scale_val(offset2, a);
168			offset = isl_aff_scale_val(offset, b);
169			offset = isl_aff_add(offset, offset2);
170		}
171	}
172
173	data->found = 1;
174	data->stride = stride;
175	if (data->want_offset)
176		data->offset = offset;
177	else
178		isl_aff_free(offset);
179	if (!data->stride || (data->want_offset && !data->offset))
180		return isl_stat_error;
181
182	return isl_stat_ok;
183error:
184	isl_val_free(stride);
185	isl_aff_free(offset);
186	return isl_stat_error;
187}
188
189/* Check if constraint "c" imposes any stride on dimension data->pos
190 * and, if so, update the stride information in "data".
191 *
192 * In order to impose a stride on the dimension, "c" needs to be an equality
193 * and it needs to involve the dimension.  Note that "c" may also be
194 * a div constraint and thus an inequality that we cannot use.
195 *
196 * Let c be of the form
197 *
198 *	h(p) + g * v * i + g * stride * f(alpha) = 0
199 *
200 * with h(p) an expression in terms of the parameters and other dimensions
201 * and f(alpha) an expression in terms of the existentially quantified
202 * variables.
203 *
204 * If "stride" is not zero and not one, then it represents a non-trivial stride
205 * on "i".  We compute a and b such that
206 *
207 *	a v + b stride = 1
208 *
209 * We have
210 *
211 *	g v i = -h(p) + g stride f(alpha)
212 *
213 *	a g v i = -a h(p) + g stride f(alpha)
214 *
215 *	a g v i + b g stride i = -a h(p) + g stride * (...)
216 *
217 *	g i = -a h(p) + g stride * (...)
218 *
219 *	i = -a h(p)/g + stride * (...)
220 *
221 * The expression "-a h(p)/g" can therefore be used as offset.
222 */
223static isl_stat detect_stride(__isl_take isl_constraint *c, void *user)
224{
225	struct isl_detect_stride_data *data = user;
226	int i;
227	isl_size n_div;
228	isl_ctx *ctx;
229	isl_stat r = isl_stat_ok;
230	isl_val *v, *stride, *m;
231	isl_bool is_eq, relevant, has_stride;
232
233	is_eq = isl_constraint_is_equality(c);
234	relevant = isl_constraint_involves_dims(c, isl_dim_set, data->pos, 1);
235	if (is_eq < 0 || relevant < 0)
236		goto error;
237	if (!is_eq || !relevant) {
238		isl_constraint_free(c);
239		return isl_stat_ok;
240	}
241
242	n_div = isl_constraint_dim(c, isl_dim_div);
243	if (n_div < 0)
244		goto error;
245	ctx = isl_constraint_get_ctx(c);
246	stride = isl_val_zero(ctx);
247	for (i = 0; i < n_div; ++i) {
248		v = isl_constraint_get_coefficient_val(c, isl_dim_div, i);
249		stride = isl_val_gcd(stride, v);
250	}
251
252	v = isl_constraint_get_coefficient_val(c, isl_dim_set, data->pos);
253	m = isl_val_gcd(isl_val_copy(stride), isl_val_copy(v));
254	stride = isl_val_div(stride, isl_val_copy(m));
255	v = isl_val_div(v, isl_val_copy(m));
256
257	has_stride = isl_val_gt_si(stride, 1);
258	if (has_stride >= 0 && has_stride) {
259		isl_aff *aff;
260		isl_val *gcd, *a, *b;
261
262		gcd = isl_val_gcdext(v, isl_val_copy(stride), &a, &b);
263		isl_val_free(gcd);
264		isl_val_free(b);
265
266		aff = isl_constraint_get_aff(c);
267		for (i = 0; i < n_div; ++i)
268			aff = isl_aff_set_coefficient_si(aff,
269							 isl_dim_div, i, 0);
270		aff = isl_aff_set_coefficient_si(aff, isl_dim_in, data->pos, 0);
271		aff = isl_aff_remove_unused_divs(aff);
272		a = isl_val_neg(a);
273		aff = isl_aff_scale_val(aff, a);
274		aff = isl_aff_scale_down_val(aff, m);
275		r = set_stride(data, stride, aff);
276	} else {
277		isl_val_free(stride);
278		isl_val_free(m);
279		isl_val_free(v);
280	}
281
282	isl_constraint_free(c);
283	if (has_stride < 0)
284		return isl_stat_error;
285	return r;
286error:
287	isl_constraint_free(c);
288	return isl_stat_error;
289}
290
291/* Check if the constraints in "set" imply any stride on set dimension "pos" and
292 * store the results in data->stride and data->offset.
293 *
294 * In particular, compute the affine hull and then check if
295 * any of the constraints in the hull impose any stride on the dimension.
296 * If no such constraint can be found, then the offset is taken
297 * to be the zero expression and the stride is taken to be one.
298 */
299static void set_detect_stride(__isl_keep isl_set *set, int pos,
300	struct isl_detect_stride_data *data)
301{
302	isl_basic_set *hull;
303
304	hull = isl_set_affine_hull(isl_set_copy(set));
305
306	data->pos = pos;
307	data->found = 0;
308	data->stride = NULL;
309	data->offset = NULL;
310	if (isl_basic_set_foreach_constraint(hull, &detect_stride, data) < 0)
311		goto error;
312
313	if (!data->found) {
314		data->stride = isl_val_one(isl_set_get_ctx(set));
315		if (data->want_offset) {
316			isl_space *space;
317			isl_local_space *ls;
318
319			space = isl_set_get_space(set);
320			ls = isl_local_space_from_space(space);
321			data->offset = isl_aff_zero_on_domain(ls);
322		}
323	}
324	isl_basic_set_free(hull);
325	return;
326error:
327	isl_basic_set_free(hull);
328	data->stride = isl_val_free(data->stride);
329	data->offset = isl_aff_free(data->offset);
330}
331
332/* Check if the constraints in "set" imply any stride on set dimension "pos" and
333 * return the results in the form of an offset and a stride.
334 */
335__isl_give isl_stride_info *isl_set_get_stride_info(__isl_keep isl_set *set,
336	int pos)
337{
338	struct isl_detect_stride_data data;
339
340	data.want_offset = 1;
341	set_detect_stride(set, pos, &data);
342
343	return isl_stride_info_alloc(data.stride, data.offset);
344}
345
346/* Check if the constraints in "set" imply any stride on set dimension "pos" and
347 * return this stride.
348 */
349__isl_give isl_val *isl_set_get_stride(__isl_keep isl_set *set, int pos)
350{
351	struct isl_detect_stride_data data;
352
353	data.want_offset = 0;
354	set_detect_stride(set, pos, &data);
355
356	return data.stride;
357}
358
359/* Check if the constraints in "map" imply any stride on output dimension "pos",
360 * independently of any other output dimensions, and
361 * return the results in the form of an offset and a stride.
362 *
363 * Convert the input to a set with only the input dimensions and
364 * the single output dimension such that it be passed to
365 * isl_set_get_stride_info and convert the result back to
366 * an expression defined over the domain of "map".
367 */
368__isl_give isl_stride_info *isl_map_get_range_stride_info(
369	__isl_keep isl_map *map, int pos)
370{
371	isl_stride_info *si;
372	isl_set *set;
373	isl_size n_in;
374
375	n_in = isl_map_dim(map, isl_dim_in);
376	if (n_in < 0)
377		return NULL;
378	map = isl_map_copy(map);
379	map = isl_map_project_onto(map, isl_dim_out, pos, 1);
380	set = isl_map_wrap(map);
381	si = isl_set_get_stride_info(set, n_in);
382	isl_set_free(set);
383	if (!si)
384		return NULL;
385	si->offset = isl_aff_domain_factor_domain(si->offset);
386	if (!si->offset)
387		return isl_stride_info_free(si);
388	return si;
389}
390