isl_test2.cc

   1 /*
   2  * Copyright 2008-2009 Katholieke Universiteit Leuven
   3  * Copyright 2010      INRIA Saclay
   4  * Copyright 2012-2013 Ecole Normale Superieure
   5  * Copyright 2014      INRIA Rocquencourt
   6  * Copyright 2021-2022 Cerebras Systems
   7  *
   8  * Use of this software is governed by the MIT license
   9  *
  10  * Written by Sven Verdoolaege, K.U.Leuven, Departement
  11  * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
  12  * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
  13  * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
  14  * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
  15  * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
  16  * B.P. 105 - 78153 Le Chesnay, France
  17  * and Cerebras Systems, 1237 E Arques Ave, Sunnyvale, CA, USA
  18  */
  19
  20 #include <assert.h>
  21 #include <stdlib.h>
  22
  23 #include <functional>
  24 #include <iostream>
  25 #include <sstream>
  26 #include <string>
  27 #include <type_traits>
  28 #include <utility>
  29 #include <vector>
  30
  31 #include <isl/cpp.h>
  32
  33 /* A binary isl function that appears in the C++ bindings
  34  * as a unary method in a class T, taking an extra argument
  35  * of type A1 and returning an object of type R.
  36  */
  37 template <typename A1, typename R, typename T>
  38 using binary_fn = R (T::*)(A1) const;
  39
  40 /* A function for selecting an overload of a pointer to a unary C++ method
  41  * based on the single argument type.
  42  * The object type and the return type are meant to be deduced.
  43  */
  44 template <typename A1, typename R, typename T>
  45 static binary_fn<A1, R, T> const arg(const binary_fn<A1, R, T> &fn)
  46 {
  47         return fn;
  48 }
  49
  50 /* A ternary isl function that appears in the C++ bindings
  51  * as a binary method in a class T, taking extra arguments
  52  * of type A1 and A2 and returning an object of type R.
  53  */
  54 template <typename A1, typename A2, typename R, typename T>
  55 using ternary_fn = R (T::*)(A1, A2) const;
  56
  57 /* A function for selecting an overload of a pointer to a binary C++ method
  58  * based on the (first) argument type(s).
  59  * The object type and the return type are meant to be deduced.
  60  */
  61 template <typename A1, typename A2, typename R, typename T>
  62 static ternary_fn<A1, A2, R, T> const arg(const ternary_fn<A1, A2, R, T> &fn)
  63 {
  64         return fn;
  65 }
  66
  67 /* A description of the input and the output of a unary operation.
  68  */
  69 struct unary {
  70         const char *arg;
  71         const char *res;
  72 };
  73
  74 /* A description of the inputs and the output of a binary operation.
  75  */
  76 struct binary {
  77         const char *arg1;
  78         const char *arg2;
  79         const char *res;
  80 };
  81
  82 /* A description of the inputs and the output of a ternary operation.
  83  */
  84 struct ternary {
  85         const char *arg1;
  86         const char *arg2;
  87         const char *arg3;
  88         const char *res;
  89 };
  90
  91 /* A template function for checking whether two objects
  92  * of the same (isl) type are (obviously) equal.
  93  * The spelling depends on the isl type and
  94  * in particular on whether an equality method is available or
  95  * whether only obvious equality can be tested.
  96  */
  97 template <typename T, typename std::decay<decltype(
  98         std::declval<T>().is_equal(std::declval<T>()))>::type = true>
  99 static bool is_equal(const T &a, const T &b)
 100 {
 101         return a.is_equal(b);
 102 }
 103 template <typename T, typename std::decay<decltype(
 104         std::declval<T>().plain_is_equal(std::declval<T>()))>::type = true>
 105 static bool is_equal(const T &a, const T &b)
 106 {
 107         return a.plain_is_equal(b);
 108 }
 109
 110 /* A helper macro for throwing an isl::exception_invalid with message "msg".
 111  */
 112 #define THROW_INVALID(msg) \
 113         isl::exception::throw_error(isl_error_invalid, msg, __FILE__, __LINE__)
 114
 115 /* Run a sequence of tests of method "fn" with stringification "name" and
 116  * with input and output described by "test",
 117  * throwing an exception when an unexpected result is produced.
 118  */
 119 template <typename R, typename T>
 120 static void test(isl::ctx ctx, R (T::*fn)() const, const std::string &name,
 121         const std::vector<unary> &tests)
 122 {
 123         for (const auto &test : tests) {
 124                 T obj(ctx, test.arg);
 125                 R expected(ctx, test.res);
 126                 const auto &res = (obj.*fn)();
 127                 std::ostringstream ss;
 128
 129                 if (is_equal(expected, res))
 130                         continue;
 131
 132                 ss << name << "(" << test.arg << ") =\n"
 133                    << res << "\n"
 134                    << "expecting:\n"
 135                    << expected;
 136                 THROW_INVALID(ss.str().c_str());
 137         }
 138 }
 139
 140 /* Run a sequence of tests of method "fn" with stringification "name" and
 141  * with inputs and output described by "test",
 142  * throwing an exception when an unexpected result is produced.
 143  */
 144 template <typename R, typename T, typename A1>
 145 static void test(isl::ctx ctx, R (T::*fn)(A1) const, const std::string &name,
 146         const std::vector<binary> &tests)
 147 {
 148         for (const auto &test : tests) {
 149                 T obj(ctx, test.arg1);
 150                 A1 arg1(ctx, test.arg2);
 151                 R expected(ctx, test.res);
 152                 const auto &res = (obj.*fn)(arg1);
 153                 std::ostringstream ss;
 154
 155                 if (is_equal(expected, res))
 156                         continue;
 157
 158                 ss << name << "(" << test.arg1 << ", " << test.arg2 << ") =\n"
 159                    << res << "\n"
 160                    << "expecting:\n"
 161                    << expected;
 162                 THROW_INVALID(ss.str().c_str());
 163         }
 164 }
 165
 166 /* Run a sequence of tests of method "fn" with stringification "name" and
 167  * with inputs and output described by "test",
 168  * throwing an exception when an unexpected result is produced.
 169  */
 170 template <typename R, typename T, typename A1, typename A2>
 171 static void test(isl::ctx ctx, R (T::*fn)(A1, A2) const,
 172         const std::string &name, const std::vector<ternary> &tests)
 173 {
 174         for (const auto &test : tests) {
 175                 T obj(ctx, test.arg1);
 176                 A1 arg1(ctx, test.arg2);
 177                 A2 arg2(ctx, test.arg3);
 178                 R expected(ctx, test.res);
 179                 const auto &res = (obj.*fn)(arg1, arg2);
 180                 std::ostringstream ss;
 181
 182                 if (is_equal(expected, res))
 183                         continue;
 184
 185                 ss << name << "(" << test.arg1 << ", " << test.arg2 << ", "
 186                    << test.arg3 << ") =\n"
 187                    << res << "\n"
 188                    << "expecting:\n"
 189                    << expected;
 190                 THROW_INVALID(ss.str().c_str());
 191         }
 192 }
 193
 194 /* A helper macro that calls test with as implicit initial argument "ctx" and
 195  * as extra argument a stringification of "FN".
 196  */
 197 #define C(FN, ...) test(ctx, FN, #FN, __VA_ARGS__)
 198
 199 /* Perform some basic isl::space tests.
 200  */
 201 static void test_space(isl::ctx ctx)
 202 {
 203         C(&isl::space::domain, {
 204         { "{ A[] -> B[] }", "{ A[] }" },
 205         { "{ A[C[] -> D[]] -> B[E[] -> F[]] }", "{ A[C[] -> D[]] }" },
 206         });
 207
 208         C(&isl::space::range, {
 209         { "{ A[] -> B[] }", "{ B[] }" },
 210         { "{ A[C[] -> D[]] -> B[E[] -> F[]] }", "{ B[E[] -> F[]] }" },
 211         });
 212
 213         C(&isl::space::params, {
 214         { "{ A[] -> B[] }", "{ : }" },
 215         { "{ A[C[] -> D[]] -> B[E[] -> F[]] }", "{ : }" },
 216         });
 217 }
 218
 219 /* Perform some basic conversion tests.
 220  *
 221  * In particular, check that a map with an output dimension
 222  * that is equal to some integer division over a domain involving
 223  * a local variable without a known integer division expression or
 224  * to some linear combination of integer divisions
 225  * can be converted to a function expressed in the same way.
 226  */
 227 static void test_conversion(isl::ctx ctx)
 228 {
 229         C(&isl::set::as_pw_multi_aff, {
 230         { "[N=0:] -> { [] }",
 231           "[N=0:] -> { [] }" },
 232         });
 233
 234         C(&isl::multi_pw_aff::as_set, {
 235         { "[n] -> { [] : n >= 0 } ",
 236           "[n] -> { [] : n >= 0 } " },
 237         });
 238
 239         C(&isl::map::as_pw_multi_aff, {
 240         { "{ [a] -> [a//2] : "
 241             "exists (e0: 8*floor((-a + e0)/8) <= -8 - a + 8e0) }",
 242           "{ [a] -> [a//2] : "
 243             "exists (e0: 8*floor((-a + e0)/8) <= -8 - a + 8e0) }" },
 244         { "{ [a, b] -> [(2*floor((a)/8) + floor((b)/6))] }",
 245           "{ [a, b] -> [(2*floor((a)/8) + floor((b)/6))] }" },
 246         });
 247 }
 248
 249 /* Perform some basic preimage tests.
 250  */
 251 static void test_preimage(isl::ctx ctx)
 252 {
 253         C(arg<isl::multi_aff>(&isl::set::preimage), {
 254         { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
 255           "{ A[j,i] -> B[i,j] }",
 256           "{ A[j,i] : 0 <= i < 10 and 0 <= j < 100 }" },
 257         { "{ rat: B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
 258           "{ A[a,b] -> B[a/2,b/6] }",
 259           "{ rat: A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 }" },
 260         { "{ B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
 261           "{ A[a,b] -> B[a/2,b/6] }",
 262           "{ A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 and "
 263                     "exists i,j : a = 2 i and b = 6 j }" },
 264         { "[n] -> { S[i] : 0 <= i <= 100 }", "[n] -> { S[n] }",
 265           "[n] -> { : 0 <= n <= 100 }" },
 266         { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
 267           "{ A[a] -> B[2a] }",
 268           "{ A[a] : 0 <= a < 50 and exists b : a = 2 b }" },
 269         { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
 270           "{ A[a] -> B[([a/2])] }",
 271           "{ A[a] : 0 <= a < 200 and exists b : [a/2] = 4 b }" },
 272         { "{ B[i,j,k] : 0 <= i,j,k <= 100 }",
 273           "{ A[a] -> B[a,a,a/3] }",
 274           "{ A[a] : 0 <= a <= 100 and exists b : a = 3 b }" },
 275         { "{ B[i,j] : j = [(i)/2] } ", "{ A[i,j] -> B[i/3,j] }",
 276           "{ A[i,j] : j = [(i)/6] and exists a : i = 3 a }" },
 277         });
 278
 279         C(arg<isl::pw_multi_aff>(&isl::set::preimage), {
 280         { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
 281           "{ A[j,i] -> B[i,j] : false }",
 282           "{ A[j,i] : false }" },
 283         });
 284
 285         C(arg<isl::multi_aff>(&isl::union_map::preimage_domain), {
 286         { "{ B[i,j] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }",
 287           "{ A[j,i] -> B[i,j] }",
 288           "{ A[j,i] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }" },
 289         { "{ B[i] -> C[i]; D[i] -> E[i] }",
 290           "{ A[i] -> B[i + 1] }",
 291           "{ A[i] -> C[i + 1] }" },
 292         { "{ B[i] -> C[i]; B[i] -> E[i] }",
 293           "{ A[i] -> B[i + 1] }",
 294           "{ A[i] -> C[i + 1]; A[i] -> E[i + 1] }" },
 295         { "{ B[i] -> C[([i/2])] }",
 296           "{ A[i] -> B[2i] }",
 297           "{ A[i] -> C[i] }" },
 298         { "{ B[i,j] -> C[([i/2]), ([(i+j)/3])] }",
 299           "{ A[i] -> B[([i/5]), ([i/7])] }",
 300           "{ A[i] -> C[([([i/5])/2]), ([(([i/5])+([i/7]))/3])] }" },
 301         { "[N] -> { B[i] -> C[([N/2]), i, ([N/3])] }",
 302           "[N] -> { A[] -> B[([N/5])] }",
 303           "[N] -> { A[] -> C[([N/2]), ([N/5]), ([N/3])] }" },
 304         { "{ B[i] -> C[i] : exists a : i = 5 a }",
 305           "{ A[i] -> B[2i] }",
 306           "{ A[i] -> C[2i] : exists a : 2i = 5 a }" },
 307         { "{ B[i] -> C[i] : exists a : i = 2 a; "
 308             "B[i] -> D[i] : exists a : i = 2 a + 1 }",
 309           "{ A[i] -> B[2i] }",
 310           "{ A[i] -> C[2i] }" },
 311         { "{ A[i] -> B[i] }", "{ C[i] -> A[(i + floor(i/3))/2] }",
 312           "{ C[i] -> B[j] : 2j = i + floor(i/3) }" },
 313         });
 314
 315         C(arg<isl::multi_aff>(&isl::union_map::preimage_range), {
 316         { "[M] -> { A[a] -> B[a] }", "[M] -> { C[] -> B[floor(M/2)] }",
 317           "[M] -> { A[floor(M/2)] -> C[] }" },
 318         });
 319 }
 320
 321 /* Perform some basic fixed power tests.
 322  */
 323 static void test_fixed_power(isl::ctx ctx)
 324 {
 325         C(arg<isl::val>(&isl::map::fixed_power), {
 326         { "{ [i] -> [i + 1] }", "23",
 327           "{ [i] -> [i + 23] }" },
 328         { "{ [a = 0:1, b = 0:15, c = 0:1, d = 0:1, 0] -> [a, b, c, d, 1]; "
 329             "[a = 0:1, b = 0:15, c = 0:1, 0, 1] -> [a, b, c, 1, 0];  "
 330             "[a = 0:1, b = 0:15, 0, 1, 1] -> [a, b, 1, 0, 0];  "
 331             "[a = 0:1, b = 0:14, 1, 1, 1] -> [a, 1 + b, 0, 0, 0];  "
 332             "[0, 15, 1, 1, 1] -> [1, 0, 0, 0, 0] }",
 333           "128",
 334           "{ [0, b = 0:15, c = 0:1, d = 0:1, e = 0:1] -> [1, b, c, d, e] }" },
 335         });
 336 }
 337
 338 /* Perform some basic intersection tests.
 339  */
 340 static void test_intersect(isl::ctx ctx)
 341 {
 342         C(&isl::union_map::intersect_domain_wrapped_domain, {
 343         { "{ [A[x] -> B[y]] -> C[z]; [D[x] -> A[y]] -> E[z] }",
 344           "{ A[0] }",
 345           "{ [A[0] -> B[y]] -> C[z] }" },
 346         { "{ C[z] -> [A[x] -> B[y]]; E[z] -> [D[x] -> A[y]] }",
 347           "{ A[0] }",
 348           "{ }" },
 349         { "{ T[A[x] -> B[y]] -> C[z]; [D[x] -> A[y]] -> E[z] }",
 350           "{ A[0] }",
 351           "{ T[A[0] -> B[y]] -> C[z] }" },
 352         });
 353
 354         C(&isl::union_map::intersect_range_wrapped_domain, {
 355         { "{ [A[x] -> B[y]] -> C[z]; [D[x] -> A[y]] -> E[z] }",
 356           "{ A[0] }",
 357           "{ }" },
 358         { "{ C[z] -> [A[x] -> B[y]]; E[z] -> [D[x] -> A[y]] }",
 359           "{ A[0] }",
 360           "{ C[z] -> [A[0] -> B[y]] }" },
 361         { "{ C[z] -> T[A[x] -> B[y]]; E[z] -> [D[x] -> A[y]] }",
 362           "{ A[0] }",
 363           "{ C[z] -> T[A[0] -> B[y]] }" },
 364         });
 365 }
 366
 367 /* Perform some basic gist tests.
 368  */
 369 static void test_gist(isl::ctx ctx)
 370 {
 371         C(arg<isl::set>(&isl::pw_aff::gist), {
 372         { "{ [x] -> [x] : x != 0 }", "{ [x] : x < -1 or x > 1 }",
 373           "{ [x] -> [x] }" },
 374         });
 375
 376         C(&isl::pw_aff::gist_params, {
 377         { "[N] -> { D[x] -> [x] : N >= 0; D[x] -> [0] : N < 0 }",
 378           "[N] -> { : N >= 0 }",
 379           "[N] -> { D[x] -> [x] }" },
 380         });
 381
 382         C(arg<isl::set>(&isl::multi_aff::gist), {
 383         { "{ A[i] -> B[i, i] }", "{ A[0] }",
 384           "{ A[i] -> B[0, 0] }" },
 385         { "[N] -> { A[i] -> B[i, N] }", "[N] -> { A[0] : N = 5 }",
 386           "[N] -> { A[i] -> B[0, 5] }" },
 387         { "[N] -> { B[N + 1, N] }", "[N] -> { : N = 5 }",
 388           "[N] -> { B[6, 5] }" },
 389         { "[N] -> { A[i] -> B[] }", "[N] -> { A[0] : N = 5 }",
 390           "[N] -> { A[i] -> B[] }" },
 391         { "[N] -> { B[] }", "[N] -> { : N = 5 }",
 392           "[N] -> { B[] }" },
 393         });
 394
 395         C(&isl::multi_aff::gist_params, {
 396         { "[N] -> { A[i] -> B[i, N] }", "[N] -> { : N = 5 }",
 397           "[N] -> { A[i] -> B[i, 5] }" },
 398         { "[N] -> { B[N + 1, N] }", "[N] -> { : N = 5 }",
 399           "[N] -> { B[6, 5] }" },
 400         { "[N] -> { A[i] -> B[] }", "[N] -> { : N = 5 }",
 401           "[N] -> { A[i] -> B[] }" },
 402         { "[N] -> { B[] }", "[N] -> { : N = 5 }",
 403           "[N] -> { B[] }" },
 404         });
 405
 406         C(arg<isl::set>(&isl::multi_pw_aff::gist), {
 407         { "{ A[i] -> B[i, i] : i >= 0 }", "{ A[0] }",
 408           "{ A[i] -> B[0, 0] }" },
 409         { "[N] -> { A[i] -> B[i, N] : N >= 0 }", "[N] -> { A[0] : N = 5 }",
 410           "[N] -> { A[i] -> B[0, 5] }" },
 411         { "[N] -> { B[N + 1, N] }", "[N] -> { : N = 5 }",
 412           "[N] -> { B[6, 5] }" },
 413         { "[N] -> { A[i] -> B[] }", "[N] -> { A[0] : N = 5 }",
 414           "[N] -> { A[i] -> B[] }" },
 415         { "[N] -> { B[] }", "[N] -> { : N = 5 }",
 416           "[N] -> { B[] }" },
 417         { "{ A[i=0:10] -> B[i] }", "{ A[5] }",
 418           "{ A[i] -> B[5] }" },
 419         { "{ A[0:10] -> B[] }", "{ A[0:10] }",
 420           "{ A[i] -> B[] }" },
 421         { "[N] -> { A[i] -> B[] : N >= 0 }", "[N] -> { A[0] : N = 5 }",
 422           "[N] -> { A[i] -> B[] }" },
 423         { "[N] -> { B[] : N >= 0 }", "[N] -> { : N = 5 }",
 424           "[N] -> { B[] }" },
 425         { "[N] -> { B[] : N = 5 }", "[N] -> { : N >= 0 }",
 426           "[N] -> { B[] : N = 5 }" },
 427         });
 428
 429         C(&isl::multi_pw_aff::gist_params, {
 430         { "[N] -> { A[i] -> B[i, N] : N >= 0 }", "[N] -> { : N = 5 }",
 431           "[N] -> { A[i] -> B[i, 5] }" },
 432         { "[N] -> { B[N + 1, N] }", "[N] -> { : N = 5 }",
 433           "[N] -> { B[6, 5] }" },
 434         { "[N] -> { A[i] -> B[] : N >= 0 }", "[N] -> { : N = 5 }",
 435           "[N] -> { A[i] -> B[] }" },
 436         { "[N] -> { B[] : N >= 0 }", "[N] -> { : N = 5 }",
 437           "[N] -> { B[] }" },
 438         { "[N] -> { B[] : N >= 5 }", "[N] -> { : N >= 0 }",
 439           "[N] -> { B[] : N >= 5 }" },
 440         });
 441
 442         C(&isl::multi_union_pw_aff::gist, {
 443         { "C[{ B[i,i] -> [3i] }]", "{ B[i,i] }",
 444           "C[{ B[i,j] -> [3i] }]" },
 445         { "(C[] : { B[i,i] })", "{ B[i,i] }",
 446           "(C[] : { B[i,j] })" },
 447         { "[N] -> (C[] : { B[N,N] })", "[N] -> { B[N,N] }",
 448           "[N] -> (C[] : { B[i,j] })" },
 449         { "C[]", "{ B[i,i] }",
 450           "C[]" },
 451         { "[N] -> (C[] : { B[i,i] : N >= 0 })", "{ B[i,i] }",
 452           "[N] -> (C[] : { B[i,j] : N >= 0 })" },
 453         { "[N] -> (C[] : { : N >= 0 })", "{ B[i,i] }",
 454           "[N] -> (C[] : { : N >= 0 })" },
 455         { "[N] -> (C[] : { : N >= 0 })", "[N] -> { B[i,i] : N >= 0 }",
 456           "[N] -> C[]" },
 457         });
 458
 459         C(&isl::multi_union_pw_aff::gist_params, {
 460         { "[N] -> C[{ B[i,i] -> [3i + N] }]", "[N] -> { : N = 1 }",
 461           "[N] -> C[{ B[i,i] -> [3i + 1] }]" },
 462         { "C[{ B[i,i] -> [3i] }]", "[N] -> { : N >= 0 }",
 463           "[N] -> C[{ B[i,i] -> [3i] }]" },
 464         { "[N] -> C[{ B[i,i] -> [3i] : N >= 0 }]", "[N] -> { : N >= 0 }",
 465           "[N] -> C[{ B[i,i] -> [3i] }]" },
 466         { "[N] -> C[{ B[i,i] -> [3i] : N >= 1 }]", "[N] -> { : N >= 0 }",
 467           "[N] -> C[{ B[i,i] -> [3i] : N >= 1 }]" },
 468         { "[N] -> (C[] : { B[i,i] : N >= 0 })", "[N] -> { : N >= 0 }",
 469           "[N] -> (C[] : { B[i,i] })" },
 470         { "[N] -> (C[] : { : N >= 0 })", "[N] -> { : N >= 0 }",
 471           "[N] -> C[]" },
 472         { "C[{ B[i,i] -> [3i] }]", "[N] -> { : N >= 0 }",
 473           "[N] -> C[{ B[i,i] -> [3i] }]" },
 474         });
 475 }
 476
 477 /* Perform tests that project out parameters.
 478  */
 479 static void test_project(isl::ctx ctx)
 480 {
 481         C(arg<isl::id>(&isl::union_map::project_out_param), {
 482         { "[N] -> { D[i] -> A[0:N-1]; D[i] -> B[i] }", "N",
 483           "{ D[i] -> A[0:]; D[i] -> B[i] }" },
 484         { "[N] -> { D[i] -> A[0:N-1]; D[i] -> B[i] }", "M",
 485           "[N] -> { D[i] -> A[0:N-1]; D[i] -> B[i] }" },
 486         });
 487
 488         C(arg<isl::id_list>(&isl::union_map::project_out_param), {
 489         { "[M, N, O] -> { D[i] -> A[j] : i <= j < M, N, O }", "(M, N)",
 490           "[O] -> { D[i] -> A[j] : i <= j < O }" },
 491         });
 492 }
 493
 494 /* Perform some basic reverse tests.
 495  */
 496 static void test_reverse(isl::ctx ctx)
 497 {
 498         C(&isl::aff::domain_reverse, {
 499         { "{ T[A[] -> B[*]] -> [0] }",
 500           "{ [B[*] -> A[]] -> [0] }" },
 501         { "{ T[A[] -> A[]] -> [0] }",
 502           "{ T[A[] -> A[]] -> [0] }" },
 503         { "{ [A[x] -> B[y]] -> [5*(x // 2) + 7*(y // 3)] }",
 504           "{ [B[y] -> A[x]] -> [5*(x // 2) + 7*(y // 3)] }" },
 505         });
 506
 507         C(&isl::multi_aff::domain_reverse, {
 508         { "{ [A[x] -> B[y]] -> [5*(x // 2) + 7*(y // 3)] }",
 509           "{ [B[y] -> A[x]] -> [5*(x // 2) + 7*(y // 3)] }" },
 510         { "{ [A[x] -> B[y]] -> T[5*(x // 2) + 7*(y // 3), 0] }",
 511           "{ [B[y] -> A[x]] -> T[5*(x // 2) + 7*(y // 3), 0] }" },
 512         });
 513
 514         C(&isl::set::wrapped_reverse, {
 515         { "{ T[A[] -> B[*]] }",
 516           "{ [B[*] -> A[]] }" },
 517         { "{ T[A[] -> A[]] }",
 518           "{ T[A[] -> A[]] }" },
 519         { "{ [A[x] -> B[2x]] }",
 520           "{ [B[y] -> A[x]] : y = 2x }" },
 521         });
 522
 523         C(&isl::pw_aff::domain_reverse, {
 524         { "{ [A[x] -> B[y]] -> [5*(x // 2) + 7*(y // 3)] }",
 525           "{ [B[y] -> A[x]] -> [5*(x // 2) + 7*(y // 3)] }" },
 526         { "{ [A[x] -> B[y]] -> [5*(x // 2) + 7*(y // 3)] : x > y }",
 527           "{ [B[y] -> A[x]] -> [5*(x // 2) + 7*(y // 3)] : x > y }" },
 528         { "{ [A[i] -> B[i + 1]] -> [i + 2] }",
 529           "{ [B[i] -> A[i - 1]] -> [i + 1] }" },
 530         });
 531
 532         C(&isl::pw_multi_aff::domain_reverse, {
 533         { "{ [A[x] -> B[y]] -> T[5*(x // 2) + 7*(y // 3), 0] : x > y }",
 534           "{ [B[y] -> A[x]] -> T[5*(x // 2) + 7*(y // 3), 0] : x > y }" },
 535         { "{ [A[i] -> B[i + 1]] -> T[0, i + 2] }",
 536           "{ [B[i] -> A[i - 1]] -> T[0, i + 1] }" },
 537         });
 538
 539         C(&isl::multi_pw_aff::domain_reverse, {
 540         { "{ [A[x] -> B[y]] -> T[5*(x // 2) + 7*(y // 3) : x > y, 0] }",
 541           "{ [B[y] -> A[x]] -> T[5*(x // 2) + 7*(y // 3) : x > y, 0] }" },
 542         });
 543
 544         C(&isl::map::domain_reverse, {
 545         { "{ [A[] -> B[]] -> [C[] -> D[]] }",
 546           "{ [B[] -> A[]] -> [C[] -> D[]] }" },
 547         { "{ N[B[] -> C[]] -> A[] }",
 548           "{ [C[] -> B[]] -> A[] }" },
 549         { "{ N[B[x] -> B[y]] -> A[] }",
 550           "{ N[B[*] -> B[*]] -> A[] }" },
 551         });
 552
 553         C(&isl::union_map::domain_reverse, {
 554         { "{ [A[] -> B[]] -> [C[] -> D[]] }",
 555           "{ [B[] -> A[]] -> [C[] -> D[]] }" },
 556         { "{ A[] -> [B[] -> C[]]; A[] -> B[]; A[0] -> N[B[1] -> B[2]] }",
 557           "{ }" },
 558         { "{ N[B[] -> C[]] -> A[] }",
 559           "{ [C[] -> B[]] -> A[] }" },
 560         { "{ N[B[x] -> B[y]] -> A[] }",
 561           "{ N[B[*] -> B[*]] -> A[] }" },
 562         });
 563
 564         C(&isl::union_map::range_reverse, {
 565         { "{ A[] -> [B[] -> C[]]; A[] -> B[]; A[0] -> N[B[1] -> B[2]] }",
 566           "{ A[] -> [C[] -> B[]]; A[0] -> N[B[2] -> B[1]] }" },
 567         { "{ A[] -> N[B[] -> C[]] }",
 568           "{ A[] -> [C[] -> B[]] }" },
 569         { "{ A[] -> N[B[x] -> B[y]] }",
 570           "{ A[] -> N[B[*] -> B[*]] }" },
 571         });
 572 }
 573
 574 /* Perform some basic scaling tests.
 575  */
 576 static void test_scale(isl::ctx ctx)
 577 {
 578         C(arg<isl::multi_val>(&isl::pw_multi_aff::scale), {
 579         { "{ A[a] -> B[a, a + 1, a - 1] : a >= 0 }", "{ B[2, 7, 0] }",
 580           "{ A[a] -> B[2a, 7a + 7, 0] : a >= 0 }" },
 581         });
 582         C(arg<isl::multi_val>(&isl::pw_multi_aff::scale), {
 583         { "{ A[a] -> B[1, a - 1] : a >= 0 }", "{ B[1/2, 7] }",
 584           "{ A[a] -> B[1/2, 7a - 7] : a >= 0 }" },
 585         });
 586
 587         C(arg<isl::multi_val>(&isl::pw_multi_aff::scale_down), {
 588         { "{ A[a] -> B[a, a + 1] : a >= 0 }", "{ B[2, 7] }",
 589           "{ A[a] -> B[a/2, (a + 1)/7] : a >= 0 }" },
 590         });
 591         C(arg<isl::multi_val>(&isl::pw_multi_aff::scale_down), {
 592         { "{ A[a] -> B[a, a - 1] : a >= 0 }", "{ B[2, 1/7] }",
 593           "{ A[a] -> B[a/2, 7a - 7] : a >= 0 }" },
 594         });
 595 }
 596
 597 /* Perform some basic isl::id_to_id tests.
 598  */
 599 static void test_id_to_id(isl::ctx ctx)
 600 {
 601         C((arg<isl::id, isl::id>(&isl::id_to_id::set)), {
 602         { "{ }", "a", "b",
 603           "{ a: b }" },
 604         { "{ a: b }", "a", "b",
 605           "{ a: b }" },
 606         { "{ a: c }", "a", "b",
 607           "{ a: b }" },
 608         { "{ a: b }", "b", "a",
 609           "{ a: b, b: a }" },
 610         { "{ a: b }", "b", "a",
 611           "{ b: a, a: b }" },
 612         });
 613 }
 614
 615 /* The list of tests to perform.
 616  */
 617 static std::vector<std::pair<const char *, void (*)(isl::ctx)>> tests =
 618 {
 619         { "space", &test_space },
 620         { "conversion", &test_conversion },
 621         { "preimage", &test_preimage },
 622         { "fixed power", &test_fixed_power },
 623         { "intersect", &test_intersect },
 624         { "gist", &test_gist },
 625         { "project out parameters", &test_project },
 626         { "reverse", &test_reverse },
 627         { "scale", &test_scale },
 628         { "id-to-id", &test_id_to_id },
 629 };
 630
 631 /* Perform some basic checks by means of the C++ bindings.
 632  */
 633 int main(int argc, char **argv)
 634 {
 635         int ret = EXIT_SUCCESS;
 636         struct isl_ctx *ctx;
 637         struct isl_options *options;
 638
 639         options = isl_options_new_with_defaults();
 640         assert(options);
 641         argc = isl_options_parse(options, argc, argv, ISL_ARG_ALL);
 642         ctx = isl_ctx_alloc_with_options(&isl_options_args, options);
 643
 644         try {
 645                 for (const auto &f : tests) {
 646                         std::cout << f.first << "\n";
 647                         f.second(ctx);
 648                 }
 649         } catch (const isl::exception &e) {
 650                 std::cerr << e.what() << "\n";
 651                 ret = EXIT_FAILURE;
 652         }
 653
 654         isl_ctx_free(ctx);
 655         return ret;
 656 }