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
 224  * can be converted to a function expressed in the same way.
 225  */
 226 static void test_conversion(isl::ctx ctx)
 227 {
 228         C(&isl::set::as_pw_multi_aff, {
 229         { "[N=0:] -> { [] }",
 230           "[N=0:] -> { [] }" },
 231         });
 232
 233         C(&isl::multi_pw_aff::as_set, {
 234         { "[n] -> { [] : n >= 0 } ",
 235           "[n] -> { [] : n >= 0 } " },
 236         });
 237
 238         C(&isl::map::as_pw_multi_aff, {
 239         { "{ [a] -> [a//2] : "
 240             "exists (e0: 8*floor((-a + e0)/8) <= -8 - a + 8e0) }",
 241           "{ [a] -> [a//2] : "
 242             "exists (e0: 8*floor((-a + e0)/8) <= -8 - a + 8e0) }" },
 243         });
 244 }
 245
 246 /* Perform some basic preimage tests.
 247  */
 248 static void test_preimage(isl::ctx ctx)
 249 {
 250         C(arg<isl::multi_aff>(&isl::set::preimage), {
 251         { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
 252           "{ A[j,i] -> B[i,j] }",
 253           "{ A[j,i] : 0 <= i < 10 and 0 <= j < 100 }" },
 254         { "{ rat: B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
 255           "{ A[a,b] -> B[a/2,b/6] }",
 256           "{ rat: A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 }" },
 257         { "{ B[i,j] : 0 <= i, j and 3 i + 5 j <= 100 }",
 258           "{ A[a,b] -> B[a/2,b/6] }",
 259           "{ A[a,b] : 0 <= a, b and 9 a + 5 b <= 600 and "
 260                     "exists i,j : a = 2 i and b = 6 j }" },
 261         { "[n] -> { S[i] : 0 <= i <= 100 }", "[n] -> { S[n] }",
 262           "[n] -> { : 0 <= n <= 100 }" },
 263         { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
 264           "{ A[a] -> B[2a] }",
 265           "{ A[a] : 0 <= a < 50 and exists b : a = 2 b }" },
 266         { "{ B[i] : 0 <= i < 100 and exists a : i = 4 a }",
 267           "{ A[a] -> B[([a/2])] }",
 268           "{ A[a] : 0 <= a < 200 and exists b : [a/2] = 4 b }" },
 269         { "{ B[i,j,k] : 0 <= i,j,k <= 100 }",
 270           "{ A[a] -> B[a,a,a/3] }",
 271           "{ A[a] : 0 <= a <= 100 and exists b : a = 3 b }" },
 272         { "{ B[i,j] : j = [(i)/2] } ", "{ A[i,j] -> B[i/3,j] }",
 273           "{ A[i,j] : j = [(i)/6] and exists a : i = 3 a }" },
 274         });
 275
 276         C(arg<isl::pw_multi_aff>(&isl::set::preimage), {
 277         { "{ B[i,j] : 0 <= i < 10 and 0 <= j < 100 }",
 278           "{ A[j,i] -> B[i,j] : false }",
 279           "{ A[j,i] : false }" },
 280         });
 281
 282         C(arg<isl::multi_aff>(&isl::union_map::preimage_domain), {
 283         { "{ B[i,j] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }",
 284           "{ A[j,i] -> B[i,j] }",
 285           "{ A[j,i] -> C[2i + 3j] : 0 <= i < 10 and 0 <= j < 100 }" },
 286         { "{ B[i] -> C[i]; D[i] -> E[i] }",
 287           "{ A[i] -> B[i + 1] }",
 288           "{ A[i] -> C[i + 1] }" },
 289         { "{ B[i] -> C[i]; B[i] -> E[i] }",
 290           "{ A[i] -> B[i + 1] }",
 291           "{ A[i] -> C[i + 1]; A[i] -> E[i + 1] }" },
 292         { "{ B[i] -> C[([i/2])] }",
 293           "{ A[i] -> B[2i] }",
 294           "{ A[i] -> C[i] }" },
 295         { "{ B[i,j] -> C[([i/2]), ([(i+j)/3])] }",
 296           "{ A[i] -> B[([i/5]), ([i/7])] }",
 297           "{ A[i] -> C[([([i/5])/2]), ([(([i/5])+([i/7]))/3])] }" },
 298         { "[N] -> { B[i] -> C[([N/2]), i, ([N/3])] }",
 299           "[N] -> { A[] -> B[([N/5])] }",
 300           "[N] -> { A[] -> C[([N/2]), ([N/5]), ([N/3])] }" },
 301         { "{ B[i] -> C[i] : exists a : i = 5 a }",
 302           "{ A[i] -> B[2i] }",
 303           "{ A[i] -> C[2i] : exists a : 2i = 5 a }" },
 304         { "{ B[i] -> C[i] : exists a : i = 2 a; "
 305             "B[i] -> D[i] : exists a : i = 2 a + 1 }",
 306           "{ A[i] -> B[2i] }",
 307           "{ A[i] -> C[2i] }" },
 308         { "{ A[i] -> B[i] }", "{ C[i] -> A[(i + floor(i/3))/2] }",
 309           "{ C[i] -> B[j] : 2j = i + floor(i/3) }" },
 310         });
 311
 312         C(arg<isl::multi_aff>(&isl::union_map::preimage_range), {
 313         { "[M] -> { A[a] -> B[a] }", "[M] -> { C[] -> B[floor(M/2)] }",
 314           "[M] -> { A[floor(M/2)] -> C[] }" },
 315         });
 316 }
 317
 318 /* Perform some basic fixed power tests.
 319  */
 320 static void test_fixed_power(isl::ctx ctx)
 321 {
 322         C(arg<isl::val>(&isl::map::fixed_power), {
 323         { "{ [i] -> [i + 1] }", "23",
 324           "{ [i] -> [i + 23] }" },
 325         { "{ [a = 0:1, b = 0:15, c = 0:1, d = 0:1, 0] -> [a, b, c, d, 1]; "
 326             "[a = 0:1, b = 0:15, c = 0:1, 0, 1] -> [a, b, c, 1, 0];  "
 327             "[a = 0:1, b = 0:15, 0, 1, 1] -> [a, b, 1, 0, 0];  "
 328             "[a = 0:1, b = 0:14, 1, 1, 1] -> [a, 1 + b, 0, 0, 0];  "
 329             "[0, 15, 1, 1, 1] -> [1, 0, 0, 0, 0] }",
 330           "128",
 331           "{ [0, b = 0:15, c = 0:1, d = 0:1, e = 0:1] -> [1, b, c, d, e] }" },
 332         });
 333 }
 334
 335 /* Perform some basic intersection tests.
 336  */
 337 static void test_intersect(isl::ctx ctx)
 338 {
 339         C(&isl::union_map::intersect_domain_wrapped_domain, {
 340         { "{ [A[x] -> B[y]] -> C[z]; [D[x] -> A[y]] -> E[z] }",
 341           "{ A[0] }",
 342           "{ [A[0] -> B[y]] -> C[z] }" },
 343         { "{ C[z] -> [A[x] -> B[y]]; E[z] -> [D[x] -> A[y]] }",
 344           "{ A[0] }",
 345           "{ }" },
 346         { "{ T[A[x] -> B[y]] -> C[z]; [D[x] -> A[y]] -> E[z] }",
 347           "{ A[0] }",
 348           "{ T[A[0] -> B[y]] -> C[z] }" },
 349         });
 350
 351         C(&isl::union_map::intersect_range_wrapped_domain, {
 352         { "{ [A[x] -> B[y]] -> C[z]; [D[x] -> A[y]] -> E[z] }",
 353           "{ A[0] }",
 354           "{ }" },
 355         { "{ C[z] -> [A[x] -> B[y]]; E[z] -> [D[x] -> A[y]] }",
 356           "{ A[0] }",
 357           "{ C[z] -> [A[0] -> B[y]] }" },
 358         { "{ C[z] -> T[A[x] -> B[y]]; E[z] -> [D[x] -> A[y]] }",
 359           "{ A[0] }",
 360           "{ C[z] -> T[A[0] -> B[y]] }" },
 361         });
 362 }
 363
 364 /* Perform some basic gist tests.
 365  */
 366 static void test_gist(isl::ctx ctx)
 367 {
 368         C(arg<isl::set>(&isl::pw_aff::gist), {
 369         { "{ [x] -> [x] : x != 0 }", "{ [x] : x < -1 or x > 1 }",
 370           "{ [x] -> [x] }" },
 371         });
 372
 373         C(&isl::pw_aff::gist_params, {
 374         { "[N] -> { D[x] -> [x] : N >= 0; D[x] -> [0] : N < 0 }",
 375           "[N] -> { : N >= 0 }",
 376           "[N] -> { D[x] -> [x] }" },
 377         });
 378
 379         C(arg<isl::set>(&isl::multi_aff::gist), {
 380         { "{ A[i] -> B[i, i] }", "{ A[0] }",
 381           "{ A[i] -> B[0, 0] }" },
 382         { "[N] -> { A[i] -> B[i, N] }", "[N] -> { A[0] : N = 5 }",
 383           "[N] -> { A[i] -> B[0, 5] }" },
 384         { "[N] -> { B[N + 1, N] }", "[N] -> { : N = 5 }",
 385           "[N] -> { B[6, 5] }" },
 386         { "[N] -> { A[i] -> B[] }", "[N] -> { A[0] : N = 5 }",
 387           "[N] -> { A[i] -> B[] }" },
 388         { "[N] -> { B[] }", "[N] -> { : N = 5 }",
 389           "[N] -> { B[] }" },
 390         });
 391
 392         C(&isl::multi_aff::gist_params, {
 393         { "[N] -> { A[i] -> B[i, N] }", "[N] -> { : N = 5 }",
 394           "[N] -> { A[i] -> B[i, 5] }" },
 395         { "[N] -> { B[N + 1, N] }", "[N] -> { : N = 5 }",
 396           "[N] -> { B[6, 5] }" },
 397         { "[N] -> { A[i] -> B[] }", "[N] -> { : N = 5 }",
 398           "[N] -> { A[i] -> B[] }" },
 399         { "[N] -> { B[] }", "[N] -> { : N = 5 }",
 400           "[N] -> { B[] }" },
 401         });
 402
 403         C(arg<isl::set>(&isl::multi_pw_aff::gist), {
 404         { "{ A[i] -> B[i, i] : i >= 0 }", "{ A[0] }",
 405           "{ A[i] -> B[0, 0] }" },
 406         { "[N] -> { A[i] -> B[i, N] : N >= 0 }", "[N] -> { A[0] : N = 5 }",
 407           "[N] -> { A[i] -> B[0, 5] }" },
 408         { "[N] -> { B[N + 1, N] }", "[N] -> { : N = 5 }",
 409           "[N] -> { B[6, 5] }" },
 410         { "[N] -> { A[i] -> B[] }", "[N] -> { A[0] : N = 5 }",
 411           "[N] -> { A[i] -> B[] }" },
 412         { "[N] -> { B[] }", "[N] -> { : N = 5 }",
 413           "[N] -> { B[] }" },
 414         { "{ A[i=0:10] -> B[i] }", "{ A[5] }",
 415           "{ A[i] -> B[5] }" },
 416         { "{ A[0:10] -> B[] }", "{ A[0:10] }",
 417           "{ A[i] -> B[] }" },
 418         { "[N] -> { A[i] -> B[] : N >= 0 }", "[N] -> { A[0] : N = 5 }",
 419           "[N] -> { A[i] -> B[] }" },
 420         { "[N] -> { B[] : N >= 0 }", "[N] -> { : N = 5 }",
 421           "[N] -> { B[] }" },
 422         { "[N] -> { B[] : N = 5 }", "[N] -> { : N >= 0 }",
 423           "[N] -> { B[] : N = 5 }" },
 424         });
 425
 426         C(&isl::multi_pw_aff::gist_params, {
 427         { "[N] -> { A[i] -> B[i, N] : N >= 0 }", "[N] -> { : N = 5 }",
 428           "[N] -> { A[i] -> B[i, 5] }" },
 429         { "[N] -> { B[N + 1, N] }", "[N] -> { : N = 5 }",
 430           "[N] -> { B[6, 5] }" },
 431         { "[N] -> { A[i] -> B[] : N >= 0 }", "[N] -> { : N = 5 }",
 432           "[N] -> { A[i] -> B[] }" },
 433         { "[N] -> { B[] : N >= 0 }", "[N] -> { : N = 5 }",
 434           "[N] -> { B[] }" },
 435         { "[N] -> { B[] : N >= 5 }", "[N] -> { : N >= 0 }",
 436           "[N] -> { B[] : N >= 5 }" },
 437         });
 438
 439         C(&isl::multi_union_pw_aff::gist, {
 440         { "C[{ B[i,i] -> [3i] }]", "{ B[i,i] }",
 441           "C[{ B[i,j] -> [3i] }]" },
 442         { "(C[] : { B[i,i] })", "{ B[i,i] }",
 443           "(C[] : { B[i,j] })" },
 444         { "[N] -> (C[] : { B[N,N] })", "[N] -> { B[N,N] }",
 445           "[N] -> (C[] : { B[i,j] })" },
 446         { "C[]", "{ B[i,i] }",
 447           "C[]" },
 448         { "[N] -> (C[] : { B[i,i] : N >= 0 })", "{ B[i,i] }",
 449           "[N] -> (C[] : { B[i,j] : N >= 0 })" },
 450         { "[N] -> (C[] : { : N >= 0 })", "{ B[i,i] }",
 451           "[N] -> (C[] : { : N >= 0 })" },
 452         { "[N] -> (C[] : { : N >= 0 })", "[N] -> { B[i,i] : N >= 0 }",
 453           "[N] -> C[]" },
 454         });
 455
 456         C(&isl::multi_union_pw_aff::gist_params, {
 457         { "[N] -> C[{ B[i,i] -> [3i + N] }]", "[N] -> { : N = 1 }",
 458           "[N] -> C[{ B[i,i] -> [3i + 1] }]" },
 459         { "C[{ B[i,i] -> [3i] }]", "[N] -> { : N >= 0 }",
 460           "[N] -> C[{ B[i,i] -> [3i] }]" },
 461         { "[N] -> C[{ B[i,i] -> [3i] : N >= 0 }]", "[N] -> { : N >= 0 }",
 462           "[N] -> C[{ B[i,i] -> [3i] }]" },
 463         { "[N] -> C[{ B[i,i] -> [3i] : N >= 1 }]", "[N] -> { : N >= 0 }",
 464           "[N] -> C[{ B[i,i] -> [3i] : N >= 1 }]" },
 465         { "[N] -> (C[] : { B[i,i] : N >= 0 })", "[N] -> { : N >= 0 }",
 466           "[N] -> (C[] : { B[i,i] })" },
 467         { "[N] -> (C[] : { : N >= 0 })", "[N] -> { : N >= 0 }",
 468           "[N] -> C[]" },
 469         { "C[{ B[i,i] -> [3i] }]", "[N] -> { : N >= 0 }",
 470           "[N] -> C[{ B[i,i] -> [3i] }]" },
 471         });
 472 }
 473
 474 /* Perform tests that project out parameters.
 475  */
 476 static void test_project(isl::ctx ctx)
 477 {
 478         C(arg<isl::id>(&isl::union_map::project_out_param), {
 479         { "[N] -> { D[i] -> A[0:N-1]; D[i] -> B[i] }", "N",
 480           "{ D[i] -> A[0:]; D[i] -> B[i] }" },
 481         { "[N] -> { D[i] -> A[0:N-1]; D[i] -> B[i] }", "M",
 482           "[N] -> { D[i] -> A[0:N-1]; D[i] -> B[i] }" },
 483         });
 484
 485         C(arg<isl::id_list>(&isl::union_map::project_out_param), {
 486         { "[M, N, O] -> { D[i] -> A[j] : i <= j < M, N, O }", "(M, N)",
 487           "[O] -> { D[i] -> A[j] : i <= j < O }" },
 488         });
 489 }
 490
 491 /* Perform some basic reverse tests.
 492  */
 493 static void test_reverse(isl::ctx ctx)
 494 {
 495         C(&isl::aff::domain_reverse, {
 496         { "{ T[A[] -> B[*]] -> [0] }",
 497           "{ [B[*] -> A[]] -> [0] }" },
 498         { "{ T[A[] -> A[]] -> [0] }",
 499           "{ T[A[] -> A[]] -> [0] }" },
 500         { "{ [A[x] -> B[y]] -> [5*(x // 2) + 7*(y // 3)] }",
 501           "{ [B[y] -> A[x]] -> [5*(x // 2) + 7*(y // 3)] }" },
 502         });
 503
 504         C(&isl::multi_aff::domain_reverse, {
 505         { "{ [A[x] -> B[y]] -> [5*(x // 2) + 7*(y // 3)] }",
 506           "{ [B[y] -> A[x]] -> [5*(x // 2) + 7*(y // 3)] }" },
 507         { "{ [A[x] -> B[y]] -> T[5*(x // 2) + 7*(y // 3), 0] }",
 508           "{ [B[y] -> A[x]] -> T[5*(x // 2) + 7*(y // 3), 0] }" },
 509         });
 510
 511         C(&isl::set::wrapped_reverse, {
 512         { "{ T[A[] -> B[*]] }",
 513           "{ [B[*] -> A[]] }" },
 514         { "{ T[A[] -> A[]] }",
 515           "{ T[A[] -> A[]] }" },
 516         { "{ [A[x] -> B[2x]] }",
 517           "{ [B[y] -> A[x]] : y = 2x }" },
 518         });
 519
 520         C(&isl::pw_aff::domain_reverse, {
 521         { "{ [A[x] -> B[y]] -> [5*(x // 2) + 7*(y // 3)] }",
 522           "{ [B[y] -> A[x]] -> [5*(x // 2) + 7*(y // 3)] }" },
 523         { "{ [A[x] -> B[y]] -> [5*(x // 2) + 7*(y // 3)] : x > y }",
 524           "{ [B[y] -> A[x]] -> [5*(x // 2) + 7*(y // 3)] : x > y }" },
 525         { "{ [A[i] -> B[i + 1]] -> [i + 2] }",
 526           "{ [B[i] -> A[i - 1]] -> [i + 1] }" },
 527         });
 528
 529         C(&isl::pw_multi_aff::domain_reverse, {
 530         { "{ [A[x] -> B[y]] -> T[5*(x // 2) + 7*(y // 3), 0] : x > y }",
 531           "{ [B[y] -> A[x]] -> T[5*(x // 2) + 7*(y // 3), 0] : x > y }" },
 532         { "{ [A[i] -> B[i + 1]] -> T[0, i + 2] }",
 533           "{ [B[i] -> A[i - 1]] -> T[0, i + 1] }" },
 534         });
 535
 536         C(&isl::multi_pw_aff::domain_reverse, {
 537         { "{ [A[x] -> B[y]] -> T[5*(x // 2) + 7*(y // 3) : x > y, 0] }",
 538           "{ [B[y] -> A[x]] -> T[5*(x // 2) + 7*(y // 3) : x > y, 0] }" },
 539         });
 540
 541         C(&isl::map::domain_reverse, {
 542         { "{ [A[] -> B[]] -> [C[] -> D[]] }",
 543           "{ [B[] -> A[]] -> [C[] -> D[]] }" },
 544         { "{ N[B[] -> C[]] -> A[] }",
 545           "{ [C[] -> B[]] -> A[] }" },
 546         { "{ N[B[x] -> B[y]] -> A[] }",
 547           "{ N[B[*] -> B[*]] -> A[] }" },
 548         });
 549
 550         C(&isl::union_map::domain_reverse, {
 551         { "{ [A[] -> B[]] -> [C[] -> D[]] }",
 552           "{ [B[] -> A[]] -> [C[] -> D[]] }" },
 553         { "{ A[] -> [B[] -> C[]]; A[] -> B[]; A[0] -> N[B[1] -> B[2]] }",
 554           "{ }" },
 555         { "{ N[B[] -> C[]] -> A[] }",
 556           "{ [C[] -> B[]] -> A[] }" },
 557         { "{ N[B[x] -> B[y]] -> A[] }",
 558           "{ N[B[*] -> B[*]] -> A[] }" },
 559         });
 560
 561         C(&isl::union_map::range_reverse, {
 562         { "{ A[] -> [B[] -> C[]]; A[] -> B[]; A[0] -> N[B[1] -> B[2]] }",
 563           "{ A[] -> [C[] -> B[]]; A[0] -> N[B[2] -> B[1]] }" },
 564         { "{ A[] -> N[B[] -> C[]] }",
 565           "{ A[] -> [C[] -> B[]] }" },
 566         { "{ A[] -> N[B[x] -> B[y]] }",
 567           "{ A[] -> N[B[*] -> B[*]] }" },
 568         });
 569 }
 570
 571 /* Perform some basic scaling tests.
 572  */
 573 static void test_scale(isl::ctx ctx)
 574 {
 575         C(arg<isl::multi_val>(&isl::pw_multi_aff::scale), {
 576         { "{ A[a] -> B[a, a + 1, a - 1] : a >= 0 }", "{ B[2, 7, 0] }",
 577           "{ A[a] -> B[2a, 7a + 7, 0] : a >= 0 }" },
 578         });
 579         C(arg<isl::multi_val>(&isl::pw_multi_aff::scale), {
 580         { "{ A[a] -> B[1, a - 1] : a >= 0 }", "{ B[1/2, 7] }",
 581           "{ A[a] -> B[1/2, 7a - 7] : a >= 0 }" },
 582         });
 583
 584         C(arg<isl::multi_val>(&isl::pw_multi_aff::scale_down), {
 585         { "{ A[a] -> B[a, a + 1] : a >= 0 }", "{ B[2, 7] }",
 586           "{ A[a] -> B[a/2, (a + 1)/7] : a >= 0 }" },
 587         });
 588         C(arg<isl::multi_val>(&isl::pw_multi_aff::scale_down), {
 589         { "{ A[a] -> B[a, a - 1] : a >= 0 }", "{ B[2, 1/7] }",
 590           "{ A[a] -> B[a/2, 7a - 7] : a >= 0 }" },
 591         });
 592 }
 593
 594 /* Perform some basic isl::id_to_id tests.
 595  */
 596 static void test_id_to_id(isl::ctx ctx)
 597 {
 598         C((arg<isl::id, isl::id>(&isl::id_to_id::set)), {
 599         { "{ }", "a", "b",
 600           "{ a: b }" },
 601         { "{ a: b }", "a", "b",
 602           "{ a: b }" },
 603         { "{ a: c }", "a", "b",
 604           "{ a: b }" },
 605         { "{ a: b }", "b", "a",
 606           "{ a: b, b: a }" },
 607         { "{ a: b }", "b", "a",
 608           "{ b: a, a: b }" },
 609         });
 610 }
 611
 612 /* The list of tests to perform.
 613  */
 614 static std::vector<std::pair<const char *, void (*)(isl::ctx)>> tests =
 615 {
 616         { "space", &test_space },
 617         { "conversion", &test_conversion },
 618         { "preimage", &test_preimage },
 619         { "fixed power", &test_fixed_power },
 620         { "intersect", &test_intersect },
 621         { "gist", &test_gist },
 622         { "project out parameters", &test_project },
 623         { "reverse", &test_reverse },
 624         { "scale", &test_scale },
 625         { "id-to-id", &test_id_to_id },
 626 };
 627
 628 /* Perform some basic checks by means of the C++ bindings.
 629  */
 630 int main(int argc, char **argv)
 631 {
 632         int ret = EXIT_SUCCESS;
 633         struct isl_ctx *ctx;
 634         struct isl_options *options;
 635
 636         options = isl_options_new_with_defaults();
 637         assert(options);
 638         argc = isl_options_parse(options, argc, argv, ISL_ARG_ALL);
 639         ctx = isl_ctx_alloc_with_options(&isl_options_args, options);
 640
 641         try {
 642                 for (const auto &f : tests) {
 643                         std::cout << f.first << "\n";
 644                         f.second(ctx);
 645                 }
 646         } catch (const isl::exception &e) {
 647                 std::cerr << e.what() << "\n";
 648                 ret = EXIT_FAILURE;
 649         }
 650
 651         isl_ctx_free(ctx);
 652         return ret;
 653 }