1 //===- unittests/Support/MathExtrasTest.cpp - math utils tests ------------===// 2 // 3 // The LLVM Compiler Infrastructure 4 // 5 // This file is distributed under the University of Illinois Open Source 6 // License. See LICENSE.TXT for details. 7 // 8 //===----------------------------------------------------------------------===// 9 10 #include "gtest/gtest.h" 11 #include "llvm/Support/MathExtras.h" 12 13 using namespace llvm; 14 15 namespace { 16 17 TEST(MathExtras, countTrailingZeros) { 18 uint8_t Z8 = 0; 19 uint16_t Z16 = 0; 20 uint32_t Z32 = 0; 21 uint64_t Z64 = 0; 22 EXPECT_EQ(8u, countTrailingZeros(Z8)); 23 EXPECT_EQ(16u, countTrailingZeros(Z16)); 24 EXPECT_EQ(32u, countTrailingZeros(Z32)); 25 EXPECT_EQ(64u, countTrailingZeros(Z64)); 26 27 uint8_t NZ8 = 42; 28 uint16_t NZ16 = 42; 29 uint32_t NZ32 = 42; 30 uint64_t NZ64 = 42; 31 EXPECT_EQ(1u, countTrailingZeros(NZ8)); 32 EXPECT_EQ(1u, countTrailingZeros(NZ16)); 33 EXPECT_EQ(1u, countTrailingZeros(NZ32)); 34 EXPECT_EQ(1u, countTrailingZeros(NZ64)); 35 } 36 37 TEST(MathExtras, countLeadingZeros) { 38 uint8_t Z8 = 0; 39 uint16_t Z16 = 0; 40 uint32_t Z32 = 0; 41 uint64_t Z64 = 0; 42 EXPECT_EQ(8u, countLeadingZeros(Z8)); 43 EXPECT_EQ(16u, countLeadingZeros(Z16)); 44 EXPECT_EQ(32u, countLeadingZeros(Z32)); 45 EXPECT_EQ(64u, countLeadingZeros(Z64)); 46 47 uint8_t NZ8 = 42; 48 uint16_t NZ16 = 42; 49 uint32_t NZ32 = 42; 50 uint64_t NZ64 = 42; 51 EXPECT_EQ(2u, countLeadingZeros(NZ8)); 52 EXPECT_EQ(10u, countLeadingZeros(NZ16)); 53 EXPECT_EQ(26u, countLeadingZeros(NZ32)); 54 EXPECT_EQ(58u, countLeadingZeros(NZ64)); 55 56 EXPECT_EQ(8u, countLeadingZeros(0x00F000FFu)); 57 EXPECT_EQ(8u, countLeadingZeros(0x00F12345u)); 58 for (unsigned i = 0; i <= 30; ++i) { 59 EXPECT_EQ(31 - i, countLeadingZeros(1u << i)); 60 } 61 62 EXPECT_EQ(8u, countLeadingZeros(0x00F1234500F12345ULL)); 63 EXPECT_EQ(1u, countLeadingZeros(1ULL << 62)); 64 for (unsigned i = 0; i <= 62; ++i) { 65 EXPECT_EQ(63 - i, countLeadingZeros(1ULL << i)); 66 } 67 } 68 69 TEST(MathExtras, findFirstSet) { 70 uint8_t Z8 = 0; 71 uint16_t Z16 = 0; 72 uint32_t Z32 = 0; 73 uint64_t Z64 = 0; 74 EXPECT_EQ(0xFFULL, findFirstSet(Z8)); 75 EXPECT_EQ(0xFFFFULL, findFirstSet(Z16)); 76 EXPECT_EQ(0xFFFFFFFFULL, findFirstSet(Z32)); 77 EXPECT_EQ(0xFFFFFFFFFFFFFFFFULL, findFirstSet(Z64)); 78 79 uint8_t NZ8 = 42; 80 uint16_t NZ16 = 42; 81 uint32_t NZ32 = 42; 82 uint64_t NZ64 = 42; 83 EXPECT_EQ(1u, findFirstSet(NZ8)); 84 EXPECT_EQ(1u, findFirstSet(NZ16)); 85 EXPECT_EQ(1u, findFirstSet(NZ32)); 86 EXPECT_EQ(1u, findFirstSet(NZ64)); 87 } 88 89 TEST(MathExtras, findLastSet) { 90 uint8_t Z8 = 0; 91 uint16_t Z16 = 0; 92 uint32_t Z32 = 0; 93 uint64_t Z64 = 0; 94 EXPECT_EQ(0xFFULL, findLastSet(Z8)); 95 EXPECT_EQ(0xFFFFULL, findLastSet(Z16)); 96 EXPECT_EQ(0xFFFFFFFFULL, findLastSet(Z32)); 97 EXPECT_EQ(0xFFFFFFFFFFFFFFFFULL, findLastSet(Z64)); 98 99 uint8_t NZ8 = 42; 100 uint16_t NZ16 = 42; 101 uint32_t NZ32 = 42; 102 uint64_t NZ64 = 42; 103 EXPECT_EQ(5u, findLastSet(NZ8)); 104 EXPECT_EQ(5u, findLastSet(NZ16)); 105 EXPECT_EQ(5u, findLastSet(NZ32)); 106 EXPECT_EQ(5u, findLastSet(NZ64)); 107 } 108 109 TEST(MathExtras, isIntN) { 110 EXPECT_TRUE(isIntN(16, 32767)); 111 EXPECT_FALSE(isIntN(16, 32768)); 112 } 113 114 TEST(MathExtras, isUIntN) { 115 EXPECT_TRUE(isUIntN(16, 65535)); 116 EXPECT_FALSE(isUIntN(16, 65536)); 117 EXPECT_TRUE(isUIntN(1, 0)); 118 EXPECT_TRUE(isUIntN(6, 63)); 119 } 120 121 TEST(MathExtras, maxIntN) { 122 EXPECT_EQ(32767, maxIntN(16)); 123 EXPECT_EQ(2147483647, maxIntN(32)); 124 EXPECT_EQ(std::numeric_limits<int32_t>::max(), maxIntN(32)); 125 EXPECT_EQ(std::numeric_limits<int64_t>::max(), maxIntN(64)); 126 } 127 128 TEST(MathExtras, minIntN) { 129 EXPECT_EQ(-32768LL, minIntN(16)); 130 EXPECT_EQ(-64LL, minIntN(7)); 131 EXPECT_EQ(std::numeric_limits<int32_t>::min(), minIntN(32)); 132 EXPECT_EQ(std::numeric_limits<int64_t>::min(), minIntN(64)); 133 } 134 135 TEST(MathExtras, maxUIntN) { 136 EXPECT_EQ(0xffffULL, maxUIntN(16)); 137 EXPECT_EQ(0xffffffffULL, maxUIntN(32)); 138 EXPECT_EQ(0xffffffffffffffffULL, maxUIntN(64)); 139 EXPECT_EQ(1ULL, maxUIntN(1)); 140 EXPECT_EQ(0x0fULL, maxUIntN(4)); 141 } 142 143 TEST(MathExtras, reverseBits) { 144 uint8_t NZ8 = 42; 145 uint16_t NZ16 = 42; 146 uint32_t NZ32 = 42; 147 uint64_t NZ64 = 42; 148 EXPECT_EQ(0x54ULL, reverseBits(NZ8)); 149 EXPECT_EQ(0x5400ULL, reverseBits(NZ16)); 150 EXPECT_EQ(0x54000000ULL, reverseBits(NZ32)); 151 EXPECT_EQ(0x5400000000000000ULL, reverseBits(NZ64)); 152 } 153 154 TEST(MathExtras, isPowerOf2_32) { 155 EXPECT_TRUE(isPowerOf2_32(1 << 6)); 156 EXPECT_TRUE(isPowerOf2_32(1 << 12)); 157 EXPECT_FALSE(isPowerOf2_32((1 << 19) + 3)); 158 EXPECT_FALSE(isPowerOf2_32(0xABCDEF0)); 159 } 160 161 TEST(MathExtras, isPowerOf2_64) { 162 EXPECT_TRUE(isPowerOf2_64(1LL << 46)); 163 EXPECT_TRUE(isPowerOf2_64(1LL << 12)); 164 EXPECT_FALSE(isPowerOf2_64((1LL << 53) + 3)); 165 EXPECT_FALSE(isPowerOf2_64(0xABCDEF0ABCDEF0LL)); 166 } 167 168 TEST(MathExtras, PowerOf2Ceil) { 169 EXPECT_EQ(0U, PowerOf2Ceil(0U)); 170 EXPECT_EQ(8U, PowerOf2Ceil(8U)); 171 EXPECT_EQ(8U, PowerOf2Ceil(7U)); 172 } 173 174 TEST(MathExtras, PowerOf2Floor) { 175 EXPECT_EQ(0U, PowerOf2Floor(0U)); 176 EXPECT_EQ(8U, PowerOf2Floor(8U)); 177 EXPECT_EQ(4U, PowerOf2Floor(7U)); 178 } 179 180 TEST(MathExtras, ByteSwap_32) { 181 EXPECT_EQ(0x44332211u, ByteSwap_32(0x11223344)); 182 EXPECT_EQ(0xDDCCBBAAu, ByteSwap_32(0xAABBCCDD)); 183 } 184 185 TEST(MathExtras, ByteSwap_64) { 186 EXPECT_EQ(0x8877665544332211ULL, ByteSwap_64(0x1122334455667788LL)); 187 EXPECT_EQ(0x1100FFEEDDCCBBAAULL, ByteSwap_64(0xAABBCCDDEEFF0011LL)); 188 } 189 190 TEST(MathExtras, countLeadingOnes) { 191 for (int i = 30; i >= 0; --i) { 192 // Start with all ones and unset some bit. 193 EXPECT_EQ(31u - i, countLeadingOnes(0xFFFFFFFF ^ (1 << i))); 194 } 195 for (int i = 62; i >= 0; --i) { 196 // Start with all ones and unset some bit. 197 EXPECT_EQ(63u - i, countLeadingOnes(0xFFFFFFFFFFFFFFFFULL ^ (1LL << i))); 198 } 199 for (int i = 30; i >= 0; --i) { 200 // Start with all ones and unset some bit. 201 EXPECT_EQ(31u - i, countLeadingOnes(0xFFFFFFFF ^ (1 << i))); 202 } 203 } 204 205 TEST(MathExtras, FloatBits) { 206 static const float kValue = 5632.34f; 207 EXPECT_FLOAT_EQ(kValue, BitsToFloat(FloatToBits(kValue))); 208 } 209 210 TEST(MathExtras, DoubleBits) { 211 static const double kValue = 87987234.983498; 212 EXPECT_DOUBLE_EQ(kValue, BitsToDouble(DoubleToBits(kValue))); 213 } 214 215 TEST(MathExtras, MinAlign) { 216 EXPECT_EQ(1u, MinAlign(2, 3)); 217 EXPECT_EQ(2u, MinAlign(2, 4)); 218 EXPECT_EQ(1u, MinAlign(17, 64)); 219 EXPECT_EQ(256u, MinAlign(256, 512)); 220 } 221 222 TEST(MathExtras, NextPowerOf2) { 223 EXPECT_EQ(4u, NextPowerOf2(3)); 224 EXPECT_EQ(16u, NextPowerOf2(15)); 225 EXPECT_EQ(256u, NextPowerOf2(128)); 226 } 227 228 TEST(MathExtras, alignTo) { 229 EXPECT_EQ(8u, alignTo(5, 8)); 230 EXPECT_EQ(24u, alignTo(17, 8)); 231 EXPECT_EQ(0u, alignTo(~0LL, 8)); 232 233 EXPECT_EQ(7u, alignTo(5, 8, 7)); 234 EXPECT_EQ(17u, alignTo(17, 8, 1)); 235 EXPECT_EQ(3u, alignTo(~0LL, 8, 3)); 236 EXPECT_EQ(552u, alignTo(321, 255, 42)); 237 } 238 239 template<typename T> 240 void SaturatingAddTestHelper() 241 { 242 const T Max = std::numeric_limits<T>::max(); 243 bool ResultOverflowed; 244 245 EXPECT_EQ(T(3), SaturatingAdd(T(1), T(2))); 246 EXPECT_EQ(T(3), SaturatingAdd(T(1), T(2), &ResultOverflowed)); 247 EXPECT_FALSE(ResultOverflowed); 248 249 EXPECT_EQ(Max, SaturatingAdd(Max, T(1))); 250 EXPECT_EQ(Max, SaturatingAdd(Max, T(1), &ResultOverflowed)); 251 EXPECT_TRUE(ResultOverflowed); 252 253 EXPECT_EQ(Max, SaturatingAdd(T(1), T(Max - 1))); 254 EXPECT_EQ(Max, SaturatingAdd(T(1), T(Max - 1), &ResultOverflowed)); 255 EXPECT_FALSE(ResultOverflowed); 256 257 EXPECT_EQ(Max, SaturatingAdd(T(1), Max)); 258 EXPECT_EQ(Max, SaturatingAdd(T(1), Max, &ResultOverflowed)); 259 EXPECT_TRUE(ResultOverflowed); 260 261 EXPECT_EQ(Max, SaturatingAdd(Max, Max)); 262 EXPECT_EQ(Max, SaturatingAdd(Max, Max, &ResultOverflowed)); 263 EXPECT_TRUE(ResultOverflowed); 264 } 265 266 TEST(MathExtras, SaturatingAdd) { 267 SaturatingAddTestHelper<uint8_t>(); 268 SaturatingAddTestHelper<uint16_t>(); 269 SaturatingAddTestHelper<uint32_t>(); 270 SaturatingAddTestHelper<uint64_t>(); 271 } 272 273 template<typename T> 274 void SaturatingMultiplyTestHelper() 275 { 276 const T Max = std::numeric_limits<T>::max(); 277 bool ResultOverflowed; 278 279 // Test basic multiplication. 280 EXPECT_EQ(T(6), SaturatingMultiply(T(2), T(3))); 281 EXPECT_EQ(T(6), SaturatingMultiply(T(2), T(3), &ResultOverflowed)); 282 EXPECT_FALSE(ResultOverflowed); 283 284 EXPECT_EQ(T(6), SaturatingMultiply(T(3), T(2))); 285 EXPECT_EQ(T(6), SaturatingMultiply(T(3), T(2), &ResultOverflowed)); 286 EXPECT_FALSE(ResultOverflowed); 287 288 // Test multiplication by zero. 289 EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(0))); 290 EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(0), &ResultOverflowed)); 291 EXPECT_FALSE(ResultOverflowed); 292 293 EXPECT_EQ(T(0), SaturatingMultiply(T(1), T(0))); 294 EXPECT_EQ(T(0), SaturatingMultiply(T(1), T(0), &ResultOverflowed)); 295 EXPECT_FALSE(ResultOverflowed); 296 297 EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(1))); 298 EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(1), &ResultOverflowed)); 299 EXPECT_FALSE(ResultOverflowed); 300 301 EXPECT_EQ(T(0), SaturatingMultiply(Max, T(0))); 302 EXPECT_EQ(T(0), SaturatingMultiply(Max, T(0), &ResultOverflowed)); 303 EXPECT_FALSE(ResultOverflowed); 304 305 EXPECT_EQ(T(0), SaturatingMultiply(T(0), Max)); 306 EXPECT_EQ(T(0), SaturatingMultiply(T(0), Max, &ResultOverflowed)); 307 EXPECT_FALSE(ResultOverflowed); 308 309 // Test multiplication by maximum value. 310 EXPECT_EQ(Max, SaturatingMultiply(Max, T(2))); 311 EXPECT_EQ(Max, SaturatingMultiply(Max, T(2), &ResultOverflowed)); 312 EXPECT_TRUE(ResultOverflowed); 313 314 EXPECT_EQ(Max, SaturatingMultiply(T(2), Max)); 315 EXPECT_EQ(Max, SaturatingMultiply(T(2), Max, &ResultOverflowed)); 316 EXPECT_TRUE(ResultOverflowed); 317 318 EXPECT_EQ(Max, SaturatingMultiply(Max, Max)); 319 EXPECT_EQ(Max, SaturatingMultiply(Max, Max, &ResultOverflowed)); 320 EXPECT_TRUE(ResultOverflowed); 321 322 // Test interesting boundary conditions for algorithm - 323 // ((1 << A) - 1) * ((1 << B) + K) for K in [-1, 0, 1] 324 // and A + B == std::numeric_limits<T>::digits. 325 // We expect overflow iff A > B and K = 1. 326 const int Digits = std::numeric_limits<T>::digits; 327 for (int A = 1, B = Digits - 1; B >= 1; ++A, --B) { 328 for (int K = -1; K <= 1; ++K) { 329 T X = (T(1) << A) - T(1); 330 T Y = (T(1) << B) + K; 331 bool OverflowExpected = A > B && K == 1; 332 333 if(OverflowExpected) { 334 EXPECT_EQ(Max, SaturatingMultiply(X, Y)); 335 EXPECT_EQ(Max, SaturatingMultiply(X, Y, &ResultOverflowed)); 336 EXPECT_TRUE(ResultOverflowed); 337 } else { 338 EXPECT_EQ(X * Y, SaturatingMultiply(X, Y)); 339 EXPECT_EQ(X * Y, SaturatingMultiply(X, Y, &ResultOverflowed)); 340 EXPECT_FALSE(ResultOverflowed); 341 } 342 } 343 } 344 } 345 346 TEST(MathExtras, SaturatingMultiply) { 347 SaturatingMultiplyTestHelper<uint8_t>(); 348 SaturatingMultiplyTestHelper<uint16_t>(); 349 SaturatingMultiplyTestHelper<uint32_t>(); 350 SaturatingMultiplyTestHelper<uint64_t>(); 351 } 352 353 template<typename T> 354 void SaturatingMultiplyAddTestHelper() 355 { 356 const T Max = std::numeric_limits<T>::max(); 357 bool ResultOverflowed; 358 359 // Test basic multiply-add. 360 EXPECT_EQ(T(16), SaturatingMultiplyAdd(T(2), T(3), T(10))); 361 EXPECT_EQ(T(16), SaturatingMultiplyAdd(T(2), T(3), T(10), &ResultOverflowed)); 362 EXPECT_FALSE(ResultOverflowed); 363 364 // Test multiply overflows, add doesn't overflow 365 EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, T(0), &ResultOverflowed)); 366 EXPECT_TRUE(ResultOverflowed); 367 368 // Test multiply doesn't overflow, add overflows 369 EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), T(1), Max, &ResultOverflowed)); 370 EXPECT_TRUE(ResultOverflowed); 371 372 // Test multiply-add with Max as operand 373 EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), T(1), Max, &ResultOverflowed)); 374 EXPECT_TRUE(ResultOverflowed); 375 376 EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), Max, T(1), &ResultOverflowed)); 377 EXPECT_TRUE(ResultOverflowed); 378 379 EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, T(1), &ResultOverflowed)); 380 EXPECT_TRUE(ResultOverflowed); 381 382 EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, Max, &ResultOverflowed)); 383 EXPECT_TRUE(ResultOverflowed); 384 385 // Test multiply-add with 0 as operand 386 EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(1), T(1), T(0), &ResultOverflowed)); 387 EXPECT_FALSE(ResultOverflowed); 388 389 EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(1), T(0), T(1), &ResultOverflowed)); 390 EXPECT_FALSE(ResultOverflowed); 391 392 EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(0), T(0), T(1), &ResultOverflowed)); 393 EXPECT_FALSE(ResultOverflowed); 394 395 EXPECT_EQ(T(0), SaturatingMultiplyAdd(T(0), T(0), T(0), &ResultOverflowed)); 396 EXPECT_FALSE(ResultOverflowed); 397 398 } 399 400 TEST(MathExtras, SaturatingMultiplyAdd) { 401 SaturatingMultiplyAddTestHelper<uint8_t>(); 402 SaturatingMultiplyAddTestHelper<uint16_t>(); 403 SaturatingMultiplyAddTestHelper<uint32_t>(); 404 SaturatingMultiplyAddTestHelper<uint64_t>(); 405 } 406 407 TEST(MathExtras, IsShiftedUInt) { 408 EXPECT_TRUE((isShiftedUInt<1, 0>(0))); 409 EXPECT_TRUE((isShiftedUInt<1, 0>(1))); 410 EXPECT_FALSE((isShiftedUInt<1, 0>(2))); 411 EXPECT_FALSE((isShiftedUInt<1, 0>(3))); 412 EXPECT_FALSE((isShiftedUInt<1, 0>(0x8000000000000000))); 413 EXPECT_TRUE((isShiftedUInt<1, 63>(0x8000000000000000))); 414 EXPECT_TRUE((isShiftedUInt<2, 62>(0xC000000000000000))); 415 EXPECT_FALSE((isShiftedUInt<2, 62>(0xE000000000000000))); 416 417 // 0x201 is ten bits long and has a 1 in the MSB and LSB. 418 EXPECT_TRUE((isShiftedUInt<10, 5>(uint64_t(0x201) << 5))); 419 EXPECT_FALSE((isShiftedUInt<10, 5>(uint64_t(0x201) << 4))); 420 EXPECT_FALSE((isShiftedUInt<10, 5>(uint64_t(0x201) << 6))); 421 } 422 423 TEST(MathExtras, IsShiftedInt) { 424 EXPECT_TRUE((isShiftedInt<1, 0>(0))); 425 EXPECT_TRUE((isShiftedInt<1, 0>(-1))); 426 EXPECT_FALSE((isShiftedInt<1, 0>(2))); 427 EXPECT_FALSE((isShiftedInt<1, 0>(3))); 428 EXPECT_FALSE((isShiftedInt<1, 0>(0x8000000000000000))); 429 EXPECT_TRUE((isShiftedInt<1, 63>(0x8000000000000000))); 430 EXPECT_TRUE((isShiftedInt<2, 62>(0xC000000000000000))); 431 EXPECT_FALSE((isShiftedInt<2, 62>(0xE000000000000000))); 432 433 // 0x201 is ten bits long and has a 1 in the MSB and LSB. 434 EXPECT_TRUE((isShiftedInt<11, 5>(int64_t(0x201) << 5))); 435 EXPECT_FALSE((isShiftedInt<11, 5>(int64_t(0x201) << 3))); 436 EXPECT_FALSE((isShiftedInt<11, 5>(int64_t(0x201) << 6))); 437 EXPECT_TRUE((isShiftedInt<11, 5>(-(int64_t(0x201) << 5)))); 438 EXPECT_FALSE((isShiftedInt<11, 5>(-(int64_t(0x201) << 3)))); 439 EXPECT_FALSE((isShiftedInt<11, 5>(-(int64_t(0x201) << 6)))); 440 441 EXPECT_TRUE((isShiftedInt<6, 10>(-(int64_t(1) << 15)))); 442 EXPECT_FALSE((isShiftedInt<6, 10>(int64_t(1) << 15))); 443 } 444 445 } // namespace 446