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(0, PowerOf2Ceil(0)); 170 EXPECT_EQ(8, PowerOf2Ceil(8)); 171 EXPECT_EQ(8, PowerOf2Ceil(7)); 172 } 173 174 TEST(MathExtras, ByteSwap_32) { 175 EXPECT_EQ(0x44332211u, ByteSwap_32(0x11223344)); 176 EXPECT_EQ(0xDDCCBBAAu, ByteSwap_32(0xAABBCCDD)); 177 } 178 179 TEST(MathExtras, ByteSwap_64) { 180 EXPECT_EQ(0x8877665544332211ULL, ByteSwap_64(0x1122334455667788LL)); 181 EXPECT_EQ(0x1100FFEEDDCCBBAAULL, ByteSwap_64(0xAABBCCDDEEFF0011LL)); 182 } 183 184 TEST(MathExtras, countLeadingOnes) { 185 for (int i = 30; i >= 0; --i) { 186 // Start with all ones and unset some bit. 187 EXPECT_EQ(31u - i, countLeadingOnes(0xFFFFFFFF ^ (1 << i))); 188 } 189 for (int i = 62; i >= 0; --i) { 190 // Start with all ones and unset some bit. 191 EXPECT_EQ(63u - i, countLeadingOnes(0xFFFFFFFFFFFFFFFFULL ^ (1LL << i))); 192 } 193 for (int i = 30; i >= 0; --i) { 194 // Start with all ones and unset some bit. 195 EXPECT_EQ(31u - i, countLeadingOnes(0xFFFFFFFF ^ (1 << i))); 196 } 197 } 198 199 TEST(MathExtras, FloatBits) { 200 static const float kValue = 5632.34f; 201 EXPECT_FLOAT_EQ(kValue, BitsToFloat(FloatToBits(kValue))); 202 } 203 204 TEST(MathExtras, DoubleBits) { 205 static const double kValue = 87987234.983498; 206 EXPECT_DOUBLE_EQ(kValue, BitsToDouble(DoubleToBits(kValue))); 207 } 208 209 TEST(MathExtras, MinAlign) { 210 EXPECT_EQ(1u, MinAlign(2, 3)); 211 EXPECT_EQ(2u, MinAlign(2, 4)); 212 EXPECT_EQ(1u, MinAlign(17, 64)); 213 EXPECT_EQ(256u, MinAlign(256, 512)); 214 } 215 216 TEST(MathExtras, NextPowerOf2) { 217 EXPECT_EQ(4u, NextPowerOf2(3)); 218 EXPECT_EQ(16u, NextPowerOf2(15)); 219 EXPECT_EQ(256u, NextPowerOf2(128)); 220 } 221 222 TEST(MathExtras, alignTo) { 223 EXPECT_EQ(8u, alignTo(5, 8)); 224 EXPECT_EQ(24u, alignTo(17, 8)); 225 EXPECT_EQ(0u, alignTo(~0LL, 8)); 226 227 EXPECT_EQ(7u, alignTo(5, 8, 7)); 228 EXPECT_EQ(17u, alignTo(17, 8, 1)); 229 EXPECT_EQ(3u, alignTo(~0LL, 8, 3)); 230 EXPECT_EQ(552u, alignTo(321, 255, 42)); 231 } 232 233 template<typename T> 234 void SaturatingAddTestHelper() 235 { 236 const T Max = std::numeric_limits<T>::max(); 237 bool ResultOverflowed; 238 239 EXPECT_EQ(T(3), SaturatingAdd(T(1), T(2))); 240 EXPECT_EQ(T(3), SaturatingAdd(T(1), T(2), &ResultOverflowed)); 241 EXPECT_FALSE(ResultOverflowed); 242 243 EXPECT_EQ(Max, SaturatingAdd(Max, T(1))); 244 EXPECT_EQ(Max, SaturatingAdd(Max, T(1), &ResultOverflowed)); 245 EXPECT_TRUE(ResultOverflowed); 246 247 EXPECT_EQ(Max, SaturatingAdd(T(1), T(Max - 1))); 248 EXPECT_EQ(Max, SaturatingAdd(T(1), T(Max - 1), &ResultOverflowed)); 249 EXPECT_FALSE(ResultOverflowed); 250 251 EXPECT_EQ(Max, SaturatingAdd(T(1), Max)); 252 EXPECT_EQ(Max, SaturatingAdd(T(1), Max, &ResultOverflowed)); 253 EXPECT_TRUE(ResultOverflowed); 254 255 EXPECT_EQ(Max, SaturatingAdd(Max, Max)); 256 EXPECT_EQ(Max, SaturatingAdd(Max, Max, &ResultOverflowed)); 257 EXPECT_TRUE(ResultOverflowed); 258 } 259 260 TEST(MathExtras, SaturatingAdd) { 261 SaturatingAddTestHelper<uint8_t>(); 262 SaturatingAddTestHelper<uint16_t>(); 263 SaturatingAddTestHelper<uint32_t>(); 264 SaturatingAddTestHelper<uint64_t>(); 265 } 266 267 template<typename T> 268 void SaturatingMultiplyTestHelper() 269 { 270 const T Max = std::numeric_limits<T>::max(); 271 bool ResultOverflowed; 272 273 // Test basic multiplication. 274 EXPECT_EQ(T(6), SaturatingMultiply(T(2), T(3))); 275 EXPECT_EQ(T(6), SaturatingMultiply(T(2), T(3), &ResultOverflowed)); 276 EXPECT_FALSE(ResultOverflowed); 277 278 EXPECT_EQ(T(6), SaturatingMultiply(T(3), T(2))); 279 EXPECT_EQ(T(6), SaturatingMultiply(T(3), T(2), &ResultOverflowed)); 280 EXPECT_FALSE(ResultOverflowed); 281 282 // Test multiplication by zero. 283 EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(0))); 284 EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(0), &ResultOverflowed)); 285 EXPECT_FALSE(ResultOverflowed); 286 287 EXPECT_EQ(T(0), SaturatingMultiply(T(1), T(0))); 288 EXPECT_EQ(T(0), SaturatingMultiply(T(1), T(0), &ResultOverflowed)); 289 EXPECT_FALSE(ResultOverflowed); 290 291 EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(1))); 292 EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(1), &ResultOverflowed)); 293 EXPECT_FALSE(ResultOverflowed); 294 295 EXPECT_EQ(T(0), SaturatingMultiply(Max, T(0))); 296 EXPECT_EQ(T(0), SaturatingMultiply(Max, T(0), &ResultOverflowed)); 297 EXPECT_FALSE(ResultOverflowed); 298 299 EXPECT_EQ(T(0), SaturatingMultiply(T(0), Max)); 300 EXPECT_EQ(T(0), SaturatingMultiply(T(0), Max, &ResultOverflowed)); 301 EXPECT_FALSE(ResultOverflowed); 302 303 // Test multiplication by maximum value. 304 EXPECT_EQ(Max, SaturatingMultiply(Max, T(2))); 305 EXPECT_EQ(Max, SaturatingMultiply(Max, T(2), &ResultOverflowed)); 306 EXPECT_TRUE(ResultOverflowed); 307 308 EXPECT_EQ(Max, SaturatingMultiply(T(2), Max)); 309 EXPECT_EQ(Max, SaturatingMultiply(T(2), Max, &ResultOverflowed)); 310 EXPECT_TRUE(ResultOverflowed); 311 312 EXPECT_EQ(Max, SaturatingMultiply(Max, Max)); 313 EXPECT_EQ(Max, SaturatingMultiply(Max, Max, &ResultOverflowed)); 314 EXPECT_TRUE(ResultOverflowed); 315 316 // Test interesting boundary conditions for algorithm - 317 // ((1 << A) - 1) * ((1 << B) + K) for K in [-1, 0, 1] 318 // and A + B == std::numeric_limits<T>::digits. 319 // We expect overflow iff A > B and K = 1. 320 const int Digits = std::numeric_limits<T>::digits; 321 for (int A = 1, B = Digits - 1; B >= 1; ++A, --B) { 322 for (int K = -1; K <= 1; ++K) { 323 T X = (T(1) << A) - T(1); 324 T Y = (T(1) << B) + K; 325 bool OverflowExpected = A > B && K == 1; 326 327 if(OverflowExpected) { 328 EXPECT_EQ(Max, SaturatingMultiply(X, Y)); 329 EXPECT_EQ(Max, SaturatingMultiply(X, Y, &ResultOverflowed)); 330 EXPECT_TRUE(ResultOverflowed); 331 } else { 332 EXPECT_EQ(X * Y, SaturatingMultiply(X, Y)); 333 EXPECT_EQ(X * Y, SaturatingMultiply(X, Y, &ResultOverflowed)); 334 EXPECT_FALSE(ResultOverflowed); 335 } 336 } 337 } 338 } 339 340 TEST(MathExtras, SaturatingMultiply) { 341 SaturatingMultiplyTestHelper<uint8_t>(); 342 SaturatingMultiplyTestHelper<uint16_t>(); 343 SaturatingMultiplyTestHelper<uint32_t>(); 344 SaturatingMultiplyTestHelper<uint64_t>(); 345 } 346 347 template<typename T> 348 void SaturatingMultiplyAddTestHelper() 349 { 350 const T Max = std::numeric_limits<T>::max(); 351 bool ResultOverflowed; 352 353 // Test basic multiply-add. 354 EXPECT_EQ(T(16), SaturatingMultiplyAdd(T(2), T(3), T(10))); 355 EXPECT_EQ(T(16), SaturatingMultiplyAdd(T(2), T(3), T(10), &ResultOverflowed)); 356 EXPECT_FALSE(ResultOverflowed); 357 358 // Test multiply overflows, add doesn't overflow 359 EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, T(0), &ResultOverflowed)); 360 EXPECT_TRUE(ResultOverflowed); 361 362 // Test multiply doesn't overflow, add overflows 363 EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), T(1), Max, &ResultOverflowed)); 364 EXPECT_TRUE(ResultOverflowed); 365 366 // Test multiply-add with Max as operand 367 EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), T(1), Max, &ResultOverflowed)); 368 EXPECT_TRUE(ResultOverflowed); 369 370 EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), Max, T(1), &ResultOverflowed)); 371 EXPECT_TRUE(ResultOverflowed); 372 373 EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, T(1), &ResultOverflowed)); 374 EXPECT_TRUE(ResultOverflowed); 375 376 EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, Max, &ResultOverflowed)); 377 EXPECT_TRUE(ResultOverflowed); 378 379 // Test multiply-add with 0 as operand 380 EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(1), T(1), T(0), &ResultOverflowed)); 381 EXPECT_FALSE(ResultOverflowed); 382 383 EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(1), T(0), T(1), &ResultOverflowed)); 384 EXPECT_FALSE(ResultOverflowed); 385 386 EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(0), T(0), T(1), &ResultOverflowed)); 387 EXPECT_FALSE(ResultOverflowed); 388 389 EXPECT_EQ(T(0), SaturatingMultiplyAdd(T(0), T(0), T(0), &ResultOverflowed)); 390 EXPECT_FALSE(ResultOverflowed); 391 392 } 393 394 TEST(MathExtras, SaturatingMultiplyAdd) { 395 SaturatingMultiplyAddTestHelper<uint8_t>(); 396 SaturatingMultiplyAddTestHelper<uint16_t>(); 397 SaturatingMultiplyAddTestHelper<uint32_t>(); 398 SaturatingMultiplyAddTestHelper<uint64_t>(); 399 } 400 401 TEST(MathExtras, IsShiftedUInt) { 402 EXPECT_TRUE((isShiftedUInt<1, 0>(0))); 403 EXPECT_TRUE((isShiftedUInt<1, 0>(1))); 404 EXPECT_FALSE((isShiftedUInt<1, 0>(2))); 405 EXPECT_FALSE((isShiftedUInt<1, 0>(3))); 406 EXPECT_FALSE((isShiftedUInt<1, 0>(0x8000000000000000))); 407 EXPECT_TRUE((isShiftedUInt<1, 63>(0x8000000000000000))); 408 EXPECT_TRUE((isShiftedUInt<2, 62>(0xC000000000000000))); 409 EXPECT_FALSE((isShiftedUInt<2, 62>(0xE000000000000000))); 410 411 // 0x201 is ten bits long and has a 1 in the MSB and LSB. 412 EXPECT_TRUE((isShiftedUInt<10, 5>(uint64_t(0x201) << 5))); 413 EXPECT_FALSE((isShiftedUInt<10, 5>(uint64_t(0x201) << 4))); 414 EXPECT_FALSE((isShiftedUInt<10, 5>(uint64_t(0x201) << 6))); 415 } 416 417 TEST(MathExtras, IsShiftedInt) { 418 EXPECT_TRUE((isShiftedInt<1, 0>(0))); 419 EXPECT_TRUE((isShiftedInt<1, 0>(-1))); 420 EXPECT_FALSE((isShiftedInt<1, 0>(2))); 421 EXPECT_FALSE((isShiftedInt<1, 0>(3))); 422 EXPECT_FALSE((isShiftedInt<1, 0>(0x8000000000000000))); 423 EXPECT_TRUE((isShiftedInt<1, 63>(0x8000000000000000))); 424 EXPECT_TRUE((isShiftedInt<2, 62>(0xC000000000000000))); 425 EXPECT_FALSE((isShiftedInt<2, 62>(0xE000000000000000))); 426 427 // 0x201 is ten bits long and has a 1 in the MSB and LSB. 428 EXPECT_TRUE((isShiftedInt<11, 5>(int64_t(0x201) << 5))); 429 EXPECT_FALSE((isShiftedInt<11, 5>(int64_t(0x201) << 3))); 430 EXPECT_FALSE((isShiftedInt<11, 5>(int64_t(0x201) << 6))); 431 EXPECT_TRUE((isShiftedInt<11, 5>(-(int64_t(0x201) << 5)))); 432 EXPECT_FALSE((isShiftedInt<11, 5>(-(int64_t(0x201) << 3)))); 433 EXPECT_FALSE((isShiftedInt<11, 5>(-(int64_t(0x201) << 6)))); 434 435 EXPECT_TRUE((isShiftedInt<6, 10>(-(int64_t(1) << 15)))); 436 EXPECT_FALSE((isShiftedInt<6, 10>(int64_t(1) << 15))); 437 } 438 439 } // namespace 440