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 } 125 126 TEST(MathExtras, minIntN) { 127 EXPECT_EQ(-32768LL, minIntN(16)); 128 EXPECT_EQ(-64LL, minIntN(7)); 129 } 130 131 TEST(MathExtras, maxUIntN) { 132 EXPECT_EQ(0xffffULL, maxUIntN(16)); 133 EXPECT_EQ(0xffffffffULL, maxUIntN(32)); 134 EXPECT_EQ(0xffffffffffffffffULL, maxUIntN(64)); 135 EXPECT_EQ(1ULL, maxUIntN(1)); 136 EXPECT_EQ(0x0fULL, maxUIntN(4)); 137 } 138 139 TEST(MathExtras, reverseBits) { 140 uint8_t NZ8 = 42; 141 uint16_t NZ16 = 42; 142 uint32_t NZ32 = 42; 143 uint64_t NZ64 = 42; 144 EXPECT_EQ(0x54ULL, reverseBits(NZ8)); 145 EXPECT_EQ(0x5400ULL, reverseBits(NZ16)); 146 EXPECT_EQ(0x54000000ULL, reverseBits(NZ32)); 147 EXPECT_EQ(0x5400000000000000ULL, reverseBits(NZ64)); 148 } 149 150 TEST(MathExtras, isPowerOf2_32) { 151 EXPECT_TRUE(isPowerOf2_32(1 << 6)); 152 EXPECT_TRUE(isPowerOf2_32(1 << 12)); 153 EXPECT_FALSE(isPowerOf2_32((1 << 19) + 3)); 154 EXPECT_FALSE(isPowerOf2_32(0xABCDEF0)); 155 } 156 157 TEST(MathExtras, isPowerOf2_64) { 158 EXPECT_TRUE(isPowerOf2_64(1LL << 46)); 159 EXPECT_TRUE(isPowerOf2_64(1LL << 12)); 160 EXPECT_FALSE(isPowerOf2_64((1LL << 53) + 3)); 161 EXPECT_FALSE(isPowerOf2_64(0xABCDEF0ABCDEF0LL)); 162 } 163 164 TEST(MathExtras, ByteSwap_32) { 165 EXPECT_EQ(0x44332211u, ByteSwap_32(0x11223344)); 166 EXPECT_EQ(0xDDCCBBAAu, ByteSwap_32(0xAABBCCDD)); 167 } 168 169 TEST(MathExtras, ByteSwap_64) { 170 EXPECT_EQ(0x8877665544332211ULL, ByteSwap_64(0x1122334455667788LL)); 171 EXPECT_EQ(0x1100FFEEDDCCBBAAULL, ByteSwap_64(0xAABBCCDDEEFF0011LL)); 172 } 173 174 TEST(MathExtras, countLeadingOnes) { 175 for (int i = 30; i >= 0; --i) { 176 // Start with all ones and unset some bit. 177 EXPECT_EQ(31u - i, countLeadingOnes(0xFFFFFFFF ^ (1 << i))); 178 } 179 for (int i = 62; i >= 0; --i) { 180 // Start with all ones and unset some bit. 181 EXPECT_EQ(63u - i, countLeadingOnes(0xFFFFFFFFFFFFFFFFULL ^ (1LL << i))); 182 } 183 for (int i = 30; i >= 0; --i) { 184 // Start with all ones and unset some bit. 185 EXPECT_EQ(31u - i, countLeadingOnes(0xFFFFFFFF ^ (1 << i))); 186 } 187 } 188 189 TEST(MathExtras, FloatBits) { 190 static const float kValue = 5632.34f; 191 EXPECT_FLOAT_EQ(kValue, BitsToFloat(FloatToBits(kValue))); 192 } 193 194 TEST(MathExtras, DoubleBits) { 195 static const double kValue = 87987234.983498; 196 EXPECT_DOUBLE_EQ(kValue, BitsToDouble(DoubleToBits(kValue))); 197 } 198 199 TEST(MathExtras, MinAlign) { 200 EXPECT_EQ(1u, MinAlign(2, 3)); 201 EXPECT_EQ(2u, MinAlign(2, 4)); 202 EXPECT_EQ(1u, MinAlign(17, 64)); 203 EXPECT_EQ(256u, MinAlign(256, 512)); 204 } 205 206 TEST(MathExtras, NextPowerOf2) { 207 EXPECT_EQ(4u, NextPowerOf2(3)); 208 EXPECT_EQ(16u, NextPowerOf2(15)); 209 EXPECT_EQ(256u, NextPowerOf2(128)); 210 } 211 212 TEST(MathExtras, alignTo) { 213 EXPECT_EQ(8u, alignTo(5, 8)); 214 EXPECT_EQ(24u, alignTo(17, 8)); 215 EXPECT_EQ(0u, alignTo(~0LL, 8)); 216 217 EXPECT_EQ(7u, alignTo(5, 8, 7)); 218 EXPECT_EQ(17u, alignTo(17, 8, 1)); 219 EXPECT_EQ(3u, alignTo(~0LL, 8, 3)); 220 EXPECT_EQ(552u, alignTo(321, 255, 42)); 221 } 222 223 template<typename T> 224 void SaturatingAddTestHelper() 225 { 226 const T Max = std::numeric_limits<T>::max(); 227 bool ResultOverflowed; 228 229 EXPECT_EQ(T(3), SaturatingAdd(T(1), T(2))); 230 EXPECT_EQ(T(3), SaturatingAdd(T(1), T(2), &ResultOverflowed)); 231 EXPECT_FALSE(ResultOverflowed); 232 233 EXPECT_EQ(Max, SaturatingAdd(Max, T(1))); 234 EXPECT_EQ(Max, SaturatingAdd(Max, T(1), &ResultOverflowed)); 235 EXPECT_TRUE(ResultOverflowed); 236 237 EXPECT_EQ(Max, SaturatingAdd(T(1), T(Max - 1))); 238 EXPECT_EQ(Max, SaturatingAdd(T(1), T(Max - 1), &ResultOverflowed)); 239 EXPECT_FALSE(ResultOverflowed); 240 241 EXPECT_EQ(Max, SaturatingAdd(T(1), Max)); 242 EXPECT_EQ(Max, SaturatingAdd(T(1), Max, &ResultOverflowed)); 243 EXPECT_TRUE(ResultOverflowed); 244 245 EXPECT_EQ(Max, SaturatingAdd(Max, Max)); 246 EXPECT_EQ(Max, SaturatingAdd(Max, Max, &ResultOverflowed)); 247 EXPECT_TRUE(ResultOverflowed); 248 } 249 250 TEST(MathExtras, SaturatingAdd) { 251 SaturatingAddTestHelper<uint8_t>(); 252 SaturatingAddTestHelper<uint16_t>(); 253 SaturatingAddTestHelper<uint32_t>(); 254 SaturatingAddTestHelper<uint64_t>(); 255 } 256 257 template<typename T> 258 void SaturatingMultiplyTestHelper() 259 { 260 const T Max = std::numeric_limits<T>::max(); 261 bool ResultOverflowed; 262 263 // Test basic multiplication. 264 EXPECT_EQ(T(6), SaturatingMultiply(T(2), T(3))); 265 EXPECT_EQ(T(6), SaturatingMultiply(T(2), T(3), &ResultOverflowed)); 266 EXPECT_FALSE(ResultOverflowed); 267 268 EXPECT_EQ(T(6), SaturatingMultiply(T(3), T(2))); 269 EXPECT_EQ(T(6), SaturatingMultiply(T(3), T(2), &ResultOverflowed)); 270 EXPECT_FALSE(ResultOverflowed); 271 272 // Test multiplication by zero. 273 EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(0))); 274 EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(0), &ResultOverflowed)); 275 EXPECT_FALSE(ResultOverflowed); 276 277 EXPECT_EQ(T(0), SaturatingMultiply(T(1), T(0))); 278 EXPECT_EQ(T(0), SaturatingMultiply(T(1), T(0), &ResultOverflowed)); 279 EXPECT_FALSE(ResultOverflowed); 280 281 EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(1))); 282 EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(1), &ResultOverflowed)); 283 EXPECT_FALSE(ResultOverflowed); 284 285 EXPECT_EQ(T(0), SaturatingMultiply(Max, T(0))); 286 EXPECT_EQ(T(0), SaturatingMultiply(Max, T(0), &ResultOverflowed)); 287 EXPECT_FALSE(ResultOverflowed); 288 289 EXPECT_EQ(T(0), SaturatingMultiply(T(0), Max)); 290 EXPECT_EQ(T(0), SaturatingMultiply(T(0), Max, &ResultOverflowed)); 291 EXPECT_FALSE(ResultOverflowed); 292 293 // Test multiplication by maximum value. 294 EXPECT_EQ(Max, SaturatingMultiply(Max, T(2))); 295 EXPECT_EQ(Max, SaturatingMultiply(Max, T(2), &ResultOverflowed)); 296 EXPECT_TRUE(ResultOverflowed); 297 298 EXPECT_EQ(Max, SaturatingMultiply(T(2), Max)); 299 EXPECT_EQ(Max, SaturatingMultiply(T(2), Max, &ResultOverflowed)); 300 EXPECT_TRUE(ResultOverflowed); 301 302 EXPECT_EQ(Max, SaturatingMultiply(Max, Max)); 303 EXPECT_EQ(Max, SaturatingMultiply(Max, Max, &ResultOverflowed)); 304 EXPECT_TRUE(ResultOverflowed); 305 306 // Test interesting boundary conditions for algorithm - 307 // ((1 << A) - 1) * ((1 << B) + K) for K in [-1, 0, 1] 308 // and A + B == std::numeric_limits<T>::digits. 309 // We expect overflow iff A > B and K = 1. 310 const int Digits = std::numeric_limits<T>::digits; 311 for (int A = 1, B = Digits - 1; B >= 1; ++A, --B) { 312 for (int K = -1; K <= 1; ++K) { 313 T X = (T(1) << A) - T(1); 314 T Y = (T(1) << B) + K; 315 bool OverflowExpected = A > B && K == 1; 316 317 if(OverflowExpected) { 318 EXPECT_EQ(Max, SaturatingMultiply(X, Y)); 319 EXPECT_EQ(Max, SaturatingMultiply(X, Y, &ResultOverflowed)); 320 EXPECT_TRUE(ResultOverflowed); 321 } else { 322 EXPECT_EQ(X * Y, SaturatingMultiply(X, Y)); 323 EXPECT_EQ(X * Y, SaturatingMultiply(X, Y, &ResultOverflowed)); 324 EXPECT_FALSE(ResultOverflowed); 325 } 326 } 327 } 328 } 329 330 TEST(MathExtras, SaturatingMultiply) { 331 SaturatingMultiplyTestHelper<uint8_t>(); 332 SaturatingMultiplyTestHelper<uint16_t>(); 333 SaturatingMultiplyTestHelper<uint32_t>(); 334 SaturatingMultiplyTestHelper<uint64_t>(); 335 } 336 337 template<typename T> 338 void SaturatingMultiplyAddTestHelper() 339 { 340 const T Max = std::numeric_limits<T>::max(); 341 bool ResultOverflowed; 342 343 // Test basic multiply-add. 344 EXPECT_EQ(T(16), SaturatingMultiplyAdd(T(2), T(3), T(10))); 345 EXPECT_EQ(T(16), SaturatingMultiplyAdd(T(2), T(3), T(10), &ResultOverflowed)); 346 EXPECT_FALSE(ResultOverflowed); 347 348 // Test multiply overflows, add doesn't overflow 349 EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, T(0), &ResultOverflowed)); 350 EXPECT_TRUE(ResultOverflowed); 351 352 // Test multiply doesn't overflow, add overflows 353 EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), T(1), Max, &ResultOverflowed)); 354 EXPECT_TRUE(ResultOverflowed); 355 356 // Test multiply-add with Max as operand 357 EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), T(1), Max, &ResultOverflowed)); 358 EXPECT_TRUE(ResultOverflowed); 359 360 EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), Max, T(1), &ResultOverflowed)); 361 EXPECT_TRUE(ResultOverflowed); 362 363 EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, T(1), &ResultOverflowed)); 364 EXPECT_TRUE(ResultOverflowed); 365 366 EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, Max, &ResultOverflowed)); 367 EXPECT_TRUE(ResultOverflowed); 368 369 // Test multiply-add with 0 as operand 370 EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(1), T(1), T(0), &ResultOverflowed)); 371 EXPECT_FALSE(ResultOverflowed); 372 373 EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(1), T(0), T(1), &ResultOverflowed)); 374 EXPECT_FALSE(ResultOverflowed); 375 376 EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(0), T(0), T(1), &ResultOverflowed)); 377 EXPECT_FALSE(ResultOverflowed); 378 379 EXPECT_EQ(T(0), SaturatingMultiplyAdd(T(0), T(0), T(0), &ResultOverflowed)); 380 EXPECT_FALSE(ResultOverflowed); 381 382 } 383 384 TEST(MathExtras, SaturatingMultiplyAdd) { 385 SaturatingMultiplyAddTestHelper<uint8_t>(); 386 SaturatingMultiplyAddTestHelper<uint16_t>(); 387 SaturatingMultiplyAddTestHelper<uint32_t>(); 388 SaturatingMultiplyAddTestHelper<uint64_t>(); 389 } 390 391 TEST(MathExtras, IsShiftedUInt) { 392 EXPECT_TRUE((isShiftedUInt<1, 0>(0))); 393 EXPECT_TRUE((isShiftedUInt<1, 0>(1))); 394 EXPECT_FALSE((isShiftedUInt<1, 0>(2))); 395 EXPECT_FALSE((isShiftedUInt<1, 0>(3))); 396 EXPECT_FALSE((isShiftedUInt<1, 0>(0x8000000000000000))); 397 EXPECT_TRUE((isShiftedUInt<1, 63>(0x8000000000000000))); 398 EXPECT_TRUE((isShiftedUInt<2, 62>(0xC000000000000000))); 399 EXPECT_FALSE((isShiftedUInt<2, 62>(0xE000000000000000))); 400 401 // 0x201 is ten bits long and has a 1 in the MSB and LSB. 402 EXPECT_TRUE((isShiftedUInt<10, 5>(uint64_t(0x201) << 5))); 403 EXPECT_FALSE((isShiftedUInt<10, 5>(uint64_t(0x201) << 4))); 404 EXPECT_FALSE((isShiftedUInt<10, 5>(uint64_t(0x201) << 6))); 405 } 406 407 TEST(MathExtras, IsShiftedInt) { 408 EXPECT_TRUE((isShiftedInt<1, 0>(0))); 409 EXPECT_TRUE((isShiftedInt<1, 0>(-1))); 410 EXPECT_FALSE((isShiftedInt<1, 0>(2))); 411 EXPECT_FALSE((isShiftedInt<1, 0>(3))); 412 EXPECT_FALSE((isShiftedInt<1, 0>(0x8000000000000000))); 413 EXPECT_TRUE((isShiftedInt<1, 63>(0x8000000000000000))); 414 EXPECT_TRUE((isShiftedInt<2, 62>(0xC000000000000000))); 415 EXPECT_FALSE((isShiftedInt<2, 62>(0xE000000000000000))); 416 417 // 0x201 is ten bits long and has a 1 in the MSB and LSB. 418 EXPECT_TRUE((isShiftedInt<11, 5>(int64_t(0x201) << 5))); 419 EXPECT_FALSE((isShiftedInt<11, 5>(int64_t(0x201) << 3))); 420 EXPECT_FALSE((isShiftedInt<11, 5>(int64_t(0x201) << 6))); 421 EXPECT_TRUE((isShiftedInt<11, 5>(-(int64_t(0x201) << 5)))); 422 EXPECT_FALSE((isShiftedInt<11, 5>(-(int64_t(0x201) << 3)))); 423 EXPECT_FALSE((isShiftedInt<11, 5>(-(int64_t(0x201) << 6)))); 424 425 EXPECT_TRUE((isShiftedInt<6, 10>(-(int64_t(1) << 15)))); 426 EXPECT_FALSE((isShiftedInt<6, 10>(int64_t(1) << 15))); 427 } 428 429 } // namespace 430