1 //===-- llvm/Support/MathExtras.h - Useful math functions -------*- C++ -*-===// 2 // 3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. 4 // See https://llvm.org/LICENSE.txt for license information. 5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception 6 // 7 //===----------------------------------------------------------------------===// 8 // 9 // This file contains some functions that are useful for math stuff. 10 // 11 //===----------------------------------------------------------------------===// 12 13 #ifndef LLVM_SUPPORT_MATHEXTRAS_H 14 #define LLVM_SUPPORT_MATHEXTRAS_H 15 16 #include "llvm/ADT/bit.h" 17 #include "llvm/Support/Compiler.h" 18 #include <cassert> 19 #include <climits> 20 #include <cstdint> 21 #include <cstring> 22 #include <limits> 23 #include <type_traits> 24 25 namespace llvm { 26 27 /// The behavior an operation has on an input of 0. 28 enum ZeroBehavior { 29 /// The returned value is undefined. 30 ZB_Undefined, 31 /// The returned value is numeric_limits<T>::max() 32 ZB_Max 33 }; 34 35 /// Mathematical constants. 36 namespace numbers { 37 // TODO: Track C++20 std::numbers. 38 // TODO: Favor using the hexadecimal FP constants (requires C++17). 39 constexpr double e = 2.7182818284590452354, // (0x1.5bf0a8b145749P+1) https://oeis.org/A001113 40 egamma = .57721566490153286061, // (0x1.2788cfc6fb619P-1) https://oeis.org/A001620 41 ln2 = .69314718055994530942, // (0x1.62e42fefa39efP-1) https://oeis.org/A002162 42 ln10 = 2.3025850929940456840, // (0x1.24bb1bbb55516P+1) https://oeis.org/A002392 43 log2e = 1.4426950408889634074, // (0x1.71547652b82feP+0) 44 log10e = .43429448190325182765, // (0x1.bcb7b1526e50eP-2) 45 pi = 3.1415926535897932385, // (0x1.921fb54442d18P+1) https://oeis.org/A000796 46 inv_pi = .31830988618379067154, // (0x1.45f306bc9c883P-2) https://oeis.org/A049541 47 sqrtpi = 1.7724538509055160273, // (0x1.c5bf891b4ef6bP+0) https://oeis.org/A002161 48 inv_sqrtpi = .56418958354775628695, // (0x1.20dd750429b6dP-1) https://oeis.org/A087197 49 sqrt2 = 1.4142135623730950488, // (0x1.6a09e667f3bcdP+0) https://oeis.org/A00219 50 inv_sqrt2 = .70710678118654752440, // (0x1.6a09e667f3bcdP-1) 51 sqrt3 = 1.7320508075688772935, // (0x1.bb67ae8584caaP+0) https://oeis.org/A002194 52 inv_sqrt3 = .57735026918962576451, // (0x1.279a74590331cP-1) 53 phi = 1.6180339887498948482; // (0x1.9e3779b97f4a8P+0) https://oeis.org/A001622 54 constexpr float ef = 2.71828183F, // (0x1.5bf0a8P+1) https://oeis.org/A001113 55 egammaf = .577215665F, // (0x1.2788d0P-1) https://oeis.org/A001620 56 ln2f = .693147181F, // (0x1.62e430P-1) https://oeis.org/A002162 57 ln10f = 2.30258509F, // (0x1.26bb1cP+1) https://oeis.org/A002392 58 log2ef = 1.44269504F, // (0x1.715476P+0) 59 log10ef = .434294482F, // (0x1.bcb7b2P-2) 60 pif = 3.14159265F, // (0x1.921fb6P+1) https://oeis.org/A000796 61 inv_pif = .318309886F, // (0x1.45f306P-2) https://oeis.org/A049541 62 sqrtpif = 1.77245385F, // (0x1.c5bf8aP+0) https://oeis.org/A002161 63 inv_sqrtpif = .564189584F, // (0x1.20dd76P-1) https://oeis.org/A087197 64 sqrt2f = 1.41421356F, // (0x1.6a09e6P+0) https://oeis.org/A002193 65 inv_sqrt2f = .707106781F, // (0x1.6a09e6P-1) 66 sqrt3f = 1.73205081F, // (0x1.bb67aeP+0) https://oeis.org/A002194 67 inv_sqrt3f = .577350269F, // (0x1.279a74P-1) 68 phif = 1.61803399F; // (0x1.9e377aP+0) https://oeis.org/A001622 69 } // namespace numbers 70 71 /// Count number of 0's from the least significant bit to the most 72 /// stopping at the first 1. 73 /// 74 /// Only unsigned integral types are allowed. 75 /// 76 /// Returns std::numeric_limits<T>::digits on an input of 0. 77 template <typename T> unsigned countTrailingZeros(T Val) { 78 static_assert(std::is_unsigned_v<T>, 79 "Only unsigned integral types are allowed."); 80 return llvm::countr_zero(Val); 81 } 82 83 /// Count number of 0's from the most significant bit to the least 84 /// stopping at the first 1. 85 /// 86 /// Only unsigned integral types are allowed. 87 /// 88 /// Returns std::numeric_limits<T>::digits on an input of 0. 89 template <typename T> unsigned countLeadingZeros(T Val) { 90 static_assert(std::is_unsigned_v<T>, 91 "Only unsigned integral types are allowed."); 92 return llvm::countl_zero(Val); 93 } 94 95 /// Get the index of the first set bit starting from the least 96 /// significant bit. 97 /// 98 /// Only unsigned integral types are allowed. 99 /// 100 /// \param ZB the behavior on an input of 0. 101 template <typename T> T findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) { 102 if (ZB == ZB_Max && Val == 0) 103 return std::numeric_limits<T>::max(); 104 105 return llvm::countr_zero(Val); 106 } 107 108 /// Create a bitmask with the N right-most bits set to 1, and all other 109 /// bits set to 0. Only unsigned types are allowed. 110 template <typename T> T maskTrailingOnes(unsigned N) { 111 static_assert(std::is_unsigned<T>::value, "Invalid type!"); 112 const unsigned Bits = CHAR_BIT * sizeof(T); 113 assert(N <= Bits && "Invalid bit index"); 114 return N == 0 ? 0 : (T(-1) >> (Bits - N)); 115 } 116 117 /// Create a bitmask with the N left-most bits set to 1, and all other 118 /// bits set to 0. Only unsigned types are allowed. 119 template <typename T> T maskLeadingOnes(unsigned N) { 120 return ~maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N); 121 } 122 123 /// Create a bitmask with the N right-most bits set to 0, and all other 124 /// bits set to 1. Only unsigned types are allowed. 125 template <typename T> T maskTrailingZeros(unsigned N) { 126 return maskLeadingOnes<T>(CHAR_BIT * sizeof(T) - N); 127 } 128 129 /// Create a bitmask with the N left-most bits set to 0, and all other 130 /// bits set to 1. Only unsigned types are allowed. 131 template <typename T> T maskLeadingZeros(unsigned N) { 132 return maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N); 133 } 134 135 /// Get the index of the last set bit starting from the least 136 /// significant bit. 137 /// 138 /// Only unsigned integral types are allowed. 139 /// 140 /// \param ZB the behavior on an input of 0. 141 template <typename T> T findLastSet(T Val, ZeroBehavior ZB = ZB_Max) { 142 if (ZB == ZB_Max && Val == 0) 143 return std::numeric_limits<T>::max(); 144 145 // Use ^ instead of - because both gcc and llvm can remove the associated ^ 146 // in the __builtin_clz intrinsic on x86. 147 return llvm::countl_zero(Val) ^ (std::numeric_limits<T>::digits - 1); 148 } 149 150 /// Macro compressed bit reversal table for 256 bits. 151 /// 152 /// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable 153 static const unsigned char BitReverseTable256[256] = { 154 #define R2(n) n, n + 2 * 64, n + 1 * 64, n + 3 * 64 155 #define R4(n) R2(n), R2(n + 2 * 16), R2(n + 1 * 16), R2(n + 3 * 16) 156 #define R6(n) R4(n), R4(n + 2 * 4), R4(n + 1 * 4), R4(n + 3 * 4) 157 R6(0), R6(2), R6(1), R6(3) 158 #undef R2 159 #undef R4 160 #undef R6 161 }; 162 163 /// Reverse the bits in \p Val. 164 template <typename T> T reverseBits(T Val) { 165 #if __has_builtin(__builtin_bitreverse8) 166 if constexpr (std::is_same_v<T, uint8_t>) 167 return __builtin_bitreverse8(Val); 168 #endif 169 #if __has_builtin(__builtin_bitreverse16) 170 if constexpr (std::is_same_v<T, uint16_t>) 171 return __builtin_bitreverse16(Val); 172 #endif 173 #if __has_builtin(__builtin_bitreverse32) 174 if constexpr (std::is_same_v<T, uint32_t>) 175 return __builtin_bitreverse32(Val); 176 #endif 177 #if __has_builtin(__builtin_bitreverse64) 178 if constexpr (std::is_same_v<T, uint64_t>) 179 return __builtin_bitreverse64(Val); 180 #endif 181 182 unsigned char in[sizeof(Val)]; 183 unsigned char out[sizeof(Val)]; 184 std::memcpy(in, &Val, sizeof(Val)); 185 for (unsigned i = 0; i < sizeof(Val); ++i) 186 out[(sizeof(Val) - i) - 1] = BitReverseTable256[in[i]]; 187 std::memcpy(&Val, out, sizeof(Val)); 188 return Val; 189 } 190 191 // NOTE: The following support functions use the _32/_64 extensions instead of 192 // type overloading so that signed and unsigned integers can be used without 193 // ambiguity. 194 195 /// Return the high 32 bits of a 64 bit value. 196 constexpr inline uint32_t Hi_32(uint64_t Value) { 197 return static_cast<uint32_t>(Value >> 32); 198 } 199 200 /// Return the low 32 bits of a 64 bit value. 201 constexpr inline uint32_t Lo_32(uint64_t Value) { 202 return static_cast<uint32_t>(Value); 203 } 204 205 /// Make a 64-bit integer from a high / low pair of 32-bit integers. 206 constexpr inline uint64_t Make_64(uint32_t High, uint32_t Low) { 207 return ((uint64_t)High << 32) | (uint64_t)Low; 208 } 209 210 /// Checks if an integer fits into the given bit width. 211 template <unsigned N> constexpr inline bool isInt(int64_t x) { 212 if constexpr (N == 8) 213 return static_cast<int8_t>(x) == x; 214 if constexpr (N == 16) 215 return static_cast<int16_t>(x) == x; 216 if constexpr (N == 32) 217 return static_cast<int32_t>(x) == x; 218 if constexpr (N < 64) 219 return -(INT64_C(1) << (N - 1)) <= x && x < (INT64_C(1) << (N - 1)); 220 (void)x; // MSVC v19.25 warns that x is unused. 221 return true; 222 } 223 224 /// Checks if a signed integer is an N bit number shifted left by S. 225 template <unsigned N, unsigned S> 226 constexpr inline bool isShiftedInt(int64_t x) { 227 static_assert( 228 N > 0, "isShiftedInt<0> doesn't make sense (refers to a 0-bit number."); 229 static_assert(N + S <= 64, "isShiftedInt<N, S> with N + S > 64 is too wide."); 230 return isInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0); 231 } 232 233 /// Checks if an unsigned integer fits into the given bit width. 234 template <unsigned N> constexpr inline bool isUInt(uint64_t x) { 235 static_assert(N > 0, "isUInt<0> doesn't make sense"); 236 if constexpr (N == 8) 237 return static_cast<uint8_t>(x) == x; 238 if constexpr (N == 16) 239 return static_cast<uint16_t>(x) == x; 240 if constexpr (N == 32) 241 return static_cast<uint32_t>(x) == x; 242 if constexpr (N < 64) 243 return x < (UINT64_C(1) << (N)); 244 (void)x; // MSVC v19.25 warns that x is unused. 245 return true; 246 } 247 248 /// Checks if a unsigned integer is an N bit number shifted left by S. 249 template <unsigned N, unsigned S> 250 constexpr inline bool isShiftedUInt(uint64_t x) { 251 static_assert( 252 N > 0, "isShiftedUInt<0> doesn't make sense (refers to a 0-bit number)"); 253 static_assert(N + S <= 64, 254 "isShiftedUInt<N, S> with N + S > 64 is too wide."); 255 // Per the two static_asserts above, S must be strictly less than 64. So 256 // 1 << S is not undefined behavior. 257 return isUInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0); 258 } 259 260 /// Gets the maximum value for a N-bit unsigned integer. 261 inline uint64_t maxUIntN(uint64_t N) { 262 assert(N > 0 && N <= 64 && "integer width out of range"); 263 264 // uint64_t(1) << 64 is undefined behavior, so we can't do 265 // (uint64_t(1) << N) - 1 266 // without checking first that N != 64. But this works and doesn't have a 267 // branch. 268 return UINT64_MAX >> (64 - N); 269 } 270 271 /// Gets the minimum value for a N-bit signed integer. 272 inline int64_t minIntN(int64_t N) { 273 assert(N > 0 && N <= 64 && "integer width out of range"); 274 275 return UINT64_C(1) + ~(UINT64_C(1) << (N - 1)); 276 } 277 278 /// Gets the maximum value for a N-bit signed integer. 279 inline int64_t maxIntN(int64_t N) { 280 assert(N > 0 && N <= 64 && "integer width out of range"); 281 282 // This relies on two's complement wraparound when N == 64, so we convert to 283 // int64_t only at the very end to avoid UB. 284 return (UINT64_C(1) << (N - 1)) - 1; 285 } 286 287 /// Checks if an unsigned integer fits into the given (dynamic) bit width. 288 inline bool isUIntN(unsigned N, uint64_t x) { 289 return N >= 64 || x <= maxUIntN(N); 290 } 291 292 /// Checks if an signed integer fits into the given (dynamic) bit width. 293 inline bool isIntN(unsigned N, int64_t x) { 294 return N >= 64 || (minIntN(N) <= x && x <= maxIntN(N)); 295 } 296 297 /// Return true if the argument is a non-empty sequence of ones starting at the 298 /// least significant bit with the remainder zero (32 bit version). 299 /// Ex. isMask_32(0x0000FFFFU) == true. 300 constexpr inline bool isMask_32(uint32_t Value) { 301 return Value && ((Value + 1) & Value) == 0; 302 } 303 304 /// Return true if the argument is a non-empty sequence of ones starting at the 305 /// least significant bit with the remainder zero (64 bit version). 306 constexpr inline bool isMask_64(uint64_t Value) { 307 return Value && ((Value + 1) & Value) == 0; 308 } 309 310 /// Return true if the argument contains a non-empty sequence of ones with the 311 /// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true. 312 constexpr inline bool isShiftedMask_32(uint32_t Value) { 313 return Value && isMask_32((Value - 1) | Value); 314 } 315 316 /// Return true if the argument contains a non-empty sequence of ones with the 317 /// remainder zero (64 bit version.) 318 constexpr inline bool isShiftedMask_64(uint64_t Value) { 319 return Value && isMask_64((Value - 1) | Value); 320 } 321 322 /// Return true if the argument is a power of two > 0. 323 /// Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.) 324 constexpr inline bool isPowerOf2_32(uint32_t Value) { 325 return llvm::has_single_bit(Value); 326 } 327 328 /// Return true if the argument is a power of two > 0 (64 bit edition.) 329 constexpr inline bool isPowerOf2_64(uint64_t Value) { 330 return llvm::has_single_bit(Value); 331 } 332 333 /// Count the number of ones from the most significant bit to the first 334 /// zero bit. 335 /// 336 /// Ex. countLeadingOnes(0xFF0FFF00) == 8. 337 /// Only unsigned integral types are allowed. 338 /// 339 /// Returns std::numeric_limits<T>::digits on an input of all ones. 340 template <typename T> unsigned countLeadingOnes(T Value) { 341 static_assert(std::is_unsigned_v<T>, 342 "Only unsigned integral types are allowed."); 343 return llvm::countl_one<T>(Value); 344 } 345 346 /// Count the number of ones from the least significant bit to the first 347 /// zero bit. 348 /// 349 /// Ex. countTrailingOnes(0x00FF00FF) == 8. 350 /// Only unsigned integral types are allowed. 351 /// 352 /// Returns std::numeric_limits<T>::digits on an input of all ones. 353 template <typename T> unsigned countTrailingOnes(T Value) { 354 static_assert(std::is_unsigned_v<T>, 355 "Only unsigned integral types are allowed."); 356 return llvm::countr_one<T>(Value); 357 } 358 359 /// Count the number of set bits in a value. 360 /// Ex. countPopulation(0xF000F000) = 8 361 /// Returns 0 if the word is zero. 362 template <typename T> 363 inline unsigned countPopulation(T Value) { 364 static_assert(std::is_unsigned_v<T>, 365 "Only unsigned integral types are allowed."); 366 return (unsigned)llvm::popcount(Value); 367 } 368 369 /// Return true if the argument contains a non-empty sequence of ones with the 370 /// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true. 371 /// If true, \p MaskIdx will specify the index of the lowest set bit and \p 372 /// MaskLen is updated to specify the length of the mask, else neither are 373 /// updated. 374 inline bool isShiftedMask_32(uint32_t Value, unsigned &MaskIdx, 375 unsigned &MaskLen) { 376 if (!isShiftedMask_32(Value)) 377 return false; 378 MaskIdx = llvm::countr_zero(Value); 379 MaskLen = llvm::popcount(Value); 380 return true; 381 } 382 383 /// Return true if the argument contains a non-empty sequence of ones with the 384 /// remainder zero (64 bit version.) If true, \p MaskIdx will specify the index 385 /// of the lowest set bit and \p MaskLen is updated to specify the length of the 386 /// mask, else neither are updated. 387 inline bool isShiftedMask_64(uint64_t Value, unsigned &MaskIdx, 388 unsigned &MaskLen) { 389 if (!isShiftedMask_64(Value)) 390 return false; 391 MaskIdx = llvm::countr_zero(Value); 392 MaskLen = llvm::popcount(Value); 393 return true; 394 } 395 396 /// Compile time Log2. 397 /// Valid only for positive powers of two. 398 template <size_t kValue> constexpr inline size_t CTLog2() { 399 static_assert(kValue > 0 && llvm::isPowerOf2_64(kValue), 400 "Value is not a valid power of 2"); 401 return 1 + CTLog2<kValue / 2>(); 402 } 403 404 template <> constexpr inline size_t CTLog2<1>() { return 0; } 405 406 /// Return the floor log base 2 of the specified value, -1 if the value is zero. 407 /// (32 bit edition.) 408 /// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2 409 inline unsigned Log2_32(uint32_t Value) { 410 return 31 - llvm::countl_zero(Value); 411 } 412 413 /// Return the floor log base 2 of the specified value, -1 if the value is zero. 414 /// (64 bit edition.) 415 inline unsigned Log2_64(uint64_t Value) { 416 return 63 - llvm::countl_zero(Value); 417 } 418 419 /// Return the ceil log base 2 of the specified value, 32 if the value is zero. 420 /// (32 bit edition). 421 /// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3 422 inline unsigned Log2_32_Ceil(uint32_t Value) { 423 return 32 - llvm::countl_zero(Value - 1); 424 } 425 426 /// Return the ceil log base 2 of the specified value, 64 if the value is zero. 427 /// (64 bit edition.) 428 inline unsigned Log2_64_Ceil(uint64_t Value) { 429 return 64 - llvm::countl_zero(Value - 1); 430 } 431 432 /// This function takes a 64-bit integer and returns the bit equivalent double. 433 inline double BitsToDouble(uint64_t Bits) { 434 static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes"); 435 return llvm::bit_cast<double>(Bits); 436 } 437 438 /// This function takes a 32-bit integer and returns the bit equivalent float. 439 inline float BitsToFloat(uint32_t Bits) { 440 static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes"); 441 return llvm::bit_cast<float>(Bits); 442 } 443 444 /// This function takes a double and returns the bit equivalent 64-bit integer. 445 /// Note that copying doubles around changes the bits of NaNs on some hosts, 446 /// notably x86, so this routine cannot be used if these bits are needed. 447 inline uint64_t DoubleToBits(double Double) { 448 static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes"); 449 return llvm::bit_cast<uint64_t>(Double); 450 } 451 452 /// This function takes a float and returns the bit equivalent 32-bit integer. 453 /// Note that copying floats around changes the bits of NaNs on some hosts, 454 /// notably x86, so this routine cannot be used if these bits are needed. 455 inline uint32_t FloatToBits(float Float) { 456 static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes"); 457 return llvm::bit_cast<uint32_t>(Float); 458 } 459 460 /// A and B are either alignments or offsets. Return the minimum alignment that 461 /// may be assumed after adding the two together. 462 constexpr inline uint64_t MinAlign(uint64_t A, uint64_t B) { 463 // The largest power of 2 that divides both A and B. 464 // 465 // Replace "-Value" by "1+~Value" in the following commented code to avoid 466 // MSVC warning C4146 467 // return (A | B) & -(A | B); 468 return (A | B) & (1 + ~(A | B)); 469 } 470 471 /// Returns the next power of two (in 64-bits) that is strictly greater than A. 472 /// Returns zero on overflow. 473 constexpr inline uint64_t NextPowerOf2(uint64_t A) { 474 A |= (A >> 1); 475 A |= (A >> 2); 476 A |= (A >> 4); 477 A |= (A >> 8); 478 A |= (A >> 16); 479 A |= (A >> 32); 480 return A + 1; 481 } 482 483 /// Returns the power of two which is less than or equal to the given value. 484 /// Essentially, it is a floor operation across the domain of powers of two. 485 inline uint64_t PowerOf2Floor(uint64_t A) { 486 return llvm::bit_floor(A); 487 } 488 489 /// Returns the power of two which is greater than or equal to the given value. 490 /// Essentially, it is a ceil operation across the domain of powers of two. 491 inline uint64_t PowerOf2Ceil(uint64_t A) { 492 if (!A) 493 return 0; 494 return NextPowerOf2(A - 1); 495 } 496 497 /// Returns the next integer (mod 2**64) that is greater than or equal to 498 /// \p Value and is a multiple of \p Align. \p Align must be non-zero. 499 /// 500 /// Examples: 501 /// \code 502 /// alignTo(5, 8) = 8 503 /// alignTo(17, 8) = 24 504 /// alignTo(~0LL, 8) = 0 505 /// alignTo(321, 255) = 510 506 /// \endcode 507 inline uint64_t alignTo(uint64_t Value, uint64_t Align) { 508 assert(Align != 0u && "Align can't be 0."); 509 return (Value + Align - 1) / Align * Align; 510 } 511 512 inline uint64_t alignToPowerOf2(uint64_t Value, uint64_t Align) { 513 assert(Align != 0 && (Align & (Align - 1)) == 0 && 514 "Align must be a power of 2"); 515 return (Value + Align - 1) & -Align; 516 } 517 518 /// If non-zero \p Skew is specified, the return value will be a minimal integer 519 /// that is greater than or equal to \p Size and equal to \p A * N + \p Skew for 520 /// some integer N. If \p Skew is larger than \p A, its value is adjusted to '\p 521 /// Skew mod \p A'. \p Align must be non-zero. 522 /// 523 /// Examples: 524 /// \code 525 /// alignTo(5, 8, 7) = 7 526 /// alignTo(17, 8, 1) = 17 527 /// alignTo(~0LL, 8, 3) = 3 528 /// alignTo(321, 255, 42) = 552 529 /// \endcode 530 inline uint64_t alignTo(uint64_t Value, uint64_t Align, uint64_t Skew) { 531 assert(Align != 0u && "Align can't be 0."); 532 Skew %= Align; 533 return alignTo(Value - Skew, Align) + Skew; 534 } 535 536 /// Returns the next integer (mod 2**64) that is greater than or equal to 537 /// \p Value and is a multiple of \c Align. \c Align must be non-zero. 538 template <uint64_t Align> constexpr inline uint64_t alignTo(uint64_t Value) { 539 static_assert(Align != 0u, "Align must be non-zero"); 540 return (Value + Align - 1) / Align * Align; 541 } 542 543 /// Returns the integer ceil(Numerator / Denominator). 544 inline uint64_t divideCeil(uint64_t Numerator, uint64_t Denominator) { 545 return alignTo(Numerator, Denominator) / Denominator; 546 } 547 548 /// Returns the integer nearest(Numerator / Denominator). 549 inline uint64_t divideNearest(uint64_t Numerator, uint64_t Denominator) { 550 return (Numerator + (Denominator / 2)) / Denominator; 551 } 552 553 /// Returns the largest uint64_t less than or equal to \p Value and is 554 /// \p Skew mod \p Align. \p Align must be non-zero 555 inline uint64_t alignDown(uint64_t Value, uint64_t Align, uint64_t Skew = 0) { 556 assert(Align != 0u && "Align can't be 0."); 557 Skew %= Align; 558 return (Value - Skew) / Align * Align + Skew; 559 } 560 561 /// Sign-extend the number in the bottom B bits of X to a 32-bit integer. 562 /// Requires 0 < B <= 32. 563 template <unsigned B> constexpr inline int32_t SignExtend32(uint32_t X) { 564 static_assert(B > 0, "Bit width can't be 0."); 565 static_assert(B <= 32, "Bit width out of range."); 566 return int32_t(X << (32 - B)) >> (32 - B); 567 } 568 569 /// Sign-extend the number in the bottom B bits of X to a 32-bit integer. 570 /// Requires 0 < B <= 32. 571 inline int32_t SignExtend32(uint32_t X, unsigned B) { 572 assert(B > 0 && "Bit width can't be 0."); 573 assert(B <= 32 && "Bit width out of range."); 574 return int32_t(X << (32 - B)) >> (32 - B); 575 } 576 577 /// Sign-extend the number in the bottom B bits of X to a 64-bit integer. 578 /// Requires 0 < B <= 64. 579 template <unsigned B> constexpr inline int64_t SignExtend64(uint64_t x) { 580 static_assert(B > 0, "Bit width can't be 0."); 581 static_assert(B <= 64, "Bit width out of range."); 582 return int64_t(x << (64 - B)) >> (64 - B); 583 } 584 585 /// Sign-extend the number in the bottom B bits of X to a 64-bit integer. 586 /// Requires 0 < B <= 64. 587 inline int64_t SignExtend64(uint64_t X, unsigned B) { 588 assert(B > 0 && "Bit width can't be 0."); 589 assert(B <= 64 && "Bit width out of range."); 590 return int64_t(X << (64 - B)) >> (64 - B); 591 } 592 593 /// Subtract two unsigned integers, X and Y, of type T and return the absolute 594 /// value of the result. 595 template <typename T> 596 std::enable_if_t<std::is_unsigned<T>::value, T> AbsoluteDifference(T X, T Y) { 597 return X > Y ? (X - Y) : (Y - X); 598 } 599 600 /// Add two unsigned integers, X and Y, of type T. Clamp the result to the 601 /// maximum representable value of T on overflow. ResultOverflowed indicates if 602 /// the result is larger than the maximum representable value of type T. 603 template <typename T> 604 std::enable_if_t<std::is_unsigned<T>::value, T> 605 SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) { 606 bool Dummy; 607 bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy; 608 // Hacker's Delight, p. 29 609 T Z = X + Y; 610 Overflowed = (Z < X || Z < Y); 611 if (Overflowed) 612 return std::numeric_limits<T>::max(); 613 else 614 return Z; 615 } 616 617 /// Add multiple unsigned integers of type T. Clamp the result to the 618 /// maximum representable value of T on overflow. 619 template <class T, class... Ts> 620 std::enable_if_t<std::is_unsigned_v<T>, T> SaturatingAdd(T X, T Y, T Z, 621 Ts... Args) { 622 bool Overflowed = false; 623 T XY = SaturatingAdd(X, Y, &Overflowed); 624 if (Overflowed) 625 return SaturatingAdd(std::numeric_limits<T>::max(), T(1), Args...); 626 return SaturatingAdd(XY, Z, Args...); 627 } 628 629 /// Multiply two unsigned integers, X and Y, of type T. Clamp the result to the 630 /// maximum representable value of T on overflow. ResultOverflowed indicates if 631 /// the result is larger than the maximum representable value of type T. 632 template <typename T> 633 std::enable_if_t<std::is_unsigned<T>::value, T> 634 SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) { 635 bool Dummy; 636 bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy; 637 638 // Hacker's Delight, p. 30 has a different algorithm, but we don't use that 639 // because it fails for uint16_t (where multiplication can have undefined 640 // behavior due to promotion to int), and requires a division in addition 641 // to the multiplication. 642 643 Overflowed = false; 644 645 // Log2(Z) would be either Log2Z or Log2Z + 1. 646 // Special case: if X or Y is 0, Log2_64 gives -1, and Log2Z 647 // will necessarily be less than Log2Max as desired. 648 int Log2Z = Log2_64(X) + Log2_64(Y); 649 const T Max = std::numeric_limits<T>::max(); 650 int Log2Max = Log2_64(Max); 651 if (Log2Z < Log2Max) { 652 return X * Y; 653 } 654 if (Log2Z > Log2Max) { 655 Overflowed = true; 656 return Max; 657 } 658 659 // We're going to use the top bit, and maybe overflow one 660 // bit past it. Multiply all but the bottom bit then add 661 // that on at the end. 662 T Z = (X >> 1) * Y; 663 if (Z & ~(Max >> 1)) { 664 Overflowed = true; 665 return Max; 666 } 667 Z <<= 1; 668 if (X & 1) 669 return SaturatingAdd(Z, Y, ResultOverflowed); 670 671 return Z; 672 } 673 674 /// Multiply two unsigned integers, X and Y, and add the unsigned integer, A to 675 /// the product. Clamp the result to the maximum representable value of T on 676 /// overflow. ResultOverflowed indicates if the result is larger than the 677 /// maximum representable value of type T. 678 template <typename T> 679 std::enable_if_t<std::is_unsigned<T>::value, T> 680 SaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed = nullptr) { 681 bool Dummy; 682 bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy; 683 684 T Product = SaturatingMultiply(X, Y, &Overflowed); 685 if (Overflowed) 686 return Product; 687 688 return SaturatingAdd(A, Product, &Overflowed); 689 } 690 691 /// Use this rather than HUGE_VALF; the latter causes warnings on MSVC. 692 extern const float huge_valf; 693 694 695 /// Add two signed integers, computing the two's complement truncated result, 696 /// returning true if overflow occurred. 697 template <typename T> 698 std::enable_if_t<std::is_signed<T>::value, T> AddOverflow(T X, T Y, T &Result) { 699 #if __has_builtin(__builtin_add_overflow) 700 return __builtin_add_overflow(X, Y, &Result); 701 #else 702 // Perform the unsigned addition. 703 using U = std::make_unsigned_t<T>; 704 const U UX = static_cast<U>(X); 705 const U UY = static_cast<U>(Y); 706 const U UResult = UX + UY; 707 708 // Convert to signed. 709 Result = static_cast<T>(UResult); 710 711 // Adding two positive numbers should result in a positive number. 712 if (X > 0 && Y > 0) 713 return Result <= 0; 714 // Adding two negatives should result in a negative number. 715 if (X < 0 && Y < 0) 716 return Result >= 0; 717 return false; 718 #endif 719 } 720 721 /// Subtract two signed integers, computing the two's complement truncated 722 /// result, returning true if an overflow ocurred. 723 template <typename T> 724 std::enable_if_t<std::is_signed<T>::value, T> SubOverflow(T X, T Y, T &Result) { 725 #if __has_builtin(__builtin_sub_overflow) 726 return __builtin_sub_overflow(X, Y, &Result); 727 #else 728 // Perform the unsigned addition. 729 using U = std::make_unsigned_t<T>; 730 const U UX = static_cast<U>(X); 731 const U UY = static_cast<U>(Y); 732 const U UResult = UX - UY; 733 734 // Convert to signed. 735 Result = static_cast<T>(UResult); 736 737 // Subtracting a positive number from a negative results in a negative number. 738 if (X <= 0 && Y > 0) 739 return Result >= 0; 740 // Subtracting a negative number from a positive results in a positive number. 741 if (X >= 0 && Y < 0) 742 return Result <= 0; 743 return false; 744 #endif 745 } 746 747 /// Multiply two signed integers, computing the two's complement truncated 748 /// result, returning true if an overflow ocurred. 749 template <typename T> 750 std::enable_if_t<std::is_signed<T>::value, T> MulOverflow(T X, T Y, T &Result) { 751 // Perform the unsigned multiplication on absolute values. 752 using U = std::make_unsigned_t<T>; 753 const U UX = X < 0 ? (0 - static_cast<U>(X)) : static_cast<U>(X); 754 const U UY = Y < 0 ? (0 - static_cast<U>(Y)) : static_cast<U>(Y); 755 const U UResult = UX * UY; 756 757 // Convert to signed. 758 const bool IsNegative = (X < 0) ^ (Y < 0); 759 Result = IsNegative ? (0 - UResult) : UResult; 760 761 // If any of the args was 0, result is 0 and no overflow occurs. 762 if (UX == 0 || UY == 0) 763 return false; 764 765 // UX and UY are in [1, 2^n], where n is the number of digits. 766 // Check how the max allowed absolute value (2^n for negative, 2^(n-1) for 767 // positive) divided by an argument compares to the other. 768 if (IsNegative) 769 return UX > (static_cast<U>(std::numeric_limits<T>::max()) + U(1)) / UY; 770 else 771 return UX > (static_cast<U>(std::numeric_limits<T>::max())) / UY; 772 } 773 774 } // End llvm namespace 775 776 #endif 777