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/Support/Compiler.h" 17 #include <cassert> 18 #include <climits> 19 #include <cmath> 20 #include <cstdint> 21 #include <cstring> 22 #include <limits> 23 #include <type_traits> 24 25 #ifdef __ANDROID_NDK__ 26 #include <android/api-level.h> 27 #endif 28 29 #ifdef _MSC_VER 30 // Declare these intrinsics manually rather including intrin.h. It's very 31 // expensive, and MathExtras.h is popular. 32 // #include <intrin.h> 33 extern "C" { 34 unsigned char _BitScanForward(unsigned long *_Index, unsigned long _Mask); 35 unsigned char _BitScanForward64(unsigned long *_Index, unsigned __int64 _Mask); 36 unsigned char _BitScanReverse(unsigned long *_Index, unsigned long _Mask); 37 unsigned char _BitScanReverse64(unsigned long *_Index, unsigned __int64 _Mask); 38 } 39 #endif 40 41 namespace llvm { 42 43 /// The behavior an operation has on an input of 0. 44 enum ZeroBehavior { 45 /// The returned value is undefined. 46 ZB_Undefined, 47 /// The returned value is numeric_limits<T>::max() 48 ZB_Max, 49 /// The returned value is numeric_limits<T>::digits 50 ZB_Width 51 }; 52 53 /// Mathematical constants. 54 namespace numbers { 55 // TODO: Track C++20 std::numbers. 56 // TODO: Favor using the hexadecimal FP constants (requires C++17). 57 constexpr double e = 2.7182818284590452354, // (0x1.5bf0a8b145749P+1) https://oeis.org/A001113 58 egamma = .57721566490153286061, // (0x1.2788cfc6fb619P-1) https://oeis.org/A001620 59 ln2 = .69314718055994530942, // (0x1.62e42fefa39efP-1) https://oeis.org/A002162 60 ln10 = 2.3025850929940456840, // (0x1.24bb1bbb55516P+1) https://oeis.org/A002392 61 log2e = 1.4426950408889634074, // (0x1.71547652b82feP+0) 62 log10e = .43429448190325182765, // (0x1.bcb7b1526e50eP-2) 63 pi = 3.1415926535897932385, // (0x1.921fb54442d18P+1) https://oeis.org/A000796 64 inv_pi = .31830988618379067154, // (0x1.45f306bc9c883P-2) https://oeis.org/A049541 65 sqrtpi = 1.7724538509055160273, // (0x1.c5bf891b4ef6bP+0) https://oeis.org/A002161 66 inv_sqrtpi = .56418958354775628695, // (0x1.20dd750429b6dP-1) https://oeis.org/A087197 67 sqrt2 = 1.4142135623730950488, // (0x1.6a09e667f3bcdP+0) https://oeis.org/A00219 68 inv_sqrt2 = .70710678118654752440, // (0x1.6a09e667f3bcdP-1) 69 sqrt3 = 1.7320508075688772935, // (0x1.bb67ae8584caaP+0) https://oeis.org/A002194 70 inv_sqrt3 = .57735026918962576451, // (0x1.279a74590331cP-1) 71 phi = 1.6180339887498948482; // (0x1.9e3779b97f4a8P+0) https://oeis.org/A001622 72 constexpr float ef = 2.71828183F, // (0x1.5bf0a8P+1) https://oeis.org/A001113 73 egammaf = .577215665F, // (0x1.2788d0P-1) https://oeis.org/A001620 74 ln2f = .693147181F, // (0x1.62e430P-1) https://oeis.org/A002162 75 ln10f = 2.30258509F, // (0x1.26bb1cP+1) https://oeis.org/A002392 76 log2ef = 1.44269504F, // (0x1.715476P+0) 77 log10ef = .434294482F, // (0x1.bcb7b2P-2) 78 pif = 3.14159265F, // (0x1.921fb6P+1) https://oeis.org/A000796 79 inv_pif = .318309886F, // (0x1.45f306P-2) https://oeis.org/A049541 80 sqrtpif = 1.77245385F, // (0x1.c5bf8aP+0) https://oeis.org/A002161 81 inv_sqrtpif = .564189584F, // (0x1.20dd76P-1) https://oeis.org/A087197 82 sqrt2f = 1.41421356F, // (0x1.6a09e6P+0) https://oeis.org/A002193 83 inv_sqrt2f = .707106781F, // (0x1.6a09e6P-1) 84 sqrt3f = 1.73205081F, // (0x1.bb67aeP+0) https://oeis.org/A002194 85 inv_sqrt3f = .577350269F, // (0x1.279a74P-1) 86 phif = 1.61803399F; // (0x1.9e377aP+0) https://oeis.org/A001622 87 } // namespace numbers 88 89 namespace detail { 90 template <typename T, std::size_t SizeOfT> struct TrailingZerosCounter { countTrailingZerosCounter91 static unsigned count(T Val, ZeroBehavior) { 92 if (!Val) 93 return std::numeric_limits<T>::digits; 94 if (Val & 0x1) 95 return 0; 96 97 // Bisection method. 98 unsigned ZeroBits = 0; 99 T Shift = std::numeric_limits<T>::digits >> 1; 100 T Mask = std::numeric_limits<T>::max() >> Shift; 101 while (Shift) { 102 if ((Val & Mask) == 0) { 103 Val >>= Shift; 104 ZeroBits |= Shift; 105 } 106 Shift >>= 1; 107 Mask >>= Shift; 108 } 109 return ZeroBits; 110 } 111 }; 112 113 #if defined(__GNUC__) || defined(_MSC_VER) 114 template <typename T> struct TrailingZerosCounter<T, 4> { 115 static unsigned count(T Val, ZeroBehavior ZB) { 116 if (ZB != ZB_Undefined && Val == 0) 117 return 32; 118 119 #if __has_builtin(__builtin_ctz) || defined(__GNUC__) 120 return __builtin_ctz(Val); 121 #elif defined(_MSC_VER) 122 unsigned long Index; 123 _BitScanForward(&Index, Val); 124 return Index; 125 #endif 126 } 127 }; 128 129 #if !defined(_MSC_VER) || defined(_M_X64) 130 template <typename T> struct TrailingZerosCounter<T, 8> { 131 static unsigned count(T Val, ZeroBehavior ZB) { 132 if (ZB != ZB_Undefined && Val == 0) 133 return 64; 134 135 #if __has_builtin(__builtin_ctzll) || defined(__GNUC__) 136 return __builtin_ctzll(Val); 137 #elif defined(_MSC_VER) 138 unsigned long Index; 139 _BitScanForward64(&Index, Val); 140 return Index; 141 #endif 142 } 143 }; 144 #endif 145 #endif 146 } // namespace detail 147 148 /// Count number of 0's from the least significant bit to the most 149 /// stopping at the first 1. 150 /// 151 /// Only unsigned integral types are allowed. 152 /// 153 /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are 154 /// valid arguments. 155 template <typename T> 156 unsigned countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) { 157 static_assert(std::numeric_limits<T>::is_integer && 158 !std::numeric_limits<T>::is_signed, 159 "Only unsigned integral types are allowed."); 160 return llvm::detail::TrailingZerosCounter<T, sizeof(T)>::count(Val, ZB); 161 } 162 163 namespace detail { 164 template <typename T, std::size_t SizeOfT> struct LeadingZerosCounter { 165 static unsigned count(T Val, ZeroBehavior) { 166 if (!Val) 167 return std::numeric_limits<T>::digits; 168 169 // Bisection method. 170 unsigned ZeroBits = 0; 171 for (T Shift = std::numeric_limits<T>::digits >> 1; Shift; Shift >>= 1) { 172 T Tmp = Val >> Shift; 173 if (Tmp) 174 Val = Tmp; 175 else 176 ZeroBits |= Shift; 177 } 178 return ZeroBits; 179 } 180 }; 181 182 #if defined(__GNUC__) || defined(_MSC_VER) 183 template <typename T> struct LeadingZerosCounter<T, 4> { 184 static unsigned count(T Val, ZeroBehavior ZB) { 185 if (ZB != ZB_Undefined && Val == 0) 186 return 32; 187 188 #if __has_builtin(__builtin_clz) || defined(__GNUC__) 189 return __builtin_clz(Val); 190 #elif defined(_MSC_VER) 191 unsigned long Index; 192 _BitScanReverse(&Index, Val); 193 return Index ^ 31; 194 #endif 195 } 196 }; 197 198 #if !defined(_MSC_VER) || defined(_M_X64) 199 template <typename T> struct LeadingZerosCounter<T, 8> { 200 static unsigned count(T Val, ZeroBehavior ZB) { 201 if (ZB != ZB_Undefined && Val == 0) 202 return 64; 203 204 #if __has_builtin(__builtin_clzll) || defined(__GNUC__) 205 return __builtin_clzll(Val); 206 #elif defined(_MSC_VER) 207 unsigned long Index; 208 _BitScanReverse64(&Index, Val); 209 return Index ^ 63; 210 #endif 211 } 212 }; 213 #endif 214 #endif 215 } // namespace detail 216 217 /// Count number of 0's from the most significant bit to the least 218 /// stopping at the first 1. 219 /// 220 /// Only unsigned integral types are allowed. 221 /// 222 /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are 223 /// valid arguments. 224 template <typename T> 225 unsigned countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) { 226 static_assert(std::numeric_limits<T>::is_integer && 227 !std::numeric_limits<T>::is_signed, 228 "Only unsigned integral types are allowed."); 229 return llvm::detail::LeadingZerosCounter<T, sizeof(T)>::count(Val, ZB); 230 } 231 232 /// Get the index of the first set bit starting from the least 233 /// significant bit. 234 /// 235 /// Only unsigned integral types are allowed. 236 /// 237 /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are 238 /// valid arguments. 239 template <typename T> T findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) { 240 if (ZB == ZB_Max && Val == 0) 241 return std::numeric_limits<T>::max(); 242 243 return countTrailingZeros(Val, ZB_Undefined); 244 } 245 246 /// Create a bitmask with the N right-most bits set to 1, and all other 247 /// bits set to 0. Only unsigned types are allowed. 248 template <typename T> T maskTrailingOnes(unsigned N) { 249 static_assert(std::is_unsigned<T>::value, "Invalid type!"); 250 const unsigned Bits = CHAR_BIT * sizeof(T); 251 assert(N <= Bits && "Invalid bit index"); 252 return N == 0 ? 0 : (T(-1) >> (Bits - N)); 253 } 254 255 /// Create a bitmask with the N left-most bits set to 1, and all other 256 /// bits set to 0. Only unsigned types are allowed. 257 template <typename T> T maskLeadingOnes(unsigned N) { 258 return ~maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N); 259 } 260 261 /// Create a bitmask with the N right-most bits set to 0, and all other 262 /// bits set to 1. Only unsigned types are allowed. 263 template <typename T> T maskTrailingZeros(unsigned N) { 264 return maskLeadingOnes<T>(CHAR_BIT * sizeof(T) - N); 265 } 266 267 /// Create a bitmask with the N left-most bits set to 0, and all other 268 /// bits set to 1. Only unsigned types are allowed. 269 template <typename T> T maskLeadingZeros(unsigned N) { 270 return maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N); 271 } 272 273 /// Get the index of the last set bit starting from the least 274 /// significant bit. 275 /// 276 /// Only unsigned integral types are allowed. 277 /// 278 /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are 279 /// valid arguments. 280 template <typename T> T findLastSet(T Val, ZeroBehavior ZB = ZB_Max) { 281 if (ZB == ZB_Max && Val == 0) 282 return std::numeric_limits<T>::max(); 283 284 // Use ^ instead of - because both gcc and llvm can remove the associated ^ 285 // in the __builtin_clz intrinsic on x86. 286 return countLeadingZeros(Val, ZB_Undefined) ^ 287 (std::numeric_limits<T>::digits - 1); 288 } 289 290 /// Macro compressed bit reversal table for 256 bits. 291 /// 292 /// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable 293 static const unsigned char BitReverseTable256[256] = { 294 #define R2(n) n, n + 2 * 64, n + 1 * 64, n + 3 * 64 295 #define R4(n) R2(n), R2(n + 2 * 16), R2(n + 1 * 16), R2(n + 3 * 16) 296 #define R6(n) R4(n), R4(n + 2 * 4), R4(n + 1 * 4), R4(n + 3 * 4) 297 R6(0), R6(2), R6(1), R6(3) 298 #undef R2 299 #undef R4 300 #undef R6 301 }; 302 303 /// Reverse the bits in \p Val. 304 template <typename T> 305 T reverseBits(T Val) { 306 unsigned char in[sizeof(Val)]; 307 unsigned char out[sizeof(Val)]; 308 std::memcpy(in, &Val, sizeof(Val)); 309 for (unsigned i = 0; i < sizeof(Val); ++i) 310 out[(sizeof(Val) - i) - 1] = BitReverseTable256[in[i]]; 311 std::memcpy(&Val, out, sizeof(Val)); 312 return Val; 313 } 314 315 #if __has_builtin(__builtin_bitreverse8) 316 template<> 317 inline uint8_t reverseBits<uint8_t>(uint8_t Val) { 318 return __builtin_bitreverse8(Val); 319 } 320 #endif 321 322 #if __has_builtin(__builtin_bitreverse16) 323 template<> 324 inline uint16_t reverseBits<uint16_t>(uint16_t Val) { 325 return __builtin_bitreverse16(Val); 326 } 327 #endif 328 329 #if __has_builtin(__builtin_bitreverse32) 330 template<> 331 inline uint32_t reverseBits<uint32_t>(uint32_t Val) { 332 return __builtin_bitreverse32(Val); 333 } 334 #endif 335 336 #if __has_builtin(__builtin_bitreverse64) 337 template<> 338 inline uint64_t reverseBits<uint64_t>(uint64_t Val) { 339 return __builtin_bitreverse64(Val); 340 } 341 #endif 342 343 // NOTE: The following support functions use the _32/_64 extensions instead of 344 // type overloading so that signed and unsigned integers can be used without 345 // ambiguity. 346 347 /// Return the high 32 bits of a 64 bit value. 348 constexpr inline uint32_t Hi_32(uint64_t Value) { 349 return static_cast<uint32_t>(Value >> 32); 350 } 351 352 /// Return the low 32 bits of a 64 bit value. 353 constexpr inline uint32_t Lo_32(uint64_t Value) { 354 return static_cast<uint32_t>(Value); 355 } 356 357 /// Make a 64-bit integer from a high / low pair of 32-bit integers. 358 constexpr inline uint64_t Make_64(uint32_t High, uint32_t Low) { 359 return ((uint64_t)High << 32) | (uint64_t)Low; 360 } 361 362 /// Checks if an integer fits into the given bit width. 363 template <unsigned N> constexpr inline bool isInt(int64_t x) { 364 return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1))); 365 } 366 // Template specializations to get better code for common cases. 367 template <> constexpr inline bool isInt<8>(int64_t x) { 368 return static_cast<int8_t>(x) == x; 369 } 370 template <> constexpr inline bool isInt<16>(int64_t x) { 371 return static_cast<int16_t>(x) == x; 372 } 373 template <> constexpr inline bool isInt<32>(int64_t x) { 374 return static_cast<int32_t>(x) == x; 375 } 376 377 /// Checks if a signed integer is an N bit number shifted left by S. 378 template <unsigned N, unsigned S> 379 constexpr inline bool isShiftedInt(int64_t x) { 380 static_assert( 381 N > 0, "isShiftedInt<0> doesn't make sense (refers to a 0-bit number."); 382 static_assert(N + S <= 64, "isShiftedInt<N, S> with N + S > 64 is too wide."); 383 return isInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0); 384 } 385 386 /// Checks if an unsigned integer fits into the given bit width. 387 /// 388 /// This is written as two functions rather than as simply 389 /// 390 /// return N >= 64 || X < (UINT64_C(1) << N); 391 /// 392 /// to keep MSVC from (incorrectly) warning on isUInt<64> that we're shifting 393 /// left too many places. 394 template <unsigned N> 395 constexpr inline std::enable_if_t<(N < 64), bool> isUInt(uint64_t X) { 396 static_assert(N > 0, "isUInt<0> doesn't make sense"); 397 return X < (UINT64_C(1) << (N)); 398 } 399 template <unsigned N> 400 constexpr inline std::enable_if_t<N >= 64, bool> isUInt(uint64_t) { 401 return true; 402 } 403 404 // Template specializations to get better code for common cases. 405 template <> constexpr inline bool isUInt<8>(uint64_t x) { 406 return static_cast<uint8_t>(x) == x; 407 } 408 template <> constexpr inline bool isUInt<16>(uint64_t x) { 409 return static_cast<uint16_t>(x) == x; 410 } 411 template <> constexpr inline bool isUInt<32>(uint64_t x) { 412 return static_cast<uint32_t>(x) == x; 413 } 414 415 /// Checks if a unsigned integer is an N bit number shifted left by S. 416 template <unsigned N, unsigned S> 417 constexpr inline bool isShiftedUInt(uint64_t x) { 418 static_assert( 419 N > 0, "isShiftedUInt<0> doesn't make sense (refers to a 0-bit number)"); 420 static_assert(N + S <= 64, 421 "isShiftedUInt<N, S> with N + S > 64 is too wide."); 422 // Per the two static_asserts above, S must be strictly less than 64. So 423 // 1 << S is not undefined behavior. 424 return isUInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0); 425 } 426 427 /// Gets the maximum value for a N-bit unsigned integer. 428 inline uint64_t maxUIntN(uint64_t N) { 429 assert(N > 0 && N <= 64 && "integer width out of range"); 430 431 // uint64_t(1) << 64 is undefined behavior, so we can't do 432 // (uint64_t(1) << N) - 1 433 // without checking first that N != 64. But this works and doesn't have a 434 // branch. 435 return UINT64_MAX >> (64 - N); 436 } 437 438 /// Gets the minimum value for a N-bit signed integer. 439 inline int64_t minIntN(int64_t N) { 440 assert(N > 0 && N <= 64 && "integer width out of range"); 441 442 return UINT64_C(1) + ~(UINT64_C(1) << (N - 1)); 443 } 444 445 /// Gets the maximum value for a N-bit signed integer. 446 inline int64_t maxIntN(int64_t N) { 447 assert(N > 0 && N <= 64 && "integer width out of range"); 448 449 // This relies on two's complement wraparound when N == 64, so we convert to 450 // int64_t only at the very end to avoid UB. 451 return (UINT64_C(1) << (N - 1)) - 1; 452 } 453 454 /// Checks if an unsigned integer fits into the given (dynamic) bit width. 455 inline bool isUIntN(unsigned N, uint64_t x) { 456 return N >= 64 || x <= maxUIntN(N); 457 } 458 459 /// Checks if an signed integer fits into the given (dynamic) bit width. 460 inline bool isIntN(unsigned N, int64_t x) { 461 return N >= 64 || (minIntN(N) <= x && x <= maxIntN(N)); 462 } 463 464 /// Return true if the argument is a non-empty sequence of ones starting at the 465 /// least significant bit with the remainder zero (32 bit version). 466 /// Ex. isMask_32(0x0000FFFFU) == true. 467 constexpr inline bool isMask_32(uint32_t Value) { 468 return Value && ((Value + 1) & Value) == 0; 469 } 470 471 /// Return true if the argument is a non-empty sequence of ones starting at the 472 /// least significant bit with the remainder zero (64 bit version). 473 constexpr inline bool isMask_64(uint64_t Value) { 474 return Value && ((Value + 1) & Value) == 0; 475 } 476 477 /// Return true if the argument contains a non-empty sequence of ones with the 478 /// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true. 479 constexpr inline bool isShiftedMask_32(uint32_t Value) { 480 return Value && isMask_32((Value - 1) | Value); 481 } 482 483 /// Return true if the argument contains a non-empty sequence of ones with the 484 /// remainder zero (64 bit version.) 485 constexpr inline bool isShiftedMask_64(uint64_t Value) { 486 return Value && isMask_64((Value - 1) | Value); 487 } 488 489 /// Return true if the argument is a power of two > 0. 490 /// Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.) 491 constexpr inline bool isPowerOf2_32(uint32_t Value) { 492 return Value && !(Value & (Value - 1)); 493 } 494 495 /// Return true if the argument is a power of two > 0 (64 bit edition.) 496 constexpr inline bool isPowerOf2_64(uint64_t Value) { 497 return Value && !(Value & (Value - 1)); 498 } 499 500 /// Count the number of ones from the most significant bit to the first 501 /// zero bit. 502 /// 503 /// Ex. countLeadingOnes(0xFF0FFF00) == 8. 504 /// Only unsigned integral types are allowed. 505 /// 506 /// \param ZB the behavior on an input of all ones. Only ZB_Width and 507 /// ZB_Undefined are valid arguments. 508 template <typename T> 509 unsigned countLeadingOnes(T Value, ZeroBehavior ZB = ZB_Width) { 510 static_assert(std::numeric_limits<T>::is_integer && 511 !std::numeric_limits<T>::is_signed, 512 "Only unsigned integral types are allowed."); 513 return countLeadingZeros<T>(~Value, ZB); 514 } 515 516 /// Count the number of ones from the least significant bit to the first 517 /// zero bit. 518 /// 519 /// Ex. countTrailingOnes(0x00FF00FF) == 8. 520 /// Only unsigned integral types are allowed. 521 /// 522 /// \param ZB the behavior on an input of all ones. Only ZB_Width and 523 /// ZB_Undefined are valid arguments. 524 template <typename T> 525 unsigned countTrailingOnes(T Value, ZeroBehavior ZB = ZB_Width) { 526 static_assert(std::numeric_limits<T>::is_integer && 527 !std::numeric_limits<T>::is_signed, 528 "Only unsigned integral types are allowed."); 529 return countTrailingZeros<T>(~Value, ZB); 530 } 531 532 namespace detail { 533 template <typename T, std::size_t SizeOfT> struct PopulationCounter { 534 static unsigned count(T Value) { 535 // Generic version, forward to 32 bits. 536 static_assert(SizeOfT <= 4, "Not implemented!"); 537 #if defined(__GNUC__) 538 return __builtin_popcount(Value); 539 #else 540 uint32_t v = Value; 541 v = v - ((v >> 1) & 0x55555555); 542 v = (v & 0x33333333) + ((v >> 2) & 0x33333333); 543 return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24; 544 #endif 545 } 546 }; 547 548 template <typename T> struct PopulationCounter<T, 8> { 549 static unsigned count(T Value) { 550 #if defined(__GNUC__) 551 return __builtin_popcountll(Value); 552 #else 553 uint64_t v = Value; 554 v = v - ((v >> 1) & 0x5555555555555555ULL); 555 v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL); 556 v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL; 557 return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56); 558 #endif 559 } 560 }; 561 } // namespace detail 562 563 /// Count the number of set bits in a value. 564 /// Ex. countPopulation(0xF000F000) = 8 565 /// Returns 0 if the word is zero. 566 template <typename T> 567 inline unsigned countPopulation(T Value) { 568 static_assert(std::numeric_limits<T>::is_integer && 569 !std::numeric_limits<T>::is_signed, 570 "Only unsigned integral types are allowed."); 571 return detail::PopulationCounter<T, sizeof(T)>::count(Value); 572 } 573 574 /// Compile time Log2. 575 /// Valid only for positive powers of two. 576 template <size_t kValue> constexpr inline size_t CTLog2() { 577 static_assert(kValue > 0 && llvm::isPowerOf2_64(kValue), 578 "Value is not a valid power of 2"); 579 return 1 + CTLog2<kValue / 2>(); 580 } 581 582 template <> constexpr inline size_t CTLog2<1>() { return 0; } 583 584 /// Return the log base 2 of the specified value. 585 inline double Log2(double Value) { 586 #if defined(__ANDROID_API__) && __ANDROID_API__ < 18 587 return __builtin_log(Value) / __builtin_log(2.0); 588 #else 589 return log2(Value); 590 #endif 591 } 592 593 /// Return the floor log base 2 of the specified value, -1 if the value is zero. 594 /// (32 bit edition.) 595 /// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2 596 inline unsigned Log2_32(uint32_t Value) { 597 return 31 - countLeadingZeros(Value); 598 } 599 600 /// Return the floor log base 2 of the specified value, -1 if the value is zero. 601 /// (64 bit edition.) 602 inline unsigned Log2_64(uint64_t Value) { 603 return 63 - countLeadingZeros(Value); 604 } 605 606 /// Return the ceil log base 2 of the specified value, 32 if the value is zero. 607 /// (32 bit edition). 608 /// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3 609 inline unsigned Log2_32_Ceil(uint32_t Value) { 610 return 32 - countLeadingZeros(Value - 1); 611 } 612 613 /// Return the ceil log base 2 of the specified value, 64 if the value is zero. 614 /// (64 bit edition.) 615 inline unsigned Log2_64_Ceil(uint64_t Value) { 616 return 64 - countLeadingZeros(Value - 1); 617 } 618 619 /// Return the greatest common divisor of the values using Euclid's algorithm. 620 template <typename T> 621 inline T greatestCommonDivisor(T A, T B) { 622 while (B) { 623 T Tmp = B; 624 B = A % B; 625 A = Tmp; 626 } 627 return A; 628 } 629 630 inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) { 631 return greatestCommonDivisor<uint64_t>(A, B); 632 } 633 634 /// This function takes a 64-bit integer and returns the bit equivalent double. 635 inline double BitsToDouble(uint64_t Bits) { 636 double D; 637 static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes"); 638 memcpy(&D, &Bits, sizeof(Bits)); 639 return D; 640 } 641 642 /// This function takes a 32-bit integer and returns the bit equivalent float. 643 inline float BitsToFloat(uint32_t Bits) { 644 float F; 645 static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes"); 646 memcpy(&F, &Bits, sizeof(Bits)); 647 return F; 648 } 649 650 /// This function takes a double and returns the bit equivalent 64-bit integer. 651 /// Note that copying doubles around changes the bits of NaNs on some hosts, 652 /// notably x86, so this routine cannot be used if these bits are needed. 653 inline uint64_t DoubleToBits(double Double) { 654 uint64_t Bits; 655 static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes"); 656 memcpy(&Bits, &Double, sizeof(Double)); 657 return Bits; 658 } 659 660 /// This function takes a float and returns the bit equivalent 32-bit integer. 661 /// Note that copying floats around changes the bits of NaNs on some hosts, 662 /// notably x86, so this routine cannot be used if these bits are needed. 663 inline uint32_t FloatToBits(float Float) { 664 uint32_t Bits; 665 static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes"); 666 memcpy(&Bits, &Float, sizeof(Float)); 667 return Bits; 668 } 669 670 /// A and B are either alignments or offsets. Return the minimum alignment that 671 /// may be assumed after adding the two together. 672 constexpr inline uint64_t MinAlign(uint64_t A, uint64_t B) { 673 // The largest power of 2 that divides both A and B. 674 // 675 // Replace "-Value" by "1+~Value" in the following commented code to avoid 676 // MSVC warning C4146 677 // return (A | B) & -(A | B); 678 return (A | B) & (1 + ~(A | B)); 679 } 680 681 /// Returns the next power of two (in 64-bits) that is strictly greater than A. 682 /// Returns zero on overflow. 683 inline uint64_t NextPowerOf2(uint64_t A) { 684 A |= (A >> 1); 685 A |= (A >> 2); 686 A |= (A >> 4); 687 A |= (A >> 8); 688 A |= (A >> 16); 689 A |= (A >> 32); 690 return A + 1; 691 } 692 693 /// Returns the power of two which is less than or equal to the given value. 694 /// Essentially, it is a floor operation across the domain of powers of two. 695 inline uint64_t PowerOf2Floor(uint64_t A) { 696 if (!A) return 0; 697 return 1ull << (63 - countLeadingZeros(A, ZB_Undefined)); 698 } 699 700 /// Returns the power of two which is greater than or equal to the given value. 701 /// Essentially, it is a ceil operation across the domain of powers of two. 702 inline uint64_t PowerOf2Ceil(uint64_t A) { 703 if (!A) 704 return 0; 705 return NextPowerOf2(A - 1); 706 } 707 708 /// Returns the next integer (mod 2**64) that is greater than or equal to 709 /// \p Value and is a multiple of \p Align. \p Align must be non-zero. 710 /// 711 /// If non-zero \p Skew is specified, the return value will be a minimal 712 /// integer that is greater than or equal to \p Value and equal to 713 /// \p Align * N + \p Skew for some integer N. If \p Skew is larger than 714 /// \p Align, its value is adjusted to '\p Skew mod \p Align'. 715 /// 716 /// Examples: 717 /// \code 718 /// alignTo(5, 8) = 8 719 /// alignTo(17, 8) = 24 720 /// alignTo(~0LL, 8) = 0 721 /// alignTo(321, 255) = 510 722 /// 723 /// alignTo(5, 8, 7) = 7 724 /// alignTo(17, 8, 1) = 17 725 /// alignTo(~0LL, 8, 3) = 3 726 /// alignTo(321, 255, 42) = 552 727 /// \endcode 728 inline uint64_t alignTo(uint64_t Value, uint64_t Align, uint64_t Skew = 0) { 729 assert(Align != 0u && "Align can't be 0."); 730 Skew %= Align; 731 return (Value + Align - 1 - Skew) / Align * Align + Skew; 732 } 733 734 /// Returns the next integer (mod 2**64) that is greater than or equal to 735 /// \p Value and is a multiple of \c Align. \c Align must be non-zero. 736 template <uint64_t Align> constexpr inline uint64_t alignTo(uint64_t Value) { 737 static_assert(Align != 0u, "Align must be non-zero"); 738 return (Value + Align - 1) / Align * Align; 739 } 740 741 /// Returns the integer ceil(Numerator / Denominator). 742 inline uint64_t divideCeil(uint64_t Numerator, uint64_t Denominator) { 743 return alignTo(Numerator, Denominator) / Denominator; 744 } 745 746 /// Returns the integer nearest(Numerator / Denominator). 747 inline uint64_t divideNearest(uint64_t Numerator, uint64_t Denominator) { 748 return (Numerator + (Denominator / 2)) / Denominator; 749 } 750 751 /// Returns the largest uint64_t less than or equal to \p Value and is 752 /// \p Skew mod \p Align. \p Align must be non-zero 753 inline uint64_t alignDown(uint64_t Value, uint64_t Align, uint64_t Skew = 0) { 754 assert(Align != 0u && "Align can't be 0."); 755 Skew %= Align; 756 return (Value - Skew) / Align * Align + Skew; 757 } 758 759 /// Sign-extend the number in the bottom B bits of X to a 32-bit integer. 760 /// Requires 0 < B <= 32. 761 template <unsigned B> constexpr inline int32_t SignExtend32(uint32_t X) { 762 static_assert(B > 0, "Bit width can't be 0."); 763 static_assert(B <= 32, "Bit width out of range."); 764 return int32_t(X << (32 - B)) >> (32 - B); 765 } 766 767 /// Sign-extend the number in the bottom B bits of X to a 32-bit integer. 768 /// Requires 0 < B <= 32. 769 inline int32_t SignExtend32(uint32_t X, unsigned B) { 770 assert(B > 0 && "Bit width can't be 0."); 771 assert(B <= 32 && "Bit width out of range."); 772 return int32_t(X << (32 - B)) >> (32 - B); 773 } 774 775 /// Sign-extend the number in the bottom B bits of X to a 64-bit integer. 776 /// Requires 0 < B <= 64. 777 template <unsigned B> constexpr inline int64_t SignExtend64(uint64_t x) { 778 static_assert(B > 0, "Bit width can't be 0."); 779 static_assert(B <= 64, "Bit width out of range."); 780 return int64_t(x << (64 - B)) >> (64 - B); 781 } 782 783 /// Sign-extend the number in the bottom B bits of X to a 64-bit integer. 784 /// Requires 0 < B <= 64. 785 inline int64_t SignExtend64(uint64_t X, unsigned B) { 786 assert(B > 0 && "Bit width can't be 0."); 787 assert(B <= 64 && "Bit width out of range."); 788 return int64_t(X << (64 - B)) >> (64 - B); 789 } 790 791 /// Subtract two unsigned integers, X and Y, of type T and return the absolute 792 /// value of the result. 793 template <typename T> 794 std::enable_if_t<std::is_unsigned<T>::value, T> AbsoluteDifference(T X, T Y) { 795 return X > Y ? (X - Y) : (Y - X); 796 } 797 798 /// Add two unsigned integers, X and Y, of type T. Clamp the result to the 799 /// maximum representable value of T on overflow. ResultOverflowed indicates if 800 /// the result is larger than the maximum representable value of type T. 801 template <typename T> 802 std::enable_if_t<std::is_unsigned<T>::value, T> 803 SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) { 804 bool Dummy; 805 bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy; 806 // Hacker's Delight, p. 29 807 T Z = X + Y; 808 Overflowed = (Z < X || Z < Y); 809 if (Overflowed) 810 return std::numeric_limits<T>::max(); 811 else 812 return Z; 813 } 814 815 /// Multiply two unsigned integers, X and Y, of type T. Clamp the result to the 816 /// maximum representable value of T on overflow. ResultOverflowed indicates if 817 /// the result is larger than the maximum representable value of type T. 818 template <typename T> 819 std::enable_if_t<std::is_unsigned<T>::value, T> 820 SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) { 821 bool Dummy; 822 bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy; 823 824 // Hacker's Delight, p. 30 has a different algorithm, but we don't use that 825 // because it fails for uint16_t (where multiplication can have undefined 826 // behavior due to promotion to int), and requires a division in addition 827 // to the multiplication. 828 829 Overflowed = false; 830 831 // Log2(Z) would be either Log2Z or Log2Z + 1. 832 // Special case: if X or Y is 0, Log2_64 gives -1, and Log2Z 833 // will necessarily be less than Log2Max as desired. 834 int Log2Z = Log2_64(X) + Log2_64(Y); 835 const T Max = std::numeric_limits<T>::max(); 836 int Log2Max = Log2_64(Max); 837 if (Log2Z < Log2Max) { 838 return X * Y; 839 } 840 if (Log2Z > Log2Max) { 841 Overflowed = true; 842 return Max; 843 } 844 845 // We're going to use the top bit, and maybe overflow one 846 // bit past it. Multiply all but the bottom bit then add 847 // that on at the end. 848 T Z = (X >> 1) * Y; 849 if (Z & ~(Max >> 1)) { 850 Overflowed = true; 851 return Max; 852 } 853 Z <<= 1; 854 if (X & 1) 855 return SaturatingAdd(Z, Y, ResultOverflowed); 856 857 return Z; 858 } 859 860 /// Multiply two unsigned integers, X and Y, and add the unsigned integer, A to 861 /// the product. Clamp the result to the maximum representable value of T on 862 /// overflow. ResultOverflowed indicates if the result is larger than the 863 /// maximum representable value of type T. 864 template <typename T> 865 std::enable_if_t<std::is_unsigned<T>::value, T> 866 SaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed = nullptr) { 867 bool Dummy; 868 bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy; 869 870 T Product = SaturatingMultiply(X, Y, &Overflowed); 871 if (Overflowed) 872 return Product; 873 874 return SaturatingAdd(A, Product, &Overflowed); 875 } 876 877 /// Use this rather than HUGE_VALF; the latter causes warnings on MSVC. 878 extern const float huge_valf; 879 880 881 /// Add two signed integers, computing the two's complement truncated result, 882 /// returning true if overflow occured. 883 template <typename T> 884 std::enable_if_t<std::is_signed<T>::value, T> AddOverflow(T X, T Y, T &Result) { 885 #if __has_builtin(__builtin_add_overflow) 886 return __builtin_add_overflow(X, Y, &Result); 887 #else 888 // Perform the unsigned addition. 889 using U = std::make_unsigned_t<T>; 890 const U UX = static_cast<U>(X); 891 const U UY = static_cast<U>(Y); 892 const U UResult = UX + UY; 893 894 // Convert to signed. 895 Result = static_cast<T>(UResult); 896 897 // Adding two positive numbers should result in a positive number. 898 if (X > 0 && Y > 0) 899 return Result <= 0; 900 // Adding two negatives should result in a negative number. 901 if (X < 0 && Y < 0) 902 return Result >= 0; 903 return false; 904 #endif 905 } 906 907 /// Subtract two signed integers, computing the two's complement truncated 908 /// result, returning true if an overflow ocurred. 909 template <typename T> 910 std::enable_if_t<std::is_signed<T>::value, T> SubOverflow(T X, T Y, T &Result) { 911 #if __has_builtin(__builtin_sub_overflow) 912 return __builtin_sub_overflow(X, Y, &Result); 913 #else 914 // Perform the unsigned addition. 915 using U = std::make_unsigned_t<T>; 916 const U UX = static_cast<U>(X); 917 const U UY = static_cast<U>(Y); 918 const U UResult = UX - UY; 919 920 // Convert to signed. 921 Result = static_cast<T>(UResult); 922 923 // Subtracting a positive number from a negative results in a negative number. 924 if (X <= 0 && Y > 0) 925 return Result >= 0; 926 // Subtracting a negative number from a positive results in a positive number. 927 if (X >= 0 && Y < 0) 928 return Result <= 0; 929 return false; 930 #endif 931 } 932 933 /// Multiply two signed integers, computing the two's complement truncated 934 /// result, returning true if an overflow ocurred. 935 template <typename T> 936 std::enable_if_t<std::is_signed<T>::value, T> MulOverflow(T X, T Y, T &Result) { 937 // Perform the unsigned multiplication on absolute values. 938 using U = std::make_unsigned_t<T>; 939 const U UX = X < 0 ? (0 - static_cast<U>(X)) : static_cast<U>(X); 940 const U UY = Y < 0 ? (0 - static_cast<U>(Y)) : static_cast<U>(Y); 941 const U UResult = UX * UY; 942 943 // Convert to signed. 944 const bool IsNegative = (X < 0) ^ (Y < 0); 945 Result = IsNegative ? (0 - UResult) : UResult; 946 947 // If any of the args was 0, result is 0 and no overflow occurs. 948 if (UX == 0 || UY == 0) 949 return false; 950 951 // UX and UY are in [1, 2^n], where n is the number of digits. 952 // Check how the max allowed absolute value (2^n for negative, 2^(n-1) for 953 // positive) divided by an argument compares to the other. 954 if (IsNegative) 955 return UX > (static_cast<U>(std::numeric_limits<T>::max()) + U(1)) / UY; 956 else 957 return UX > (static_cast<U>(std::numeric_limits<T>::max())) / UY; 958 } 959 960 } // End llvm namespace 961 962 #endif 963