1193323Sed//===-- llvm/Support/MathExtras.h - Useful math functions -------*- C++ -*-===// 2193323Sed// 3353358Sdim// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. 4353358Sdim// See https://llvm.org/LICENSE.txt for license information. 5353358Sdim// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception 6193323Sed// 7193323Sed//===----------------------------------------------------------------------===// 8193323Sed// 9193323Sed// This file contains some functions that are useful for math stuff. 10193323Sed// 11193323Sed//===----------------------------------------------------------------------===// 12193323Sed 13193323Sed#ifndef LLVM_SUPPORT_MATHEXTRAS_H 14193323Sed#define LLVM_SUPPORT_MATHEXTRAS_H 15193323Sed 16261991Sdim#include "llvm/Support/Compiler.h" 17218893Sdim#include "llvm/Support/SwapByteOrder.h" 18309124Sdim#include <algorithm> 19276479Sdim#include <cassert> 20321369Sdim#include <climits> 21261991Sdim#include <cstring> 22321369Sdim#include <limits> 23276479Sdim#include <type_traits> 24261991Sdim 25288943Sdim#ifdef __ANDROID_NDK__ 26288943Sdim#include <android/api-level.h> 27288943Sdim#endif 28288943Sdim 29341825Sdim#ifdef _MSC_VER 30341825Sdim// Declare these intrinsics manually rather including intrin.h. It's very 31341825Sdim// expensive, and MathExtras.h is popular. 32341825Sdim// #include <intrin.h> 33341825Sdimextern "C" { 34341825Sdimunsigned char _BitScanForward(unsigned long *_Index, unsigned long _Mask); 35341825Sdimunsigned char _BitScanForward64(unsigned long *_Index, unsigned __int64 _Mask); 36341825Sdimunsigned char _BitScanReverse(unsigned long *_Index, unsigned long _Mask); 37341825Sdimunsigned char _BitScanReverse64(unsigned long *_Index, unsigned __int64 _Mask); 38341825Sdim} 39341825Sdim#endif 40341825Sdim 41193323Sednamespace llvm { 42360784Sdim 43341825Sdim/// The behavior an operation has on an input of 0. 44261991Sdimenum ZeroBehavior { 45341825Sdim /// The returned value is undefined. 46261991Sdim ZB_Undefined, 47341825Sdim /// The returned value is numeric_limits<T>::max() 48261991Sdim ZB_Max, 49341825Sdim /// The returned value is numeric_limits<T>::digits 50261991Sdim ZB_Width 51261991Sdim}; 52193323Sed 53360784Sdim/// Mathematical constants. 54360784Sdimnamespace numbers { 55360784Sdim// TODO: Track C++20 std::numbers. 56360784Sdim// TODO: Favor using the hexadecimal FP constants (requires C++17). 57360784Sdimconstexpr double e = 2.7182818284590452354, // (0x1.5bf0a8b145749P+1) https://oeis.org/A001113 58360784Sdim egamma = .57721566490153286061, // (0x1.2788cfc6fb619P-1) https://oeis.org/A001620 59360784Sdim ln2 = .69314718055994530942, // (0x1.62e42fefa39efP-1) https://oeis.org/A002162 60360784Sdim ln10 = 2.3025850929940456840, // (0x1.24bb1bbb55516P+1) https://oeis.org/A002392 61360784Sdim log2e = 1.4426950408889634074, // (0x1.71547652b82feP+0) 62360784Sdim log10e = .43429448190325182765, // (0x1.bcb7b1526e50eP-2) 63360784Sdim pi = 3.1415926535897932385, // (0x1.921fb54442d18P+1) https://oeis.org/A000796 64360784Sdim inv_pi = .31830988618379067154, // (0x1.45f306bc9c883P-2) https://oeis.org/A049541 65360784Sdim sqrtpi = 1.7724538509055160273, // (0x1.c5bf891b4ef6bP+0) https://oeis.org/A002161 66360784Sdim inv_sqrtpi = .56418958354775628695, // (0x1.20dd750429b6dP-1) https://oeis.org/A087197 67360784Sdim sqrt2 = 1.4142135623730950488, // (0x1.6a09e667f3bcdP+0) https://oeis.org/A00219 68360784Sdim inv_sqrt2 = .70710678118654752440, // (0x1.6a09e667f3bcdP-1) 69360784Sdim sqrt3 = 1.7320508075688772935, // (0x1.bb67ae8584caaP+0) https://oeis.org/A002194 70360784Sdim inv_sqrt3 = .57735026918962576451, // (0x1.279a74590331cP-1) 71360784Sdim phi = 1.6180339887498948482; // (0x1.9e3779b97f4a8P+0) https://oeis.org/A001622 72360784Sdimconstexpr float ef = 2.71828183F, // (0x1.5bf0a8P+1) https://oeis.org/A001113 73360784Sdim egammaf = .577215665F, // (0x1.2788d0P-1) https://oeis.org/A001620 74360784Sdim ln2f = .693147181F, // (0x1.62e430P-1) https://oeis.org/A002162 75360784Sdim ln10f = 2.30258509F, // (0x1.26bb1cP+1) https://oeis.org/A002392 76360784Sdim log2ef = 1.44269504F, // (0x1.715476P+0) 77360784Sdim log10ef = .434294482F, // (0x1.bcb7b2P-2) 78360784Sdim pif = 3.14159265F, // (0x1.921fb6P+1) https://oeis.org/A000796 79360784Sdim inv_pif = .318309886F, // (0x1.45f306P-2) https://oeis.org/A049541 80360784Sdim sqrtpif = 1.77245385F, // (0x1.c5bf8aP+0) https://oeis.org/A002161 81360784Sdim inv_sqrtpif = .564189584F, // (0x1.20dd76P-1) https://oeis.org/A087197 82360784Sdim sqrt2f = 1.41421356F, // (0x1.6a09e6P+0) https://oeis.org/A002193 83360784Sdim inv_sqrt2f = .707106781F, // (0x1.6a09e6P-1) 84360784Sdim sqrt3f = 1.73205081F, // (0x1.bb67aeP+0) https://oeis.org/A002194 85360784Sdim inv_sqrt3f = .577350269F, // (0x1.279a74P-1) 86360784Sdim phif = 1.61803399F; // (0x1.9e377aP+0) https://oeis.org/A001622 87360784Sdim} // namespace numbers 88360784Sdim 89288943Sdimnamespace detail { 90288943Sdimtemplate <typename T, std::size_t SizeOfT> struct TrailingZerosCounter { 91353358Sdim static unsigned count(T Val, ZeroBehavior) { 92288943Sdim if (!Val) 93288943Sdim return std::numeric_limits<T>::digits; 94288943Sdim if (Val & 0x1) 95288943Sdim return 0; 96261991Sdim 97288943Sdim // Bisection method. 98353358Sdim unsigned ZeroBits = 0; 99288943Sdim T Shift = std::numeric_limits<T>::digits >> 1; 100288943Sdim T Mask = std::numeric_limits<T>::max() >> Shift; 101288943Sdim while (Shift) { 102288943Sdim if ((Val & Mask) == 0) { 103288943Sdim Val >>= Shift; 104288943Sdim ZeroBits |= Shift; 105288943Sdim } 106288943Sdim Shift >>= 1; 107288943Sdim Mask >>= Shift; 108261991Sdim } 109288943Sdim return ZeroBits; 110261991Sdim } 111288943Sdim}; 112261991Sdim 113360784Sdim#if defined(__GNUC__) || defined(_MSC_VER) 114288943Sdimtemplate <typename T> struct TrailingZerosCounter<T, 4> { 115353358Sdim static unsigned count(T Val, ZeroBehavior ZB) { 116288943Sdim if (ZB != ZB_Undefined && Val == 0) 117288943Sdim return 32; 118261991Sdim 119360784Sdim#if __has_builtin(__builtin_ctz) || defined(__GNUC__) 120288943Sdim return __builtin_ctz(Val); 121296417Sdim#elif defined(_MSC_VER) 122288943Sdim unsigned long Index; 123288943Sdim _BitScanForward(&Index, Val); 124288943Sdim return Index; 125261991Sdim#endif 126288943Sdim } 127288943Sdim}; 128261991Sdim 129261991Sdim#if !defined(_MSC_VER) || defined(_M_X64) 130288943Sdimtemplate <typename T> struct TrailingZerosCounter<T, 8> { 131353358Sdim static unsigned count(T Val, ZeroBehavior ZB) { 132288943Sdim if (ZB != ZB_Undefined && Val == 0) 133288943Sdim return 64; 134261991Sdim 135360784Sdim#if __has_builtin(__builtin_ctzll) || defined(__GNUC__) 136288943Sdim return __builtin_ctzll(Val); 137296417Sdim#elif defined(_MSC_VER) 138288943Sdim unsigned long Index; 139288943Sdim _BitScanForward64(&Index, Val); 140288943Sdim return Index; 141261991Sdim#endif 142288943Sdim } 143288943Sdim}; 144261991Sdim#endif 145261991Sdim#endif 146288943Sdim} // namespace detail 147261991Sdim 148341825Sdim/// Count number of 0's from the least significant bit to the most 149261991Sdim/// stopping at the first 1. 150261991Sdim/// 151261991Sdim/// Only unsigned integral types are allowed. 152261991Sdim/// 153261991Sdim/// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are 154261991Sdim/// valid arguments. 155261991Sdimtemplate <typename T> 156353358Sdimunsigned countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) { 157288943Sdim static_assert(std::numeric_limits<T>::is_integer && 158288943Sdim !std::numeric_limits<T>::is_signed, 159288943Sdim "Only unsigned integral types are allowed."); 160321369Sdim return llvm::detail::TrailingZerosCounter<T, sizeof(T)>::count(Val, ZB); 161288943Sdim} 162261991Sdim 163288943Sdimnamespace detail { 164288943Sdimtemplate <typename T, std::size_t SizeOfT> struct LeadingZerosCounter { 165353358Sdim static unsigned count(T Val, ZeroBehavior) { 166288943Sdim if (!Val) 167288943Sdim return std::numeric_limits<T>::digits; 168261991Sdim 169288943Sdim // Bisection method. 170353358Sdim unsigned ZeroBits = 0; 171288943Sdim for (T Shift = std::numeric_limits<T>::digits >> 1; Shift; Shift >>= 1) { 172288943Sdim T Tmp = Val >> Shift; 173288943Sdim if (Tmp) 174288943Sdim Val = Tmp; 175288943Sdim else 176288943Sdim ZeroBits |= Shift; 177288943Sdim } 178288943Sdim return ZeroBits; 179261991Sdim } 180288943Sdim}; 181261991Sdim 182360784Sdim#if defined(__GNUC__) || defined(_MSC_VER) 183288943Sdimtemplate <typename T> struct LeadingZerosCounter<T, 4> { 184353358Sdim static unsigned count(T Val, ZeroBehavior ZB) { 185288943Sdim if (ZB != ZB_Undefined && Val == 0) 186288943Sdim return 32; 187261991Sdim 188360784Sdim#if __has_builtin(__builtin_clz) || defined(__GNUC__) 189288943Sdim return __builtin_clz(Val); 190296417Sdim#elif defined(_MSC_VER) 191288943Sdim unsigned long Index; 192288943Sdim _BitScanReverse(&Index, Val); 193288943Sdim return Index ^ 31; 194261991Sdim#endif 195288943Sdim } 196288943Sdim}; 197261991Sdim 198261991Sdim#if !defined(_MSC_VER) || defined(_M_X64) 199288943Sdimtemplate <typename T> struct LeadingZerosCounter<T, 8> { 200353358Sdim static unsigned count(T Val, ZeroBehavior ZB) { 201288943Sdim if (ZB != ZB_Undefined && Val == 0) 202288943Sdim return 64; 203261991Sdim 204360784Sdim#if __has_builtin(__builtin_clzll) || defined(__GNUC__) 205288943Sdim return __builtin_clzll(Val); 206296417Sdim#elif defined(_MSC_VER) 207288943Sdim unsigned long Index; 208288943Sdim _BitScanReverse64(&Index, Val); 209288943Sdim return Index ^ 63; 210261991Sdim#endif 211288943Sdim } 212288943Sdim}; 213261991Sdim#endif 214261991Sdim#endif 215288943Sdim} // namespace detail 216261991Sdim 217341825Sdim/// Count number of 0's from the most significant bit to the least 218288943Sdim/// stopping at the first 1. 219288943Sdim/// 220288943Sdim/// Only unsigned integral types are allowed. 221288943Sdim/// 222288943Sdim/// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are 223288943Sdim/// valid arguments. 224288943Sdimtemplate <typename T> 225353358Sdimunsigned countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) { 226288943Sdim static_assert(std::numeric_limits<T>::is_integer && 227288943Sdim !std::numeric_limits<T>::is_signed, 228288943Sdim "Only unsigned integral types are allowed."); 229321369Sdim return llvm::detail::LeadingZerosCounter<T, sizeof(T)>::count(Val, ZB); 230288943Sdim} 231288943Sdim 232341825Sdim/// Get the index of the first set bit starting from the least 233261991Sdim/// significant bit. 234261991Sdim/// 235261991Sdim/// Only unsigned integral types are allowed. 236261991Sdim/// 237261991Sdim/// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are 238261991Sdim/// valid arguments. 239288943Sdimtemplate <typename T> T findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) { 240261991Sdim if (ZB == ZB_Max && Val == 0) 241261991Sdim return std::numeric_limits<T>::max(); 242261991Sdim 243261991Sdim return countTrailingZeros(Val, ZB_Undefined); 244261991Sdim} 245261991Sdim 246341825Sdim/// Create a bitmask with the N right-most bits set to 1, and all other 247321369Sdim/// bits set to 0. Only unsigned types are allowed. 248321369Sdimtemplate <typename T> T maskTrailingOnes(unsigned N) { 249321369Sdim static_assert(std::is_unsigned<T>::value, "Invalid type!"); 250321369Sdim const unsigned Bits = CHAR_BIT * sizeof(T); 251321369Sdim assert(N <= Bits && "Invalid bit index"); 252321369Sdim return N == 0 ? 0 : (T(-1) >> (Bits - N)); 253321369Sdim} 254321369Sdim 255341825Sdim/// Create a bitmask with the N left-most bits set to 1, and all other 256321369Sdim/// bits set to 0. Only unsigned types are allowed. 257321369Sdimtemplate <typename T> T maskLeadingOnes(unsigned N) { 258321369Sdim return ~maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N); 259321369Sdim} 260321369Sdim 261341825Sdim/// Create a bitmask with the N right-most bits set to 0, and all other 262321369Sdim/// bits set to 1. Only unsigned types are allowed. 263321369Sdimtemplate <typename T> T maskTrailingZeros(unsigned N) { 264321369Sdim return maskLeadingOnes<T>(CHAR_BIT * sizeof(T) - N); 265321369Sdim} 266321369Sdim 267341825Sdim/// Create a bitmask with the N left-most bits set to 0, and all other 268321369Sdim/// bits set to 1. Only unsigned types are allowed. 269321369Sdimtemplate <typename T> T maskLeadingZeros(unsigned N) { 270321369Sdim return maskTrailingOnes<T>(CHAR_BIT * sizeof(T) - N); 271321369Sdim} 272321369Sdim 273341825Sdim/// Get the index of the last set bit starting from the least 274261991Sdim/// significant bit. 275261991Sdim/// 276261991Sdim/// Only unsigned integral types are allowed. 277261991Sdim/// 278261991Sdim/// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are 279261991Sdim/// valid arguments. 280288943Sdimtemplate <typename T> T findLastSet(T Val, ZeroBehavior ZB = ZB_Max) { 281261991Sdim if (ZB == ZB_Max && Val == 0) 282261991Sdim return std::numeric_limits<T>::max(); 283261991Sdim 284261991Sdim // Use ^ instead of - because both gcc and llvm can remove the associated ^ 285261991Sdim // in the __builtin_clz intrinsic on x86. 286261991Sdim return countLeadingZeros(Val, ZB_Undefined) ^ 287261991Sdim (std::numeric_limits<T>::digits - 1); 288261991Sdim} 289261991Sdim 290341825Sdim/// Macro compressed bit reversal table for 256 bits. 291261991Sdim/// 292261991Sdim/// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable 293261991Sdimstatic const unsigned char BitReverseTable256[256] = { 294261991Sdim#define R2(n) n, n + 2 * 64, n + 1 * 64, n + 3 * 64 295261991Sdim#define R4(n) R2(n), R2(n + 2 * 16), R2(n + 1 * 16), R2(n + 3 * 16) 296261991Sdim#define R6(n) R4(n), R4(n + 2 * 4), R4(n + 1 * 4), R4(n + 3 * 4) 297261991Sdim R6(0), R6(2), R6(1), R6(3) 298276479Sdim#undef R2 299276479Sdim#undef R4 300276479Sdim#undef R6 301261991Sdim}; 302261991Sdim 303341825Sdim/// Reverse the bits in \p Val. 304261991Sdimtemplate <typename T> 305261991SdimT reverseBits(T Val) { 306261991Sdim unsigned char in[sizeof(Val)]; 307261991Sdim unsigned char out[sizeof(Val)]; 308261991Sdim std::memcpy(in, &Val, sizeof(Val)); 309261991Sdim for (unsigned i = 0; i < sizeof(Val); ++i) 310261991Sdim out[(sizeof(Val) - i) - 1] = BitReverseTable256[in[i]]; 311261991Sdim std::memcpy(&Val, out, sizeof(Val)); 312261991Sdim return Val; 313261991Sdim} 314261991Sdim 315193323Sed// NOTE: The following support functions use the _32/_64 extensions instead of 316193323Sed// type overloading so that signed and unsigned integers can be used without 317193323Sed// ambiguity. 318193323Sed 319321369Sdim/// Return the high 32 bits of a 64 bit value. 320314564Sdimconstexpr inline uint32_t Hi_32(uint64_t Value) { 321193323Sed return static_cast<uint32_t>(Value >> 32); 322193323Sed} 323193323Sed 324321369Sdim/// Return the low 32 bits of a 64 bit value. 325314564Sdimconstexpr inline uint32_t Lo_32(uint64_t Value) { 326193323Sed return static_cast<uint32_t>(Value); 327193323Sed} 328193323Sed 329321369Sdim/// Make a 64-bit integer from a high / low pair of 32-bit integers. 330314564Sdimconstexpr inline uint64_t Make_64(uint32_t High, uint32_t Low) { 331276479Sdim return ((uint64_t)High << 32) | (uint64_t)Low; 332276479Sdim} 333276479Sdim 334321369Sdim/// Checks if an integer fits into the given bit width. 335314564Sdimtemplate <unsigned N> constexpr inline bool isInt(int64_t x) { 336206083Srdivacky return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1))); 337193323Sed} 338206083Srdivacky// Template specializations to get better code for common cases. 339314564Sdimtemplate <> constexpr inline bool isInt<8>(int64_t x) { 340206083Srdivacky return static_cast<int8_t>(x) == x; 341193323Sed} 342314564Sdimtemplate <> constexpr inline bool isInt<16>(int64_t x) { 343206083Srdivacky return static_cast<int16_t>(x) == x; 344193323Sed} 345314564Sdimtemplate <> constexpr inline bool isInt<32>(int64_t x) { 346206083Srdivacky return static_cast<int32_t>(x) == x; 347193323Sed} 348193323Sed 349321369Sdim/// Checks if a signed integer is an N bit number shifted left by S. 350314564Sdimtemplate <unsigned N, unsigned S> 351314564Sdimconstexpr inline bool isShiftedInt(int64_t x) { 352309124Sdim static_assert( 353309124Sdim N > 0, "isShiftedInt<0> doesn't make sense (refers to a 0-bit number."); 354309124Sdim static_assert(N + S <= 64, "isShiftedInt<N, S> with N + S > 64 is too wide."); 355309124Sdim return isInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0); 356234353Sdim} 357234353Sdim 358321369Sdim/// Checks if an unsigned integer fits into the given bit width. 359314564Sdim/// 360314564Sdim/// This is written as two functions rather than as simply 361314564Sdim/// 362314564Sdim/// return N >= 64 || X < (UINT64_C(1) << N); 363314564Sdim/// 364314564Sdim/// to keep MSVC from (incorrectly) warning on isUInt<64> that we're shifting 365314564Sdim/// left too many places. 366314564Sdimtemplate <unsigned N> 367314564Sdimconstexpr inline typename std::enable_if<(N < 64), bool>::type 368314564SdimisUInt(uint64_t X) { 369314564Sdim static_assert(N > 0, "isUInt<0> doesn't make sense"); 370314564Sdim return X < (UINT64_C(1) << (N)); 371198090Srdivacky} 372314564Sdimtemplate <unsigned N> 373314564Sdimconstexpr inline typename std::enable_if<N >= 64, bool>::type 374314564SdimisUInt(uint64_t X) { 375314564Sdim return true; 376314564Sdim} 377309124Sdim 378206083Srdivacky// Template specializations to get better code for common cases. 379314564Sdimtemplate <> constexpr inline bool isUInt<8>(uint64_t x) { 380206083Srdivacky return static_cast<uint8_t>(x) == x; 381206083Srdivacky} 382314564Sdimtemplate <> constexpr inline bool isUInt<16>(uint64_t x) { 383206083Srdivacky return static_cast<uint16_t>(x) == x; 384206083Srdivacky} 385314564Sdimtemplate <> constexpr inline bool isUInt<32>(uint64_t x) { 386206083Srdivacky return static_cast<uint32_t>(x) == x; 387206083Srdivacky} 388198090Srdivacky 389309124Sdim/// Checks if a unsigned integer is an N bit number shifted left by S. 390314564Sdimtemplate <unsigned N, unsigned S> 391314564Sdimconstexpr inline bool isShiftedUInt(uint64_t x) { 392309124Sdim static_assert( 393309124Sdim N > 0, "isShiftedUInt<0> doesn't make sense (refers to a 0-bit number)"); 394309124Sdim static_assert(N + S <= 64, 395309124Sdim "isShiftedUInt<N, S> with N + S > 64 is too wide."); 396309124Sdim // Per the two static_asserts above, S must be strictly less than 64. So 397309124Sdim // 1 << S is not undefined behavior. 398309124Sdim return isUInt<N + S>(x) && (x % (UINT64_C(1) << S) == 0); 399234353Sdim} 400234353Sdim 401309124Sdim/// Gets the maximum value for a N-bit unsigned integer. 402309124Sdiminline uint64_t maxUIntN(uint64_t N) { 403309124Sdim assert(N > 0 && N <= 64 && "integer width out of range"); 404309124Sdim 405309124Sdim // uint64_t(1) << 64 is undefined behavior, so we can't do 406309124Sdim // (uint64_t(1) << N) - 1 407309124Sdim // without checking first that N != 64. But this works and doesn't have a 408309124Sdim // branch. 409309124Sdim return UINT64_MAX >> (64 - N); 410309124Sdim} 411309124Sdim 412309124Sdim/// Gets the minimum value for a N-bit signed integer. 413309124Sdiminline int64_t minIntN(int64_t N) { 414309124Sdim assert(N > 0 && N <= 64 && "integer width out of range"); 415309124Sdim 416309124Sdim return -(UINT64_C(1)<<(N-1)); 417309124Sdim} 418309124Sdim 419309124Sdim/// Gets the maximum value for a N-bit signed integer. 420309124Sdiminline int64_t maxIntN(int64_t N) { 421309124Sdim assert(N > 0 && N <= 64 && "integer width out of range"); 422309124Sdim 423309124Sdim // This relies on two's complement wraparound when N == 64, so we convert to 424309124Sdim // int64_t only at the very end to avoid UB. 425309124Sdim return (UINT64_C(1) << (N - 1)) - 1; 426309124Sdim} 427309124Sdim 428321369Sdim/// Checks if an unsigned integer fits into the given (dynamic) bit width. 429218893Sdiminline bool isUIntN(unsigned N, uint64_t x) { 430309124Sdim return N >= 64 || x <= maxUIntN(N); 431218893Sdim} 432218893Sdim 433321369Sdim/// Checks if an signed integer fits into the given (dynamic) bit width. 434218893Sdiminline bool isIntN(unsigned N, int64_t x) { 435309124Sdim return N >= 64 || (minIntN(N) <= x && x <= maxIntN(N)); 436218893Sdim} 437218893Sdim 438321369Sdim/// Return true if the argument is a non-empty sequence of ones starting at the 439321369Sdim/// least significant bit with the remainder zero (32 bit version). 440321369Sdim/// Ex. isMask_32(0x0000FFFFU) == true. 441314564Sdimconstexpr inline bool isMask_32(uint32_t Value) { 442193323Sed return Value && ((Value + 1) & Value) == 0; 443193323Sed} 444193323Sed 445321369Sdim/// Return true if the argument is a non-empty sequence of ones starting at the 446321369Sdim/// least significant bit with the remainder zero (64 bit version). 447314564Sdimconstexpr inline bool isMask_64(uint64_t Value) { 448193323Sed return Value && ((Value + 1) & Value) == 0; 449193323Sed} 450193323Sed 451321369Sdim/// Return true if the argument contains a non-empty sequence of ones with the 452321369Sdim/// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true. 453314564Sdimconstexpr inline bool isShiftedMask_32(uint32_t Value) { 454288943Sdim return Value && isMask_32((Value - 1) | Value); 455193323Sed} 456193323Sed 457321369Sdim/// Return true if the argument contains a non-empty sequence of ones with the 458321369Sdim/// remainder zero (64 bit version.) 459314564Sdimconstexpr inline bool isShiftedMask_64(uint64_t Value) { 460288943Sdim return Value && isMask_64((Value - 1) | Value); 461193323Sed} 462193323Sed 463321369Sdim/// Return true if the argument is a power of two > 0. 464321369Sdim/// Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.) 465314564Sdimconstexpr inline bool isPowerOf2_32(uint32_t Value) { 466193323Sed return Value && !(Value & (Value - 1)); 467193323Sed} 468193323Sed 469321369Sdim/// Return true if the argument is a power of two > 0 (64 bit edition.) 470314564Sdimconstexpr inline bool isPowerOf2_64(uint64_t Value) { 471327952Sdim return Value && !(Value & (Value - 1)); 472193323Sed} 473193323Sed 474321369Sdim/// Return a byte-swapped representation of the 16-bit argument. 475193323Sedinline uint16_t ByteSwap_16(uint16_t Value) { 476218893Sdim return sys::SwapByteOrder_16(Value); 477193323Sed} 478193323Sed 479321369Sdim/// Return a byte-swapped representation of the 32-bit argument. 480193323Sedinline uint32_t ByteSwap_32(uint32_t Value) { 481218893Sdim return sys::SwapByteOrder_32(Value); 482193323Sed} 483193323Sed 484321369Sdim/// Return a byte-swapped representation of the 64-bit argument. 485193323Sedinline uint64_t ByteSwap_64(uint64_t Value) { 486218893Sdim return sys::SwapByteOrder_64(Value); 487193323Sed} 488193323Sed 489341825Sdim/// Count the number of ones from the most significant bit to the first 490288943Sdim/// zero bit. 491288943Sdim/// 492321369Sdim/// Ex. countLeadingOnes(0xFF0FFF00) == 8. 493288943Sdim/// Only unsigned integral types are allowed. 494288943Sdim/// 495288943Sdim/// \param ZB the behavior on an input of all ones. Only ZB_Width and 496288943Sdim/// ZB_Undefined are valid arguments. 497288943Sdimtemplate <typename T> 498353358Sdimunsigned countLeadingOnes(T Value, ZeroBehavior ZB = ZB_Width) { 499288943Sdim static_assert(std::numeric_limits<T>::is_integer && 500288943Sdim !std::numeric_limits<T>::is_signed, 501288943Sdim "Only unsigned integral types are allowed."); 502341825Sdim return countLeadingZeros<T>(~Value, ZB); 503193323Sed} 504193323Sed 505341825Sdim/// Count the number of ones from the least significant bit to the first 506288943Sdim/// zero bit. 507288943Sdim/// 508288943Sdim/// Ex. countTrailingOnes(0x00FF00FF) == 8. 509288943Sdim/// Only unsigned integral types are allowed. 510288943Sdim/// 511288943Sdim/// \param ZB the behavior on an input of all ones. Only ZB_Width and 512288943Sdim/// ZB_Undefined are valid arguments. 513288943Sdimtemplate <typename T> 514353358Sdimunsigned countTrailingOnes(T Value, ZeroBehavior ZB = ZB_Width) { 515288943Sdim static_assert(std::numeric_limits<T>::is_integer && 516288943Sdim !std::numeric_limits<T>::is_signed, 517288943Sdim "Only unsigned integral types are allowed."); 518341825Sdim return countTrailingZeros<T>(~Value, ZB); 519193323Sed} 520193323Sed 521288943Sdimnamespace detail { 522288943Sdimtemplate <typename T, std::size_t SizeOfT> struct PopulationCounter { 523288943Sdim static unsigned count(T Value) { 524288943Sdim // Generic version, forward to 32 bits. 525288943Sdim static_assert(SizeOfT <= 4, "Not implemented!"); 526360784Sdim#if defined(__GNUC__) 527288943Sdim return __builtin_popcount(Value); 528288943Sdim#else 529288943Sdim uint32_t v = Value; 530288943Sdim v = v - ((v >> 1) & 0x55555555); 531288943Sdim v = (v & 0x33333333) + ((v >> 2) & 0x33333333); 532288943Sdim return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24; 533288943Sdim#endif 534288943Sdim } 535288943Sdim}; 536193323Sed 537288943Sdimtemplate <typename T> struct PopulationCounter<T, 8> { 538288943Sdim static unsigned count(T Value) { 539360784Sdim#if defined(__GNUC__) 540288943Sdim return __builtin_popcountll(Value); 541193323Sed#else 542288943Sdim uint64_t v = Value; 543288943Sdim v = v - ((v >> 1) & 0x5555555555555555ULL); 544288943Sdim v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL); 545288943Sdim v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL; 546288943Sdim return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56); 547193323Sed#endif 548288943Sdim } 549288943Sdim}; 550288943Sdim} // namespace detail 551288943Sdim 552341825Sdim/// Count the number of set bits in a value. 553288943Sdim/// Ex. countPopulation(0xF000F000) = 8 554288943Sdim/// Returns 0 if the word is zero. 555288943Sdimtemplate <typename T> 556288943Sdiminline unsigned countPopulation(T Value) { 557288943Sdim static_assert(std::numeric_limits<T>::is_integer && 558288943Sdim !std::numeric_limits<T>::is_signed, 559288943Sdim "Only unsigned integral types are allowed."); 560288943Sdim return detail::PopulationCounter<T, sizeof(T)>::count(Value); 561193323Sed} 562193323Sed 563360784Sdim/// Compile time Log2. 564360784Sdim/// Valid only for positive powers of two. 565360784Sdimtemplate <size_t kValue> constexpr inline size_t CTLog2() { 566360784Sdim static_assert(kValue > 0 && llvm::isPowerOf2_64(kValue), 567360784Sdim "Value is not a valid power of 2"); 568360784Sdim return 1 + CTLog2<kValue / 2>(); 569360784Sdim} 570360784Sdim 571360784Sdimtemplate <> constexpr inline size_t CTLog2<1>() { return 0; } 572360784Sdim 573321369Sdim/// Return the log base 2 of the specified value. 574288943Sdiminline double Log2(double Value) { 575288943Sdim#if defined(__ANDROID_API__) && __ANDROID_API__ < 18 576288943Sdim return __builtin_log(Value) / __builtin_log(2.0); 577193323Sed#else 578288943Sdim return log2(Value); 579193323Sed#endif 580193323Sed} 581193323Sed 582321369Sdim/// Return the floor log base 2 of the specified value, -1 if the value is zero. 583321369Sdim/// (32 bit edition.) 584193323Sed/// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2 585193323Sedinline unsigned Log2_32(uint32_t Value) { 586261991Sdim return 31 - countLeadingZeros(Value); 587193323Sed} 588193323Sed 589321369Sdim/// Return the floor log base 2 of the specified value, -1 if the value is zero. 590321369Sdim/// (64 bit edition.) 591193323Sedinline unsigned Log2_64(uint64_t Value) { 592261991Sdim return 63 - countLeadingZeros(Value); 593193323Sed} 594193323Sed 595321369Sdim/// Return the ceil log base 2 of the specified value, 32 if the value is zero. 596321369Sdim/// (32 bit edition). 597193323Sed/// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3 598193323Sedinline unsigned Log2_32_Ceil(uint32_t Value) { 599261991Sdim return 32 - countLeadingZeros(Value - 1); 600193323Sed} 601193323Sed 602321369Sdim/// Return the ceil log base 2 of the specified value, 64 if the value is zero. 603321369Sdim/// (64 bit edition.) 604193323Sedinline unsigned Log2_64_Ceil(uint64_t Value) { 605261991Sdim return 64 - countLeadingZeros(Value - 1); 606193323Sed} 607193323Sed 608321369Sdim/// Return the greatest common divisor of the values using Euclid's algorithm. 609353358Sdimtemplate <typename T> 610353358Sdiminline T greatestCommonDivisor(T A, T B) { 611193323Sed while (B) { 612353358Sdim T Tmp = B; 613193323Sed B = A % B; 614353358Sdim A = Tmp; 615193323Sed } 616193323Sed return A; 617193323Sed} 618193323Sed 619353358Sdiminline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) { 620353358Sdim return greatestCommonDivisor<uint64_t>(A, B); 621353358Sdim} 622353358Sdim 623321369Sdim/// This function takes a 64-bit integer and returns the bit equivalent double. 624193323Sedinline double BitsToDouble(uint64_t Bits) { 625314564Sdim double D; 626314564Sdim static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes"); 627314564Sdim memcpy(&D, &Bits, sizeof(Bits)); 628314564Sdim return D; 629193323Sed} 630193323Sed 631321369Sdim/// This function takes a 32-bit integer and returns the bit equivalent float. 632193323Sedinline float BitsToFloat(uint32_t Bits) { 633314564Sdim float F; 634314564Sdim static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes"); 635314564Sdim memcpy(&F, &Bits, sizeof(Bits)); 636314564Sdim return F; 637193323Sed} 638193323Sed 639321369Sdim/// This function takes a double and returns the bit equivalent 64-bit integer. 640321369Sdim/// Note that copying doubles around changes the bits of NaNs on some hosts, 641321369Sdim/// notably x86, so this routine cannot be used if these bits are needed. 642193323Sedinline uint64_t DoubleToBits(double Double) { 643314564Sdim uint64_t Bits; 644314564Sdim static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes"); 645314564Sdim memcpy(&Bits, &Double, sizeof(Double)); 646314564Sdim return Bits; 647193323Sed} 648193323Sed 649321369Sdim/// This function takes a float and returns the bit equivalent 32-bit integer. 650321369Sdim/// Note that copying floats around changes the bits of NaNs on some hosts, 651321369Sdim/// notably x86, so this routine cannot be used if these bits are needed. 652193323Sedinline uint32_t FloatToBits(float Float) { 653314564Sdim uint32_t Bits; 654314564Sdim static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes"); 655314564Sdim memcpy(&Bits, &Float, sizeof(Float)); 656314564Sdim return Bits; 657193323Sed} 658193323Sed 659321369Sdim/// A and B are either alignments or offsets. Return the minimum alignment that 660321369Sdim/// may be assumed after adding the two together. 661314564Sdimconstexpr inline uint64_t MinAlign(uint64_t A, uint64_t B) { 662193323Sed // The largest power of 2 that divides both A and B. 663249423Sdim // 664296417Sdim // Replace "-Value" by "1+~Value" in the following commented code to avoid 665249423Sdim // MSVC warning C4146 666249423Sdim // return (A | B) & -(A | B); 667249423Sdim return (A | B) & (1 + ~(A | B)); 668193323Sed} 669193323Sed 670321369Sdim/// Returns the next power of two (in 64-bits) that is strictly greater than A. 671321369Sdim/// Returns zero on overflow. 672239462Sdiminline uint64_t NextPowerOf2(uint64_t A) { 673193323Sed A |= (A >> 1); 674193323Sed A |= (A >> 2); 675193323Sed A |= (A >> 4); 676193323Sed A |= (A >> 8); 677193323Sed A |= (A >> 16); 678193323Sed A |= (A >> 32); 679193323Sed return A + 1; 680193323Sed} 681193323Sed 682276479Sdim/// Returns the power of two which is less than or equal to the given value. 683276479Sdim/// Essentially, it is a floor operation across the domain of powers of two. 684276479Sdiminline uint64_t PowerOf2Floor(uint64_t A) { 685276479Sdim if (!A) return 0; 686276479Sdim return 1ull << (63 - countLeadingZeros(A, ZB_Undefined)); 687276479Sdim} 688276479Sdim 689314564Sdim/// Returns the power of two which is greater than or equal to the given value. 690314564Sdim/// Essentially, it is a ceil operation across the domain of powers of two. 691314564Sdiminline uint64_t PowerOf2Ceil(uint64_t A) { 692314564Sdim if (!A) 693314564Sdim return 0; 694314564Sdim return NextPowerOf2(A - 1); 695314564Sdim} 696314564Sdim 697243830Sdim/// Returns the next integer (mod 2**64) that is greater than or equal to 698243830Sdim/// \p Value and is a multiple of \p Align. \p Align must be non-zero. 699193323Sed/// 700296417Sdim/// If non-zero \p Skew is specified, the return value will be a minimal 701296417Sdim/// integer that is greater than or equal to \p Value and equal to 702296417Sdim/// \p Align * N + \p Skew for some integer N. If \p Skew is larger than 703296417Sdim/// \p Align, its value is adjusted to '\p Skew mod \p Align'. 704296417Sdim/// 705193323Sed/// Examples: 706243830Sdim/// \code 707309124Sdim/// alignTo(5, 8) = 8 708309124Sdim/// alignTo(17, 8) = 24 709309124Sdim/// alignTo(~0LL, 8) = 0 710309124Sdim/// alignTo(321, 255) = 510 711296417Sdim/// 712309124Sdim/// alignTo(5, 8, 7) = 7 713309124Sdim/// alignTo(17, 8, 1) = 17 714309124Sdim/// alignTo(~0LL, 8, 3) = 3 715309124Sdim/// alignTo(321, 255, 42) = 552 716243830Sdim/// \endcode 717309124Sdiminline uint64_t alignTo(uint64_t Value, uint64_t Align, uint64_t Skew = 0) { 718314564Sdim assert(Align != 0u && "Align can't be 0."); 719296417Sdim Skew %= Align; 720296417Sdim return (Value + Align - 1 - Skew) / Align * Align + Skew; 721193323Sed} 722193323Sed 723314564Sdim/// Returns the next integer (mod 2**64) that is greater than or equal to 724314564Sdim/// \p Value and is a multiple of \c Align. \c Align must be non-zero. 725314564Sdimtemplate <uint64_t Align> constexpr inline uint64_t alignTo(uint64_t Value) { 726314564Sdim static_assert(Align != 0u, "Align must be non-zero"); 727314564Sdim return (Value + Align - 1) / Align * Align; 728314564Sdim} 729314564Sdim 730327952Sdim/// Returns the integer ceil(Numerator / Denominator). 731327952Sdiminline uint64_t divideCeil(uint64_t Numerator, uint64_t Denominator) { 732327952Sdim return alignTo(Numerator, Denominator) / Denominator; 733327952Sdim} 734327952Sdim 735360784Sdim/// Returns the integer nearest(Numerator / Denominator). 736360784Sdiminline uint64_t divideNearest(uint64_t Numerator, uint64_t Denominator) { 737360784Sdim return (Numerator + (Denominator / 2)) / Denominator; 738360784Sdim} 739314564Sdim 740309124Sdim/// Returns the largest uint64_t less than or equal to \p Value and is 741309124Sdim/// \p Skew mod \p Align. \p Align must be non-zero 742309124Sdiminline uint64_t alignDown(uint64_t Value, uint64_t Align, uint64_t Skew = 0) { 743314564Sdim assert(Align != 0u && "Align can't be 0."); 744309124Sdim Skew %= Align; 745309124Sdim return (Value - Skew) / Align * Align + Skew; 746309124Sdim} 747309124Sdim 748309124Sdim/// Sign-extend the number in the bottom B bits of X to a 32-bit integer. 749309124Sdim/// Requires 0 < B <= 32. 750314564Sdimtemplate <unsigned B> constexpr inline int32_t SignExtend32(uint32_t X) { 751309124Sdim static_assert(B > 0, "Bit width can't be 0."); 752309124Sdim static_assert(B <= 32, "Bit width out of range."); 753309124Sdim return int32_t(X << (32 - B)) >> (32 - B); 754206124Srdivacky} 755206124Srdivacky 756309124Sdim/// Sign-extend the number in the bottom B bits of X to a 32-bit integer. 757309124Sdim/// Requires 0 < B < 32. 758243830Sdiminline int32_t SignExtend32(uint32_t X, unsigned B) { 759309124Sdim assert(B > 0 && "Bit width can't be 0."); 760309124Sdim assert(B <= 32 && "Bit width out of range."); 761243830Sdim return int32_t(X << (32 - B)) >> (32 - B); 762243830Sdim} 763243830Sdim 764309124Sdim/// Sign-extend the number in the bottom B bits of X to a 64-bit integer. 765309124Sdim/// Requires 0 < B < 64. 766314564Sdimtemplate <unsigned B> constexpr inline int64_t SignExtend64(uint64_t x) { 767309124Sdim static_assert(B > 0, "Bit width can't be 0."); 768309124Sdim static_assert(B <= 64, "Bit width out of range."); 769206274Srdivacky return int64_t(x << (64 - B)) >> (64 - B); 770206124Srdivacky} 771206124Srdivacky 772309124Sdim/// Sign-extend the number in the bottom B bits of X to a 64-bit integer. 773309124Sdim/// Requires 0 < B < 64. 774243830Sdiminline int64_t SignExtend64(uint64_t X, unsigned B) { 775309124Sdim assert(B > 0 && "Bit width can't be 0."); 776309124Sdim assert(B <= 64 && "Bit width out of range."); 777243830Sdim return int64_t(X << (64 - B)) >> (64 - B); 778243830Sdim} 779243830Sdim 780309124Sdim/// Subtract two unsigned integers, X and Y, of type T and return the absolute 781309124Sdim/// value of the result. 782296417Sdimtemplate <typename T> 783296417Sdimtypename std::enable_if<std::is_unsigned<T>::value, T>::type 784309124SdimAbsoluteDifference(T X, T Y) { 785309124Sdim return std::max(X, Y) - std::min(X, Y); 786309124Sdim} 787309124Sdim 788309124Sdim/// Add two unsigned integers, X and Y, of type T. Clamp the result to the 789309124Sdim/// maximum representable value of T on overflow. ResultOverflowed indicates if 790309124Sdim/// the result is larger than the maximum representable value of type T. 791309124Sdimtemplate <typename T> 792309124Sdimtypename std::enable_if<std::is_unsigned<T>::value, T>::type 793296417SdimSaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) { 794296417Sdim bool Dummy; 795296417Sdim bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy; 796296417Sdim // Hacker's Delight, p. 29 797296417Sdim T Z = X + Y; 798296417Sdim Overflowed = (Z < X || Z < Y); 799296417Sdim if (Overflowed) 800296417Sdim return std::numeric_limits<T>::max(); 801296417Sdim else 802296417Sdim return Z; 803296417Sdim} 804296417Sdim 805309124Sdim/// Multiply two unsigned integers, X and Y, of type T. Clamp the result to the 806309124Sdim/// maximum representable value of T on overflow. ResultOverflowed indicates if 807309124Sdim/// the result is larger than the maximum representable value of type T. 808296417Sdimtemplate <typename T> 809296417Sdimtypename std::enable_if<std::is_unsigned<T>::value, T>::type 810296417SdimSaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) { 811296417Sdim bool Dummy; 812296417Sdim bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy; 813296417Sdim 814296417Sdim // Hacker's Delight, p. 30 has a different algorithm, but we don't use that 815296417Sdim // because it fails for uint16_t (where multiplication can have undefined 816296417Sdim // behavior due to promotion to int), and requires a division in addition 817296417Sdim // to the multiplication. 818296417Sdim 819296417Sdim Overflowed = false; 820296417Sdim 821296417Sdim // Log2(Z) would be either Log2Z or Log2Z + 1. 822296417Sdim // Special case: if X or Y is 0, Log2_64 gives -1, and Log2Z 823296417Sdim // will necessarily be less than Log2Max as desired. 824296417Sdim int Log2Z = Log2_64(X) + Log2_64(Y); 825296417Sdim const T Max = std::numeric_limits<T>::max(); 826296417Sdim int Log2Max = Log2_64(Max); 827296417Sdim if (Log2Z < Log2Max) { 828296417Sdim return X * Y; 829296417Sdim } 830296417Sdim if (Log2Z > Log2Max) { 831296417Sdim Overflowed = true; 832296417Sdim return Max; 833296417Sdim } 834296417Sdim 835296417Sdim // We're going to use the top bit, and maybe overflow one 836296417Sdim // bit past it. Multiply all but the bottom bit then add 837296417Sdim // that on at the end. 838296417Sdim T Z = (X >> 1) * Y; 839296417Sdim if (Z & ~(Max >> 1)) { 840296417Sdim Overflowed = true; 841296417Sdim return Max; 842296417Sdim } 843296417Sdim Z <<= 1; 844296417Sdim if (X & 1) 845296417Sdim return SaturatingAdd(Z, Y, ResultOverflowed); 846296417Sdim 847296417Sdim return Z; 848296417Sdim} 849296417Sdim 850309124Sdim/// Multiply two unsigned integers, X and Y, and add the unsigned integer, A to 851309124Sdim/// the product. Clamp the result to the maximum representable value of T on 852309124Sdim/// overflow. ResultOverflowed indicates if the result is larger than the 853309124Sdim/// maximum representable value of type T. 854296417Sdimtemplate <typename T> 855296417Sdimtypename std::enable_if<std::is_unsigned<T>::value, T>::type 856296417SdimSaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed = nullptr) { 857296417Sdim bool Dummy; 858296417Sdim bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy; 859296417Sdim 860296417Sdim T Product = SaturatingMultiply(X, Y, &Overflowed); 861296417Sdim if (Overflowed) 862296417Sdim return Product; 863296417Sdim 864296417Sdim return SaturatingAdd(A, Product, &Overflowed); 865296417Sdim} 866296417Sdim 867309124Sdim/// Use this rather than HUGE_VALF; the latter causes warnings on MSVC. 868280031Sdimextern const float huge_valf; 869360784Sdim 870360784Sdim 871360784Sdim/// Add two signed integers, computing the two's complement truncated result, 872360784Sdim/// returning true if overflow occured. 873360784Sdimtemplate <typename T> 874360784Sdimtypename std::enable_if<std::is_signed<T>::value, T>::type 875360784SdimAddOverflow(T X, T Y, T &Result) { 876360784Sdim#if __has_builtin(__builtin_add_overflow) 877360784Sdim return __builtin_add_overflow(X, Y, &Result); 878360784Sdim#else 879360784Sdim // Perform the unsigned addition. 880360784Sdim using U = typename std::make_unsigned<T>::type; 881360784Sdim const U UX = static_cast<U>(X); 882360784Sdim const U UY = static_cast<U>(Y); 883360784Sdim const U UResult = UX + UY; 884360784Sdim 885360784Sdim // Convert to signed. 886360784Sdim Result = static_cast<T>(UResult); 887360784Sdim 888360784Sdim // Adding two positive numbers should result in a positive number. 889360784Sdim if (X > 0 && Y > 0) 890360784Sdim return Result <= 0; 891360784Sdim // Adding two negatives should result in a negative number. 892360784Sdim if (X < 0 && Y < 0) 893360784Sdim return Result >= 0; 894360784Sdim return false; 895360784Sdim#endif 896360784Sdim} 897360784Sdim 898360784Sdim/// Subtract two signed integers, computing the two's complement truncated 899360784Sdim/// result, returning true if an overflow ocurred. 900360784Sdimtemplate <typename T> 901360784Sdimtypename std::enable_if<std::is_signed<T>::value, T>::type 902360784SdimSubOverflow(T X, T Y, T &Result) { 903360784Sdim#if __has_builtin(__builtin_sub_overflow) 904360784Sdim return __builtin_sub_overflow(X, Y, &Result); 905360784Sdim#else 906360784Sdim // Perform the unsigned addition. 907360784Sdim using U = typename std::make_unsigned<T>::type; 908360784Sdim const U UX = static_cast<U>(X); 909360784Sdim const U UY = static_cast<U>(Y); 910360784Sdim const U UResult = UX - UY; 911360784Sdim 912360784Sdim // Convert to signed. 913360784Sdim Result = static_cast<T>(UResult); 914360784Sdim 915360784Sdim // Subtracting a positive number from a negative results in a negative number. 916360784Sdim if (X <= 0 && Y > 0) 917360784Sdim return Result >= 0; 918360784Sdim // Subtracting a negative number from a positive results in a positive number. 919360784Sdim if (X >= 0 && Y < 0) 920360784Sdim return Result <= 0; 921360784Sdim return false; 922360784Sdim#endif 923360784Sdim} 924360784Sdim 925360784Sdim 926360784Sdim/// Multiply two signed integers, computing the two's complement truncated 927360784Sdim/// result, returning true if an overflow ocurred. 928360784Sdimtemplate <typename T> 929360784Sdimtypename std::enable_if<std::is_signed<T>::value, T>::type 930360784SdimMulOverflow(T X, T Y, T &Result) { 931360784Sdim // Perform the unsigned multiplication on absolute values. 932360784Sdim using U = typename std::make_unsigned<T>::type; 933360784Sdim const U UX = X < 0 ? (0 - static_cast<U>(X)) : static_cast<U>(X); 934360784Sdim const U UY = Y < 0 ? (0 - static_cast<U>(Y)) : static_cast<U>(Y); 935360784Sdim const U UResult = UX * UY; 936360784Sdim 937360784Sdim // Convert to signed. 938360784Sdim const bool IsNegative = (X < 0) ^ (Y < 0); 939360784Sdim Result = IsNegative ? (0 - UResult) : UResult; 940360784Sdim 941360784Sdim // If any of the args was 0, result is 0 and no overflow occurs. 942360784Sdim if (UX == 0 || UY == 0) 943360784Sdim return false; 944360784Sdim 945360784Sdim // UX and UY are in [1, 2^n], where n is the number of digits. 946360784Sdim // Check how the max allowed absolute value (2^n for negative, 2^(n-1) for 947360784Sdim // positive) divided by an argument compares to the other. 948360784Sdim if (IsNegative) 949360784Sdim return UX > (static_cast<U>(std::numeric_limits<T>::max()) + U(1)) / UY; 950360784Sdim else 951360784Sdim return UX > (static_cast<U>(std::numeric_limits<T>::max())) / UY; 952360784Sdim} 953360784Sdim 954193323Sed} // End llvm namespace 955193323Sed 956193323Sed#endif 957