//===-- llvm/Support/MathExtras.h - Useful math functions -------*- C++ -*-===// // // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. // See https://llvm.org/LICENSE.txt for license information. // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception // //===----------------------------------------------------------------------===// // // This file contains some functions that are useful for math stuff. // //===----------------------------------------------------------------------===// #ifndef LLVM_SUPPORT_MATHEXTRAS_H #define LLVM_SUPPORT_MATHEXTRAS_H #include "llvm/Support/Compiler.h" #include "llvm/Support/SwapByteOrder.h" #include #include #include #include #include #include #ifdef __ANDROID_NDK__ #include #endif #ifdef _MSC_VER // Declare these intrinsics manually rather including intrin.h. It's very // expensive, and MathExtras.h is popular. // #include extern "C" { unsigned char _BitScanForward(unsigned long *_Index, unsigned long _Mask); unsigned char _BitScanForward64(unsigned long *_Index, unsigned __int64 _Mask); unsigned char _BitScanReverse(unsigned long *_Index, unsigned long _Mask); unsigned char _BitScanReverse64(unsigned long *_Index, unsigned __int64 _Mask); } #endif namespace llvm { /// The behavior an operation has on an input of 0. enum ZeroBehavior { /// The returned value is undefined. ZB_Undefined, /// The returned value is numeric_limits::max() ZB_Max, /// The returned value is numeric_limits::digits ZB_Width }; /// Mathematical constants. namespace numbers { // TODO: Track C++20 std::numbers. // TODO: Favor using the hexadecimal FP constants (requires C++17). constexpr double e = 2.7182818284590452354, // (0x1.5bf0a8b145749P+1) https://oeis.org/A001113 egamma = .57721566490153286061, // (0x1.2788cfc6fb619P-1) https://oeis.org/A001620 ln2 = .69314718055994530942, // (0x1.62e42fefa39efP-1) https://oeis.org/A002162 ln10 = 2.3025850929940456840, // (0x1.24bb1bbb55516P+1) https://oeis.org/A002392 log2e = 1.4426950408889634074, // (0x1.71547652b82feP+0) log10e = .43429448190325182765, // (0x1.bcb7b1526e50eP-2) pi = 3.1415926535897932385, // (0x1.921fb54442d18P+1) https://oeis.org/A000796 inv_pi = .31830988618379067154, // (0x1.45f306bc9c883P-2) https://oeis.org/A049541 sqrtpi = 1.7724538509055160273, // (0x1.c5bf891b4ef6bP+0) https://oeis.org/A002161 inv_sqrtpi = .56418958354775628695, // (0x1.20dd750429b6dP-1) https://oeis.org/A087197 sqrt2 = 1.4142135623730950488, // (0x1.6a09e667f3bcdP+0) https://oeis.org/A00219 inv_sqrt2 = .70710678118654752440, // (0x1.6a09e667f3bcdP-1) sqrt3 = 1.7320508075688772935, // (0x1.bb67ae8584caaP+0) https://oeis.org/A002194 inv_sqrt3 = .57735026918962576451, // (0x1.279a74590331cP-1) phi = 1.6180339887498948482; // (0x1.9e3779b97f4a8P+0) https://oeis.org/A001622 constexpr float ef = 2.71828183F, // (0x1.5bf0a8P+1) https://oeis.org/A001113 egammaf = .577215665F, // (0x1.2788d0P-1) https://oeis.org/A001620 ln2f = .693147181F, // (0x1.62e430P-1) https://oeis.org/A002162 ln10f = 2.30258509F, // (0x1.26bb1cP+1) https://oeis.org/A002392 log2ef = 1.44269504F, // (0x1.715476P+0) log10ef = .434294482F, // (0x1.bcb7b2P-2) pif = 3.14159265F, // (0x1.921fb6P+1) https://oeis.org/A000796 inv_pif = .318309886F, // (0x1.45f306P-2) https://oeis.org/A049541 sqrtpif = 1.77245385F, // (0x1.c5bf8aP+0) https://oeis.org/A002161 inv_sqrtpif = .564189584F, // (0x1.20dd76P-1) https://oeis.org/A087197 sqrt2f = 1.41421356F, // (0x1.6a09e6P+0) https://oeis.org/A002193 inv_sqrt2f = .707106781F, // (0x1.6a09e6P-1) sqrt3f = 1.73205081F, // (0x1.bb67aeP+0) https://oeis.org/A002194 inv_sqrt3f = .577350269F, // (0x1.279a74P-1) phif = 1.61803399F; // (0x1.9e377aP+0) https://oeis.org/A001622 } // namespace numbers namespace detail { template struct TrailingZerosCounter { static unsigned count(T Val, ZeroBehavior) { if (!Val) return std::numeric_limits::digits; if (Val & 0x1) return 0; // Bisection method. unsigned ZeroBits = 0; T Shift = std::numeric_limits::digits >> 1; T Mask = std::numeric_limits::max() >> Shift; while (Shift) { if ((Val & Mask) == 0) { Val >>= Shift; ZeroBits |= Shift; } Shift >>= 1; Mask >>= Shift; } return ZeroBits; } }; #if defined(__GNUC__) || defined(_MSC_VER) template struct TrailingZerosCounter { static unsigned count(T Val, ZeroBehavior ZB) { if (ZB != ZB_Undefined && Val == 0) return 32; #if __has_builtin(__builtin_ctz) || defined(__GNUC__) return __builtin_ctz(Val); #elif defined(_MSC_VER) unsigned long Index; _BitScanForward(&Index, Val); return Index; #endif } }; #if !defined(_MSC_VER) || defined(_M_X64) template struct TrailingZerosCounter { static unsigned count(T Val, ZeroBehavior ZB) { if (ZB != ZB_Undefined && Val == 0) return 64; #if __has_builtin(__builtin_ctzll) || defined(__GNUC__) return __builtin_ctzll(Val); #elif defined(_MSC_VER) unsigned long Index; _BitScanForward64(&Index, Val); return Index; #endif } }; #endif #endif } // namespace detail /// Count number of 0's from the least significant bit to the most /// stopping at the first 1. /// /// Only unsigned integral types are allowed. /// /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are /// valid arguments. template unsigned countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) { static_assert(std::numeric_limits::is_integer && !std::numeric_limits::is_signed, "Only unsigned integral types are allowed."); return llvm::detail::TrailingZerosCounter::count(Val, ZB); } namespace detail { template struct LeadingZerosCounter { static unsigned count(T Val, ZeroBehavior) { if (!Val) return std::numeric_limits::digits; // Bisection method. unsigned ZeroBits = 0; for (T Shift = std::numeric_limits::digits >> 1; Shift; Shift >>= 1) { T Tmp = Val >> Shift; if (Tmp) Val = Tmp; else ZeroBits |= Shift; } return ZeroBits; } }; #if defined(__GNUC__) || defined(_MSC_VER) template struct LeadingZerosCounter { static unsigned count(T Val, ZeroBehavior ZB) { if (ZB != ZB_Undefined && Val == 0) return 32; #if __has_builtin(__builtin_clz) || defined(__GNUC__) return __builtin_clz(Val); #elif defined(_MSC_VER) unsigned long Index; _BitScanReverse(&Index, Val); return Index ^ 31; #endif } }; #if !defined(_MSC_VER) || defined(_M_X64) template struct LeadingZerosCounter { static unsigned count(T Val, ZeroBehavior ZB) { if (ZB != ZB_Undefined && Val == 0) return 64; #if __has_builtin(__builtin_clzll) || defined(__GNUC__) return __builtin_clzll(Val); #elif defined(_MSC_VER) unsigned long Index; _BitScanReverse64(&Index, Val); return Index ^ 63; #endif } }; #endif #endif } // namespace detail /// Count number of 0's from the most significant bit to the least /// stopping at the first 1. /// /// Only unsigned integral types are allowed. /// /// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are /// valid arguments. template unsigned countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) { static_assert(std::numeric_limits::is_integer && !std::numeric_limits::is_signed, "Only unsigned integral types are allowed."); return llvm::detail::LeadingZerosCounter::count(Val, ZB); } /// Get the index of the first set bit starting from the least /// significant bit. /// /// Only unsigned integral types are allowed. /// /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are /// valid arguments. template T findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) { if (ZB == ZB_Max && Val == 0) return std::numeric_limits::max(); return countTrailingZeros(Val, ZB_Undefined); } /// Create a bitmask with the N right-most bits set to 1, and all other /// bits set to 0. Only unsigned types are allowed. template T maskTrailingOnes(unsigned N) { static_assert(std::is_unsigned::value, "Invalid type!"); const unsigned Bits = CHAR_BIT * sizeof(T); assert(N <= Bits && "Invalid bit index"); return N == 0 ? 0 : (T(-1) >> (Bits - N)); } /// Create a bitmask with the N left-most bits set to 1, and all other /// bits set to 0. Only unsigned types are allowed. template T maskLeadingOnes(unsigned N) { return ~maskTrailingOnes(CHAR_BIT * sizeof(T) - N); } /// Create a bitmask with the N right-most bits set to 0, and all other /// bits set to 1. Only unsigned types are allowed. template T maskTrailingZeros(unsigned N) { return maskLeadingOnes(CHAR_BIT * sizeof(T) - N); } /// Create a bitmask with the N left-most bits set to 0, and all other /// bits set to 1. Only unsigned types are allowed. template T maskLeadingZeros(unsigned N) { return maskTrailingOnes(CHAR_BIT * sizeof(T) - N); } /// Get the index of the last set bit starting from the least /// significant bit. /// /// Only unsigned integral types are allowed. /// /// \param ZB the behavior on an input of 0. Only ZB_Max and ZB_Undefined are /// valid arguments. template T findLastSet(T Val, ZeroBehavior ZB = ZB_Max) { if (ZB == ZB_Max && Val == 0) return std::numeric_limits::max(); // Use ^ instead of - because both gcc and llvm can remove the associated ^ // in the __builtin_clz intrinsic on x86. return countLeadingZeros(Val, ZB_Undefined) ^ (std::numeric_limits::digits - 1); } /// Macro compressed bit reversal table for 256 bits. /// /// http://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable static const unsigned char BitReverseTable256[256] = { #define R2(n) n, n + 2 * 64, n + 1 * 64, n + 3 * 64 #define R4(n) R2(n), R2(n + 2 * 16), R2(n + 1 * 16), R2(n + 3 * 16) #define R6(n) R4(n), R4(n + 2 * 4), R4(n + 1 * 4), R4(n + 3 * 4) R6(0), R6(2), R6(1), R6(3) #undef R2 #undef R4 #undef R6 }; /// Reverse the bits in \p Val. template T reverseBits(T Val) { unsigned char in[sizeof(Val)]; unsigned char out[sizeof(Val)]; std::memcpy(in, &Val, sizeof(Val)); for (unsigned i = 0; i < sizeof(Val); ++i) out[(sizeof(Val) - i) - 1] = BitReverseTable256[in[i]]; std::memcpy(&Val, out, sizeof(Val)); return Val; } // NOTE: The following support functions use the _32/_64 extensions instead of // type overloading so that signed and unsigned integers can be used without // ambiguity. /// Return the high 32 bits of a 64 bit value. constexpr inline uint32_t Hi_32(uint64_t Value) { return static_cast(Value >> 32); } /// Return the low 32 bits of a 64 bit value. constexpr inline uint32_t Lo_32(uint64_t Value) { return static_cast(Value); } /// Make a 64-bit integer from a high / low pair of 32-bit integers. constexpr inline uint64_t Make_64(uint32_t High, uint32_t Low) { return ((uint64_t)High << 32) | (uint64_t)Low; } /// Checks if an integer fits into the given bit width. template constexpr inline bool isInt(int64_t x) { return N >= 64 || (-(INT64_C(1)<<(N-1)) <= x && x < (INT64_C(1)<<(N-1))); } // Template specializations to get better code for common cases. template <> constexpr inline bool isInt<8>(int64_t x) { return static_cast(x) == x; } template <> constexpr inline bool isInt<16>(int64_t x) { return static_cast(x) == x; } template <> constexpr inline bool isInt<32>(int64_t x) { return static_cast(x) == x; } /// Checks if a signed integer is an N bit number shifted left by S. template constexpr inline bool isShiftedInt(int64_t x) { static_assert( N > 0, "isShiftedInt<0> doesn't make sense (refers to a 0-bit number."); static_assert(N + S <= 64, "isShiftedInt with N + S > 64 is too wide."); return isInt(x) && (x % (UINT64_C(1) << S) == 0); } /// Checks if an unsigned integer fits into the given bit width. /// /// This is written as two functions rather than as simply /// /// return N >= 64 || X < (UINT64_C(1) << N); /// /// to keep MSVC from (incorrectly) warning on isUInt<64> that we're shifting /// left too many places. template constexpr inline typename std::enable_if<(N < 64), bool>::type isUInt(uint64_t X) { static_assert(N > 0, "isUInt<0> doesn't make sense"); return X < (UINT64_C(1) << (N)); } template constexpr inline typename std::enable_if= 64, bool>::type isUInt(uint64_t X) { return true; } // Template specializations to get better code for common cases. template <> constexpr inline bool isUInt<8>(uint64_t x) { return static_cast(x) == x; } template <> constexpr inline bool isUInt<16>(uint64_t x) { return static_cast(x) == x; } template <> constexpr inline bool isUInt<32>(uint64_t x) { return static_cast(x) == x; } /// Checks if a unsigned integer is an N bit number shifted left by S. template constexpr inline bool isShiftedUInt(uint64_t x) { static_assert( N > 0, "isShiftedUInt<0> doesn't make sense (refers to a 0-bit number)"); static_assert(N + S <= 64, "isShiftedUInt with N + S > 64 is too wide."); // Per the two static_asserts above, S must be strictly less than 64. So // 1 << S is not undefined behavior. return isUInt(x) && (x % (UINT64_C(1) << S) == 0); } /// Gets the maximum value for a N-bit unsigned integer. inline uint64_t maxUIntN(uint64_t N) { assert(N > 0 && N <= 64 && "integer width out of range"); // uint64_t(1) << 64 is undefined behavior, so we can't do // (uint64_t(1) << N) - 1 // without checking first that N != 64. But this works and doesn't have a // branch. return UINT64_MAX >> (64 - N); } /// Gets the minimum value for a N-bit signed integer. inline int64_t minIntN(int64_t N) { assert(N > 0 && N <= 64 && "integer width out of range"); return -(UINT64_C(1)<<(N-1)); } /// Gets the maximum value for a N-bit signed integer. inline int64_t maxIntN(int64_t N) { assert(N > 0 && N <= 64 && "integer width out of range"); // This relies on two's complement wraparound when N == 64, so we convert to // int64_t only at the very end to avoid UB. return (UINT64_C(1) << (N - 1)) - 1; } /// Checks if an unsigned integer fits into the given (dynamic) bit width. inline bool isUIntN(unsigned N, uint64_t x) { return N >= 64 || x <= maxUIntN(N); } /// Checks if an signed integer fits into the given (dynamic) bit width. inline bool isIntN(unsigned N, int64_t x) { return N >= 64 || (minIntN(N) <= x && x <= maxIntN(N)); } /// Return true if the argument is a non-empty sequence of ones starting at the /// least significant bit with the remainder zero (32 bit version). /// Ex. isMask_32(0x0000FFFFU) == true. constexpr inline bool isMask_32(uint32_t Value) { return Value && ((Value + 1) & Value) == 0; } /// Return true if the argument is a non-empty sequence of ones starting at the /// least significant bit with the remainder zero (64 bit version). constexpr inline bool isMask_64(uint64_t Value) { return Value && ((Value + 1) & Value) == 0; } /// Return true if the argument contains a non-empty sequence of ones with the /// remainder zero (32 bit version.) Ex. isShiftedMask_32(0x0000FF00U) == true. constexpr inline bool isShiftedMask_32(uint32_t Value) { return Value && isMask_32((Value - 1) | Value); } /// Return true if the argument contains a non-empty sequence of ones with the /// remainder zero (64 bit version.) constexpr inline bool isShiftedMask_64(uint64_t Value) { return Value && isMask_64((Value - 1) | Value); } /// Return true if the argument is a power of two > 0. /// Ex. isPowerOf2_32(0x00100000U) == true (32 bit edition.) constexpr inline bool isPowerOf2_32(uint32_t Value) { return Value && !(Value & (Value - 1)); } /// Return true if the argument is a power of two > 0 (64 bit edition.) constexpr inline bool isPowerOf2_64(uint64_t Value) { return Value && !(Value & (Value - 1)); } /// Return a byte-swapped representation of the 16-bit argument. inline uint16_t ByteSwap_16(uint16_t Value) { return sys::SwapByteOrder_16(Value); } /// Return a byte-swapped representation of the 32-bit argument. inline uint32_t ByteSwap_32(uint32_t Value) { return sys::SwapByteOrder_32(Value); } /// Return a byte-swapped representation of the 64-bit argument. inline uint64_t ByteSwap_64(uint64_t Value) { return sys::SwapByteOrder_64(Value); } /// Count the number of ones from the most significant bit to the first /// zero bit. /// /// Ex. countLeadingOnes(0xFF0FFF00) == 8. /// Only unsigned integral types are allowed. /// /// \param ZB the behavior on an input of all ones. Only ZB_Width and /// ZB_Undefined are valid arguments. template unsigned countLeadingOnes(T Value, ZeroBehavior ZB = ZB_Width) { static_assert(std::numeric_limits::is_integer && !std::numeric_limits::is_signed, "Only unsigned integral types are allowed."); return countLeadingZeros(~Value, ZB); } /// Count the number of ones from the least significant bit to the first /// zero bit. /// /// Ex. countTrailingOnes(0x00FF00FF) == 8. /// Only unsigned integral types are allowed. /// /// \param ZB the behavior on an input of all ones. Only ZB_Width and /// ZB_Undefined are valid arguments. template unsigned countTrailingOnes(T Value, ZeroBehavior ZB = ZB_Width) { static_assert(std::numeric_limits::is_integer && !std::numeric_limits::is_signed, "Only unsigned integral types are allowed."); return countTrailingZeros(~Value, ZB); } namespace detail { template struct PopulationCounter { static unsigned count(T Value) { // Generic version, forward to 32 bits. static_assert(SizeOfT <= 4, "Not implemented!"); #if defined(__GNUC__) return __builtin_popcount(Value); #else uint32_t v = Value; v = v - ((v >> 1) & 0x55555555); v = (v & 0x33333333) + ((v >> 2) & 0x33333333); return ((v + (v >> 4) & 0xF0F0F0F) * 0x1010101) >> 24; #endif } }; template struct PopulationCounter { static unsigned count(T Value) { #if defined(__GNUC__) return __builtin_popcountll(Value); #else uint64_t v = Value; v = v - ((v >> 1) & 0x5555555555555555ULL); v = (v & 0x3333333333333333ULL) + ((v >> 2) & 0x3333333333333333ULL); v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL; return unsigned((uint64_t)(v * 0x0101010101010101ULL) >> 56); #endif } }; } // namespace detail /// Count the number of set bits in a value. /// Ex. countPopulation(0xF000F000) = 8 /// Returns 0 if the word is zero. template inline unsigned countPopulation(T Value) { static_assert(std::numeric_limits::is_integer && !std::numeric_limits::is_signed, "Only unsigned integral types are allowed."); return detail::PopulationCounter::count(Value); } /// Compile time Log2. /// Valid only for positive powers of two. template constexpr inline size_t CTLog2() { static_assert(kValue > 0 && llvm::isPowerOf2_64(kValue), "Value is not a valid power of 2"); return 1 + CTLog2(); } template <> constexpr inline size_t CTLog2<1>() { return 0; } /// Return the log base 2 of the specified value. inline double Log2(double Value) { #if defined(__ANDROID_API__) && __ANDROID_API__ < 18 return __builtin_log(Value) / __builtin_log(2.0); #else return log2(Value); #endif } /// Return the floor log base 2 of the specified value, -1 if the value is zero. /// (32 bit edition.) /// Ex. Log2_32(32) == 5, Log2_32(1) == 0, Log2_32(0) == -1, Log2_32(6) == 2 inline unsigned Log2_32(uint32_t Value) { return 31 - countLeadingZeros(Value); } /// Return the floor log base 2 of the specified value, -1 if the value is zero. /// (64 bit edition.) inline unsigned Log2_64(uint64_t Value) { return 63 - countLeadingZeros(Value); } /// Return the ceil log base 2 of the specified value, 32 if the value is zero. /// (32 bit edition). /// Ex. Log2_32_Ceil(32) == 5, Log2_32_Ceil(1) == 0, Log2_32_Ceil(6) == 3 inline unsigned Log2_32_Ceil(uint32_t Value) { return 32 - countLeadingZeros(Value - 1); } /// Return the ceil log base 2 of the specified value, 64 if the value is zero. /// (64 bit edition.) inline unsigned Log2_64_Ceil(uint64_t Value) { return 64 - countLeadingZeros(Value - 1); } /// Return the greatest common divisor of the values using Euclid's algorithm. template inline T greatestCommonDivisor(T A, T B) { while (B) { T Tmp = B; B = A % B; A = Tmp; } return A; } inline uint64_t GreatestCommonDivisor64(uint64_t A, uint64_t B) { return greatestCommonDivisor(A, B); } /// This function takes a 64-bit integer and returns the bit equivalent double. inline double BitsToDouble(uint64_t Bits) { double D; static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes"); memcpy(&D, &Bits, sizeof(Bits)); return D; } /// This function takes a 32-bit integer and returns the bit equivalent float. inline float BitsToFloat(uint32_t Bits) { float F; static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes"); memcpy(&F, &Bits, sizeof(Bits)); return F; } /// This function takes a double and returns the bit equivalent 64-bit integer. /// Note that copying doubles around changes the bits of NaNs on some hosts, /// notably x86, so this routine cannot be used if these bits are needed. inline uint64_t DoubleToBits(double Double) { uint64_t Bits; static_assert(sizeof(uint64_t) == sizeof(double), "Unexpected type sizes"); memcpy(&Bits, &Double, sizeof(Double)); return Bits; } /// This function takes a float and returns the bit equivalent 32-bit integer. /// Note that copying floats around changes the bits of NaNs on some hosts, /// notably x86, so this routine cannot be used if these bits are needed. inline uint32_t FloatToBits(float Float) { uint32_t Bits; static_assert(sizeof(uint32_t) == sizeof(float), "Unexpected type sizes"); memcpy(&Bits, &Float, sizeof(Float)); return Bits; } /// A and B are either alignments or offsets. Return the minimum alignment that /// may be assumed after adding the two together. constexpr inline uint64_t MinAlign(uint64_t A, uint64_t B) { // The largest power of 2 that divides both A and B. // // Replace "-Value" by "1+~Value" in the following commented code to avoid // MSVC warning C4146 // return (A | B) & -(A | B); return (A | B) & (1 + ~(A | B)); } /// Returns the next power of two (in 64-bits) that is strictly greater than A. /// Returns zero on overflow. inline uint64_t NextPowerOf2(uint64_t A) { A |= (A >> 1); A |= (A >> 2); A |= (A >> 4); A |= (A >> 8); A |= (A >> 16); A |= (A >> 32); return A + 1; } /// Returns the power of two which is less than or equal to the given value. /// Essentially, it is a floor operation across the domain of powers of two. inline uint64_t PowerOf2Floor(uint64_t A) { if (!A) return 0; return 1ull << (63 - countLeadingZeros(A, ZB_Undefined)); } /// Returns the power of two which is greater than or equal to the given value. /// Essentially, it is a ceil operation across the domain of powers of two. inline uint64_t PowerOf2Ceil(uint64_t A) { if (!A) return 0; return NextPowerOf2(A - 1); } /// Returns the next integer (mod 2**64) that is greater than or equal to /// \p Value and is a multiple of \p Align. \p Align must be non-zero. /// /// If non-zero \p Skew is specified, the return value will be a minimal /// integer that is greater than or equal to \p Value and equal to /// \p Align * N + \p Skew for some integer N. If \p Skew is larger than /// \p Align, its value is adjusted to '\p Skew mod \p Align'. /// /// Examples: /// \code /// alignTo(5, 8) = 8 /// alignTo(17, 8) = 24 /// alignTo(~0LL, 8) = 0 /// alignTo(321, 255) = 510 /// /// alignTo(5, 8, 7) = 7 /// alignTo(17, 8, 1) = 17 /// alignTo(~0LL, 8, 3) = 3 /// alignTo(321, 255, 42) = 552 /// \endcode inline uint64_t alignTo(uint64_t Value, uint64_t Align, uint64_t Skew = 0) { assert(Align != 0u && "Align can't be 0."); Skew %= Align; return (Value + Align - 1 - Skew) / Align * Align + Skew; } /// Returns the next integer (mod 2**64) that is greater than or equal to /// \p Value and is a multiple of \c Align. \c Align must be non-zero. template constexpr inline uint64_t alignTo(uint64_t Value) { static_assert(Align != 0u, "Align must be non-zero"); return (Value + Align - 1) / Align * Align; } /// Returns the integer ceil(Numerator / Denominator). inline uint64_t divideCeil(uint64_t Numerator, uint64_t Denominator) { return alignTo(Numerator, Denominator) / Denominator; } /// Returns the largest uint64_t less than or equal to \p Value and is /// \p Skew mod \p Align. \p Align must be non-zero inline uint64_t alignDown(uint64_t Value, uint64_t Align, uint64_t Skew = 0) { assert(Align != 0u && "Align can't be 0."); Skew %= Align; return (Value - Skew) / Align * Align + Skew; } /// Sign-extend the number in the bottom B bits of X to a 32-bit integer. /// Requires 0 < B <= 32. template constexpr inline int32_t SignExtend32(uint32_t X) { static_assert(B > 0, "Bit width can't be 0."); static_assert(B <= 32, "Bit width out of range."); return int32_t(X << (32 - B)) >> (32 - B); } /// Sign-extend the number in the bottom B bits of X to a 32-bit integer. /// Requires 0 < B < 32. inline int32_t SignExtend32(uint32_t X, unsigned B) { assert(B > 0 && "Bit width can't be 0."); assert(B <= 32 && "Bit width out of range."); return int32_t(X << (32 - B)) >> (32 - B); } /// Sign-extend the number in the bottom B bits of X to a 64-bit integer. /// Requires 0 < B < 64. template constexpr inline int64_t SignExtend64(uint64_t x) { static_assert(B > 0, "Bit width can't be 0."); static_assert(B <= 64, "Bit width out of range."); return int64_t(x << (64 - B)) >> (64 - B); } /// Sign-extend the number in the bottom B bits of X to a 64-bit integer. /// Requires 0 < B < 64. inline int64_t SignExtend64(uint64_t X, unsigned B) { assert(B > 0 && "Bit width can't be 0."); assert(B <= 64 && "Bit width out of range."); return int64_t(X << (64 - B)) >> (64 - B); } /// Subtract two unsigned integers, X and Y, of type T and return the absolute /// value of the result. template typename std::enable_if::value, T>::type AbsoluteDifference(T X, T Y) { return std::max(X, Y) - std::min(X, Y); } /// Add two unsigned integers, X and Y, of type T. Clamp the result to the /// maximum representable value of T on overflow. ResultOverflowed indicates if /// the result is larger than the maximum representable value of type T. template typename std::enable_if::value, T>::type SaturatingAdd(T X, T Y, bool *ResultOverflowed = nullptr) { bool Dummy; bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy; // Hacker's Delight, p. 29 T Z = X + Y; Overflowed = (Z < X || Z < Y); if (Overflowed) return std::numeric_limits::max(); else return Z; } /// Multiply two unsigned integers, X and Y, of type T. Clamp the result to the /// maximum representable value of T on overflow. ResultOverflowed indicates if /// the result is larger than the maximum representable value of type T. template typename std::enable_if::value, T>::type SaturatingMultiply(T X, T Y, bool *ResultOverflowed = nullptr) { bool Dummy; bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy; // Hacker's Delight, p. 30 has a different algorithm, but we don't use that // because it fails for uint16_t (where multiplication can have undefined // behavior due to promotion to int), and requires a division in addition // to the multiplication. Overflowed = false; // Log2(Z) would be either Log2Z or Log2Z + 1. // Special case: if X or Y is 0, Log2_64 gives -1, and Log2Z // will necessarily be less than Log2Max as desired. int Log2Z = Log2_64(X) + Log2_64(Y); const T Max = std::numeric_limits::max(); int Log2Max = Log2_64(Max); if (Log2Z < Log2Max) { return X * Y; } if (Log2Z > Log2Max) { Overflowed = true; return Max; } // We're going to use the top bit, and maybe overflow one // bit past it. Multiply all but the bottom bit then add // that on at the end. T Z = (X >> 1) * Y; if (Z & ~(Max >> 1)) { Overflowed = true; return Max; } Z <<= 1; if (X & 1) return SaturatingAdd(Z, Y, ResultOverflowed); return Z; } /// Multiply two unsigned integers, X and Y, and add the unsigned integer, A to /// the product. Clamp the result to the maximum representable value of T on /// overflow. ResultOverflowed indicates if the result is larger than the /// maximum representable value of type T. template typename std::enable_if::value, T>::type SaturatingMultiplyAdd(T X, T Y, T A, bool *ResultOverflowed = nullptr) { bool Dummy; bool &Overflowed = ResultOverflowed ? *ResultOverflowed : Dummy; T Product = SaturatingMultiply(X, Y, &Overflowed); if (Overflowed) return Product; return SaturatingAdd(A, Product, &Overflowed); } /// Use this rather than HUGE_VALF; the latter causes warnings on MSVC. extern const float huge_valf; /// Add two signed integers, computing the two's complement truncated result, /// returning true if overflow occured. template typename std::enable_if::value, T>::type AddOverflow(T X, T Y, T &Result) { #if __has_builtin(__builtin_add_overflow) return __builtin_add_overflow(X, Y, &Result); #else // Perform the unsigned addition. using U = typename std::make_unsigned::type; const U UX = static_cast(X); const U UY = static_cast(Y); const U UResult = UX + UY; // Convert to signed. Result = static_cast(UResult); // Adding two positive numbers should result in a positive number. if (X > 0 && Y > 0) return Result <= 0; // Adding two negatives should result in a negative number. if (X < 0 && Y < 0) return Result >= 0; return false; #endif } /// Subtract two signed integers, computing the two's complement truncated /// result, returning true if an overflow ocurred. template typename std::enable_if::value, T>::type SubOverflow(T X, T Y, T &Result) { #if __has_builtin(__builtin_sub_overflow) return __builtin_sub_overflow(X, Y, &Result); #else // Perform the unsigned addition. using U = typename std::make_unsigned::type; const U UX = static_cast(X); const U UY = static_cast(Y); const U UResult = UX - UY; // Convert to signed. Result = static_cast(UResult); // Subtracting a positive number from a negative results in a negative number. if (X <= 0 && Y > 0) return Result >= 0; // Subtracting a negative number from a positive results in a positive number. if (X >= 0 && Y < 0) return Result <= 0; return false; #endif } /// Multiply two signed integers, computing the two's complement truncated /// result, returning true if an overflow ocurred. template typename std::enable_if::value, T>::type MulOverflow(T X, T Y, T &Result) { // Perform the unsigned multiplication on absolute values. using U = typename std::make_unsigned::type; const U UX = X < 0 ? (0 - static_cast(X)) : static_cast(X); const U UY = Y < 0 ? (0 - static_cast(Y)) : static_cast(Y); const U UResult = UX * UY; // Convert to signed. const bool IsNegative = (X < 0) ^ (Y < 0); Result = IsNegative ? (0 - UResult) : UResult; // If any of the args was 0, result is 0 and no overflow occurs. if (UX == 0 || UY == 0) return false; // UX and UY are in [1, 2^n], where n is the number of digits. // Check how the max allowed absolute value (2^n for negative, 2^(n-1) for // positive) divided by an argument compares to the other. if (IsNegative) return UX > (static_cast(std::numeric_limits::max()) + U(1)) / UY; else return UX > (static_cast(std::numeric_limits::max())) / UY; } } // End llvm namespace #endif