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Diffstat (limited to 'third_party/llvm-project/include/llvm/Support/MathExtras.h')
| -rw-r--r-- | third_party/llvm-project/include/llvm/Support/MathExtras.h | 951 |
1 files changed, 951 insertions, 0 deletions
diff --git a/third_party/llvm-project/include/llvm/Support/MathExtras.h b/third_party/llvm-project/include/llvm/Support/MathExtras.h new file mode 100644 index 000000000..004a6f5f6 --- /dev/null +++ b/third_party/llvm-project/include/llvm/Support/MathExtras.h @@ -0,0 +1,951 @@ +//===-- 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 <algorithm> +#include <cassert> +#include <climits> +#include <cstring> +#include <limits> +#include <type_traits> + +#ifdef __ANDROID_NDK__ +#include <android/api-level.h> +#endif + +#ifdef _MSC_VER +// Declare these intrinsics manually rather including intrin.h. It's very +// expensive, and MathExtras.h is popular. +// #include <intrin.h> +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<T>::max() + ZB_Max, + /// The returned value is numeric_limits<T>::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 <typename T, std::size_t SizeOfT> struct TrailingZerosCounter { + static unsigned count(T Val, ZeroBehavior) { + if (!Val) + return std::numeric_limits<T>::digits; + if (Val & 0x1) + return 0; + + // Bisection method. + unsigned ZeroBits = 0; + T Shift = std::numeric_limits<T>::digits >> 1; + T Mask = std::numeric_limits<T>::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 <typename T> struct TrailingZerosCounter<T, 4> { + 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 <typename T> struct TrailingZerosCounter<T, 8> { + 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 <typename T> +unsigned countTrailingZeros(T Val, ZeroBehavior ZB = ZB_Width) { + static_assert(std::numeric_limits<T>::is_integer && + !std::numeric_limits<T>::is_signed, + "Only unsigned integral types are allowed."); + return llvm::detail::TrailingZerosCounter<T, sizeof(T)>::count(Val, ZB); +} + +namespace detail { +template <typename T, std::size_t SizeOfT> struct LeadingZerosCounter { + static unsigned count(T Val, ZeroBehavior) { + if (!Val) + return std::numeric_limits<T>::digits; + + // Bisection method. + unsigned ZeroBits = 0; + for (T Shift = std::numeric_limits<T>::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 <typename T> struct LeadingZerosCounter<T, 4> { + 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 <typename T> struct LeadingZerosCounter<T, 8> { + 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 <typename T> +unsigned countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) { + static_assert(std::numeric_limits<T>::is_integer && + !std::numeric_limits<T>::is_signed, + "Only unsigned integral types are allowed."); + return llvm::detail::LeadingZerosCounter<T, sizeof(T)>::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 <typename T> T findFirstSet(T Val, ZeroBehavior ZB = ZB_Max) { + if (ZB == ZB_Max && Val == 0) + return std::numeric_limits<T>::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 <typename T> T maskTrailingOnes(unsigned N) { + static_assert(std::is_unsigned<T>::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 <typename T> T maskLeadingOnes(unsigned N) { + return ~maskTrailingOnes<T>(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 <typename T> T maskTrailingZeros(unsigned N) { + return maskLeadingOnes<T>(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 <typename T> T maskLeadingZeros(unsigned N) { + return maskTrailingOnes<T>(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 <typename T> T findLastSet(T Val, ZeroBehavior ZB = ZB_Max) { + if (ZB == ZB_Max && Val == 0) + return std::numeric_limits<T>::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<T>::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 <typename T> +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<uint32_t>(Value >> 32); +} + +/// Return the low 32 bits of a 64 bit value. +constexpr inline uint32_t Lo_32(uint64_t Value) { + return static_cast<uint32_t>(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 <unsigned N> 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<int8_t>(x) == x; +} +template <> constexpr inline bool isInt<16>(int64_t x) { + return static_cast<int16_t>(x) == x; +} +template <> constexpr inline bool isInt<32>(int64_t x) { + return static_cast<int32_t>(x) == x; +} + +/// Checks if a signed integer is an N bit number shifted left by S. +template <unsigned N, unsigned S> +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<N, S> with N + S > 64 is too wide."); + return isInt<N + S>(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 <unsigned N> +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 <unsigned N> +constexpr inline typename std::enable_if<N >= 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<uint8_t>(x) == x; +} +template <> constexpr inline bool isUInt<16>(uint64_t x) { + return static_cast<uint16_t>(x) == x; +} +template <> constexpr inline bool isUInt<32>(uint64_t x) { + return static_cast<uint32_t>(x) == x; +} + +/// Checks if a unsigned integer is an N bit number shifted left by S. +template <unsigned N, unsigned S> +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<N, S> 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<N + S>(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 <typename T> +unsigned countLeadingOnes(T Value, ZeroBehavior ZB = ZB_Width) { + static_assert(std::numeric_limits<T>::is_integer && + !std::numeric_limits<T>::is_signed, + "Only unsigned integral types are allowed."); + return countLeadingZeros<T>(~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 <typename T> +unsigned countTrailingOnes(T Value, ZeroBehavior ZB = ZB_Width) { + static_assert(std::numeric_limits<T>::is_integer && + !std::numeric_limits<T>::is_signed, + "Only unsigned integral types are allowed."); + return countTrailingZeros<T>(~Value, ZB); +} + +namespace detail { +template <typename T, std::size_t SizeOfT> 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 <typename T> struct PopulationCounter<T, 8> { + 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 <typename T> +inline unsigned countPopulation(T Value) { + static_assert(std::numeric_limits<T>::is_integer && + !std::numeric_limits<T>::is_signed, + "Only unsigned integral types are allowed."); + return detail::PopulationCounter<T, sizeof(T)>::count(Value); +} + +/// Compile time Log2. +/// Valid only for positive powers of two. +template <size_t kValue> constexpr inline size_t CTLog2() { + static_assert(kValue > 0 && llvm::isPowerOf2_64(kValue), + "Value is not a valid power of 2"); + return 1 + CTLog2<kValue / 2>(); +} + +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 <typename T> +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<uint64_t>(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 <uint64_t Align> 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 <unsigned B> 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 <unsigned B> 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 T> +typename std::enable_if<std::is_unsigned<T>::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 T> +typename std::enable_if<std::is_unsigned<T>::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<T>::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 T> +typename std::enable_if<std::is_unsigned<T>::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<T>::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 T> +typename std::enable_if<std::is_unsigned<T>::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 T> +typename std::enable_if<std::is_signed<T>::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<T>::type; + const U UX = static_cast<U>(X); + const U UY = static_cast<U>(Y); + const U UResult = UX + UY; + + // Convert to signed. + Result = static_cast<T>(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 T> +typename std::enable_if<std::is_signed<T>::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<T>::type; + const U UX = static_cast<U>(X); + const U UY = static_cast<U>(Y); + const U UResult = UX - UY; + + // Convert to signed. + Result = static_cast<T>(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 T> +typename std::enable_if<std::is_signed<T>::value, T>::type +MulOverflow(T X, T Y, T &Result) { + // Perform the unsigned multiplication on absolute values. + using U = typename std::make_unsigned<T>::type; + const U UX = X < 0 ? (0 - static_cast<U>(X)) : static_cast<U>(X); + const U UY = Y < 0 ? (0 - static_cast<U>(Y)) : static_cast<U>(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<U>(std::numeric_limits<T>::max()) + U(1)) / UY; + else + return UX > (static_cast<U>(std::numeric_limits<T>::max())) / UY; +} + +} // End llvm namespace + +#endif |