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// Copyright 2020 The Abseil Authors // // Licensed under the Apache License, Version 2.0 (the "License"); // you may not use this file except in compliance with the License. // You may obtain a copy of the License at // // https://www.apache.org/licenses/LICENSE-2.0 // // Unless required by applicable law or agreed to in writing, software // distributed under the License is distributed on an "AS IS" BASIS, // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. // See the License for the specific language governing permissions and // limitations under the License. #ifndef ABSL_NUMERIC_INTERNAL_BITS_H_ #define ABSL_NUMERIC_INTERNAL_BITS_H_ #include #include #include // Clang on Windows has __builtin_clzll; otherwise we need to use the // windows intrinsic functions. #if defined(_MSC_VER) && !defined(__clang__) #include #endif #include "absl/base/attributes.h" #include "absl/base/config.h" #if defined(__GNUC__) && !defined(__clang__) // GCC #define ABSL_NUMERIC_INTERNAL_HAVE_BUILTIN_OR_GCC(x) 1 #else #define ABSL_NUMERIC_INTERNAL_HAVE_BUILTIN_OR_GCC(x) ABSL_HAVE_BUILTIN(x) #endif #if ABSL_NUMERIC_INTERNAL_HAVE_BUILTIN_OR_GCC(__builtin_popcountl) && \ ABSL_NUMERIC_INTERNAL_HAVE_BUILTIN_OR_GCC(__builtin_popcountll) #define ABSL_INTERNAL_CONSTEXPR_POPCOUNT constexpr #define ABSL_INTERNAL_HAS_CONSTEXPR_POPCOUNT 1 #else #define ABSL_INTERNAL_CONSTEXPR_POPCOUNT #define ABSL_INTERNAL_HAS_CONSTEXPR_POPCOUNT 0 #endif #if ABSL_NUMERIC_INTERNAL_HAVE_BUILTIN_OR_GCC(__builtin_clz) && \ ABSL_NUMERIC_INTERNAL_HAVE_BUILTIN_OR_GCC(__builtin_clzll) #define ABSL_INTERNAL_CONSTEXPR_CLZ constexpr #define ABSL_INTERNAL_HAS_CONSTEXPR_CLZ 1 #else #define ABSL_INTERNAL_CONSTEXPR_CLZ #define ABSL_INTERNAL_HAS_CONSTEXPR_CLZ 0 #endif #if ABSL_NUMERIC_INTERNAL_HAVE_BUILTIN_OR_GCC(__builtin_ctz) && \ ABSL_NUMERIC_INTERNAL_HAVE_BUILTIN_OR_GCC(__builtin_ctzll) #define ABSL_INTERNAL_CONSTEXPR_CTZ constexpr #define ABSL_INTERNAL_HAS_CONSTEXPR_CTZ 1 #else #define ABSL_INTERNAL_CONSTEXPR_CTZ #define ABSL_INTERNAL_HAS_CONSTEXPR_CTZ 0 #endif namespace absl { ABSL_NAMESPACE_BEGIN namespace numeric_internal { constexpr bool IsPowerOf2(unsigned int x) noexcept { return x != 0 && (x & (x - 1)) == 0; } template [[nodiscard]] ABSL_ATTRIBUTE_ALWAYS_INLINE constexpr T RotateRight( T x, int s) noexcept { static_assert(std::is_unsigned::value, "T must be unsigned"); static_assert(IsPowerOf2(std::numeric_limits::digits), "T must have a power-of-2 size"); // Rotate by s mod the number of digits to avoid unnecessary rotations. // // A negative s represents a left rotation instead of a right rotation. // We compute it as an equivalent complementary right rotation by leveraging // its two's complement representation. // // For example, suppose we rotate a 3-bit number by -2. // In that case: // * s = 0b11111111111111111111111111111110 // * n = 8 // * r = (0b11111111111111111111111111111110 & 0b111) = 0b110 // // Instead of rotating by 2 to the left, we rotate by 6 to the right, which // is equivalent. const int n = std::numeric_limits::digits; const int r = s & (n - 1); if (r == 0) { return x; } else { return (x >> r) | (x << (n - r)); } } template [[nodiscard]] ABSL_ATTRIBUTE_ALWAYS_INLINE constexpr T RotateLeft( T x, int s) noexcept { static_assert(std::is_unsigned::value, "T must be unsigned"); static_assert(IsPowerOf2(std::numeric_limits::digits), "T must have a power-of-2 size"); // Rotate by s mod the number of digits to avoid unnecessary rotations. // See comment in RotateRight for a detailed explanation of the logic below. const int n = std::numeric_limits::digits; const int r = s & (n - 1); if (r == 0) { return x; } else { return (x << r) | (x >> (n - r)); } } ABSL_ATTRIBUTE_ALWAYS_INLINE ABSL_INTERNAL_CONSTEXPR_POPCOUNT inline int Popcount32(uint32_t x) noexcept { #if ABSL_NUMERIC_INTERNAL_HAVE_BUILTIN_OR_GCC(__builtin_popcount) static_assert(sizeof(unsigned int) == sizeof(x), "__builtin_popcount does not take 32-bit arg"); return __builtin_popcount(x); #else x -= ((x >> 1) & 0x55555555); x = ((x >> 2) & 0x33333333) + (x & 0x33333333); return static_cast((((x + (x >> 4)) & 0xF0F0F0F) * 0x1010101) >> 24); #endif } ABSL_ATTRIBUTE_ALWAYS_INLINE ABSL_INTERNAL_CONSTEXPR_POPCOUNT inline int Popcount64(uint64_t x) noexcept { #if ABSL_NUMERIC_INTERNAL_HAVE_BUILTIN_OR_GCC(__builtin_popcountll) static_assert(sizeof(unsigned long long) == sizeof(x), // NOLINT(runtime/int) "__builtin_popcount does not take 64-bit arg"); return __builtin_popcountll(x); #else x -= (x >> 1) & 0x5555555555555555ULL; x = ((x >> 2) & 0x3333333333333333ULL) + (x & 0x3333333333333333ULL); return static_cast( (((x + (x >> 4)) & 0xF0F0F0F0F0F0F0FULL) * 0x101010101010101ULL) >> 56); #endif } template ABSL_ATTRIBUTE_ALWAYS_INLINE ABSL_INTERNAL_CONSTEXPR_POPCOUNT inline int Popcount(T x) noexcept { static_assert(std::is_unsigned::value, "T must be unsigned"); static_assert(IsPowerOf2(std::numeric_limits::digits), "T must have a power-of-2 size"); static_assert(sizeof(x) <= sizeof(uint64_t), "T is too large"); if constexpr (sizeof(x) <= sizeof(uint32_t)) { return Popcount32(x); } else { return Popcount64(x); } } ABSL_ATTRIBUTE_ALWAYS_INLINE ABSL_INTERNAL_CONSTEXPR_CLZ inline int CountLeadingZeroes32(uint32_t x) { #if ABSL_NUMERIC_INTERNAL_HAVE_BUILTIN_OR_GCC(__builtin_clz) // Use __builtin_clz, which uses the following instructions: // x86: bsr, lzcnt // ARM64: clz // PPC: cntlzd static_assert(sizeof(unsigned int) == sizeof(x), "__builtin_clz does not take 32-bit arg"); // Handle 0 as a special case because __builtin_clz(0) is undefined. return x == 0 ? 32 : __builtin_clz(x); #elif defined(_MSC_VER) && !defined(__clang__) unsigned long result = 0; // NOLINT(runtime/int) if (_BitScanReverse(&result, x)) { return 31 - result; } return 32; #else int zeroes = 28; if (x >> 16) { zeroes -= 16; x >>= 16; } if (x >> 8) { zeroes -= 8; x >>= 8; } if (x >> 4) { zeroes -= 4; x >>= 4; } return "\4\3\2\2\1\1\1\1\0\0\0\0\0\0\0"[x] + zeroes; #endif } ABSL_ATTRIBUTE_ALWAYS_INLINE ABSL_INTERNAL_CONSTEXPR_CLZ inline int CountLeadingZeroes16(uint16_t x) { #if ABSL_HAVE_BUILTIN(__builtin_clzg) return x == 0 ? 16 : __builtin_clzg(x); #elif ABSL_HAVE_BUILTIN(__builtin_clzs) static_assert(sizeof(unsigned short) == sizeof(x), // NOLINT(runtime/int) "__builtin_clzs does not take 16-bit arg"); return x == 0 ? 16 : __builtin_clzs(x); #else return CountLeadingZeroes32(x) - 16; #endif } ABSL_ATTRIBUTE_ALWAYS_INLINE ABSL_INTERNAL_CONSTEXPR_CLZ inline int CountLeadingZeroes64(uint64_t x) { #if ABSL_NUMERIC_INTERNAL_HAVE_BUILTIN_OR_GCC(__builtin_clzll) // Use __builtin_clzll, which uses the following instructions: // x86: bsr, lzcnt // ARM64: clz // PPC: cntlzd static_assert(sizeof(unsigned long long) == sizeof(x), // NOLINT(runtime/int) "__builtin_clzll does not take 64-bit arg"); // Handle 0 as a special case because __builtin_clzll(0) is undefined. return x == 0 ? 64 : __builtin_clzll(x); #elif defined(_MSC_VER) && !defined(__clang__) && \ (defined(_M_X64) || defined(_M_ARM64)) // MSVC does not have __buitin_clzll. Use _BitScanReverse64. unsigned long result = 0; // NOLINT(runtime/int) if (_BitScanReverse64(&result, x)) { return 63 - result; } return 64; #elif defined(_MSC_VER) && !defined(__clang__) // MSVC does not have __buitin_clzll. Compose two calls to _BitScanReverse unsigned long result = 0; // NOLINT(runtime/int) if ((x >> 32) && _BitScanReverse(&result, static_cast(x >> 32))) { return 31 - result; } if (_BitScanReverse(&result, static_cast(x))) { return 63 - result; } return 64; #else int zeroes = 60; if (x >> 32) { zeroes -= 32; x >>= 32; } if (x >> 16) { zeroes -= 16; x >>= 16; } if (x >> 8) { zeroes -= 8; x >>= 8; } if (x >> 4) { zeroes -= 4; x >>= 4; } return "\4\3\2\2\1\1\1\1\0\0\0\0\0\0\0"[x] + zeroes; #endif } template ABSL_ATTRIBUTE_ALWAYS_INLINE ABSL_INTERNAL_CONSTEXPR_CLZ inline int CountLeadingZeroes(T x) { static_assert(std::is_unsigned::value, "T must be unsigned"); static_assert(IsPowerOf2(std::numeric_limits::digits), "T must have a power-of-2 size"); static_assert(sizeof(T) <= sizeof(uint64_t), "T too large"); return sizeof(T) <= sizeof(uint16_t) ? CountLeadingZeroes16(static_cast(x)) - (std::numeric_limits::digits - std::numeric_limits::digits) : (sizeof(T) <= sizeof(uint32_t) ? CountLeadingZeroes32(static_cast(x)) - (std::numeric_limits::digits - std::numeric_limits::digits) : CountLeadingZeroes64(x)); } ABSL_ATTRIBUTE_ALWAYS_INLINE ABSL_INTERNAL_CONSTEXPR_CTZ inline int CountTrailingZeroesNonzero32(uint32_t x) { #if ABSL_NUMERIC_INTERNAL_HAVE_BUILTIN_OR_GCC(__builtin_ctz) static_assert(sizeof(unsigned int) == sizeof(x), "__builtin_ctz does not take 32-bit arg"); return __builtin_ctz(x); #elif defined(_MSC_VER) && !defined(__clang__) unsigned long result = 0; // NOLINT(runtime/int) _BitScanForward(&result, x); return result; #else int c = 31; x &= ~x + 1; if (x & 0x0000FFFF) c -= 16; if (x & 0x00FF00FF) c -= 8; if (x & 0x0F0F0F0F) c -= 4; if (x & 0x33333333) c -= 2; if (x & 0x55555555) c -= 1; return c; #endif } ABSL_ATTRIBUTE_ALWAYS_INLINE ABSL_INTERNAL_CONSTEXPR_CTZ inline int CountTrailingZeroesNonzero64(uint64_t x) { #if ABSL_NUMERIC_INTERNAL_HAVE_BUILTIN_OR_GCC(__builtin_ctzll) static_assert(sizeof(unsigned long long) == sizeof(x), // NOLINT(runtime/int) "__builtin_ctzll does not take 64-bit arg"); return __builtin_ctzll(x); #elif defined(_MSC_VER) && !defined(__clang__) && \ (defined(_M_X64) || defined(_M_ARM64)) unsigned long result = 0; // NOLINT(runtime/int) _BitScanForward64(&result, x); return result; #elif defined(_MSC_VER) && !defined(__clang__) unsigned long result = 0; // NOLINT(runtime/int) if (static_cast(x) == 0) { _BitScanForward(&result, static_cast(x >> 32)); return result + 32; } _BitScanForward(&result, static_cast(x)); return result; #else int c = 63; x &= ~x + 1; if (x & 0x00000000FFFFFFFF) c -= 32; if (x & 0x0000FFFF0000FFFF) c -= 16; if (x & 0x00FF00FF00FF00FF) c -= 8; if (x & 0x0F0F0F0F0F0F0F0F) c -= 4; if (x & 0x3333333333333333) c -= 2; if (x & 0x5555555555555555) c -= 1; return c; #endif } ABSL_ATTRIBUTE_ALWAYS_INLINE ABSL_INTERNAL_CONSTEXPR_CTZ inline int CountTrailingZeroesNonzero16(uint16_t x) { #if ABSL_HAVE_BUILTIN(__builtin_ctzg) return __builtin_ctzg(x); #elif ABSL_HAVE_BUILTIN(__builtin_ctzs) static_assert(sizeof(unsigned short) == sizeof(x), // NOLINT(runtime/int) "__builtin_ctzs does not take 16-bit arg"); return __builtin_ctzs(x); #else return CountTrailingZeroesNonzero32(x); #endif } template ABSL_ATTRIBUTE_ALWAYS_INLINE ABSL_INTERNAL_CONSTEXPR_CTZ inline int CountTrailingZeroes(T x) noexcept { static_assert(std::is_unsigned::value, "T must be unsigned"); static_assert(IsPowerOf2(std::numeric_limits::digits), "T must have a power-of-2 size"); static_assert(sizeof(T) <= sizeof(uint64_t), "T too large"); return x == 0 ? std::numeric_limits::digits : (sizeof(T) <= sizeof(uint16_t) ? CountTrailingZeroesNonzero16(static_cast(x)) : (sizeof(T) <= sizeof(uint32_t) ? CountTrailingZeroesNonzero32( static_cast(x)) : CountTrailingZeroesNonzero64(x))); } // If T is narrower than unsigned, T{1} << bit_width will be promoted. We // want to force it to wraparound so that bit_ceil of an invalid value are not // core constant expressions. template ABSL_ATTRIBUTE_ALWAYS_INLINE ABSL_INTERNAL_CONSTEXPR_CLZ inline typename std::enable_if::value, T>::type BitCeilPromotionHelper(T x, T promotion) { return (T{1} << (x + promotion)) >> promotion; } template ABSL_ATTRIBUTE_ALWAYS_INLINE ABSL_INTERNAL_CONSTEXPR_CLZ inline typename std::enable_if::value, T>::type BitCeilNonPowerOf2(T x) { // If T is narrower than unsigned, it undergoes promotion to unsigned when we // shift. We calculate the number of bits added by the wider type. return BitCeilPromotionHelper( static_cast(std::numeric_limits::digits - CountLeadingZeroes(x)), T{sizeof(T) >= sizeof(unsigned) ? 0 : std::numeric_limits::digits - std::numeric_limits::digits}); } } // namespace numeric_internal ABSL_NAMESPACE_END } // namespace absl #endif // ABSL_NUMERIC_INTERNAL_BITS_H_