// Copyright 2002 and onwards Google Inc. // // A collection of useful (static) bit-twiddling functions. #pragma once #include "gutil/integral_types.h" // IWYU pragma: no_include #include "gutil/macros.h" // IWYU pragma: keep class Bits { public: // Return the number of one bits in the given integer. static int CountOnesInByte(unsigned char n); static int CountOnes(uint32 n) { n -= ((n >> 1) & 0x55555555); n = ((n >> 2) & 0x33333333) + (n & 0x33333333); return (((n + (n >> 4)) & 0xF0F0F0F) * 0x1010101) >> 24; } // Count bits using sideways addition [WWG'57]. See Knuth TAOCP v4 7.1.3(59) static inline int CountOnes64(uint64 n) { #if defined(__x86_64__) n -= (n >> 1) & 0x5555555555555555ULL; n = ((n >> 2) & 0x3333333333333333ULL) + (n & 0x3333333333333333ULL); return (((n + (n >> 4)) & 0xF0F0F0F0F0F0F0FULL) * 0x101010101010101ULL) >> 56; #else return CountOnes(n >> 32) + CountOnes(n & 0xffffffff); #endif } // Count bits using popcnt instruction (available on argo machines). // Doesn't check if the instruction exists. // Please use TestCPUFeature(POPCNT) from base/cpuid/cpuid.h before using this. static inline int CountOnes64withPopcount(uint64 n) { #if defined(__x86_64__) && defined __GNUC__ int64 count = 0; asm("popcnt %1,%0" : "=r"(count) : "rm"(n) : "cc"); return count; #else return CountOnes64(n); #endif } // Reverse the bits in the given integer. static uint8 ReverseBits8(uint8 n); static uint32 ReverseBits32(uint32 n); static uint64 ReverseBits64(uint64 n); // Return the number of one bits in the byte sequence. static int Count(const void* m, int num_bytes); // Return the number of different bits in the given byte sequences. // (i.e., the Hamming distance) static int Difference(const void* m1, const void* m2, int num_bytes); // Return the number of different bits in the given byte sequences, // up to a maximum. Values larger than the maximum may be returned // (because multiple bits are checked at a time), but the function // may exit early if the cap is exceeded. static int CappedDifference(const void* m1, const void* m2, int num_bytes, int cap); // Return floor(log2(n)) for positive integer n. Returns -1 iff n == 0. static int Log2Floor(uint32 n); static int Log2Floor64(uint64 n); // Potentially faster version of Log2Floor() that returns an // undefined value if n == 0 static int Log2FloorNonZero(uint32 n); static int Log2FloorNonZero64(uint64 n); // Return ceiling(log2(n)) for positive integer n. Returns -1 iff n == 0. static int Log2Ceiling(uint32 n); static int Log2Ceiling64(uint64 n); // Return the first set least / most significant bit, 0-indexed. Returns an // undefined value if n == 0. FindLSBSetNonZero() is similar to ffs() except // that it's 0-indexed, while FindMSBSetNonZero() is the same as // Log2FloorNonZero(). static int FindLSBSetNonZero(uint32 n); static int FindLSBSetNonZero64(uint64 n); static int FindMSBSetNonZero(uint32 n) { return Log2FloorNonZero(n); } static int FindMSBSetNonZero64(uint64 n) { return Log2FloorNonZero64(n); } // Portable implementations static int Log2Floor_Portable(uint32 n); static int Log2FloorNonZero_Portable(uint32 n); static int FindLSBSetNonZero_Portable(uint32 n); static int Log2Floor64_Portable(uint64 n); static int Log2FloorNonZero64_Portable(uint64 n); static int FindLSBSetNonZero64_Portable(uint64 n); // Viewing bytes as a stream of unsigned bytes, does that stream // contain any byte equal to c? template static bool BytesContainByte(T bytes, uint8 c); // Viewing bytes as a stream of unsigned bytes, does that stream // contain any byte b < c? template static bool BytesContainByteLessThan(T bytes, uint8 c); // Viewing bytes as a stream of unsigned bytes, are all elements of that // stream in [lo, hi]? template static bool BytesAllInRange(T bytes, uint8 lo, uint8 hi); private: static const char num_bits[]; static const unsigned char bit_reverse_table[]; DISALLOW_COPY_AND_ASSIGN(Bits); }; // A utility class for some handy bit patterns. The names l and h // were chosen to match Knuth Volume 4: l is 0x010101... and h is 0x808080...; // half_ones is ones in the lower half only. We assume sizeof(T) is 1 or even. template struct BitPattern { static const T half_ones = (static_cast(1) << (sizeof(T) * 4)) - 1; static const T l = (sizeof(T) == 1) ? 1 : (half_ones / 0xff * (half_ones + 2)); static const T h = ~(l * 0x7f); }; // ------------------------------------------------------------------------ // Implementation details follow // ------------------------------------------------------------------------ // use GNU builtins where available #if defined(__GNUC__) && ((__GNUC__ == 3 && __GNUC_MINOR__ >= 4) || __GNUC__ >= 4) inline int Bits::Log2Floor(uint32 n) { return n == 0 ? -1 : 31 ^ __builtin_clz(n); } inline int Bits::Log2FloorNonZero(uint32 n) { return 31 ^ __builtin_clz(n); } inline int Bits::FindLSBSetNonZero(uint32 n) { return __builtin_ctz(n); } inline int Bits::Log2Floor64(uint64 n) { return n == 0 ? -1 : 63 ^ __builtin_clzll(n); } inline int Bits::Log2FloorNonZero64(uint64 n) { return 63 ^ __builtin_clzll(n); } inline int Bits::FindLSBSetNonZero64(uint64 n) { return __builtin_ctzll(n); } #elif defined(_MSC_VER) #include "gutil/bits-internal-windows.h" #else #include "gutil/bits-internal-unknown.h" #endif inline int Bits::CountOnesInByte(unsigned char n) { return num_bits[n]; } inline uint8 Bits::ReverseBits8(unsigned char n) { n = ((n >> 1) & 0x55) | ((n & 0x55) << 1); n = ((n >> 2) & 0x33) | ((n & 0x33) << 2); return ((n >> 4) & 0x0f) | ((n & 0x0f) << 4); } inline uint32 Bits::ReverseBits32(uint32 n) { n = ((n >> 1) & 0x55555555) | ((n & 0x55555555) << 1); n = ((n >> 2) & 0x33333333) | ((n & 0x33333333) << 2); n = ((n >> 4) & 0x0F0F0F0F) | ((n & 0x0F0F0F0F) << 4); n = ((n >> 8) & 0x00FF00FF) | ((n & 0x00FF00FF) << 8); return (n >> 16) | (n << 16); } inline uint64 Bits::ReverseBits64(uint64 n) { #if defined(__x86_64__) n = ((n >> 1) & 0x5555555555555555ULL) | ((n & 0x5555555555555555ULL) << 1); n = ((n >> 2) & 0x3333333333333333ULL) | ((n & 0x3333333333333333ULL) << 2); n = ((n >> 4) & 0x0F0F0F0F0F0F0F0FULL) | ((n & 0x0F0F0F0F0F0F0F0FULL) << 4); n = ((n >> 8) & 0x00FF00FF00FF00FFULL) | ((n & 0x00FF00FF00FF00FFULL) << 8); n = ((n >> 16) & 0x0000FFFF0000FFFFULL) | ((n & 0x0000FFFF0000FFFFULL) << 16); return (n >> 32) | (n << 32); #else return ReverseBits32(n >> 32) | (static_cast(ReverseBits32(n & 0xffffffff)) << 32); #endif } inline int Bits::Log2FloorNonZero_Portable(uint32 n) { // Just use the common routine return Log2Floor(n); } // Log2Floor64() is defined in terms of Log2Floor32(), Log2FloorNonZero32() inline int Bits::Log2Floor64_Portable(uint64 n) { const uint32 topbits = static_cast(n >> 32); if (topbits == 0) { // Top bits are zero, so scan in bottom bits return Log2Floor(static_cast(n)); } else { return 32 + Log2FloorNonZero(topbits); } } // Log2FloorNonZero64() is defined in terms of Log2FloorNonZero32() inline int Bits::Log2FloorNonZero64_Portable(uint64 n) { const uint32 topbits = static_cast(n >> 32); if (topbits == 0) { // Top bits are zero, so scan in bottom bits return Log2FloorNonZero(static_cast(n)); } else { return 32 + Log2FloorNonZero(topbits); } } // FindLSBSetNonZero64() is defined in terms of FindLSBSetNonZero() inline int Bits::FindLSBSetNonZero64_Portable(uint64 n) { const uint32 bottombits = static_cast(n); if (bottombits == 0) { // Bottom bits are zero, so scan in top bits return 32 + FindLSBSetNonZero(static_cast(n >> 32)); } else { return FindLSBSetNonZero(bottombits); } } template bool Bits::BytesContainByteLessThan(T bytes, uint8 c) { T l = BitPattern::l; T h = BitPattern::h; // The c <= 0x80 code is straight out of Knuth Volume 4. // Usually c will be manifestly constant. return c <= 0x80 ? ((h & (bytes - l * c) & ~bytes) != 0) : ((((bytes - l * c) | (bytes ^ h)) & h) != 0); } template bool Bits::BytesContainByte(T bytes, uint8 c) { // Usually c will be manifestly constant. return Bits::BytesContainByteLessThan(bytes ^ (c * BitPattern::l), 1); } template bool Bits::BytesAllInRange(T bytes, uint8 lo, uint8 hi) { T l = BitPattern::l; T h = BitPattern::h; // In the common case, lo and hi are manifest constants. if (lo > hi) { return false; } if (hi - lo < 128) { T x = bytes - l * lo; T y = bytes + l * (127 - hi); return ((x | y) & h) == 0; } return !Bits::BytesContainByteLessThan(bytes + (255 - hi) * l, lo + (255 - hi)); }