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Source file src/math/bits/bits.go

Documentation: math/bits

     1  // Copyright 2017 The Go Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  //go:generate go run make_tables.go
     6  
     7  // Package bits implements bit counting and manipulation
     8  // functions for the predeclared unsigned integer types.
     9  package bits
    10  
    11  const uintSize = 32 << (^uint(0) >> 32 & 1) // 32 or 64
    12  
    13  // UintSize is the size of a uint in bits.
    14  const UintSize = uintSize
    15  
    16  // --- LeadingZeros ---
    17  
    18  // LeadingZeros returns the number of leading zero bits in x; the result is UintSize for x == 0.
    19  func LeadingZeros(x uint) int { return UintSize - Len(x) }
    20  
    21  // LeadingZeros8 returns the number of leading zero bits in x; the result is 8 for x == 0.
    22  func LeadingZeros8(x uint8) int { return 8 - Len8(x) }
    23  
    24  // LeadingZeros16 returns the number of leading zero bits in x; the result is 16 for x == 0.
    25  func LeadingZeros16(x uint16) int { return 16 - Len16(x) }
    26  
    27  // LeadingZeros32 returns the number of leading zero bits in x; the result is 32 for x == 0.
    28  func LeadingZeros32(x uint32) int { return 32 - Len32(x) }
    29  
    30  // LeadingZeros64 returns the number of leading zero bits in x; the result is 64 for x == 0.
    31  func LeadingZeros64(x uint64) int { return 64 - Len64(x) }
    32  
    33  // --- TrailingZeros ---
    34  
    35  // See http://supertech.csail.mit.edu/papers/debruijn.pdf
    36  const deBruijn32 = 0x077CB531
    37  
    38  var deBruijn32tab = [32]byte{
    39  	0, 1, 28, 2, 29, 14, 24, 3, 30, 22, 20, 15, 25, 17, 4, 8,
    40  	31, 27, 13, 23, 21, 19, 16, 7, 26, 12, 18, 6, 11, 5, 10, 9,
    41  }
    42  
    43  const deBruijn64 = 0x03f79d71b4ca8b09
    44  
    45  var deBruijn64tab = [64]byte{
    46  	0, 1, 56, 2, 57, 49, 28, 3, 61, 58, 42, 50, 38, 29, 17, 4,
    47  	62, 47, 59, 36, 45, 43, 51, 22, 53, 39, 33, 30, 24, 18, 12, 5,
    48  	63, 55, 48, 27, 60, 41, 37, 16, 46, 35, 44, 21, 52, 32, 23, 11,
    49  	54, 26, 40, 15, 34, 20, 31, 10, 25, 14, 19, 9, 13, 8, 7, 6,
    50  }
    51  
    52  // TrailingZeros returns the number of trailing zero bits in x; the result is UintSize for x == 0.
    53  func TrailingZeros(x uint) int {
    54  	if UintSize == 32 {
    55  		return TrailingZeros32(uint32(x))
    56  	}
    57  	return TrailingZeros64(uint64(x))
    58  }
    59  
    60  // TrailingZeros8 returns the number of trailing zero bits in x; the result is 8 for x == 0.
    61  func TrailingZeros8(x uint8) int {
    62  	return int(ntz8tab[x])
    63  }
    64  
    65  // TrailingZeros16 returns the number of trailing zero bits in x; the result is 16 for x == 0.
    66  func TrailingZeros16(x uint16) (n int) {
    67  	if x == 0 {
    68  		return 16
    69  	}
    70  	// see comment in TrailingZeros64
    71  	return int(deBruijn32tab[uint32(x&-x)*deBruijn32>>(32-5)])
    72  }
    73  
    74  // TrailingZeros32 returns the number of trailing zero bits in x; the result is 32 for x == 0.
    75  func TrailingZeros32(x uint32) int {
    76  	if x == 0 {
    77  		return 32
    78  	}
    79  	// see comment in TrailingZeros64
    80  	return int(deBruijn32tab[(x&-x)*deBruijn32>>(32-5)])
    81  }
    82  
    83  // TrailingZeros64 returns the number of trailing zero bits in x; the result is 64 for x == 0.
    84  func TrailingZeros64(x uint64) int {
    85  	if x == 0 {
    86  		return 64
    87  	}
    88  	// If popcount is fast, replace code below with return popcount(^x & (x - 1)).
    89  	//
    90  	// x & -x leaves only the right-most bit set in the word. Let k be the
    91  	// index of that bit. Since only a single bit is set, the value is two
    92  	// to the power of k. Multiplying by a power of two is equivalent to
    93  	// left shifting, in this case by k bits. The de Bruijn (64 bit) constant
    94  	// is such that all six bit, consecutive substrings are distinct.
    95  	// Therefore, if we have a left shifted version of this constant we can
    96  	// find by how many bits it was shifted by looking at which six bit
    97  	// substring ended up at the top of the word.
    98  	// (Knuth, volume 4, section 7.3.1)
    99  	return int(deBruijn64tab[(x&-x)*deBruijn64>>(64-6)])
   100  }
   101  
   102  // --- OnesCount ---
   103  
   104  const m0 = 0x5555555555555555 // 01010101 ...
   105  const m1 = 0x3333333333333333 // 00110011 ...
   106  const m2 = 0x0f0f0f0f0f0f0f0f // 00001111 ...
   107  const m3 = 0x00ff00ff00ff00ff // etc.
   108  const m4 = 0x0000ffff0000ffff
   109  
   110  // OnesCount returns the number of one bits ("population count") in x.
   111  func OnesCount(x uint) int {
   112  	if UintSize == 32 {
   113  		return OnesCount32(uint32(x))
   114  	}
   115  	return OnesCount64(uint64(x))
   116  }
   117  
   118  // OnesCount8 returns the number of one bits ("population count") in x.
   119  func OnesCount8(x uint8) int {
   120  	return int(pop8tab[x])
   121  }
   122  
   123  // OnesCount16 returns the number of one bits ("population count") in x.
   124  func OnesCount16(x uint16) int {
   125  	return int(pop8tab[x>>8] + pop8tab[x&0xff])
   126  }
   127  
   128  // OnesCount32 returns the number of one bits ("population count") in x.
   129  func OnesCount32(x uint32) int {
   130  	return int(pop8tab[x>>24] + pop8tab[x>>16&0xff] + pop8tab[x>>8&0xff] + pop8tab[x&0xff])
   131  }
   132  
   133  // OnesCount64 returns the number of one bits ("population count") in x.
   134  func OnesCount64(x uint64) int {
   135  	// Implementation: Parallel summing of adjacent bits.
   136  	// See "Hacker's Delight", Chap. 5: Counting Bits.
   137  	// The following pattern shows the general approach:
   138  	//
   139  	//   x = x>>1&(m0&m) + x&(m0&m)
   140  	//   x = x>>2&(m1&m) + x&(m1&m)
   141  	//   x = x>>4&(m2&m) + x&(m2&m)
   142  	//   x = x>>8&(m3&m) + x&(m3&m)
   143  	//   x = x>>16&(m4&m) + x&(m4&m)
   144  	//   x = x>>32&(m5&m) + x&(m5&m)
   145  	//   return int(x)
   146  	//
   147  	// Masking (& operations) can be left away when there's no
   148  	// danger that a field's sum will carry over into the next
   149  	// field: Since the result cannot be > 64, 8 bits is enough
   150  	// and we can ignore the masks for the shifts by 8 and up.
   151  	// Per "Hacker's Delight", the first line can be simplified
   152  	// more, but it saves at best one instruction, so we leave
   153  	// it alone for clarity.
   154  	const m = 1<<64 - 1
   155  	x = x>>1&(m0&m) + x&(m0&m)
   156  	x = x>>2&(m1&m) + x&(m1&m)
   157  	x = (x>>4 + x) & (m2 & m)
   158  	x += x >> 8
   159  	x += x >> 16
   160  	x += x >> 32
   161  	return int(x) & (1<<7 - 1)
   162  }
   163  
   164  // --- RotateLeft ---
   165  
   166  // RotateLeft returns the value of x rotated left by (k mod UintSize) bits.
   167  // To rotate x right by k bits, call RotateLeft(x, -k).
   168  func RotateLeft(x uint, k int) uint {
   169  	if UintSize == 32 {
   170  		return uint(RotateLeft32(uint32(x), k))
   171  	}
   172  	return uint(RotateLeft64(uint64(x), k))
   173  }
   174  
   175  // RotateLeft8 returns the value of x rotated left by (k mod 8) bits.
   176  // To rotate x right by k bits, call RotateLeft8(x, -k).
   177  func RotateLeft8(x uint8, k int) uint8 {
   178  	const n = 8
   179  	s := uint(k) & (n - 1)
   180  	return x<<s | x>>(n-s)
   181  }
   182  
   183  // RotateLeft16 returns the value of x rotated left by (k mod 16) bits.
   184  // To rotate x right by k bits, call RotateLeft16(x, -k).
   185  func RotateLeft16(x uint16, k int) uint16 {
   186  	const n = 16
   187  	s := uint(k) & (n - 1)
   188  	return x<<s | x>>(n-s)
   189  }
   190  
   191  // RotateLeft32 returns the value of x rotated left by (k mod 32) bits.
   192  // To rotate x right by k bits, call RotateLeft32(x, -k).
   193  func RotateLeft32(x uint32, k int) uint32 {
   194  	const n = 32
   195  	s := uint(k) & (n - 1)
   196  	return x<<s | x>>(n-s)
   197  }
   198  
   199  // RotateLeft64 returns the value of x rotated left by (k mod 64) bits.
   200  // To rotate x right by k bits, call RotateLeft64(x, -k).
   201  func RotateLeft64(x uint64, k int) uint64 {
   202  	const n = 64
   203  	s := uint(k) & (n - 1)
   204  	return x<<s | x>>(n-s)
   205  }
   206  
   207  // --- Reverse ---
   208  
   209  // Reverse returns the value of x with its bits in reversed order.
   210  func Reverse(x uint) uint {
   211  	if UintSize == 32 {
   212  		return uint(Reverse32(uint32(x)))
   213  	}
   214  	return uint(Reverse64(uint64(x)))
   215  }
   216  
   217  // Reverse8 returns the value of x with its bits in reversed order.
   218  func Reverse8(x uint8) uint8 {
   219  	return rev8tab[x]
   220  }
   221  
   222  // Reverse16 returns the value of x with its bits in reversed order.
   223  func Reverse16(x uint16) uint16 {
   224  	return uint16(rev8tab[x>>8]) | uint16(rev8tab[x&0xff])<<8
   225  }
   226  
   227  // Reverse32 returns the value of x with its bits in reversed order.
   228  func Reverse32(x uint32) uint32 {
   229  	const m = 1<<32 - 1
   230  	x = x>>1&(m0&m) | x&(m0&m)<<1
   231  	x = x>>2&(m1&m) | x&(m1&m)<<2
   232  	x = x>>4&(m2&m) | x&(m2&m)<<4
   233  	x = x>>8&(m3&m) | x&(m3&m)<<8
   234  	return x>>16 | x<<16
   235  }
   236  
   237  // Reverse64 returns the value of x with its bits in reversed order.
   238  func Reverse64(x uint64) uint64 {
   239  	const m = 1<<64 - 1
   240  	x = x>>1&(m0&m) | x&(m0&m)<<1
   241  	x = x>>2&(m1&m) | x&(m1&m)<<2
   242  	x = x>>4&(m2&m) | x&(m2&m)<<4
   243  	x = x>>8&(m3&m) | x&(m3&m)<<8
   244  	x = x>>16&(m4&m) | x&(m4&m)<<16
   245  	return x>>32 | x<<32
   246  }
   247  
   248  // --- ReverseBytes ---
   249  
   250  // ReverseBytes returns the value of x with its bytes in reversed order.
   251  func ReverseBytes(x uint) uint {
   252  	if UintSize == 32 {
   253  		return uint(ReverseBytes32(uint32(x)))
   254  	}
   255  	return uint(ReverseBytes64(uint64(x)))
   256  }
   257  
   258  // ReverseBytes16 returns the value of x with its bytes in reversed order.
   259  func ReverseBytes16(x uint16) uint16 {
   260  	return x>>8 | x<<8
   261  }
   262  
   263  // ReverseBytes32 returns the value of x with its bytes in reversed order.
   264  func ReverseBytes32(x uint32) uint32 {
   265  	const m = 1<<32 - 1
   266  	x = x>>8&(m3&m) | x&(m3&m)<<8
   267  	return x>>16 | x<<16
   268  }
   269  
   270  // ReverseBytes64 returns the value of x with its bytes in reversed order.
   271  func ReverseBytes64(x uint64) uint64 {
   272  	const m = 1<<64 - 1
   273  	x = x>>8&(m3&m) | x&(m3&m)<<8
   274  	x = x>>16&(m4&m) | x&(m4&m)<<16
   275  	return x>>32 | x<<32
   276  }
   277  
   278  // --- Len ---
   279  
   280  // Len returns the minimum number of bits required to represent x; the result is 0 for x == 0.
   281  func Len(x uint) int {
   282  	if UintSize == 32 {
   283  		return Len32(uint32(x))
   284  	}
   285  	return Len64(uint64(x))
   286  }
   287  
   288  // Len8 returns the minimum number of bits required to represent x; the result is 0 for x == 0.
   289  func Len8(x uint8) int {
   290  	return int(len8tab[x])
   291  }
   292  
   293  // Len16 returns the minimum number of bits required to represent x; the result is 0 for x == 0.
   294  func Len16(x uint16) (n int) {
   295  	if x >= 1<<8 {
   296  		x >>= 8
   297  		n = 8
   298  	}
   299  	return n + int(len8tab[x])
   300  }
   301  
   302  // Len32 returns the minimum number of bits required to represent x; the result is 0 for x == 0.
   303  func Len32(x uint32) (n int) {
   304  	if x >= 1<<16 {
   305  		x >>= 16
   306  		n = 16
   307  	}
   308  	if x >= 1<<8 {
   309  		x >>= 8
   310  		n += 8
   311  	}
   312  	return n + int(len8tab[x])
   313  }
   314  
   315  // Len64 returns the minimum number of bits required to represent x; the result is 0 for x == 0.
   316  func Len64(x uint64) (n int) {
   317  	if x >= 1<<32 {
   318  		x >>= 32
   319  		n = 32
   320  	}
   321  	if x >= 1<<16 {
   322  		x >>= 16
   323  		n += 16
   324  	}
   325  	if x >= 1<<8 {
   326  		x >>= 8
   327  		n += 8
   328  	}
   329  	return n + int(len8tab[x])
   330  }
   331  

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