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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
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
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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