-
Notifications
You must be signed in to change notification settings - Fork 17.5k
/
bits.go
330 lines (280 loc) · 9.53 KB
/
bits.go
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
// Copyright 2017 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
//go:generate go run make_tables.go
// Package bits implements bit counting and manipulation
// functions for the predeclared unsigned integer types.
package bits
const uintSize = 32 << (^uint(0) >> 32 & 1) // 32 or 64
// UintSize is the size of a uint in bits.
const UintSize = uintSize
// --- LeadingZeros ---
// LeadingZeros returns the number of leading zero bits in x; the result is UintSize for x == 0.
func LeadingZeros(x uint) int { return UintSize - Len(x) }
// LeadingZeros8 returns the number of leading zero bits in x; the result is 8 for x == 0.
func LeadingZeros8(x uint8) int { return 8 - Len8(x) }
// LeadingZeros16 returns the number of leading zero bits in x; the result is 16 for x == 0.
func LeadingZeros16(x uint16) int { return 16 - Len16(x) }
// LeadingZeros32 returns the number of leading zero bits in x; the result is 32 for x == 0.
func LeadingZeros32(x uint32) int { return 32 - Len32(x) }
// LeadingZeros64 returns the number of leading zero bits in x; the result is 64 for x == 0.
func LeadingZeros64(x uint64) int { return 64 - Len64(x) }
// --- TrailingZeros ---
// See http://supertech.csail.mit.edu/papers/debruijn.pdf
const deBruijn32 = 0x077CB531
var deBruijn32tab = [32]byte{
0, 1, 28, 2, 29, 14, 24, 3, 30, 22, 20, 15, 25, 17, 4, 8,
31, 27, 13, 23, 21, 19, 16, 7, 26, 12, 18, 6, 11, 5, 10, 9,
}
const deBruijn64 = 0x03f79d71b4ca8b09
var deBruijn64tab = [64]byte{
0, 1, 56, 2, 57, 49, 28, 3, 61, 58, 42, 50, 38, 29, 17, 4,
62, 47, 59, 36, 45, 43, 51, 22, 53, 39, 33, 30, 24, 18, 12, 5,
63, 55, 48, 27, 60, 41, 37, 16, 46, 35, 44, 21, 52, 32, 23, 11,
54, 26, 40, 15, 34, 20, 31, 10, 25, 14, 19, 9, 13, 8, 7, 6,
}
// TrailingZeros returns the number of trailing zero bits in x; the result is UintSize for x == 0.
func TrailingZeros(x uint) int {
if UintSize == 32 {
return TrailingZeros32(uint32(x))
}
return TrailingZeros64(uint64(x))
}
// TrailingZeros8 returns the number of trailing zero bits in x; the result is 8 for x == 0.
func TrailingZeros8(x uint8) int {
return int(ntz8tab[x])
}
// TrailingZeros16 returns the number of trailing zero bits in x; the result is 16 for x == 0.
func TrailingZeros16(x uint16) (n int) {
if x == 0 {
return 16
}
// see comment in TrailingZeros64
return int(deBruijn32tab[uint32(x&-x)*deBruijn32>>(32-5)])
}
// TrailingZeros32 returns the number of trailing zero bits in x; the result is 32 for x == 0.
func TrailingZeros32(x uint32) int {
if x == 0 {
return 32
}
// see comment in TrailingZeros64
return int(deBruijn32tab[(x&-x)*deBruijn32>>(32-5)])
}
// TrailingZeros64 returns the number of trailing zero bits in x; the result is 64 for x == 0.
func TrailingZeros64(x uint64) int {
if x == 0 {
return 64
}
// If popcount is fast, replace code below with return popcount(^x & (x - 1)).
//
// x & -x leaves only the right-most bit set in the word. Let k be the
// index of that bit. Since only a single bit is set, the value is two
// to the power of k. Multiplying by a power of two is equivalent to
// left shifting, in this case by k bits. The de Bruijn (64 bit) constant
// is such that all six bit, consecutive substrings are distinct.
// Therefore, if we have a left shifted version of this constant we can
// find by how many bits it was shifted by looking at which six bit
// substring ended up at the top of the word.
// (Knuth, volume 4, section 7.3.1)
return int(deBruijn64tab[(x&-x)*deBruijn64>>(64-6)])
}
// --- OnesCount ---
const m0 = 0x5555555555555555 // 01010101 ...
const m1 = 0x3333333333333333 // 00110011 ...
const m2 = 0x0f0f0f0f0f0f0f0f // 00001111 ...
const m3 = 0x00ff00ff00ff00ff // etc.
const m4 = 0x0000ffff0000ffff
// OnesCount returns the number of one bits ("population count") in x.
func OnesCount(x uint) int {
if UintSize == 32 {
return OnesCount32(uint32(x))
}
return OnesCount64(uint64(x))
}
// OnesCount8 returns the number of one bits ("population count") in x.
func OnesCount8(x uint8) int {
return int(pop8tab[x])
}
// OnesCount16 returns the number of one bits ("population count") in x.
func OnesCount16(x uint16) int {
return int(pop8tab[x>>8] + pop8tab[x&0xff])
}
// OnesCount32 returns the number of one bits ("population count") in x.
func OnesCount32(x uint32) int {
return int(pop8tab[x>>24] + pop8tab[x>>16&0xff] + pop8tab[x>>8&0xff] + pop8tab[x&0xff])
}
// OnesCount64 returns the number of one bits ("population count") in x.
func OnesCount64(x uint64) int {
// Implementation: Parallel summing of adjacent bits.
// See "Hacker's Delight", Chap. 5: Counting Bits.
// The following pattern shows the general approach:
//
// x = x>>1&(m0&m) + x&(m0&m)
// x = x>>2&(m1&m) + x&(m1&m)
// x = x>>4&(m2&m) + x&(m2&m)
// x = x>>8&(m3&m) + x&(m3&m)
// x = x>>16&(m4&m) + x&(m4&m)
// x = x>>32&(m5&m) + x&(m5&m)
// return int(x)
//
// Masking (& operations) can be left away when there's no
// danger that a field's sum will carry over into the next
// field: Since the result cannot be > 64, 8 bits is enough
// and we can ignore the masks for the shifts by 8 and up.
// Per "Hacker's Delight", the first line can be simplified
// more, but it saves at best one instruction, so we leave
// it alone for clarity.
const m = 1<<64 - 1
x = x>>1&(m0&m) + x&(m0&m)
x = x>>2&(m1&m) + x&(m1&m)
x = (x>>4 + x) & (m2 & m)
x += x >> 8
x += x >> 16
x += x >> 32
return int(x) & (1<<7 - 1)
}
// --- RotateLeft ---
// RotateLeft returns the value of x rotated left by (k mod UintSize) bits.
// To rotate x right by k bits, call RotateLeft(x, -k).
func RotateLeft(x uint, k int) uint {
if UintSize == 32 {
return uint(RotateLeft32(uint32(x), k))
}
return uint(RotateLeft64(uint64(x), k))
}
// RotateLeft8 returns the value of x rotated left by (k mod 8) bits.
// To rotate x right by k bits, call RotateLeft8(x, -k).
func RotateLeft8(x uint8, k int) uint8 {
const n = 8
s := uint(k) & (n - 1)
return x<<s | x>>(n-s)
}
// RotateLeft16 returns the value of x rotated left by (k mod 16) bits.
// To rotate x right by k bits, call RotateLeft16(x, -k).
func RotateLeft16(x uint16, k int) uint16 {
const n = 16
s := uint(k) & (n - 1)
return x<<s | x>>(n-s)
}
// RotateLeft32 returns the value of x rotated left by (k mod 32) bits.
// To rotate x right by k bits, call RotateLeft32(x, -k).
func RotateLeft32(x uint32, k int) uint32 {
const n = 32
s := uint(k) & (n - 1)
return x<<s | x>>(n-s)
}
// RotateLeft64 returns the value of x rotated left by (k mod 64) bits.
// To rotate x right by k bits, call RotateLeft64(x, -k).
func RotateLeft64(x uint64, k int) uint64 {
const n = 64
s := uint(k) & (n - 1)
return x<<s | x>>(n-s)
}
// --- Reverse ---
// Reverse returns the value of x with its bits in reversed order.
func Reverse(x uint) uint {
if UintSize == 32 {
return uint(Reverse32(uint32(x)))
}
return uint(Reverse64(uint64(x)))
}
// Reverse8 returns the value of x with its bits in reversed order.
func Reverse8(x uint8) uint8 {
return rev8tab[x]
}
// Reverse16 returns the value of x with its bits in reversed order.
func Reverse16(x uint16) uint16 {
return uint16(rev8tab[x>>8]) | uint16(rev8tab[x&0xff])<<8
}
// Reverse32 returns the value of x with its bits in reversed order.
func Reverse32(x uint32) uint32 {
const m = 1<<32 - 1
x = x>>1&(m0&m) | x&(m0&m)<<1
x = x>>2&(m1&m) | x&(m1&m)<<2
x = x>>4&(m2&m) | x&(m2&m)<<4
x = x>>8&(m3&m) | x&(m3&m)<<8
return x>>16 | x<<16
}
// Reverse64 returns the value of x with its bits in reversed order.
func Reverse64(x uint64) uint64 {
const m = 1<<64 - 1
x = x>>1&(m0&m) | x&(m0&m)<<1
x = x>>2&(m1&m) | x&(m1&m)<<2
x = x>>4&(m2&m) | x&(m2&m)<<4
x = x>>8&(m3&m) | x&(m3&m)<<8
x = x>>16&(m4&m) | x&(m4&m)<<16
return x>>32 | x<<32
}
// --- ReverseBytes ---
// ReverseBytes returns the value of x with its bytes in reversed order.
func ReverseBytes(x uint) uint {
if UintSize == 32 {
return uint(ReverseBytes32(uint32(x)))
}
return uint(ReverseBytes64(uint64(x)))
}
// ReverseBytes16 returns the value of x with its bytes in reversed order.
func ReverseBytes16(x uint16) uint16 {
return x>>8 | x<<8
}
// ReverseBytes32 returns the value of x with its bytes in reversed order.
func ReverseBytes32(x uint32) uint32 {
const m = 1<<32 - 1
x = x>>8&(m3&m) | x&(m3&m)<<8
return x>>16 | x<<16
}
// ReverseBytes64 returns the value of x with its bytes in reversed order.
func ReverseBytes64(x uint64) uint64 {
const m = 1<<64 - 1
x = x>>8&(m3&m) | x&(m3&m)<<8
x = x>>16&(m4&m) | x&(m4&m)<<16
return x>>32 | x<<32
}
// --- Len ---
// Len returns the minimum number of bits required to represent x; the result is 0 for x == 0.
func Len(x uint) int {
if UintSize == 32 {
return Len32(uint32(x))
}
return Len64(uint64(x))
}
// Len8 returns the minimum number of bits required to represent x; the result is 0 for x == 0.
func Len8(x uint8) int {
return int(len8tab[x])
}
// Len16 returns the minimum number of bits required to represent x; the result is 0 for x == 0.
func Len16(x uint16) (n int) {
if x >= 1<<8 {
x >>= 8
n = 8
}
return n + int(len8tab[x])
}
// Len32 returns the minimum number of bits required to represent x; the result is 0 for x == 0.
func Len32(x uint32) (n int) {
if x >= 1<<16 {
x >>= 16
n = 16
}
if x >= 1<<8 {
x >>= 8
n += 8
}
return n + int(len8tab[x])
}
// Len64 returns the minimum number of bits required to represent x; the result is 0 for x == 0.
func Len64(x uint64) (n int) {
if x >= 1<<32 {
x >>= 32
n = 32
}
if x >= 1<<16 {
x >>= 16
n += 16
}
if x >= 1<<8 {
x >>= 8
n += 8
}
return n + int(len8tab[x])
}