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
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
|
/* Copyright (c) 2016 Vladimir Makarov <vmakarov@gcc.gnu.org>
Permission is hereby granted, free of charge, to any person
obtaining a copy of this software and associated documentation
files (the "Software"), to deal in the Software without
restriction, including without limitation the rights to use, copy,
modify, merge, publish, distribute, sublicense, and/or sell copies
of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be
included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
/* This file implements MUM (MUltiply and Mix) hashing. We randomize
input data by 64x64-bit multiplication and mixing hi- and low-parts
of the multiplication result by using an addition and then mix it
into the current state. We use prime numbers randomly generated
with the equal probability of their bit values for the
multiplication. When all primes are used once, the state is
randomized and the same prime numbers are used again for data
randomization.
The MUM hashing passes all SMHasher tests. Pseudo Random Number
Generator based on MUM also passes NIST Statistical Test Suite for
Random and Pseudorandom Number Generators for Cryptographic
Applications (version 2.2.1) with 1000 bitstreams each containing
1M bits. MUM hashing is also faster Spooky64 and City64 on small
strings (at least upto 512-bit) on Haswell and Power7. The MUM bulk
speed (speed on very long data) is bigger than Spooky and City on
Power7. On Haswell the bulk speed is bigger than Spooky one and
close to City speed. */
#ifndef __MUM_HASH__
#define __MUM_HASH__
#include <stddef.h>
#include <stdlib.h>
#include <string.h>
#include <limits.h>
#ifdef _MSC_VER
typedef unsigned __int16 uint16_t;
typedef unsigned __int32 uint32_t;
typedef unsigned __int64 uint64_t;
#else
#include <stdint.h>
#endif
/* Macro saying to use 128-bit integers implemented by GCC for some
targets. */
#ifndef _MUM_USE_INT128
/* In GCC uint128_t is defined if HOST_BITS_PER_WIDE_INT >= 64.
HOST_WIDE_INT is long if HOST_BITS_PER_LONG > HOST_BITS_PER_INT,
otherwise int. */
#ifdef __SIZEOF_INT128__
#define _MUM_USE_INT128 1
#else
#define _MUM_USE_INT128 0
#endif
#endif
#if defined(__GNUC__) && ((__GNUC__ == 4) && (__GNUC_MINOR__ >= 9) || (__GNUC__ > 4))
#define _MUM_FRESH_GCC
#endif
#if !defined(__llvm__) && defined(_MUM_FRESH_GCC)
#define _MUM_ATTRIBUTE_UNUSED __attribute__((unused))
#define _MUM_OPTIMIZE(opts) __attribute__((__optimize__ (opts)))
#define _MUM_TARGET(opts) __attribute__((__target__ (opts)))
#else
#define _MUM_ATTRIBUTE_UNUSED
#define _MUM_OPTIMIZE(opts)
#define _MUM_TARGET(opts)
#endif
/* Here are different primes randomly generated with the equal
probability of their bit values. They are used to randomize input
values. */
static uint64_t _mum_hash_step_prime = 0x2e0bb864e9ea7df5ULL;
static uint64_t _mum_key_step_prime = 0xcdb32970830fcaa1ULL;
static uint64_t _mum_block_start_prime = 0xc42b5e2e6480b23bULL;
static uint64_t _mum_unroll_prime = 0x7b51ec3d22f7096fULL;
static uint64_t _mum_tail_prime = 0xaf47d47c99b1461bULL;
static uint64_t _mum_finish_prime1 = 0xa9a7ae7ceff79f3fULL;
static uint64_t _mum_finish_prime2 = 0xaf47d47c99b1461bULL;
static uint64_t _mum_primes [] = {
0X9ebdcae10d981691, 0X32b9b9b97a27ac7d, 0X29b5584d83d35bbd, 0X4b04e0e61401255f,
0X25e8f7b1f1c9d027, 0X80d4c8c000f3e881, 0Xbd1255431904b9dd, 0X8a3bd4485eee6d81,
0X3bc721b2aad05197, 0X71b1a19b907d6e33, 0X525e6c1084a8534b, 0X9e4c2cd340c1299f,
0Xde3add92e94caa37, 0X7e14eadb1f65311d, 0X3f5aa40f89812853, 0X33b15a3b587d15c9,
};
/* Multiply 64-bit V and P and return sum of high and low parts of the
result. */
static inline uint64_t
_mum (uint64_t v, uint64_t p) {
uint64_t hi, lo;
#if _MUM_USE_INT128
#if defined(__aarch64__)
/* AARCH64 needs 2 insns to calculate 128-bit result of the
multiplication. If we use a generic code we actually call a
function doing 128x128->128 bit multiplication. The function is
very slow. */
lo = v * p, hi;
asm ("umulh %0, %1, %2" : "=r" (hi) : "r" (v), "r" (p));
#else
__uint128_t r = (__uint128_t) v * (__uint128_t) p;
hi = (uint64_t) (r >> 64);
lo = (uint64_t) r;
#endif
#else
/* Implementation of 64x64->128-bit multiplication by four 32x32->64
bit multiplication. */
uint64_t hv = v >> 32, hp = p >> 32;
uint64_t lv = (uint32_t) v, lp = (uint32_t) p;
uint64_t rh = hv * hp;
uint64_t rm_0 = hv * lp;
uint64_t rm_1 = hp * lv;
uint64_t rl = lv * lp;
uint64_t t, carry = 0;
/* We could ignore a carry bit here if we did not care about the
same hash for 32-bit and 64-bit targets. */
t = rl + (rm_0 << 32);
#ifdef MUM_TARGET_INDEPENDENT_HASH
carry = t < rl;
#endif
lo = t + (rm_1 << 32);
#ifdef MUM_TARGET_INDEPENDENT_HASH
carry += lo < t;
#endif
hi = rh + (rm_0 >> 32) + (rm_1 >> 32) + carry;
#endif
/* We could use XOR here too but, for some reasons, on Haswell and
Power7 using an addition improves hashing performance by 10% for
small strings. */
return hi + lo;
}
#if defined(_MSC_VER)
#define _mum_bswap_32(x) _byteswap_uint32_t (x)
#define _mum_bswap_64(x) _byteswap_uint64_t (x)
#elif defined(__APPLE__)
#include <libkern/OSByteOrder.h>
#define _mum_bswap_32(x) OSSwapInt32 (x)
#define _mum_bswap_64(x) OSSwapInt64 (x)
#elif defined(__GNUC__)
#define _mum_bswap32(x) __builtin_bswap32 (x)
#define _mum_bswap64(x) __builtin_bswap64 (x)
#else
#include <byteswap.h>
#define _mum_bswap32(x) bswap32 (x)
#define _mum_bswap64(x) bswap64 (x)
#endif
static inline uint64_t
_mum_le (uint64_t v) {
#if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ || !defined(MUM_TARGET_INDEPENDENT_HASH)
return v;
#elif __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__
return _mum_bswap64 (v);
#else
#error "Unknown endianess"
#endif
}
static inline uint32_t
_mum_le32 (uint32_t v) {
#if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ || !defined(MUM_TARGET_INDEPENDENT_HASH)
return v;
#elif __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__
return _mum_bswap32 (v);
#else
#error "Unknown endianess"
#endif
}
/* Macro defining how many times the most nested loop in
_mum_hash_aligned will be unrolled by the compiler (although it can
make an own decision:). Use only a constant here to help a
compiler to unroll a major loop.
The macro value affects the result hash for strings > 128 bit. The
unroll factor greatly affects the hashing speed. We prefer the
speed. */
#ifndef _MUM_UNROLL_FACTOR_POWER
#if defined(__PPC64__) && !defined(MUM_TARGET_INDEPENDENT_HASH)
#define _MUM_UNROLL_FACTOR_POWER 3
#elif defined(__aarch64__) && !defined(MUM_TARGET_INDEPENDENT_HASH)
#define _MUM_UNROLL_FACTOR_POWER 4
#else
#define _MUM_UNROLL_FACTOR_POWER 2
#endif
#endif
#if _MUM_UNROLL_FACTOR_POWER < 1
#error "too small unroll factor"
#elif _MUM_UNROLL_FACTOR_POWER > 4
#error "We have not enough primes for such unroll factor"
#endif
#define _MUM_UNROLL_FACTOR (1 << _MUM_UNROLL_FACTOR_POWER)
static inline uint64_t _MUM_OPTIMIZE("unroll-loops")
_mum_hash_aligned (uint64_t start, const void *key, size_t len) {
uint64_t result = start;
const unsigned char *str = (const unsigned char *) key;
uint64_t u64;
int i;
size_t n;
result = _mum (result, _mum_block_start_prime);
while (len > _MUM_UNROLL_FACTOR * sizeof (uint64_t)) {
/* This loop could be vectorized when we have vector insns for
64x64->128-bit multiplication. AVX2 currently only have a
vector insn for 4 32x32->64-bit multiplication. */
for (i = 0; i < _MUM_UNROLL_FACTOR; i++)
result ^= _mum (_mum_le (((uint64_t *) str)[i]), _mum_primes[i]);
len -= _MUM_UNROLL_FACTOR * sizeof (uint64_t);
str += _MUM_UNROLL_FACTOR * sizeof (uint64_t);
/* We will use the same prime numbers on the next iterations --
randomize the state. */
result = _mum (result, _mum_unroll_prime);
}
n = len / sizeof (uint64_t);
for (i = 0; i < (int)n; i++)
result ^= _mum (_mum_le (((uint64_t *) str)[i]), _mum_primes[i]);
len -= n * sizeof (uint64_t); str += n * sizeof (uint64_t);
switch (len) {
case 7:
u64 = _mum_le32 (*(uint32_t *) str);
u64 |= (uint64_t) str[4] << 32;
u64 |= (uint64_t) str[5] << 40;
u64 |= (uint64_t) str[6] << 48;
return result ^ _mum (u64, _mum_tail_prime);
case 6:
u64 = _mum_le32 (*(uint32_t *) str);
u64 |= (uint64_t) str[4] << 32;
u64 |= (uint64_t) str[5] << 40;
return result ^ _mum (u64, _mum_tail_prime);
case 5:
u64 = _mum_le32 (*(uint32_t *) str);
u64 |= (uint64_t) str[4] << 32;
return result ^ _mum (u64, _mum_tail_prime);
case 4:
u64 = _mum_le32 (*(uint32_t *) str);
return result ^ _mum (u64, _mum_tail_prime);
case 3:
u64 = str[0];
u64 |= (uint64_t) str[1] << 8;
u64 |= (uint64_t) str[2] << 16;
return result ^ _mum (u64, _mum_tail_prime);
case 2:
u64 = str[0];
u64 |= (uint64_t) str[1] << 8;
return result ^ _mum (u64, _mum_tail_prime);
case 1:
u64 = str[0];
return result ^ _mum (u64, _mum_tail_prime);
}
return result;
}
/* Final randomization of H. */
static inline uint64_t
_mum_final (uint64_t h) {
h ^= _mum (h, _mum_finish_prime1);
h ^= _mum (h, _mum_finish_prime2);
return h;
}
#if defined(__x86_64__) && defined(_MUM_FRESH_GCC)
/* We want to use AVX2 insn MULX instead of generic x86-64 MULQ where
it is possible. Although on modern Intel processors MULQ takes
3-cycles vs. 4 for MULX, MULX permits more freedom in insn
scheduling as it uses less fixed registers. */
static inline uint64_t _MUM_TARGET("arch=haswell")
_mum_hash_avx2 (const void * key, size_t len, uint64_t seed) {
return _mum_final (_mum_hash_aligned (seed + len, key, len));
}
#endif
#ifndef _MUM_UNALIGNED_ACCESS
#if defined(__x86_64__) || defined(__i386__) || defined(__PPC64__) \
|| defined(__s390__) || defined(__m32c__) || defined(cris) \
|| defined(__CR16__) || defined(__vax__) || defined(__m68k__) \
|| defined(__aarch64__)
#define _MUM_UNALIGNED_ACCESS 1
#else
#define _MUM_UNALIGNED_ACCESS 0
#endif
#endif
/* When we need an aligned access to data being hashed we move part of
the unaligned data to an aligned block of given size and then
process it, repeating processing the data by the block. */
#ifndef _MUM_BLOCK_LEN
#define _MUM_BLOCK_LEN 1024
#endif
#if _MUM_BLOCK_LEN < 8
#error "too small block length"
#endif
static inline uint64_t
#if defined(__x86_64__)
_MUM_TARGET("inline-all-stringops")
#endif
_mum_hash_default (const void *key, size_t len, uint64_t seed) {
uint64_t result;
const unsigned char *str = (const unsigned char *) key;
size_t block_len;
uint64_t buf[_MUM_BLOCK_LEN / sizeof (uint64_t)];
result = seed + len;
if (_MUM_UNALIGNED_ACCESS || ((size_t) str & 0x7) == 0)
result = _mum_hash_aligned (result, key, len);
else {
while (len != 0) {
block_len = len < _MUM_BLOCK_LEN ? len : _MUM_BLOCK_LEN;
memmove (buf, str, block_len);
result = _mum_hash_aligned (result, buf, block_len);
len -= block_len;
str += block_len;
}
}
return _mum_final (result);
}
static inline uint64_t
_mum_next_factor (void) {
uint64_t start = 0;
int i;
for (i = 0; i < 8; i++)
start = (start << 8) | rand() % 256;
return start;
}
/* ++++++++++++++++++++++++++ Interface functions: +++++++++++++++++++ */
/* Set random multiplicators depending on SEED. */
static inline void
mum_hash_randomize (uint64_t seed) {
int i;
srand (seed);
_mum_hash_step_prime = _mum_next_factor ();
_mum_key_step_prime = _mum_next_factor ();
_mum_finish_prime1 = _mum_next_factor ();
_mum_finish_prime2 = _mum_next_factor ();
_mum_block_start_prime = _mum_next_factor ();
_mum_unroll_prime = _mum_next_factor ();
_mum_tail_prime = _mum_next_factor ();
for (i = 0; i < (int)(sizeof (_mum_primes) / sizeof (uint64_t)); i++)
_mum_primes[i] = _mum_next_factor ();
}
/* Start hashing data with SEED. Return the state. */
static inline uint64_t
mum_hash_init (uint64_t seed) {
return seed;
}
/* Process data KEY with the state H and return the updated state. */
static inline uint64_t
mum_hash_step (uint64_t h, uint64_t key)
{
return _mum (h, _mum_hash_step_prime) ^ _mum (key, _mum_key_step_prime);
}
/* Return the result of hashing using the current state H. */
static inline uint64_t
mum_hash_finish (uint64_t h) {
return _mum_final (h);
}
/* Fast hashing of KEY with SEED. The hash is always the same for the
same key on any target. */
static inline size_t
mum_hash64 (uint64_t key, uint64_t seed) {
return mum_hash_finish (mum_hash_step (mum_hash_init (seed), key));
}
/* Hash data KEY of length LEN and SEED. The hash depends on the
target endianess and the unroll factor. */
static inline uint64_t
mum_hash (const void *key, size_t len, uint64_t seed) {
#if defined(__x86_64__) && defined(_MUM_FRESH_GCC)
static int avx2_support = 0;
if (avx2_support > 0)
return _mum_hash_avx2 (key, len, seed);
else if (! avx2_support) {
__builtin_cpu_init ();
avx2_support = __builtin_cpu_supports ("avx2") ? 1 : -1;
if (avx2_support > 0)
return _mum_hash_avx2 (key, len, seed);
}
#endif
return _mum_hash_default (key, len, seed);
}
#endif
|