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utils.cpp
1
2 /**
3 * Copyright (c) 2015-present, Facebook, Inc.
4 * All rights reserved.
5 *
6 * This source code is licensed under the CC-by-NC license found in the
7 * LICENSE file in the root directory of this source tree.
8 */
9
10 // Copyright 2004-present Facebook. All Rights Reserved
11 // -*- c++ -*-
12
13 #include "utils.h"
14
15 #include <cstdio>
16 #include <cassert>
17 #include <cstring>
18 #include <cmath>
19
20 #include <smmintrin.h>
21 #include <mmintrin.h>
22
23 #include <sys/time.h>
24 #include <sys/types.h>
25 #include <unistd.h>
26
27 #include <omp.h>
28
29
30 #include <algorithm>
31 #include <vector>
32
33 #include "AuxIndexStructures.h"
34 #include "FaissAssert.h"
35
36
37
38 #ifndef FINTEGER
39 #define FINTEGER long
40 #endif
41
42
43 extern "C" {
44
45 /* declare BLAS functions, see http://www.netlib.org/clapack/cblas/ */
46
47 int sgemm_ (const char *transa, const char *transb, FINTEGER *m, FINTEGER *
48 n, FINTEGER *k, const float *alpha, const float *a,
49 FINTEGER *lda, const float *b, FINTEGER *
50 ldb, float *beta, float *c, FINTEGER *ldc);
51
52 /* Lapack functions, see http://www.netlib.org/clapack/old/single/sgeqrf.c */
53
54 int sgeqrf_ (FINTEGER *m, FINTEGER *n, float *a, FINTEGER *lda,
55 float *tau, float *work, FINTEGER *lwork, FINTEGER *info);
56
57 int sorgqr_(FINTEGER *m, FINTEGER *n, FINTEGER *k, float *a,
58 FINTEGER *lda, float *tau, float *work,
59 FINTEGER *lwork, FINTEGER *info);
60
61
62 }
63
64
65 /**************************************************
66 * Get some stats about the system
67 **************************************************/
68
69 namespace faiss {
70
71 double getmillisecs () {
72 struct timeval tv;
73 gettimeofday (&tv, nullptr);
74 return tv.tv_sec * 1e3 + tv.tv_usec * 1e-3;
75 }
76
77
78 #ifdef __linux__
79
80 size_t get_mem_usage_kb ()
81 {
82 int pid = getpid ();
83 char fname[256];
84 snprintf (fname, 256, "/proc/%d/status", pid);
85 FILE * f = fopen (fname, "r");
86 FAISS_ASSERT (f || !"cannot open proc status file") ;
87 size_t sz = 0;
88 for (;;) {
89 char buf [256];
90 if (!fgets (buf, 256, f)) break;
91 if (sscanf (buf, "VmRSS: %ld kB", &sz) == 1) break;
92 }
93 fclose (f);
94 return sz;
95 }
96
97 #elif __APPLE__
98
99 size_t get_mem_usage_kb ()
100 {
101 fprintf(stderr, "WARN: get_mem_usage_kb not implemented on the mac\n");
102 return 0;
103 }
104
105 #endif
106
107
108
109 /**************************************************
110 * Random data generation functions
111 **************************************************/
112
113 /**
114 * The definition of random functions depends on the architecture:
115 *
116 * - for Linux, we rely on re-entrant functions (random_r). This
117 * provides good quality reproducible random sequences.
118 *
119 * - for Apple, we use rand_r. Apple is trying so hard to deprecate
120 * this function that it removed its definition form stdlib.h, so we
121 * re-declare it below. Fortunately, since it is deprecated, its
122 * prototype should not change much in the forerseeable future.
123 *
124 * Unfortunately, system designers are more concerned with making the
125 * most unpredictable random sequences for cryptographic use, when in
126 * scientific contexts what acutally matters is having reproducible
127 * squences in multi-threaded contexts.
128 */
129
130
131 #ifdef __linux__
132
133
134
135
136 int RandomGenerator::rand_int ()
137 {
138 int32_t a;
139 random_r (&rand_data, &a);
140 return a;
141 }
142
143 long RandomGenerator::rand_long ()
144 {
145 int32_t a, b;
146 random_r (&rand_data, &a);
147 random_r (&rand_data, &b);
148 return long(a) | long(b) << 31;
149 }
150
151
152 RandomGenerator::RandomGenerator (long seed)
153 {
154 memset (&rand_data, 0, sizeof (rand_data));
155 initstate_r (seed, rand_state, sizeof (rand_state), &rand_data);
156 }
157
158
159 RandomGenerator::RandomGenerator (const RandomGenerator & other)
160 {
161 memcpy (rand_state, other.rand_state, sizeof(rand_state));
162 rand_data = other.rand_data;
163 setstate_r (rand_state, &rand_data);
164 }
165
166
167 #elif __APPLE__
168
169 extern "C" {
170 int rand_r(unsigned *seed);
171 }
172
173 RandomGenerator::RandomGenerator (long seed)
174 {
175 rand_state = seed;
176 }
177
178
179 RandomGenerator::RandomGenerator (const RandomGenerator & other)
180 {
181 rand_state = other.rand_state;
182 }
183
184
185 int RandomGenerator::rand_int ()
186 {
187 // RAND_MAX is 31 bits
188 // try to add more randomness in the lower bits
189 int lowbits = rand_r(&rand_state) >> 15;
190 return rand_r(&rand_state) ^ lowbits;
191 }
192
193 long RandomGenerator::rand_long ()
194 {
195 return long(random()) | long(random()) << 31;
196 }
197
198
199
200 #endif
201
202 int RandomGenerator::rand_int (int max)
203 { // this suffers form non-uniform probabilities when max is not a
204 // power of 2, but if RAND_MAX >> max the bias is limited.
205 return rand_int () % max;
206 }
207
208 float RandomGenerator::rand_float ()
209 {
210 return rand_int() / float(1L << 31);
211 }
212
213 double RandomGenerator::rand_double ()
214 {
215 return rand_long() / double(1L << 62);
216 }
217
218
219 /***********************************************************************
220 * Random functions in this C file only exist because Torch
221 * counterparts are slow and not multi-threaded. Typical use is for
222 * more than 1-100 billion values. */
223
224
225 /* Generate a set of random floating point values such that x[i] in [0,1]
226 multi-threading. For this reason, we rely on re-entreant functions. */
227 void float_rand (float * x, size_t n, long seed)
228 {
229 // only try to parallelize on large enough arrays
230 const size_t nblock = n < 1024 ? 1 : 1024;
231
232 RandomGenerator rng0 (seed);
233 int a0 = rng0.rand_int (), b0 = rng0.rand_int ();
234
235 #pragma omp parallel for
236 for (size_t j = 0; j < nblock; j++) {
237
238 RandomGenerator rng (a0 + j * b0);
239
240 const size_t istart = j * n / nblock;
241 const size_t iend = (j + 1) * n / nblock;
242
243 for (size_t i = istart; i < iend; i++)
244 x[i] = rng.rand_float ();
245 }
246 }
247
248
249 void float_randn (float * x, size_t n, long seed)
250 {
251 // only try to parallelize on large enough arrays
252 const size_t nblock = n < 1024 ? 1 : 1024;
253
254 RandomGenerator rng0 (seed);
255 int a0 = rng0.rand_int (), b0 = rng0.rand_int ();
256
257 #pragma omp parallel for
258 for (size_t j = 0; j < nblock; j++) {
259 RandomGenerator rng (a0 + j * b0);
260
261 double a = 0, b = 0, s = 0;
262 int state = 0; /* generate two number per "do-while" loop */
263
264 const size_t istart = j * n / nblock;
265 const size_t iend = (j + 1) * n / nblock;
266
267 for (size_t i = istart; i < iend; i++) {
268 /* Marsaglia's method (see Knuth) */
269 if (state == 0) {
270 do {
271 a = 2.0 * rng.rand_double () - 1;
272 b = 2.0 * rng.rand_double () - 1;
273 s = a * a + b * b;
274 } while (s >= 1.0);
275 x[i] = a * sqrt(-2.0 * log(s) / s);
276 }
277 else
278 x[i] = b * sqrt(-2.0 * log(s) / s);
279 state = 1 - state;
280 }
281 }
282 }
283
284
285 /* Integer versions */
286 void long_rand (long * x, size_t n, long seed)
287 {
288 // only try to parallelize on large enough arrays
289 const size_t nblock = n < 1024 ? 1 : 1024;
290
291 RandomGenerator rng0 (seed);
292 int a0 = rng0.rand_int (), b0 = rng0.rand_int ();
293
294 #pragma omp parallel for
295 for (size_t j = 0; j < nblock; j++) {
296
297 RandomGenerator rng (a0 + j * b0);
298
299 const size_t istart = j * n / nblock;
300 const size_t iend = (j + 1) * n / nblock;
301 for (size_t i = istart; i < iend; i++)
302 x[i] = rng.rand_long ();
303 }
304 }
305
306
307
308 void rand_perm (int *perm, size_t n, long seed)
309 {
310 for (size_t i = 0; i < n; i++) perm[i] = i;
311
312 RandomGenerator rng (seed);
313
314 for (size_t i = 0; i + 1 < n; i++) {
315 int i2 = i + rng.rand_int (n - i);
316 std::swap(perm[i], perm[i2]);
317 }
318 }
319
320
321
322
323 void byte_rand (uint8_t * x, size_t n, long seed)
324 {
325 // only try to parallelize on large enough arrays
326 const size_t nblock = n < 1024 ? 1 : 1024;
327
328 RandomGenerator rng0 (seed);
329 int a0 = rng0.rand_int (), b0 = rng0.rand_int ();
330
331 #pragma omp parallel for
332 for (size_t j = 0; j < nblock; j++) {
333
334 RandomGenerator rng (a0 + j * b0);
335
336 const size_t istart = j * n / nblock;
337 const size_t iend = (j + 1) * n / nblock;
338
339 size_t i;
340 for (i = istart; i < iend; i++)
341 x[i] = rng.rand_long ();
342 }
343 }
344
345
346
347 void reflection (const float * __restrict u,
348 float * __restrict x,
349 size_t n, size_t d, size_t nu)
350 {
351 size_t i, j, l;
352 for (i = 0; i < n; i++) {
353 const float * up = u;
354 for (l = 0; l < nu; l++) {
355 float ip1 = 0, ip2 = 0;
356
357 for (j = 0; j < d; j+=2) {
358 ip1 += up[j] * x[j];
359 ip2 += up[j+1] * x[j+1];
360 }
361 float ip = 2 * (ip1 + ip2);
362
363 for (j = 0; j < d; j++)
364 x[j] -= ip * up[j];
365 up += d;
366 }
367 x += d;
368 }
369 }
370
371
372 /* Reference implementation (slower) */
373 void reflection_ref (const float * u, float * x, size_t n, size_t d, size_t nu)
374 {
375 size_t i, j, l;
376 for (i = 0; i < n; i++) {
377 const float * up = u;
378 for (l = 0; l < nu; l++) {
379 double ip = 0;
380
381 for (j = 0; j < d; j++)
382 ip += up[j] * x[j];
383 ip *= 2;
384
385 for (j = 0; j < d; j++)
386 x[j] -= ip * up[j];
387
388 up += d;
389 }
390 x += d;
391 }
392 }
393
394 /*********************************************************
395 * Optimized distance computations
396 *********************************************************/
397
398
399
400 /* Functions to compute:
401 - L2 distance between 2 vectors
402 - inner product between 2 vectors
403 - L2 norm of a vector
404
405 The functions should probably not be invoked when a large number of
406 vectors are be processed in batch (in which case Matrix multiply
407 is faster), but may be useful for comparing vectors isolated in
408 memory.
409
410 Works with any vectors of any dimension, even unaligned (in which
411 case they are slower).
412
413 */
414
415
416 // set some of the floats in x to 0 so that there are d floats remaining
417 // 0 <= d <= 4
418 static inline __m128 maskout (int d, __m128 x)
419 {
420 // check which values to clear out
421 __m128i d4 = _mm_set1_epi32 (d);
422 __m128i lim = _mm_set_epi32 (3, 2, 1, 0);
423 __m128i mask = _mm_cmpgt_epi32 (d4, lim);
424
425 return _mm_and_ps (x, (__m128)mask);
426 }
427
428
429 /* SSE-implementation of L2 distance */
430 float fvec_L2sqr (const float * x,
431 const float * y,
432 size_t d)
433 {
434 __m128 mx, my;
435 __m128 msum1 = _mm_setzero_ps();
436
437 while (d > 4) {
438 mx = _mm_loadu_ps (x); x += 4;
439 my = _mm_loadu_ps (y); y += 4;
440 const __m128 a_m_b1 = _mm_sub_ps (mx, my);
441 msum1 = _mm_add_ps (msum1, _mm_mul_ps (a_m_b1, a_m_b1));
442 d -= 4;
443 }
444
445 // add the last 1, 2, 3, or 4 values
446 mx = _mm_loadu_ps (x);
447 my = _mm_loadu_ps (y);
448 __m128 a_m_b1 = maskout (d, _mm_sub_ps (mx, my));
449
450 msum1 = _mm_add_ps (msum1, _mm_mul_ps (a_m_b1, a_m_b1));
451
452 msum1 = _mm_hadd_ps (msum1, msum1);
453 msum1 = _mm_hadd_ps (msum1, msum1);
454 return _mm_cvtss_f32 (msum1);
455 }
456
457
458 /* same without SSE */
459 float fvec_L2sqr_ref (const float * x,
460 const float * y,
461 size_t d)
462 {
463 size_t i;
464 float res_ = 0;
465 for (i = 0; i < d; i++) {
466 const float tmp = x[i] - y[i];
467 res_ += tmp * tmp;
468 }
469 return res_;
470 }
471
472 float fvec_inner_product (const float * x,
473 const float * y,
474 size_t d)
475 {
476 __m128 mx, my;
477 __m128 msum1 = _mm_setzero_ps();
478
479 while (d > 4) {
480 mx = _mm_loadu_ps (x); x += 4;
481 my = _mm_loadu_ps (y); y += 4;
482 msum1 = _mm_add_ps (msum1, _mm_mul_ps (mx, my));
483 d -= 4;
484 }
485
486 // add the last 1, 2, 3, or 4 values
487 mx = _mm_loadu_ps (x);
488 my = _mm_loadu_ps (y);
489 __m128 prod = maskout (d, _mm_mul_ps (mx, my));
490
491 msum1 = _mm_add_ps (msum1, prod);
492
493 msum1 = _mm_hadd_ps (msum1, msum1);
494 msum1 = _mm_hadd_ps (msum1, msum1);
495 return _mm_cvtss_f32 (msum1);
496 }
497
498
499 float fvec_inner_product_ref (const float * x,
500 const float * y,
501 size_t d)
502 {
503 size_t i;
504 float res_ = 0;
505 for (i = 0; i < d; i++)
506 res_ += x[i] * y[i];
507 return res_;
508 }
509
510
511 float fvec_norm_L2sqr (const float * x,
512 size_t d)
513 {
514 __m128 mx;
515 __m128 msum1 = _mm_setzero_ps();
516
517 while (d > 4) {
518 mx = _mm_loadu_ps (x); x += 4;
519 msum1 = _mm_add_ps (msum1, _mm_mul_ps (mx, mx));
520 d -= 4;
521 }
522
523 mx = maskout (d, _mm_loadu_ps (x));
524 msum1 = _mm_add_ps (msum1, _mm_mul_ps (mx, mx));
525
526 msum1 = _mm_hadd_ps (msum1, msum1);
527 msum1 = _mm_hadd_ps (msum1, msum1);
528 return _mm_cvtss_f32 (msum1);
529 }
530
531
532 float fvec_norm_L2sqr_ref (const float * __restrict x,
533 size_t d)
534 {
535 size_t i;
536 double res_ = 0;
537 for (i = 0; i < d; i++)
538 res_ += x[i] * x[i];
539 return res_;
540 }
541
542
543
544
545 /* Compute the inner product between a vector x and
546 a set of ny vectors y.
547 These functions are not intended to replace BLAS matrix-matrix, as they
548 would be significantly less efficient in this case. */
549 void fvec_inner_products_ny (float * __restrict ip,
550 const float * x,
551 const float * y,
552 size_t d, size_t ny)
553 {
554 for (size_t i = 0; i < ny; i++) {
555 ip[i] = fvec_inner_product (x, y, d);
556 y += d;
557 }
558 }
559
560
561
562
563 /* compute ny L2 distances between x and a set of vectors y */
564 void fvec_L2sqr_ny (float * __restrict dis,
565 const float * x,
566 const float * y,
567 size_t d, size_t ny)
568 {
569 for (size_t i = 0; i < ny; i++) {
570 dis[i] = fvec_L2sqr (x, y, d);
571 y += d;
572 }
573 }
574
575
576
577
578 /* Compute the L2 norm of a set of nx vectors */
579 void fvec_norms_L2 (float * __restrict nr,
580 const float * __restrict x,
581 size_t d, size_t nx)
582 {
583
584 #pragma omp parallel for
585 for (size_t i = 0; i < nx; i++) {
586 nr[i] = sqrtf (fvec_norm_L2sqr (x + i * d, d));
587 }
588 }
589
590 void fvec_norms_L2sqr (float * __restrict nr,
591 const float * __restrict x,
592 size_t d, size_t nx)
593 {
594 #pragma omp parallel for
595 for (size_t i = 0; i < nx; i++)
596 nr[i] = fvec_norm_L2sqr (x + i * d, d);
597 }
598
599
600
601 void fvec_renorm_L2 (size_t d, size_t nx, float * __restrict x)
602 {
603 #pragma omp parallel for
604 for (size_t i = 0; i < nx; i++) {
605 float * __restrict xi = x + i * d;
606
607 float nr = fvec_norm_L2sqr (xi, d);
608
609 if (nr > 0) {
610 size_t j;
611 const float inv_nr = 1.0 / sqrtf (nr);
612 for (j = 0; j < d; j++)
613 xi[j] *= inv_nr;
614 }
615 }
616 }
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634 /***************************************************************************
635 * KNN functions
636 ***************************************************************************/
637
638
639
640 /* Find the nearest neighbors for nx queries in a set of ny vectors */
641 static void knn_inner_product_sse (const float * x,
642 const float * y,
643 size_t d, size_t nx, size_t ny,
644 float_minheap_array_t * res)
645 {
646 size_t k = res->k;
647
648 #pragma omp parallel for
649 for (size_t i = 0; i < nx; i++) {
650 const float * x_ = x + i * d;
651 const float * y_ = y;
652
653 float * __restrict simi = res->get_val(i);
654 long * __restrict idxi = res->get_ids (i);
655
656 minheap_heapify (k, simi, idxi);
657
658 for (size_t j = 0; j < ny; j++) {
659 float ip = fvec_inner_product (x_, y_, d);
660
661 if (ip > simi[0]) {
662 minheap_pop (k, simi, idxi);
663 minheap_push (k, simi, idxi, ip, j);
664 }
665 y_ += d;
666 }
667 minheap_reorder (k, simi, idxi);
668 }
669
670 }
671
672 static void knn_L2sqr_sse (
673 const float * x,
674 const float * y,
675 size_t d, size_t nx, size_t ny,
676 float_maxheap_array_t * res)
677 {
678 size_t k = res->k;
679
680 #pragma omp parallel for
681 for (size_t i = 0; i < nx; i++) {
682 const float * x_ = x + i * d;
683 const float * y_ = y;
684 size_t j;
685 float * __restrict simi = res->get_val(i);
686 long * __restrict idxi = res->get_ids (i);
687
688 maxheap_heapify (k, simi, idxi);
689 for (j = 0; j < ny; j++) {
690 float disij = fvec_L2sqr (x_, y_, d);
691
692 if (disij < simi[0]) {
693 maxheap_pop (k, simi, idxi);
694 maxheap_push (k, simi, idxi, disij, j);
695 }
696 y_ += d;
697 }
698 maxheap_reorder (k, simi, idxi);
699 }
700
701 }
702
703
704 /** Find the nearest neighbors for nx queries in a set of ny vectors */
705 static void knn_inner_product_blas (
706 const float * x,
707 const float * y,
708 size_t d, size_t nx, size_t ny,
709 float_minheap_array_t * res)
710 {
711 res->heapify ();
712
713 // BLAS does not like empty matrices
714 if (nx == 0 || ny == 0) return;
715
716 /* block sizes */
717 const size_t bs_x = 4096, bs_y = 1024;
718 // const size_t bs_x = 16, bs_y = 16;
719 float *ip_block = new float[bs_x * bs_y];
720
721 for (size_t i0 = 0; i0 < nx; i0 += bs_x) {
722 size_t i1 = i0 + bs_x;
723 if(i1 > nx) i1 = nx;
724
725 for (size_t j0 = 0; j0 < ny; j0 += bs_y) {
726 size_t j1 = j0 + bs_y;
727 if (j1 > ny) j1 = ny;
728 /* compute the actual dot products */
729 {
730 float one = 1, zero = 0;
731 FINTEGER nyi = j1 - j0, nxi = i1 - i0, di = d;
732 sgemm_ ("Transpose", "Not transpose", &nyi, &nxi, &di, &one,
733 y + j0 * d, &di,
734 x + i0 * d, &di, &zero,
735 ip_block, &nyi);
736 }
737
738 /* collect maxima */
739 res->addn (j1 - j0, ip_block, j0, i0, i1 - i0);
740 }
741 }
742 delete [] ip_block;
743 res->reorder ();
744 }
745
746 // distance correction is an operator that can be applied to transform
747 // the distances
748 template<class DistanceCorrection>
749 static void knn_L2sqr_blas (const float * x,
750 const float * y,
751 size_t d, size_t nx, size_t ny,
752 float_maxheap_array_t * res,
753 const DistanceCorrection &corr)
754 {
755 res->heapify ();
756
757 // BLAS does not like empty matrices
758 if (nx == 0 || ny == 0) return;
759
760 size_t k = res->k;
761
762 /* block sizes */
763 const size_t bs_x = 4096, bs_y = 1024;
764 // const size_t bs_x = 16, bs_y = 16;
765 float *ip_block = new float[bs_x * bs_y];
766
767 float *x_norms = new float[nx];
768 fvec_norms_L2sqr (x_norms, x, d, nx);
769
770 float *y_norms = new float[ny];
771 fvec_norms_L2sqr (y_norms, y, d, ny);
772
773 for (size_t i0 = 0; i0 < nx; i0 += bs_x) {
774 size_t i1 = i0 + bs_x;
775 if(i1 > nx) i1 = nx;
776
777 for (size_t j0 = 0; j0 < ny; j0 += bs_y) {
778 size_t j1 = j0 + bs_y;
779 if (j1 > ny) j1 = ny;
780 /* compute the actual dot products */
781 {
782 float one = 1, zero = 0;
783 FINTEGER nyi = j1 - j0, nxi = i1 - i0, di = d;
784 sgemm_ ("Transpose", "Not transpose", &nyi, &nxi, &di, &one,
785 y + j0 * d, &di,
786 x + i0 * d, &di, &zero,
787 ip_block, &nyi);
788 }
789
790 /* collect minima */
791 #pragma omp parallel for
792 for (size_t i = i0; i < i1; i++) {
793 float * __restrict simi = res->get_val(i);
794 long * __restrict idxi = res->get_ids (i);
795 const float *ip_line = ip_block + (i - i0) * (j1 - j0);
796
797 for (size_t j = j0; j < j1; j++) {
798 float ip = *ip_line++;
799 float dis = x_norms[i] + y_norms[j] - 2 * ip;
800
801 dis = corr (dis, i, j);
802
803 if (dis < simi[0]) {
804 maxheap_pop (k, simi, idxi);
805 maxheap_push (k, simi, idxi, dis, j);
806 }
807 }
808 }
809 }
810 }
811 res->reorder ();
812
813 delete [] ip_block;
814 delete [] x_norms;
815 delete [] y_norms;
816 }
817
818
819
820
821
822
823
824
825
826 /*******************************************************
827 * KNN driver functions
828 *******************************************************/
829
830 void knn_inner_product (const float * x,
831 const float * y,
832 size_t d, size_t nx, size_t ny,
833 float_minheap_array_t * res)
834 {
835 if (d % 4 == 0 && nx < 20) {
836 knn_inner_product_sse (x, y, d, nx, ny, res);
837 } else {
838 knn_inner_product_blas (x, y, d, nx, ny, res);
839 }
840 }
841
842
843
844 struct NopDistanceCorrection {
845 float operator()(float dis, size_t qno, size_t bno) const {
846 return dis;
847 }
848 };
849
850 void knn_L2sqr (const float * x,
851 const float * y,
852 size_t d, size_t nx, size_t ny,
853 float_maxheap_array_t * res)
854 {
855 if (d % 4 == 0 && nx < 20) {
856 knn_L2sqr_sse (x, y, d, nx, ny, res);
857 } else {
858 NopDistanceCorrection nop;
859 knn_L2sqr_blas (x, y, d, nx, ny, res, nop);
860 }
861 }
862
863 struct BaseShiftDistanceCorrection {
864 const float *base_shift;
865 float operator()(float dis, size_t qno, size_t bno) const {
866 return dis - base_shift[bno];
867 }
868 };
869
870 void knn_L2sqr_base_shift (
871 const float * x,
872 const float * y,
873 size_t d, size_t nx, size_t ny,
874 float_maxheap_array_t * res,
875 const float *base_shift)
876 {
877 BaseShiftDistanceCorrection corr = {base_shift};
878 knn_L2sqr_blas (x, y, d, nx, ny, res, corr);
879 }
880
881
882
883 /***************************************************************************
884 * compute a subset of distances
885 ***************************************************************************/
886
887 /* compute the inner product between x and a subset y of ny vectors,
888 whose indices are given by idy. */
889 void fvec_inner_products_by_idx (float * __restrict ip,
890 const float * x,
891 const float * y,
892 const long * __restrict ids, /* for y vecs */
893 size_t d, size_t nx, size_t ny)
894 {
895 #pragma omp parallel for
896 for (size_t j = 0; j < nx; j++) {
897 const long * __restrict idsj = ids + j * ny;
898 const float * xj = x + j * d;
899 float * __restrict ipj = ip + j * ny;
900 for (size_t i = 0; i < ny; i++) {
901 if (idsj[i] < 0)
902 continue;
903 ipj[i] = fvec_inner_product (xj, y + d * idsj[i], d);
904 }
905 }
906 }
907
908 /* compute the inner product between x and a subset y of ny vectors,
909 whose indices are given by idy. */
910 void fvec_L2sqr_by_idx (float * __restrict dis,
911 const float * x,
912 const float * y,
913 const long * __restrict ids, /* ids of y vecs */
914 size_t d, size_t nx, size_t ny)
915 {
916 #pragma omp parallel for
917 for (size_t j = 0; j < nx; j++) {
918 const long * __restrict idsj = ids + j * ny;
919 const float * xj = x + j * d;
920 float * __restrict disj = dis + j * ny;
921 for (size_t i = 0; i < ny; i++) {
922 if (idsj[i] < 0)
923 continue;
924 disj[i] = fvec_L2sqr (xj, y + d * idsj[i], d);
925 }
926 }
927 }
928
929
930
931
932
933 /* Find the nearest neighbors for nx queries in a set of ny vectors
934 indexed by ids. May be useful for re-ranking a pre-selected vector list */
935 void knn_inner_products_by_idx (const float * x,
936 const float * y,
937 const long * __restrict ids,
938 size_t d, size_t nx, size_t ny,
939 float_minheap_array_t * res)
940 {
941 size_t k = res->k;
942
943
944
945 #pragma omp parallel for
946 for (size_t i = 0; i < nx; i++) {
947 const float * x_ = x + i * d;
948 const long * idsi = ids + i * ny;
949 size_t j;
950 float * __restrict simi = res->get_val(i);
951 long * __restrict idxi = res->get_ids (i);
952 minheap_heapify (k, simi, idxi);
953
954 for (j = 0; j < ny; j++) {
955 if (idsi[j] < 0) break;
956 float ip = fvec_inner_product (x_, y + d * idsi[j], d);
957
958 if (ip > simi[0]) {
959 minheap_pop (k, simi, idxi);
960 minheap_push (k, simi, idxi, ip, idsi[j]);
961 }
962 }
963 minheap_reorder (k, simi, idxi);
964 }
965
966 }
967
968 void knn_L2sqr_by_idx (const float * x,
969 const float * y,
970 const long * __restrict ids,
971 size_t d, size_t nx, size_t ny,
972 float_maxheap_array_t * res)
973 {
974 size_t k = res->k;
975
976 #pragma omp parallel for
977 for (size_t i = 0; i < nx; i++) {
978 const float * x_ = x + i * d;
979 const long * __restrict idsi = ids + i * ny;
980 float * __restrict simi = res->get_val(i);
981 long * __restrict idxi = res->get_ids (i);
982 maxheap_heapify (res->k, simi, idxi);
983 for (size_t j = 0; j < ny; j++) {
984 float disij = fvec_L2sqr (x_, y + d * idsi[j], d);
985
986 if (disij < simi[0]) {
987 maxheap_pop (k, simi, idxi);
988 maxheap_push (k, simi, idxi, disij, idsi[j]);
989 }
990 }
991 maxheap_reorder (res->k, simi, idxi);
992 }
993
994 }
995
996
997
998
999
1000 /***************************************************************************
1001 * Range search
1002 ***************************************************************************/
1003
1004 /** Find the nearest neighbors for nx queries in a set of ny vectors
1005 * compute_l2 = compute pairwise squared L2 distance rather than inner prod
1006 */
1007 template <bool compute_l2>
1008 static void range_search_blas (
1009 const float * x,
1010 const float * y,
1011 size_t d, size_t nx, size_t ny,
1012 float radius,
1013 RangeSearchResult *result)
1014 {
1015
1016 // BLAS does not like empty matrices
1017 if (nx == 0 || ny == 0) return;
1018
1019 /* block sizes */
1020 const size_t bs_x = 4096, bs_y = 1024;
1021 // const size_t bs_x = 16, bs_y = 16;
1022 float *ip_block = new float[bs_x * bs_y];
1023
1024 float *x_norms = nullptr, *y_norms = nullptr;
1025
1026 if (compute_l2) {
1027 x_norms = new float[nx];
1028 fvec_norms_L2sqr (x_norms, x, d, nx);
1029 y_norms = new float[ny];
1030 fvec_norms_L2sqr (y_norms, y, d, ny);
1031 }
1032
1033 std::vector <RangeSearchPartialResult *> partial_results;
1034
1035 for (size_t j0 = 0; j0 < ny; j0 += bs_y) {
1036 size_t j1 = j0 + bs_y;
1037 if (j1 > ny) j1 = ny;
1038 RangeSearchPartialResult * pres = new RangeSearchPartialResult (result);
1039 partial_results.push_back (pres);
1040
1041 for (size_t i0 = 0; i0 < nx; i0 += bs_x) {
1042 size_t i1 = i0 + bs_x;
1043 if(i1 > nx) i1 = nx;
1044
1045 /* compute the actual dot products */
1046 {
1047 float one = 1, zero = 0;
1048 FINTEGER nyi = j1 - j0, nxi = i1 - i0, di = d;
1049 sgemm_ ("Transpose", "Not transpose", &nyi, &nxi, &di, &one,
1050 y + j0 * d, &di,
1051 x + i0 * d, &di, &zero,
1052 ip_block, &nyi);
1053 }
1054
1055
1056 for (size_t i = i0; i < i1; i++) {
1057 const float *ip_line = ip_block + (i - i0) * (j1 - j0);
1058
1059 RangeSearchPartialResult::QueryResult & qres =
1060 pres->new_result (i);
1061
1062 for (size_t j = j0; j < j1; j++) {
1063 float ip = *ip_line++;
1064 if (compute_l2) {
1065 float dis = x_norms[i] + y_norms[j] - 2 * ip;
1066 if (dis < radius) {
1067 qres.add (dis, j);
1068 }
1069 } else {
1070 if (ip > radius) {
1071 qres.add (ip, j);
1072 }
1073 }
1074 }
1075 }
1076 }
1077
1078 }
1079 delete [] ip_block;
1080 delete [] x_norms;
1081 delete [] y_norms;
1082
1083 { // merge the partial results
1084 int npres = partial_results.size();
1085 // count
1086 for (size_t i = 0; i < nx; i++) {
1087 for (int j = 0; j < npres; j++)
1088 result->lims[i] += partial_results[j]->queries[i].nres;
1089 }
1090 result->do_allocation ();
1091 for (int j = 0; j < npres; j++) {
1092 partial_results[j]->set_result (true);
1093 delete partial_results[j];
1094 }
1095
1096 // reset the limits
1097 for (size_t i = nx; i > 0; i--) {
1098 result->lims [i] = result->lims [i - 1];
1099 }
1100 result->lims [0] = 0;
1101 }
1102 }
1103
1104
1105 template <bool compute_l2>
1106 static void range_search_sse (const float * x,
1107 const float * y,
1108 size_t d, size_t nx, size_t ny,
1109 float radius,
1110 RangeSearchResult *res)
1111 {
1112 FAISS_ASSERT (d % 4 == 0);
1113
1114 #pragma omp parallel
1115 {
1116 RangeSearchPartialResult pres (res);
1117
1118 #pragma omp for
1119 for (size_t i = 0; i < nx; i++) {
1120 const float * x_ = x + i * d;
1121 const float * y_ = y;
1122 size_t j;
1123
1124 RangeSearchPartialResult::QueryResult & qres =
1125 pres.new_result (i);
1126
1127 for (j = 0; j < ny; j++) {
1128 if (compute_l2) {
1129 float disij = fvec_L2sqr (x_, y_, d);
1130 if (disij < radius) {
1131 qres.add (disij, j);
1132 }
1133 } else {
1134 float ip = fvec_inner_product (x_, y_, d);
1135 if (ip > radius) {
1136 qres.add (ip, j);
1137 }
1138 }
1139 y_ += d;
1140 }
1141
1142 }
1143 pres.finalize ();
1144 }
1145 }
1146
1147
1148
1149
1150
1151 void range_search_L2sqr (
1152 const float * x,
1153 const float * y,
1154 size_t d, size_t nx, size_t ny,
1155 float radius,
1156 RangeSearchResult *res)
1157 {
1158
1159 if (d % 4 == 0 && nx < 20) {
1160 range_search_sse<true> (x, y, d, nx, ny, radius, res);
1161 } else {
1162 range_search_blas<true> (x, y, d, nx, ny, radius, res);
1163 }
1164 }
1165
1166 void range_search_inner_product (
1167 const float * x,
1168 const float * y,
1169 size_t d, size_t nx, size_t ny,
1170 float radius,
1171 RangeSearchResult *res)
1172 {
1173
1174 if (d % 4 == 0 && nx < 20) {
1175 range_search_sse<false> (x, y, d, nx, ny, radius, res);
1176 } else {
1177 range_search_blas<false> (x, y, d, nx, ny, radius, res);
1178 }
1179 }
1180
1181
1182
1183 /***************************************************************************
1184 * Some matrix manipulation functions
1185 ***************************************************************************/
1186
1187
1188 /* This function exists because the Torch counterpart is extremly slow
1189 (not multi-threaded + unexpected overhead even in single thread).
1190 It is here to implement the usual property |x-y|^2=|x|^2+|y|^2-2<x|y> */
1191 void inner_product_to_L2sqr (float * __restrict dis,
1192 const float * nr1,
1193 const float * nr2,
1194 size_t n1, size_t n2)
1195 {
1196
1197 #pragma omp parallel for
1198 for (size_t j = 0 ; j < n1 ; j++) {
1199 float * disj = dis + j * n2;
1200 for (size_t i = 0 ; i < n2 ; i++)
1201 disj[i] = nr1[j] + nr2[i] - 2 * disj[i];
1202 }
1203 }
1204
1205
1206 void matrix_qr (int m, int n, float *a)
1207 {
1208 FAISS_ASSERT(m >= n);
1209 FINTEGER mi = m, ni = n, ki = mi < ni ? mi : ni;
1210 std::vector<float> tau (ki);
1211 FINTEGER lwork = -1, info;
1212 float work_size;
1213
1214 sgeqrf_ (&mi, &ni, a, &mi, tau.data(),
1215 &work_size, &lwork, &info);
1216 lwork = size_t(work_size);
1217 std::vector<float> work (lwork);
1218
1219 sgeqrf_ (&mi, &ni, a, &mi,
1220 tau.data(), work.data(), &lwork, &info);
1221
1222 sorgqr_ (&mi, &ni, &ki, a, &mi, tau.data(),
1223 work.data(), &lwork, &info);
1224
1225 }
1226
1227
1228 void pairwise_L2sqr (long d,
1229 long nq, const float *xq,
1230 long nb, const float *xb,
1231 float *dis,
1232 long ldq, long ldb, long ldd)
1233 {
1234 if (nq == 0 || nb == 0) return;
1235 if (ldq == -1) ldq = d;
1236 if (ldb == -1) ldb = d;
1237 if (ldd == -1) ldd = nb;
1238
1239 // store in beginning of distance matrix to avoid malloc
1240 float *b_norms = dis;
1241
1242 #pragma omp parallel for
1243 for (long i = 0; i < nb; i++)
1244 b_norms [i] = fvec_norm_L2sqr (xb + i * ldb, d);
1245
1246 #pragma omp parallel for
1247 for (long i = 1; i < nq; i++) {
1248 float q_norm = fvec_norm_L2sqr (xq + i * ldq, d);
1249 for (long j = 0; j < nb; j++)
1250 dis[i * ldd + j] = q_norm + b_norms [j];
1251 }
1252
1253 {
1254 float q_norm = fvec_norm_L2sqr (xq, d);
1255 for (long j = 0; j < nb; j++)
1256 dis[j] += q_norm;
1257 }
1258
1259 {
1260 FINTEGER nbi = nb, nqi = nq, di = d, ldqi = ldq, ldbi = ldb, lddi = ldd;
1261 float one = 1.0, minus_2 = -2.0;
1262
1263 sgemm_ ("Transposed", "Not transposed",
1264 &nbi, &nqi, &di,
1265 &minus_2,
1266 xb, &ldbi,
1267 xq, &ldqi,
1268 &one, dis, &lddi);
1269 }
1270
1271
1272 }
1273
1274
1275
1276 /***************************************************************************
1277 * Kmeans subroutine
1278 ***************************************************************************/
1279
1280 // a bit above machine epsilon for float16
1281
1282 #define EPS (1 / 1024.)
1283
1284 /* For k-means, compute centroids given assignment of vectors to centroids */
1285 /* NOTE: This could be multi-threaded (use histogram of indexes) */
1286 int km_update_centroids (const float * x,
1287 float * centroids,
1288 long * assign,
1289 size_t d, size_t k, size_t n)
1290 {
1291 std::vector<size_t> hassign(k);
1292 memset (centroids, 0, sizeof(*centroids) * d * k);
1293
1294
1295 #pragma omp parallel
1296 {
1297 int nt = omp_get_num_threads();
1298 int rank = omp_get_thread_num();
1299 // this thread is taking care of centroids c0:c1
1300 size_t c0 = (k * rank) / nt;
1301 size_t c1 = (k * (rank + 1)) / nt;
1302 const float *xi = x;
1303 // printf("thread %d/%d: centroids %ld:%ld\n", rank, nt, c0, c1);
1304 size_t nacc = 0;
1305
1306 for (size_t i = 0; i < n; i++) {
1307 long ci = assign[i];
1308 assert (ci >= 0 && ci < k);
1309 if (ci >= c0 && ci < c1) {
1310 float * c = centroids + ci * d;
1311 hassign[ci]++;
1312 for (size_t j = 0; j < d; j++)
1313 c[j] += xi[j];
1314 nacc++;
1315 }
1316 xi += d;
1317 }
1318 // printf("thread %d/%d: nacc = %ld/%ld\n", rank, nt, nacc, n);
1319
1320 }
1321
1322 #pragma omp parallel for
1323 for (size_t ci = 0; ci < k; ci++) {
1324 float * c = centroids + ci * d;
1325 float ni = (float) hassign[ci];
1326 if (ni != 0) {
1327 for (size_t j = 0; j < d; j++)
1328 c[j] /= ni;
1329 }
1330 }
1331
1332 /* Take care of void clusters */
1333 size_t nsplit = 0;
1334 RandomGenerator rng (1234);
1335 for (size_t ci = 0; ci < k; ci++) {
1336 if (hassign[ci] == 0) { /* need to redefine a centroid */
1337 size_t cj;
1338 for (cj = 0; 1; cj = (cj+1) % k) {
1339 /* probability to pick this cluster for split */
1340 float p = (hassign[cj] - 1.0) / (float) (n - k);
1341 float r = rng.rand_float ();
1342 if (r < p) {
1343 break; /* found our cluster to be split */
1344 }
1345 }
1346 memcpy (centroids+ci*d, centroids+cj*d, sizeof(*centroids) * d);
1347
1348 /* small symmetric pertubation. Much better than */
1349 for (size_t j = 0; j < d; j++)
1350 if (j % 2 == 0) {
1351 centroids[ci * d + j] *= 1 + EPS;
1352 centroids[cj * d + j] *= 1 - EPS;
1353 }
1354 else {
1355 centroids[ci * d + j] *= 1 + EPS;
1356 centroids[cj * d + j] *= 1 - EPS;
1357 }
1358
1359 /* assume even split of the cluster */
1360 hassign[ci] = hassign[cj] / 2;
1361 hassign[cj] -= hassign[ci];
1362 nsplit++;
1363 }
1364 }
1365
1366 return nsplit;
1367 }
1368
1369 #undef EPS
1370
1371
1372
1373 /***************************************************************************
1374 * Result list routines
1375 ***************************************************************************/
1376
1377
1378 void ranklist_handle_ties (int k, long *idx, const float *dis)
1379 {
1380 float prev_dis = -1e38;
1381 int prev_i = -1;
1382 for (int i = 0; i < k; i++) {
1383 if (dis[i] != prev_dis) {
1384 if (i > prev_i + 1) {
1385 // sort between prev_i and i - 1
1386 std::sort (idx + prev_i, idx + i);
1387 }
1388 prev_i = i;
1389 prev_dis = dis[i];
1390 }
1391 }
1392 }
1393
1394 size_t ranklist_intersection_size (size_t k1, const long *v1,
1395 size_t k2, const long *v2_in)
1396 {
1397 if (k2 > k1) return ranklist_intersection_size (k2, v2_in, k1, v1);
1398 long *v2 = new long [k2];
1399 memcpy (v2, v2_in, sizeof (long) * k2);
1400 std::sort (v2, v2 + k2);
1401 { // de-dup v2
1402 long prev = -1;
1403 size_t wp = 0;
1404 for (size_t i = 0; i < k2; i++) {
1405 if (v2 [i] != prev) {
1406 v2[wp++] = prev = v2 [i];
1407 }
1408 }
1409 k2 = wp;
1410 }
1411 const long seen_flag = 1L << 60;
1412 size_t count = 0;
1413 for (size_t i = 0; i < k1; i++) {
1414 long q = v1 [i];
1415 size_t i0 = 0, i1 = k2;
1416 while (i0 + 1 < i1) {
1417 size_t imed = (i1 + i0) / 2;
1418 long piv = v2 [imed] & ~seen_flag;
1419 if (piv <= q) i0 = imed;
1420 else i1 = imed;
1421 }
1422 if (v2 [i0] == q) {
1423 count++;
1424 v2 [i0] |= seen_flag;
1425 }
1426 }
1427 delete [] v2;
1428
1429 return count;
1430 }
1431
1432 double imbalance_factor (int k, const int *hist) {
1433 double tot = 0, uf = 0;
1434
1435 for (int i = 0 ; i < k ; i++) {
1436 tot += hist[i];
1437 uf += hist[i] * (double) hist[i];
1438 }
1439 uf = uf * k / (tot * tot);
1440
1441 return uf;
1442 }
1443
1444
1445 double imbalance_factor (int n, int k, const long *assign) {
1446 std::vector<int> hist(k, 0);
1447 for (int i = 0; i < n; i++) {
1448 hist[assign[i]]++;
1449 }
1450
1451 return imbalance_factor (k, hist.data());
1452 }
1453
1454
1455
1456 int ivec_hist (size_t n, const int * v, int vmax, int *hist) {
1457 memset (hist, 0, sizeof(hist[0]) * vmax);
1458 int nout = 0;
1459 while (n--) {
1460 if (v[n] < 0 || v[n] >= vmax) nout++;
1461 else hist[v[n]]++;
1462 }
1463 return nout;
1464 }
1465
1466
1467 void bincode_hist(size_t n, size_t nbits, const uint8_t *codes, int *hist)
1468 {
1469 FAISS_ASSERT (nbits % 8 == 0);
1470 size_t d = nbits / 8;
1471 std::vector<int> accu(d * 256);
1472 const uint8_t *c = codes;
1473 for (size_t i = 0; i < n; i++)
1474 for(int j = 0; j < d; j++)
1475 accu[j * 256 + *c++]++;
1476 memset (hist, 0, sizeof(*hist) * nbits);
1477 for (int i = 0; i < d; i++) {
1478 const int *ai = accu.data() + i * 256;
1479 int * hi = hist + i * 8;
1480 for (int j = 0; j < 256; j++)
1481 for (int k = 0; k < 8; k++)
1482 if ((j >> k) & 1)
1483 hi[k] += ai[j];
1484 }
1485
1486 }
1487
1488
1489
1490 size_t ivec_checksum (size_t n, const int *a)
1491 {
1492 size_t cs = 112909;
1493 while (n--) cs = cs * 65713 + a[n] * 1686049;
1494 return cs;
1495 }
1496
1497
1498 namespace {
1499 struct ArgsortComparator {
1500 const float *vals;
1501 bool operator() (const size_t a, const size_t b) const {
1502 return vals[a] < vals[b];
1503 }
1504 };
1505
1506 struct SegmentS {
1507 size_t i0; // begin pointer in the permutation array
1508 size_t i1; // end
1509 size_t len() const {
1510 return i1 - i0;
1511 }
1512 };
1513
1514 // see https://en.wikipedia.org/wiki/Merge_algorithm#Parallel_merge
1515 // extended to > 1 merge thread
1516
1517 // merges 2 ranges that should be consecutive on the source into
1518 // the union of the two on the destination
1519 template<typename T>
1520 void parallel_merge (const T *src, T *dst,
1521 SegmentS &s1, SegmentS & s2, int nt,
1522 const ArgsortComparator & comp) {
1523 if (s2.len() > s1.len()) { // make sure that s1 larger than s2
1524 std::swap(s1, s2);
1525 }
1526
1527 // compute sub-ranges for each thread
1528 SegmentS s1s[nt], s2s[nt], sws[nt];
1529 s2s[0].i0 = s2.i0;
1530 s2s[nt - 1].i1 = s2.i1;
1531
1532 // not sure parallel actually helps here
1533 #pragma omp parallel for num_threads(nt)
1534 for (int t = 0; t < nt; t++) {
1535 s1s[t].i0 = s1.i0 + s1.len() * t / nt;
1536 s1s[t].i1 = s1.i0 + s1.len() * (t + 1) / nt;
1537
1538 if (t + 1 < nt) {
1539 T pivot = src[s1s[t].i1];
1540 size_t i0 = s2.i0, i1 = s2.i1;
1541 while (i0 + 1 < i1) {
1542 size_t imed = (i1 + i0) / 2;
1543 if (comp (pivot, src[imed])) {i1 = imed; }
1544 else {i0 = imed; }
1545 }
1546 s2s[t].i1 = s2s[t + 1].i0 = i1;
1547 }
1548 }
1549 s1.i0 = std::min(s1.i0, s2.i0);
1550 s1.i1 = std::max(s1.i1, s2.i1);
1551 s2 = s1;
1552 sws[0].i0 = s1.i0;
1553 for (int t = 0; t < nt; t++) {
1554 sws[t].i1 = sws[t].i0 + s1s[t].len() + s2s[t].len();
1555 if (t + 1 < nt) {
1556 sws[t + 1].i0 = sws[t].i1;
1557 }
1558 }
1559 assert(sws[nt - 1].i1 == s1.i1);
1560
1561 // do the actual merging
1562 #pragma omp parallel for num_threads(nt)
1563 for (int t = 0; t < nt; t++) {
1564 SegmentS sw = sws[t];
1565 SegmentS s1t = s1s[t];
1566 SegmentS s2t = s2s[t];
1567 if (s1t.i0 < s1t.i1 && s2t.i0 < s2t.i1) {
1568 for (;;) {
1569 // assert (sw.len() == s1t.len() + s2t.len());
1570 if (comp(src[s1t.i0], src[s2t.i0])) {
1571 dst[sw.i0++] = src[s1t.i0++];
1572 if (s1t.i0 == s1t.i1) break;
1573 } else {
1574 dst[sw.i0++] = src[s2t.i0++];
1575 if (s2t.i0 == s2t.i1) break;
1576 }
1577 }
1578 }
1579 if (s1t.len() > 0) {
1580 assert(s1t.len() == sw.len());
1581 memcpy(dst + sw.i0, src + s1t.i0, s1t.len() * sizeof(dst[0]));
1582 } else if (s2t.len() > 0) {
1583 assert(s2t.len() == sw.len());
1584 memcpy(dst + sw.i0, src + s2t.i0, s2t.len() * sizeof(dst[0]));
1585 }
1586 }
1587 }
1588
1589 };
1590
1591 void fvec_argsort (size_t n, const float *vals,
1592 size_t *perm)
1593 {
1594 for (size_t i = 0; i < n; i++) perm[i] = i;
1595 ArgsortComparator comp = {vals};
1596 std::sort (perm, perm + n, comp);
1597 }
1598
1599 void fvec_argsort_parallel (size_t n, const float *vals,
1600 size_t *perm)
1601 {
1602 size_t * perm2 = new size_t[n];
1603 // 2 result tables, during merging, flip between them
1604 size_t *permB = perm2, *permA = perm;
1605
1606 int nt = omp_get_max_threads();
1607 { // prepare correct permutation so that the result ends in perm
1608 // at final iteration
1609 int nseg = nt;
1610 while (nseg > 1) {
1611 nseg = (nseg + 1) / 2;
1612 std::swap (permA, permB);
1613 }
1614 }
1615
1616 #pragma omp parallel
1617 for (size_t i = 0; i < n; i++) permA[i] = i;
1618
1619 ArgsortComparator comp = {vals};
1620
1621 SegmentS segs[nt];
1622
1623 // independent sorts
1624 #pragma omp parallel for
1625 for (int t = 0; t < nt; t++) {
1626 size_t i0 = t * n / nt;
1627 size_t i1 = (t + 1) * n / nt;
1628 SegmentS seg = {i0, i1};
1629 std::sort (permA + seg.i0, permA + seg.i1, comp);
1630 segs[t] = seg;
1631 }
1632 int prev_nested = omp_get_nested();
1633 omp_set_nested(1);
1634
1635 int nseg = nt;
1636 while (nseg > 1) {
1637 int nseg1 = (nseg + 1) / 2;
1638 int sub_nt = nseg % 2 == 0 ? nt : nt - 1;
1639 int sub_nseg1 = nseg / 2;
1640
1641 #pragma omp parallel for num_threads(nseg1)
1642 for (int s = 0; s < nseg; s += 2) {
1643 if (s + 1 == nseg) { // otherwise isolated segment
1644 memcpy(permB + segs[s].i0, permA + segs[s].i0,
1645 segs[s].len() * sizeof(size_t));
1646 } else {
1647 int t0 = s * sub_nt / sub_nseg1;
1648 int t1 = (s + 1) * sub_nt / sub_nseg1;
1649 printf("merge %d %d, %d threads\n", s, s + 1, t1 - t0);
1650 parallel_merge(permA, permB, segs[s], segs[s + 1],
1651 t1 - t0, comp);
1652 }
1653 }
1654 for (int s = 0; s < nseg; s += 2)
1655 segs[s / 2] = segs[s];
1656 nseg = nseg1;
1657 std::swap (permA, permB);
1658 }
1659 assert (permA == perm);
1660 omp_set_nested(prev_nested);
1661 delete [] perm2;
1662 }
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679 /***************************************************************************
1680 * heavily optimized table computations
1681 ***************************************************************************/
1682
1683
1684 static inline void fvec_madd_ref (size_t n, const float *a,
1685 float bf, const float *b, float *c) {
1686 for (size_t i = 0; i < n; i++)
1687 c[i] = a[i] + bf * b[i];
1688 }
1689
1690
1691 static inline void fvec_madd_sse (size_t n, const float *a,
1692 float bf, const float *b, float *c) {
1693 n >>= 2;
1694 __m128 bf4 = _mm_set_ps1 (bf);
1695 __m128 * a4 = (__m128*)a;
1696 __m128 * b4 = (__m128*)b;
1697 __m128 * c4 = (__m128*)c;
1698
1699 while (n--) {
1700 *c4 = _mm_add_ps (*a4, _mm_mul_ps (bf4, *b4));
1701 b4++;
1702 a4++;
1703 c4++;
1704 }
1705 }
1706
1707 void fvec_madd (size_t n, const float *a,
1708 float bf, const float *b, float *c)
1709 {
1710 if ((n & 3) == 0 &&
1711 ((((long)a) | ((long)b) | ((long)c)) & 15) == 0)
1712 fvec_madd_sse (n, a, bf, b, c);
1713 else
1714 fvec_madd_ref (n, a, bf, b, c);
1715 }
1716
1717 static inline int fvec_madd_and_argmin_ref (size_t n, const float *a,
1718 float bf, const float *b, float *c) {
1719 float vmin = 1e20;
1720 int imin = -1;
1721
1722 for (size_t i = 0; i < n; i++) {
1723 c[i] = a[i] + bf * b[i];
1724 if (c[i] < vmin) {
1725 vmin = c[i];
1726 imin = i;
1727 }
1728 }
1729 return imin;
1730 }
1731
1732 static inline int fvec_madd_and_argmin_sse (size_t n, const float *a,
1733 float bf, const float *b, float *c) {
1734 n >>= 2;
1735 __m128 bf4 = _mm_set_ps1 (bf);
1736 __m128 vmin4 = _mm_set_ps1 (1e20);
1737 __m128i imin4 = _mm_set1_epi32 (-1);
1738 __m128i idx4 = _mm_set_epi32 (3, 2, 1, 0);
1739 __m128i inc4 = _mm_set1_epi32 (4);
1740 __m128 * a4 = (__m128*)a;
1741 __m128 * b4 = (__m128*)b;
1742 __m128 * c4 = (__m128*)c;
1743
1744 while (n--) {
1745 __m128 vc4 = _mm_add_ps (*a4, _mm_mul_ps (bf4, *b4));
1746 *c4 = vc4;
1747 __m128i mask = (__m128i)_mm_cmpgt_ps (vmin4, vc4);
1748 // imin4 = _mm_blendv_epi8 (imin4, idx4, mask); // slower!
1749
1750 imin4 = _mm_or_si128 (_mm_and_si128 (mask, idx4),
1751 _mm_andnot_si128 (mask, imin4));
1752 vmin4 = _mm_min_ps (vmin4, vc4);
1753 b4++;
1754 a4++;
1755 c4++;
1756 idx4 = _mm_add_epi32 (idx4, inc4);
1757 }
1758
1759 // 4 values -> 2
1760 {
1761 idx4 = _mm_shuffle_epi32 (imin4, 3 << 2 | 2);
1762 __m128 vc4 = _mm_shuffle_ps (vmin4, vmin4, 3 << 2 | 2);
1763 __m128i mask = (__m128i)_mm_cmpgt_ps (vmin4, vc4);
1764 imin4 = _mm_or_si128 (_mm_and_si128 (mask, idx4),
1765 _mm_andnot_si128 (mask, imin4));
1766 vmin4 = _mm_min_ps (vmin4, vc4);
1767 }
1768 // 2 values -> 1
1769 {
1770 idx4 = _mm_shuffle_epi32 (imin4, 1);
1771 __m128 vc4 = _mm_shuffle_ps (vmin4, vmin4, 1);
1772 __m128i mask = (__m128i)_mm_cmpgt_ps (vmin4, vc4);
1773 imin4 = _mm_or_si128 (_mm_and_si128 (mask, idx4),
1774 _mm_andnot_si128 (mask, imin4));
1775 // vmin4 = _mm_min_ps (vmin4, vc4);
1776 }
1777 return _mm_extract_epi32 (imin4, 0);
1778 }
1779
1780
1781 int fvec_madd_and_argmin (size_t n, const float *a,
1782 float bf, const float *b, float *c)
1783 {
1784 if ((n & 3) == 0 &&
1785 ((((long)a) | ((long)b) | ((long)c)) & 15) == 0)
1786 return fvec_madd_and_argmin_sse (n, a, bf, b, c);
1787 else
1788 return fvec_madd_and_argmin_ref (n, a, bf, b, c);
1789 }
1790
1791
1792
1793
1794
1795 } // namespace faiss
faiss::RandomGenerator
random generator that can be used in multithreaded contexts
Definition: utils.h:49
faiss::knn_L2sqr_base_shift
void knn_L2sqr_base_shift(const float *x, const float *y, size_t d, size_t nx, size_t ny, float_maxheap_array_t *res, const float *base_shift)
Definition: utils.cpp:870
faiss::RandomGenerator::RandomGenerator
RandomGenerator(long seed=1234)
initialize
faiss::km_update_centroids
int km_update_centroids(const float *x, float *centroids, long *assign, size_t d, size_t k, size_t n)
Definition: utils.cpp:1286
faiss::fvec_L2sqr
float fvec_L2sqr(const float *x, const float *y, size_t d)
Squared L2 distance between two vectors.
Definition: utils.cpp:430
faiss::bincode_hist
void bincode_hist(size_t n, size_t nbits, const uint8_t *codes, int *hist)
Definition: utils.cpp:1467
faiss::ranklist_handle_ties
void ranklist_handle_ties(int k, long *idx, const float *dis)
Definition: utils.cpp:1378
faiss::RandomGenerator::rand_float
float rand_float()
between 0 and 1
Definition: utils.cpp:208
faiss::fvec_madd
void fvec_madd(size_t n, const float *a, float bf, const float *b, float *c)
Definition: utils.cpp:1707
faiss::get_mem_usage_kb
size_t get_mem_usage_kb()
get current RSS usage in kB
faiss::ivec_hist
int ivec_hist(size_t n, const int *v, int vmax, int *hist)
compute histogram on v
Definition: utils.cpp:1456
faiss::RandomGenerator::rand_long
long rand_long()
random long &lt; 2 ^ 62
faiss::RandomGenerator::rand_int
int rand_int()
random 31-bit positive integer
faiss::HeapArray
Definition: Heap.h:351
faiss::ranklist_intersection_size
size_t ranklist_intersection_size(size_t k1, const long *v1, size_t k2, const long *v2_in)
Definition: utils.cpp:1394
faiss::pairwise_L2sqr
void pairwise_L2sqr(long d, long nq, const float *xq, long nb, const float *xb, float *dis, long ldq, long ldb, long ldd)
Definition: utils.cpp:1228
faiss::range_search_inner_product
void range_search_inner_product(const float *x, const float *y, size_t d, size_t nx, size_t ny, float radius, RangeSearchResult *res)
same as range_search_L2sqr for the inner product similarity
Definition: utils.cpp:1166
faiss::knn_inner_product
void knn_inner_product(const float *x, const float *y, size_t d, size_t nx, size_t ny, float_minheap_array_t *res)
Definition: utils.cpp:830
faiss::getmillisecs
double getmillisecs()
ms elapsed since some arbitrary epoch
Definition: utils.cpp:71
faiss::NopDistanceCorrection
Definition: utils.cpp:844
faiss::imbalance_factor
double imbalance_factor(int k, const int *hist)
same, takes a histogram as input
Definition: utils.cpp:1432
faiss::fvec_norm_L2sqr
float fvec_norm_L2sqr(const float *x, size_t d)
Definition: utils.cpp:511
faiss::range_search_L2sqr
void range_search_L2sqr(const float *x, const float *y, size_t d, size_t nx, size_t ny, float radius, RangeSearchResult *res)
Definition: utils.cpp:1151
faiss::matrix_qr
void matrix_qr(int m, int n, float *a)
Definition: utils.cpp:1206
faiss::RangeSearchResult
Definition: AuxIndexStructures.h:35
faiss::ivec_checksum
size_t ivec_checksum(size_t n, const int *a)
compute a checksum on a table.
Definition: utils.cpp:1490
faiss::BaseShiftDistanceCorrection
Definition: utils.cpp:863
faiss::fvec_madd_and_argmin
int fvec_madd_and_argmin(size_t n, const float *a, float bf, const float *b, float *c)
Definition: utils.cpp:1781
faiss::knn_L2sqr
void knn_L2sqr(const float *x, const float *y, size_t d, size_t nx, size_t ny, float_maxheap_array_t *res)
Definition: utils.cpp:850