666 lines
19 KiB
C++
666 lines
19 KiB
C++
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/**
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* Copyright (c) 2015-present, Facebook, Inc.
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* All rights reserved.
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*
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* This source code is licensed under the CC-by-NC license found in the
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* LICENSE file in the root directory of this source tree.
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*/
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/* Copyright 2004-present Facebook. All Rights Reserved.
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Index based on product quantiztion.
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*/
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#include "ProductQuantizer.h"
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#include <cstddef>
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#include <cstring>
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#include <cstdio>
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#include <algorithm>
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#include "FaissAssert.h"
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#include "VectorTransform.h"
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#include "IndexFlat.h"
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#include "utils.h"
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extern "C" {
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/* declare BLAS functions, see http://www.netlib.org/clapack/cblas/ */
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int sgemm_ (const char *transa, const char *transb, FINTEGER *m, FINTEGER *
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n, FINTEGER *k, const float *alpha, const float *a,
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FINTEGER *lda, const float *b, FINTEGER *
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ldb, float *beta, float *c, FINTEGER *ldc);
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}
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namespace faiss {
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/* compute an estimator using look-up tables for typical values of M */
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template <typename CT, class C>
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void pq_estimators_from_tables_Mmul4 (int M, const CT * codes,
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size_t ncodes,
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const float * __restrict dis_table,
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size_t ksub,
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size_t k,
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float * heap_dis,
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long * heap_ids)
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{
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for (size_t j = 0; j < ncodes; j++) {
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float dis = 0;
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const float *dt = dis_table;
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for (size_t m = 0; m < M; m+=4) {
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float dism = 0;
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dism = dt[*codes++]; dt += ksub;
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dism += dt[*codes++]; dt += ksub;
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dism += dt[*codes++]; dt += ksub;
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dism += dt[*codes++]; dt += ksub;
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dis += dism;
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}
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if (C::cmp (heap_dis[0], dis)) {
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heap_pop<C> (k, heap_dis, heap_ids);
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heap_push<C> (k, heap_dis, heap_ids, dis, j);
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}
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}
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}
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template <typename CT, class C>
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void pq_estimators_from_tables_M4 (const CT * codes,
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size_t ncodes,
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const float * __restrict dis_table,
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size_t ksub,
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size_t k,
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float * heap_dis,
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long * heap_ids)
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{
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for (size_t j = 0; j < ncodes; j++) {
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float dis = 0;
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const float *dt = dis_table;
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dis = dt[*codes++]; dt += ksub;
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dis += dt[*codes++]; dt += ksub;
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dis += dt[*codes++]; dt += ksub;
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dis += dt[*codes++];
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if (C::cmp (heap_dis[0], dis)) {
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heap_pop<C> (k, heap_dis, heap_ids);
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heap_push<C> (k, heap_dis, heap_ids, dis, j);
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}
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}
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}
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template <typename CT, class C>
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static inline void pq_estimators_from_tables (const ProductQuantizer * pq,
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const CT * codes,
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size_t ncodes,
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const float * dis_table,
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size_t k,
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float * heap_dis,
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long * heap_ids)
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{
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if (pq->M == 4) {
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pq_estimators_from_tables_M4<CT, C> (codes, ncodes,
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dis_table, pq->ksub, k,
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heap_dis, heap_ids);
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return;
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}
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if (pq->M % 4 == 0) {
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pq_estimators_from_tables_Mmul4<CT, C> (pq->M, codes, ncodes,
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dis_table, pq->ksub, k,
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heap_dis, heap_ids);
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return;
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}
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/* Default is relatively slow */
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const size_t M = pq->M;
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const size_t ksub = pq->ksub;
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for (size_t j = 0; j < ncodes; j++) {
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float dis = 0;
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const float * __restrict dt = dis_table;
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for (int m = 0; m < M; m++) {
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dis += dt[*codes++];
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dt += ksub;
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}
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if (C::cmp (heap_dis[0], dis)) {
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heap_pop<C> (k, heap_dis, heap_ids);
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heap_push<C> (k, heap_dis, heap_ids, dis, j);
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}
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}
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}
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/*********************************************
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* PQ implementation
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*********************************************/
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ProductQuantizer::ProductQuantizer (size_t d, size_t M, size_t nbits):
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d(d), M(M), nbits(nbits)
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{
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set_derived_values ();
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}
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ProductQuantizer::ProductQuantizer ():
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d(0), M(1), nbits(0)
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{
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set_derived_values ();
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}
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void ProductQuantizer::set_derived_values () {
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// quite a few derived values
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FAISS_ASSERT (d % M == 0);
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dsub = d / M;
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byte_per_idx = (nbits + 7) / 8;
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code_size = byte_per_idx * M;
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ksub = 1 << nbits;
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centroids.resize (d * ksub);
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verbose = false;
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train_type = Train_default;
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}
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void ProductQuantizer::set_params (const float * centroids_, int m)
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{
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memcpy (get_centroids(m, 0), centroids_,
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ksub * dsub * sizeof (centroids_[0]));
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}
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static void init_hypercube (int d, int nbits,
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int n, const float * x,
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float *centroids)
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{
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std::vector<float> mean (d);
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for (int i = 0; i < n; i++)
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for (int j = 0; j < d; j++)
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mean [j] += x[i * d + j];
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float maxm = 0;
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for (int j = 0; j < d; j++) {
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mean [j] /= n;
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if (fabs(mean[j]) > maxm) maxm = fabs(mean[j]);
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}
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for (int i = 0; i < (1 << nbits); i++) {
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float * cent = centroids + i * d;
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for (int j = 0; j < nbits; j++)
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cent[j] = mean [j] + (((i >> j) & 1) ? 1 : -1) * maxm;
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for (int j = nbits; j < d; j++)
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cent[j] = mean [j];
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}
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}
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static void init_hypercube_pca (int d, int nbits,
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int n, const float * x,
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float *centroids)
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{
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PCAMatrix pca (d, nbits);
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pca.train (n, x);
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for (int i = 0; i < (1 << nbits); i++) {
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float * cent = centroids + i * d;
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for (int j = 0; j < d; j++) {
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cent[j] = pca.mean[j];
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float f = 1.0;
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for (int k = 0; k < nbits; k++)
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cent[j] += f *
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sqrt (pca.eigenvalues [k]) *
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(((i >> k) & 1) ? 1 : -1) *
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pca.PCAMat [j + k * d];
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}
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}
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}
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void ProductQuantizer::train (int n, const float * x)
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{
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if (train_type != Train_shared) {
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train_type_t final_train_type;
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final_train_type = train_type;
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if (train_type == Train_hypercube ||
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train_type == Train_hypercube_pca) {
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if (dsub < nbits) {
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final_train_type = Train_default;
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printf ("cannot train hypercube: nbits=%ld > log2(d=%ld)\n",
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nbits, dsub);
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}
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}
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float * xslice = new float[n * dsub];
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for (int m = 0; m < M; m++) {
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for (int j = 0; j < n; j++)
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memcpy (xslice + j * dsub,
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x + j * d + m * dsub,
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dsub * sizeof(float));
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Clustering clus (dsub, ksub, cp);
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// we have some initialization for the centroids
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if (final_train_type != Train_default) {
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clus.centroids.resize (dsub * ksub);
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}
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switch (final_train_type) {
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case Train_hypercube:
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init_hypercube (dsub, nbits, n, xslice,
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clus.centroids.data ());
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break;
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case Train_hypercube_pca:
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init_hypercube_pca (dsub, nbits, n, xslice,
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clus.centroids.data ());
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break;
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case Train_hot_start:
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memcpy (clus.centroids.data(),
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get_centroids (m, 0),
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dsub * ksub * sizeof (float));
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break;
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default: ;
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}
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if(verbose) {
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clus.verbose = true;
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printf ("Training PQ slice %d/%zd\n", m, M);
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}
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IndexFlatL2 index (dsub);
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clus.train (n, xslice, index);
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set_params (clus.centroids.data(), m);
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}
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delete [] xslice;
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} else {
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Clustering clus (dsub, ksub, cp);
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if(verbose) {
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clus.verbose = true;
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printf ("Training all PQ slices at once\n");
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}
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IndexFlatL2 index (dsub);
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clus.train (n * M, x, index);
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for (int m = 0; m < M; m++) {
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set_params (clus.centroids.data(), m);
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}
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}
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}
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void ProductQuantizer::compute_code (const float * x, uint8_t * code) const
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{
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float distances [ksub];
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for (size_t m = 0; m < M; m++) {
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float mindis = 1e20;
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int idxm = -1;
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const float * xsub = x + m * dsub;
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fvec_L2sqr_ny (distances, xsub, get_centroids(m, 0), dsub, ksub);
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/* Find best centroid */
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size_t i;
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for (i = 0; i < ksub; i++) {
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float dis = distances [i];
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if (dis < mindis) {
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mindis = dis;
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idxm = i;
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}
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}
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switch (byte_per_idx) {
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case 1: code[m] = (uint8_t) idxm; break;
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case 2: ((uint16_t *) code)[m] = (uint16_t) idxm; break;
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}
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}
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}
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void ProductQuantizer::decode (const uint8_t *code, float *x) const
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{
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if (byte_per_idx == 1) {
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for (size_t m = 0; m < M; m++) {
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memcpy (x + m * dsub, get_centroids(m, code[m]),
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sizeof(float) * dsub);
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}
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} else {
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const uint16_t *c = (const uint16_t*) code;
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for (size_t m = 0; m < M; m++) {
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memcpy (x + m * dsub, get_centroids(m, c[m]),
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sizeof(float) * dsub);
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}
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}
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}
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void ProductQuantizer::decode (const uint8_t *code, float *x, size_t n) const
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{
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for (size_t i = 0; i < n; i++) {
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this->decode (code + M * i, x + d * i);
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}
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}
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void ProductQuantizer::compute_code_from_distance_table (const float *tab,
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uint8_t *code) const
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{
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for (size_t m = 0; m < M; m++) {
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float mindis = 1e20;
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int idxm = -1;
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/* Find best centroid */
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for (size_t j = 0; j < ksub; j++) {
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float dis = *tab++;
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if (dis < mindis) {
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mindis = dis;
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idxm = j;
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}
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}
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switch (byte_per_idx) {
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case 1: code[m] = (uint8_t) idxm; break;
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case 2: ((uint16_t *) code)[m] = (uint16_t) idxm; break;
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}
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}
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}
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void ProductQuantizer::compute_codes (const float * x,
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uint8_t * codes,
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size_t n) const
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{
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if (dsub < 16) { // simple direct computation
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#pragma omp parallel for
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for (size_t i = 0; i < n; i++)
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compute_code (x + i * d, codes + i * code_size);
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} else { // worthwile to use BLAS
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float *dis_tables = new float [n * ksub * M];
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compute_distance_tables (n, x, dis_tables);
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#pragma omp parallel for
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for (size_t i = 0; i < n; i++) {
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uint8_t * code = codes + i * code_size;
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const float * tab = dis_tables + i * ksub * M;
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compute_code_from_distance_table (tab, code);
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}
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delete [] dis_tables;
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}
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}
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void ProductQuantizer::compute_distance_table (const float * x,
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float * dis_table) const
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{
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size_t m;
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for (m = 0; m < M; m++) {
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fvec_L2sqr_ny (dis_table + m * ksub,
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x + m * dsub,
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get_centroids(m, 0),
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dsub,
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ksub);
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}
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}
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void ProductQuantizer::compute_inner_prod_table (const float * x,
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float * dis_table) const
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{
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size_t m;
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for (m = 0; m < M; m++) {
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fvec_inner_products_ny (dis_table + m * ksub,
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x + m * dsub,
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get_centroids(m, 0),
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dsub,
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ksub);
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}
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}
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void ProductQuantizer::compute_distance_tables (
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size_t nx,
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const float * x,
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float * dis_tables) const
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{
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if (dsub < 16) {
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#pragma omp parallel for
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for (size_t i = 0; i < nx; i++) {
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compute_distance_table (x + i * d, dis_tables + i * ksub * M);
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}
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} else { // use BLAS
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for (int m = 0; m < M; m++) {
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pairwise_L2sqr (dsub,
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nx, x + dsub * m,
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ksub, centroids.data() + m * dsub * ksub,
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dis_tables + ksub * m,
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d, dsub, ksub * M);
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}
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}
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}
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void ProductQuantizer::compute_inner_prod_tables (
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size_t nx,
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const float * x,
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float * dis_tables) const
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{
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if (dsub < 16) {
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#pragma omp parallel for
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for (size_t i = 0; i < nx; i++) {
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compute_inner_prod_table (x + i * d, dis_tables + i * ksub * M);
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}
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} else { // use BLAS
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// compute distance tables
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for (int m = 0; m < M; m++) {
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FINTEGER ldc = ksub * M, nxi = nx, ksubi = ksub,
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dsubi = dsub, di = d;
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float one = 1.0, zero = 0;
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sgemm_ ("Transposed", "Not transposed",
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&ksubi, &nxi, &dsubi,
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&one, ¢roids [m * dsub * ksub], &dsubi,
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x + dsub * m, &di,
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&zero, dis_tables + ksub * m, &ldc);
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}
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}
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}
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template <typename CT, class C>
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static void pq_knn_search_with_tables (
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const ProductQuantizer * pq,
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const float *dis_tables,
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const uint8_t * codes,
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const size_t ncodes,
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HeapArray<C> * res,
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bool init_finalize_heap)
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{
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size_t k = res->k, nx = res->nh;
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size_t ksub = pq->ksub, M = pq->M;
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#pragma omp parallel for
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for (size_t i = 0; i < nx; i++) {
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/* query preparation for asymmetric search: compute look-up tables */
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const float* dis_table = dis_tables + i * ksub * M;
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/* Compute distances and keep smallest values */
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long * __restrict heap_ids = res->ids + i * k;
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float * __restrict heap_dis = res->val + i * k;
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if (init_finalize_heap) {
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heap_heapify<C> (k, heap_dis, heap_ids);
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}
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pq_estimators_from_tables<CT, C> (pq,
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(CT*)codes, ncodes,
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dis_table,
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k, heap_dis, heap_ids);
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if (init_finalize_heap) {
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heap_reorder<C> (k, heap_dis, heap_ids);
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}
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}
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}
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/*
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static inline void pq_estimators_from_tables (const ProductQuantizer * pq,
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const CT * codes,
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size_t ncodes,
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const float * dis_table,
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size_t k,
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float * heap_dis,
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long * heap_ids)
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*/
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void ProductQuantizer::search (const float * __restrict x,
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size_t nx,
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const uint8_t * codes,
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const size_t ncodes,
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float_maxheap_array_t * res,
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bool init_finalize_heap) const
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{
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float * dis_tables = new float [nx * ksub * M];
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compute_distance_tables (nx, x, dis_tables);
|
|
FAISS_ASSERT(nx == res->nh);
|
|
|
|
if (byte_per_idx == 1) {
|
|
|
|
pq_knn_search_with_tables<uint8_t, CMax<float, long> > (
|
|
this, dis_tables, codes, ncodes, res, init_finalize_heap);
|
|
|
|
} else if (byte_per_idx == 2) {
|
|
pq_knn_search_with_tables<uint16_t, CMax<float, long> > (
|
|
this, dis_tables, codes, ncodes, res, init_finalize_heap);
|
|
|
|
}
|
|
delete [] dis_tables;
|
|
}
|
|
|
|
void ProductQuantizer::search_ip (const float * __restrict x,
|
|
size_t nx,
|
|
const uint8_t * codes,
|
|
const size_t ncodes,
|
|
float_minheap_array_t * res,
|
|
bool init_finalize_heap) const
|
|
{
|
|
float * dis_tables = new float [nx * ksub * M];
|
|
compute_inner_prod_tables (nx, x, dis_tables);
|
|
FAISS_ASSERT(nx == res->nh);
|
|
|
|
if (byte_per_idx == 1) {
|
|
|
|
pq_knn_search_with_tables<uint8_t, CMin<float, long> > (
|
|
this, dis_tables, codes, ncodes, res, init_finalize_heap);
|
|
|
|
} else if (byte_per_idx == 2) {
|
|
pq_knn_search_with_tables<uint16_t, CMin<float, long> > (
|
|
this, dis_tables, codes, ncodes, res, init_finalize_heap);
|
|
}
|
|
delete [] dis_tables;
|
|
}
|
|
|
|
|
|
|
|
static float sqr (float x) {
|
|
return x * x;
|
|
}
|
|
|
|
void ProductQuantizer::compute_sdc_table ()
|
|
{
|
|
sdc_table.resize (M * ksub * ksub);
|
|
|
|
for (int m = 0; m < M; m++) {
|
|
|
|
const float *cents = centroids.data() + m * ksub * dsub;
|
|
float * dis_tab = sdc_table.data() + m * ksub * ksub;
|
|
|
|
// TODO optimize with BLAS
|
|
for (int i = 0; i < ksub; i++) {
|
|
const float *centi = cents + i * dsub;
|
|
for (int j = 0; j < ksub; j++) {
|
|
float accu = 0;
|
|
const float *centj = cents + j * dsub;
|
|
for (int k = 0; k < dsub; k++)
|
|
accu += sqr (centi[k] - centj[k]);
|
|
dis_tab [i + j * ksub] = accu;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
void ProductQuantizer::search_sdc (const uint8_t * qcodes,
|
|
size_t nq,
|
|
const uint8_t * bcodes,
|
|
const size_t nb,
|
|
float_maxheap_array_t * res,
|
|
bool init_finalize_heap) const
|
|
{
|
|
FAISS_ASSERT (sdc_table.size() == M * ksub * ksub);
|
|
size_t k = res->k;
|
|
|
|
FAISS_ASSERT (byte_per_idx == 1);
|
|
|
|
#pragma omp parallel for
|
|
for (size_t i = 0; i < nq; i++) {
|
|
|
|
/* Compute distances and keep smallest values */
|
|
long * heap_ids = res->ids + i * k;
|
|
float * heap_dis = res->val + i * k;
|
|
const uint8_t * qcode = qcodes + i * code_size;
|
|
|
|
if (init_finalize_heap)
|
|
maxheap_heapify (k, heap_dis, heap_ids);
|
|
|
|
const uint8_t * bcode = bcodes;
|
|
for (size_t j = 0; j < nb; j++) {
|
|
float dis = 0;
|
|
const float * tab = sdc_table.data();
|
|
for (int m = 0; m < M; m++) {
|
|
dis += tab[bcode[m] + qcode[m] * ksub];
|
|
tab += ksub * ksub;
|
|
}
|
|
if (dis < heap_dis[0]) {
|
|
maxheap_pop (k, heap_dis, heap_ids);
|
|
maxheap_push (k, heap_dis, heap_ids, dis, j);
|
|
}
|
|
bcode += code_size;
|
|
}
|
|
|
|
if (init_finalize_heap)
|
|
maxheap_reorder (k, heap_dis, heap_ids);
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
} // namespace faiss
|