utils_simd.cpp 16.3 KB
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687
/**
 * Copyright (c) 2015-present, Facebook, Inc.
 * All rights reserved.
 *
 * This source code is licensed under the BSD+Patents license found in the
 * LICENSE file in the root directory of this source tree.
 */

// -*- c++ -*-

#include "utils.h"

#include <cstdio>
#include <cassert>
#include <cstring>
#include <cmath>

#ifdef __SSE__
#include <immintrin.h>
#endif

#ifdef __aarch64__
#include  <arm_neon.h>
#endif

#include <omp.h>



/**************************************************
 * Get some stats about the system
 **************************************************/

namespace faiss {

#ifdef __AVX__
#define USE_AVX
#endif


/*********************************************************
 * Optimized distance computations
 *********************************************************/


/* Functions to compute:
   - L2 distance between 2 vectors
   - inner product between 2 vectors
   - L2 norm of a vector

   The functions should probably not be invoked when a large number of
   vectors are be processed in batch (in which case Matrix multiply
   is faster), but may be useful for comparing vectors isolated in
   memory.

   Works with any vectors of any dimension, even unaligned (in which
   case they are slower).

*/


/*********************************************************
 * Reference implementations
 */

/* same without SSE */
float fvec_L2sqr_ref (const float * x,
                     const float * y,
                     size_t d)
{
    size_t i;
    float res = 0;
    for (i = 0; i < d; i++) {
        const float tmp = x[i] - y[i];
       res += tmp * tmp;
    }
    return res;
}

float fvec_inner_product_ref (const float * x,
                             const float * y,
                             size_t d)
{
    size_t i;
    float res = 0;
    for (i = 0; i < d; i++)
       res += x[i] * y[i];
    return res;
}

float fvec_norm_L2sqr_ref (const float *x, size_t d)
{
    size_t i;
    double res = 0;
    for (i = 0; i < d; i++)
       res += x[i] * x[i];
    return res;
}


void fvec_L2sqr_ny_ref (float * dis,
                    const float * x,
                    const float * y,
                    size_t d, size_t ny)
{
    for (size_t i = 0; i < ny; i++) {
        dis[i] = fvec_L2sqr (x, y, d);
        y += d;
    }
}




/*********************************************************
 * SSE and AVX implementations
 */

#ifdef __SSE__

// reads 0 <= d < 4 floats as __m128
static inline __m128 masked_read (int d, const float *x)
{
    assert (0 <= d && d < 4);
    __attribute__((__aligned__(16))) float buf[4] = {0, 0, 0, 0};
    switch (d) {
      case 3:
        buf[2] = x[2];
      case 2:
        buf[1] = x[1];
      case 1:
        buf[0] = x[0];
    }
    return _mm_load_ps (buf);
    // cannot use AVX2 _mm_mask_set1_epi32
}

float fvec_norm_L2sqr (const float *  x,
                      size_t d)
{
    __m128 mx;
    __m128 msum1 = _mm_setzero_ps();

    while (d >= 4) {
        mx = _mm_loadu_ps (x); x += 4;
        msum1 = _mm_add_ps (msum1, _mm_mul_ps (mx, mx));
        d -= 4;
    }

    mx = masked_read (d, x);
    msum1 = _mm_add_ps (msum1, _mm_mul_ps (mx, mx));

    msum1 = _mm_hadd_ps (msum1, msum1);
    msum1 = _mm_hadd_ps (msum1, msum1);
    return  _mm_cvtss_f32 (msum1);
}

namespace {

float sqr (float x) {
    return x * x;
}


void fvec_L2sqr_ny_D1 (float * dis, const float * x,
                       const float * y, size_t ny)
{
    float x0s = x[0];
    __m128 x0 = _mm_set_ps (x0s, x0s, x0s, x0s);

    size_t i;
    for (i = 0; i + 3 < ny; i += 4) {
        __m128 tmp, accu;
        tmp = x0 - _mm_loadu_ps (y); y += 4;
        accu = tmp * tmp;
        dis[i] = _mm_cvtss_f32 (accu);
        tmp = _mm_shuffle_ps (accu, accu, 1);
        dis[i + 1] = _mm_cvtss_f32 (tmp);
        tmp = _mm_shuffle_ps (accu, accu, 2);
        dis[i + 2] = _mm_cvtss_f32 (tmp);
        tmp = _mm_shuffle_ps (accu, accu, 3);
        dis[i + 3] = _mm_cvtss_f32 (tmp);
    }
    while (i < ny) { // handle non-multiple-of-4 case
        dis[i++] = sqr(x0s - *y++);
    }
}


void fvec_L2sqr_ny_D2 (float * dis, const float * x,
                       const float * y, size_t ny)
{
    __m128 x0 = _mm_set_ps (x[1], x[0], x[1], x[0]);

    size_t i;
    for (i = 0; i + 1 < ny; i += 2) {
        __m128 tmp, accu;
        tmp = x0 - _mm_loadu_ps (y); y += 4;
        accu = tmp * tmp;
        accu = _mm_hadd_ps (accu, accu);
        dis[i] = _mm_cvtss_f32 (accu);
        accu = _mm_shuffle_ps (accu, accu, 3);
        dis[i + 1] = _mm_cvtss_f32 (accu);
    }
    if (i < ny) { // handle odd case
        dis[i] = sqr(x[0] - y[0]) + sqr(x[1] - y[1]);
    }
}



void fvec_L2sqr_ny_D4 (float * dis, const float * x,
                        const float * y, size_t ny)
{
    __m128 x0 = _mm_loadu_ps(x);

    for (size_t i = 0; i < ny; i++) {
        __m128 tmp, accu;
        tmp = x0 - _mm_loadu_ps (y); y += 4;
        accu = tmp * tmp;
        accu = _mm_hadd_ps (accu, accu);
        accu = _mm_hadd_ps (accu, accu);
        dis[i] = _mm_cvtss_f32 (accu);
    }
}


void fvec_L2sqr_ny_D8 (float * dis, const float * x,
                        const float * y, size_t ny)
{
    __m128 x0 = _mm_loadu_ps(x);
    __m128 x1 = _mm_loadu_ps(x + 4);

    for (size_t i = 0; i < ny; i++) {
        __m128 tmp, accu;
        tmp = x0 - _mm_loadu_ps (y); y += 4;
        accu = tmp * tmp;
        tmp = x1 - _mm_loadu_ps (y); y += 4;
        accu += tmp * tmp;
        accu = _mm_hadd_ps (accu, accu);
        accu = _mm_hadd_ps (accu, accu);
        dis[i] = _mm_cvtss_f32 (accu);
    }
}


void fvec_L2sqr_ny_D12 (float * dis, const float * x,
                        const float * y, size_t ny)
{
    __m128 x0 = _mm_loadu_ps(x);
    __m128 x1 = _mm_loadu_ps(x + 4);
    __m128 x2 = _mm_loadu_ps(x + 8);

    for (size_t i = 0; i < ny; i++) {
        __m128 tmp, accu;
        tmp = x0 - _mm_loadu_ps (y); y += 4;
        accu = tmp * tmp;
        tmp = x1 - _mm_loadu_ps (y); y += 4;
        accu += tmp * tmp;
        tmp = x2 - _mm_loadu_ps (y); y += 4;
        accu += tmp * tmp;
        accu = _mm_hadd_ps (accu, accu);
        accu = _mm_hadd_ps (accu, accu);
        dis[i] = _mm_cvtss_f32 (accu);
    }
}


} // anonymous namespace

void fvec_L2sqr_ny (float * dis, const float * x,
                        const float * y, size_t d, size_t ny) {
    // optimized for a few special cases
    switch(d) {
    case 1:
        fvec_L2sqr_ny_D1 (dis, x, y, ny);
        return;
    case 2:
        fvec_L2sqr_ny_D2 (dis, x, y, ny);
        return;
    case 4:
        fvec_L2sqr_ny_D4 (dis, x, y, ny);
        return;
    case 8:
        fvec_L2sqr_ny_D8 (dis, x, y, ny);
        return;
    case 12:
        fvec_L2sqr_ny_D12 (dis, x, y, ny);
        return;
    default:
        fvec_L2sqr_ny_ref (dis, x, y, d, ny);
        return;
    }
}



#endif

#ifdef USE_AVX

// reads 0 <= d < 8 floats as __m256
static inline __m256 masked_read_8 (int d, const float *x)
{
    assert (0 <= d && d < 8);
    if (d < 4) {
        __m256 res = _mm256_setzero_ps ();
        res = _mm256_insertf128_ps (res, masked_read (d, x), 0);
        return res;
    } else {
        __m256 res = _mm256_setzero_ps ();
        res = _mm256_insertf128_ps (res, _mm_loadu_ps (x), 0);
        res = _mm256_insertf128_ps (res, masked_read (d - 4, x + 4), 1);
        return res;
    }
}

float fvec_inner_product (const float * x,
                          const float * y,
                          size_t d)
{
    __m256 msum1 = _mm256_setzero_ps();

    while (d >= 8) {
        __m256 mx = _mm256_loadu_ps (x); x += 8;
        __m256 my = _mm256_loadu_ps (y); y += 8;
        msum1 = _mm256_add_ps (msum1, _mm256_mul_ps (mx, my));
        d -= 8;
    }

    __m128 msum2 = _mm256_extractf128_ps(msum1, 1);
    msum2 +=       _mm256_extractf128_ps(msum1, 0);

    if (d >= 4) {
        __m128 mx = _mm_loadu_ps (x); x += 4;
        __m128 my = _mm_loadu_ps (y); y += 4;
        msum2 = _mm_add_ps (msum2, _mm_mul_ps (mx, my));
        d -= 4;
    }

    if (d > 0) {
        __m128 mx = masked_read (d, x);
        __m128 my = masked_read (d, y);
        msum2 = _mm_add_ps (msum2, _mm_mul_ps (mx, my));
    }

    msum2 = _mm_hadd_ps (msum2, msum2);
    msum2 = _mm_hadd_ps (msum2, msum2);
    return  _mm_cvtss_f32 (msum2);
}

float fvec_L2sqr (const float * x,
                 const float * y,
                 size_t d)
{
    __m256 msum1 = _mm256_setzero_ps();

    while (d >= 8) {
        __m256 mx = _mm256_loadu_ps (x); x += 8;
        __m256 my = _mm256_loadu_ps (y); y += 8;
        const __m256 a_m_b1 = mx - my;
        msum1 += a_m_b1 * a_m_b1;
        d -= 8;
    }

    __m128 msum2 = _mm256_extractf128_ps(msum1, 1);
    msum2 +=       _mm256_extractf128_ps(msum1, 0);

    if (d >= 4) {
        __m128 mx = _mm_loadu_ps (x); x += 4;
        __m128 my = _mm_loadu_ps (y); y += 4;
        const __m128 a_m_b1 = mx - my;
        msum2 += a_m_b1 * a_m_b1;
        d -= 4;
    }

    if (d > 0) {
        __m128 mx = masked_read (d, x);
        __m128 my = masked_read (d, y);
        __m128 a_m_b1 = mx - my;
        msum2 += a_m_b1 * a_m_b1;
    }

    msum2 = _mm_hadd_ps (msum2, msum2);
    msum2 = _mm_hadd_ps (msum2, msum2);
    return  _mm_cvtss_f32 (msum2);
}

#elif defined(__SSE__)

/* SSE-implementation of L2 distance */
float fvec_L2sqr (const float * x,
                 const float * y,
                 size_t d)
{
    __m128 msum1 = _mm_setzero_ps();

    while (d >= 4) {
        __m128 mx = _mm_loadu_ps (x); x += 4;
        __m128 my = _mm_loadu_ps (y); y += 4;
        const __m128 a_m_b1 = mx - my;
        msum1 += a_m_b1 * a_m_b1;
        d -= 4;
    }

    if (d > 0) {
        // add the last 1, 2 or 3 values
        __m128 mx = masked_read (d, x);
        __m128 my = masked_read (d, y);
        __m128 a_m_b1 = mx - my;
        msum1 += a_m_b1 * a_m_b1;
    }

    msum1 = _mm_hadd_ps (msum1, msum1);
    msum1 = _mm_hadd_ps (msum1, msum1);
    return  _mm_cvtss_f32 (msum1);
}


float fvec_inner_product (const float * x,
                         const float * y,
                         size_t d)
{
    __m128 mx, my;
    __m128 msum1 = _mm_setzero_ps();

    while (d >= 4) {
        mx = _mm_loadu_ps (x); x += 4;
        my = _mm_loadu_ps (y); y += 4;
        msum1 = _mm_add_ps (msum1, _mm_mul_ps (mx, my));
        d -= 4;
    }

    // add the last 1, 2, or 3 values
    mx = masked_read (d, x);
    my = masked_read (d, y);
    __m128 prod = _mm_mul_ps (mx, my);

    msum1 = _mm_add_ps (msum1, prod);

    msum1 = _mm_hadd_ps (msum1, msum1);
    msum1 = _mm_hadd_ps (msum1, msum1);
    return  _mm_cvtss_f32 (msum1);
}

#elif defined(__aarch64__)


float fvec_L2sqr (const float * x,
                  const float * y,
                  size_t d)
{
    if (d & 3) return fvec_L2sqr_ref (x, y, d);
    float32x4_t accu = vdupq_n_f32 (0);
    for (size_t i = 0; i < d; i += 4) {
        float32x4_t xi = vld1q_f32 (x + i);
        float32x4_t yi = vld1q_f32 (y + i);
        float32x4_t sq = vsubq_f32 (xi, yi);
        accu = vfmaq_f32 (accu, sq, sq);
    }
    float32x4_t a2 = vpaddq_f32 (accu, accu);
    return vdups_laneq_f32 (a2, 0) + vdups_laneq_f32 (a2, 1);
}

float fvec_inner_product (const float * x,
                          const float * y,
                          size_t d)
{
    if (d & 3) return fvec_inner_product_ref (x, y, d);
    float32x4_t accu = vdupq_n_f32 (0);
    for (size_t i = 0; i < d; i += 4) {
        float32x4_t xi = vld1q_f32 (x + i);
        float32x4_t yi = vld1q_f32 (y + i);
        accu = vfmaq_f32 (accu, xi, yi);
    }
    float32x4_t a2 = vpaddq_f32 (accu, accu);
    return vdups_laneq_f32 (a2, 0) + vdups_laneq_f32 (a2, 1);
}

float fvec_norm_L2sqr (const float *x, size_t d)
{
    if (d & 3) return fvec_norm_L2sqr_ref (x, d);
    float32x4_t accu = vdupq_n_f32 (0);
    for (size_t i = 0; i < d; i += 4) {
        float32x4_t xi = vld1q_f32 (x + i);
        accu = vfmaq_f32 (accu, xi, xi);
    }
    float32x4_t a2 = vpaddq_f32 (accu, accu);
    return vdups_laneq_f32 (a2, 0) + vdups_laneq_f32 (a2, 1);
}

// not optimized for ARM
void fvec_L2sqr_ny (float * dis, const float * x,
                        const float * y, size_t d, size_t ny) {
    fvec_L2sqr_ny_ref (dis, x, y, d, ny);
}


#else
// scalar implementation

float fvec_L2sqr (const float * x,
                  const float * y,
                  size_t d)
{
    return fvec_L2sqr_ref (x, y, d);
}

float fvec_inner_product (const float * x,
                             const float * y,
                             size_t d)
{
    return fvec_inner_product_ref (x, y, d);
}

float fvec_norm_L2sqr (const float *x, size_t d)
{
    return fvec_norm_L2sqr_ref (x, d);
}

void fvec_L2sqr_ny (float * dis, const float * x,
                        const float * y, size_t d, size_t ny) {
    fvec_L2sqr_ny_ref (dis, x, y, d, ny);
}


#endif




















/***************************************************************************
 * heavily optimized table computations
 ***************************************************************************/


static inline void fvec_madd_ref (size_t n, const float *a,
                           float bf, const float *b, float *c) {
    for (size_t i = 0; i < n; i++)
        c[i] = a[i] + bf * b[i];
}

#ifdef __SSE__

static inline void fvec_madd_sse (size_t n, const float *a,
                                  float bf, const float *b, float *c) {
    n >>= 2;
    __m128 bf4 = _mm_set_ps1 (bf);
    __m128 * a4 = (__m128*)a;
    __m128 * b4 = (__m128*)b;
    __m128 * c4 = (__m128*)c;

    while (n--) {
        *c4 = _mm_add_ps (*a4, _mm_mul_ps (bf4, *b4));
        b4++;
        a4++;
        c4++;
    }
}

void fvec_madd (size_t n, const float *a,
                float bf, const float *b, float *c)
{
    if ((n & 3) == 0 &&
        ((((long)a) | ((long)b) | ((long)c)) & 15) == 0)
        fvec_madd_sse (n, a, bf, b, c);
    else
        fvec_madd_ref (n, a, bf, b, c);
}

#else

void fvec_madd (size_t n, const float *a,
                float bf, const float *b, float *c)
{
    fvec_madd_ref (n, a, bf, b, c);
}

#endif

static inline int fvec_madd_and_argmin_ref (size_t n, const float *a,
                                         float bf, const float *b, float *c) {
    float vmin = 1e20;
    int imin = -1;

    for (size_t i = 0; i < n; i++) {
        c[i] = a[i] + bf * b[i];
        if (c[i] < vmin) {
            vmin = c[i];
            imin = i;
        }
    }
    return imin;
}

#ifdef __SSE__

static inline int fvec_madd_and_argmin_sse (
        size_t n, const float *a,
        float bf, const float *b, float *c) {
    n >>= 2;
    __m128 bf4 = _mm_set_ps1 (bf);
    __m128 vmin4 = _mm_set_ps1 (1e20);
    __m128i imin4 = _mm_set1_epi32 (-1);
    __m128i idx4 = _mm_set_epi32 (3, 2, 1, 0);
    __m128i inc4 = _mm_set1_epi32 (4);
    __m128 * a4 = (__m128*)a;
    __m128 * b4 = (__m128*)b;
    __m128 * c4 = (__m128*)c;

    while (n--) {
        __m128 vc4 = _mm_add_ps (*a4, _mm_mul_ps (bf4, *b4));
        *c4 = vc4;
        __m128i mask = (__m128i)_mm_cmpgt_ps (vmin4, vc4);
        // imin4 = _mm_blendv_epi8 (imin4, idx4, mask); // slower!

        imin4 = _mm_or_si128 (_mm_and_si128 (mask, idx4),
                              _mm_andnot_si128 (mask, imin4));
        vmin4 = _mm_min_ps (vmin4, vc4);
        b4++;
        a4++;
        c4++;
        idx4 = _mm_add_epi32 (idx4, inc4);
    }

    // 4 values -> 2
    {
        idx4 = _mm_shuffle_epi32 (imin4, 3 << 2 | 2);
        __m128 vc4 = _mm_shuffle_ps (vmin4, vmin4, 3 << 2 | 2);
        __m128i mask = (__m128i)_mm_cmpgt_ps (vmin4, vc4);
        imin4 = _mm_or_si128 (_mm_and_si128 (mask, idx4),
                              _mm_andnot_si128 (mask, imin4));
        vmin4 = _mm_min_ps (vmin4, vc4);
    }
    // 2 values -> 1
    {
        idx4 = _mm_shuffle_epi32 (imin4, 1);
        __m128 vc4 = _mm_shuffle_ps (vmin4, vmin4, 1);
        __m128i mask = (__m128i)_mm_cmpgt_ps (vmin4, vc4);
        imin4 = _mm_or_si128 (_mm_and_si128 (mask, idx4),
                              _mm_andnot_si128 (mask, imin4));
        // vmin4 = _mm_min_ps (vmin4, vc4);
    }
    return _mm_cvtsi128_si32 (imin4);
}


int fvec_madd_and_argmin (size_t n, const float *a,
                          float bf, const float *b, float *c)
{
    if ((n & 3) == 0 &&
        ((((long)a) | ((long)b) | ((long)c)) & 15) == 0)
        return fvec_madd_and_argmin_sse (n, a, bf, b, c);
    else
        return fvec_madd_and_argmin_ref (n, a, bf, b, c);
}

#else

int fvec_madd_and_argmin (size_t n, const float *a,
                          float bf, const float *b, float *c)
{
  return fvec_madd_and_argmin_ref (n, a, bf, b, c);
}

#endif




} // namespace faiss