text: /* adler32_simd.c
   *
   * Copyright 2017 The Chromium Authors. All rights reserved.
   * Use of this source code is governed by a BSD-style license that can be
   * found in the Chromium source repository LICENSE file.
   *
   * Per http://en.wikipedia.org/wiki/Adler-32 the adler32 A value (aka s1) is
   * the sum of N input data bytes D1 ... DN,
   *
   *   A = A0 + D1 + D2 + ... + DN
   *
   * where A0 is the initial value.
   *
   * SSE2 _mm_sad_epu8() can be used for byte sums (see http://bit.ly/2wpUOeD,
   * for example) and accumulating the byte sums can use SSE shuffle-adds (see
   * the "Integer" section of http://bit.ly/2erPT8t for details). Arm NEON has
   * similar instructions.
   *
   * The adler32 B value (aka s2) sums the A values from each step:
   *
   *   B0 + (A0 + D1) + (A0 + D1 + D2) + ... + (A0 + D1 + D2 + ... + DN) or
   *
   *       B0 + N.A0 + N.D1 + (N-1).D2 + (N-2).D3 + ... + (N-(N-1)).DN
   *
   * B0 being the initial value. For 32 bytes (ideal for garden-variety SIMD):
   *
   *   B = B0 + 32.A0 + [D1 D2 D3 ... D32] x [32 31 30 ... 1].
   *
   * Adjacent blocks of 32 input bytes can be iterated with the expressions to
   * compute the adler32 s1 s2 of M >> 32 input bytes [1].
   *
   * As M grows, the s1 s2 sums grow. If left unchecked, they would eventually
   * overflow the precision of their integer representation (bad). However, s1
   * and s2 also need to be computed modulo the adler BASE value (reduced). If
   * at most NMAX bytes are processed before a reduce, s1 s2 _cannot_ overflow
   * a uint32_t type (the NMAX constraint) [2].
   *
   * [1] the iterative equations for s2 contain constant factors; these can be
   * hoisted from the n-blocks do loop of the SIMD code.
   *
   * [2] zlib adler32_z() uses this fact to implement NMAX-block-based updates
   * of the adler s1 s2 of uint32_t type (see adler32.c).
   */
  
  #include "adler32_simd.h"
  
  /* Definitions from adler32.c: largest prime smaller than 65536 */
  #define BASE 65521U
  /* NMAX is the largest n such that 255n(n+1)/2 + (n+1)(BASE-1) <= 2^32-1 */
  #define NMAX 5552
  
  #include <tmmintrin.h>
  
  uint32_t ZLIB_INTERNAL adler32_simd_(  /* SSSE3 */
      uint32_t adler,
      const unsigned char *buf,
      z_size_t len)
  {
      /* initial Adler-32 value */
      if (buf == Z_NULL)
          return 1L;
  
      /*
       * Split Adler-32 into component sums.
       */
      uint32_t s1 = adler & 0xffff;
      uint32_t s2 = adler >> 16;
  
      /*
       * Process the data in blocks.
       */
      const unsigned BLOCK_SIZE = 1 << 5;
  
      z_size_t blocks = len / BLOCK_SIZE;
      len -= blocks * BLOCK_SIZE;
  
      while (blocks)
      {
          unsigned n = NMAX / BLOCK_SIZE;  /* The NMAX constraint. */
          if (n > blocks)
              n = (unsigned) blocks;
          blocks -= n;
  
          const __m128i tap1 =
              _mm_setr_epi8(32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17);
          const __m128i tap2 =
              _mm_setr_epi8(16,15,14,13,12,11,10, 9, 8, 7, 6, 5, 4, 3, 2, 1);
          const __m128i zero =
              _mm_setr_epi8( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
          const __m128i ones =
              _mm_set_epi16( 1, 1, 1, 1, 1, 1, 1, 1);
  
          /*
           * Process n blocks of data. At most NMAX data bytes can be
           * processed before s2 must be reduced modulo BASE.
           */
          __m128i v_ps = _mm_set_epi32(0, 0, 0, s1 * n);
          __m128i v_s2 = _mm_set_epi32(0, 0, 0, s2);
          __m128i v_s1 = _mm_set_epi32(0, 0, 0, 0);
  
          do {
              /*
               * Load 32 input bytes.
               */
              const __m128i bytes1 = _mm_loadu_si128((__m128i*)(buf));
              const __m128i bytes2 = _mm_loadu_si128((__m128i*)(buf + 16));
  
              /*
               * Add previous block byte sum to v_ps.
               */
              v_ps = _mm_add_epi32(v_ps, v_s1);
  
              /*
               * Horizontally add the bytes for s1, multiply-adds the
               * bytes by [ 32, 31, 30, ... ] for s2.
               */
              v_s1 = _mm_add_epi32(v_s1, _mm_sad_epu8(bytes1, zero));
              const __m128i mad1 = _mm_maddubs_epi16(bytes1, tap1);
              v_s2 = _mm_add_epi32(v_s2, _mm_madd_epi16(mad1, ones));
  
              v_s1 = _mm_add_epi32(v_s1, _mm_sad_epu8(bytes2, zero));
              const __m128i mad2 = _mm_maddubs_epi16(bytes2, tap2);
              v_s2 = _mm_add_epi32(v_s2, _mm_madd_epi16(mad2, ones));
  
              buf += BLOCK_SIZE;
  
          } while (--n);
  
          v_s2 = _mm_add_epi32(v_s2, _mm_slli_epi32(v_ps, 5));
  
          /*
           * Sum epi32 ints v_s1(s2) and accumulate in s1(s2).
           */
  
  #define S23O1 _MM_SHUFFLE(2,3,0,1)  /* A B C D -> B A D C */
  #define S1O32 _MM_SHUFFLE(1,0,3,2)  /* A B C D -> C D A B */
  
          v_s1 = _mm_add_epi32(v_s1, _mm_shuffle_epi32(v_s1, S23O1));
          v_s1 = _mm_add_epi32(v_s1, _mm_shuffle_epi32(v_s1, S1O32));
  
          s1 += _mm_cvtsi128_si32(v_s1);
  
          v_s2 = _mm_add_epi32(v_s2, _mm_shuffle_epi32(v_s2, S23O1));
          v_s2 = _mm_add_epi32(v_s2, _mm_shuffle_epi32(v_s2, S1O32));
  
          s2 = _mm_cvtsi128_si32(v_s2);
  
  #undef S23O1
  #undef S1O32
  
          /*
           * Reduce.
           */
          s1 %= BASE;
          s2 %= BASE;
      }
  
      /*
       * Handle leftover data.
       */
      if (len) {
          if (len >= 16) {
              s2 += (s1 += *buf++);
              s2 += (s1 += *buf++);
              s2 += (s1 += *buf++);
              s2 += (s1 += *buf++);
  
              s2 += (s1 += *buf++);
              s2 += (s1 += *buf++);
              s2 += (s1 += *buf++);
              s2 += (s1 += *buf++);
  
              s2 += (s1 += *buf++);
              s2 += (s1 += *buf++);
              s2 += (s1 += *buf++);
              s2 += (s1 += *buf++);
  
              s2 += (s1 += *buf++);
              s2 += (s1 += *buf++);
              s2 += (s1 += *buf++);
              s2 += (s1 += *buf++);
  
              len -= 16;
          }
  
          while (len--) {
              s2 += (s1 += *buf++);
          }
  
          if (s1 >= BASE)
              s1 -= BASE;
          s2 %= BASE;
      }
  
      /*
       * Return the recombined sums.
       */
      return s1 | (s2 << 16);
  }
  