text: /* Adler32 for POWER8 using VSX instructions.
   * Copyright (C) 2020 IBM Corporation
   * Author: Rogerio Alves <rcardoso@linux.ibm.com>
   * For conditions of distribution and use, see copyright notice in zlib.h
   *
   * Calculate adler32 checksum for 16 bytes at once using POWER8+ VSX (vector)
   * instructions.
   *
   * If adler32 do 1 byte at time on the first iteration s1 is s1_0 (_n means
   * iteration n) is the initial value of adler - at start  _0 is 1 unless
   * adler initial value is different than 1. So s1_1 = s1_0 + c[0] after
   * the first calculation. For the iteration s1_2 = s1_1 + c[1] and so on.
   * Hence, for iteration N, s1_N = s1_(N-1) + c[N] is the value of s1 on
   * after iteration N.
   *
   * Therefore, for s2 and iteration N, s2_N = s2_0 + N*s1_N + N*c[0] +
   * N-1*c[1] + ... + c[N]
   *
   * In a more general way:
   *
   * s1_N = s1_0 + sum(i=1 to N)c[i]
   * s2_N = s2_0 + N*s1 + sum (i=1 to N)(N-i+1)*c[i]
   *
   * Where s1_N, s2_N are the values for s1, s2 after N iterations. So if we
   * can process N-bit at time we can do this at once.
   *
   * Since VSX can support 16-bit vector instructions, we can process
   * 16-bit at time using N = 16 we have:
   *
   * s1 = s1_16 = s1_(16-1) + c[16] = s1_0 + sum(i=1 to 16)c[i]
   * s2 = s2_16 = s2_0 + 16*s1 + sum(i=1 to 16)(16-i+1)*c[i]
   *
   * After the first iteration we calculate the adler32 checksum for 16 bytes.
   *
   * For more background about adler32 please check the RFC:
   * https://www.ietf.org/rfc/rfc1950.txt
   */
  
  #ifdef POWER8_VSX_ADLER32
  
  #include <altivec.h>
  #include "zbuild.h"
  #include "zutil.h"
  #include "adler32_p.h"
  
  /* Vector across sum unsigned int (saturate).  */
  inline vector unsigned int vec_sumsu(vector unsigned int __a, vector unsigned int __b) {
      __b = vec_sld(__a, __a, 8);
      __b = vec_add(__b, __a);
      __a = vec_sld(__b, __b, 4);
      __a = vec_add(__a, __b);
  
      return __a;
  }
  
  uint32_t adler32_power8(uint32_t adler, const unsigned char* buf, size_t len) {
      uint32_t s1 = adler & 0xffff;
      uint32_t s2 = (adler >> 16) & 0xffff;
  
      /* in case user likes doing a byte at a time, keep it fast */
      if (UNLIKELY(len == 1))
          return adler32_len_1(s1, buf, s2);
  
      /* If buffer is empty or len=0 we need to return adler initial value.  */
      if (UNLIKELY(buf == NULL))
          return 1;
  
      /* This is faster than VSX code for len < 64.  */
      if (len < 64)
          return adler32_len_64(s1, buf, len, s2);
  
      /* Use POWER VSX instructions for len >= 64. */
      const vector unsigned int v_zeros = { 0 };
      const vector unsigned char v_mul = {16, 15, 14, 13, 12, 11, 10, 9, 8, 7,
           6, 5, 4, 3, 2, 1};
      const vector unsigned char vsh = vec_splat_u8(4);
      const vector unsigned int vmask = {0xffffffff, 0x0, 0x0, 0x0};
      vector unsigned int vs1 = { 0 };
      vector unsigned int vs2 = { 0 };
      vector unsigned int vs1_save = { 0 };
      vector unsigned int vsum1, vsum2;
      vector unsigned char vbuf;
      int n;
  
      vs1[0] = s1;
      vs2[0] = s2;
  
      /* Do length bigger than NMAX in blocks of NMAX size.  */
      while (len >= NMAX) {
          len -= NMAX;
          n = NMAX / 16;
          do {
              vbuf = vec_xl(0, (unsigned char *) buf);
              vsum1 = vec_sum4s(vbuf, v_zeros); /* sum(i=1 to 16) buf[i].  */
              /* sum(i=1 to 16) buf[i]*(16-i+1).  */
              vsum2 = vec_msum(vbuf, v_mul, v_zeros);
              /* Save vs1.  */
              vs1_save = vec_add(vs1_save, vs1);
              /* Accumulate the sums.  */
              vs1 = vec_add(vsum1, vs1);
              vs2 = vec_add(vsum2, vs2);
  
              buf += 16;
          } while (--n);
          /* Once each block of NMAX size.  */
          vs1 = vec_sumsu(vs1, vsum1);
          vs1_save = vec_sll(vs1_save, vsh); /* 16*vs1_save.  */
          vs2 = vec_add(vs1_save, vs2);
          vs2 = vec_sumsu(vs2, vsum2);
  
          /* vs1[0] = (s1_i + sum(i=1 to 16)buf[i]) mod 65521.  */
          vs1[0] = vs1[0] % BASE;
          /* vs2[0] = s2_i + 16*s1_save +
             sum(i=1 to 16)(16-i+1)*buf[i] mod 65521.  */
          vs2[0] = vs2[0] % BASE;
  
          vs1 = vec_and(vs1, vmask);
          vs2 = vec_and(vs2, vmask);
          vs1_save = v_zeros;
      }
  
      /* len is less than NMAX one modulo is needed.  */
      if (len >= 16) {
          while (len >= 16) {
              len -= 16;
  
              vbuf = vec_xl(0, (unsigned char *) buf);
  
              vsum1 = vec_sum4s(vbuf, v_zeros); /* sum(i=1 to 16) buf[i].  */
              /* sum(i=1 to 16) buf[i]*(16-i+1).  */
              vsum2 = vec_msum(vbuf, v_mul, v_zeros);
              /* Save vs1.  */
              vs1_save = vec_add(vs1_save, vs1);
              /* Accumulate the sums.  */
              vs1 = vec_add(vsum1, vs1);
              vs2 = vec_add(vsum2, vs2);
  
              buf += 16;
          }
          /* Since the size will be always less than NMAX we do this once.  */
          vs1 = vec_sumsu(vs1, vsum1);
          vs1_save = vec_sll(vs1_save, vsh); /* 16*vs1_save.  */
          vs2 = vec_add(vs1_save, vs2);
          vs2 = vec_sumsu(vs2, vsum2);
      }
      /* Copy result back to s1, s2 (mod 65521).  */
      s1 = vs1[0] % BASE;
      s2 = vs2[0] % BASE;
  
      /* Process tail (len < 16).and return  */
      return adler32_len_16(s1, buf, len, s2);
  }
  
  #endif /* POWER8_VSX_ADLER32 */
  