libpopcnt.h

/*
 * libpopcnt.h - C/C++ library for counting the number of 1 bits (bit
 * population count) in an array as quickly as possible using
 * specialized CPU instructions i.e. POPCNT, AVX2, AVX512, NEON.
 *
 * Copyright (c) 2016 - 2019, Kim Walisch
 * Copyright (c) 2016 - 2018, Wojciech Muła
 *
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:
 *
 * 1. Redistributions of source code must retain the above copyright notice, this
 *    list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright notice,
 *    this list of conditions and the following disclaimer in the documentation
 *    and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
 * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
 * ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
 * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

#ifndef LIBPOPCNT_H
#define LIBPOPCNT_H

#include <stdint.h>

#ifndef __has_builtin
  #define __has_builtin(x) 0
#endif

#ifndef __has_attribute
  #define __has_attribute(x) 0
#endif

#ifdef __GNUC__
  #define GNUC_PREREQ(x, y) \
      (__GNUC__ > x || (__GNUC__ == x && __GNUC_MINOR__ >= y))
#else
  #define GNUC_PREREQ(x, y) 0
#endif

#ifdef __clang__
  #define CLANG_PREREQ(x, y) \
      (__clang_major__ > x || (__clang_major__ == x && __clang_minor__ >= y))
#else
  #define CLANG_PREREQ(x, y) 0
#endif

#if (_MSC_VER < 1900) && \
    !defined(__cplusplus)
  #define inline __inline
#endif

#if (defined(__i386__) || \
     defined(__x86_64__) || \
     defined(_M_IX86) || \
     defined(_M_X64))
  #define X86_OR_X64
#endif

#if defined(X86_OR_X64) && \
   (defined(__cplusplus) || \
    defined(_MSC_VER) || \
   (GNUC_PREREQ(4, 2) || \
    __has_builtin(__sync_val_compare_and_swap)))
  #define HAVE_CPUID
#endif

#if GNUC_PREREQ(4, 2) || \
    __has_builtin(__builtin_popcount)
  #define HAVE_BUILTIN_POPCOUNT
#endif

#if GNUC_PREREQ(4, 2) || \
    CLANG_PREREQ(3, 0)
  #define HAVE_ASM_POPCNT
#endif

#if defined(HAVE_CPUID) && \
   (defined(HAVE_ASM_POPCNT) || \
    defined(_MSC_VER))
  #define HAVE_POPCNT
#endif

#if defined(HAVE_CPUID) && \
    GNUC_PREREQ(4, 9)
  #define HAVE_AVX2
#endif

#if defined(HAVE_CPUID) && \
    GNUC_PREREQ(5, 0)
  #define HAVE_AVX512
#endif

#if defined(HAVE_CPUID) && \
    defined(_MSC_VER) && \
    defined(__AVX2__)
  #define HAVE_AVX2
#endif

#if defined(HAVE_CPUID) && \
    defined(_MSC_VER) && \
    defined(__AVX512__)
  #define HAVE_AVX512
#endif

#if defined(HAVE_CPUID) && \
    CLANG_PREREQ(3, 8) && \
    __has_attribute(target) && \
   (!defined(_MSC_VER) || defined(__AVX2__)) && \
   (!defined(__apple_build_version__) || __apple_build_version__ >= 8000000)
  #define HAVE_AVX2
  #define HAVE_AVX512
#endif

#ifdef __cplusplus
extern "C" {
#endif

/*
 * This uses fewer arithmetic operations than any other known
 * implementation on machines with fast multiplication.
 * It uses 12 arithmetic operations, one of which is a multiply.
 * http://en.wikipedia.org/wiki/Hamming_weight#Efficient_implementation
 */
static inline uint64_t popcount64(uint64_t x)
{
  uint64_t m1 = 0x5555555555555555ll;
  uint64_t m2 = 0x3333333333333333ll;
  uint64_t m4 = 0x0F0F0F0F0F0F0F0Fll;
  uint64_t h01 = 0x0101010101010101ll;

  x -= (x >> 1) & m1;
  x = (x & m2) + ((x >> 2) & m2);
  x = (x + (x >> 4)) & m4;

  return (x * h01) >> 56;
}

#if defined(HAVE_ASM_POPCNT) && \
    defined(__x86_64__)

static inline uint64_t popcnt64(uint64_t x)
{
  __asm__ ("popcnt %1, %0" : "=r" (x) : "0" (x));
  return x;
}

#elif defined(HAVE_ASM_POPCNT) && \
      defined(__i386__)

static inline uint32_t popcnt32(uint32_t x)
{
  __asm__ ("popcnt %1, %0" : "=r" (x) : "0" (x));
  return x;
}

static inline uint64_t popcnt64(uint64_t x)
{
  return popcnt32((uint32_t) x) +
         popcnt32((uint32_t)(x >> 32));
}

#elif defined(_MSC_VER) && \
      defined(_M_X64)

#include <nmmintrin.h>

static inline uint64_t popcnt64(uint64_t x)
{
  return _mm_popcnt_u64(x);
}

#elif defined(_MSC_VER) && \
      defined(_M_IX86)

#include <nmmintrin.h>

static inline uint64_t popcnt64(uint64_t x)
{
  return _mm_popcnt_u32((uint32_t) x) + 
         _mm_popcnt_u32((uint32_t)(x >> 32));
}

/* non x86 CPUs */
#elif defined(HAVE_BUILTIN_POPCOUNT)

static inline uint64_t popcnt64(uint64_t x)
{
  return __builtin_popcountll(x);
}

/* no hardware POPCNT,
 * use pure integer algorithm */
#else

static inline uint64_t popcnt64(uint64_t x)
{
  return popcount64(x);
}

#endif

static inline uint64_t popcnt64_unrolled(const uint64_t* data, uint64_t size)
{
  uint64_t i = 0;
  uint64_t limit = size - size % 4;
  uint64_t cnt = 0;

  for (; i < limit; i += 4)
  {
    cnt += popcnt64(data[i+0]);
    cnt += popcnt64(data[i+1]);
    cnt += popcnt64(data[i+2]);
    cnt += popcnt64(data[i+3]);
  }

  for (; i < size; i++)
    cnt += popcnt64(data[i]);

  return cnt;
}

#if defined(HAVE_CPUID)

#if defined(_MSC_VER)
  #include <intrin.h>
  #include <immintrin.h>
#endif

/* %ecx bit flags */
#define bit_POPCNT (1 << 23)

/* %ebx bit flags */
#define bit_AVX2   (1 << 5)
#define bit_AVX512 (1 << 30)

/* xgetbv bit flags */
#define XSTATE_SSE (1 << 1)
#define XSTATE_YMM (1 << 2)
#define XSTATE_ZMM (7 << 5)

static inline void run_cpuid(int eax, int ecx, int* abcd)
{
#if defined(_MSC_VER)
  __cpuidex(abcd, eax, ecx);
#else
  int ebx = 0;
  int edx = 0;

  #if defined(__i386__) && \
      defined(__PIC__)
    /* in case of PIC under 32-bit EBX cannot be clobbered */
    __asm__ ("movl %%ebx, %%edi;"
             "cpuid;"
             "xchgl %%ebx, %%edi;"
             : "=D" (ebx),
               "+a" (eax),
               "+c" (ecx),
               "=d" (edx));
  #else
    __asm__ ("cpuid;"
             : "+b" (ebx),
               "+a" (eax),
               "+c" (ecx),
               "=d" (edx));
  #endif

  abcd[0] = eax;
  abcd[1] = ebx;
  abcd[2] = ecx;
  abcd[3] = edx;
#endif
}

#if defined(HAVE_AVX2) || \
    defined(HAVE_AVX512)

static inline int get_xcr0()
{
  int xcr0;

#if defined(_MSC_VER)
  xcr0 = (int) _xgetbv(0);
#else
  __asm__ ("xgetbv" : "=a" (xcr0) : "c" (0) : "%edx" );
#endif

  return xcr0;
}

#endif

static inline int get_cpuid()
{
  int flags = 0;
  int abcd[4];

  run_cpuid(1, 0, abcd);

  if ((abcd[2] & bit_POPCNT) == bit_POPCNT)
    flags |= bit_POPCNT;

#if defined(HAVE_AVX2) || \
    defined(HAVE_AVX512)

  int osxsave_mask = (1 << 27);

  /* ensure OS supports extended processor state management */
  if ((abcd[2] & osxsave_mask) != osxsave_mask)
    return 0;

  int ymm_mask = XSTATE_SSE | XSTATE_YMM;
  int zmm_mask = XSTATE_SSE | XSTATE_YMM | XSTATE_ZMM;

  int xcr0 = get_xcr0();

  if ((xcr0 & ymm_mask) == ymm_mask)
  {
    run_cpuid(7, 0, abcd);

    if ((abcd[1] & bit_AVX2) == bit_AVX2)
      flags |= bit_AVX2;

    if ((xcr0 & zmm_mask) == zmm_mask)
    {
      if ((abcd[1] & bit_AVX512) == bit_AVX512)
        flags |= bit_AVX512;
    }
  }

#endif

  return flags;
}

#endif /* cpuid */

#if defined(HAVE_AVX2)

#include <immintrin.h>

#if !defined(_MSC_VER)
  __attribute__ ((target ("avx2")))
#endif
static inline void CSA256(__m256i* h, __m256i* l, __m256i a, __m256i b, __m256i c)
{
  __m256i u = _mm256_xor_si256(a, b);
  *h = _mm256_or_si256(_mm256_and_si256(a, b), _mm256_and_si256(u, c));
  *l = _mm256_xor_si256(u, c);
}

#if !defined(_MSC_VER)
  __attribute__ ((target ("avx2")))
#endif
static inline __m256i popcnt256(__m256i v)
{
  __m256i lookup1 = _mm256_setr_epi8(
      4, 5, 5, 6, 5, 6, 6, 7,
      5, 6, 6, 7, 6, 7, 7, 8,
      4, 5, 5, 6, 5, 6, 6, 7,
      5, 6, 6, 7, 6, 7, 7, 8
  );

  __m256i lookup2 = _mm256_setr_epi8(
      4, 3, 3, 2, 3, 2, 2, 1,
      3, 2, 2, 1, 2, 1, 1, 0,
      4, 3, 3, 2, 3, 2, 2, 1,
      3, 2, 2, 1, 2, 1, 1, 0
  );

  __m256i low_mask = _mm256_set1_epi8(0x0f);
  __m256i lo = _mm256_and_si256(v, low_mask);
  __m256i hi = _mm256_and_si256(_mm256_srli_epi16(v, 4), low_mask);
  __m256i popcnt1 = _mm256_shuffle_epi8(lookup1, lo);
  __m256i popcnt2 = _mm256_shuffle_epi8(lookup2, hi);

  return _mm256_sad_epu8(popcnt1, popcnt2);
}

/*
 * AVX2 Harley-Seal popcount (4th iteration).
 * The algorithm is based on the paper "Faster Population Counts
 * using AVX2 Instructions" by Daniel Lemire, Nathan Kurz and
 * Wojciech Mula (23 Nov 2016).
 * @see https://arxiv.org/abs/1611.07612
 */
#if !defined(_MSC_VER)
  __attribute__ ((target ("avx2")))
#endif
static inline uint64_t popcnt_avx2(const __m256i* data, uint64_t size)
{
  __m256i cnt = _mm256_setzero_si256();
  __m256i ones = _mm256_setzero_si256();
  __m256i twos = _mm256_setzero_si256();
  __m256i fours = _mm256_setzero_si256();
  __m256i eights = _mm256_setzero_si256();
  __m256i sixteens = _mm256_setzero_si256();
  __m256i twosA, twosB, foursA, foursB, eightsA, eightsB;

  uint64_t i = 0;
  uint64_t limit = size - size % 16;
  uint64_t* cnt64;

  for(; i < limit; i += 16)
  {
    CSA256(&twosA, &ones, ones, data[i+0], data[i+1]);
    CSA256(&twosB, &ones, ones, data[i+2], data[i+3]);
    CSA256(&foursA, &twos, twos, twosA, twosB);
    CSA256(&twosA, &ones, ones, data[i+4], data[i+5]);
    CSA256(&twosB, &ones, ones, data[i+6], data[i+7]);
    CSA256(&foursB, &twos, twos, twosA, twosB);
    CSA256(&eightsA, &fours, fours, foursA, foursB);
    CSA256(&twosA, &ones, ones, data[i+8], data[i+9]);
    CSA256(&twosB, &ones, ones, data[i+10], data[i+11]);
    CSA256(&foursA, &twos, twos, twosA, twosB);
    CSA256(&twosA, &ones, ones, data[i+12], data[i+13]);
    CSA256(&twosB, &ones, ones, data[i+14], data[i+15]);
    CSA256(&foursB, &twos, twos, twosA, twosB);
    CSA256(&eightsB, &fours, fours, foursA, foursB);
    CSA256(&sixteens, &eights, eights, eightsA, eightsB);

    cnt = _mm256_add_epi64(cnt, popcnt256(sixteens));
  }

  cnt = _mm256_slli_epi64(cnt, 4);
  cnt = _mm256_add_epi64(cnt, _mm256_slli_epi64(popcnt256(eights), 3));
  cnt = _mm256_add_epi64(cnt, _mm256_slli_epi64(popcnt256(fours), 2));
  cnt = _mm256_add_epi64(cnt, _mm256_slli_epi64(popcnt256(twos), 1));
  cnt = _mm256_add_epi64(cnt, popcnt256(ones));

  for(; i < size; i++)
    cnt = _mm256_add_epi64(cnt, popcnt256(data[i]));

  cnt64 = (uint64_t*) &cnt;

  return cnt64[0] +
         cnt64[1] +
         cnt64[2] +
         cnt64[3];
}

/* Align memory to 32 bytes boundary */
static inline void align_avx2(const uint8_t** p, uint64_t* size, uint64_t* cnt)
{
  for (; (uintptr_t) *p % 8; (*p)++)
  {
    *cnt += popcnt64(**p);
    *size -= 1;
  }
  for (; (uintptr_t) *p % 32; (*p) += 8)
  {
    *cnt += popcnt64(
        *(const uint64_t*) *p);
    *size -= 8;
  }
}

#endif

#if defined(HAVE_AVX512)

#include <immintrin.h>

#if !defined(_MSC_VER)
  __attribute__ ((target ("avx512bw")))
#endif
static inline __m512i popcnt512(__m512i v)
{
  __m512i m1 = _mm512_set1_epi8(0x55);
  __m512i m2 = _mm512_set1_epi8(0x33);
  __m512i m4 = _mm512_set1_epi8(0x0F);
  __m512i t1 = _mm512_sub_epi8(v, (_mm512_srli_epi16(v, 1) & m1));
  __m512i t2 = _mm512_add_epi8(t1 & m2, (_mm512_srli_epi16(t1, 2) & m2));
  __m512i t3 = _mm512_add_epi8(t2, _mm512_srli_epi16(t2, 4)) & m4;

  return _mm512_sad_epu8(t3, _mm512_setzero_si512());
}

#if !defined(_MSC_VER)
  __attribute__ ((target ("avx512bw")))
#endif
static inline void CSA512(__m512i* h, __m512i* l, __m512i a, __m512i b, __m512i c)
{
  *l = _mm512_ternarylogic_epi32(c, b, a, 0x96);
  *h = _mm512_ternarylogic_epi32(c, b, a, 0xe8);
}

/*
 * AVX512 Harley-Seal popcount (4th iteration).
 * The algorithm is based on the paper "Faster Population Counts
 * using AVX2 Instructions" by Daniel Lemire, Nathan Kurz and
 * Wojciech Mula (23 Nov 2016).
 * @see https://arxiv.org/abs/1611.07612
 */
#if !defined(_MSC_VER)
  __attribute__ ((target ("avx512bw")))
#endif
static inline uint64_t popcnt_avx512(const __m512i* data, const uint64_t size)
{
  __m512i cnt = _mm512_setzero_si512();
  __m512i ones = _mm512_setzero_si512();
  __m512i twos = _mm512_setzero_si512();
  __m512i fours = _mm512_setzero_si512();
  __m512i eights = _mm512_setzero_si512();
  __m512i sixteens = _mm512_setzero_si512();
  __m512i twosA, twosB, foursA, foursB, eightsA, eightsB;

  uint64_t i = 0;
  uint64_t limit = size - size % 16;
  uint64_t* cnt64;

  for(; i < limit; i += 16)
  {
    CSA512(&twosA, &ones, ones, data[i+0], data[i+1]);
    CSA512(&twosB, &ones, ones, data[i+2], data[i+3]);
    CSA512(&foursA, &twos, twos, twosA, twosB);
    CSA512(&twosA, &ones, ones, data[i+4], data[i+5]);
    CSA512(&twosB, &ones, ones, data[i+6], data[i+7]);
    CSA512(&foursB, &twos, twos, twosA, twosB);
    CSA512(&eightsA, &fours, fours, foursA, foursB);
    CSA512(&twosA, &ones, ones, data[i+8], data[i+9]);
    CSA512(&twosB, &ones, ones, data[i+10], data[i+11]);
    CSA512(&foursA, &twos, twos, twosA, twosB);
    CSA512(&twosA, &ones, ones, data[i+12], data[i+13]);
    CSA512(&twosB, &ones, ones, data[i+14], data[i+15]);
    CSA512(&foursB, &twos, twos, twosA, twosB);
    CSA512(&eightsB, &fours, fours, foursA, foursB);
    CSA512(&sixteens, &eights, eights, eightsA, eightsB);

    cnt = _mm512_add_epi64(cnt, popcnt512(sixteens));
  }

  cnt = _mm512_slli_epi64(cnt, 4);
  cnt = _mm512_add_epi64(cnt, _mm512_slli_epi64(popcnt512(eights), 3));
  cnt = _mm512_add_epi64(cnt, _mm512_slli_epi64(popcnt512(fours), 2));
  cnt = _mm512_add_epi64(cnt, _mm512_slli_epi64(popcnt512(twos), 1));
  cnt = _mm512_add_epi64(cnt, popcnt512(ones));

  for(; i < size; i++)
    cnt = _mm512_add_epi64(cnt, popcnt512(data[i]));

  cnt64 = (uint64_t*) &cnt;

  return cnt64[0] +
         cnt64[1] +
         cnt64[2] +
         cnt64[3] +
         cnt64[4] +
         cnt64[5] +
         cnt64[6] +
         cnt64[7];
}

/* Align memory to 64 bytes boundary */
static inline void align_avx512(const uint8_t** p, uint64_t* size, uint64_t* cnt)
{
  for (; (uintptr_t) *p % 8; (*p)++)
  {
    *cnt += popcnt64(**p);
    *size -= 1;
  }
  for (; (uintptr_t) *p % 64; (*p) += 8)
  {
    *cnt += popcnt64(
        *(const uint64_t*) *p);
    *size -= 8;
  }
}

#endif

/* x86 CPUs */
#if defined(X86_OR_X64)

/* Align memory to 8 bytes boundary */
static inline void align_8(const uint8_t** p, uint64_t* size, uint64_t* cnt)
{
  for (; *size > 0 && (uintptr_t) *p % 8; (*p)++)
  {
    *cnt += popcount64(**p);
    *size -= 1;
  }
}

static inline uint64_t popcount64_unrolled(const uint64_t* data, uint64_t size)
{
  uint64_t i = 0;
  uint64_t limit = size - size % 4;
  uint64_t cnt = 0;

  for (; i < limit; i += 4)
  {
    cnt += popcount64(data[i+0]);
    cnt += popcount64(data[i+1]);
    cnt += popcount64(data[i+2]);
    cnt += popcount64(data[i+3]);
  }

  for (; i < size; i++)
    cnt += popcount64(data[i]);

  return cnt;
}

/*
 * Count the number of 1 bits in the data array
 * @data: An array
 * @size: Size of data in bytes
 */
static inline uint64_t popcnt(const void* data, uint64_t size)
{
  const uint8_t* ptr = (const uint8_t*) data;
  uint64_t cnt = 0;
  uint64_t i;

#if defined(HAVE_CPUID)
  #if defined(__cplusplus)
    /* C++11 thread-safe singleton */
    static const int cpuid = get_cpuid();
  #else
    static int cpuid_ = -1;
    int cpuid = cpuid_;
    if (cpuid == -1)
    {
      cpuid = get_cpuid();

      #if defined(_MSC_VER)
        _InterlockedCompareExchange(&cpuid_, cpuid, -1);
      #else
        __sync_val_compare_and_swap(&cpuid_, -1, cpuid);
      #endif
    }
  #endif
#endif

#if defined(HAVE_AVX512)

  /* AVX512 requires arrays >= 1024 bytes */
  if ((cpuid & bit_AVX512) &&
      size >= 1024)
  {
    align_avx512(&ptr, &size, &cnt);
    cnt += popcnt_avx512((const __m512i*) ptr, size / 64);
    ptr += size - size % 64;
    size = size % 64;
  }

#endif

#if defined(HAVE_AVX2)

  /* AVX2 requires arrays >= 512 bytes */
  if ((cpuid & bit_AVX2) &&
      size >= 512)
  {
    align_avx2(&ptr, &size, &cnt);
    cnt += popcnt_avx2((const __m256i*) ptr, size / 32);
    ptr += size - size % 32;
    size = size % 32;
  }

#endif

#if defined(HAVE_POPCNT)

  if (cpuid & bit_POPCNT)
  {
    cnt += popcnt64_unrolled((const uint64_t*) ptr, size / 8);
    ptr += size - size % 8;
    size = size % 8;
    for (i = 0; i < size; i++)
      cnt += popcnt64(ptr[i]);

    return cnt;
  }

#endif

  /* pure integer popcount algorithm */
  if (size >= 8)
  {
    align_8(&ptr, &size, &cnt);
    cnt += popcount64_unrolled((const uint64_t*) ptr, size / 8);
    ptr += size - size % 8;
    size = size % 8;
  }

  /* pure integer popcount algorithm */
  for (i = 0; i < size; i++)
    cnt += popcount64(ptr[i]);

  return cnt;
}

#elif defined(__ARM_NEON) || \
      defined(__aarch64__)

#include <arm_neon.h>

/* Align memory to 8 bytes boundary */
static inline void align_8(const uint8_t** p, uint64_t* size, uint64_t* cnt)
{
  for (; *size > 0 && (uintptr_t) *p % 8; (*p)++)
  {
    *cnt += popcnt64(**p);
    *size -= 1;
  }
}

static inline uint64x2_t vpadalq(uint64x2_t sum, uint8x16_t t)
{
  return vpadalq_u32(sum, vpaddlq_u16(vpaddlq_u8(t)));
}

/*
 * Count the number of 1 bits in the data array
 * @data: An array
 * @size: Size of data in bytes
 */
static inline uint64_t popcnt(const void* data, uint64_t size)
{
  uint64_t cnt = 0;
  uint64_t chunk_size = 64;
  const uint8_t* ptr = (const uint8_t*) data;

  if (size >= chunk_size)
  {
    uint64_t i = 0;
    uint64_t iters = size / chunk_size;
    uint64x2_t sum = vcombine_u64(vcreate_u64(0), vcreate_u64(0));
    uint8x16_t zero = vcombine_u8(vcreate_u8(0), vcreate_u8(0));

    do
    {
      uint8x16_t t0 = zero;
      uint8x16_t t1 = zero;
      uint8x16_t t2 = zero;
      uint8x16_t t3 = zero;

      /*
       * After every 31 iterations we need to add the
       * temporary sums (t0, t1, t2, t3) to the total sum.
       * We must ensure that the temporary sums <= 255
       * and 31 * 8 bits = 248 which is OK.
       */
      uint64_t limit = (i + 31 < iters) ? i + 31 : iters;
  
      /* Each iteration processes 64 bytes */
      for (; i < limit; i++)
      {
        uint8x16x4_t input = vld4q_u8(ptr);
        ptr += chunk_size;

        t0 = vaddq_u8(t0, vcntq_u8(input.val[0]));
        t1 = vaddq_u8(t1, vcntq_u8(input.val[1]));
        t2 = vaddq_u8(t2, vcntq_u8(input.val[2]));
        t3 = vaddq_u8(t3, vcntq_u8(input.val[3]));
      }

      sum = vpadalq(sum, t0);
      sum = vpadalq(sum, t1);
      sum = vpadalq(sum, t2);
      sum = vpadalq(sum, t3);
    }
    while (i < iters);

    uint64_t tmp[2];
    vst1q_u64(tmp, sum);
    cnt += tmp[0];
    cnt += tmp[1];
  }

  size %= chunk_size;
  align_8(&ptr, &size, &cnt);
  const uint64_t* ptr64 = (const uint64_t*) ptr;
  uint64_t iters = size / 8;

  for (uint64_t i = 0; i < iters; i++)
    cnt += popcnt64(ptr64[i]);

  ptr += size - size % 8;
  size = size % 8;

  for (uint64_t i = 0; i < size; i++)
    cnt += popcnt64(ptr[i]);

  return cnt;
}

/* all other CPUs */
#else

/* Align memory to 8 bytes boundary */
static inline void align_8(const uint8_t** p, uint64_t* size, uint64_t* cnt)
{
  for (; *size > 0 && (uintptr_t) *p % 8; (*p)++)
  {
    *cnt += popcnt64(**p);
    *size -= 1;
  }
}

/*
 * Count the number of 1 bits in the data array
 * @data: An array
 * @size: Size of data in bytes
 */
static inline uint64_t popcnt(const void* data, uint64_t size)
{
  const uint8_t* ptr = (const uint8_t*) data;
  uint64_t cnt = 0;
  uint64_t i;

  align_8(&ptr, &size, &cnt);
  cnt += popcnt64_unrolled((const uint64_t*) ptr, size / 8);
  ptr += size - size % 8;
  size = size % 8;
  for (i = 0; i < size; i++)
    cnt += popcnt64(ptr[i]);

  return cnt;
}

#endif

#ifdef __cplusplus
} /* extern "C" */
#endif

#endif /* LIBPOPCNT_H */