From 590f3f0ec6d4b1b2b54859577b221ba8cc11e291 Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Sun, 26 Feb 2017 22:03:58 +0100
Subject: [PATCH 01/37] Add AVX2 popcount algorithm

---
 CMakeLists.txt          |  52 +++++--
 include/popcnt.hpp      |  92 +-----------
 src/BitSieve-popcnt.cpp | 309 ++++++++++++++++++++++++++++++++++++++++
 src/BitSieve.cpp        |  92 ++++--------
 4 files changed, 383 insertions(+), 162 deletions(-)
 create mode 100644 src/BitSieve-popcnt.cpp

diff --git a/CMakeLists.txt b/CMakeLists.txt
index af33ec780..fb2987231 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -8,13 +8,12 @@ set(CMAKE_BUILD_TYPE Release)
 
 # Build options ######################################################
 
-option(ENABLE_POPCNT "Enable POPCNT instruction" ON)
 option(ENABLE_MPI "Enable MPI (Message Passing Interface)" OFF)
 
 # Include Check* #####################################################
 
-include(CheckCXXCompilerFlag)
 include(CheckCXXSourceRuns)
+include(CheckCXXSourceCompiles)
 include(CheckTypeSize)
 
 # primecount binary source files #####################################
@@ -26,6 +25,7 @@ set(BIN_SRC src/app/cmdoptions.cpp
 # primecount library source files ####################################
 
 set(LIB_SRC src/BitSieve.cpp
+            src/BitSieve-popcnt.cpp
             src/FactorTable.cpp
             src/Li.cpp
             src/P2.cpp
@@ -107,15 +107,51 @@ if (OPENMP_FOUND)
     set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${OpenMP_CXX_FLAGS}")
 endif()
 
-# Check for -mpopcnt compiler option #################################
+# Reset CMAKE_CXX_FLAGS for compiler checks ##########################
 
-if(ENABLE_POPCNT)
-    CHECK_CXX_COMPILER_FLAG(-mpopcnt MPOPCNT_FLAG)
-    if(MPOPCNT_FLAG)
-        set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mpopcnt")
-    endif()
+set(CXX_FLAGS "${CMAKE_CXX_FLAGS}")
+set(CMAKE_CXX_FLAGS "")
+
+# Check -mpopcnt compiler flag #######################################
+
+set(CMAKE_CXX_FLAGS "-mpopcnt -Werror")
+
+check_cxx_source_compiles(
+    "int main(int, char**) { return 0; }"
+    mpopcnt)
+
+if(mpopcnt)
+    set(CXX_FLAGS "${CXX_FLAGS} -mpopcnt")
 endif()
 
+# Check -mpopcntd compiler flag ######################################
+
+set(CMAKE_CXX_FLAGS "-mpopcntd -Werror")
+
+check_cxx_source_compiles(
+    "int main(int, char**) { return 0; }"
+    mpopcntd)
+
+if(mpopcntd)
+    set(CXX_FLAGS "${CXX_FLAGS} -mpopcntd")
+endif()
+
+# Check -mavx2 compiler flag #########################################
+
+set(CMAKE_CXX_FLAGS "-mavx2 -Werror")
+
+check_cxx_source_compiles(
+    "int main(int, char**) { return 0; }"
+    mavx2)
+
+if(mavx2)
+    set_source_files_properties(src/BitSieve-popcnt.cpp PROPERTIES COMPILE_FLAGS -mavx2)
+endif()
+
+# Restore CMAKE_CXX_FLAGS ############################################
+
+set(CMAKE_CXX_FLAGS "${CXX_FLAGS}")
+
 # Check if int128_t type exists ######################################
 
 check_type_size("int128_t" INT128_T)
diff --git a/include/popcnt.hpp b/include/popcnt.hpp
index c95e1d3bc..af730787c 100644
--- a/include/popcnt.hpp
+++ b/include/popcnt.hpp
@@ -1,7 +1,7 @@
 ///
-/// @file    popcnt.hpp
-/// @brief   Functions to count the number of 1 bits inside a 64-bit
-///          word or a 64-bit array.
+/// @file  popcnt.hpp
+/// @brief Functions to count the number of 1 bits
+///        inside a 64-bit word.
 ///
 /// Copyright (C) 2016 Kim Walisch, <kim.walisch@gmail.com>
 ///
@@ -59,9 +59,6 @@ inline uint64_t popcnt64(uint64_t x)
 
 #else
 
-/// Fallback mode if POPCNT intrinsic is not available
-#define NO_POPCNT_INTRINSIC
-
 inline uint64_t popcnt64(uint64_t x)
 {
   const uint64_t m1 = 0x5555555555555555ll;
@@ -76,89 +73,6 @@ inline uint64_t popcnt64(uint64_t x)
   return (x * h01) >> 56;
 }
 
-inline void CSA(uint64_t& h, uint64_t& l, uint64_t a, uint64_t b, uint64_t c)
-{
-  uint64_t u = a ^ b; 
-  h = (a & b) | (u & c);
-  l = u ^ c;
-}
-
-/// Harley-Seal popcount (4th iteration).
-/// The Harley-Seal popcount algorithm is one of the fastest algorithms
-/// for counting 1 bits in an array using only integer operations.
-/// This implementation uses only 5.69 instructions per 64-bit word.
-/// @see Chapter 5 in "Hacker's Delight" 2nd edition.
-///
-inline uint64_t popcnt64(const uint64_t* data, uint64_t size)
-{
-  uint64_t total = 0;
-  uint64_t ones = 0, twos = 0, fours = 0, eights = 0, sixteens = 0;
-  uint64_t twosA, twosB, foursA, foursB, eightsA, eightsB;
-  uint64_t limit = size - size % 16;
-  uint64_t i = 0;
-
-  for(; i < limit; i += 16)
-  {
-    CSA(twosA, ones, ones, data[i+0], data[i+1]);
-    CSA(twosB, ones, ones, data[i+2], data[i+3]);
-    CSA(foursA, twos, twos, twosA, twosB);
-    CSA(twosA, ones, ones, data[i+4], data[i+5]);
-    CSA(twosB, ones, ones, data[i+6], data[i+7]);
-    CSA(foursB, twos, twos, twosA, twosB);
-    CSA(eightsA,fours, fours, foursA, foursB);
-    CSA(twosA, ones, ones, data[i+8], data[i+9]);
-    CSA(twosB, ones, ones, data[i+10], data[i+11]);
-    CSA(foursA, twos, twos, twosA, twosB);
-    CSA(twosA, ones, ones, data[i+12], data[i+13]);
-    CSA(twosB, ones, ones, data[i+14], data[i+15]);
-    CSA(foursB, twos, twos, twosA, twosB);
-    CSA(eightsB, fours, fours, foursA, foursB);
-    CSA(sixteens, eights, eights, eightsA, eightsB);
-
-    total += popcnt64(sixteens);
-  }
-
-  total *= 16;
-  total += 8 * popcnt64(eights);
-  total += 4 * popcnt64(fours);
-  total += 2 * popcnt64(twos);
-  total += 1 * popcnt64(ones);
-
-  for(; i < size; i++)
-    total += popcnt64(data[i]);
-
-  return total;
-}
-
-#endif
-
-#if !defined(NO_POPCNT_INTRINSIC)
-
-/// Count the number of 1 bits inside the data array
-/// using the POPCNT instruction.
-///
-inline uint64_t popcnt64(const uint64_t* data, uint64_t size)
-{
-  uint64_t sum0 = 0, sum1 = 0, sum2 = 0, sum3 = 0;
-  uint64_t limit = size - size % 4;
-  uint64_t i = 0;
-
-  for (; i < limit; i += 4)
-  {
-    sum0 += popcnt64(data[i+0]);
-    sum1 += popcnt64(data[i+1]);
-    sum2 += popcnt64(data[i+2]);
-    sum3 += popcnt64(data[i+3]);
-  }
-
-  uint64_t total = sum0 + sum1 + sum2 + sum3;
-
-  for (; i < size; i++)
-    total += popcnt64(data[i]);
-
-  return total;
-}
-
 #endif
 
 #endif /* POPCNT_HPP */
diff --git a/src/BitSieve-popcnt.cpp b/src/BitSieve-popcnt.cpp
new file mode 100644
index 000000000..2f76cd242
--- /dev/null
+++ b/src/BitSieve-popcnt.cpp
@@ -0,0 +1,309 @@
+///
+/// @file  BitSieve-popcnt.cpp
+/// @brief Count the number of 1 bits inside a 64-bit array.
+///        The vectorized popcount algorithms used in this file are
+///        described in the paper "Faster Population Counts using AVX2
+///        Instructions" by Wojciech Muła, Nathan Kurz, Daniel Lemire.
+/// @see   https://arxiv.org/abs/1611.07612
+/// @see   https://github.com/WojciechMula/sse-popcount
+///
+/// Copyright (C) 2016 Kim Walisch, <kim.walisch@gmail.com>
+///
+/// This file is distributed under the BSD License. See the COPYING
+/// file in the top level directory.
+///
+
+#include <BitSieve.hpp>
+#include <popcnt.hpp>
+
+#include <stdint.h>
+#include <cassert>
+#include <vector>
+
+namespace {
+namespace DEFAULT {
+
+void CSA(uint64_t& h, uint64_t& l, uint64_t a, uint64_t b, uint64_t c)
+{
+  uint64_t u = a ^ b; 
+  h = (a & b) | (u & c);
+  l = u ^ c;
+}
+
+/// Harley-Seal popcount (4th iteration).
+/// The Harley-Seal popcount algorithm is one of the fastest algorithms
+/// for counting 1 bits in an array using only integer operations.
+/// This implementation uses only 5.69 instructions per 64-bit word.
+/// @see Chapter 5 in "Hacker's Delight" 2nd edition.
+///
+uint64_t popcnt(const uint64_t* data, uint64_t size)
+{
+  uint64_t total = 0;
+  uint64_t ones = 0, twos = 0, fours = 0, eights = 0, sixteens = 0;
+  uint64_t twosA, twosB, foursA, foursB, eightsA, eightsB;
+  uint64_t limit = size - size % 16;
+  uint64_t i = 0;
+
+  for(; i < limit; i += 16)
+  {
+    CSA(twosA, ones, ones, data[i+0], data[i+1]);
+    CSA(twosB, ones, ones, data[i+2], data[i+3]);
+    CSA(foursA, twos, twos, twosA, twosB);
+    CSA(twosA, ones, ones, data[i+4], data[i+5]);
+    CSA(twosB, ones, ones, data[i+6], data[i+7]);
+    CSA(foursB, twos, twos, twosA, twosB);
+    CSA(eightsA,fours, fours, foursA, foursB);
+    CSA(twosA, ones, ones, data[i+8], data[i+9]);
+    CSA(twosB, ones, ones, data[i+10], data[i+11]);
+    CSA(foursA, twos, twos, twosA, twosB);
+    CSA(twosA, ones, ones, data[i+12], data[i+13]);
+    CSA(twosB, ones, ones, data[i+14], data[i+15]);
+    CSA(foursB, twos, twos, twosA, twosB);
+    CSA(eightsB, fours, fours, foursA, foursB);
+    CSA(sixteens, eights, eights, eightsA, eightsB);
+
+    total += popcnt64(sixteens);
+  }
+
+  total *= 16;
+  total += 8 * popcnt64(eights);
+  total += 4 * popcnt64(fours);
+  total += 2 * popcnt64(twos);
+  total += 1 * popcnt64(ones);
+
+  for(; i < size; i++)
+    total += popcnt64(data[i]);
+
+  return total;
+}
+
+} // namespace DEFAULT
+} // namespace
+
+namespace {
+namespace POPCNT {
+
+/// Count the number of 1 bits inside the data
+/// array using the POPCNT instruction.
+///
+uint64_t popcnt(const uint64_t* data, uint64_t size)
+{
+  uint64_t sum0 = 0, sum1 = 0, sum2 = 0, sum3 = 0;
+  uint64_t limit = size - size % 4;
+  uint64_t i = 0;
+
+  for (; i < limit; i += 4)
+  {
+    sum0 += popcnt64(data[i+0]);
+    sum1 += popcnt64(data[i+1]);
+    sum2 += popcnt64(data[i+2]);
+    sum3 += popcnt64(data[i+3]);
+  }
+
+  uint64_t total = sum0 + sum1 + sum2 + sum3;
+
+  for (; i < size; i++)
+    total += popcnt64(data[i]);
+
+  return total;
+}
+
+} // namespace POPCNT
+} // namespace
+
+#if defined(__x86_64__) && \
+    defined(__GNUC__) && \
+           (__GNUC__ > 4 || \
+           (__GNUC__ == 4 && __GNUC_MINOR__ >= 8))
+
+#include <immintrin.h>
+
+namespace {
+namespace AVX2 {
+
+__m256i popcnt(const __m256i v)
+{
+  __m256i m1 = _mm256_set1_epi8(0x55);
+  __m256i m2 = _mm256_set1_epi8(0x33);
+  __m256i m4 = _mm256_set1_epi8(0x0F);
+
+  __m256i t1 = _mm256_sub_epi8(v, (_mm256_srli_epi16(v,  1) & m1));
+  __m256i t2 = _mm256_add_epi8(t1 & m2, (_mm256_srli_epi16(t1, 2) & m2));
+  __m256i t3 = _mm256_add_epi8(t2, _mm256_srli_epi16(t2, 4)) & m4;
+
+  return _mm256_sad_epu8(t3, _mm256_setzero_si256());
+}
+
+void CSA(__m256i& h, __m256i& l, __m256i a, __m256i b, __m256i c)
+{
+  __m256i u = a ^ b;
+  h = (a & b) | (u & c);
+  l = u ^ c;
+}
+
+/// 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
+///
+uint64_t popcnt(const __m256i* data, uint64_t size)
+{
+  __m256i total = _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 limit = size - size % 16;
+  uint64_t i = 0;
+
+  for(; i < limit; i += 16)
+  {
+    CSA(twosA, ones, ones, data[i+0], data[i+1]);
+    CSA(twosB, ones, ones, data[i+2], data[i+3]);
+    CSA(foursA, twos, twos, twosA, twosB);
+    CSA(twosA, ones, ones, data[i+4], data[i+5]);
+    CSA(twosB, ones, ones, data[i+6], data[i+7]);
+    CSA(foursB, twos, twos, twosA, twosB);
+    CSA(eightsA,fours, fours, foursA, foursB);
+    CSA(twosA, ones, ones, data[i+8], data[i+9]);
+    CSA(twosB, ones, ones, data[i+10], data[i+11]);
+    CSA(foursA, twos, twos, twosA, twosB);
+    CSA(twosA, ones, ones, data[i+12], data[i+13]);
+    CSA(twosB, ones, ones, data[i+14], data[i+15]);
+    CSA(foursB, twos, twos, twosA, twosB);
+    CSA(eightsB, fours, fours, foursA, foursB);
+    CSA(sixteens, eights, eights, eightsA, eightsB);
+
+    total = _mm256_add_epi64(total, popcnt(sixteens));
+  }
+
+  total = _mm256_slli_epi64(total, 4);
+  total = _mm256_add_epi64(total, _mm256_slli_epi64(popcnt(eights), 3));
+  total = _mm256_add_epi64(total, _mm256_slli_epi64(popcnt(fours), 2));
+  total = _mm256_add_epi64(total, _mm256_slli_epi64(popcnt(twos), 1));
+  total = _mm256_add_epi64(total, popcnt(ones));
+
+  for(; i < size; i++)
+    total = _mm256_add_epi64(total, popcnt(data[i]));
+
+  uint64_t* total64 = (uint64_t*) &total;
+
+  return total64[0] +
+         total64[1] +
+         total64[2] +
+         total64[3];
+}
+
+/// Align memory to 32 bytes boundary
+void align(const uint64_t*& data, uint64_t* size, uint64_t* total)
+{
+  for (; *size > 0 && (uintptr_t) data % 32 != 0; data++)
+  {
+    *total += popcnt64(*data);
+    *size -= 1;
+  }
+}
+
+/// AVX2 popcount algorithm for 64-bit arrays.
+/// @param data  A 64-bit array
+/// @param size  Length of data array
+///
+uint64_t popcnt(const uint64_t* data, uint64_t size)
+{
+  uint64_t total = 0;
+
+  // AVX2 popcount is faster than POPCNT 
+  // for array sizes >= 1 kilobyte
+  if (size * 8 >= 1024)
+  {
+    align(data, &size, &total);
+    total += popcnt((const __m256i*) data, size / 4);
+    data += size - size % 4;
+    size = size % 4;
+  }
+
+  // process remaining words
+  total += POPCNT::popcnt(data, size);
+
+  return total;
+}
+
+} // namespace AVX2
+} // namespace
+
+#endif /* AVX2 */
+
+/// Function multi-versioning is currently (February 2017)
+/// only supported by GCC >= 4.8
+///
+#if defined(__x86_64__) && \
+    defined(__GNUC__) && \
+           (__GNUC__ > 4 || \
+           (__GNUC__ == 4 && __GNUC_MINOR__ >= 8))
+
+namespace {
+
+__attribute__ ((target ("default")))
+uint64_t popcnt(const uint64_t* data, uint64_t size)
+{
+  return DEFAULT::popcnt(data, size);
+}
+
+__attribute__ ((target ("popcnt")))
+uint64_t popcnt(const uint64_t* data, uint64_t size)
+{
+  return POPCNT::popcnt(data, size);
+}
+
+__attribute__ ((target ("avx2")))
+uint64_t popcnt(const uint64_t* data, uint64_t size)
+{
+  return AVX2::popcnt(data, size);
+}
+
+} // namespace
+
+#else
+
+uint64_t popcnt(const uint64_t* data, uint64_t size)
+{
+  return POPCNT::popcnt(data, size);
+}
+
+#endif
+
+namespace primecount {
+
+/// Count the number of 1 bits inside [start, stop]
+uint64_t BitSieve::count(uint64_t start,
+                         uint64_t stop) const
+{
+  if (start > stop)
+    return 0;
+
+  assert(stop < size_);
+
+  uint64_t start_idx = start / 64;
+  uint64_t stop_idx = stop / 64;
+  uint64_t m1 = 0xffffffffffffffffull << (start % 64);
+  uint64_t m2 = 0xffffffffffffffffull >> (63 - stop % 64);
+  uint64_t bit_count;
+
+  if (start_idx == stop_idx)
+    bit_count = popcnt64(sieve_[start_idx] & (m1 & m2));
+  else
+  {
+    bit_count = popcnt64(sieve_[start_idx] & m1);
+    bit_count += popcnt(&sieve_[start_idx + 1], stop_idx - (start_idx + 1));
+    bit_count += popcnt64(sieve_[stop_idx] & m2);
+  }
+
+  return bit_count;
+}
+
+} // namespace
+
diff --git a/src/BitSieve.cpp b/src/BitSieve.cpp
index 2f4874d3f..cd664f6e2 100644
--- a/src/BitSieve.cpp
+++ b/src/BitSieve.cpp
@@ -11,12 +11,7 @@
 /// file in the top level directory.
 ///
 
-#if !defined(__STDC_CONSTANT_MACROS)
-  #define __STDC_CONSTANT_MACROS
-#endif
-
 #include <BitSieve.hpp>
-#include <popcnt.hpp>
 #include <imath.hpp>
 
 #include <stdint.h>
@@ -35,16 +30,16 @@ const uint64_t primes[] = { 0, 2, 3, 5, 7, 11, 13, 17, 19, 23 };
 /// Bitmasks with multiples of the i-th prime set
 const uint64_t masks[] =
 {
-  UINT64_C(0x0000000000000000),
-  UINT64_C(0x5555555555555555), // 2
-  UINT64_C(0x9249249249249249), // 3
-  UINT64_C(0x1084210842108421), // 5
-  UINT64_C(0x8102040810204081), // 7
-  UINT64_C(0x0080100200400801), // 11
-  UINT64_C(0x0010008004002001), // 13
-  UINT64_C(0x0008000400020001), // 17
-  UINT64_C(0x0200004000080001), // 19
-  UINT64_C(0x0000400000800001)  // 23
+  0x0000000000000000ull,
+  0x5555555555555555ull, // 2
+  0x9249249249249249ull, // 3
+  0x1084210842108421ull, // 5
+  0x8102040810204081ull, // 7
+  0x0080100200400801ull, // 11
+  0x0010008004002001ull, // 13
+  0x0008000400020001ull, // 17
+  0x0200004000080001ull, // 19
+  0x0000400000800001ull  // 23
 };
 
 /// Get bitmask with unset multiples
@@ -61,34 +56,28 @@ uint64_t fast_modulo(uint64_t x, uint64_t y)
   return x;
 }
 
-}
+} // namespace
 
 namespace primecount {
 
 const uint64_t BitSieve::unset_bit_[64] =
 {
-  ~(UINT64_C(1) <<  0), ~(UINT64_C(1) <<  1), ~(UINT64_C(1) <<  2),
-  ~(UINT64_C(1) <<  3), ~(UINT64_C(1) <<  4), ~(UINT64_C(1) <<  5),
-  ~(UINT64_C(1) <<  6), ~(UINT64_C(1) <<  7), ~(UINT64_C(1) <<  8),
-  ~(UINT64_C(1) <<  9), ~(UINT64_C(1) << 10), ~(UINT64_C(1) << 11),
-  ~(UINT64_C(1) << 12), ~(UINT64_C(1) << 13), ~(UINT64_C(1) << 14),
-  ~(UINT64_C(1) << 15), ~(UINT64_C(1) << 16), ~(UINT64_C(1) << 17),
-  ~(UINT64_C(1) << 18), ~(UINT64_C(1) << 19), ~(UINT64_C(1) << 20),
-  ~(UINT64_C(1) << 21), ~(UINT64_C(1) << 22), ~(UINT64_C(1) << 23),
-  ~(UINT64_C(1) << 24), ~(UINT64_C(1) << 25), ~(UINT64_C(1) << 26),
-  ~(UINT64_C(1) << 27), ~(UINT64_C(1) << 28), ~(UINT64_C(1) << 29),
-  ~(UINT64_C(1) << 30), ~(UINT64_C(1) << 31), ~(UINT64_C(1) << 32),
-  ~(UINT64_C(1) << 33), ~(UINT64_C(1) << 34), ~(UINT64_C(1) << 35),
-  ~(UINT64_C(1) << 36), ~(UINT64_C(1) << 37), ~(UINT64_C(1) << 38),
-  ~(UINT64_C(1) << 39), ~(UINT64_C(1) << 40), ~(UINT64_C(1) << 41),
-  ~(UINT64_C(1) << 42), ~(UINT64_C(1) << 43), ~(UINT64_C(1) << 44),
-  ~(UINT64_C(1) << 45), ~(UINT64_C(1) << 46), ~(UINT64_C(1) << 47),
-  ~(UINT64_C(1) << 48), ~(UINT64_C(1) << 49), ~(UINT64_C(1) << 50),
-  ~(UINT64_C(1) << 51), ~(UINT64_C(1) << 52), ~(UINT64_C(1) << 53),
-  ~(UINT64_C(1) << 54), ~(UINT64_C(1) << 55), ~(UINT64_C(1) << 56),
-  ~(UINT64_C(1) << 57), ~(UINT64_C(1) << 58), ~(UINT64_C(1) << 59),
-  ~(UINT64_C(1) << 60), ~(UINT64_C(1) << 61), ~(UINT64_C(1) << 62),
-  ~(UINT64_C(1) << 63)
+  ~(1ull <<  0), ~(1ull <<  1), ~(1ull <<  2), ~(1ull <<  3),
+  ~(1ull <<  4), ~(1ull <<  5), ~(1ull <<  6), ~(1ull <<  7),
+  ~(1ull <<  8), ~(1ull <<  9), ~(1ull << 10), ~(1ull << 11),
+  ~(1ull << 12), ~(1ull << 13), ~(1ull << 14), ~(1ull << 15),
+  ~(1ull << 16), ~(1ull << 17), ~(1ull << 18), ~(1ull << 19),
+  ~(1ull << 20), ~(1ull << 21), ~(1ull << 22), ~(1ull << 23),
+  ~(1ull << 24), ~(1ull << 25), ~(1ull << 26), ~(1ull << 27),
+  ~(1ull << 28), ~(1ull << 29), ~(1ull << 30), ~(1ull << 31),
+  ~(1ull << 32), ~(1ull << 33), ~(1ull << 34), ~(1ull << 35),
+  ~(1ull << 36), ~(1ull << 37), ~(1ull << 38), ~(1ull << 39),
+  ~(1ull << 40), ~(1ull << 41), ~(1ull << 42), ~(1ull << 43),
+  ~(1ull << 44), ~(1ull << 45), ~(1ull << 46), ~(1ull << 47),
+  ~(1ull << 48), ~(1ull << 49), ~(1ull << 50), ~(1ull << 51),
+  ~(1ull << 52), ~(1ull << 53), ~(1ull << 54), ~(1ull << 55),
+  ~(1ull << 56), ~(1ull << 57), ~(1ull << 58), ~(1ull << 59),
+  ~(1ull << 60), ~(1ull << 61), ~(1ull << 62), ~(1ull << 63)
 };
 
 BitSieve::BitSieve(std::size_t size) :
@@ -158,31 +147,4 @@ void BitSieve::pre_sieve(uint64_t c, uint64_t low)
   }
 }
 
-/// Count the number of 1 bits inside [start, stop]
-uint64_t BitSieve::count(uint64_t start,
-                         uint64_t stop) const
-{
-  if (start > stop)
-    return 0;
-
-  assert(stop < size_);
-
-  uint64_t start_idx = start / 64;
-  uint64_t stop_idx = stop / 64;
-  uint64_t m1 = UINT64_C(0xffffffffffffffff) << (start % 64);
-  uint64_t m2 = UINT64_C(0xffffffffffffffff) >> (63 - stop % 64);
-  uint64_t bit_count;
-
-  if (start_idx == stop_idx)
-    bit_count = popcnt64(sieve_[start_idx] & (m1 & m2));
-  else
-  {
-    bit_count = popcnt64(sieve_[start_idx] & m1);
-    bit_count += popcnt64(&sieve_[start_idx + 1], stop_idx - (start_idx + 1));
-    bit_count += popcnt64(sieve_[stop_idx] & m2);
-  }
-
-  return bit_count;
-}
-
 } // namespace

From 056961a668071851e25beded709a24f5647c956a Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Sun, 26 Feb 2017 22:29:32 +0100
Subject: [PATCH 02/37] Silence OS X warning

---
 CMakeLists.txt | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/CMakeLists.txt b/CMakeLists.txt
index fb2987231..4797963f8 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -1,4 +1,4 @@
-cmake_minimum_required(VERSION 2.8.4)
+cmake_minimum_required(VERSION 3.0)
 project(primecount)
 set(PRIMECOUNT_VERSION_MAJOR 3)
 set(PRIMECOUNT_VERSION_MINOR 5)

From 0c57ad679fac77dea544449c3696ddb4a06716a0 Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Sun, 26 Feb 2017 22:48:51 +0100
Subject: [PATCH 03/37] Update comment

---
 src/BitSieve-popcnt.cpp | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/BitSieve-popcnt.cpp b/src/BitSieve-popcnt.cpp
index 2f76cd242..941180f23 100644
--- a/src/BitSieve-popcnt.cpp
+++ b/src/BitSieve-popcnt.cpp
@@ -1,8 +1,8 @@
 ///
 /// @file  BitSieve-popcnt.cpp
 /// @brief Count the number of 1 bits inside a 64-bit array.
-///        The vectorized popcount algorithms used in this file are
-///        described in the paper "Faster Population Counts using AVX2
+///        The AVX2 popcount algorithm used in this file is described
+///        in the paper "Faster Population Counts using AVX2
 ///        Instructions" by Wojciech Muła, Nathan Kurz, Daniel Lemire.
 /// @see   https://arxiv.org/abs/1611.07612
 /// @see   https://github.com/WojciechMula/sse-popcount

From 0c836db1634bd639057a7ed78861b52a1cd31722 Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Sun, 26 Feb 2017 22:59:13 +0100
Subject: [PATCH 04/37] Remove newline

---
 src/BitSieve-popcnt.cpp | 1 -
 1 file changed, 1 deletion(-)

diff --git a/src/BitSieve-popcnt.cpp b/src/BitSieve-popcnt.cpp
index 941180f23..9c3919ac1 100644
--- a/src/BitSieve-popcnt.cpp
+++ b/src/BitSieve-popcnt.cpp
@@ -306,4 +306,3 @@ uint64_t BitSieve::count(uint64_t start,
 }
 
 } // namespace
-

From 7582d6bc6a7f47e858f755874bb6ae3a991c05f8 Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Mon, 27 Feb 2017 08:15:52 +0100
Subject: [PATCH 05/37] Install CMake 3.x

---
 .travis.yml | 1 +
 1 file changed, 1 insertion(+)

diff --git a/.travis.yml b/.travis.yml
index 8b468277c..050f67269 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -11,6 +11,7 @@ env:
     - OMP_NUM_THREADS=4
 
 before_install:
+  - sudo add-apt-repository ppa:george-edison55/precise-backports
   - sudo apt-get update -qq
 
 # Install cmake, OpenMPI, cppcheck

From f8cc9b7077cb7d21c2441328e02b617c8bf3a02f Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Mon, 27 Feb 2017 08:31:27 +0100
Subject: [PATCH 06/37] Add --yes option

---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index 050f67269..3df3e84d0 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -11,7 +11,7 @@ env:
     - OMP_NUM_THREADS=4
 
 before_install:
-  - sudo add-apt-repository ppa:george-edison55/precise-backports
+  - sudo add-apt-repository ppa:george-edison55/precise-backports -y
   - sudo apt-get update -qq
 
 # Install cmake, OpenMPI, cppcheck

From 8c4d4ae16503a12a2a5cd636aed9030f63e04c2e Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Mon, 27 Feb 2017 08:33:41 +0100
Subject: [PATCH 07/37] Improved compiler flag checks

---
 CMakeLists.txt | 27 ++++++---------------------
 1 file changed, 6 insertions(+), 21 deletions(-)

diff --git a/CMakeLists.txt b/CMakeLists.txt
index 4797963f8..28db3f216 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -13,7 +13,7 @@ option(ENABLE_MPI "Enable MPI (Message Passing Interface)" OFF)
 # Include Check* #####################################################
 
 include(CheckCXXSourceRuns)
-include(CheckCXXSourceCompiles)
+include(CheckCXXCompilerFlag)
 include(CheckTypeSize)
 
 # primecount binary source files #####################################
@@ -107,43 +107,28 @@ if (OPENMP_FOUND)
     set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${OpenMP_CXX_FLAGS}")
 endif()
 
-# Reset CMAKE_CXX_FLAGS for compiler checks ##########################
+# Use -Werror for compiler checks ####################################
 
 set(CXX_FLAGS "${CMAKE_CXX_FLAGS}")
-set(CMAKE_CXX_FLAGS "")
+set(CMAKE_CXX_FLAGS -Werror)
 
 # Check -mpopcnt compiler flag #######################################
 
-set(CMAKE_CXX_FLAGS "-mpopcnt -Werror")
-
-check_cxx_source_compiles(
-    "int main(int, char**) { return 0; }"
-    mpopcnt)
-
+check_cxx_compiler_flag(-mpopcnt mpopcnt)
 if(mpopcnt)
     set(CXX_FLAGS "${CXX_FLAGS} -mpopcnt")
 endif()
 
 # Check -mpopcntd compiler flag ######################################
 
-set(CMAKE_CXX_FLAGS "-mpopcntd -Werror")
-
-check_cxx_source_compiles(
-    "int main(int, char**) { return 0; }"
-    mpopcntd)
-
+check_cxx_compiler_flag(-mpopcntd mpopcntd)
 if(mpopcntd)
     set(CXX_FLAGS "${CXX_FLAGS} -mpopcntd")
 endif()
 
 # Check -mavx2 compiler flag #########################################
 
-set(CMAKE_CXX_FLAGS "-mavx2 -Werror")
-
-check_cxx_source_compiles(
-    "int main(int, char**) { return 0; }"
-    mavx2)
-
+check_cxx_compiler_flag(-mavx2 mavx2)
 if(mavx2)
     set_source_files_properties(src/BitSieve-popcnt.cpp PROPERTIES COMPILE_FLAGS -mavx2)
 endif()

From 578cda71b07c239407b38d2ef946272081c2cde8 Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Mon, 27 Feb 2017 08:53:24 +0100
Subject: [PATCH 08/37] Fix CMake 3.x installation

---
 .travis.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.travis.yml b/.travis.yml
index 3df3e84d0..6dcdc13ba 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -16,7 +16,7 @@ before_install:
 
 # Install cmake, OpenMPI, cppcheck
 install:
-  - sudo apt-get install -y cmake openmpi-bin libopenmpi-dev cppcheck
+  - sudo apt-get install -y cmake cmake-data openmpi-bin libopenmpi-dev cppcheck
 
 # Test build.sh script
 before_script:

From 9dc07a599d4246f1501387954d0c9185b5acc511 Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Mon, 27 Feb 2017 13:57:13 +0100
Subject: [PATCH 09/37] CMake check __attribute__ target("avx2")

---
 CMakeLists.txt          | 49 +++++++++++++--------
 src/BitSieve-popcnt.cpp | 95 +++++------------------------------------
 2 files changed, 41 insertions(+), 103 deletions(-)

diff --git a/CMakeLists.txt b/CMakeLists.txt
index 28db3f216..2b5069cd2 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -8,10 +8,12 @@ set(CMAKE_BUILD_TYPE Release)
 
 # Build options ######################################################
 
-option(ENABLE_MPI "Enable MPI (Message Passing Interface)" OFF)
+option(ENABLE_POPCNT "Enable POPCNT instruction" ON)
+option(ENABLE_MPI    "Enable MPI (Message Passing Interface)" OFF)
 
 # Include Check* #####################################################
 
+include(CheckCXXSourceCompiles)
 include(CheckCXXSourceRuns)
 include(CheckCXXCompilerFlag)
 include(CheckTypeSize)
@@ -103,39 +105,50 @@ endif()
 # Check for OpenMP ###################################################
 
 find_package(OpenMP QUIET)
-if (OPENMP_FOUND)
+if(OPENMP_FOUND)
     set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${OpenMP_CXX_FLAGS}")
 endif()
 
 # Use -Werror for compiler checks ####################################
 
-set(CXX_FLAGS "${CMAKE_CXX_FLAGS}")
+set(COPY_CXX_FLAGS "${CMAKE_CXX_FLAGS}")
 set(CMAKE_CXX_FLAGS -Werror)
 
 # Check -mpopcnt compiler flag #######################################
 
-check_cxx_compiler_flag(-mpopcnt mpopcnt)
-if(mpopcnt)
-    set(CXX_FLAGS "${CXX_FLAGS} -mpopcnt")
+if(ENABLE_POPCNT)
+    check_cxx_compiler_flag(-mpopcnt mpopcnt)
+    if(mpopcnt)
+        set(COPY_CXX_FLAGS "${COPY_CXX_FLAGS} -mpopcnt")
+    endif()
 endif()
 
 # Check -mpopcntd compiler flag ######################################
 
-check_cxx_compiler_flag(-mpopcntd mpopcntd)
-if(mpopcntd)
-    set(CXX_FLAGS "${CXX_FLAGS} -mpopcntd")
+if(ENABLE_POPCNT)
+    check_cxx_compiler_flag(-mpopcntd mpopcntd)
+    if(mpopcntd)
+        set(COPY_CXX_FLAGS "${COPY_CXX_FLAGS} -mpopcntd")
+    endif()
 endif()
 
-# Check -mavx2 compiler flag #########################################
+# Restore CMAKE_CXX_FLAGS ############################################
 
-check_cxx_compiler_flag(-mavx2 mavx2)
-if(mavx2)
-    set_source_files_properties(src/BitSieve-popcnt.cpp PROPERTIES COMPILE_FLAGS -mavx2)
-endif()
+set(CMAKE_CXX_FLAGS "${COPY_CXX_FLAGS}")
 
-# Restore CMAKE_CXX_FLAGS ############################################
+# Check target("avx2") ###############################################
+
+check_cxx_source_compiles("
+    __attribute__ ((target (\"default\")))
+    int func() { return 0; }
+    __attribute__ ((target (\"avx2\")))
+    int func() { return 1; }
+    int main() { return func(); }"
+    target_avx2)
 
-set(CMAKE_CXX_FLAGS "${CXX_FLAGS}")
+if(target_avx2)
+    add_definitions(-DHAVE_TARGET_AVX2)
+endif()
 
 # Check if int128_t type exists ######################################
 
@@ -185,11 +198,11 @@ check_cxx_source_runs("
 
         return 0;
     }"
-    HAVE_LIBDIVIDE)
+    use_libdivide)
 
 # Include S2_easy* source files ######################################
 
-if(HAVE_LIBDIVIDE)
+if(use_libdivide)
     set(LIB_SRC ${LIB_SRC} src/deleglise-rivat/S2_easy_libdivide.cpp)
     if(ENABLE_MPI)
         set(LIB_SRC ${LIB_SRC} src/mpi/deleglise-rivat/S2_easy_mpi_libdivide.cpp)
diff --git a/src/BitSieve-popcnt.cpp b/src/BitSieve-popcnt.cpp
index 9c3919ac1..6e48b8de4 100644
--- a/src/BitSieve-popcnt.cpp
+++ b/src/BitSieve-popcnt.cpp
@@ -20,66 +20,6 @@
 #include <cassert>
 #include <vector>
 
-namespace {
-namespace DEFAULT {
-
-void CSA(uint64_t& h, uint64_t& l, uint64_t a, uint64_t b, uint64_t c)
-{
-  uint64_t u = a ^ b; 
-  h = (a & b) | (u & c);
-  l = u ^ c;
-}
-
-/// Harley-Seal popcount (4th iteration).
-/// The Harley-Seal popcount algorithm is one of the fastest algorithms
-/// for counting 1 bits in an array using only integer operations.
-/// This implementation uses only 5.69 instructions per 64-bit word.
-/// @see Chapter 5 in "Hacker's Delight" 2nd edition.
-///
-uint64_t popcnt(const uint64_t* data, uint64_t size)
-{
-  uint64_t total = 0;
-  uint64_t ones = 0, twos = 0, fours = 0, eights = 0, sixteens = 0;
-  uint64_t twosA, twosB, foursA, foursB, eightsA, eightsB;
-  uint64_t limit = size - size % 16;
-  uint64_t i = 0;
-
-  for(; i < limit; i += 16)
-  {
-    CSA(twosA, ones, ones, data[i+0], data[i+1]);
-    CSA(twosB, ones, ones, data[i+2], data[i+3]);
-    CSA(foursA, twos, twos, twosA, twosB);
-    CSA(twosA, ones, ones, data[i+4], data[i+5]);
-    CSA(twosB, ones, ones, data[i+6], data[i+7]);
-    CSA(foursB, twos, twos, twosA, twosB);
-    CSA(eightsA,fours, fours, foursA, foursB);
-    CSA(twosA, ones, ones, data[i+8], data[i+9]);
-    CSA(twosB, ones, ones, data[i+10], data[i+11]);
-    CSA(foursA, twos, twos, twosA, twosB);
-    CSA(twosA, ones, ones, data[i+12], data[i+13]);
-    CSA(twosB, ones, ones, data[i+14], data[i+15]);
-    CSA(foursB, twos, twos, twosA, twosB);
-    CSA(eightsB, fours, fours, foursA, foursB);
-    CSA(sixteens, eights, eights, eightsA, eightsB);
-
-    total += popcnt64(sixteens);
-  }
-
-  total *= 16;
-  total += 8 * popcnt64(eights);
-  total += 4 * popcnt64(fours);
-  total += 2 * popcnt64(twos);
-  total += 1 * popcnt64(ones);
-
-  for(; i < size; i++)
-    total += popcnt64(data[i]);
-
-  return total;
-}
-
-} // namespace DEFAULT
-} // namespace
-
 namespace {
 namespace POPCNT {
 
@@ -111,22 +51,19 @@ uint64_t popcnt(const uint64_t* data, uint64_t size)
 } // namespace POPCNT
 } // namespace
 
-#if defined(__x86_64__) && \
-    defined(__GNUC__) && \
-           (__GNUC__ > 4 || \
-           (__GNUC__ == 4 && __GNUC_MINOR__ >= 8))
+#if defined(HAVE_TARGET_AVX2)
 
 #include <immintrin.h>
 
 namespace {
 namespace AVX2 {
 
+__attribute__ ((target ("avx2")))
 __m256i popcnt(const __m256i v)
 {
   __m256i m1 = _mm256_set1_epi8(0x55);
   __m256i m2 = _mm256_set1_epi8(0x33);
   __m256i m4 = _mm256_set1_epi8(0x0F);
-
   __m256i t1 = _mm256_sub_epi8(v, (_mm256_srli_epi16(v,  1) & m1));
   __m256i t2 = _mm256_add_epi8(t1 & m2, (_mm256_srli_epi16(t1, 2) & m2));
   __m256i t3 = _mm256_add_epi8(t2, _mm256_srli_epi16(t2, 4)) & m4;
@@ -134,6 +71,7 @@ __m256i popcnt(const __m256i v)
   return _mm256_sad_epu8(t3, _mm256_setzero_si256());
 }
 
+__attribute__ ((target ("avx2")))
 void CSA(__m256i& h, __m256i& l, __m256i a, __m256i b, __m256i c)
 {
   __m256i u = a ^ b;
@@ -147,6 +85,7 @@ void CSA(__m256i& h, __m256i& l, __m256i a, __m256i b, __m256i c)
 /// Wojciech Mula (23 Nov 2016).
 /// @see https://arxiv.org/abs/1611.07612
 ///
+__attribute__ ((target ("avx2")))
 uint64_t popcnt(const __m256i* data, uint64_t size)
 {
   __m256i total = _mm256_setzero_si256();
@@ -199,16 +138,18 @@ uint64_t popcnt(const __m256i* data, uint64_t size)
 }
 
 /// Align memory to 32 bytes boundary
-void align(const uint64_t*& data, uint64_t* size, uint64_t* total)
+void align(const uint64_t*& p,
+           uint64_t* size,
+           uint64_t* total)
 {
-  for (; *size > 0 && (uintptr_t) data % 32 != 0; data++)
+  for (; *size > 0 && (uintptr_t) p % 32 != 0; p++)
   {
-    *total += popcnt64(*data);
+    *total += popcnt64(*p);
     *size -= 1;
   }
 }
 
-/// AVX2 popcount algorithm for 64-bit arrays.
+/// AVX2 popcount algorithm.
 /// @param data  A 64-bit array
 /// @param size  Length of data array
 ///
@@ -235,26 +176,10 @@ uint64_t popcnt(const uint64_t* data, uint64_t size)
 } // namespace AVX2
 } // namespace
 
-#endif /* AVX2 */
-
-/// Function multi-versioning is currently (February 2017)
-/// only supported by GCC >= 4.8
-///
-#if defined(__x86_64__) && \
-    defined(__GNUC__) && \
-           (__GNUC__ > 4 || \
-           (__GNUC__ == 4 && __GNUC_MINOR__ >= 8))
-
 namespace {
 
 __attribute__ ((target ("default")))
 uint64_t popcnt(const uint64_t* data, uint64_t size)
-{
-  return DEFAULT::popcnt(data, size);
-}
-
-__attribute__ ((target ("popcnt")))
-uint64_t popcnt(const uint64_t* data, uint64_t size)
 {
   return POPCNT::popcnt(data, size);
 }

From d01354855463cd01322c337b6ae01a84f4cfabe3 Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Mon, 27 Feb 2017 18:17:16 +0100
Subject: [PATCH 10/37] Update year

---
 COPYING | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/COPYING b/COPYING
index 07dc6aed2..f5323e3b5 100644
--- a/COPYING
+++ b/COPYING
@@ -1,6 +1,6 @@
 BSD 2-Clause License
 
-Copyright (c) 2013 - 2016, Kim Walisch.
+Copyright (c) 2013 - 2017, Kim Walisch.
 All rights reserved.
 
 Redistribution and use in source and binary forms, with or without

From 8c20892ab70aa4881675afd9327b31a02377d799 Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Mon, 27 Feb 2017 18:18:55 +0100
Subject: [PATCH 11/37] Update copyright year

---
 src/app/help.cpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/app/help.cpp b/src/app/help.cpp
index 05600f297..94a2db17d 100644
--- a/src/app/help.cpp
+++ b/src/app/help.cpp
@@ -58,7 +58,7 @@ const string helpMenu(
 
 const string versionInfo(
   "primecount " PRIMECOUNT_VERSION ", <https://github.com/kimwalisch/primecount>\n"
-  "Copyright (C) 2016 Kim Walisch\n"
+  "Copyright (C) 2013 - 2017 Kim Walisch\n"
   "BSD 2-Clause License <http://opensource.org/licenses/BSD-2-Clause>"
 );
 

From 7f5744c69e0d3c756e8f6736eea3a295346059ae Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Mon, 27 Feb 2017 18:31:27 +0100
Subject: [PATCH 12/37] Changes in version 3.6

---
 ChangeLog | 11 +++++++++++
 1 file changed, 11 insertions(+)

diff --git a/ChangeLog b/ChangeLog
index 6560689ba..7791412d1 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,14 @@
+2017-02-27 Kim Walisch  <kim.walisch@gmail.com>
+
+  Version 3.6 work in progress.
+
+  This version features a new AVX2 popcount algorithm which
+  computes the hard special leaves up to 15% faster on x86 CPUs
+  with AVX2 support (2013 or later).
+
+  * BitSieve-popcnt.cpp: New AVX2 popcount algorithm.
+  * CMakeLists.txt: Add AVX2 check.
+
 2016-12-16 Kim Walisch  <kim.walisch@gmail.com>
 
   Version 3.5 released.

From 7ae5e8a4873a0b7b345866a4fe5e2039aa58e75d Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Mon, 27 Feb 2017 20:21:48 +0100
Subject: [PATCH 13/37] Improve code readability

---
 src/BitSieve-popcnt.cpp | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/src/BitSieve-popcnt.cpp b/src/BitSieve-popcnt.cpp
index 6e48b8de4..7990801b8 100644
--- a/src/BitSieve-popcnt.cpp
+++ b/src/BitSieve-popcnt.cpp
@@ -176,6 +176,10 @@ uint64_t popcnt(const uint64_t* data, uint64_t size)
 } // namespace AVX2
 } // namespace
 
+#endif
+
+#if defined(HAVE_TARGET_AVX2)
+
 namespace {
 
 __attribute__ ((target ("default")))

From c98c51710627db631c4e74842b8606cd55514b0e Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Mon, 27 Feb 2017 20:36:00 +0100
Subject: [PATCH 14/37] Fix clang performance bug

On x86_64 when compiled with clang++ the popcnt64() was erroneously
defined as:

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

Instead of:

inline uint64_t popcnt64(uint64_t x)
{
  return __builtin_popcountll(x);
}
---
 include/popcnt.hpp | 14 ++------------
 1 file changed, 2 insertions(+), 12 deletions(-)

diff --git a/include/popcnt.hpp b/include/popcnt.hpp
index af730787c..63cf068d1 100644
--- a/include/popcnt.hpp
+++ b/include/popcnt.hpp
@@ -39,18 +39,8 @@ inline uint64_t popcnt64(uint64_t x)
          _mm_popcnt_u32((uint32_t)(x >> 32));
 }
 
-#elif __has_builtin(__builtin_popcount) || \
-      (defined(__GNUC__) && \
-       defined(__i386__))
-
-inline uint64_t popcnt64(uint64_t x)
-{
-  return __builtin_popcount((uint32_t) x) +
-         __builtin_popcount((uint32_t)(x >> 32));
-}
-
-#elif __has_builtin(__builtin_popcountll) || \
-      defined(__GNUC__)
+#elif defined(__GNUC__) || \
+      __has_builtin(__builtin_popcountll)
 
 inline uint64_t popcnt64(uint64_t x)
 {

From e0c6fd3d7151c03bf5d14e54bef990c289f92ee7 Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Mon, 27 Feb 2017 21:17:09 +0100
Subject: [PATCH 15/37] Changes in version 3.6

---
 ChangeLog | 1 +
 1 file changed, 1 insertion(+)

diff --git a/ChangeLog b/ChangeLog
index 7791412d1..11f0975e6 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -7,6 +7,7 @@
   with AVX2 support (2013 or later).
 
   * BitSieve-popcnt.cpp: New AVX2 popcount algorithm.
+  * popcnt.hpp: Fix clang performance bug.
   * CMakeLists.txt: Add AVX2 check.
 
 2016-12-16 Kim Walisch  <kim.walisch@gmail.com>

From f89d0267d395a13dd0e93a84576e25b0f7282217 Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Tue, 28 Feb 2017 10:16:21 +0100
Subject: [PATCH 16/37] Minor performance improvement

---
 src/BitSieve-popcnt.cpp | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/src/BitSieve-popcnt.cpp b/src/BitSieve-popcnt.cpp
index 7990801b8..d2d23e310 100644
--- a/src/BitSieve-popcnt.cpp
+++ b/src/BitSieve-popcnt.cpp
@@ -142,8 +142,9 @@ void align(const uint64_t*& p,
            uint64_t* size,
            uint64_t* total)
 {
-  for (; *size > 0 && (uintptr_t) p % 32 != 0; p++)
+  for (; (uintptr_t) p % 32 != 0; p++)
   {
+    assert(*size > 0);
     *total += popcnt64(*p);
     *size -= 1;
   }

From b19ade06d560d7e99def23c6dab37f1f1d21aff8 Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Tue, 28 Feb 2017 18:01:43 +0100
Subject: [PATCH 17/37] Update timings

---
 README.md | 26 +++++++++++++-------------
 1 file changed, 13 insertions(+), 13 deletions(-)

diff --git a/README.md b/README.md
index 9f46fe082..146da4aac 100644
--- a/README.md
+++ b/README.md
@@ -207,7 +207,7 @@ Benchmarks
     <td>3,204,941,750,802</td>
     <td>4.01s</td>
     <td>1.96s</td>
-    <td>0.43s</td>
+    <td>0.38s</td>
     <td>0.22s</td>
   </tr>
   <tr align="right">
@@ -215,32 +215,32 @@ Benchmarks
     <td>29,844,570,422,669</td>
     <td>27.75s</td>
     <td>12.08s</td>
-    <td>1.65s</td>
-    <td>0.77s</td>
+    <td>1.52s</td>
+    <td>0.76s</td>
   </tr>
   <tr align="right">
     <td>10<sup>16</sup></td>
     <td>279,238,341,033,925</td>
     <td>232.30s</td>
     <td>92.09s</td>
-    <td>7.31s</td>
-    <td>2.83s</td>
+    <td>6.87s</td>
+    <td>2.67s</td>
   </tr>
   <tr align="right">
     <td>10<sup>17</sup></td>
     <td>2,623,557,157,654,233</td>
     <td>1,836.73s</td>
     <td>731.35s</td>
-    <td>33.66s</td>
-    <td>11.20s</td>
+    <td>31.63s</td>
+    <td>10.66s</td>
   </tr>
   <tr align="right">
     <td>10<sup>18</sup></td>
     <td>24,739,954,287,740,860</td>
     <td>14,949.16s</td>
     <td>6,631.73s</td>
-    <td>157.15s</td>
-    <td>47.07s</td>
+    <td>146.55s</td>
+    <td>44.54s</td>
   </tr>
   <tr align="right">
     <td>10<sup>19</sup></td>
@@ -248,7 +248,7 @@ Benchmarks
     <td>NaN</td>
     <td>NaN</td>
     <td>NaN</td>
-    <td>225.08s</td>
+    <td>209.57s</td>
   </tr>
   <tr align="right">
     <td>10<sup>20</sup></td>
@@ -256,7 +256,7 @@ Benchmarks
     <td>NaN</td>
     <td>NaN</td>
     <td>NaN</td>
-    <td>1,029.41s</td>
+    <td>939.88s</td>
   </tr>
   <tr align="right">
     <td>10<sup>21</sup></td>
@@ -264,7 +264,7 @@ Benchmarks
     <td>NaN</td>
     <td>NaN</td>
     <td>NaN</td>
-    <td>4,867.45s</td>
+    <td>4,536.14s</td>
   </tr>
   <tr align="right">
     <td>10<sup>22</sup></td>
@@ -278,7 +278,7 @@ Benchmarks
 
 The benchmarks above were run on an Intel Core i7-6700 CPU (4 x 3.4 GHz) from
 2015 using a Linux x64 operating system and primecount was compiled using
-GCC 5.2.
+GCC 5.4.
 
 Build instructions
 ------------------

From 8beb6ac3a92263501ccf4d2d4c26d08a9e927017 Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Tue, 28 Feb 2017 18:54:30 +0100
Subject: [PATCH 18/37] update copyright year

---
 src/BitSieve-popcnt.cpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/BitSieve-popcnt.cpp b/src/BitSieve-popcnt.cpp
index d2d23e310..99a92f22b 100644
--- a/src/BitSieve-popcnt.cpp
+++ b/src/BitSieve-popcnt.cpp
@@ -7,7 +7,7 @@
 /// @see   https://arxiv.org/abs/1611.07612
 /// @see   https://github.com/WojciechMula/sse-popcount
 ///
-/// Copyright (C) 2016 Kim Walisch, <kim.walisch@gmail.com>
+/// Copyright (C) 2017 Kim Walisch, <kim.walisch@gmail.com>
 ///
 /// This file is distributed under the BSD License. See the COPYING
 /// file in the top level directory.

From 7176e600aca350eff7d91f31c0cf746d75f94829 Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Tue, 28 Feb 2017 19:12:07 +0100
Subject: [PATCH 19/37] Update version to 3.6

---
 CMakeLists.txt         | 2 +-
 README.md              | 8 ++++----
 doc/primecount-MPI.md  | 2 +-
 include/primecount.hpp | 4 ++--
 4 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/CMakeLists.txt b/CMakeLists.txt
index 2b5069cd2..eafe3441a 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -1,7 +1,7 @@
 cmake_minimum_required(VERSION 3.0)
 project(primecount)
 set(PRIMECOUNT_VERSION_MAJOR 3)
-set(PRIMECOUNT_VERSION_MINOR 5)
+set(PRIMECOUNT_VERSION_MINOR 6)
 set(PRIMECOUNT_VERSION "${PRIMECOUNT_VERSION_MAJOR}.${PRIMECOUNT_VERSION_MINOR}")
 include_directories(include src/primesieve/include)
 set(CMAKE_BUILD_TYPE Release)
diff --git a/README.md b/README.md
index 146da4aac..af9f08a5a 100644
--- a/README.md
+++ b/README.md
@@ -30,9 +30,9 @@ Below are the latest precompiled binaries for Windows 64-bit, Linux and OS X.
 These binaries are statically linked and require a CPU which supports the POPCNT
 instruction (2010 or later).
 
-* [primecount-3.5-win64.zip](https://dl.bintray.com/kimwalisch/primecount/primecount-3.5-win64.zip), 404K
-* [primecount-3.5-linux-x64.tar.gz](https://dl.bintray.com/kimwalisch/primecount/primecount-3.5-linux-x64.tar.gz), 915K
-* [primecount-3.5-macOS-x64.tar.gz](https://dl.bintray.com/kimwalisch/primecount/primecount-3.5-macOS-x64.tar.gz), 688K
+* [primecount-3.6-win64.zip](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-win64.zip), 404K
+* [primecount-3.6-linux-x64.tar.gz](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-linux-x64.tar.gz), 915K
+* [primecount-3.6-macOS-x64.tar.gz](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-macOS-x64.tar.gz), 688K
 * Binaries with backup functionality are available [here](https://github.com/kimwalisch/primecount/tree/backup#primecount-backup)
 
 Usage examples
@@ -285,7 +285,7 @@ Build instructions
 You need to have installed a C++ compiler, cmake and make to build primecount.
 
 Download
-[primecount-3.5.zip](https://github.com/kimwalisch/primecount/archive/v3.5.zip)
+[primecount-3.6.zip](https://github.com/kimwalisch/primecount/archive/v3.6.zip)
 and build it using:
 
 ```sh
diff --git a/doc/primecount-MPI.md b/doc/primecount-MPI.md
index 4daa47182..dfa951563 100644
--- a/doc/primecount-MPI.md
+++ b/doc/primecount-MPI.md
@@ -25,7 +25,7 @@ sudo apt-get install g++ make cmake libopenmpi-dev openmpi-bin
 ```
 
 Then download
-[primecount-3.5.zip](https://github.com/kimwalisch/primecount/archive/v3.5.zip)
+[primecount-3.6.zip](https://github.com/kimwalisch/primecount/archive/v3.6.zip)
 and build it using:
 ```sh
 cmake -DENABLE_MPI=ON .
diff --git a/include/primecount.hpp b/include/primecount.hpp
index 6d2a123a0..5d536c50c 100644
--- a/include/primecount.hpp
+++ b/include/primecount.hpp
@@ -13,9 +13,9 @@
 #include <string>
 #include <stdint.h>
 
-#define PRIMECOUNT_VERSION "3.5"
+#define PRIMECOUNT_VERSION "3.6"
 #define PRIMECOUNT_VERSION_MAJOR 3
-#define PRIMECOUNT_VERSION_MINOR 5
+#define PRIMECOUNT_VERSION_MINOR 6
 
 namespace primecount {
 

From f7c9f336def978e8eb8d1cd5854d18ecf99ef209 Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Tue, 28 Feb 2017 22:29:09 +0100
Subject: [PATCH 20/37] Update file sizes

---
 README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index af9f08a5a..5e711fa11 100644
--- a/README.md
+++ b/README.md
@@ -31,8 +31,8 @@ These binaries are statically linked and require a CPU which supports the POPCNT
 instruction (2010 or later).
 
 * [primecount-3.6-win64.zip](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-win64.zip), 404K
-* [primecount-3.6-linux-x64.tar.gz](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-linux-x64.tar.gz), 915K
-* [primecount-3.6-macOS-x64.tar.gz](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-macOS-x64.tar.gz), 688K
+* [primecount-3.6-linux-x64.tar.gz](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-linux-x64.tar.gz), 1018K
+* [primecount-3.6-macOS-x64.tar.gz](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-macOS-x64.tar.gz), 897K
 * Binaries with backup functionality are available [here](https://github.com/kimwalisch/primecount/tree/backup#primecount-backup)
 
 Usage examples

From 6f286c604f1ab370f47b7af8fd86a465c70f3238 Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Wed, 1 Mar 2017 17:52:20 +0100
Subject: [PATCH 21/37] Improved AVX2 check

---
 CMakeLists.txt | 35 ++++++++++++++++-------------------
 1 file changed, 16 insertions(+), 19 deletions(-)

diff --git a/CMakeLists.txt b/CMakeLists.txt
index eafe3441a..19f150b8f 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -109,45 +109,42 @@ if(OPENMP_FOUND)
     set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${OpenMP_CXX_FLAGS}")
 endif()
 
-# Use -Werror for compiler checks ####################################
-
-set(COPY_CXX_FLAGS "${CMAKE_CXX_FLAGS}")
-set(CMAKE_CXX_FLAGS -Werror)
-
 # Check -mpopcnt compiler flag #######################################
 
 if(ENABLE_POPCNT)
+    set(COPY_CXX_FLAGS "${CMAKE_CXX_FLAGS}")
+    set(CMAKE_CXX_FLAGS -Werror)
     check_cxx_compiler_flag(-mpopcnt mpopcnt)
+    set(CMAKE_CXX_FLAGS "${COPY_CXX_FLAGS}")
     if(mpopcnt)
-        set(COPY_CXX_FLAGS "${COPY_CXX_FLAGS} -mpopcnt")
+        set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mpopcnt")
     endif()
 endif()
 
 # Check -mpopcntd compiler flag ######################################
 
 if(ENABLE_POPCNT)
+    set(COPY_CXX_FLAGS "${CMAKE_CXX_FLAGS}")
+    set(CMAKE_CXX_FLAGS -Werror)
     check_cxx_compiler_flag(-mpopcntd mpopcntd)
+    set(CMAKE_CXX_FLAGS "${COPY_CXX_FLAGS}")
     if(mpopcntd)
-        set(COPY_CXX_FLAGS "${COPY_CXX_FLAGS} -mpopcntd")
+        set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -mpopcntd")
     endif()
 endif()
 
-# Restore CMAKE_CXX_FLAGS ############################################
-
-set(CMAKE_CXX_FLAGS "${COPY_CXX_FLAGS}")
-
-# Check target("avx2") ###############################################
+# Check AVX2 (x86_64) compiler support  ##############################
 
 check_cxx_source_compiles("
-    __attribute__ ((target (\"default\")))
-    int func() { return 0; }
+    #include <immintrin.h>
     __attribute__ ((target (\"avx2\")))
-    int func() { return 1; }
-    int main() { return func(); }"
-    target_avx2)
+    void func() { __m256i v = _mm256_setzero_si256(); }
+    int x = __builtin_cpu_supports(\"avx2\");
+    int main() { return 0; }"
+    have_avx2)
 
-if(target_avx2)
-    add_definitions(-DHAVE_TARGET_AVX2)
+if(have_avx2)
+    add_definitions(-DHAVE_AVX2)
 endif()
 
 # Check if int128_t type exists ######################################

From 1b64c39d48650a5b378abbc91ecf9bf0ff0d538d Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Wed, 1 Mar 2017 18:03:01 +0100
Subject: [PATCH 22/37] Get rid of GCC Function Multiversioning

GCC Function Multiversioning only works on Linux. The new code uses __builtin_cpu_supports() and works on Windows, Linux and macOS with GCC. Clang will likely also work in near future.
---
 src/BitSieve-popcnt.cpp | 23 +++++++++++------------
 1 file changed, 11 insertions(+), 12 deletions(-)

diff --git a/src/BitSieve-popcnt.cpp b/src/BitSieve-popcnt.cpp
index 99a92f22b..97799af7c 100644
--- a/src/BitSieve-popcnt.cpp
+++ b/src/BitSieve-popcnt.cpp
@@ -51,7 +51,7 @@ uint64_t popcnt(const uint64_t* data, uint64_t size)
 } // namespace POPCNT
 } // namespace
 
-#if defined(HAVE_TARGET_AVX2)
+#if defined(HAVE_AVX2)
 
 #include <immintrin.h>
 
@@ -179,24 +179,21 @@ uint64_t popcnt(const uint64_t* data, uint64_t size)
 
 #endif
 
-#if defined(HAVE_TARGET_AVX2)
-
 namespace {
 
-__attribute__ ((target ("default")))
-uint64_t popcnt(const uint64_t* data, uint64_t size)
-{
-  return POPCNT::popcnt(data, size);
-}
+#if defined(HAVE_AVX2)
+
+// calls CPUID at program startup
+const int avx2 = __builtin_cpu_supports("avx2");
 
-__attribute__ ((target ("avx2")))
 uint64_t popcnt(const uint64_t* data, uint64_t size)
 {
-  return AVX2::popcnt(data, size);
+  if (avx2)
+    return AVX2::popcnt(data, size);
+  else
+    return POPCNT::popcnt(data, size);
 }
 
-} // namespace
-
 #else
 
 uint64_t popcnt(const uint64_t* data, uint64_t size)
@@ -206,6 +203,8 @@ uint64_t popcnt(const uint64_t* data, uint64_t size)
 
 #endif
 
+} // namespace
+
 namespace primecount {
 
 /// Count the number of 1 bits inside [start, stop]

From e121431306355e2150b5b4fb2bc07d9c590a0fab Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Wed, 1 Mar 2017 18:06:50 +0100
Subject: [PATCH 23/37] Test all branches

---
 appveyor.yml | 4 ----
 1 file changed, 4 deletions(-)

diff --git a/appveyor.yml b/appveyor.yml
index 500475c8f..50cbf8b37 100644
--- a/appveyor.yml
+++ b/appveyor.yml
@@ -3,10 +3,6 @@
 
 version: 1.0.{build}
 
-branches:
-  only:
-  - master
-
 platform:
   - x86
   - x64

From 9f606ac4b53e77db3764af4a0f89c842c62cdb4d Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Wed, 1 Mar 2017 18:23:08 +0100
Subject: [PATCH 24/37] Rename AVX2 test

---
 CMakeLists.txt | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/CMakeLists.txt b/CMakeLists.txt
index 19f150b8f..91dc32214 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -141,9 +141,9 @@ check_cxx_source_compiles("
     void func() { __m256i v = _mm256_setzero_si256(); }
     int x = __builtin_cpu_supports(\"avx2\");
     int main() { return 0; }"
-    have_avx2)
+    AVX2)
 
-if(have_avx2)
+if(AVX2)
     add_definitions(-DHAVE_AVX2)
 endif()
 

From fa507c6ca90f8f0ec11157281458b62b13145a75 Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Wed, 1 Mar 2017 22:45:15 +0100
Subject: [PATCH 25/37] Fix AVX2 detection

---
 src/BitSieve-popcnt.cpp | 15 ++++++++++++---
 1 file changed, 12 insertions(+), 3 deletions(-)

diff --git a/src/BitSieve-popcnt.cpp b/src/BitSieve-popcnt.cpp
index 97799af7c..3bb1db67d 100644
--- a/src/BitSieve-popcnt.cpp
+++ b/src/BitSieve-popcnt.cpp
@@ -183,12 +183,21 @@ namespace {
 
 #if defined(HAVE_AVX2)
 
-// calls CPUID at program startup
-const int avx2 = __builtin_cpu_supports("avx2");
+struct CpuInfo
+{
+  int has_avx2;
+  CpuInfo()
+  {
+    __builtin_cpu_init();
+    has_avx2 = __builtin_cpu_supports("avx2");
+  }
+};
+
+const CpuInfo cpuInfo;
 
 uint64_t popcnt(const uint64_t* data, uint64_t size)
 {
-  if (avx2)
+  if (cpuInfo.has_avx2)
     return AVX2::popcnt(data, size);
   else
     return POPCNT::popcnt(data, size);

From ef1302be1a13332279e1b75c55b255aa8a229367 Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Wed, 1 Mar 2017 22:58:00 +0100
Subject: [PATCH 26/37] Refactor PhiTiny code

---
 include/PhiTiny.hpp | 6 +++---
 src/PhiTiny.cpp     | 4 ++--
 2 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/include/PhiTiny.hpp b/include/PhiTiny.hpp
index cd01d9b84..d721b8246 100644
--- a/include/PhiTiny.hpp
+++ b/include/PhiTiny.hpp
@@ -1,7 +1,7 @@
 ///
 /// @file  PhiTiny.hpp
 ///
-/// Copyright (C) 2016 Kim Walisch, <kim.walisch@gmail.com>
+/// Copyright (C) 2017 Kim Walisch, <kim.walisch@gmail.com>
 ///
 /// This file is distributed under the BSD License. See the COPYING
 /// file in the top level directory.
@@ -56,6 +56,8 @@ class PhiTiny {
   static const int totients[7];
 };
 
+extern const PhiTiny phiTiny;
+
 inline bool is_phi_tiny(int64_t a)
 {
   return PhiTiny::is_tiny(a);
@@ -66,7 +68,6 @@ inline bool is_phi_tiny(int64_t a)
 template <typename X, typename A>
 typename prt::make_signed<X>::type phi_tiny(X x, A a)
 {
-  extern const PhiTiny phiTiny;
   return phiTiny.phi(x, a);
 }
 
@@ -75,7 +76,6 @@ typename prt::make_signed<X>::type phi_tiny(X x, A a)
 template <typename X, typename A>
 X phi_tiny(X x, A a)
 {
-  extern const PhiTiny phiTiny;
   return phiTiny.phi(x, a);
 }
 
diff --git a/src/PhiTiny.cpp b/src/PhiTiny.cpp
index 5c009a021..b1edcc8bc 100644
--- a/src/PhiTiny.cpp
+++ b/src/PhiTiny.cpp
@@ -7,7 +7,7 @@
 ///        phi(x, a) = (x / pp) * φ(pp) + phi(x % pp, a)
 ///        with pp = 2 * 3 * ... * prime[a]
 ///
-/// Copyright (C) 2016 Kim Walisch, <kim.walisch@gmail.com>
+/// Copyright (C) 2017 Kim Walisch, <kim.walisch@gmail.com>
 ///
 /// This file is distributed under the BSD License. See the COPYING
 /// file in the top level directory.
@@ -21,7 +21,7 @@
 
 namespace primecount {
 
-extern const PhiTiny phiTiny = PhiTiny();
+const PhiTiny phiTiny;
 
 const int PhiTiny::pi[20] = { 0, 0, 1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8 };
 

From 409075d98b3d682fffb98330189f48e33dbceb76 Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Thu, 2 Mar 2017 11:23:40 +0100
Subject: [PATCH 27/37] Refactor CPU detection code

---
 src/BitSieve-popcnt.cpp | 16 +++-------------
 1 file changed, 3 insertions(+), 13 deletions(-)

diff --git a/src/BitSieve-popcnt.cpp b/src/BitSieve-popcnt.cpp
index 3bb1db67d..e93f8010b 100644
--- a/src/BitSieve-popcnt.cpp
+++ b/src/BitSieve-popcnt.cpp
@@ -183,21 +183,11 @@ namespace {
 
 #if defined(HAVE_AVX2)
 
-struct CpuInfo
-{
-  int has_avx2;
-  CpuInfo()
-  {
-    __builtin_cpu_init();
-    has_avx2 = __builtin_cpu_supports("avx2");
-  }
-};
-
-const CpuInfo cpuInfo;
-
 uint64_t popcnt(const uint64_t* data, uint64_t size)
 {
-  if (cpuInfo.has_avx2)
+  static const int has_avx2 = __builtin_cpu_supports("avx2");
+
+  if (has_avx2)
     return AVX2::popcnt(data, size);
   else
     return POPCNT::popcnt(data, size);

From 7b2d62e95585626f5c6fc8451f519d3ce9eaaac2 Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Thu, 2 Mar 2017 17:25:27 +0100
Subject: [PATCH 28/37] Refactor

---
 src/BitSieve-popcnt.cpp | 24 ++++++++++++++----------
 1 file changed, 14 insertions(+), 10 deletions(-)

diff --git a/src/BitSieve-popcnt.cpp b/src/BitSieve-popcnt.cpp
index e93f8010b..3d55d21a5 100644
--- a/src/BitSieve-popcnt.cpp
+++ b/src/BitSieve-popcnt.cpp
@@ -28,9 +28,13 @@ namespace POPCNT {
 ///
 uint64_t popcnt(const uint64_t* data, uint64_t size)
 {
-  uint64_t sum0 = 0, sum1 = 0, sum2 = 0, sum3 = 0;
-  uint64_t limit = size - size % 4;
+  uint64_t sum0 = 0;
+  uint64_t sum1 = 0;
+  uint64_t sum2 = 0;
+  uint64_t sum3 = 0;
+
   uint64_t i = 0;
+  uint64_t limit = size - size % 4;
 
   for (; i < limit; i += 4)
   {
@@ -64,7 +68,7 @@ __m256i popcnt(const __m256i v)
   __m256i m1 = _mm256_set1_epi8(0x55);
   __m256i m2 = _mm256_set1_epi8(0x33);
   __m256i m4 = _mm256_set1_epi8(0x0F);
-  __m256i t1 = _mm256_sub_epi8(v, (_mm256_srli_epi16(v,  1) & m1));
+  __m256i t1 = _mm256_sub_epi8(v, (_mm256_srli_epi16(v, 1) & m1));
   __m256i t2 = _mm256_add_epi8(t1 & m2, (_mm256_srli_epi16(t1, 2) & m2));
   __m256i t3 = _mm256_add_epi8(t2, _mm256_srli_epi16(t2, 4)) & m4;
 
@@ -96,8 +100,8 @@ uint64_t popcnt(const __m256i* data, uint64_t size)
   __m256i sixteens = _mm256_setzero_si256();
   __m256i twosA, twosB, foursA, foursB, eightsA, eightsB;
 
-  uint64_t limit = size - size % 16;
   uint64_t i = 0;
+  uint64_t limit = size - size % 16;
 
   for(; i < limit; i += 16)
   {
@@ -139,14 +143,14 @@ uint64_t popcnt(const __m256i* data, uint64_t size)
 
 /// Align memory to 32 bytes boundary
 void align(const uint64_t*& p,
-           uint64_t* size,
-           uint64_t* total)
+           uint64_t& size,
+           uint64_t& total)
 {
   for (; (uintptr_t) p % 32 != 0; p++)
   {
-    assert(*size > 0);
-    *total += popcnt64(*p);
-    *size -= 1;
+    assert(size > 0);
+    total += popcnt64(*p);
+    size -= 1;
   }
 }
 
@@ -162,7 +166,7 @@ uint64_t popcnt(const uint64_t* data, uint64_t size)
   // for array sizes >= 1 kilobyte
   if (size * 8 >= 1024)
   {
-    align(data, &size, &total);
+    align(data, size, total);
     total += popcnt((const __m256i*) data, size / 4);
     data += size - size % 4;
     size = size % 4;

From 49a786e83710b4e6e6dd0a074209cfc3375b076b Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Thu, 2 Mar 2017 20:26:17 +0100
Subject: [PATCH 29/37] Fix time measuring

When OpenMP was disabled the elapsed time was not accurate.
---
 src/primecount.cpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/primecount.cpp b/src/primecount.cpp
index 6f139e047..6a78e8755 100644
--- a/src/primecount.cpp
+++ b/src/primecount.cpp
@@ -275,7 +275,7 @@ double get_wtime()
 #ifdef _OPENMP
   return omp_get_wtime();
 #else
-  return (double) (std::clock() / CLOCKS_PER_SEC);
+  return (double) std::clock() / CLOCKS_PER_SEC;
 #endif
 }
 

From 18e97d8880519508f2436e13fecb2d14499444a3 Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Thu, 2 Mar 2017 20:53:17 +0100
Subject: [PATCH 30/37] Update file sizes

---
 README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index 5e711fa11..3bd68a92c 100644
--- a/README.md
+++ b/README.md
@@ -30,9 +30,9 @@ Below are the latest precompiled binaries for Windows 64-bit, Linux and OS X.
 These binaries are statically linked and require a CPU which supports the POPCNT
 instruction (2010 or later).
 
-* [primecount-3.6-win64.zip](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-win64.zip), 404K
+* [primecount-3.6-win64.zip](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-win64.zip), 400K
 * [primecount-3.6-linux-x64.tar.gz](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-linux-x64.tar.gz), 1018K
-* [primecount-3.6-macOS-x64.tar.gz](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-macOS-x64.tar.gz), 897K
+* [primecount-3.6-macOS-x64.tar.gz](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-macOS-x64.tar.gz), 922K
 * Binaries with backup functionality are available [here](https://github.com/kimwalisch/primecount/tree/backup#primecount-backup)
 
 Usage examples

From 8a469d2014a2a656697bce2992890e54e3987652 Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Thu, 2 Mar 2017 21:37:04 +0100
Subject: [PATCH 31/37] Describe AVX2 usage

---
 README.md | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index 3bd68a92c..419bf411c 100644
--- a/README.md
+++ b/README.md
@@ -26,9 +26,10 @@ used to compute several world records e.g.
 
 Binaries
 --------
-Below are the latest precompiled binaries for Windows 64-bit, Linux and OS X.
+Below are the latest primecount binaries for Windows 64-bit, Linux and macOS.
 These binaries are statically linked and require a CPU which supports the POPCNT
-instruction (2010 or later).
+instruction (2010 or later). primecount also uses the AVX2 instruction set (if
+available) to speed up the computation of the hard special leaves. 
 
 * [primecount-3.6-win64.zip](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-win64.zip), 400K
 * [primecount-3.6-linux-x64.tar.gz](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-linux-x64.tar.gz), 1018K

From f90dddfa2b0513f30ada60a520107b56850feb6e Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Thu, 2 Mar 2017 22:01:59 +0100
Subject: [PATCH 32/37] Changes in version 3.6

---
 ChangeLog | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/ChangeLog b/ChangeLog
index 11f0975e6..c59273394 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,6 +1,6 @@
-2017-02-27 Kim Walisch  <kim.walisch@gmail.com>
+2017-03-02 Kim Walisch  <kim.walisch@gmail.com>
 
-  Version 3.6 work in progress.
+  Version 3.6 released.
 
   This version features a new AVX2 popcount algorithm which
   computes the hard special leaves up to 15% faster on x86 CPUs
@@ -8,6 +8,7 @@
 
   * BitSieve-popcnt.cpp: New AVX2 popcount algorithm.
   * popcnt.hpp: Fix clang performance bug.
+  * primecount.cpp: Fix clang time measuring.
   * CMakeLists.txt: Add AVX2 check.
 
 2016-12-16 Kim Walisch  <kim.walisch@gmail.com>

From fa33c9b0eda8d36f39d80a02ca01b4392d554595 Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Thu, 2 Mar 2017 23:12:21 +0100
Subject: [PATCH 33/37] Update file sizes

---
 README.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/README.md b/README.md
index 419bf411c..194507234 100644
--- a/README.md
+++ b/README.md
@@ -31,9 +31,9 @@ These binaries are statically linked and require a CPU which supports the POPCNT
 instruction (2010 or later). primecount also uses the AVX2 instruction set (if
 available) to speed up the computation of the hard special leaves. 
 
-* [primecount-3.6-win64.zip](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-win64.zip), 400K
-* [primecount-3.6-linux-x64.tar.gz](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-linux-x64.tar.gz), 1018K
-* [primecount-3.6-macOS-x64.tar.gz](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-macOS-x64.tar.gz), 922K
+* [primecount-3.6-win64.zip](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-win64.zip), 400 KB
+* [primecount-3.6-linux-x64.tar.gz](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-linux-x64.tar.gz), 1 MB
+* [primecount-3.6-macOS-x64.tar.gz](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-macOS-x64.tar.gz), 922 KB
 * Binaries with backup functionality are available [here](https://github.com/kimwalisch/primecount/tree/backup#primecount-backup)
 
 Usage examples

From ca82262412bbf6fff9a67b120befa0e313064b0a Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Sat, 4 Mar 2017 14:21:49 +0100
Subject: [PATCH 34/37] Improved AVX2 popcount

---
 src/BitSieve-popcnt.cpp | 41 +++++++++++++++++++++++++++--------------
 1 file changed, 27 insertions(+), 14 deletions(-)

diff --git a/src/BitSieve-popcnt.cpp b/src/BitSieve-popcnt.cpp
index 3d55d21a5..71b9d3ff4 100644
--- a/src/BitSieve-popcnt.cpp
+++ b/src/BitSieve-popcnt.cpp
@@ -62,19 +62,6 @@ uint64_t popcnt(const uint64_t* data, uint64_t size)
 namespace {
 namespace AVX2 {
 
-__attribute__ ((target ("avx2")))
-__m256i popcnt(const __m256i v)
-{
-  __m256i m1 = _mm256_set1_epi8(0x55);
-  __m256i m2 = _mm256_set1_epi8(0x33);
-  __m256i m4 = _mm256_set1_epi8(0x0F);
-  __m256i t1 = _mm256_sub_epi8(v, (_mm256_srli_epi16(v, 1) & m1));
-  __m256i t2 = _mm256_add_epi8(t1 & m2, (_mm256_srli_epi16(t1, 2) & m2));
-  __m256i t3 = _mm256_add_epi8(t2, _mm256_srli_epi16(t2, 4)) & m4;
-
-  return _mm256_sad_epu8(t3, _mm256_setzero_si256());
-}
-
 __attribute__ ((target ("avx2")))
 void CSA(__m256i& h, __m256i& l, __m256i a, __m256i b, __m256i c)
 {
@@ -83,6 +70,32 @@ void CSA(__m256i& h, __m256i& l, __m256i a, __m256i b, __m256i c)
   l = u ^ c;
 }
 
+__attribute__ ((target ("avx2")))
+__m256i popcnt(__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 = v & low_mask;
+    __m256i hi = _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
@@ -163,7 +176,7 @@ uint64_t popcnt(const uint64_t* data, uint64_t size)
   uint64_t total = 0;
 
   // AVX2 popcount is faster than POPCNT 
-  // for array sizes >= 1 kilobyte
+  // for array sizes >= 1 KB
   if (size * 8 >= 1024)
   {
     align(data, size, total);

From ad888114f22db116d2c9e0da80d589d7ab36a537 Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Sat, 4 Mar 2017 15:22:08 +0100
Subject: [PATCH 35/37] Update macOS file size

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 194507234..e69c8584c 100644
--- a/README.md
+++ b/README.md
@@ -33,7 +33,7 @@ available) to speed up the computation of the hard special leaves.
 
 * [primecount-3.6-win64.zip](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-win64.zip), 400 KB
 * [primecount-3.6-linux-x64.tar.gz](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-linux-x64.tar.gz), 1 MB
-* [primecount-3.6-macOS-x64.tar.gz](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-macOS-x64.tar.gz), 922 KB
+* [primecount-3.6-macOS-x64.tar.gz](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-macOS-x64.tar.gz), 899 KB
 * Binaries with backup functionality are available [here](https://github.com/kimwalisch/primecount/tree/backup#primecount-backup)
 
 Usage examples

From 0af058008f324461128048e6d61ea87230c30717 Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Sat, 4 Mar 2017 15:24:14 +0100
Subject: [PATCH 36/37] Update macOS file extension

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index e69c8584c..ccdfe5dc6 100644
--- a/README.md
+++ b/README.md
@@ -33,7 +33,7 @@ available) to speed up the computation of the hard special leaves.
 
 * [primecount-3.6-win64.zip](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-win64.zip), 400 KB
 * [primecount-3.6-linux-x64.tar.gz](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-linux-x64.tar.gz), 1 MB
-* [primecount-3.6-macOS-x64.tar.gz](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-macOS-x64.tar.gz), 899 KB
+* [primecount-3.6-macOS-x64.zip](https://dl.bintray.com/kimwalisch/primecount/primecount-3.6-macOS-x64.zip), 899 KB
 * Binaries with backup functionality are available [here](https://github.com/kimwalisch/primecount/tree/backup#primecount-backup)
 
 Usage examples

From 8f082a3bb133b93b7c13cb560de7189ab8584662 Mon Sep 17 00:00:00 2001
From: Kim Walisch <kim.walisch@gmail.com>
Date: Sat, 4 Mar 2017 15:26:44 +0100
Subject: [PATCH 37/37] Changes in version 3.6

---
 ChangeLog | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/ChangeLog b/ChangeLog
index c59273394..3600ffdd5 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,4 +1,4 @@
-2017-03-02 Kim Walisch  <kim.walisch@gmail.com>
+2017-03-04 Kim Walisch  <kim.walisch@gmail.com>
 
   Version 3.6 released.