add boost on mac

macx64/include/boost/histogram/accumulators/sum.hpp

@@ -0,0 +1,107 @@
+// Copyright 2018 Hans Dembinski
+//
+// Distributed under the Boost Software License, version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_HISTOGRAM_ACCUMULATORS_SUM_HPP
+#define BOOST_HISTOGRAM_ACCUMULATORS_SUM_HPP
+
+#include <boost/histogram/fwd.hpp>
+#include <cmath>
+#include <type_traits>
+
+namespace boost {
+namespace histogram {
+namespace accumulators {
+
+/**
+  Uses Neumaier algorithm to compute accurate sums.
+
+  The algorithm uses memory for two floats and is three to
+  five times slower compared to a simple floating point
+  number used to accumulate a sum, but the relative error
+  of the sum is at the level of the machine precision,
+  independent of the number of samples.
+
+  A. Neumaier, Zeitschrift fuer Angewandte Mathematik
+  und Mechanik 54 (1974) 39-51.
+*/
+template <typename RealType>
+class sum {
+public:
+  sum() = default;
+
+  /// Initialize sum to value
+  explicit sum(const RealType& value) noexcept : large_(value) {}
+
+  /// Set sum to value
+  sum& operator=(const RealType& value) noexcept {
+    large_ = value;
+    small_ = 0;
+    return *this;
+  }
+
+  /// Increment sum by one
+  sum& operator++() { return operator+=(1); }
+
+  /// Increment sum by value
+  sum& operator+=(const RealType& value) {
+    auto temp = large_ + value; // prevent optimization
+    if (std::abs(large_) >= std::abs(value))
+      small_ += (large_ - temp) + value;
+    else
+      small_ += (value - temp) + large_;
+    large_ = temp;
+    return *this;
+  }
+
+  /// Scale by value
+  sum& operator*=(const RealType& value) {
+    large_ *= value;
+    small_ *= value;
+    return *this;
+  }
+
+  template <class T>
+  bool operator==(const sum<T>& rhs) const noexcept {
+    return large_ == rhs.large_ && small_ == rhs.small_;
+  }
+
+  template <class T>
+  bool operator!=(const T& rhs) const noexcept {
+    return !operator==(rhs);
+  }
+
+  /// Return large part of the sum.
+  const RealType& large() const { return large_; }
+
+  /// Return small part of the sum.
+  const RealType& small() const { return small_; }
+
+  // allow implicit conversion to RealType
+  operator RealType() const { return large_ + small_; }
+
+  template <class Archive>
+  void serialize(Archive&, unsigned /* version */);
+
+private:
+  RealType large_ = RealType();
+  RealType small_ = RealType();
+};
+
+} // namespace accumulators
+} // namespace histogram
+} // namespace boost
+
+#ifndef BOOST_HISTOGRAM_DOXYGEN_INVOKED
+namespace std {
+template <class T, class U>
+struct common_type<boost::histogram::accumulators::sum<T>,
+                   boost::histogram::accumulators::sum<U>> {
+  using type = boost::histogram::accumulators::sum<common_type_t<T, U>>;
+};
+} // namespace std
+#endif
+
+#endif