From 3099e6be6c1874573109d1f8fa68800c32164b5b Mon Sep 17 00:00:00 2001
From: Danny Robson <danny@nerdcruft.net>
Date: Tue, 25 Aug 2015 17:25:55 +1000
Subject: [PATCH] maths: add kahan summation

---
 maths.hpp | 25 +++++++++++++++++++++++++
 1 file changed, 25 insertions(+)

diff --git a/maths.hpp b/maths.hpp
index d896c90e..a87ae18c 100644
--- a/maths.hpp
+++ b/maths.hpp
@@ -253,6 +253,31 @@ combination [[gnu::pure]] (unsigned n, unsigned k)
 }
 
 
+//-----------------------------------------------------------------------------
+// kahan summation for long floating point sequences
+
+template <class InputIt>
+typename std::iterator_traits<InputIt>::value_type
+fsum (InputIt first, InputIt last)
+{
+    using T = typename std::iterator_traits<InputIt>::value_type;
+    static_assert (std::is_floating_point<T>::value,
+                   "fsum only works for floating point types");
+
+    T sum = 0;
+    T c = 0;
+
+    for (auto cursor = first; cursor != last; ++cursor) {
+        T y = *cursor - c;
+        T t = sum + y;
+        c = (t - sum) - y;
+        sum = t;
+    }
+
+    return sum;
+}
+
+
 //-----------------------------------------------------------------------------
 /// Variadic minimum
 namespace util {