[lmi] fma() is not a speed optimization: self-documenting patch

[Greg Chicares]

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diff --git a/financial.hpp b/financial.hpp
index 7eba93bb6..ee5aea5ff 100644
--- a/financial.hpp
+++ b/financial.hpp
@@ -30,6 +30,7 @@
 #include "miscellany.hpp"               // ios_out_app_binary()
 #include "zero.hpp"                     // decimal_root()
 
+#include <cmath>                        // fma()
 #include <fstream>
 #include <iterator>                     // iterator_traits
 
@@ -56,13 +57,31 @@ long double fv
     // Symbol v, meaning 1/(1+i), is standard. A corresponding
     // symbol u, meaning (1+i), is not standard, but should be.
     long double const u = 1.0L + i;
-    long double z = 0.0L;
-    for(InputIterator j = first; j != last; ++j)
+    long double z = *first;
+    for(InputIterator j = 1 + first; j != last; ++j)
         {
-        z += *j;
-        z *= u;
+// several options tested with:
+//   $make $coefficiency unit_tests unit_test_targets=financial_test 2>&1 
|grep form
+// all unit tests pass for all options; only speed varies
+//
+// HEAD (without the other modifications here):
+//      z += *j;
+//      z *= u;
+// iterator  form: 1.440e-02 s mean;      13512 us least of  70 runs
+// container form: 1.361e-02 s mean;      13387 us least of  74 runs
+
+// Rearranged calculation (multiply, then add):
+//      z = (z * u) + *j;
+// iterator  form: 1.519e-02 s mean;      13450 us least of  66 runs
+// container form: 1.368e-02 s mean;      13456 us least of  74 runs
+
+// Fused multiply-add...expecting a speed gain?
+        z = std::fma(z, u, *j);
+// iterator  form: 3.343e-01 s mean;     333474 us least of   3 runs
+// container form: 3.338e-01 s mean;     333260 us least of   3 runs
+// no material difference observed with std::fmal() instead of std::fma()
         }
-    return z;
+    return z * u;
 }
 
 /// IRR: internal rate of return
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