Change merged black&scholes benchmark to use tie() for loop fusion

demo/blackscholes/nt2_merged/blackandscholes_nt2_merged.cpp

@@ -21,6 +21,7 @@
 #include <nt2/include/functions/unary_minus.hpp>
 #include <nt2/include/functions/plus.hpp>
 #include <nt2/include/functions/minus.hpp>
+#include <nt2/include/functions/tie.hpp>
 #include <nt2/include/constants/half.hpp>
 #include <vector>
 #include <iostream>
@@ -82,6 +83,9 @@ template<typename T> struct blackandscholes_nt2_merged
     Ta.resize(nt2::of_size(size_));
     ra.resize(nt2::of_size(size_));
     va.resize(nt2::of_size(size_));
+    da.resize(nt2::of_size(size_));
+    d1.resize(nt2::of_size(size_));
+    d2.resize(nt2::of_size(size_));
     R.resize(nt2::of_size(size_));
 
     for(std::size_t i = 1; i <= size_; ++i)
@@ -90,7 +94,11 @@ template<typename T> struct blackandscholes_nt2_merged
 
   void operator()()
   {
-    R = nt2::blackandscholes(Sa, Xa, Ta, ra, va);
+    nt2::tie(da,d1,d2,R) = nt2::tie ( nt2::sqrt(Ta)
+                                    , nt2::log(Sa/Xa) + (nt2::fma(nt2::sqr(va),T(0.5),ra)*Ta)/(va*da)
+                                    , nt2::fnms(va,da,d1)
+                                    , nt2::fnms(Xa*nt2::exp(-ra*Ta),nt2::fastnormcdf(d2),Sa*nt2::fastnormcdf(d1))
+                                    );
   }
 
   friend std::ostream& operator<<(std::ostream& os, blackandscholes_nt2_merged<T> const& p)
@@ -101,7 +109,7 @@ template<typename T> struct blackandscholes_nt2_merged
   std::size_t size() const { return size_; }
 
   private:
-  nt2::table<T> Sa, Xa, Ta, ra, va, R;
+  nt2::table<T> Sa, Xa, Ta, ra, va, R, da, d1, d2;
   std::size_t size_;
 };