Static derivative computation test added (boost::proto).

examples/firstAndSecondDerivative.cpp

@@ -29,14 +29,14 @@ T ddf(const T & x)
 int main()
 {
 	double xdbl = 1.5;
-	
+
 	{
 		cout << "Analytical\n";
 		cout << "f(x)      = " << f(xdbl) << endl;
 		cout << "df(x)/dt  = " << df(xdbl) << endl;
 		cout << "d²f(x)/dt = " << ddf(xdbl) << endl;
 	}
-	
+
 	// 1st derivative forward
 	{
 		using Fd = Dual<double>;
@@ -47,7 +47,7 @@ int main()
 		cout << "f(x)      = " << y.a << endl;
 		cout << "df(x)/dt  = " << y.d(0) << endl;
 	}
-	
+
 	// 2nd derivative forward
 	/*
 	{

tests/compile_time_derivative/Makefile

@@ -0,0 +1,33 @@
+# Declaration of variables
+C = clang
+C_FLAGS = -Wall
+CC = clang++
+CC_FLAGS = -Wall -std=c++17 -O0
+LD_FLAGS =
+INCLUDES =
+
+# File names
+EXEC = run
+CSOURCES = $(wildcard *.c)
+COBJECTS = $(CSOURCES:.c=.o)
+SOURCES = $(wildcard *.cpp)
+OBJECTS = $(SOURCES:.cpp=.o)
+
+# Main target
+$(EXEC): $(COBJECTS) $(OBJECTS)
+	$(CC) $(LD_FLAGS) $(COBJECTS) $(OBJECTS) -o $(EXEC)
+
+# To obtain object files
+%.o: %.cpp
+	$(CC) $(INCLUDES) $(CC_FLAGS) -o $@ -c $<
+
+# To obtain object files
+%.o: %.c
+	$(C) $(INCLUDES) $(C_FLAGS) -o $@ -c $<
+
+# To remove generated files
+clean:
+	rm -f $(COBJECTS) $(OBJECTS)
+
+cleaner:
+	rm -f $(EXEC) $(COBJECTS) $(OBJECTS)

tests/compile_time_derivative/compile_time_derivative.hpp

@@ -0,0 +1,112 @@
+#ifndef DEF_compile_time_derivative
+#define DEF_compile_time_derivative
+
+#include <boost/proto/proto.hpp>
+
+using namespace boost::proto;
+
+// Assuming derivative of one variable, the 'unknown'
+struct unknown {};
+
+// Boost.Proto calls this the expression wrapper
+// elements of the EDSL will have this type
+template<typename Expr>
+struct expression;
+
+// Boost.Proto calls this the domain
+struct derived_domain
+: domain<generator<expression>> {};
+
+// We will use a context to evaluate expression templates
+struct evaluation_context: callable_context<evaluation_context const> {
+    double value;
+
+    explicit evaluation_context(double value)
+        : value(value)
+    {}
+
+    typedef double result_type;
+
+    double operator()(tag::terminal, unknown) const
+    { return value; }
+};
+// And now we can do:
+// evaluation_context context(42);
+// eval(expr, context);
+// to evaluate an expression as though the unknown had value 42
+
+template<typename Expr>
+struct expression: extends<Expr, expression<Expr>, derived_domain> {
+    typedef extends<Expr, expression<Expr>, derived_domain> base_type;
+
+    expression(Expr const& expr = Expr())
+        : base_type(expr)
+    {}
+
+    typedef double result_type;
+
+    // We spare ourselves the need to write eval(expr, context)
+    // Instead, expr(42) is available
+    double operator()(double d) const
+    {
+        evaluation_context context(d);
+        return eval(*this, context);
+    }
+};
+
+// Boost.Proto calls this a transform -- we use this to operate
+// on the expression templates
+struct Derivative
+: or_<
+    when<
+        terminal<unknown>
+        , boost::mpl::int_<1>()
+    >
+    , when<
+        terminal<_>
+        , boost::mpl::int_<0>()
+    >
+    , when<
+        plus<Derivative, Derivative>
+        , _make_plus(Derivative(_left), Derivative(_right))
+    >
+    , when<
+        minus<Derivative, Derivative>
+        , _make_minus(Derivative(_left), Derivative(_right))
+    >
+    , when<
+        multiplies<Derivative, Derivative>
+        , _make_plus(
+            _make_multiplies(Derivative(_left), _right)
+            , _make_multiplies(_left, Derivative(_right))
+        )
+    >
+    //*
+    , when<
+        divides<Derivative, Derivative>
+        , _make_divides
+        (
+            _make_minus
+            (
+                _make_multiplies
+                (
+                    _right,
+                    Derivative(_left)
+                ),
+                _make_multiplies
+                (
+                    _left,
+                    Derivative(_right)
+                )
+            ),
+            _make_multiplies
+            (
+                _right,
+                _right
+            )
+        )
+    >
+    , otherwise<_>
+> {};
+
+#endif

tests/compile_time_derivative/main.cpp

@@ -0,0 +1,39 @@
+#include <iostream>
+
+#include "utils.hpp"
+#include "compile_time_derivative.hpp"
+
+using std::cout;
+using std::endl;
+
+// x is the unknown
+expression<terminal<unknown>::type> const x;
+
+// A transform works as a functor
+Derivative const derivative;
+
+template<typename T>
+T fct(const T & x) {
+	return (3)*x*x + (2)*x - (3) + (1)/x;
+}
+template<typename T>
+T dfct(const T & x) {
+	return (6)*x + (2) - (1)/(x*x);
+}
+
+// The file must be compiled with -O0 because with -O2 and up
+int main()
+{
+	auto func = (3*x*x + 2*x - 3 + 1./x);
+	// auto func = fct(x);
+	auto dfunc = derivative(func);
+
+	cout.precision(16);
+    for(double i = 0.1 ; i < 2. ; i+=.1)
+		std::cout << func(i) << "\t" << fct(i) << '\n';
+
+    for(double i = 0.1 ; i < 2. ; i+=.1)
+		std::cout << func(i) << "\t" << fct(i) << "\t" << dfunc(i) << "\t" << dfct(i) << '\n';
+
+	return 0;
+}