+
+
+double diff_aux(lmm_variable_t var, double x)
+{
+ double tmp_fpi, result;
+
+ XBT_IN2("(var (%p), x (%1.20f))", var, x);
+ xbt_assert0(var->func_fpi,
+ "Initialize the protocol functions first create variables before.");
+
+ tmp_fpi = var->func_fpi(var, x);
+ result = - tmp_fpi;
+
+ XBT_OUT;
+ return result;
+}
+
+/** \brief Attribute the value bound to var->bound.
+ *
+ * \param func_fpi inverse of the partial differential of f (f prime inverse, (f')^{-1})
+ *
+ * Set default functions to the ones passed as parameters. This is a polimorfism in C pure, enjoy the roots of programming.
+ *
+ */
+void lmm_set_default_protocol_function(double (* func_fpi) (lmm_variable_t var, double x))
+{
+ func_fpi_def = func_fpi;
+}
+
+
+/**************** Vegas and Reno functions *************************/
+/*
+ * NOTE for Reno: all functions consider the network
+ * coeficient (alpha) equal to 1.
+ */
+
+/*
+ * For Vegas: $f(x) = \alpha D_f\ln(x)$
+ * Therefore: $fpi(x) = \frac{\alpha D_f}{x}$
+ */
+#define VEGAS_SCALING 1000.0
+double func_vegas_fpi(lmm_variable_t var, double x){
+ xbt_assert0(x>0.0,"Don't call me with stupid values!");
+ return VEGAS_SCALING*var->df/x;
+}
+
+/*
+ * For Reno: $f(x) = \frac{\sqrt{3/2}}{D_f} atan(\sqrt{3/2}D_f x)$
+ * Therefore: $fpi(x) = \sqrt{\frac{1}{{D_f}^2 x} - \frac{2}{3{D_f}^2}}$
+ */
+#define RENO_SCALING 1000.0
+double func_reno_fpi(lmm_variable_t var, double x){
+ double res_fpi;
+
+ xbt_assert0(var->df>0.0,"Don't call me with stupid values!");
+ xbt_assert0(x>0.0,"Don't call me with stupid values!");
+
+ res_fpi = 1/(var->df*var->df*x) - 2/(3*var->df*var->df);
+ if(res_fpi<=0.0) return 0.0;
+/* xbt_assert0(res_fpi>0.0,"Don't call me with stupid values!"); */
+ return sqrt(RENO_SCALING*res_fpi);
+}
+