+/** \brief Attribute the value bound to var->bound.
+ *
+ * \param func_f default function f associated with the chosen protocol flavor
+ * \param func_fp partial differential of f (f prime, f')
+ * \param func_fpi inverse of the partial differential of f (f prime inverse, (f')^{-1})
+ * \param func_fpip partial differential of the inverse of the partial differential of f (f prime inverse prime, ((f')^{-1})')
+ *
+ * Set default functions to the ones passed as parameters.
+ *
+ */
+void lmm_set_default_protocol_functions(double (* func_f) (lmm_variable_t var, double x),
+ double (* func_fp) (lmm_variable_t var, double x),
+ double (* func_fpi) (lmm_variable_t var, double x),
+ double (* func_fpip) (lmm_variable_t var, double x))
+
+{
+ func_f_def = func_f;
+ func_fp_def = func_fp;
+ func_fpi_def = func_fpi;
+ func_fpip_def = func_fpip;
+}
+
+
+/*
+ * NOTE for Reno: all functions consider the network
+ * coeficient (alpha) equal to 1.
+ */
+
+/*
+ * For Reno f: $\alpha_f d_f \log\left(x_f\right)$
+ */
+double func_reno_f(lmm_variable_t var, double x){
+ xbt_assert0(x,"Please report this bug.");
+ return var->df * log(x);
+}
+
+/*
+ * For Reno fp: $\frac{\alpha D_f}{x}$
+ */
+double func_reno_fp(lmm_variable_t var, double x){
+ xbt_assert0(x,"Please report this bug.");
+ return var->df/x;
+}
+
+/*
+ * For Reno fpi: $\frac{\alpha D_f}{x}$
+ */
+double func_reno_fpi(lmm_variable_t var, double x){
+ xbt_assert0(x,"Please report this bug.");
+ return var->df/x;
+}
+
+/*
+ * For Reno fpip: $-\frac{\alpha D_f}{x^2}$
+ */
+double func_reno_fpip(lmm_variable_t var, double x){
+ xbt_assert0(x,"Please report this bug.");
+ return -( var->df/(x*x) ) ;
+}
+
+
+/*
+ * For Vegas f: $\frac{\sqrt{\frac{3}{2}}}{D_f} \arctan\left(\sqrt{\frac{3}{2}}x_f D_f\right)$
+ */
+double func_vegas_f(lmm_variable_t var, double x){
+ xbt_assert0(x,"Please report this bug.");
+ // \sqrt{3/2} = 0.8164965808
+ return (0.8164965808 / var->df) * atan( (0.8164965808 / var->df)*x );
+}
+
+/*
+ * For Vegas fp: $\frac{3{D_f}^2}{3{D_f}^2x^2 + 2}$
+ */
+double func_vegas_fp(lmm_variable_t var, double x){
+ xbt_assert0(x,"Please report this bug.");
+ return (3*var->df*var->df) / (3*var->df*var->df*x*x + 2);
+}
+
+/*
+ * For Vegas fpi: $\sqrt{\frac{1}{x} - \frac{2}{3{D_f}^2}}$
+ */
+double func_vegas_fpi(lmm_variable_t var, double x){
+ double res_fpi;
+ xbt_assert0( (x<0.0) ,"Please report this bug.");
+ xbt_assert0( (var->df<0.0), "Please report this bug.");
+ res_fpi = (1/x) - 2/(3*var->df*var->df);
+ return sqrt(res_fpi);
+}
+
+/*
+ * For Vegas fpip: $-\frac{1}{2x^2\sqrt{\frac{1}{x} - \frac{2}{3{D_f}^2}}}$
+ */
+double func_vegas_fpip(lmm_variable_t var, double x){
+ double res_fpip;
+ xbt_assert0(x,"Please report this bug.");
+ xbt_assert0( (x<0.0), "Please report this bug.");
+ res_fpip = sqrt(1/x - 2/(3*var->df*var->df));
+ return -(1/(2*x*x*res_fpip));
+}