Correct the equation for the entropy time derivative in GADGET2_SPH

This fixes #183 (closed) meaning that energy is now correctly conserved.

It also:

• Adds a parameter file and run script for the perturbed box test case.
• Adds entropy to the diagnostics file.
• Replace the MPI_AllReduce in the statistics collection by an MPI_Reduce since only rank 0 writes anyway.
• Gives a better documentation for the approx_exp() function.
• Adds an accuracy test for the approximate maths functions (currently only exp())
• Adds a test no make sure the symmetric and non-symmetric versions of the SPH interaction routines give the same answer. That was the origin of the energy non-conservation bug.

examples/PerturbedBox/makeIC.py

@@ -19,6 +19,7 @@
  ##############################################################################
 
 import h5py
+import sys
 import random
 from numpy import *
 
@@ -26,13 +27,13 @@ from numpy import *
 # at a constant density and pressure in a cubic box
 
 # Parameters
-periodic= 1      # 1 For periodic box
+periodic= 1          # 1 For periodic box
 boxSize = 1.
-L = 50           # Number of particles along one axis
-rho = 1.         # Density
-P = 1.           # Pressure
-gamma = 5./3.    # Gas adiabatic index
-pert = 0.01      # Perturbation scale (in units of the interparticle separation)
+L = int(sys.argv[1]) # Number of particles along one axis
+rho = 1.             # Density
+P = 1.               # Pressure
+gamma = 5./3.        # Gas adiabatic index
+pert = 0.01          # Perturbation scale (in units of the interparticle separation)
 fileName = "perturbedBox.hdf5"