#! /usr/bin/env python # def r8_factorial_values ( n_data ): #*****************************************************************************80 # ## R8_FACTORIAL_VALUES returns values of the real factorial function. # # Discussion: # # 0! = 1 # I! = Product ( 1 <= J <= I ) J # # Although the factorial is an integer valued function, it quickly # becomes too large for an integer to hold. This routine still accepts # an integer as the input argument, but returns the function value # as a real number. # # In Mathematica, the function can be evaluated by: # # n! # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 27 December 2014 # # Author: # # John Burkardt # # Reference: # # Milton Abramowitz and Irene Stegun, # Handbook of Mathematical Functions, # US Department of Commerce, 1964. # # Stephen Wolfram, # The Mathematica Book, # Fourth Edition, # Wolfram Media / Cambridge University Press, 1999. # # Parameters: # # Input/output, integer N_DATA. The user sets N_DATA to 0 before the # first call. On each call, the routine increments N_DATA by 1, and # returns the corresponding data; when there is no more data, the # output value of N_DATA will be 0 again. # # Output, integer N, the argument of the function. # # Output, real FN, the value of the function. # import numpy as np n_max = 25 fn_vec = np.array ( [ \ 0.1000000000000000E+01, \ 0.1000000000000000E+01, \ 0.2000000000000000E+01, \ 0.6000000000000000E+01, \ 0.2400000000000000E+02, \ 0.1200000000000000E+03, \ 0.7200000000000000E+03, \ 0.5040000000000000E+04, \ 0.4032000000000000E+05, \ 0.3628800000000000E+06, \ 0.3628800000000000E+07, \ 0.3991680000000000E+08, \ 0.4790016000000000E+09, \ 0.6227020800000000E+10, \ 0.8717829120000000E+11, \ 0.1307674368000000E+13, \ 0.2092278988800000E+14, \ 0.3556874280960000E+15, \ 0.6402373705728000E+16, \ 0.1216451004088320E+18, \ 0.2432902008176640E+19, \ 0.1551121004333099E+26, \ 0.3041409320171338E+65, \ 0.9332621544394415E+158, \ 0.5713383956445855E+263 ] ) n_vec = np.array ( [ \ 0, \ 1, \ 2, \ 3, \ 4, \ 5, \ 6, \ 7, \ 8, \ 9, \ 10, \ 11, \ 12, \ 13, \ 14, \ 15, \ 16, \ 17, \ 18, \ 19, \ 20, \ 25, \ 50, \ 100, \ 150 ] ) if ( n_data < 0 ): n_data = 0 if ( n_max <= n_data ): n_data = 0 n = 0 fn = 0 else: n = n_vec[n_data] fn = fn_vec[n_data] n_data = n_data + 1 return n_data, n, fn def r8_factorial_values_test ( ): #*****************************************************************************80 # ## R8_FACTORIAL_VALUES_TEST tests R8_FACTORIAL_VALUES. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 27 December 2014 # # Author: # # John Burkardt # import platform print ( '' ) print ( 'R8_FACTORIAL_VALUES_TEST:' ) print ( ' Python version: %s' % ( platform.python_version ( ) ) ) print ( ' R8_FACTORIAL_VALUES returns values of the real factorial function.' ) print ( '' ) print ( ' N R8_FACTORIAL(N)' ) print ( '' ) n_data = 0 while ( True ): n_data, n, fn = r8_factorial_values ( n_data ) if ( n_data == 0 ): break print ( ' %8d %14.6g' % ( n, fn ) ) # # Terminate. # print ( '' ) print ( 'R8_FACTORIAL_VALUES_TEST:' ) print ( ' Normal end of execution.' ) return if ( __name__ == '__main__' ): from timestamp import timestamp timestamp ( ) r8_factorial_values_test ( ) timestamp ( )