Question

CS 153 Program 4 - Stirling Approximation (separate compilation) 1. Write a pure function double factoriallint Ni that computes N! N 1023°4 ... N-1)'N Do this the obvious way by initializing a product to one and then multiplying the integers together using a loop. Zero factorial is defined to be one. Now write a pure function double atining in Ni that uses the Stirling approximation to compute: approx[e!) - V22) In this formula, n is an integer, and e is base of the natural logarithm. Use the pre-processor constants from math.h: ME and M_PL Don't even dream of typing in your own literals, . Write your own function de la myPon (double x, int that computes Do this in a counting loop. Don't use the library function powil. Assume that n is a non-negative integer. Use your function Pow(in your function for the Stirling approximation. Put all three functions in a source file atirling Fun.c. This file will need some include files at the top. Except for debugging, don't have main) in this file 2. Create a header file still marun.ls that contains prototypes for three functions 3. Write a main function that asks the user for N, and then writes out a table forn from 1 to N where each line hasnt, and the Stirling approximation ton! Of course, for fairly small, will overflow. Put main in a source file called stirlingen. This file will need appropriate header files, including the one from above. Your three files should all be in the same subdirectory. Try to make the output look reasonably neat at least for small values of N You will need to fiddle with formats with printf. Compile your files and link them together using C:\CSourcege string Puno stilingain. n! Approx. 0.0000 1307674368000 1300430722199.4680 Use ANSI-C syntax Compile and run using the goc environment. Do not mix tabs and spaces in the source file. Debug thoroughly. Turn in three source files named as above using Blackboard.

program in C. please paste code, thanks!

Answer 1

Code :-

stirlingFun.h

double myPow(double x,int n);
double factorial(int N);
double stirling(int N);

stirlingFun.c

#include<math.h>
#include"stirlingFun.h"
double factorial(int N)
{
   int count;
   double product = 1;
   for (count = 1 ; count <= N ;count++)
   {
       product = product * count;
   }
   return product;
}
double stirling(int N)
{
   double rootTerm=0.0,powerTerm=0.0,product=0.0;
   rootTerm = sqrt(2*M_PI*N);
   powerTerm = N/M_E;
   powerTerm = myPow(powerTerm,N);
   product = rootTerm*powerTerm;
   return product;
}
double myPow(double x,int n)
{
   //Assuming n is positive integer
   double power = 1;
   int count;
   for (count = 1;count<=n;count++)
   {
       power = power * x;
   }
   return power;
}

stirlingMain.c

#include<stdio.h>
#include"stirlingFun.h"
int main()
{
   double pureFactorial=0.0,stirlingFactorial=0.0;
   int number,count;
   printf("Enter a number : ");
   scanf("%d",&number);
   printf("\tn\t\tn!\t\tapprox.\t\t\n");
   printf("-------------+-------------------+------------------------\n");
   for(count = 0;count<=number;count++)
   {
       pureFactorial = factorial(count);
       stirlingFactorial = stirling(count);
       printf("\t%3d %20.0f %20.4f\n",count,pureFactorial,stirlingFactorial);
   }
   return 0;
}

Note :- 20.0 means float with 0 decimal places

Output :-

C: \2020\27-02-2020>gcc - Wall stirlingFun.c stirlingMain.c -o file C:\ 12020\27-02-2020>file.exe Enter a number : 15 approx. 0.0000 0.9221 OHNMON00OONM 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000 5.8362 23.5062 118.0192 710.0782 4980.3958 39902.3955 359536.8728 3598695.6187 39615625.0506 475687486.4728 6187239475.1927 86661001740.5988 1300430722199.4680