Infinite series approximation of pi in C not terminating

Question

Here is my code, when using print statements it appeared to be an infinite loop:

some potential issues i can troubleshoot are integer division, and perhaps figuring out if the algorithm terminates, and if it always has the correct output, perhaps there is some idiosyncrasy of the C language that I do not understand causing this issue?

From my understanding as the sum tends to negative infinity it will cause the break statement to be triggered ending the algorithm once it reaches an approximation of epsilon precision.

#include <stdio.h>

int main()
{

  double pi, sum, epsilon;
  long long i=1;
  long long max = 2147483647;
  printf("Pleas enter the desired accuracy epsilon : ");
  scanf("%f", &epsilon);
  while (i<max){
    if (i%2 == 0){
      sum = -4.0/(2.0*i-1);
    }else if (i%2 ==1){
      sum = (4.0/(2.0*i-1));
    }
    if (sum < epsilon){
      break;
    }
    pi += sum;
  }
  printf("The value of pi approximated to epsion : %f is %f\n", epsilon, pi);
  return 0;
}

Use a `for` loop instead, then such mistakes are easier to find. — Some programmer dude, Nov 06 '18 at 05:23
thanks for the feedback, i added the increment within the loop, however it appears the final awnser is still 4.0, i will continue to troubleshoot. — Ben French, Nov 06 '18 at 05:26
If you're using C99 or newer, `printf` `%lf` is pointless (it's equivalent to `%f`). If you're using C90, `printf` `%lf` has undefined behavior. — melpomene, Nov 06 '18 at 05:50
@melpomene I have got the algorithm working, however I need to display more than the 6 digits standard with double, how would you recommend doing that — Ben French, Nov 06 '18 at 05:53
I just used %20.18f for 18 digits of precision, is that common/accurate for floating point arithmetic? — Ben French, Nov 06 '18 at 05:56
Please read [How to debug small programs](https://ericlippert.com/2014/03/05/how-to-debug-small-programs/) — Basile Starynkevitch, Nov 06 '18 at 05:59
Please stop changing your question in a way that invalidates existing answers. — melpomene, Nov 06 '18 at 06:00
Read also the documentation of every function you are using, notably of [scanf](https://en.cppreference.com/w/c/io/fscanf) and of [printf](https://en.cppreference.com/w/c/io/printf). Read http://floating-point-gui.de/ — Basile Starynkevitch, Nov 06 '18 at 06:07
Welcome to Stack Overflow! Do not edit the question to [invalidate existing answers](https://meta.stackoverflow.com/a/290704/3956566) — , Nov 06 '18 at 07:59

P.W · Accepted Answer · 2018-11-06T05:44:42.807

1

You are not increment the value of i in your while loop. As a result its value always remains 1.

Increment i after your processing is done before the closing } of the while loop.

Initialize the values of pi, sum, epsilon so that you do not run into undefined behavior when you try to read their values for the first time.

Also, with proper options enabled (-Wall with GCC) the compiler will warn you, that you are trying to read a float into a double.

warning: format '%f' expects argument of type 'float *', but argument 2 has type 'double *' [-Wformat=]

   scanf("%f", &epsilon);

          ~^   ~~~~~~~~

So you have to use the correct conversion specifier: %lf instead of %f in your scanf statement.

If you are not very particular about the number 2147483647 and just want a large value, you can also use ULLONG_MAX (from limits.h) to initialize max instead of hard-coding the value.

edited Nov 06 '18 at 05:44

answered Nov 06 '18 at 05:21

P.W

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`ULLONG_MAX` is guaranteed not to be `2147483647`. – melpomene Nov 06 '18 at 05:34
the arithmetic is still not working properly however – Ben French Nov 06 '18 at 05:43
@BenFrench: Have you initialized `pi, sum, epsilon` at the beginning? – P.W Nov 06 '18 at 05:45
yeah i have initialized it and fixed the arithmetic, its working now, however it only displays to 6 decimal places, i am working on extending the floating point decimals displayed, thanks for your help so far though – Ben French Nov 06 '18 at 05:51

vinayawsm · Answer 2 · 2018-11-06T05:27:13.327

1

You need to increment i value in while loop.

Your looping condition while(i < max) is always satisfied (infinite loop). So the value of i or max should be changed inside the loop to ever end the loop.

edited Nov 06 '18 at 05:27

answered Nov 06 '18 at 05:21

vinayawsm

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melpomene · Answer 3 · 2018-11-06T05:30:05.380

1

Your code has undefined behavior:

scanf("%f", &epsilon);

scanf %f takes a float *, not double *. The correct format for double * is %lf.

Your loop condition while (i<max) is equivalent to while (1) as neither i nor max change their value inside the loop.

This also means sum is always 4:

sum = (4.0/(2.0*i-1));
// 4 / (2 * 1 - 1) = 4 / (2 - 1) = 4 / 1 = 4

pi += sum;

also has undefined behavior: pi is uninitialized.

edited Nov 06 '18 at 05:30

answered Nov 06 '18 at 05:24

melpomene

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yeah, it appears that sum is always 4, correct, I will try to fix this – Ben French Nov 06 '18 at 05:33

Infinite series approximation of pi in C not terminating

3 Answers3