The 'nan' output.

**Smriti P. Suman** · 06-08-2016

The following is a very simple code to generate the points in the graph of a function. However, I'm getting 'nan' as the output of 'ret' (marked in red).

insert

Code:

#include<iostream>
#include<math.h>


using namespace std;




float fun_1(float z)
{


   int k;


   float ret1=0;


   for(k=1; k<=1000; k++)
     {


       int c, d;
       int pk=1;
       int factk=1;


       for(c=1; c<=k; c++)
          {
             pk= pk*(3*c-2);
          }




        for(d=1; d<=3*k; d++)
          {
             factk=factk*d;
          }




       ret1= ret1+((pk*pow(z,3*k))/(factk));


     }


return(ret1);


}




float fun_2(float z)
{


   int k;


   float ret2=0;


   for(k=1; k<=1000; k++)
     {


       int c, d;
       int qk=1;
       int factk=1;


       for(c=1; c<=k; c++)
          {
             qk= qk*(3*c-1);
          }




        for(d=1; d<=3*k+1; d++)
          {
             factk=factk*d;
          }




       ret2= ret2+((qk*pow(z,(3*k+1)))/(factk));


     }


return(ret2);


}










float fun_main(float z, float c1, float c2)
{


  float ret1, ret2, ret;
  ret1=fun_1(z);
  ret2=fun_2(z);
  ret= c1*(1+ret1)-c2*(z+ret2);


  return(ret);


}




int main()


{


  float c1= 0.355028053887817;
  float c2= 0.258819403792807;


  float z;




  float fun_main(float z, float c1, float c2);
  float fun_1(float z);
  float fun_2(float z);


  for(z=-10; z<=10;)


  {
    float ret;
    ret= fun_main(z, c1, c2);


    cout<<z<<" "<<" "<<ret<<endl;


    z=z+0.01;
  }


return 0;
}

Kindly help me sort this problem out.

Thanks!

**Salem** · 06-08-2016

Use a debugger

Code:

$ g++ -Wall -g bar.cpp
$ gdb -q ./a.out 
Reading symbols from /home/sc/Documents/a.out...done.
(gdb) b fun_main
Breakpoint 1 at 0x400a89: file bar.cpp, line 53.
(gdb) run
Starting program: /home/sc/Documents/a.out 

Breakpoint 1, fun_main (z=-10, c1=0.355028063, c2=0.258819401) at bar.cpp:53
53        ret1=fun_1(z);
(gdb) n
54        ret2=fun_2(z);
(gdb) p ret1
$1 = -nan(0x400000)
(gdb) n
55        ret= c1*(1+ret1)-c2*(z+ret2);
(gdb) p ret2
$2 = -nan(0x400000)

OK, so now we know where all the nan's are coming from.

So delete the first breakpoint and set one at the start of fun_1 instead, and let's analyse it's behaviour.

Code:

(gdb) delete 1
(gdb) b fun_1
Breakpoint 2 at 0x400881: file bar.cpp, line 9.
(gdb) c
Continuing.
-10  -nan

Breakpoint 2, fun_1 (z=-9.98999977) at bar.cpp:9
9         float ret1=0;
(gdb) list
4       using namespace std;
5
6       float fun_1(float z)
7       {
8         int k;
9         float ret1=0;
10        for(k=1; k<=1000; k++)
11        {
12          int c, d;
13          int pk=1;
(gdb) 
14          int factk=1;
15          for(c=1; c<=k; c++)
16          {
17            pk= pk*(3*c-2);
18          }
19          for(d=1; d<=3*k; d++)
20          {
21            factk=factk*d;
22          }
23          ret1= ret1+((pk*pow(z,3*k))/(factk));
(gdb) b 23
Breakpoint 3 at 0x4008fc: file bar.cpp, line 23.
(gdb) c
Continuing.

Breakpoint 3, fun_1 (z=-9.98999977) at bar.cpp:23
23          ret1= ret1+((pk*pow(z,3*k))/(factk));
(gdb) printf "%d %d %d\n", k, pk, factk
1 1 6
(gdb) c
Continuing.

Breakpoint 3, fun_1 (z=-9.98999977) at bar.cpp:23
23          ret1= ret1+((pk*pow(z,3*k))/(factk));
(gdb) printf "%d %d %d\n", k, pk, factk
2 4 720
(gdb) c
Continuing.

Breakpoint 3, fun_1 (z=-9.98999977) at bar.cpp:23
23          ret1= ret1+((pk*pow(z,3*k))/(factk));
(gdb) printf "%d %d %d\n", k, pk, factk
3 28 362880
(gdb) c
Continuing.

Breakpoint 3, fun_1 (z=-9.98999977) at bar.cpp:23
23          ret1= ret1+((pk*pow(z,3*k))/(factk));
(gdb) printf "%d %d %d\n", k, pk, factk
4 280 479001600

Do you see just how quickly factk is growing.
It's only iteration 4 out of 1000 and it's already approaching the numeric limit for an integer.

You have a serious numeric overflow issue (or possibly several).

**Smriti P. Suman** · 06-08-2016

Thanks for pointing this out. I should have checked this out by myself.

Regards.

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