floating point rounding errors

Question

The output is

x=1000300  y=1000000,  z=1000300

I can understand how I got x and z but ~~c's~~ y's output makes no sense.

 #include <stdio.h> 
 int main() 
 { int i=0; 
  float a = 100; 
  a = a*a*a*a*a;  

 float c = 3; 
 float x = 1000000*c + a; 
 float y = a; 
 float z = 0; 

  for (i=0; i<1000000; i++) 
  { y += c; 
    z += c; 
  } 

  z += a; 
  x /= 10000; 
  y /= 10000; 
  z /= 10000; 

 printf("x=%.0f  y=%.0f,  z=%.0f\n", x, y, z); 
 }

Am I missing something? Where is c's output? – Marlon Feb 21 '11 at 01:10 — Marlon, Feb 21 '11 at 01:10

Jonathan Leffler · Accepted Answer · 2011-02-21T01:27:34.877

5

The value in y starts out at 1E10 (from the assignment to a). You add 3 to this a million times.

The trouble is that a float has at most 7 significant decimal digits, so you effectively do not change y each time, hence the result divided by 10,000 is ~~10,000,000~~ 1,000,000 as displayed.

If you coded it with double, you would see more nearly the result you expect.

edited Feb 21 '11 at 01:27

answered Feb 21 '11 at 01:16

Jonathan Leffler

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Thank you for explanation though isn't y = 1,000,000? – foo Feb 21 '11 at 01:22
@Mateo - yes - I can't count zeroes. There are reasons why commas are used, and exponential notation. I'll fix my answer. (I should know that 1E10 / 1E4 == 1E6 too; I was careless.) – Jonathan Leffler Feb 21 '11 at 01:26

floating point rounding errors

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