C++ Double size/ overflow questions

Question

I have recently come across something weird that I am having trouble understanding.

Basically I was trying to estimate the number of seconds that have passed in the last 2014 years. However the results that I was getting were negative numbers. I thought at first that it was some kind of overflow due to the size limitations of a double floating point variable, however after looking into that it seems that this is not the case. So I started to play around with the following code:

double test = 1.8*pow(10,308);
cout << test << endl;
test = 1.7*pow(10,308);
cout << test << endl;
test = 2*1000000000;
cout << test << endl;
test = 2*100*100*100*100*100;
cout << test << endl;
test = 1*1000000000;
cout << test << endl;
test = 1*100*100*100*100*100;
cout << test << endl;

This returned the following output:

inf
1.7e+308
2e+009
-1.47484e+009
1e+009
1.41007e+009

The first two results make sense to me. I am under the impression that 1.7e+308 is the maximum possible value that can be stores in a double, which means that 1.8e+308 wouldn't work - so the compiler interprets this as infinity? However after that things become a little confusing.

I don't understand why 2*10000000000 and 2*100*100*100*100*100 return different values?

Or why 1*10000000000 and 1*100*100*100*100*100 don't return that same value?

I also don't understand why 2*100*100*100*100*100 returns a negative value?

Also where is the 1.4... coming from when I am only multiplaying by 1 or 2?

If someone could help me understand this better it would be appreciated!

Answer 1

All of these except the first two are performing integer arithmetic, then converting the integer result to double. The strange values are the result of integer overflow (which gives undefined behaviour). You should get the results you expect if you use floating-point constants, for example

test = 2. * 100. * 100. * 100. * 100. * 100.;