Re: GUB and mpfr/mpc

[Dan Eble]

On Dec 4, 2014, at 09:58 , Masamichi HOSODA <address@hidden> wrote:
> 
>> Also, the mention of optimization reminds me of one of the horrors of 
>> floating point types: a value in a register can quietly be changed when it 
>> is written to memory.  Take a look at some of the “myths” in section 1 of 
>> https://hal.archives-ouvertes.fr/hal-00128124/en/ .
[…]
> I think that floating point can be used as long as it's used correct.
> 
> operator== shouldn't be used for comparison of floating point values.
> operator!= shouldn't be used too.
> operator< and operator> may be used.

The issue is more complex than that.  Sit down and try this:

#include <iostream>

int main(void)
{
  double a = 0;
  double b = 0;

  std::cin >> a;
  std::cin >> b;

  double x = a/b;
  if (x < a/b) {
    std::cout << "x:" << x << " < " << (a/b) << std::endl;
  }
  volatile double y = x;
  if (y < a/b) {
    std::cout << "y:" << y << " < " << (a/b) << std::endl;
  }

  return 0;
}

Results in LilyDev 3:

$ g++ fp.cc -o fp && (echo "2 3" | ./fp)
x:0.666667 < 0.666667
y:0.666667 < 0.666667

$ g++ -O3 fp.cc -o fp && (echo "2 3" | ./fp)
y:0.666667 < 0.666667

Add looping and you’ve got fatal issues.  (And if you’re like me, steam will 
erupt from your ears any second now...)
— 
Dan