Graceful Underflow

Question

I have been searching about this for so long, but i am not able to understand what this question means.

Question:

Write a program in any language to determine how your computer handles graceful 
underflow.

I understand that a overflow condition is something like this: if an integer can store a maximum value of x and if we assign a value of x+1, the value x+1 will be converted to the the lowest value the integer can hold. I understand that underflow is just the reverse.

How does it stand from High performance scientific computing / Linear algebra point of view ?

I have read this link , but i think it's the same underflow/ overflow stuff that i mentioned above. What does the graceful underflow stand for?

Answer 1

Okay,as per the link posted by @StoneBird in this link was particularly helpful. Here i have created a program in c that demonstrates the same.

#include <stdio.h>
#include <math.h>

int main(int argc, char **argv)
{
    unsigned int s,e,m;
    unsigned int* ptr;
    float a,temp=0;
    a=1;
    float min=pow(2,-129);
    while(a>min){
        temp=a;
        a=a/2;
    }
    printf("Value=%e\n",temp);
    ptr=(unsigned int*)&temp;
    s = *ptr >> 31;
    e = *ptr & 0x7f800000;
    e >>= 23;
    m = *ptr & 0x07fffff;
    printf("sign = %x\n",s);
    printf("exponent = %x\n",e);
    printf("mantissa = %x\n",m);
    return 0;
}

Here the min variable is used to change the final number...i used min=pow(2,-129), pow(2,-128) and pow(2,-130) to see the results and the saw the Denormal number appear.This wiki page explains it all.