CODEWITHSUNDEEP
cbit
user1697083
user1697083

Reputation:

Calculate epsilon for a float in C

I have to use bit/integer ops to figure out the epsilon for a given value in C. I know in terms of bit patterns that computing the next neighbor involves incrementing the mantissa, and if that overflows, to increment the exponent - but I'm not sure where to begin in terms of calculating the epsilon.

I can't use floating point math - so I need to generate the bit pattern directly. This makes it trickier because I cannot subtract.

Here's my understanding (based on some research I've done here on SO): the range changes obviously as the numbers get bigger, but I'm not sure how to use FLT_EPSILON to generate the right numbers. For 2^2x numbers, perhaps it is (FLT_EPSILON - 1) * number?

Upvotes: 2

Views: 3260

Answers (2)

Ivan Ivanov
Ivan Ivanov

Reputation: 2096

due to IEEE 754 format you need 1 in mantissa and 127 shifted to 23

float x;

*((int*) &x) = 1;
*((int*) &x) = *((int*) &x) | 104 << 23;

printf("%.12f\n", FLT_EPSILON);
printf("%.12f\n", x);

Upvotes: 2

MooseBoys
MooseBoys

Reputation: 6793

If your epsilon is simply the value of one LSB increment to the mantissa, the value should be 2^(exp-23). So if your input is [s][exp][mantissa] your epsilon should be [0][exp-23][0]. Sure enough, when given an input of 1.0 ([0][127][0]), the result is [0][104][0] = 2^-23 = FLT_EPSILON.

Upvotes: 4

Related Questions