Number of floats between two floats

Question

Say I have two Python floats a and b, is there an easy way to find out how many representable real numbers are between the two in IEEE-754 representati

Answer 1

I would look at the frexp function in the math module. The example below extracts the mantissa and converts it to an integer. The difference should be the number of floats between to the two values.

>>> math.frexp(1.1234567890)[0] * 2**53
5059599576307254.0
>>> math.frexp(1.12345678901)[0] * 2**53
5059599576352290.0

The following code should do it:

import math
import sys

def delta(x,y):
    '''Return the number of floats between x and y.'''
    x = float(x)
    y = float(y)
    if x == y:
        return 0
    elif x < y:
        return -delta(y,x)
    else:
        x_mant, x_exp = math.frexp(x)
        y_mant, y_exp = math.frexp(y)
        x_int = int(x_mant * 2**(sys.float_info.mant_dig + x_exp - y_exp))
        y_int = int(y_mant * 2**sys.float_info.mant_dig)
        return x_int - y_int

print(delta(1.123456789, 1.1234567889999))
450
>>>