# Next floating point number

Steven D'Aprano steve at REMOVETHIScyber.com.au
Fri Dec 16 22:23:38 EST 2005

```I'm looking for some way to get the next floating point number after any
particular float.

(Any mathematicians out there: I am aware that there is no "next real
number". But floats are not real numbers, they only have a finite
precision.)

According to the IEEE standard, there should be a routine like next(x,y)
which returns the next float starting from x in the direction of y.

Unless I have missed something, Python doesn't appear to give an interface
to the C library's next float function. I assume that most C floating
point libraries will have such a function.

So I came up with a pure Python implementation, and hoped that somebody
who had experience with numerical programming in Python would comment.

def nextfloat(x, y=None):
"""Return the next floating point number starting at x in the
direction of y. If y is not given, the direction is away from zero.
"""
from math import frexp # Returns a tuple (mantissa, exponent)
x = float(x)
if y is None:
if x < 0.0:
op = sub
else:
elif y > x:
elif y < x:
op = sub
else:
raise ValueError("direction float is equal to starting float")
# We find the next float by finding the smallest float epsilon which
# is distinguishable from x. We know epsilon will be a power of two,
# because floats are implemented internally in binary.
# We get our initial estimate for epsilon from the floating point
# exponent of x.
epsilon = 2.0**(frexp(x)) # epsilon > abs(x)
lasteps = epsilon # Save a copy of our last epsilon for later use.
while op(x, epsilon) != x:
lasteps = epsilon
epsilon /= 2.0
# When we get here, we've halved epsilon one time too many.
# We can't just double it, because that fails for the case where x is
# zero - epsilon will underflow to zero. So we need to save and use
# the previous iteration of epsilon.
return op(x, lasteps)

Thanks,

--
Steven.

```