why numpy's nextafter(0,inf) will raise err when flag under(flow) enabled?

Question

from numpy import nextafter,seterr
print(nextafter(0.,1.)) #5e-324
seterr(under="raise")
print(nextafter(0.,1.)) #FloatingPointError: underflow encountered in nextafter

Why is this code truggering the error below ?

FloatingPointError: underflow encountered in nextafter.

According to my tests, similar code works in C.

Answer 1

help(numpy.seterr) describes underflow as

Underflow: result so close to zero that some precision was lost

This corresponds to the more precise description in man feenableexcept:

The underflow exception occurs when a result has to be represented as a floating-point number, but has smaller absolute value than the smallest positive normalized floating-point number (and would lose much accuracy when represented as a denormalized number)

Zero is not a denormalized number. The next higher or lower value after zero is denormalized. Therefore a floating point exception is raised if you enable it. See also: What is a subnormal floating point number?

The following C code also signals a floating point exception:

#define _GNU_SOURCE
#include <fenv.h>
#include <math.h>
#include <stdio.h>

int main(void)
{
  double f = 0.;
  feenableexcept(FE_UNDERFLOW);
  f = nextafter(f, 1.);
  printf("%g\n", f);
}

If you want to skip over the subnormal values, go from zero straight to numpy.finfo('f8').smallest_normal (2.2250738585072014e-308)