It would be nice if math.hypot had the property

If
  0 < y1 < y2
then
  math.hypot(x, y1) <= math.hypot(x, y2)

This is not the case in python3 with

  x  = 0.6102683302836215
  y1 = 0.7906090004346522
  y2 = y1 + 1e-16

python2's implementation of math.hypot is OK with these inputs.

Thanks for the report.  This is fixed in Python 3.10 where your script outputs:   [1.1102230246251565e-16, 1.1102230246251565e-16]

There isn't much that can be done about it for Python 3.9.

I agree this doesn't occur in 3.10, but think Raymond pasted wrong outputs. Here:

Python 3.10.0a4+ (heads/master:64fc105b2d, Jan 28 2021, 15:31:11)
[MSC v.1928 64 bit (AMD64)] on win32
>>> x  = 0.6102683302836215
>>> y1 = 0.7906090004346522
>>> y2 = y1 + 1e-16
>>> from math import hypot
>>> hypot(x, y1)
0.998744224772008
>>> hypot(x, y2)
0.9987442247720081

Those both appear to be the results "as if" computed to infinite precision and then correctly rounded back to Python's float precision.

Many thanks!  Was the 3.9 version of hypot introduced in 3.0?  I'm fixing my code to call sqrt(x**2 + y**2) if necessary and I'd like to know what range of versions this version should apply for.

>  I'd like to know what range of versions this version should apply for.

Only 3.8 and 3.9.

Prior to that, we used the C compiler's hypot() which tended to be very good but was implementation dependent, only covered the two argument case, and made no particular guarantees about accuracy, commutativity, or monotonicity.

Thanks for the info.