Update: it looks like IEEE 754-1985 does require that
roundtripping works, at least when the rounding mode
is round-to-nearest.  From section 5.6 again:

"""
When rounding to nearest, conversion from binary to decimal and back to
binary shall be the identity as long as the decimal string is carried to the
maximum precision specified in Table 2, namely, 9 digits for single and 17
digits for double.
"""

Mark
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