[Numpy-discussion] precision isn't just precision

[Paul F. Dubois]

Before we all rattle on too long about precision, I'd like to point out that
selecting a precision actually carries two consequences in the context of
computer languages:

1. Expected: The number of digits of accuracy in the representation of a
floating point number.
2. Unexpected: The range of numbers that can be represented by this type.

Thus, to a scientist it is perfectly logical that if d is a double and f is
a single,

d * f

has only single precision validity.

Unfortunately in a computer if you hold this answer in a single, then it may
fail if the contents of d include numbers outside the single range, even if
f is 1.0.

Thus the rules in C and Fortran that coercion is UP had to do as much with
range as precision.