Paul D. Anderson wrote:
> Multiplying two floats produces a number whose potential precision is the sum 
> of the operands' precision. We need a method to determine what the precision 
> of the product should be. Not that it's difficult to come up with an answer 
> -- but we have to agree on something.

Not more precision than the input data deserve.  The decimal
floating-point numbers of the new IEEE 754-2008 carry with them a notion
of “how precise is this result?”; this might be a good starting point
for discussion.

—Joel Salomon

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