Question for Joe Horn, Dieter, and other

[Dieter]

(11-01-2017 05:32 PM)Namir Wrote:  If I represent R using complex number notation (I, e), would the use of complex math operations (adding, subtracting, etc.) between two near-integer-value floating-point numbers, yield more accurate results than straight forward operations between these same numbers? That is, for example:

R1 * R1 is less accurate than? (I1, e1) * (I2, e2)

For addition and subtraction it seems obvious that adding/subtracting the integer parts and "e" separately improves accuracy. On the one hand because "e" may be represeted exactly where I+e may already show roundoff errors, on the other hand because the result (I1+I2, e1+e2) may yield a more exact value for e1+e2 as both I1+I2 and e1+e2 may be represented with, say, 10 or 12 significant digits each.

But how do you want to multiply two numbers with this method?
(I1+e1)*(I2+e2) equals I1*I2+e1*I2+I1*e2+e1*e2 while (I1, e1)*(I2, e2) is (I1*I2–e1*e2,  I1*e2+I2*e1). Note the minus !

Dieter