[Cfp-interest 1475] Re: complex multiplication and division

[Damian McGuckin]

Hi Paul,

On Fri, 7 Feb 2020, paul zimmermann wrote:

>  /* generated with ./mpcheck-double -seed 1473128 */
>  x = -8.2287892462057963e+188 + I * 4.7082627796239037e+122;
>  y = -1.0987942433164555e-323 + I * 6.4181344246145655e-324;

Just looking at 'y', both of these numbers are subnormal. Your own output 
says that 'y' (as represented) is nothing like the numbers that you typed 
above. Your program printed:

> y=(-9.8813129168249309e-324,4.9406564584124654e-324)

The reason for the difference is that representing the components of 'y' 
as a double will underflow and loose lots of the least significant digits.

If I change your program to use

 	y = -9.8813129168249309e-324 + I * 4.9406564584124654e-324

where this number is the actual value of what you are representing, the 
results are still what you saw, i.e.

 	x*y=(8.1311241468363422e-135,-4.0655620734181711e-135)

I reran your problem with 'long double complex' but again with

 	y = -9.8813129168249309e-324 + I * 4.9406564584124654e-324

It produces the same results as you say with doubles. Your might like to 
rerun MFPR with this number.

The issue you are seeing is related to representational error, not any
rounding issues.

What Jim has said still stands but your phenomena are something different.

Regards - Damian

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