Purpose of epsilon, why relative error can't be lower?

[jaimecoj]

I was trying calculating integrals of tiny orders. Between 1e-20 and 1e-60. And setting the relative error bellow epsilon throws error.

I'm using double and it is floating point representation, so I deduct it shouldn't be a problem if I use tiny numbers since it is stored as a chain of significant numbers and exponent.

[mcsauder]

Hi @jaimecoj , this is a correct error to be thrown for the case you described. Here is a description of what machine epsilon is: https://en.wikipedia.org/wiki/Machine_epsilon.

Your hardware will only carry a certain set limit on how many decimal places can be carried. If you are interested in extending your level of precision, using the MPFRC++ capability of the library should help: https://github.com/tbs1980/NumericalIntegration#multiprecision-usage-note.

Let us know if this answers your question!