Is double-double 128 bit?

Yes, double-double is an unevaluated sum of two doubles. From high-level perspective you can imagine it as double with 106-bit mantissa.

Which kind of error analysis do you use?

To analyse error of interpolating polynomial, I split function domain into intervals of constant ULP, bound the absolute error of approximation (with

Sollya) and evaluation (with

Gappa), compute the total ULP error on each interval, and choose the maximum of all intervals. Other kinds of errors (range reduction and reconstruction) are analysed on case-by-case basis.