Paul Zimmermann wrote:
>        Hi,
> 
> as a followup on the "Arbitrary precision in cython" thread, I'd like to
> mention that one can directly use mpfr's implementation from within Sage:
> 
> sage: RealField(150)(10).eint()
> 2492.2289762418777591384401439985248489896471
> 
> It only works for real numbers, but has the advantage to guarantee correct
> rounding (for the 150-bit binary result; if you are using the decimal
> result above, you have to take into account the binary->decimal conversion
> error, which is at most 1/2 ulp).


Just a note:

sage: pari(RealField(500)(10)).eint1().python()
4.15696892968532427740285981027818038434629008241953313262759569712786222819608803586147163177527802101305497591041862309918139192016097135380721447598904e-6
sage: RealField(500)(10).eint()
2492.22897624187775913844014399852484898964710143094234538818526713774122742888744417794599665663156560488342454657568480015672868779475213684965774390
sage:
sage: pari(RealField(500)(-10)).eint1().python()
-2492.22897624187775913844014399852484898964710143094234538818526713774122742888744417794599665663156560488342454657568480015672868779475213684965774390402
sage: RealField(500)(-10).eint()
NaN



Jason


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