Extra precision hidden

[user202729]

Looks like pari real objects are always displayed to ≈ 15 digits of precision regardless of internal precision:

sage: pari(RealField(100)(sqrt(2)))
1.41421356237310
sage: pari(RealField(300)(sqrt(2)))
1.41421356237310

internally stored precision can be seen to be higher:

sage: pari(RealField(100)(sqrt(2)))^2-2
-1.47595429215023 E-30
sage: pari(RealField(300)(sqrt(2)))^2-2
1.27815007960614 E-90

[tornaria]

Indeed, pari has a "default display precision":

sage: pari.default("realprecision")
15
sage: pari(RealField(100)(sqrt(2)))
1.41421356237310
sage: pari.default("realprecision", 100)
sage: pari(RealField(100)(sqrt(2)))
1.41421356237309504880168872420917624993
sage: pari(RealField(335)(sqrt(2)))
1.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573

Note that it won't print 100 digits if the precision of the object is smaller. Note also that the internal precision is stored in bits and a multiple of 64 bits:

sage: pari.default("realprecision", 100)
sage: pari.default("realprecision")
115
sage: pari.default("realbitprecision")
384
sage: pari.default()
[...]
   realbitprecision = 384 significant bits (100 decimal digits displayed)
   realprecision = 115 significant digits (100 digits displayed)
[...]

[user202729]

I see.

Then the next question is whether this behavior is desirable? On one hand it is consistent with pari's default display precision, on the other hand we're using pari from inside sage, so it should conform to sage's convention.

Looking at RealField having everything displayed by default, maybe pari should follow that. Or at least have a global flag that configures the setting.