HP 40gs, error in calculator?

[Claudio L.]

(11-03-2017 08:04 PM)Massimo Gnerucci Wrote:  

(11-03-2017 05:40 PM)Jake Schwartz Wrote:  ..and the WP-34S in "double mode" returns -1.158028306006248917735787454453501 E-34.

Jake

While SHOW on the DM42 returns: -1.158028306006248941790250554076922E-34
Who's right? Or, better, closer to truth?

newRPL solving the mystery...

-1.158028306006248941790250554076922E-34

is the correct answer for 34 digits precision.
To obtain this answer:
34 SETPREC π0 0 + SIN
the 0 + is intentional, to round π0 to 34 digits, since it's provided with twice the current precision by default.
The actual answer for 34 SETPREC π0 SIN is:
9.862803482534211.E-80
which is only 17 digits, and the last one is not correctly rounded (should be a 2). It actually looks like an incorrect answer, but let's look deeper:
Due to internal precision multiples of 8, when 34 digits are selected it needs to work with 40 internally, then π0 provides twice that = 80 digits (hence the 10^-80 answer, those 16 first digits are the correct answer for pi with 80 digits precision).
But in reality, for the selected 34 digit precision, the digits that really matter are the ones from 10^-34 to 10^-68, which are correctly given as zero.