real precision again

[Walter Neumann <neumann@cpw.math.columbia.edu>]

At large precision (over 395 digits) sin(Pi*2.) claims to have twice as
many significant digits as it should:


? \p300
   realprecision = 308 significant digits (300 digits displayed)
? Pi*2.
%1 = 6.28318530717958647692528676655900576839433879875021164194988918461563281257241799725606965068423413596429617302656461329418768921910116446345071881625696223490056820540387704221111928924589790986076392885762195133186689225695129646757356633054240381829129713384692069722090865329642678721452049828255
? sin(%)
%2 = 0.E-307
? \p400
   realprecision = 404 significant digits (400 digits displayed)
? Pi*2.
%3 = 6.283185307179586476925286766559005768394338798750211641949889184615632812572417997256069650684234135964296173026564613294187689219101164463450718816256962234900568205403877042211119289245897909860763928857621951331866892256951296467573566330542403818291297133846920697220908653296426787214520498282547449174013212631176349763041841925658508183430728735785180720022661061097640933042768293903883023219
? sin(%)
%4 = 2.083415134163379771317306786512007684572941095163701634157290887739967165726519878072310347834290217941711584606256087453734814712822486064338376377290291271528114660633609372113745774583418171579011473210390805058843715841645813527378491473322289166282480743273765616722933205149866985251359777695245970930844694020475677754390894758209754567147135178467574886857510516861792192562776849904346531125 E-404
? \q
Goodbye!


--walter neumann