Toward an API for the real numbers

[Albert Chan]

(10-08-2020 03:26 AM)Paul Dale Wrote:  It's an interesting approach. It still boils down to deceiving the user about results. Albeit, it is giving "good" approximations.

E.g. it seems like it only deals with single transcendental functions. Something like log(log(x)) would throw it off.

Can you elaborate what is the "interesting approach" ?

From what I've read, this API seems able to do whole expression, returning correctly rounded results.

I were thinking it does calculations like spigot, a command-line exact real calculator
All digits it returns guaranteed correct (the down side, take lots of time, sometimes literally stuck)

Lets try first example from Why and how to use arbitrary precision

>spigot --printf="%.34g" "173746*sin(1e22) + 94228*log(17.1) - 78487*exp(0.42)"
-1.341818957829619549704278684230959e-12

Free42-Decimal, RAD mode:

1e22 SIN 173746 ×     → -148066.4888436499855528005582160138
17.1 LN 94228 × +     →  119454.1966158397094008651162133881
0.42 EXP 78487 ×      →  119454.1966158397107426840740430076
-                     →      -0.0000000000013418189578296195