RE: HP48-HP50G : Error functions ERF(z), FRESNEL integrals, PROBIT, etc.

[Gil]

New version 11c

Slight changes (uniformization) in the DOERR messages.

Subroutine inv¦z was completed (in bold) for special cases.

The rest remains mostly the same for the functions
ERF & ERFc, their inverse INV¦ & INV¦c
& PROBIT ERFi iERFc ERFcx FADDEEVA DAWSON according to Wolfram Alpha or Wikipedia definitions.

As previously, all of them take a single argument input and accept, as argument input, a real or complex number, according to the explanation given at the beginning of each function.

inv¦z
\<<
DO 9 \-> p z \<-max.z
\<< z DUP ERF 4 ROLLD 3 DROPN p - DUP \-> f
\<< '2/\v/\pi*EXP(-z^2)+f*z' / - \->NUM DUP DUP RE ABS \<-max.z > SWAP IM ABS \<-max.z > OR
IF
THEN ROT DROP "To get here a sol,
try & let 
\<-max.z 
=

99
, instead of 
9
,
in 
inv
\166
z
 & in 
ERF
" SWAP "
Failure
 as
Interm.Newton
result (
a
,
b
)=
" SWAP 1 RND + ", &
|
a
|" + \<-max.z 10 < " or " "or" IFTE + "|
b
| \>=" + \<-max.z R\->I + " not OK in 
ERF
" + UNROT SWAP ROT POP DOERR
END p SWAP z
\>>
\>>
UNTIL OVER - DUP RE ABS .0000000001 < SWAP IM ABS .0000000001 < AND
END UNROT DROP2
\>>