HP-71B: 1^Inf Error

[Albert Chan]

(06-09-2023 01:03 PM)J-F Garnier Wrote:  In this particular example [acos(2+0j)], the signed zero is not managed properly in the complex domain.
Maybe an additional reason for having abandoned it?

I believe it is asin/acos sign bug in code.
Calculate acos(2+0j) by "hand", I am getting correct answer.

Implementing the complex arcsine and arccosine functions ... (page 326 for acos(z) algorithm),

lua> x, y = 2, 0
lua> signy = signbit(y) and -1 or 1
lua> r = sqrt((x+1)^2 + y^2)
lua> s = sqrt((x-1)^2 + y^2)
lua> a = (r+s)/2
lua> b = x/a
lua> I.new(acos(b), -signy * acosh(a))      -- = acos(2+0j)
(0-1.3169578969248166*I)

sign(y) bug is in cpr.a, which sometimes use -sign(x) instead. (docasc code comment)
Because asin(z) + acos(z) = pi/2, this bug affected both asin and acos.

Code:

*      with sign(y,x)=sign(y) if y<>0, -sgn(x) if y=0

>acos((2,0))
(0,1.31695789692)      ✘
>acos((-2,0))
(3.14159265359,-1.31695789692)      ✔