HP-71B: 1^Inf Error

[J-F Garnier]

(06-09-2023 11:56 AM)Albert Chan Wrote:  But, HP71B IEEE implementation is not perfect ...

>E=1e-9 @ Z=0.
>acos((2,E))
(5.7735026919E-10,-1.31695789692)
>acos((2,Z))
(0,1.31695789692)      ! ???
>acos((2,-Z))
(0,1.31695789692)
>acos((2,-E))
(5.7735026919E-10,1.31695789692)

Note that the complex inverse trig functions are supported on the 71B only with the MATH version 2B that I wrote. You would get however, the same result on a HP-48, except you can't do acos((2,-0)) because there is no signed zero on the 48.

I remember that the HP-71B MATH ROM developers reported (in the HP Journal I guess), that they had trouble to extend the IEEE concepts to the complex domain. It was very new at the time. So they did their best and this was basically unchanged in the next 28C/S and series 48.
In this particular example, the signed zero is not managed properly in the complex domain. Maybe an additional reason for having abandoned it?

J-F