(38G) Neighbour Function (Dedekind Cut)

[Gerald H]

The three programmes below together perform the Neighbour function & Dedekind cut.

For the development of the programmes please see:

http://www.hpmuseum.org/forum/thread-9170.html

The Neighbour function for a real number N finds the nearest number to N that the calculator can represent.

The Dedekind cut returns for real input N the upper & lower nearest numbers to N that the calculator can represent.

The first programme accepts a real number input on the Home screen & returns the upper nearest number in Ans.

NXTUP

Code:

Ans►N:
IFTE(Ans,10^(XPON(Ans)),1.E-488)►T:
N/T:
T*(Ans+10^((Ans≠-1)-12)):

The next programme accepts a complex number as input on the Home screen, say

(x,P)

where you require the neighbour of x & P is either 1 or -1, 1 indicating the upper neighbour & -1 the lower, & returns the result in Ans.

NEIGHBOR

Code:

Ans►Z0:
RE(Ans)►R:
IM(Z0)►I:
IF I==-1
THEN
-R:
RUN NXTUP:
-Ans:
ELSE
R:
RUN NXTUP:
END:

Finally for real number input in the Home screen the programme DCUT returns a complex number in Ans, the real part being the upper & the imaginary part the lower neighbour.

DCUT

Code:

Ans►D:
(D,1):
RUN NEIGHBOR:
Ans►U:
(D,-1):
RUN NEIGHBOR:
(U,Ans):