+- HP Forums (https://www.hpmuseum.org/forum)
+-- Forum: HP Software Libraries (/forum-10.html)
+--- Forum: General Software Library (/forum-13.html)
+--- Thread: (38G) Neighbour Function (Dedekind Cut) (/thread-9180.html)
(38G) Neighbour Function (Dedekind Cut) - Gerald H - 09-28-2017 10:11 AM
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):