Wednesday, January 17, 2018

integer floats with remainder theory

integer floats with remainder theory - copyright RS

The float is formed of 2 integers...

One being the integer and the remainder being the floating component....

thusly we need two integers per float for example 2 32bit integers will make one single float instruction....

integer A : Remainder B

A + B = float
(A + B) x (A²+B²)

= float C dislocating A and B by a certain number of places = a float that travels as the integer.

Expansion data sets:

A1 : B1
A2 : B2
Ar : Br

F1 : Bf1
F2 : Bf2
Fr : Bfr

A : Integer
F : Float
r : Remainder

The data set expansion can be infinite and the expansion of the data set doubles the precision,
With the remainder... infinite computation = infinite precision.

Not only that but the computation can be executed as an Integer or as a float or indeed with both.
Relevance is that on computers there are a lot of integer registers; Float also..
Also the data can be compressed in ram without using larger buffer widths.

copyright Rupert Summerskill

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