Interval arithmetic by Robert Elton Maas:

Demonstration of my newly-written general utilities for interval arithmetic
with rational endpoints:


* (ratio-make-smaller+simpler 160025413/50937671) (float * 1d0)

120748342/38435391
*
3.1415926534999996d0
* (ratio-make-smaller+simpler **) (float * 1d0)

81471271/25933111
*
3.1415926534999987d0
* (ratio-make-smaller+simpler **) (float * 1d0)

42194200/13430831
*
3.1415926534999956d0
* (ratio-make-smaller+simpler **) (float * 1d0)

2917129/928551
*
3.1415926534999157d0
* (ratio-make-smaller+simpler **) (float * 1d0)

1562735/497434
*
3.1415926534977503d0
* (ratio-make-smaller+simpler **) (float * 1d0)

208341/66317
*
3.1415926534674368d0
* (ratio-make-smaller+simpler **) (float * 1d0)

103993/33102
*
3.1415926530119025d0


* (ratio-make-larger+simpler 160025413/50937671) (float * 1d0)

39277071/12502280
*
3.1415926535000014d0
* (ratio-make-larger+simpler **) (float * 1d0)

36359942/11573729
*
3.1415926535000085d0
* (ratio-make-larger+simpler **) (float * 1d0)

33442813/10645178
*
3.1415926535000165d0
* (ratio-make-larger+simpler **) (float * 1d0)

30525684/9716627
*
3.1415926535000263d0
* (ratio-make-larger+simpler **) (float * 1d0)

27608555/8788076
*
3.141592653500038d0
* (ratio-make-larger+simpler **) (float * 1d0)

24691426/7859525
*
3.1415926535000525d0


* (setq rat 160025413/50937671)

160025413/50937671
* (setq rats (ratio-to-simpler-interval rat))

(120748342/38435391 39277071/12502280)
* (< (car rats) rat (cadr rats))

T


;rats left over from above:
* (loop for rat in rats collect (float rat 1d0))

(3.1415926534999996d0 3.1415926535000014d0)
* (setq rats (ratio-interval-make-wider+simpler rats))

(81471271/25933111 39277071/12502280)
* (loop for rat in rats collect (float rat 1d0))

(3.1415926534999987d0 3.1415926535000014d0)
* (setq rats (ratio-interval-make-wider+simpler rats))

(42194200/13430831 39277071/12502280)
* (loop for rat in rats collect (float rat 1d0))

(3.1415926534999956d0 3.1415926535000014d0)


;rats left over from above:
* (ratio-interval-simplify-expand-to-threshold rats 50000000)

(2917129/928551 36359942/11573729)
* (loop for rat in * collect (float rat 1d0))

(3.1415926534999157d0 3.1415926535000085d0)
* (ratio-interval-simplify-expand-to-threshold rats 1000000)

(208341/66317 729371/232166)
* (loop for rat in * collect (float rat 1d0))

(3.1415926534674368d0 3.141592653532386d0)
* (ratio-interval-simplify-expand-to-threshold rats 100000)

(75593/24062 355/113)
* (loop for rat in * collect (float rat 1d0))

(3.141592552572521d0 3.1415929203539825d0)
* (ratio-interval-simplify-expand-to-threshold rats 10000)

(7433/2366 355/113)
* (loop for rat in * collect (float rat 1d0))

(3.1415891800507185d0 3.1415929203539825d0)
* (ratio-interval-simplify-expand-to-threshold rats 1000)

(688/219 355/113)
* (loop for rat in * collect (float rat 1d0))

(3.141552511415525d0 3.1415929203539825d0)
* (ratio-interval-simplify-expand-to-threshold rats 100)

(69/22 22/7)
* (loop for rat in * collect (float rat 1d0))

(3.1363636363636362d0 3.142857142857143d0)
* (ratio-interval-simplify-expand-to-threshold rats 50)

(25/8 22/7)
* (loop for rat in * collect (float rat 1d0))

(3.125d0 3.142857142857143d0)
* (ratio-interval-simplify-expand-to-threshold rats 30)

(3 22/7)
* (loop for rat in * collect (float rat 1d0))

(3.0d0 3.142857142857143d0)


* (intervals-divide '(3/4 4/5) '(1 11/10))

(15/22 4/5)


(ratio-interval-to-simplest-ratio-within
  (list (rational 3.14) (rational 3.15)))
22/7


* (ratio-interval-format-f (list (rational 1.234275) (rational 1.234657)))

"1.234[2..7]"
* (ratio-interval-format-f (list (rational 1.234567) (rational 1.234657)))

"1.2345[6..G]"
* (ratio-interval-format-f '(15/22 4/5))

"0.6[8..K]"
* (ratio-interval-format-f '(208341/66317 729371/232166))

"3.1415926534[6..E]"
* (ratio-interval-format-f '(75593/24062 355/113))

"3.141592[5..A]"


* (setq oldint (list 0 1))

(0 1)
* (setq newint (list (rational 0.37) (rational 0.48)))

(3103785/8388608 16106127/33554432)
* (show-interval-refinement oldint newint)
[-------------------------!!!!!!!!!------------------------------------]
(3103785/8388608 16106127/33554432)
* (setq oldint (list 75593/24062 355/113))

(75593/24062 355/113)
* (setq newint (list 208341/66317 729371/232166))

(208341/66317 729371/232166)
* (show-interval-refinement oldint newint)
[-------------------!--------------------------------------------------]
(208341/66317 729371/232166)

* (setq oldint (list 1/2 3/2))

(1/2 3/2)
* (setq newint (list 2/3 2))

(2/3 2)
* (show-interval-refinement oldint newint)

** WARNING: New interval not included within old interval,
**  so I'll have to intersect the two to get a valid interval refinement.
[-----------!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!]
(2/3 3/2)


Would you like me to set up this software as a
Web-server-side application so that you-all can play
with it?

Urgent note: I'm in desperate financial circumstances.
I desperately need a source of income to avoid becoming
homeless. Please refer me to somebody who has money to
hire me for writing software.