(Plus 42) Fraction approximation equation
02-17-2022, 01:38 PM (This post was last modified: 02-17-2022 08:41 PM by Vincent Weber.)
Post: #1
 Vincent Weber Senior Member Posts: 359 Joined: May 2015
(Plus 42) Fraction approximation equation
Hi all,

Since Plus42 does not (have) yet a fraction mode à la 32SII/35S, and since this mode is anyway limited (4096 denominator maximum, no expression of tolerance, just max denominator) I made an equation for it.

It has no intelligence whatsoever, no limited fractions algorithm, just plain stupid brute force try of every possible denominator. Plus42 is so fast anyway :)

Just enter X, the value to be approximated, and TOL (e.g. 1E-8), the tolerance of the approximation. Press EVAL, now N holds the numerator of the approximated fraction, D the denominator, and RES the difference with the original number.

Cheers

FRAC:0×FOR(SEQ(L(N:IP(X)):L(D:1)):L(RES:ABS(N÷D-X))>TOL:0:SEQ(L(D:D+1):L(N:RND(D×X:0))))+RES
02-17-2022, 02:14 PM
Post: #2
 Thomas Okken Senior Member Posts: 1,894 Joined: Feb 2014
RE: (Plus 42) Fraction approximation equation
(02-17-2022 01:38 PM)Vincent Weber Wrote:  FRAC:0×FOR(SEQ(L(N:IP(X)):L(D:1)):L(RES:ABS(N÷D-X))>TOL:0:SEQ(L(D+1):L(N:RND(D×X:0))))+RES

You can prevent :‌D from turning into by putting a zero-width space or a zero-width non-joiner between the : and the D.
(The difference is whether a line break may occur or not.)

https://unicode-table.com/en/200B/
https://unicode-table.com/en/200C/
02-17-2022, 02:50 PM
Post: #3
 Massimo Gnerucci Senior Member Posts: 2,682 Joined: Dec 2013
RE: (Plus 42) Fraction approximation equation
(02-17-2022 02:14 PM)Thomas Okken Wrote:
(02-17-2022 01:38 PM)Vincent Weber Wrote:  FRAC:0×FOR(SEQ(L(N:IP(X)):L(D:1)):L(RES:ABS(N÷D-X))>TOL:0:SEQ(L(D:D+1):L(N:RND(D×X:0))))+RES

You can prevent :‌D from turning into :D by putting a zero-width space or a zero-width non-joiner between the : and the D.
(The difference is whether a line break may occur or not.)

https://unicode-table.com/en/200B/
https://unicode-table.com/en/200C/

Isn't it simpler to just "Disable Smilies"?

Greetings,
Massimo

-+×÷ ↔ left is right and right is wrong
02-17-2022, 03:47 PM
Post: #4
 Vincent Weber Senior Member Posts: 359 Joined: May 2015
RE: (Plus 42) Fraction approximation equation
(02-17-2022 02:50 PM)Massimo Gnerucci Wrote:
(02-17-2022 02:14 PM)Thomas Okken Wrote:  You can prevent :‌D from turning into by putting a zero-width space or a zero-width non-joiner between the : and the D.
(The difference is whether a line break may occur or not.)

https://unicode-table.com/en/200B/
https://unicode-table.com/en/200C/

Isn't it simpler to just "Disable Smilies"?

Thanks Thomas and Massimo, I didn't notice that !
Since I'm lazy, I chose the "disable smilies" option
Cheers
02-17-2022, 08:38 PM
Post: #5
 ijabbott Senior Member Posts: 1,306 Joined: Jul 2015
RE: (Plus 42) Fraction approximation equation
(02-17-2022 02:50 PM)Massimo Gnerucci Wrote:
(02-17-2022 02:14 PM)Thomas Okken Wrote:  You can prevent :‌D from turning into by putting a zero-width space or a zero-width non-joiner between the : and the D.
(The difference is whether a line break may occur or not.)

https://unicode-table.com/en/200B/
https://unicode-table.com/en/200C/

Isn't it simpler to just "Disable Smilies"?

Disabling smilies is also better for cut and pasting.

— Ian Abbott
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