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**Lance Edmonds** · 11 May 2000, 04:56 AM

as you already have your numerator and denominator, you can calculate the whole number directly, and then use some of the bbs code to create the fractional part.

a search of the bbs for "fraction" brings up some code that should help with this problem... try some of the following:

------------------
lance
powerbasic support
mailto:[email protected][email protected]</a>

**Fred Buffington** · 12 May 2000, 05:32 PM

how bout this
input "Enter a decimal",num$
for k%=1 to len(num$)
if mid$(num$,k%,1)="." then
if k%<>1 then whole&=val(mid$(num$,1,k%))
numerator&=val(mid$(num$,k%+1))
denom&=10^(len(num$)-k%)
end if
next k%

for m&=numerator&/2 to numerator&-1
if numerator&/m&=int(numerator&/m&) and denom&/m&=int (denom&/m&) then divisor&=m&
next m&
if divisor&<>0 then numerator&=numerator&/divisor& :
denim&=denom&/m&

print whole&;ltrim$(str$(numerator&));"/";ltrim$(str$(denim&))

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**Fred Buffington** · 12 May 2000, 05:43 PM

I think i had a mental breakdown there LOL
the routine to check for a divisor should go
from 2 to numerator/2 instead

you could also check for a "/" entered then use the smaller
of numerator or denuminator for finding a divisor.

Actually you could do it from 1 to numerator&-1
but there is no need to do all of those calcuilations.

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**Fred Buffington** · 12 May 2000, 06:19 PM

That's still not right sorry.
This is better

for m&=numerator to 2 step -1
if numerator&/m&=int(numerator&/m&) and denom&/m&=int
(denom&/m&) then
divisor&=m&
exit for
end if
next m&
**and there was a mistake on a later line too
if divisor&<>0 then numerator&=numerator&/divisor& :
denim&=denom&/m&
print whole&;ltrim$(str$(numerator&));"/";ltrim$(str$(denim&))

should be
if divisor&<>0 then numerator&=numerator&/divisor& :
denom&=denom&/divisor&
print whole&;ltrim$(str$(numerator&));"/";ltrim$(str$(denom&))

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**Michael Torrie** · 13 May 2000, 11:43 AM

Oops. I posted before really reading the original question. I do have an algorithm for creating fractions from decimal, and reducing them, based on an algorithm by Euclid. It's very efficient. But It doesn't handle creating mixed fractions. But if someone's interested, I'll post it to the source code forum

[This message has been edited by Michael Torrie (edited May 13, 2000).]

**Donald R. Darden** · 9 Apr 2001, 07:25 AM

There is a program I wrote that does what you want --
It converts any decimal number to a rational
equivalent, even for "irrational" numbers. It
depends upon how many places of accuracy you are
willing to settle for. It is called RATIONAL, and
it has been posted at the ABC (All BASIC Code) web
site. I wrote the original version on a TI SR-52
calculator many years ago, and adapt it to every
new computer language that I learn. It can be
handy to have.

Rational numbers have the form of P/Q, so that you
get both the P and the Q as integer values. If you
want to convert the result to a integer and fraction
form. you would just complete the division, take the
INT part for your integer, then use RATIONAL to
convert the decimal portion into another P/Q
expression for the fraction.

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**Daniel Corbier** · 9 Apr 2001, 09:07 PM

Lance, it seems like two of the links you mentioned return an
"HTTP 404 - File not found" error. However I searched in the
archived forums, and found those messages there.

You guys may be interested in the code listed at VbToTheMax.com
( http://www.vb2themax.com/Item.asp?Pa...odeBank&ID=344 )
designed just for that purpose. The algorithm is based on the
concept of Continued Fractions. And it can return results for
use in the form "a/b" or "a b/c".

------------------
Daniel Corbier
UCalc Fast Math Parser
http://www.ucalc.com

[This message has been edited by Daniel Corbier (edited April 09, 2001).]

**Lance Edmonds** · 10 Apr 2001, 07:38 PM

Daniel, I posted that message in May 2000, so normal archiving has shifted their location.

------------------
Lance
PowerBASIC Support
mailto:[email protected][email protected]ic.com</A>

**Jerry Fielden** · 11 Apr 2001, 09:00 AM

I missed it on the first try. This one should reduce

Code:

num = 10
denom = 8
whole = FIX(num/denom)
num = num MOD denom

DO 
   FOR x = 2 TO num
     IF num MOD x = 0 AND denom MOD x = 0 THEN
        num = num / x : denom = denom / x
        ITERATE DO
     END IF
  NEXT X
  EXIT DO
LOOP


print  STR$(whole) + " " + STR$(num) + "/" + LTRIM$(STR$(denom))

[This message has been edited by Jerry Fielden (edited July 04, 2001).]

**Daniel Corbier** · 11 Apr 2001, 12:20 PM

Oops. Lance, I hadn't noticed the date of the original message.
The more recent post made the topic seem like a new one.
By the way, are messages in the archive forums conserved
indefinitely, or are they purged after a certain time?

As for reducing fractions, the VbToTheMax.com code doesn't
have the same limitations as some of the code I've seen posted.
It allows you to reduce fractions, and it can also convert a
floating point value to a clean-cut accurate fraction, using
a minimum of iterations. For instance:

DecToProperFrac(5655/5423, a, b, c)
would return 1 8/187 (in the values a, b, and c)

------------------
Daniel Corbier
UCalc Fast Math Parser
http://www.ucalc.com

**Tom Hanlin** · 11 Apr 2001, 01:26 PM

We don't generally archive messages unless necessary. What with improvements to the
UBB forum software and moving to a much faster server, we have not had to archive
messages for some time...

------------------
Tom Hanlin
PowerBASIC Staff

**Petar Petrenko** · 19 May 2001, 12:04 PM

Sorry I react so late (and my bad English), but I bought PB 3.5 few days ago. I read that you want a routine for reducing fractions and mixed numbers. I saw all the routines you got, but my opinion is that you must try mine. The fastest and simpliest routine you need is based upon prime numbers (they can be divided only by 1 and themselves) but it will complicate the program too much, because you need a generator of prime numbers. If we ignore that routine, then this one is next to it by speed. The routine that Jerry Fielden sent to you is very near to what you want but it is as fast as a snail. Why? Let me analyze my routine.
If you input number 990 in line (03) and number 60 in line (04) - in lines (06) through (15) you will get 16 30 / 60. In other words you are "normalizing" the fraction. Numerator becomes smaller than denominator. In lines (16) - (23) you divide numerator and denominator only with number 2 because there is no further need for dividing with even numbers (they are not prime numbers). This is the first part of the acceleration, and this is the reason why, in line (25) in the FOR...NEXT loop, STEP is equal to 2. After line (23) the fraction is 16 15 / 30.
The real stuff is hidden in line (25). Instead to evaluate the FOR...NEXT loop to the value of denominator it is quite enough to evaluate to square root of it!!! If you need an explanation then take a piece of paper and write down all numbers from 3 to 100. Cross over all even numbers. Circle number 3 and after that cross over all numbers that are multiply of 3 (6, 9... 99). After that find the first number after 3 that is not crossed over (number 5) and then repeat the same (cross over numbers 10, 15... 95). Then try the same with number 7 and so on. You will find out that after number 10 (and 10 is square root of 100) there is no other numbers to cross over and all other numbers left are prime numbers!!! And, this is the algorithm for prime numbers routine. At the end the fraction is 16 1 / 2.

(01) DEFDBL A-Z
(02) CLS

(03) INPUT "Numerator: ", num
(04) INPUT "Denominator: ", denom
(05) PRINT

(06) IF num > denom THEN
(07) whole = FIX(num / denom)
(08) num = num MOD denom
(09) IF num = 0 THEN
(10) PRINT whole
(11) PRINT
(12) PRINT "END"
(13) END
(14) END IF
(15) END IF

(16) DO WHILE ind = 0
(17) ind = 1
(18) IF (num MOD 2) = 0 AND (denom MOD 2) = 0 THEN
(19) ind = 0
(20) num = num \ 2
(21) denom = denom \ 2
(22) END IF
(23) LOOP

(24) ind = 0

(25) FOR i = 3 TO SQR(denom) + 1 STEP 2
(26) IF i > denom THEN EXIT FOR
(27) DO WHILE ind = 0
(28) ind = 1
(29) IF (num MOD i) = 0 AND (denom MOD i) = 0 THEN
(30) ind = 0
(31) num = num \ i
(32) denom = denom \ i
(33) END IF
(34) LOOP
(35) NEXT i

(36) IF whole <> 0 THEN
(37) PRINT whole;" "; num; "/"; denom
(38) ELSE
(39) PRINT num; "/"; denom
(40) END IF

(41) PRINT
(42) PRINT "END"

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**Jerry Fielden** · 19 May 2001, 03:55 PM

Sorry Petar,

Your code is kicking out the wrong answers. You may need to
modify it a little.

I entered 5655 for the Numerator and 5423 for the Denominator.
your answer is like the rest. 1 232/5423. The correct answer is
1 8/187.

MTIMER reports 600 microseconds using my code for that problem.
Thats not that slow. Of course my machine is not that slow either.

Just a little more and you will be there.

------------------

**Petar Petrenko** · 21 May 2001, 01:50 PM

Sorry Jerry. The mistake was in the IND variable that controls DO...LOOP. Maybe my program is longer but it is optimized as much as possible. I started programing on "Spectrum 64" were optimize code was necessary if you need real-time results. Nowadays speed maybe is not so critical but it is fine to make an effort and optimize your programs as much as possible.

Best regards,
Petar

DEFWRD A-Z
CLS

INPUT "Numerator: ", num
INPUT "Denominator: ", denom
PRINT

IF num > denom THEN
whole = FIX(num / denom)
num = num MOD denom
IF num = 0 THEN
PRINT whole
PRINT "END"
END
END IF
END IF

ind = 1
DO WHILE ind = 1
ind = 0
IF num MOD 2 = 0 AND denom MOD 2 = 0 THEN
ind = 1
num = num / 2
denom = denom / 2
END IF
LOOP

FOR i = 3 TO SQR(denom) STEP 2
IF i > denom THEN EXIT FOR
ind = 1
DO WHILE ind = 1
ind = 0
IF num MOD i = 0 AND denom MOD i = 0 THEN
ind = 1
num = num / i
denom = denom / i
END IF
LOOP
NEXT i

IF whole <> 0 THEN
PRINT whole; " "; num; "/"; denom
ELSE
PRINT num; "/"; denom
END IF

PRINT "END"

------------------

**Jerry Fielden** · 21 May 2001, 06:55 PM

Sorry Petar,

MTIMER is reporting that your progam to be slower.

To further check it, I Hard coded 5655 as num and 5423 as denom.
I wrapped it in a 1000 loop FOR NEXT and zeroed out all variables
at the bottom of the loop. I Booted straight to DOS and ran it
about 20 times. Your average speed was 39695 microseconds.

I did the same thing with my snail with an average speed of
38651.

You must have left something else out, I'm sure you will fix it.

------------------

[This message has been edited by Jerry Fielden (edited May 21, 2001).]

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