Post by: bplus on April 22, 2019, 11:34:25 am
https://www.qb64.org/forum/index.php?topic=1085.msg102795#msg102795
and became interested in DEC_FRAC.BAS:
Code: QB64: [Select]
- ' DEC_FRAC.BAS - Fraction/Decimal conversion functions
- ' and sample program
- ' by Antonio and Alfonso De Pasquale
- ' Copyright (C) 1993 DOS Resource Guide
- ' Published in Issue #10, July 1993, page 46
- MAIN:
- CONVERT:
- CASE "Q"
- CASE "D"
- fraction$ = DecToFrac$(decimal)
- CASE "F"
- decimal = FracToDec(fraction$)
- GOTO MAIN
- '*********************************************************
- '
- ' ACTUAL CONVERSION FUNCTIONS BEGIN HERE
- '
- '*********************************************************
- decimal$ = "0" + decimal$
- index = index + 1
- whole$ = ""
- num = dec
- den = 1000
- num = (num / index)
- den = (den / index)
- NEXT index
- NEXT pass
- DecToFrac$ = fraction$
- decimal = 0
- dp = 0
- f$ = fraction$
- dp = num / den
- FracToDec = decimal
I tried a couple of 6 digit decimals .125125 and .333111 and saw that the method only seemed to handle 3 digits, ie answers back were for .125 and .333. The method used was a little curious too...
I thought I'd challenge folks to see if anyone could come up with better, elegant method, one that could at least come up with better answers for the tests mentioned.
Post by: Pete on April 22, 2019, 03:15:36 pm
Pete
Post by: Jack002 on April 22, 2019, 04:00:13 pm
If you had to do it yourself, you'd be able to see X/10, X/5, X/3, X/9. Some know the pattern of 1/7 and might see that.
I saw a cool youtube vid where they claim any number no matter how long (like 15-20 digits mostly) they could tell you if it was prime or what factors it had. Some tricky little hacks to do it.
If I find that link, I'll post it here.
[edit]
Not the one I saw, but seems similar
Post by: bplus on April 22, 2019, 05:30:14 pm
27 lines of code, .333111 >>> 333111 / 1,000,000 .125125 >>> 1001 / 8000
Bonus .125125125 >>> 1001001 / 8,000,000
Post by: bplus on April 23, 2019, 12:51:21 pm
Code: QB64: [Select]
- WHILE 1
- d&& = 10 ^ p%%
- g&& = gcd&&(n&&, d&&): sn&& = n&& / g&&: sd&& = d&& / g&&
- convert2Fraction$ = decimal$
- 'a and b will be changed unless make copies
- c&& = a&&: d&& = b&&
- gcd&& = c&& + d&&
Post by: Pete on April 23, 2019, 02:40:18 pm
Pete
Post by: bplus on April 23, 2019, 04:25:08 pm
If you enter too many digits, it just returns 1/1. Large decimals like 1 / 97 cannot be properly evaluated. Because it can't round, it would just give a giant numerator and denominator, anyway. It works great for common fractions.
Pete
Works for up to 18 digits, a little better than 3 don't ya think?
Because it can't reduce (not round) it will give giant denominators. I only promised a fraction not convenience nor practicality. :D
Post by: Pete on April 23, 2019, 10:10:48 pm
Pete :D
Post by: Jack002 on April 23, 2019, 11:44:12 pm
If you enter too many digits, it just returns 1/1. Large decimals like 1 / 97 cannot be properly evaluated. Because it can't round, it would just give a giant numerator and denominator, anyway. It works great for common fractions.Oh but if you ever get a chance, look at the recip of 97, its pretty cool. I did it in LISP once.
Pete
Post by: Pete on April 24, 2019, 12:20:48 am
Works for up to 18 digits, a little better than 3 don't ya think?
Because it can't reduce (not round) it will give giant denominators. I only promised a fraction not convenience nor practicality. :D
It has to round to some degree to reduce properly. To try and get that for all possible decimal to fraction conversion would be a real... challenge.
Pete
Post by: Qwerkey on April 24, 2019, 04:33:46 am
Works for up to 18 digits, a little better than 3 don't ya think?
bplus, another brilliancy. But what does WHILE 1 mean? My brain doesn't like that statement at all. Clearly it's not 0 and therefore NOT False and therefore the condition is True, but it just looks horrible (to me). I think that I'd be happier with WHILE -1 (which is the BASIC convention for True), but even that I don't like. I'd have to write: Condition%% = -1, WHILE Condition%%. Good thing that I never got a job requiring programming.
Post by: bplus on April 24, 2019, 09:40:37 am
How about: WHILE 1 = 1 ?
Actually with QB64 you can do infinite loops (or loops with escape or end coded inside) with DO... LOOP so:
Code: QB64: [Select]
might satisfy your QB senses. :)
Post by: Jack002 on April 24, 2019, 09:47:38 am
For i = 1 to 2 step 0
REM Now you're stuck here
next i
;)
Post by: bplus on April 24, 2019, 09:54:57 am
Oh but if you ever get a chance, look at the recip of 97, its pretty cool. I did it in LISP once.
It has to round to some degree to reduce properly. To try and get that for all possible decimal to fraction conversion would be a real... challenge.
Pete
Hi Jack002,
Yes, I know what you are talking about and I have some code floating about that calculates precisely the decimal and the repeating digits part of the decimal like we learned in school for 1/7 = .142857 with a bar over the digits that repeat forever.
Hi Pete,
Yes, I think it is possible to do any fraction BUT first you must express the decimal with a special notation to handle the repeating part. I like 1/3 = .R3 = .33333... 1/6 = .1R6 = .16666...
I will try to dig up the code I had that did that and then I will try to reverse it back from the special decimal notation eg, .1R6 back to 1/6. There will likely be a limit on digits again until/unless you convert the code to employ your string math.
Post by: bplus on April 24, 2019, 11:38:54 am
Code: QB64: [Select]
- ' from:"Decimal Expansion of Division without Dividing by bplus 2017-12-03"
- ' dove tailing Adrians and my recent dividing programs
- ' 2019-04-24
- ' I want to isolate the repeated section immdeiately not write the fraction out and then repeat the repeated section
- ' not 1/6 = .16R6 >>> but .1R6
- 'hmm... look like have to cycle through twice to get the length of the repeat section
- ' but before returning backup to start of repeat section insert the R where it starts the first time
- ' and end it where " repeat " starts.
- DEFLNG A-Z
- WHILE 1
- INPUT nd$
- 'n = original product or numerator (preserve value of n)
- 'd = divisor (also preserve value)
- c = n 'copy of n to be reduced until <= d, c will be the remainder part of division
- a = 0 'a is for answer or accumulate, the integer part of the division result
- 'find lowest power of 10 such that: d * 10^p > n
- p = 0 'power of 10
- p = p + 1
- WHILE c >= d
- p = p - 1
- m = 0
- m = m + 1
- m = m - 1
- c = c - d * m * 10 ^ p
- a = a + m * 10 ^ p
- 'Now for the decimal expansion isolating the repeating part if one
- b$ = "."
- 'emergency bug out!
- loopct = loopct + 1 'loop count should not exceed 1000 for numbers I am testing
- 'track repeats b() tracks been here once, b2() tracks been here twice
- b2(c) = 1
- rFlag = 1
- b$ = b$ + " repeat "
- b2(c) = 1
- b(c) = 1
- 'c was last remainder, mult by 10 and see if some m * d > can reduce it
- tc = 10 * c
- flag = 0
- c = tc - d * m
- 'OK either d divided n eventually or there is a repeated pattern recorded in b$
- skip: '< needed for debugging
- PRINT "Check string before chopping redundant section:"
- PRINT r$
- pete$ = " repeat "
- divide$ = r$
Yeah, 1/97 is looking like it would need string math to process. :D yikes! that's long!
Post by: Pete on April 24, 2019, 11:42:50 am
Pete
Post by: Jack002 on April 24, 2019, 04:14:59 pm
Well done.
Post by: bplus on April 24, 2019, 09:10:04 pm
The trick to converting a repeating decimal number to fraction is to align a second repeating section over the first by multiplying by some power of 10, p, = length of repeating section. This way when you subtract x * 10 ^ p - x = a definite finite decimal, d st.
x * (10 ^ p - 1) = d
then x = d / (10 ^ p - 1) a fraction!
QB64 can only process p up to around 14 digits in the repeating section of the decimal.
Code: QB64: [Select]
- ' from:"Decimal Expansion of Division without Dividing by bplus 2017-12-03"
- ' dove tailing Adrians and my recent dividing programs
- ' 2019-04-24
- ' I want to isolate the repeated section immediately not write the fraction out and then repeat the repeated section
- ' not 1/6 = .16R6 >>> but .1R6
- 'hmm... look like have to cycle through twice to get the length of the repeat section
- ' but before returning backup to start of repeat section insert the R where it starts the first time
- ' and end it where " repeat " starts.
- '2019-04-24
- ' just for kicks, convert the R notation back to fraction if possible.
- ' Had to revert back to the redundant " repeat " form of R notation.
- DEFLNG A-Z
- INPUT nd$
- d$ = divide$(numerator, dvsr)
- 'and now arttemp"t to convert back to fraction
- result$ = convertRnotation2Fraction$(d$)
- 'check if R in the decimal
- 'still here? we have an R and a decimal
- PRINT "Debug: repeat length ="; p
- PRINT "The length of the repeat section of: "
- PRINT rNotedDecimal$
- PRINT " is too long to convert back to fraction."
- PRINT "Debug: converting dec$ "; dec$
- 'remove " repeat "
- 'mult by 10^p to get the 2nd repeat part in dec1$ aligned to 1st repeat part in dec2$
- n## = vd1## - vd2## 'subtract dec2$ from dec1$
- adj&& = 1 'convert to whole numbers
- adj&& = adj&& * 10
- n## = n## * 10
- 'reevaluate to avoid rounding errors from crazy floating point math
- n1&& = vd1## * adj&& - vd2## * adj&&
- PRINT "Debug values: vd1, vd2, adj&&, n1&& (difference * adj&& for whole number):"
- d&& = (10 ^ p - 1) * adj&&
- 'reduce giant numbers by Gretaest Common Divisor between them
- g&& = gcd&&(n1&&, d&&): sn&& = n1&& / g&&: sd&& = d&& / g&&
- d&& = 10 ^ p%%
- g&& = gcd&&(n&&, d&&): sn&& = n&& / g&&: sd&& = d&& / g&&
- convert2Fraction$ = decimal$
- 'a and b will be changed unless make copies
- c&& = a&&: d&& = b&&
- gcd&& = c&& + d&&
- 'n = original product or numerator (preserve value of n)
- 'd = divisor (also preserve value)
- c = n 'copy of n to be reduced until <= d, c will be the remainder part of division
- a = 0 'a is for answer or accumulate, the integer part of the division result
- 'find lowest power of 10 such that: d * 10^p > n
- p = 0 'power of 10
- p = p + 1
- WHILE c >= d
- p = p - 1
- m = 0
- m = m + 1
- m = m - 1
- c = c - d * m * 10 ^ p
- a = a + m * 10 ^ p
- 'Now for the decimal expansion isolating the repeating part if one
- b$ = "."
- 'emergency bug out!
- loopct = loopct + 1 'loop count should not exceed 1000 for numbers I am testing
- 'track repeats b() tracks been here once, b2() tracks been here twice
- b2(c) = 1
- rFlag = 1
- b$ = b$ + " repeat "
- b2(c) = 1
- b(c) = 1
- 'c was last remainder, mult by 10 and see if some m * d > can reduce it
- tc = 10 * c
- flag = 0
- c = tc - d * m
- 'OK either d divided n eventually or there is a repeated pattern recorded in b$
- skip: '< needed for debugging
- divide$ = r$
Post by: Jack002 on April 25, 2019, 11:20:08 am
[edit]
No, I think its just me. I am not on the new version yet. I replaced _trim$ with ltrim$. Seems that didn't work.
Post by: bplus on April 25, 2019, 12:00:43 pm
I crashed it with 1/62
[edit]
No, I think its just me. I am not on the new version yet. I replaced _trim$ with ltrim$. Seems that didn't work.
Hi Jack002,
Oh! looks like I was allowing repeat sections up to 15 because 1/62 was 15. OK on my system QB64 v1.3 on Windows 10, the code works and arrives back at 1/62.
Post by: Jack002 on April 25, 2019, 04:11:13 pm
(all the posts here seem to use the new functions of 1.3, so this version is no good for any of those)
Post by: bplus on April 25, 2019, 04:21:08 pm
I'm on V 1.2, I need to get the new 1.3 version installed.
(all the posts here seem to use the new functions of 1.3, so this version is no good for any of those)
I think _TRIM$ is the only new function I am using from v1.3 and replacing it with LTRIM$ should be fine, the only thing it is doing is formatting the output display, it shouldn't interfere with main code. (Though I don't want to discourage you from updating. :)
Jack002 are you using Windows 10 for OS?
Post by: Jack002 on April 25, 2019, 10:59:12 pm
Post by: FellippeHeitor on April 25, 2019, 11:12:29 pm
Post by: bplus on April 26, 2019, 10:21:01 am
A variable type is different, I can see that in the negative numbers in Jack002's last line of output and also adj&& is different, I have 10, Jack002s' code has way more for adj&&. Perhaps Jack002 changed more than _TRIM$??
I'd like to compare the code Jack002 is running with mine through WinMerge.
Post by: Jack002 on April 26, 2019, 04:51:46 pm
[edit]
I just now changed all my ltrims to rtrim$(ltrim$()), no change. It still does the same thing
Code: QB64: [Select]
- ' from:"Decimal Expansion of Division without Dividing by bplus 2017-12-03"
- ' dove tailing Adrians and my recent dividing programs
- ' 2019-04-24
- ' I want to isolate the repeated section immediately not write the fraction out and then repeat the repeated section
- ' not 1/6 = .16R6 >>> but .1R6
- 'hmm... look like have to cycle through twice to get the length of the repeat section
- ' but before returning backup to start of repeat section insert the R where it starts the first time
- ' and end it where " repeat " starts.
- '2019-04-24
- ' just for kicks, convert the R notation back to fraction if possible.
- ' Had to revert back to the redundant " repeat " form of R notation.
- DEFLNG A-Z
- INPUT nd$
- d$ = divide$(numerator, dvsr)
- 'and now arttemp"t to convert back to fraction
- result$ = convertRnotation2Fraction$(d$)
- 'check if R in the decimal
- 'still here? we have an R and a decimal
- PRINT "Debug: repeat length ="; p
- PRINT "The length of the repeat section of: "
- PRINT rNotedDecimal$
- PRINT " is too long to convert back to fraction."
- PRINT "Debug: converting dec$ "; dec$
- 'remove " repeat "
- 'mult by 10^p to get the 2nd repeat part in dec1$ aligned to 1st repeat part in dec2$
- n## = vd1## - vd2## 'subtract dec2$ from dec1$
- adj&& = 1 'convert to whole numbers
- adj&& = adj&& * 10
- n## = n## * 10
- 'reevaluate to avoid rounding errors from crazy floating point math
- n1&& = vd1## * adj&& - vd2## * adj&&
- PRINT "Debug values: vd1, vd2, adj&&, n1&& (difference * adj&& for whole number):"
- d&& = (10 ^ p - 1) * adj&&
- 'reduce giant numbers by Gretaest Common Divisor between them
- g&& = gcd&&(n1&&, d&&): sn&& = n1&& / g&&: sd&& = d&& / g&&
- d&& = 10 ^ p%%
- g&& = gcd&&(n&&, d&&): sn&& = n&& / g&&: sd&& = d&& / g&&
- convert2Fraction$ = decimal$
- 'a and b will be changed unless make copies
- c&& = a&&: d&& = b&&
- gcd&& = c&& + d&&
- 'n = original product or numerator (preserve value of n)
- 'd = divisor (also preserve value)
- c = n 'copy of n to be reduced until <= d, c will be the remainder part of division
- a = 0 'a is for answer or accumulate, the integer part of the division result
- 'find lowest power of 10 such that: d * 10^p > n
- p = 0 'power of 10
- p = p + 1
- WHILE c >= d
- p = p - 1
- m = 0
- m = m + 1
- m = m - 1
- c = c - d * m * 10 ^ p
- a = a + m * 10 ^ p
- 'Now for the decimal expansion isolating the repeating part if one
- b$ = "."
- 'emergency bug out!
- loopct = loopct + 1 'loop count should not exceed 1000 for numbers I am testing
- 'track repeats b() tracks been here once, b2() tracks been here twice
- b2(c) = 1
- rFlag = 1
- b$ = b$ + " repeat "
- b2(c) = 1
- b(c) = 1
- 'c was last remainder, mult by 10 and see if some m * d > can reduce it
- tc = 10 * c
- flag = 0
- c = tc - d * m
- 'OK either d divided n eventually or there is a repeated pattern recorded in b$
- skip: '< needed for debugging
- divide$ = r$
Post by: bplus on April 26, 2019, 05:19:41 pm
Yeah, I run very same and do get back to 1/62 on last line.
Don't know what our difference is????
Post by: Jack002 on April 26, 2019, 10:17:56 pm
LOL
[edit]
It fails on this line
g&& = gcd&&(n1&&, d&&)
I don't follow all the logic here, once you make vd1 and vd2 etc you start to lose me.
Does it matter that the value of vd1 is not an integer? Its 16129032258064.52
Post by: bplus on April 27, 2019, 12:18:58 am
Here is an example of converting 1/6 in English:
Quote
Convert a repeating decimal back to fraction:
1/6 = .16R6 = x
10x = 1.666... VD1
- x = .166... VD2
=============
9x = 1.5 VD1 - VD2
adj = 10 a multiplier to get rid of decimal
90x = 15 or x = 15 /90
GCD(15, 90) = greatest common denominator of 15 and 90 is 15
15/15 = 1 and 90/15 = 6 so 15/90 = 1/6
x = 1/6
Post by: Jack002 on April 27, 2019, 09:17:23 am
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Post by: Jack002 on April 27, 2019, 09:22:01 am
{1/56 also fails for the same reason, both numbers given to GCD are negative}
Post by: bplus on April 27, 2019, 09:37:27 am
Ok so vd1 is larger than vd2. You multiply both by adj and take a difference. Won't that number be positive? If so, why is this negative?
Yes why are your numerator and denominator negative? The only time I see that is when the number exceeds it's TYPE limit.
And why is your adj 1000000 when mine is 10? That might make VD1 and VD2 too big even for _INTEGER64 limit.
So the crux of our difference might begin here with the calculation of adj&&
Code: QB64: [Select]
adj&& is the multiplier needed to get VD1-VD2 (which becomes the numerator of the fraction) into a whole number.We are using the same code. Is there a version 1.3 difference in handling the variable types?
Has anyone else tried 1/62? What do you get with what version of QB64?
OK I am still getting good results with Jack002 code on an older version of QB64.
Jack002 are you using 32 bit of even X86 versions of QB64?
Post by: bplus on April 27, 2019, 10:23:57 am
After some more experimenting I see it also fails for 1/60. GCD is given two numbers, one is negative. It seems to always happen when one or both numbers given GCD are negative
{1/56 also fails for the same reason, both numbers given to GCD are negative}
The 3rd number from left of the 2nd line from bottom adj&& is supposed to be a simple power of 10, eg 10, 100, 1000, 10000...
Code: QB64: [Select]
So there is a type limit problem.
Post by: bplus on April 27, 2019, 10:39:58 am
1/60 has a suspiciously high adj&&
Post by: Jack002 on April 27, 2019, 05:32:17 pm
I don't know why this is failing. The number and the INT are the same.
Code: QB64: [Select]
I see it keeps going till ADJ is 1.5D+19!!
Post by: Jack002 on April 27, 2019, 05:39:00 pm
Code: QB64: [Select]
EDIT
I made two changes to the while loop. Now it seems to work
Code: QB64: [Select]
- adj&& = adj&& * 10
- n## = n## * 10 + 1.0D+15
Post by: bplus on April 27, 2019, 08:46:33 pm
Yep! I was convinced something was screwy when I saw the adj&& for 1/60.
Here is another way around adj&& calc:
Code: QB64: [Select]
- 'adj&& = 1 'convert to whole numbers
- 'WHILE n## <> INT(n##)
- ' adj&& = adj&& * 10
- ' n## = n## * 10
- 'WEND
- adj&& = 10 ^ p2
I also had to reduce max length of the repeat section below 13 because 1/79 was getting negative numerator and denominator like you were getting, which means the type limit was exceeded.
Modified code:
Code: QB64: [Select]
- ' from:"Decimal Expansion of Division without Dividing by bplus 2017-12-03"
- ' dove tailing Adrians and my recent dividing programs
- ' 2019-04-24
- ' I want to isolate the repeated section immediately not write the fraction out and then repeat the repeated section
- ' not 1/6 = .16R6 >>> but .1R6
- 'hmm... look like have to cycle through twice to get the length of the repeat section
- ' but before returning backup to start of repeat section insert the R where it starts the first time
- ' and end it where " repeat " starts.
- '2019-04-24
- ' just for kicks, convert the R notation back to fraction if possible.
- ' Had to revert back to the redundant " repeat " form of R notation.
- '2019-04-27 Thanks to Jack002's comments and replies this code to calculate adj&& may have been improved.
- DEFLNG A-Z
- INPUT nd$
- d$ = divide$(numerator, dvsr)
- 'and now arttemp"t to convert back to fraction
- result$ = convertRnotation2Fraction$(d$)
- 'check if R in the decimal
- 'still here? we have an R and a decimal
- PRINT "Debug: repeat length ="; p
- PRINT "The length of the repeat section of: "
- PRINT rNotedDecimal$
- PRINT " is too long to convert back to fraction."
- PRINT "Debug: converting dec$ "; dec$
- 'remove " repeat "
- 'mult by 10^p to get the 2nd repeat part in dec1$ aligned to 1st repeat part in dec2$
- n## = vd1## - vd2## 'subtract dec2$ from dec1$
- 'adj&& = 1 'convert to whole numbers
- 'WHILE n## <> INT(n##)
- ' adj&& = adj&& * 10
- ' n## = n## * 10
- 'WEND
- 'calculate adj&& from length of decimal
- adj&& = 10 ^ p2
- 'reevaluate to avoid rounding errors from crazy floating point math
- n1&& = vd1## * adj&& - vd2## * adj&&
- PRINT "Debug values: vd1, vd2, adj&&, n1&& (difference * adj&& for whole number):"
- d&& = (10 ^ p - 1) * adj&&
- 'reduce giant numbers by Gretaest Common Divisor between them
- g&& = gcd&&(n1&&, d&&): sn&& = n1&& / g&&: sd&& = d&& / g&&
- d&& = 10 ^ p%%
- g&& = gcd&&(n&&, d&&): sn&& = n&& / g&&: sd&& = d&& / g&&
- convert2Fraction$ = decimal$
- 'a and b will be changed unless make copies
- c&& = a&&: d&& = b&&
- gcd&& = c&& + d&&
- 'n = original product or numerator (preserve value of n)
- 'd = divisor (also preserve value)
- c = n 'copy of n to be reduced until <= d, c will be the remainder part of division
- a = 0 'a is for answer or accumulate, the integer part of the division result
- 'find lowest power of 10 such that: d * 10^p > n
- p = 0 'power of 10
- p = p + 1
- WHILE c >= d
- p = p - 1
- m = 0
- m = m + 1
- m = m - 1
- c = c - d * m * 10 ^ p
- a = a + m * 10 ^ p
- 'Now for the decimal expansion isolating the repeating part if one
- b$ = "."
- 'emergency bug out!
- loopct = loopct + 1 'loop count should not exceed 1000 for numbers I am testing
- 'track repeats b() tracks been here once, b2() tracks been here twice
- b2(c) = 1
- rFlag = 1
- b$ = b$ + " repeat "
- b2(c) = 1
- b(c) = 1
- 'c was last remainder, mult by 10 and see if some m * d > can reduce it
- tc = 10 * c
- flag = 0
- c = tc - d * m
- 'OK either d divided n eventually or there is a repeated pattern recorded in b$
- skip: '< needed for debugging
- divide$ = r$
Post by: Jack002 on April 28, 2019, 12:19:01 am
Why do you suppose there is so much rounding error between the versions? This is like the old 8 bit days when you do 1/3 and then * 3 and get this long line of 9s. I know I saw that on the commodore 64.
Post by: bplus on April 28, 2019, 09:45:54 am
I was proud to hack some kind of solution. I had my doubts. I have written one like your first part that does the dec equivalent, but never thought to make it go back again. Well done (in spite of any problems)
Why do you suppose there is so much rounding error between the versions? This is like the old 8 bit days when you do 1/3 and then * 3 and get this long line of 9s. I know I saw that on the commodore 64.
Hi Jack002,
I am sorry I missed the experience with a Commodore 64, you have obviously been deeply affected by it. I did have experience with GW BASIC and DOS and loved the way the two worked together, then later VB for DOS and DOS great stuff!
The great difference between our different results of this code, I am still attributing to the possibility you are using a 32 bit version of QB64 or even x86. You have not said X64, x32 or even x86 that your version of QB64 is. If you are using a X64 bit version of QB64 I am completely baffled! LOL wouldn't be first time!
Post by: SMcNeill on April 28, 2019, 12:46:57 pm
Hi Jack002,
I am sorry I missed the experience with a Commodore 64, you have obviously been deeply affected by it. I did have experience with GW BASIC and DOS and loved the way the two worked together, then later VB for DOS and DOS great stuff!
The great difference between our different results of this code, I am still attributing to the possibility you are using a 32 bit version of QB64 or even x86. You have not said X64, x32 or even x86 that your version of QB64 is. If you are using a X64 bit version of QB64 I am completely baffled! LOL wouldn't be first time!
We’ve seen some drastic differences in the past with how Windows does math with 32-bit and 64-bit code, so I’m guessing that’s probably the difference as well.
Post by: Jack002 on April 28, 2019, 04:15:03 pm
If we can't expect every computer to make the same calculations in things like this how can we ever plan to write a program that works for everyone? I'm stumped.
Post by: bplus on April 28, 2019, 05:37:03 pm
Until version 1.3 all stable versions of QB64 were 32 bit, didn't matter if your computer was 64 bit.
Post by: Jack002 on April 28, 2019, 05:39:12 pm
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Post by: Pete on April 28, 2019, 08:19:17 pm
Pete
Post by: Jack002 on April 28, 2019, 11:55:29 pm
Post by: bplus on April 30, 2019, 10:46:48 am
The new method of calculating adj&& is ruined when STR$(n##) produces a string with scientific or exponential notation.
Code: QB64: [Select]
Also the longer the string of zeros to the right of the decimal the less repeat length this convert back to fraction can tolerate.
I actually started reconsidering picking up string math to attempt larger fraction conversions but then I would need GCD function for number strings also... just doesn't seem worth the trouble. Like Pete said, who uses such cumbersome fractions anyway?
Just neat to see that they could (if only in theory) be converted back (but not with rounding).
I can see rounding decimals to closest 1/2, 1/4, 1/8, 1/16, 1/32, 1/64 of a unit as being useful.
Post by: jack on April 30, 2019, 02:24:45 pm
just for fun, expand the decimal to continued fraction convergents https://en.wikipedia.org/wiki/Continued_fraction, see the comments
you will wind up with successive approximations to Pi in this instance
3/1, 22/7, 333/106, 355/113
the only problem is how to know when you reached the optimum
Code: [Select]
DIM n1 AS DOUBLE, n2 AS DOUBLE, n3 AS DOUBLE
DIM d1 AS DOUBLE, d2 AS DOUBLE, d3 AS DOUBLE
DIM fp AS DOUBLE, ip AS DOUBLE
'expand a decimal number to a fraction using continued fraction convergents
'take Pi for instance
'int(Pi) = 3, frac = Pi-3 = .1415926535897932384626433832795
' | 3
'0 1 |
'1 0 |
'3 * 1 + 0 = 3
'3 * 0 + 1 = 1
' | 3 |
'0 1 | 3 |
'1 0 | 1 |
'frac = 1/ frac : int(frac) = 7 : frac = frac - 7
'
'7 * 3 + 1 = 22
'7 * 1 + 0 = 7
' | 3 | 7
'0 1 | 3 | 22
'1 0 | 1 | 7
'frac = 1/ frac : int(frac) = 15 : frac = frac - 15
'
'15 * 22 + 3 = 333
'15 * 7 + 1 = 106
' | 3 | 7 | 15
'0 1 | 3 | 22 | 333
'1 0 | 1 | 7 | 106
'frac = 1/ frac : int(frac) = 1 : frac = frac - 1
'
'1 * 333 + 22 = 355
'1 * 106 + 7 = 113
' | 3 | 7 | 15 | 1
'0 1 | 3 | 22 | 333 | 355
'1 0 | 1 | 7 | 106 | 113
n1 = 0: n2 = 1
d1 = 1: d2 = 0
fp = 3.1415926535897932384626433832795
'fp = .125125
FOR i = 1 TO 6
ip = INT(fp)
n3 = ip * n2 + n1
d3 = ip * d2 + d1
n1 = n2: n2 = n3
d1 = d2: d2 = d3
fp = 1 / (fp - ip)
PRINT n3; "/"; d3
NEXT
Post by: bplus on April 30, 2019, 03:06:02 pm
Would that sequence continue to get better, if you could extend the precision of the calculations?
Post by: jack on April 30, 2019, 04:12:37 pm