Is it possible to store a fraction like 3/6 in a variable of some sort?
When I try this it only stores the numbers before the /. I know that I can use 2 variables and divide them, but the input is from a single text field. Is this at all possible?
I want to do this because I need to calculate the fractions to decimal odds.
A bonus question ;) - Is there an easy way to calculate a decimal value to a fraction? Thanks..
Well in short, there is no true way to extract the original fraction out of a decimal.
Example: take 5/10
you will get 0.5
now, 0.5 also translates back to 1/2, 2/4, 3/6, etc.
Your best bet is to store each integer separately, and perform the calculation later on.
The best thing to do is to implement a fraction class (or rational number class). Normally it would take a numerator and denominator and be able to provide a double, and do basic math with other fraction objects. It should also be able to parse and format fractions.
Rational Arithmetic on Rosetta Code looks like something good to start with.
I'm afraid there aren't any easy answers for you on this. For creating the fraction, you'll have to split the text field on the '/', convert the two halves to doubles, and divide them out. As for converting it back to a fraction, you'll have to crack open a math textbook and figure it out. (Even worse, a double is not actually precise—you may think it has 0.1 in it, but it really has 0.09999999999999998726 or something like that, so you'll have to choose a precision and go for it, or write some sort of fraction class that's based on a pair of integers.)
The method, as been said, is to store the numerator and denominator, much in the way you can write it on paper.
for 'C' use the
GNU Multiple Precision Arithmetic Library
look for 'rational' in the docs.
Is there an easy way to calculate a decimal value to a fraction?
If you limit your decimal values to a certain number of decimal points you could create a lookup table.
0.3333, 1/3
0.6666, 2/3
0.0625, 1/16
0.1250, 1/8
0.2500, 1/4
0.5000, 1/2
0.7500, 3/4
etc...
So if the user input 0.5 you pad it with 0's until you got 4 decimal places. You would then use the lookup table to return "1/2". The lookup table should probably be a dictionary of sorts.
It wouldn't be too difficult to do estimating either. For example, if the user entered 0.0624 you could easily select the value in the table closest to that decimal. In this case it would return "1/16."
Don't let typing/entering of the finite set of decimal/fraction pairs scares you (it's really not that large depending on the precision you choose).
If all else fails perhaps a google search would reveal a library that does this sort of this for you.
Related
I have a task to use Marie Simulator to calculate the area of a circle
requiring its radius
I know that in Marie Language there is no multiplication operator so we use multiplication by adding numbers several times so If I wanted to multiply 2*3 I could write it down like 3+3 or 2+2+2
but when using the area of a circle there is pi which is 3.14 I can't imagine how could I get it so can anyone give me the algorithm or code for that ?
thanks in advance.
MARIE does not have floating point support.
So, should refer to your course work or ask your instructors what to do, as it is not obvious.
It is, of course, possible to do floating point in software, but the complexity is extraordinary, so unlikely to be what the're looking for.
You could use fixed point arithmetic, fractions, or decimal.
Here's one solution that might be appropriate: multiply one of the numbers (having decimal places) by some fixed constant factor, do the arithmetic, then interpret answers accordingly. For example, let's use 100 as the factor, so 3.14 is represented by 314. Let's say r is 9, so we can square that (9x9=81), then multiply 81 x 314 = 25434. Now we know that value is 100x too large, so the real answer is 254.34. (You can choose to ignore the .34, or, round it, then ignore. 254 is still more accurate than 243 which we would get from 9x9x3.)
Fixed point multiplies all numbers by the constant (usually a power of 2, so that the binary point is in the same bit position). Additions are relatively straightforward, but multiplications need to interpret results by factoring in (or out) that both sources are in scaled, meaning the answer is doubly scaled.
If you need to measure radius also with decimal digits, e.g. 9.5, then you could scale both 9.5 and 3.14 by 100. Then we need 950x950, and multiply by 314. The answer will be 100x100x100 too large, so 1000000x too large. With this approach, 16 bits that MARIE offers will overflow, so you would need to use at least 32-bit arithmetic (not trivial on 16-bit machine).
You can use two different scaling factors, e.g. 9.5 as 95 and 3.14 as 314. Take 95x95x314, is 10000x too large, so interpret the answer accordingly. Still this will overflow MARIE's 16-bits
Fractions would maintain both a numerator and denominator for all numbers. So, 3.14 could be 314/100, and 9.5 could be 95/10 — and simplified 157/50 and 19/2. To add you have to find a common denominator, convert, then sum numerators. To multiply you multiply both numerators and denominators: numerator = 19x19x157, denominator = 2x2x50. Just fits in 16-bit unsigned arithmetic, but still overflows 16-bit signed arithmetic..
And finally binary coded decimal is more like a string format, where numbers are stored one decimal digit per byte or per nibble (packed decimal). Algorithms for addition and subtraction need to account for variable length inputs.
Big integer forms also use similar to binary coded decimal but compose much larger elements instead of single decimal digits.
All of these approaches require some thought, and the more limitations you want to remove, the more work required. So, I'd suggest to go back to your course to find what they really want.
I am having a problem with a simple division from two integers. I need it to be as accurate as possible, but for some reason the double type is working strange.
For example, if I execute the following code:
double res = (29970.0/1000.0);
The result is 29.969999999999999, when it should be 29.970.
Any idea why this is happening?
Thanks
Any idea why this is happening?
Because double representation is finite. For example, IEEE754 double-precision standard has 52 bits for fraction. So, not all the real numbers are covered. So, some of the values can not be ideally precise. In your case the result is 10^-15 away from the ideal.
I need it to be as accurate as possible
You shouldn't use doubles, then. In Java, for example, you would use BigDecimal instead (most languages provide a similar facility). double operations are intrinsically inaccurate to some degree. This is due to the internal representation of floating point numbers.
floating point numbers of type float and double are stored in binary format. Therefore numbers cant have precise decimal values. Those values are instead quantisized. If you hypothetically had only 2 bits fraction number type you would be able to represent only 2^-2 quantums: 0.00 0.25 0.50 0.75, nothing between.
I need it to be as accurate as possible
There is no silver bullet, but if you want only basic arithmetic operations (which map ℚ to ℚ), and you REALLY want exact results, then your best bet is rational type composed of two unlimited integers (a.k.a. BigInteger, BigInt, etc.) - but even then, memory is not infinite, and you must think about it.
For the rest of the question, please read about fixed size floating-point numbers, there's plenty of good sources.
We can write a simple Rational Number class using two integers representing A/B with B != 0.
If we want to represent an irrational number class (storing and computing), the first thing came to my mind is to use floating point, which means use IEEE 754 standard (binary fraction). This is because irrational number must be approximated.
Is there another way to write irrational number class other than using binary fraction (whether they conserve memory space or not) ?
I studied jsbeuno's solution using Python: Irrational number representation in any programming language?
He's still using the built-in floating point to store.
This is not homework.
Thank you for your time.
With a cardinality argument, there are much more irrational numbers than rational ones. (and the number of IEEE754 floating point numbers is finite, probably less than 2^64).
You can represent numbers with something else than fractions (e.g. logarithmically).
jsbeuno is storing the number as a base and a radix and using those when doing calcs with other irrational numbers; he's only using the float representation for output.
If you want to get fancier, you can define the base and the radix as rational numbers (with two integers) as described above, or make them themselves irrational numbers.
To make something thoroughly useful, though, you'll end up replicating a symbolic math package.
You can always use symbolic math, where items are stored exactly as they are and calculations are deferred until they can be performed with precision above some threshold.
For example, say you performed two operations on a non-irrational number like 2, one to take the square root and then one to square that. With limited precision, you may get something like:
(√2)²
= 1.414213562²
= 1.999999999
However, storing symbolic math would allow you to store the result of √2 as √2 rather than an approximation of it, then realise that (√x)² is equivalent to x, removing the possibility of error.
Now that obviously involves a more complicated encoding that simple IEEE754 but it's not impossible to achieve.
I have some inputs on my site representing floating point numbers with up to ten precision digits (in decimal). At some point, in the client side validation code, I need to compare a couple of those values to see if they are equal or not, and here, as you would expect, the intrinsics of IEEE754 make that simple check fails with things like (2.0000000000==2.0000000001) = true.
I may break the floating point number in two longs for each side of the dot, make each side a 64 bit long and do my comparisons manually, but it looks so ugly!
Any decent Javascript library to handle arbitrary (or at least guaranteed) precision float numbers on Javascript?
Thanks in advance!
PS: A GWT based solution has a ++
There is the GWT-MATH library at http://code.google.com/p/gwt-math/.
However, I warn you, it's a GWT jsni overlay of a java->javascript automated conversion of java.BigDecimal (actually the old com.ibm.math.BigDecimal).
It works, but speedy it is not. (Nor lean. It will pad on a good 70k into your project).
At my workplace, we are working on a fixed point simple decimal, but nothing worth releasing yet. :(
Use an arbitrary precision integer library such as silentmatt’s javascript-biginteger, which can store and calculate with integers of any arbitrary size.
Since you want ten decimal places, you’ll need to store the value n as n×10^10. For example, store 1 as 10000000000 (ten zeroes), 1.5 as 15000000000 (nine zeroes), etc. To display the value to the user, simply place a decimal point in front of the tenth-last character (and then cut off any trailing zeroes if you want).
Alternatively you could store a numerator and a denominator as bigintegers, which would then allow you arbitrarily precise fractional values (but beware – fractional values tend to get very big very quickly).
I tried to assign a very small number to a double value, like so:
double verySmall = 0.000000001;
9 fractional digits. For some reason, when I multiplicate this value by 10, I get something like 0.000000007. I slighly remember there were problems writing big numbers like this in plain text into source code. Do I have to wrap it in some function or a directive in order to feed it correctly to the compiler? Or is it fine to type in such small numbers in text?
The problem is with floating point arithmetic not with writing literals in source code. It is not designed to be exact. The best way around is to not use the built in double - use integers only (if possible) with power of 10 coefficients, sum everything up and display the final useful figure after rounding.
Standard floating point numbers are not stored in a perfect format, they're stored in a format that's fairly compact and fairly easy to perform math on. They are imprecise at surprisingly small precision levels. But fast. More here.
If you're dealing with very small numbers, you'll want to see if Objective-C or Cocoa provides something analagous to the java.math.BigDecimal class in Java. This is precisely for dealing with numbers where precision is more important than speed. If there isn't one, you may need to port it (the source to BigDecimal is available and fairly straightforward).
EDIT: iKenndac points out the NSDecimalNumber class, which is the analogue for java.math.BigDecimal. No port required.
As usual, you need to read stuff like this in order to learn more about how floating-point numbers work on computers. You cannot expect to be able to store any random fraction with perfect results, just as you can't expect to store any random integer. There are bits at the bottom, and their numbers are limited.