1.824999999999999.round(2)
# => 1.82
1.82499999999999999.round(2)
# => 1.83
I don't understand why the result in the first case is 1.82 and for the latter 1.83. My desired result is 1.82 for both cases.
As is well known, a floating number in computer has errors. Notice that both numbers that you have are close to 1.825. In your first case, the number is small enough to be differentiated from 1.825.
1.824999999999999
# => 1.824999999999999
In your second case, having enough 9s makes the value close enough to be considered exactly as 1.825:
1.82499999999999999
# => 1.825
Then, when you apply round, you get 1.83.
In addition to the many excellent explanations here, I'd like to give an example using BigDecimal
o = BigDecimal.new('1.82499999999999999', 17)
2.0.0p247 :011 > o.round(2).to_f
=> 1.82
Also notice that #round takes various modes for rounding, as per the docs.
Ref:
http://www.ruby-doc.org/stdlib-2.1.0/libdoc/bigdecimal/rdoc/BigDecimal.html#method-c-mode
http://www.ruby-doc.org/stdlib-2.1.0/libdoc/bigdecimal/rdoc/BigDecimal.html#method-i-round
After a certain number of (binary) digits, Ruby cannot represent differences between Float literals, even if you've entered the value directly in source code or the console
1.82499999999999999 == 1.825
# => true
If you really need a high level of precision, then you could look at the BigDecimal class. Although you could still enter enough 9s to reach limits in that class.
Floats are notoriously imprecise as sawa and Neil have pointed out.
If this is mainly an issue for testing, you can use assert_in_delta if you're using minitest, or be_within with rSpec
Related
I'm currently doing a project Euler problem that requires me to find patterns in repeating decimals. However, Ruby rounds too soon and I can't find a way to flesh out decimals to the nth place.
For instance:
1/7.to_f => 0.14285714285714285
but I'm trying to make it so:
1/7.to_f => 0.14285714285714285714285714285757142857142857
Any help would be greatly appreciated!
All languages support being able to define the precision of floating point in output. Ruby uses the common format strings:
pi = 355.0/113.0
'%1.5f' % pi # => "3.14159"
Or, in your case:
'%1.20f' % (1.0/7.0) # => "0.14285714285714284921"
'%1.20f' % (1.to_f/7) # => "0.14285714285714284921"
'%1.20f' % (1/7.to_f) # => "0.14285714285714284921"
I'd recommend reading the documentation for String's % and Kernel::sprintf. How Ruby determines to use fixed or floating math and the uses of to_f is covered in any decent Ruby tutorial.
You can easily get as many repeating digits as you like, by scaling up the computation by a power of 10
10**100/7
=> 1428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428
I'm using ruby's Rational library to convert the width & height of images to aspect ratios.
I've noticed that string arguments are treated differently than numeric arguments.
>> Rational('1.91','1')
=> (191/100)
>> Rational(1.91,1)
=> (8601875288277647/4503599627370496)
>> RUBY_VERSION
=> "2.1.5"
>> RUBY_ENGINE
=> "ruby"
FYI 1.91:1 is an aspect ratio recommended by Facebook for images on their platform.
Values like 191 and 100 are much more convenient to store in my database than 8601875288277647 and 4503599627370496. But I'd like to understand where this different originates before deciding which approach to use.
The Rational test suite doesn't seem to cover this exact case.
Disclaimer: This is only an educated guess, based on some knowledge on how to implement such a feat.
As Kent Dahl already said, Floats are not precise, they have a fixed precision, which means 1.91 is really 1.910000000000000000001 or something like that, which ruby "knows" should be displayed as 1.91.
"1.91" on the other hand is a string, basically an array of characters: '1', '.', '9', '1'.
This said, here is what you need to do, to build the rational out of floats:
Get rid of the . (mathematically by multiplying the numerator and denominator with 10^x, or multiplying with ten as many times, as there are numbers behind the .)
Find the greatest common denominator (gcd)
Divide num and denom with the gcd
Step 1 however, is a little different for Float and String:
The Float, we will have to multiply with 10^x, where x is (because of the precision) not 2 (as one would think with 1.91), but more something like 16 (remember: 1.9100...1).
For the String, we COULD cast it into a float and do the same trick, but hey, there is an easier way: We just count the number of characters behind the dot (which is 2), remove the dot and multiply the denom with 10^2... This is not only the easier, but also the more precise way.
The big numbers might disappear again, when applying step 3, that's why you will not always get those strange results when dealing with rationals from floats.
TLDR: The numbers will be built differently based on the arguments being String, or FLoat. FLoats can produce long-ass numbers, because precision.
The Float 1.91 is stored as a double which has a given amount of precision, limited by binary presentation. The equivalent Rational object retains this precision a such as possible, so it is huge. There is no way of storing 1.91 exactly in a double, but the value you get is close enough for most uses.
As for the String, it represents a different value - the exact value of 1.91 - and as you create a Rational it retains it better. It is more correct than the Float, UT takes longer to use for calculations.
This is similar to the problem with 1.0/3 as it "goes on forever" 0.333333...etc, but Rational can represent it exactly.
Weird..
$ (9.95*100).to_i
=> 994
And then,
$ (9.95*100).round.to_i
=> 995
It seems like the floating point value is (approximately) 9.9499999... and
to_i
chops the decimal value, hence the 994.
But does anyone know why?
Read more about the problems with accuracy here: https://en.wikipedia.org/wiki/Floating_point#Accuracy_problems
Short version: Never use floats as representation for currencies.
Your call to #round is rounding it "up" from (its internal representation of 9.95, which is a number slightly inaccurate and just below it). So that one works, whereas calling straight #to_i just (always) truncates, so it sees 994.99999 and truncates it down to 994. With Ruby 1.9.x+ it shows this more plainly (for better or worse), so you can see what is going on.
>> 9.95*100
=> 994.9999999999999
>> (9.95*100).round
=> 995
ree-1.8.7-2010.02 :003 > (10015.8*100.0).to_i
=> 1001579
ree-1.8.7-2010.02 :004 > 10015.8*100.0
=> 1001580.0
ree-1.8.7-2010.02 :005 > 1001580.0.to_i
=> 1001580
ruby 1.8.7 produces the same.
Does anybody knows how to eradicate this heresy? =)
Actually, all of this make sense.
Because 0.8 cannot be represented exactly by any series of 1 / 2 ** x for various x, it must be represented approximately, and it happens that this is slightly less than 10015.8.
So, when you just print it, it is rounded reasonably.
When you convert it to an integer without adding 0.5, it truncates .79999999... to .7
When you type in 10001580.0, well, that has an exact representation in all formats, including float and double. So you don't see the truncation of a value ever so slightly less than the next integral step.
Floating point is not inaccurate, it just has limitations on what can be represented. Yes, FP is perfectly accurate but cannot necessarily represent every number we can easily type in using base 10. (Update/clarification: well, ironically, it can represent exactly every integer, because every integer has a 2 ** x composition, but "every fraction" is another story. Only certain decimal fractions can be exactly composed using a 1/2**x series.)
In fact, JavaScript implementations use floating point storage and arithmetic for all numeric values. This is because FP hardware produces exact results for integers, so this got the JS guys 52-bit math using existing hardware on (at the time) almost-entirely 32-bit machines.
Due to truncation error in float calculation, 10015.8*100.0 is actually calculated as 1001579.999999... So if you simply apply to_i, it cuts off the decimal part and returns 1001579
http://en.wikipedia.org/wiki/Floating_point#Accuracy_problems
>> sprintf("%.16f", 10015.8*100.0)
=> "1001579.9999999999000000"
And Float#to_i truncates this to 1001579.
I'm making an application which is listening to prices being updated regularly, but occasionally my data source throws me something like "1.79769313486232e+308". The numbers that get sent will never by really big numbers (eg. "179769313486232e+308"), but as with the example above, they come with a lot of precision.
I'd be happy to drop everything after the first couple of decimal places, and end up with something like "1.798", but the following code isn't working for me:
irb(main):001:0> s = '1.79769313486232e+308'
=> "1.79769313486232e+308"
irb(main):002:0> ("%.3f" % s).to_f
(irb):2: warning: Float 1.79769313486232e+30... out of range
=> 0.0
Any graceful ways to handle these kind of numbers in Ruby?
You need to find out from your data source what those really big numbers mean. The price isn't actually 1.797e+308, but it probably also isn't 1.797. How you deal with those numbers depends entirely on what value you should be interpreting them as.
Update: I'm not sure you understand what this number means. 1.79769313486232e+308 is 1.79769313486232 times ten to the 308th power. It's a number with more than 300 digits to the left of the decimal point. This isn't a price, it's a mistake. It's the upper limit of what double-precision floating point can represent.
In other words, you're getting the equivalent of 0xFFFFFFFF or something like that, but interpreted as a floating point number.
That's right at the top of the range of "doubles". In Python for example it's converted to the special float called "inf".
The graceful way to handle this one might be to treat it as infinity
you could strip out extra decimals using regexp
>> s =~ /\.\d\d\d(\d+)/
>> s.gsub($1, '')
=> "1.797e+308"