0.06 == 0.06 returns false in Ruby?

[Jason_G]

Hi

I wrote a simple test program, basically the program asks the user to
enter floats. the entered values shall be used as keys for Hash (the
values are irrelavent).

The program tries to find the lowest untaken key/float (floats are used
as keys).

please see attachment.

please run the prog, and enter the following:
0.01 - OK
0.02 - OK
0.03 - OK
0.04 - OK
0.05 - OK
0.06 - Problem

Can anyone explain to me what's going on here?

thanks
jason

Attachments:
http://www.ruby-forum.com/attachment/193/test.rb

···

--
Posted via http://www.ruby-forum.com/.

[Dan_Zwell]

Jason G. wrote:

Hi

I wrote a simple test program, basically the program asks the user to
enter floats. the entered values shall be used as keys for Hash (the
values are irrelavent).

The program tries to find the lowest untaken key/float (floats are used
as keys).

please see attachment.

please run the prog, and enter the following:
0.01 - OK
0.02 - OK
0.03 - OK
0.04 - OK
0.05 - OK
0.06 - Problem

Can anyone explain to me what's going on here?

You should never compare floating point numbers for equality in any language. This is true at least for C, C++, .NET, and Java, to name a few. It just won't be accurate. Unlike integers, floats are not stored as their true Platonic forms ;). If you really wanted to see how the digits differed, you could print both numbers to a large number of digits (printf("%.20f", my_number)). You don't even need to do any math to see the roundoff error.

>> printf("%.50f", 1.1)
1.10000000000000008881784197001252323389053344726562

To compare floats, you must ask whether they are within a certain threshold of each other.
Epsilon = 0.00000000001
return (num1-num2).abs < Epsilon # num1 == num2

Dan

[_Pena_Botp1 ("Peña, Botp")]

# Subject: 0.06 == 0.06 returns false in Ruby?
# http://www.ruby-forum.com/attachment/193/test.rb

oops, careful w your statement/subject

obviously, 0.06 == 0.06. any language can vouch on that.

irb(main):008:0> 0.06 == 0.06
=> true

the problem crops out here (they trigger when you do operations),

irb(main):009:0> 0.05+0.01 == 0.06
=> false

you can check the diff

irb(main):010:0> (0.05+0.01) - 0.06
=> 6.93889390390723e-18

as mentioned by Dan, careful on comparing floats. And as to any precision subject, there is what we call significant digits..

this floating problem is a faq and is very surprising on such a very high language such as ruby. can we address this? maybe create flag like $EPSILON=0 or something, or may flag to revert to rational or bigdeci like $FLOAT_PROCESSOR=RATIONAL...

just a thought.

kind regards -botp

···

From: Jason G. [mailto:jasonpurchase@yahoo.com]

[Martin_Jansson]

This is why I prefer to use fixed decimal. In your own private code,
it's easy enough to implement. You just decide how many "decimals" your
int's should have.

Getting correct programs using floats are really hard. Heck, MS Excell
don't even get Sum and Mean right. (Microsoft, usually, use naïve
algorithm's that don't take care of underflow and rounding errors).

···

--
Posted via http://www.ruby-forum.com/.

[Jason_G]

thanks for the help

···

--
Posted via http://www.ruby-forum.com/.

[Dan_Zwell]

Dan Zwell wrote:

To compare floats, you must ask whether they are within a certain threshold of each other.
Epsilon = 0.00000000001
return (num1-num2).abs < Epsilon # num1 == num2

Dan

Oops, I didn't realize that Ruby comes with an Epsilon. This should be a fine test for equality:

return (num1-num2).abs < Float::EPSILON

Now, whether Float#==(other) should make this check might be worth thinking about, but I really have no opinion on the matter--I'm used to not comparing floats like this.

Dan

[Michael_Ulm]

Peña wrote:
--snip--

irb(main):010:0> (0.05+0.01) - 0.06
=> 6.93889390390723e-18

as mentioned by Dan, careful on comparing floats. And as to any
precision subject, there is what we call significant digits..

this floating problem is a faq and is very surprising on such a
very high language such as ruby. can we address this? maybe create
flag like $EPSILON=0 or something, or may flag to revert to rational
or bigdeci like $FLOAT_PROCESSOR=RATIONAL...

Unfortunately, there is no easy solution to this problem. Here is a
catalog of often proposed solutions and why they do not work:

1 (proposed by doug meyer in this thread) Always use
  (x-y).abs < Float::EPSILON
  as a test for equality.

  This won't work because the rounding error easily can get bigger than
  Float::EPSILON, especially when dealing with numbers that are bigger
  than unity. e.g.
  y = 100.1 + 0.3
  y - 100.4 # => -1.421e-14, while Float::EPSILON = 2.22e-16

2 Always use (x-y).abs < (x.abs + y.abs) * Float::EPSILON) as a test for equality.

  Better than the first proposal, but won't work if the rounding error
  gets too large after a complex computation.
  In addition, (1) and (2) suffer from the problem that x==y and y==z do
  not imply x==z.

3 Use Bigdezimal

  This only shifts the problem a few decimal places down, and tests for
  equality will fail as with the normal floats.

4 Use Rationals

  Works if you only have to deal with rational operations. But doesn't
  solve the following
  x = sqrt(2)
  y = x + 1
  x + 0.2 == y - 0.8 # => false
  In addition, rational arithmetic can produce huge numbers pretty fast,
  and this will slow down computations enormously.

5 Use a symbolic math package

  This could in theory solve the issue with equality, but in practice there
  is no way to decide that two symbolic representations of a number are the
  same, like
  1 / (sqrt(2) - 1) == sqrt(2) + 1
  Also, very, very slow.

6 Use interval arithmetic

  Gives you strict bounds on your solution, but can't answer x==y.

Summing up, when using floating point arithmetic there is no one true way.
There is no substitute for understanding numbers and analyzing your problem.

HTH,

Michael

[doug_meyer]

There is also a class called BigDecimal (or something like that) if
you want to have really accurate numbers and no floating-point errors.

···

On 8/30/07, Dan Zwell <dzwell@gmail.com> wrote:

Dan Zwell wrote:
> To compare floats, you must ask whether they are within a certain
> threshold of each other.
> Epsilon = 0.00000000001
> return (num1-num2).abs < Epsilon # num1 == num2
>
> Dan
>
>

Oops, I didn't realize that Ruby comes with an Epsilon. This should be a
fine test for equality:

return (num1-num2).abs < Float::EPSILON

Now, whether Float#==(other) should make this check might be worth
thinking about, but I really have no opinion on the matter--I'm used to
not comparing floats like this.

Dan

[M_Edward_Ed_Borasky1 (M. Edward (Ed) Borasky)]

Michael Ulm wrote:

Unfortunately, there is no easy solution to this problem. Here is a
catalog of often proposed solutions and why they do not work:

1 (proposed by doug meyer in this thread) Always use
(x-y).abs < Float::EPSILON
as a test for equality.

This won't work because the rounding error easily can get bigger than
Float::EPSILON, especially when dealing with numbers that are bigger
than unity. e.g.
y = 100.1 + 0.3
y - 100.4 # => -1.421e-14, while Float::EPSILON = 2.22e-16

2 Always use (x-y).abs < (x.abs + y.abs) * Float::EPSILON) as a test
for equality.

Better than the first proposal, but won't work if the rounding error
gets too large after a complex computation.
In addition, (1) and (2) suffer from the problem that x==y and y==z do
not imply x==z.

3 Use Bigdezimal

This only shifts the problem a few decimal places down, and tests for
equality will fail as with the normal floats.

4 Use Rationals

Works if you only have to deal with rational operations. But doesn't
solve the following
x = sqrt(2)
y = x + 1
x + 0.2 == y - 0.8 # => false
In addition, rational arithmetic can produce huge numbers pretty fast,
and this will slow down computations enormously.
5 Use a symbolic math package

This could in theory solve the issue with equality, but in practice there
is no way to decide that two symbolic representations of a number are the
same, like
1 / (sqrt(2) - 1) == sqrt(2) + 1
Also, very, very slow.

6 Use interval arithmetic

Gives you strict bounds on your solution, but can't answer x==y.

Summing up, when using floating point arithmetic there is no one true way.
There is no substitute for understanding numbers and analyzing your
problem.

Well ... OK ... but ...

This whole floating-point thing comes up here on a weekly basis, and
I'll bet it comes up on all the other language mailing lists too. No
matter how many times you repeat this, no matter how many web sites
explaining floating point arithmetic you point people to, etc., you are
still going to get people who don't know how it works and have
expectations that aren't realistic. An awful lot of calculators have
been built using decimal arithmetic just because there are a few less
"anomalies" that need to be explained.

People like me who do number crunching for a living know all this stuff
inside and out. I actually learned the basics of scientific computing in
scaled fixed-point arithmetic, and it's only been in recent years (since
the Pentium, in fact) that just about every computer you're likely to
touch has had floating point hardware. Before that, you were likely to
be dealing with slow and inaccurate libraries emulating the hardware
unless you were in a scientific research environment. And it's also been
only a few more years since nearly all new architectures supported
(mostly) the IEEE floating point standard.

Before that, it was chaos -- most 32-bit floating point arithmetic was
unusable except for data storage, the reigning supercomputers had
floating point units optimized for speed at the expense of correctness,
you actually had to pay for good math libraries and whole books of
garbage number crunching algorithms were popular best-sellers. In short,
even the folks who knew very well how it *should* be done made both
necessary compromises and serious mistakes. It took some brave souls
like William Kahan several years to get some of the more obvious garbage
out of "common practice".

So give the newbies a break on this issue -- the professionals have only
been doing it mostly right since about 1990.

[Daniel_DeLorme]

Michael Ulm wrote:

this floating problem is a faq and is very surprising on such a
very high language such as ruby. can we address this? maybe create
flag like $EPSILON=0 or something, or may flag to revert to rational
or bigdeci like $FLOAT_PROCESSOR=RATIONAL...

Unfortunately, there is no easy solution to this problem. Here is a
catalog of often proposed solutions and why they do not work:

2 Always use (x-y).abs < (x.abs + y.abs) * Float::EPSILON) as a test for equality.

Better than the first proposal, but won't work if the rounding error
gets too large after a complex computation.
In addition, (1) and (2) suffer from the problem that x==y and y==z do
not imply x==z.

But it would fix 99% of problems. It would be worth it just for the sake of reducing those questions on the list

Seriously though, since floating point calculations are approximative to start with, what would be wrong with making them more intuitive approximations? IMHO Float should use the above algorithm for == and reserve normal floating point arithmetic for eql?

Daniel

[W_James]

How about
  (a - b).abs / [a, b].map{|x| a.abs}.min < Float::EPSILON
?

def eq( a, b )
  (a - b).abs / [a, b].map{|x| a.abs}.min < Float::EPSILON
end

DATA.each{|s|
  strings = s.chomp.split(";")
  floats = strings.map{|s| eval(s) }
  puts strings.join( " == " ) +
    " : #{floats[0]==floats[1]} #{ eq( *floats ) }"
}

__END__
(0.05+0.01);0.06
(0.34+0.01);0.35
9.123456789;9.1234567891
9.123456789012345;9.1234567890123451
9.12345678901234e-9;9.123456789012341e-9

=== output ===
(0.05+0.01) == 0.06 : false true
(0.34+0.01) == 0.35 : false true
9.123456789 == 9.1234567891 : false false
9.123456789012345 == 9.1234567890123451 : false true
9.12345678901234e-9 == 9.123456789012341e-9 : false true

···

On Aug 31, 1:25 am, Michael Ulm <michael....@isis-papyrus.com> wrote:

2 Always use
  (x-y).abs < (x.abs + y.abs) * Float::EPSILON)
  as a test for equality.

  Better than the first proposal, but won't work if the rounding error
  gets too large after a complex computation.
  In addition, (1) and (2) suffer from the problem that x==y and y==z do
  not imply x==z.

[Daniel_Berger2 (Daniel Berger)]

<snip>

Unfortunately, there is no easy solution to this problem.

<snip>

Here's my naive, DWIM approach:

class Float
   def ==(other)
      self.to_s == other.to_s
   end
end

Regards,

Dan

···

On Aug 31, 12:25 am, Michael Ulm <michael....@isis-papyrus.com> wrote:

[RaL]

+1

···

2007/8/31, doug meyer <doug.meyer@sigeps.org>:

There is also a class called BigDecimal (or something like that) if
you want to have really accurate numbers and no floating-point errors.

[Dan_Zwell]

Daniel DeLorme wrote:

Michael Ulm wrote:

this floating problem is a faq and is very surprising on such a
very high language such as ruby. can we address this? maybe create
flag like $EPSILON=0 or something, or may flag to revert to rational
or bigdeci like $FLOAT_PROCESSOR=RATIONAL...

Unfortunately, there is no easy solution to this problem. Here is a
catalog of often proposed solutions and why they do not work:

2 Always use (x-y).abs < (x.abs + y.abs) * Float::EPSILON) as a test for equality.

Better than the first proposal, but won't work if the rounding error
gets too large after a complex computation.
In addition, (1) and (2) suffer from the problem that x==y and y==z do
not imply x==z.

But it would fix 99% of problems. It would be worth it just for the sake of reducing those questions on the list

Seriously though, since floating point calculations are approximative to start with, what would be wrong with making them more intuitive approximations? IMHO Float should use the above algorithm for == and reserve normal floating point arithmetic for eql?

Daniel

Michael wrote very convincingly that there is no simple solution that will work in all cases. I'm convinced, at least. If there is no solution that works 100% of the time, we can't give the illusion that there is. To do so would be to teach bad programming practices to newcomers, and that's not fair.

The current "==" in okay because it works the way a moderately experienced programmer would expect. A perfect "==" that could deal with floats would be even better, but we aren't gonna get that. A "==" that seems like magic and almost always works is really pretty dangerous.

Dan

[Bertram_Scharpf]

Hi,

···

Am Freitag, 31. Aug 2007, 17:03:38 +0900 schrieb Daniel DeLorme:

Unfortunately, there is no easy solution to this problem. Here is a
catalog of often proposed solutions and why they do not work:

But it would fix 99% of problems. It would be worth it just for the sake of
reducing those questions on the list

Seriously though, since floating point calculations are approximative to
start with, what would be wrong with making them more intuitive
approximations? IMHO Float should use the above algorithm for == and
reserve normal floating point arithmetic for eql?

I alway liked it to be forced to decide what are countable
dimensions and what are continuous ones. This made my
programming style much clearer.

Bertram

--
Bertram Scharpf
Stuttgart, Deutschland/Germany
http://www.bertram-scharpf.de

[Robert_K1 (Robert K.)]

And who decides about the size of epsilon and which algorithm to
choose? There is no one size fits all answer to that hence leaving
Float#== the way it is (i.e. compare for exact identical values) is
the only viable option. Otherwise you would soon see similar
questions on the list, i.e., "how come it sometimes works and
sometimes it doesn't". And they become more difficult to answer as
the cases are likely less easy to spot / explain.

Kind regards

robert

···

2007/8/31, Daniel DeLorme <dan-ml@dan42.com>:

Michael Ulm wrote:
>> this floating problem is a faq and is very surprising on such a
>> very high language such as ruby. can we address this? maybe create
>> flag like $EPSILON=0 or something, or may flag to revert to rational
>> or bigdeci like $FLOAT_PROCESSOR=RATIONAL...
>
> Unfortunately, there is no easy solution to this problem. Here is a
> catalog of often proposed solutions and why they do not work:
>
> 2 Always use (x-y).abs < (x.abs + y.abs) * Float::EPSILON) as a test
> for equality.
>
> Better than the first proposal, but won't work if the rounding error
> gets too large after a complex computation.
> In addition, (1) and (2) suffer from the problem that x==y and y==z do
> not imply x==z.

But it would fix 99% of problems. It would be worth it just for the sake
of reducing those questions on the list

Seriously though, since floating point calculations are approximative to
start with, what would be wrong with making them more intuitive
approximations? IMHO Float should use the above algorithm for == and
reserve normal floating point arithmetic for eql?

[Kyle_Schmitt]

A warning on things like BigDecimal.
Unless I'm mistaken it's still stored in twos compliment, which means
you'll still end up with the same sort of floating point problems
(albeit further down), and the same numbers that you can't express
exactly with a normal float, can't be expressed exactly with a
BigDecimal.

You'd think some fixed point math libraries would help, but be
careful, because many of those _also_ store in twos compliment.

--Kyle

···

On 8/30/07, doug meyer <doug.meyer@sigeps.org> wrote:

There is also a class called BigDecimal (or something like that) if
you want to have really accurate numbers and no floating-point errors.

[Michael_Ulm]

Daniel Berger wrote:

<snip>

Unfortunately, there is no easy solution to this problem.

<snip>

Here's my naive, DWIM approach:

class Float
   def ==(other)
      self.to_s == other.to_s
   end
end

Oh yes, nice one. This fulfills

'from x==y and y==z follows x==z'

Unfortunately it does not fulfill some other properties one
wants to have; e.g. it violates

'from x==y follows x+z==y+z'

for example

x, y = 1.0/3.0, 0.333333333333333
x.to_s == y.to_s # => true
(x+x).to_s == (y+x).to_s # => false

In particular, you don't have

'from x==y follows x-y==0'

for example

x, y = 0.6, 6 * 0.1
x.to_s == y.to_s # => true
(x - y).to_s == 0.to_s # => false

HTH,

Michael

···

On Aug 31, 12:25 am, Michael Ulm <michael....@isis-papyrus.com> wrote:

[_Pena_Botp1 ("Peña, Botp")]

# And who decides about the size of epsilon and which algorithm to
# choose? There is no one size fits all answer to that hence leaving
# Float#== the way it is (i.e. compare for exact identical values) is
# the only viable option. Otherwise you would soon see similar
# questions on the list, i.e., "how come it sometimes works and
# sometimes it doesn't". And they become more difficult to answer as
# the cases are likely less easy to spot / explain.

indeed

maybe i'm not "realistic" but i thought

   0.05 + 0.01 == 0.06 => false

was "unrealistic" enough for a simple and plain 2 decimal arithmetic. Even people w zero-know on computers would laugh about it (yes, try explaining it to your wife or kids, eg).

For simple math (eg those dealing w money):
  i can live w slowness in simple math (quite a paradox if you ask me).
  i can live w 1/3 == 0.3333333333 =>false
  or that sqrt(2) == 1.1414213562 => false
  i use bigdecimal. bigdecimal handles 0.05 + 0.01 == 0.06 => true

For complex math,
  i can live w slowness (no question there).
  bigdecimal easily handles sqrt(2) at 100 digits: 2.sqrt(100) => #<BigDecimal:b7d74094,'0.1414213562 3730950488 0168872420 9698078569 6718753769 4807317667 9737990732 4784621070 3885038753 4327641572 7350138462 309122925E1',124(124)
  so yes, i still use bigdecimal for complex math.

so regardless, of whether its simple or complex (or "highly precise" or not), i use bigdecimal. counting ang looping otoh has no problem w me since fixnum/bignum handles this flawlessly. (Also, note that big RDBMS like oracle and postgresql use BCD and fixed pt math for numerics).

So, my question probably is (maybe this could be addressed to Matz): How can i make ruby use a particular arithmetic, like bigdecimal eg, so that literals like 1.05, and operations like 1+1.01 are now handled as bigdecimals.

thank you and kind regards -botp

···

From: Robert Klemme [mailto:shortcutter@googlemail.com]

[M_Edward_Ed_Borasky1 (M. Edward (Ed) Borasky)]

Bertram Scharpf wrote:

Hi,

Unfortunately, there is no easy solution to this problem. Here is a
catalog of often proposed solutions and why they do not work:

But it would fix 99% of problems. It would be worth it just for the sake of
reducing those questions on the list

Seriously though, since floating point calculations are approximative to
start with, what would be wrong with making them more intuitive
approximations? IMHO Float should use the above algorithm for == and
reserve normal floating point arithmetic for eql?

I alway liked it to be forced to decide what are countable
dimensions and what are continuous ones. This made my
programming style much clearer.

Bertram

Well ... since *everything* in computing is countable ...

But seriously, real computing on real digital machines involves
translation from infinite and/or continuous semantics to very large
finite discrete processes. About the only thing that's truly infinite is
the time it takes to complete

while true do
end

But there are some techniques not terribly well known that improve on
floating point arithmetic as normally implemented in hardware. They're
too expensive for mass-market hardware, so they're usually implemented
in software. Interval arithmetic has already been mentioned, but there
are some others. Try "A New Approach to Scientific Computation" by
Kulisch and Miranker.

Most of these are historical curiosities these days because of the
widespread distribution of high-performance open-source libraries for
exact and symbolic computation, such as GiNaC, GMP, CLN, etc. And it's
pretty easy using SWIG to interface one or more of these to Ruby.

···

Am Freitag, 31. Aug 2007, 17:03:38 +0900 schrieb Daniel DeLorme: