I found this blog entry:
Which shows the following…
irb(main):011:0> require ‘bigdecimal’
=> true
irb(main):012:0> x = BigDecimal(“123.6”) - BigDecimal(“123”)
=> #BigDecimal:28c5b84,‘0.6E0’,4(16)
irb(main):013:0> puts x.to_f
0.6
=> nil
irb(main):014:0> puts f=123.6 - 123
0.599999999999994
=> nil
irb(main):015:0> 123.6 - 123
=> 0.599999999999994
irb(main):016:0> 123.6 - 123.0
=> 0.599999999999994
irb(main):017:0>
That’s a little strange… Isn’t it?
On Thu, 29 Oct 2009, Aldric G. wrote:
=> nil
irb(main):014:0> puts f=123.6 - 123
0.599999999999994
=> nil
irb(main):015:0> 123.6 - 123
=> 0.599999999999994
irb(main):016:0> 123.6 - 123.0
=> 0.599999999999994
irb(main):017:0>That’s a little strange… Isn’t it?
No, it’s not. Welcome to the wonderfully confusing world of floating
point math…
Matthew K. Williams wrote:
irb(main):016:0> 123.6 - 123.0
=> 0.599999999999994That’s a little strange… Isn’t it?
No, it’s not. Welcome to the wonderfully confusing world of floating
point math…
Oh, thanks. Can I have some pop-corn and an introductory pamphlet before
I bash my head against the wall? 
Matthew K. Williams wrote:
On Thu, 29 Oct 2009, Aldric G. wrote:
I bash my head against the wall?
Pamphlet → IEEE 754-2008 revision - WikipediaPopcorn, well, it’s kinda hard to transmit over the wire.
As a rule of thumb, if you really care about the decimals, either use
BigDecimal or integers (and keep track of where the decimal should be –
this is common for $$$$). Unfortunately, this is not limited to ruby,
either – C, Java, and a host of other languages all are subject.Matt
Thanks. Both my head and the wall are safe for now. As one may have
surmised, I don’t deal with floating point values much, but this is
frustrating. I do see that there are a couple of people who wrote gems
on Rubyforge to handle this issue 
On Thu, 29 Oct 2009, Aldric G. wrote:
I bash my head against the wall?
Pamphlet → IEEE 754-2008 revision - Wikipedia
Popcorn, well, it’s kinda hard to transmit over the wire. 
As a rule of thumb, if you really care about the decimals, either use
BigDecimal or integers (and keep track of where the decimal should be –
this is common for $$$$). Unfortunately, this is not limited to ruby,
either – C, Java, and a host of other languages all are subject.
Matt
On 28.10.2009 19:21, Matthew K. Williams wrote:
I bash my head against the wall?
Pamphlet → IEEE 754-2008 revision - Wikipedia
Popcorn, well, it’s kinda hard to transmit over the wire.
Easy to do with a modern email client - just needs support for POP3 and
a working firewall (for the heat).
As a rule of thumb, if you really care about the decimals, either use
BigDecimal or integers (and keep track of where the decimal should be –
this is common for $$$$). Unfortunately, this is not limited to ruby,
either – C, Java, and a host of other languages all are subject.
Absolutely: this is a common issue in all programming languages which
are not systems for symbolic math (like Mathematica) because they do not
work with real numbers but just rational numbers.
Cheers
robert
Aldric G. wrote:
Matthew K. Williams wrote:
irb(main):016:0> 123.6 - 123.0
=> 0.599999999999994That’s a little strange… Isn’t it?
No, it’s not. Welcome to the wonderfully confusing world of floating
point math…Oh, thanks. Can I have some pop-corn and an introductory pamphlet before
I bash my head against the wall?
Most languages these days use IEEE 754-style floats, which leads to the
imprecision you saw.
http://c2.com/cgi/wiki?IeeeSevenFiftyFour
Don’t use floats for serious arithmetic.
Marnen Laibow-Koser
http://www.marnen.org
[email protected]
Robert K. wrote:
On 28.10.2009 19:21, Matthew K. Williams wrote:
I bash my head against the wall?
Pamphlet → IEEE 754-2008 revision - Wikipedia
Popcorn, well, it’s kinda hard to transmit over the wire.
Easy to do with a modern email client - just needs support for POP3 and
a working firewall (for the heat).
LOL!
As a rule of thumb, if you really care about the decimals, either use
BigDecimal or integers (and keep track of where the decimal should be –
this is common for $$$$). Unfortunately, this is not limited to ruby,
either – C, Java, and a host of other languages all are subject.Absolutely: this is a common issue in all programming languages which
are not systems for symbolic math (like Mathematica) because they do not
work with real numbers but just rational numbers.
That is not the issue here – after all, BigDecimal does precise
arithmetic, but only with rational numbers. The issue is rather that
IEEE 754 does an inadequate job of representing arbitrary rational
numbers, and the small errors are accumulated and magnified in
calculations.
Cheers
robert
Marnen Laibow-Koser
http://www.marnen.org
[email protected]
Gary W. wrote:
[…].
Many people don’t realize that floating point literals written
in base 10 (such as 123.6) may not have an exact finite
representation when converted to base 2
Right. 0.6 in binary has a repeating decimal – 0.1001 repeating or
something like that.
and similarly a finite
base 2 floating point value may not have a finite representation
in base 10.
[…]
I think not. Every number of the form 1/(2^n) has a terminating decimal
in base 10. Am I wrong?
The problems, of course, arise with numbers like 1/3, which doesn’t
terminate in either base. This is what the Rational class is good for.
Marnen Laibow-Koser
http://www.marnen.org
[email protected]
On Oct 28, 2009, at 5:14 PM, Marnen Laibow-Koser wrote:
terminate in either base. This is what the Rational class is good
for.
I spoke to quickly and had in mind what you just
suggested, that there are numbers that don’t terminate
in either base.
But my main point was that people become aware of
these issues via the conversion problem rather than
via the nuances of IEEE floating point arithmetic.
Gary W.
On Oct 28, 2009, at 3:30 PM, Marnen Laibow-Koser wrote:
That is not the issue here – after all, BigDecimal does precise
arithmetic, but only with rational numbers. The issue is rather that
IEEE 754 does an inadequate job of representing arbitrary rational
numbers, and the small errors are accumulated and magnified in
calculations.
I’d like to emphasize the fact that it is a very specific
representation problem that most often leads to a thread such
as this. That problem is a misunderstanding about the nature
of converting between a base 10 literal and a base 2 internal
value.
Many people don’t realize that floating point literals written
in base 10 (such as 123.6) may not have an exact finite
representation when converted to base 2 and similarly a finite
base 2 floating point value may not have a finite representation
in base 10.
In the original post the floating point subtraction in the
expression (123.6 - 123.0) is handled just fine. The problem
is that 123.6 can’t be represented exactly as a base 2 floating
point value so the subtraction that actually gets done is
123.599999999999994315658113919198513031005859375 - 123.0
and the result
0.599999999999994315658113919198513031005859375
is rounded via Ruby’s Float#to_s method to
0.599999999999994
Gary W.
Rajinder Y. wrote:
[…]
I’ve been following this thread and am wondering if there are other
numerical
classes for Ruby other than BigDecimal?
Well, I mentioned Rational. There’s also Bignum, but that’s
transparent, so it doesn’t need to be called explicitly as BigDecimal
does. Check the standard library docs.
Were you looking for something specific?
–
Kind Regards,
Rajinder Y.Do Good! - Share Freely, Enrich and Empower people to Transform their
lives.
Best,
–
Marnen Laibow-Koser
http://www.marnen.org
[email protected]
Marnen Laibow-Koser wrote:
Were you looking for something specific?
Hi Marnen,
thanks for the reply. I am aware of Bignum and understand how Ruby does
the
translation transparently from Fixnum. I was just seeking more knowledge
outside
my current understanding of Ruby.
I had imagined there might be a class Currency =), again just wanting to
know
what’s available to me through Ruby.
Best,
Marnen Laibow-Koser
http://www.marnen.org
[email protected]
–
Kind Regards,
Rajinder Y.
Do Good! - Share Freely, Enrich and Empower people to Transform their
lives.
On Wed, Oct 28, 2009 at 12:30 PM, Marnen Laibow-Koser
[email protected] wrote:
work with real numbers but just rational numbers.
That is not the issue here – after all, BigDecimal does precise
arithmetic, but only with rational numbers.
BigDecimal actually works with decimal numbers, which are a subset of
rational numbers; Rational does precise math with rational numbers.
 The issue is rather that IEEE 754 does an inadequate job of representing
arbitrary rational numbers, and the small errors are accumulated and
magnified in calculations.
The bigger issue is that Ruby – like most general purpose programming
languages, though there are exceptions like Scheme – makes IEEE 754
floating point the easiest non-integer data type to use, rather than
using exact numbers by default and using inexact numbers only when
explicitly called for (or when an operation that produces inexact
results is used.)
Aldric G. wrote:
=> nil
irb(main):014:0> puts f=123.6 - 123
0.599999999999994
=> nil
irb(main):015:0> 123.6 - 123
=> 0.599999999999994
irb(main):016:0> 123.6 - 123.0
=> 0.599999999999994
irb(main):017:0>That’s a little strange… Isn’t it?
I’ve been following this thread and am wondering if there are other
numerical
classes for Ruby other than BigDecimal?
–
Kind Regards,
Rajinder Y.
Do Good! - Share Freely, Enrich and Empower people to Transform their
lives.
Rajinder Y. wrote:
I’ve been following this thread and am wondering if there are other
numerical
classes for Ruby other than BigDecimal?
http://rubyforge.org/search/?type_of_search=soft&words=float&Search=Search
That should get you started
Aldric G. wrote:
Rajinder Y. wrote:
I’ve been following this thread and am wondering if there are other
numerical
classes for Ruby other than BigDecimal?http://rubyforge.org/search/?type_of_search=soft&words=float&Search=Search
That should get you started
Thanks (Jedi) Aldric, good place to expand =)
–
Kind Regards,
Rajinder Y.
Do Good! - Share Freely, Enrich and Empower people to Transform their
lives.
Christopher D. wrote:
On Wed, Oct 28, 2009 at 12:30 PM, Marnen Laibow-Koser
[email protected] wrote:work with real numbers but just rational numbers.
That is not the issue here – after all, BigDecimal does precise
arithmetic, but only with rational numbers.BigDecimal actually works with decimal numbers, which are a subset of
rational numbers; Rational does precise math with rational numbers.
You’re quite right, and I realized that about 10 seconds after I posted.
 The issue is rather that IEEE 754 does an inadequate job of representing
arbitrary rational numbers, and the small errors are accumulated and
magnified in calculations.The bigger issue is that Ruby – like most general purpose programming
languages, though there are exceptions like Scheme – makes IEEE 754
floating point the easiest non-integer data type to use, rather than
using exact numbers by default and using inexact numbers only when
explicitly called for (or when an operation that produces inexact
results is used.)
Yup. At least Ruby took a step in the right direction by making Bignum
transparent; it would be lovely if some future version did likewise with
BigDecimal.
Marnen Laibow-Koser
http://www.marnen.org
[email protected]
On 10/31/2009 07:35 AM, George N. wrote:
It’s also worth noting that most floating point hardware is not
anywhere close to 754 compliant even though most FPUs do use the
standard number formats (at least for single and double precision).
Interesting! I wasn’t aware of that. Why is that? Do they just leave
out operations or are HW vendors actually cutting corners and digressing
from the prescribed algorithms / results?
Kind regards
robert
On Wed, 28 Oct 2009 14:30:21 -0500, Marnen Laibow-Koser
[email protected] wrote:
work with real numbers but just rational numbers.
That is not the issue here – after all, BigDecimal does precise
arithmetic, but only with rational numbers. The issue is rather that
IEEE 754 does an inadequate job of representing arbitrary rational
numbers, and the small errors are accumulated and magnified in
calculations.
The problem is that the 754 representation has finite precision. I
suppose you can call that “inadequate”, but I don’t see a good way
around it … 0.6 is still infinite in binary. BigDecimal will get
you the right answer (unless you run out of memory), but when the
significant figures pile up it tends to get you there very slowly. All
the various arbitrary precision formats suffer badly performance wise.
It’s also worth noting that most floating point hardware is not
anywhere close to 754 compliant even though most FPUs do use the
standard number formats (at least for single and double precision).
George
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