Increase significant digits in Float

Discussion in 'Ruby' started by Jason Lillywhite, Mar 2, 2010.

1. Jason LillywhiteGuest

If I want to increase my significant digits beyond 15 in a result of a
math expression involving floats, how do I do it? So, for example, I
would like more than 15 sig digits in the result of:

irb(main):001:0> 4.005 / 7
=> 0.572142857142857

Thank you!
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Jason Lillywhite, Mar 2, 2010

2. Jesús Gabriel y GalánGuest

On Tue, Mar 2, 2010 at 4:26 PM, Jason Lillywhite
<> wrote:
> If I want to increase my significant digits beyond 15 in a result of a
> math expression involving floats, how do I do it? So, for example, I
> would like more than 15 sig digits in the result of:
>
> irb(main):001:0> 4.005 / 7
> => 0.572142857142857

irb is calling inspect on the value of the expression. It's the
inspect method the one that truncates to 15 digits when it creates the
string. You can create your own strings with greater precision like
this:

irb(main):001:0> result = 4.005 / 7
=> 0.572142857142857
irb(main):002:0> "%.20f" % result
=> "0.57214285714285717521"
irb(main):003:0> "%.30f" % result
=> "0.572142857142857175212213860505"

Check the String#% method:

http://ruby-doc.org/core/classes/String.html#M000770

and the Kernel#sprintf method:

http://ruby-doc.org/core/classes/Kernel.html#M005962

Jesus.

Jesús Gabriel y Galán, Mar 2, 2010

3. Jason LillywhiteGuest

JesÃºs Gabriel y GalÃ¡n wrote:

> irb is calling inspect on the value of the expression. It's the
> inspect method the one that truncates to 15 digits when it creates the
> string.

Thank you! I forgot that IRB is returning a truncated string to the
screen.

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Jason Lillywhite, Mar 2, 2010
4. Xavier NoriaGuest

On Tue, Mar 2, 2010 at 5:00 PM, Jason Lillywhite
<> wrote:

> Thank you! I forgot that IRB is returning a truncated string to the
> screen.

That 15 is hard-coded in the definition of Float#to_s.

Xavier Noria, Mar 2, 2010
5. Siep KortelingGuest

Xavier Noria wrote:
> On Tue, Mar 2, 2010 at 5:00 PM, Jason Lillywhite
> <> wrote:
>
>> Thank you! I forgot that IRB is returning a truncated string to the
>> screen.

>
> That 15 is hard-coded in the definition of Float#to_s.

Yes, and exposing more digits is not accurate:

puts "%.70f"%(4.005 / 7)
#=>0.5721428571428571752122138605045620352029800415039062500000000000000000
require 'bigdecimal'
a = BigDecimal.new("4.005")
b = a/7
puts b
#=>0.572142857142857142857143E0
p b.precs
#=>[24, 32]

#first number is the number of significant digits in b; the second
number is the maximum precision my system can handle (not sure about
this). The float is bogus after the 16th digit.

hth,

Siep
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Siep Korteling, Mar 2, 2010
6. Jason LillywhiteGuest

Siep Korteling wrote:
> #first number is the number of significant digits in b; the second
> number is the maximum precision my system can handle (not sure about
> this). The float is bogus after the 16th digit.

Thank you Siep!

This is interesting - and good to know.

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Jason Lillywhite, Mar 2, 2010
7. Neve LeGuest

Siep Korteling wrote:
>> Xavier Noria wrote:
>> That 15 is hard-coded in the definition of Float#to_s.

>
> Yes, and exposing more digits is not accurate:
> The float is bogus after the 16th digit.

Working with big numbers here, it seems that precision is only
guaranteed to 15 digits on either side of the decimal. When a whole
number >15 digits is divided the decimal is approximated, and anything
>17 digits prints a float of n.0 no matter how it's "%n.nf" formatted.

Is the hard-coded 15 just a "safe" limit? Would I be able to recompile
ruby with a higher definition? If possible, how high could I go?
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Neve Le, Jun 30, 2010
8. Brian CandlerGuest

Neve Le wrote:
> Is the hard-coded 15 just a "safe" limit? Would I be able to recompile
> ruby with a higher definition? If possible, how high could I go?

No, it's a limit of IEEE double-precision floating-point representation.

If you want more digits of precision, use BigDecimal.
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Brian Candler, Jun 30, 2010
9. Giampiero ZanchiGuest

Giampiero Zanchi, Jun 30, 2010
10. Guest

On Wed, Jun 30, 2010 at 8:06 AM, Neve Le <> wrote:
> Siep Korteling wrote:
>>> Xavier Noria wrote:
>>> That 15 is hard-coded in the definition of Float#to_s.

>>
>> Yes, and exposing more digits is not accurate:
>> The float is bogus =A0after the 16th digit.

>
> Working with big numbers here, it seems that precision is only
> guaranteed to 15 digits on either side of the decimal. When a whole
> number >15 digits is divided the decimal is approximated, and anything
>>17 digits prints a float of n.0 no matter how it's "%n.nf" formatted.

http://ruby-doc.org/core/classes/Float.html
"Float objects represent real numbers using the native architecture=91s
double-precision floating point representation."

http://en.wikipedia.org/wiki/Double_precision_floating-point_format

You could try BigDecimal.

, Jun 30, 2010
11. Javier GoizuetaGuest

You may also want to take a look at http://flt.rubyforge.org/

It's an implementation of arbitrary precision floating point numbers
(decimal and binary). If you don't need it to be fast it has some
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Javier Goizueta, Jun 30, 2010
12. Colin BartlettGuest

[Note: parts of this message were removed to make it a legal post.]

On Wed, Jun 30, 2010 at 3:56 PM, Javier Goizueta <>wrote:

> You may also want to take a look at http://flt.rubyforge.org/
>
> It's an implementation of arbitrary precision floating point numbers
> (decimal and binary). If you don't need it to be fast it has some
> --
> Posted via http://www.ruby-forum.com/.
>

Also: I recall a short thread from December 2008:
Proposing an arbitrary precision class building on BigDecimal and being
derived from Numeric
subsequent
or as a user friendly all in one place:
https://rubyforge.org/projects/appmath/
http://appmath.rubyforge.org/
http://www.ulrichmutze.de/index.html

(I should observe that I haven't tried this code: I simply made a mental
note at the time of the thread that it might be useful.)

Colin Bartlett, Jul 1, 2010