From: Peter Vandenabeele <peter@...>
Date: 2012-01-29T03:43:22+09:00
Subject: Re: Microrant on Ruy's Math Skills

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On Fri, Jan 27, 2012 at 8:51 AM, Matthias W=C3=A4chter
<matthias@waechter.wiz.at>wrote:

> Am 25.01.2012 15:28, schrieb botp:
>
>> 2012/1/25 Matthias W=C3=A4chter<matthias@waechter.wiz.**at<matthias@waec=
hter.wiz.at>
>> >:
>>
>>> I=E2=80=99m curious to see what=E2=80=99s gonna happen once Desktop CPU=
s start to support
>>> the nice decimal floating-point types of IEEE 754-2008
>>> [http://en.wikipedia.org/wiki/**IEEE_754-2008#Basic_formats<http://en.w=
ikipedia.org/wiki/IEEE_754-2008#Basic_formats>]
>>> =E2=80=A6 maybe Ruby
>>> should already prepare syntactically for support of these types. And, i=
n
>>> theory, there is already a library from Intel
>>> [http://software.intel.com/en-**us/articles/intel-decimal-**
>>> floating-point-math-library/<http://software.intel.com/en-us/articles/i=
ntel-decimal-floating-point-math-library/>
>>> ]
>>> one can use to do decimal floating-point math.
>>>
>>
>> wow, thanks for the update. i hope ruby can indeed support that even
>> if i need to recompile manually.
>>
>
If I understand correctly, the IEEE 754-2008 decimal formats are fixed size=
,
so even the largest of them (128 bit)

  http://en.wikipedia.org/wiki/Decimal128_floating-point_format

is fixed size limited to 34 digits.

But the current Ruby BigDecimal implementation can go well beyond that:

$ ruby -v
ruby 1.9.3p0 (2011-10-30 revision 33570) [i686-linux]
002:0> require 'bigdecimal'
=3D> true
003:0> require 'bigdecimal/util'
=3D> true
005:0> a =3D
BigDecimal.new("12345678901234567890123456789012345678901234567890123456789=
0")
=3D> #<BigDecimal:985aa30,'0.1234567890 1234567890 1234567890 1234567890
1234567890 123456789E60',63(72)>
006:0> b =3D a +1
=3D> #<BigDecimal:9859324,'0.1234567890 1234567890 1234567890 1234567890
1234567890 1234567891E60',63(144)>
007:0> b - a
=3D> #<BigDecimal:98639a0,'0.1E1',9(81)>
008:0> (b - a).to_s
=3D> "0.1E1"
009:0> (b - a).to_s('F')
=3D> "1.0"

That means to remain truely backwards compatible, we would need something
like:

1.1 #=3D> Float (machine dependent)
1.1BD #=3D> BigDecimal ("unlimited" size)
1.1D #=3D> Decimal (e.g. picking the standardized IEEE 754 2008 Decimal128
fomat)

HTH,

Peter

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