Playing with DoubleDouble presicion

[TimoVJL]

Perhaps same idea ?
http://web.mit.edu/tabbott/Public/quaddouble-debian/qd-2.3.4-old/docs/qd.pdf

EDIT 2023-11-19
QDC was a QD fork in C, but never finished 

[Biterider]

Hi Timo
The idea of extending double-double to quad-double is appealing 
But before getting into that, wouldn't it be wiser to explore extending double-double with REAL10 instead of REAL8? This would give the same algorithm 8 digits more precision without increasing the complexity using today's existing x86 hardware.

Biterider

[NoCforMe]

Hey, that's clever! And even I can understand how it works. Kewl.

[jack]

it's an interesting subject, but some years ago I tested the performance of dd vs soft-float and soft-float was a bit faster
just now I did a very simple test of qd vs my kindergarten mp float routines and mine was about 45% slower than qd

[NoCforMe]

Um, what exactly is "soft-float"? It certainly can't be floating-point implemented in software if it's faster than "hard-float".

[HSE]

Perhaps same idea ?
http://web.mit.edu/tabbott/Public/quaddouble-debian/qd-2.3.4-old/docs/qd.pdf

Exactly same idea.

Apparently nobody is using qd, probably because range of exponents anyway is that of REAL8. That trigger the circle few used - hardly accepted for publication - few used.

The easy thing could be to use Lawrence Berkeley National Laboratory libraries, but they have now another licenses. I don't remember what was, just not or fun. 

[HSE]

Hi Biterider,

But before getting into that, wouldn't it be wiser to explore extending double-double with REAL10 instead of REAL8?

In the FPU, calculations between REAL10 numbers don't always have REAL10 precision (never trascendental functions, IIRC).

To make calculations between REAL8 numbers and to obtain always REAL8 precision, the FPU use REAL10 as internal representation.

No problem with REAL10 if you solve calculations by hand, instead of FPU   

HSE

[jack]

Alan Miller implemented dd and qd in FORTRAN https://jblevins.org/mirror/amiller/#nas should be easy enough to translate the code to your favorite language
btw, here's SoftFloat http://www.jhauser.us/arithmetic/SoftFloat.html

[NoCforMe]

btw, here's SoftFloat

Thanks (turned that into a clickable link for you; just posting URLs doesn't make them into links here anymore)

But but but ... if it's implemented in software, how could it possibly be faster than a FPU?

[jack]

not faster than the FPU but faster than dd
btw, the quad_nas.f90 only need 2 small changes for it to compile with gfortran
change line 51 from   INTEGER, PARAMETER    :: r10 = 3
to INTEGER, PARAMETER    :: r10 = real(10)
and line 1464 to 0.0000000000000000000_r10 ,  0.000000000000000000_r10      , &

[HSE]

Hi jack,

Alan Miller implemented dd and qd in FORTRAN https://jblevins.org/mirror/amiller/#nas should be easy enough to translate the code to your favorite language
btw, here's SoftFloat http://www.jhauser.us/arithmetic/SoftFloat.html

No. 

The latest release of SoftFloat implements five floating-point formats: 16-bit half-precision, 32-bit single-precision, 64-bit double-precision, 80-bit double-extended-precision, and 128-bit quadruple-precision

That don't have double-double-precision nor quadruple-double-precision.

HSE

[jack]

128-bit is the same as double-double 
but SoftFloat doesn't come with string to float and vice versa conversion routines, I need to look and see what I used

[HSE]

128-bit is the same as double-double 

Very funny, but no.

[jack]

dd and Soft-128 both give about 33-34 decimal digits the difference being that Soft-128 has a larger exponent range
for Soft-float you can use https://github.com/jwiegley/gdtoa for the conversions

[HSE]

dd and Soft-128 both

They are 2 diferents formats.

Double-double-precision (Real8,Real8) use FPU, then is very fast (same idea is used in Quadruple-double-precision (Real8,Real8,Real8,Real8)).

Quadruple-precision (Real16 or Soft-128) requiere a library to execute some kind of emulation in memory, that is very slow.

you can use https://github.com/jwiegley/gdtoa for the conversions

You can convert numbers between any format you can think, if they fit inside format range, eventualy loosing precision.