This is the
talk page for discussing improvements to the
Quadruple-precision floating-point format article. This is not a forum for general discussion of the article's subject. |
Article policies
|
Find sources: Google ( books · news · scholar · free images · WP refs) · FENS · JSTOR · TWL |
![]() | This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||||||||||||||||||
|
I think this article should be moved, since the title is not conform to IEEE 754r, which refers the format as quad or quadruple precision, but never quad precision. Also quad is not really an adjective like single and double. See e.g. the draft on [1]. — Ylai 08:53, 9 January 2006 (UTC)
This page on quadruple precision says:
(1/3 rounds up like double precision, because of the odd number of bits in the significand.)
However the page for double precision says:
(1/3 rounds down instead of up like single precision, because of the odd number of bits in the significand.)
These statements contradict each other.
I think it should probably be "7ffe" in the first block of four hex digits unless anyone can say why not.
7ffe
-
Jake (
talk)
04:27, 20 September 2014 (UTC)It appears that an error has crept into the example for 1/3, namely:
1) The examples states that the following bits, presented as hex numbers, denote 1/3:
3ffeh 5555h 5555h 5555h 5555h 5555h 5555h 5555h
2) When expanded into binaly notation this is:
0011b 1111b 1111b 1110b 0101b 0101b 0101b 0101b ....
3) The exponent is (15 bits):
011111111111110b = 16382d, adding the offset of -16383d the value of the exponent is found to be 16382-16383=-1d. And this is what appears wrong to me. It must be -2d. Why? Because, read on...
4) The mantissa is:
0101b 0101b 0101b .... = 1/4d + 1/16d + 1/64d + 1/256d + 1/1024d + 1/4096d ... = 0.333d... When we add the implied 1d the value of the matissa is found to be 1+0.333...=1.333d...
5) Finally we construct the floating-point number as follows:
mantissa * 2^exponent = 1.333... * 2^-1 = 1.333... * 1/2 = 0.666..., which is not 1/3 as the text states it must be. However, if the exponent was -2 then the result would be: mantissa * 2^exponent = 1.333... * 2^-2 = 1.333... * 1/4 = 0.333..., which is the correct result.
6) Bottom line: I think that the example for 1/3 must be:
3ffdh 5555h 5555h 5555h 5555h 5555h 5555h 5555h
Plamka 23:16, 17 September 2007 (UTC)
Do any hardware or CPUs support quadruple precision floating point already?
Do any programming languages?
193.74.100.50 ( talk) 08:00, 9 May 2008 (UTC)
In the first paragraph, the article claims that quadruple precision could refer to integers, fixed point numbers, or floating point numbers, but the rest of the article solely discusses floating point numbers. Could somebody rectify this? —Preceding unsigned comment added by 128.101.38.232 ( talk) 19:55, 27 October 2008 (UTC)
The IBM z Series supports quad precision. See: this paper, Figure 1. mfc ( talk) 11:59, 10 March 2009 (UTC)
IBM hex (base 16) floating point has supported extended (128 bit) precision starting with the 360/85, and all models of S/370 and successors, except that DXR (extended precision divide) was done in software emulation until part way through the ESA/390 years. Newer processors implement binary (IEEE) and decimal (IEEE) floating point, including extended (128 bit) precision. Gah4 ( talk) 00:01, 25 October 2011 (UTC)
The VAX had support for 128-bit floats (called h_float) since the 1970s, but it's not IEEE 754-compliant. —Preceding unsigned comment added by 69.54.60.34 ( talk) 14:04, 15 September 2010 (UTC)
VAX still supports H-Float, but it is implemented through software emulation on most models, or optional microcode. The VAX 11/730, implemented in microcode through the AMD2900 series bit-slice logic, normally came with H-Float. Gah4 ( talk) 00:01, 25 October 2011 (UTC)
Some (all?) PowerPC CPUs supports quadprecision nativly. Also few compilers like Intel Fortran compiler (but few others also) supports quad-precision (not sure if strictly IEEE754, but they do) on x86 and amd64 systems using only double precision numbers with additions of some refinments or software functions. There is also few (about 3), lightwaight and fast libraries for quad and octal precision using 2xdouble (or 4xfloat for old architecture) or 4xdouble, but they do not have only about 90% precision of real quad or octal floating point numbers. One of such libraries is QD and DDFUN90 library. — Preceding unsigned comment added by 91.213.255.7 ( talk) 03:16, 11 June 2011 (UTC)
A link to Multiprecision Computing Toolbox for MATLAB was added, which is fine since according to http://www.advanpix.com/2013/01/20/fast-quadruple-precision-computations/ this toolbox has specific, optimized support for IEEE quadruple precision (not just generic arbitrary precision). However this is a bit hidden. I think that some reference to this page from the changelog should be given, but I wonder what form it should take (this cannot be a real reference, since the external links appear after the references). Vincent Lefèvre ( talk) 17:39, 12 April 2013 (UTC)
Hello fellow Wikipedians,
I have just modified 2 external links on Quadruple-precision floating-point format. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at {{
Sourcecheck}}
).
An editor has reviewed this edit and fixed any errors that were found.
Cheers.— cyberbot II Talk to my owner:Online 19:07, 20 April 2016 (UTC)
0001 0000 0000 0000 0000 0000 0000 0000 ≈ -1.189731495357231765085759326628008 × 10<sup>-4932</sup> (min quadruple precision)
This probably needs to be added for those wishing to know what the minimum is in hexadecimal. However, I am not sure if it is truely `-1.189...7 + 0.0...1 x 10-4932`. I didn't calculate it.
Much love, PauSix ( talk) 03:27, 20 October 2018 (UTC)
The sentence "If a decimal string with at most 33 significant digits is converted to IEEE 754 quadruple-precision representation, and then converted back to a decimal string with the same number of digits, the final result should match the original string" is only true if the quadruple precision representation is a normal number. Subnormals have less precision and proportionately fewer decimal digits are allowed. The wikipedia article for double precision floating-point format has the same issue. 2601:18C:4200:60F0:845C:148F:C31C:6449 ( talk) 13:48, 15 August 2022 (UTC)
Reference 1, which is:
David H. Bailey; Jonathan M. Borwein (July 6, 2009). "High-Precision Computation and Mathematical Physics" (PDF).
no longer works for me. 64.16.131.2 ( talk) 21:45, 22 February 2023 (UTC)
This is the
talk page for discussing improvements to the
Quadruple-precision floating-point format article. This is not a forum for general discussion of the article's subject. |
Article policies
|
Find sources: Google ( books · news · scholar · free images · WP refs) · FENS · JSTOR · TWL |
![]() | This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||||||||||||||||||
|
I think this article should be moved, since the title is not conform to IEEE 754r, which refers the format as quad or quadruple precision, but never quad precision. Also quad is not really an adjective like single and double. See e.g. the draft on [1]. — Ylai 08:53, 9 January 2006 (UTC)
This page on quadruple precision says:
(1/3 rounds up like double precision, because of the odd number of bits in the significand.)
However the page for double precision says:
(1/3 rounds down instead of up like single precision, because of the odd number of bits in the significand.)
These statements contradict each other.
I think it should probably be "7ffe" in the first block of four hex digits unless anyone can say why not.
7ffe
-
Jake (
talk)
04:27, 20 September 2014 (UTC)It appears that an error has crept into the example for 1/3, namely:
1) The examples states that the following bits, presented as hex numbers, denote 1/3:
3ffeh 5555h 5555h 5555h 5555h 5555h 5555h 5555h
2) When expanded into binaly notation this is:
0011b 1111b 1111b 1110b 0101b 0101b 0101b 0101b ....
3) The exponent is (15 bits):
011111111111110b = 16382d, adding the offset of -16383d the value of the exponent is found to be 16382-16383=-1d. And this is what appears wrong to me. It must be -2d. Why? Because, read on...
4) The mantissa is:
0101b 0101b 0101b .... = 1/4d + 1/16d + 1/64d + 1/256d + 1/1024d + 1/4096d ... = 0.333d... When we add the implied 1d the value of the matissa is found to be 1+0.333...=1.333d...
5) Finally we construct the floating-point number as follows:
mantissa * 2^exponent = 1.333... * 2^-1 = 1.333... * 1/2 = 0.666..., which is not 1/3 as the text states it must be. However, if the exponent was -2 then the result would be: mantissa * 2^exponent = 1.333... * 2^-2 = 1.333... * 1/4 = 0.333..., which is the correct result.
6) Bottom line: I think that the example for 1/3 must be:
3ffdh 5555h 5555h 5555h 5555h 5555h 5555h 5555h
Plamka 23:16, 17 September 2007 (UTC)
Do any hardware or CPUs support quadruple precision floating point already?
Do any programming languages?
193.74.100.50 ( talk) 08:00, 9 May 2008 (UTC)
In the first paragraph, the article claims that quadruple precision could refer to integers, fixed point numbers, or floating point numbers, but the rest of the article solely discusses floating point numbers. Could somebody rectify this? —Preceding unsigned comment added by 128.101.38.232 ( talk) 19:55, 27 October 2008 (UTC)
The IBM z Series supports quad precision. See: this paper, Figure 1. mfc ( talk) 11:59, 10 March 2009 (UTC)
IBM hex (base 16) floating point has supported extended (128 bit) precision starting with the 360/85, and all models of S/370 and successors, except that DXR (extended precision divide) was done in software emulation until part way through the ESA/390 years. Newer processors implement binary (IEEE) and decimal (IEEE) floating point, including extended (128 bit) precision. Gah4 ( talk) 00:01, 25 October 2011 (UTC)
The VAX had support for 128-bit floats (called h_float) since the 1970s, but it's not IEEE 754-compliant. —Preceding unsigned comment added by 69.54.60.34 ( talk) 14:04, 15 September 2010 (UTC)
VAX still supports H-Float, but it is implemented through software emulation on most models, or optional microcode. The VAX 11/730, implemented in microcode through the AMD2900 series bit-slice logic, normally came with H-Float. Gah4 ( talk) 00:01, 25 October 2011 (UTC)
Some (all?) PowerPC CPUs supports quadprecision nativly. Also few compilers like Intel Fortran compiler (but few others also) supports quad-precision (not sure if strictly IEEE754, but they do) on x86 and amd64 systems using only double precision numbers with additions of some refinments or software functions. There is also few (about 3), lightwaight and fast libraries for quad and octal precision using 2xdouble (or 4xfloat for old architecture) or 4xdouble, but they do not have only about 90% precision of real quad or octal floating point numbers. One of such libraries is QD and DDFUN90 library. — Preceding unsigned comment added by 91.213.255.7 ( talk) 03:16, 11 June 2011 (UTC)
A link to Multiprecision Computing Toolbox for MATLAB was added, which is fine since according to http://www.advanpix.com/2013/01/20/fast-quadruple-precision-computations/ this toolbox has specific, optimized support for IEEE quadruple precision (not just generic arbitrary precision). However this is a bit hidden. I think that some reference to this page from the changelog should be given, but I wonder what form it should take (this cannot be a real reference, since the external links appear after the references). Vincent Lefèvre ( talk) 17:39, 12 April 2013 (UTC)
Hello fellow Wikipedians,
I have just modified 2 external links on Quadruple-precision floating-point format. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at {{
Sourcecheck}}
).
An editor has reviewed this edit and fixed any errors that were found.
Cheers.— cyberbot II Talk to my owner:Online 19:07, 20 April 2016 (UTC)
0001 0000 0000 0000 0000 0000 0000 0000 ≈ -1.189731495357231765085759326628008 × 10<sup>-4932</sup> (min quadruple precision)
This probably needs to be added for those wishing to know what the minimum is in hexadecimal. However, I am not sure if it is truely `-1.189...7 + 0.0...1 x 10-4932`. I didn't calculate it.
Much love, PauSix ( talk) 03:27, 20 October 2018 (UTC)
The sentence "If a decimal string with at most 33 significant digits is converted to IEEE 754 quadruple-precision representation, and then converted back to a decimal string with the same number of digits, the final result should match the original string" is only true if the quadruple precision representation is a normal number. Subnormals have less precision and proportionately fewer decimal digits are allowed. The wikipedia article for double precision floating-point format has the same issue. 2601:18C:4200:60F0:845C:148F:C31C:6449 ( talk) 13:48, 15 August 2022 (UTC)
Reference 1, which is:
David H. Bailey; Jonathan M. Borwein (July 6, 2009). "High-Precision Computation and Mathematical Physics" (PDF).
no longer works for me. 64.16.131.2 ( talk) 21:45, 22 February 2023 (UTC)