Talk:Quadruple-precision floating-point format

message: 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 . — Ylai 08:53, 9 January 2006 (UTC)
replies: text: Good point. So changed. --Jake 21:43, 9 January 2006 (UTC)
thread_title:  Title 

message: 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.
:It appears this has been cleaned up. -Jake (talk) 04:27, 20 September 2014 (UTC)
thread_title:  1/3 rounds up or down? 

message: I think it should probably be "7ffe" in the first block of four hex digits unless anyone can say why not.
:Yes, 7ffe -Jake (talk) 04:27, 20 September 2014 (UTC)
thread_title:  Max quad begins with (hex) 7fef or 7ffe? 

message: 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)
replies: text: Plamka is right and unfortunately MAX is also broken. I've changed the values accordingly. --136.172.253.11 19:17, 5 March 2008 (UTC)
thread_title:  Possible Error in the Example for 1/3 

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thread_title:  External links modified 

message: 0001 0000 0000 0000 0000 0000 0000 0000   ≈  -1.189731495357231765085759326628008 × 10-4932 
                                              (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)
replies: text: Last November I added more examples to all the various floating-point formats, so that (hopefully) they all contain the same set of examples. The minimum value mentioned above was added as "smallest positive normal number". Peter J. Acklam (talk) 07:44, 7 August 2019 (UTC)
thread_title:  Add minimum to examples? 

message: 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)
replies: text: Thanks (and this won't work either in case of overflow, though this is a bit more obvious). I've just done the correction in Quadruple-precision floating-point format, Double-precision floating-point format and Single-precision floating-point format. — Vincent Lefèvre (talk) 17:43, 17 August 2022 (UTC)
thread_title:  Conversion to binary and back 

message: 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)
replies: text: Thanks for the information. I've just updated the URL. — Vincent Lefèvre (talk) 21:58, 22 February 2023 (UTC)
thread_title:  Broken Link