# User talk:Vincent Lefèvre

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## IEEE 754 preferred width and double rounding

Someone was adding a bit to IEEE 754-2008 about expression evaluation and a bit of the standard there struck me as worth querying.

My reading of the preferred width recommendations in IEEE 754-2008 is that if you have a statement

x=y+z

where x, y, z are all double but the block has preferred width extended then y and z should be added using extended precision and then assigned to x, so one would have double rounding. Is that correct do you think? Thanks Dmcq (talk) 23:33, 6 April 2012 (UTC)

Yes, in this case, one has double rounding. In order to avoid double rounding, one can use the format-Of operations (Section 5.4) instead of the ones affected by preferredWidth. Note that IEEE 754-2008 doesn't define bindings, so that when one writes x=y+z in a language, it is up to the language to specify which kind of operation is used (depending on the context). Vincent Lefèvre (talk) 00:27, 7 April 2012 (UTC)
Thanks very much. Well setting preferred width to none should do that I believe so that's okay. I guess whatever one does something one doesn't think of will happen! Dmcq (talk) 15:09, 7 April 2012 (UTC)

## A barnstar for you!

 The Technical Barnstar I am awarding you this Technical Barnstar for your work on IEEE floating point. Good Job! Guy Macon (talk) 03:21, 13 November 2012 (UTC)

## Double-quad, quad-single, etc.

Could you take a look at Quadruple-precision floating-point format#Double-double arithmetic an perhaps expand it a bit? In particular, many embedded processors have 32-bit floating point arithmetic, and there is a lot of interest in combining two, three or four 32-bit numbers to get extended precision. Yet double-single and quad-single don't seem to be covered anywhere on Wikipedia. Thanks! --Guy Macon (talk) 08:51, 15 November 2012 (UTC)

## "Rounding" article undo (incorrect formulas)

Why the formulas are incorrect? If you mean rounding half-integer always up (like MS Excel function EVEN() do), or always down - it is not bankers' rounding.

If the fraction of number is 0.5 (half-integer), then rounded number is the even integer nearest (maybe up, maybe down) to initial number.

0.5 rounded to 0; 1.5 to 2; 2.5 to 2; 3.5 to 4; 4.5 to 4 and so on.

-0.5 rounded to 0; -1.5 to -2; -2.5 to -2; -3.5 to -4; -4.5 to -4 and so on.

On the other hand each even number has two entries of half-integers: 0 has 0.5 and -0.5; 2 has 1.5 and 2.5; -2 has -1.5 and -2.5 an so on.

That is the point of banker's rounding - unbiased rounding.

It is almost the same arguments for rounding half to odd formula.

If you are confused with multiplier (factor) before floor brackets, or addend inside floor brackets, you should understand that the floor or ceiling brackets are not usual brackets (parentheses) - you can't carry out or in anything, except integer addend (subtrahend), as usual as you do with simple brackets. Floor and ceiling functions have some unique rules. Anyway, just try my formulas with few half-integer numbers and say where I have mistaken. :-)

P.S. Sorry for my English.

Borman05 (talk) 16:49, 11 April 2014 (UTC)

The incorrectness is for non-half-integers. For Round half to even on y = 1, $q=2\lfloor\frac{y}{2}+0.5\rfloor$ gives 2 instead of 1. For Round half to odd on y = 0, $q=2\lfloor\frac{y}{2}\rfloor+1$ gives 1 instead of 0.
Vincent Lefèvre (talk) 17:00, 11 April 2014 (UTC)
I understand this, but this is not common formulas for all cases. As it was said earlier in article: "Rounding a number y to the nearest integer requires some tie-breaking rule for those cases when y is exactly half-way between two integers — that is, when the fraction part of y is exactly 0.5"
These simple formulas only for half-integers
Borman05 (talk) 17:32, 11 April 2014 (UTC)
No, there is a tie-breaking rule for special cases, but then, from this tie-breaking rule, one can find formulas that are valid for all numbers (those given for Round half up to Round half towards zero). Note that if you wanted formulas for half-integers only, such formulas could be simpler than those given.
Vincent Lefèvre (talk) 21:44, 11 April 2014 (UTC)