# IEEE 754R notes from October 13-14, 2004

Notes taken by Dan Zuras.

## October 13, 2004: Draft review

Notes for draft review at HP in Cupertino at 1:00 on Wednesday 10/13/04. Jim Thomas was our host. Dan Zuras, Jon Okada, Peter Markstein, Mike Cowlishaw (phone), Eric Schwartz (phone), Jeff Kidder (phone), Alex Liu (phone), Leonard Tsai (phone), Joe Darcy (phone) & David Hough attended.

We started with my embarrassing discovery of yesterday about decimal to binary conversions. Then draft review continued while I worked on a stronger counter example for directed rounding.

n 2n ULP 2n + ULP/2 2n + ULP
24 16777216 2 16777217 16777218
25 33554432 4 33554434 33554436
26 67108864 8 67108868 67108872
2713421772816134217736134217744
2826843545632268435472268435488
2953687091264536870944536870976
30107374182412810737418881073741952
31214748364825621474837762147483904
32429496729651242949675524294967808
n510*2nULP510*2n + ULP/2510*2n + ULP
0 9765625 1 9765625.5 9765626
1 19531250 2 19531251 19531252
2 39062500 4 39062502 39062504
3 78125000 8 78125004 78125008
4 156250000 16 156250008 156250016
5 312500000 32 312500016 312500032
6 625000000 64 625000032 625000064
71250000000 128 1250000064 1250000128
82500000000 256 2500000128 2500000256
95000000000 512 5000000256 5000000512
1010000000000 1024 10000000512 10000001024

This means that there is a counter example to convert from decimal strings to single precision with directed rounding.

In particular, for round-to-zero, the string "1073741825" will convert to 230 - 64 if the last digit is ignored because 1073741820 < 230 but we have 230 < 1073741824 = 230 + 1 < 230 + 128. Therefore, ignoring the tenth digit means that the string is converted to a binary number that is not even one of the two surrounding numbers.

I got sidetracked with a discussion of Annex Z.

## October 14, 2004: Discussion

Notes for meeting at HP in Cupertino at 1:00 on Thursday 10/14/04. Jim Thomas was our host. Dan Zuras, Jon Okada, Dick Delp, Alex Liu (phone), Eric Schwartz (phone), Peter Markstein, Joe Darcy, Leonard Tsai (phone), David Hough, Jeff Kidder (phone), Mike Cowlishaw (phone), & Ivan Godard (arter 3:00) attended.

We went through the list of subcommittee proposals in the following order:

1. Shall I write a letter to the editor for various magazines asking about the signalling NaN question? SIAM News, IEEE Computer, CACM, Dr Dobbs, comp.arch.arithmetic, NA Digest (Cleve Moler's), et al. YES
2. Should we define Annex Z with radix = 2 or 10 or not, as in pages 87 to 99 of the current draft. YES
3. Should we do integers? Pull Z.1 out of purple in pages 87 to 88 of the current draft. Write it up first.
4. Shall we accept debug.sxw? Annex D, from the subcommittee. Resubmit next time.
5. Shall we accept correctly rounded base conversion? From the proposal and subcommittee. YES

After we finished with that we continued to discuss the nature of the rounding specification we must make in light of my odd discovery of Tuesday. We'll start with the C99 specification.

We also discussed whether we should ACTUALLY demand looking at all those digits on input & PRINTING them on output. Also, what are the default number of digits to print out for each precision when the number is unspecified.

Now that Ivan is here, Dave decided to talk about modes.