Notes taken by Dan Zuras.

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 | 2^{n} |
ULP | 2^{n} + ULP/2 |
2^{n} + ULP |
---|---|---|---|---|

24 | 16777216 | 2 | 16777217 | 16777218 |

25 | 33554432 | 4 | 33554434 | 33554436 |

26 | 67108864 | 8 | 67108868 | 67108872 |

27 | 134217728 | 16 | 134217736 | 134217744 |

28 | 268435456 | 32 | 268435472 | 268435488 |

29 | 536870912 | 64 | 536870944 | 536870976 |

30 | 1073741824 | 128 | 1073741888 | 1073741952 |

31 | 2147483648 | 256 | 2147483776 | 2147483904 |

32 | 4294967296 | 512 | 4294967552 | 4294967808 |

n | 5^{10}*2^{n} | ULP | 5^{10}*2^{n} + ULP/2 | 5^{10}*2^{n} + 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 |

7 | 1250000000 | 128 | 1250000064 | 1250000128 |

8 | 2500000000 | 256 | 2500000128 | 2500000256 |

9 | 5000000000 | 512 | 5000000256 | 5000000512 |

10 | 10000000000 | 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 2^{30} - 64 if the last digit is ignored
because 1073741820 < 2^{30} but we have 2^{30} < 1073741824 =
2^{30} + 1 < 2^{30} + 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.

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:

- 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** - Should we define Annex Z with radix = 2 or 10 or not, as
in pages 87 to 99 of the current draft.
**YES** - Should we do integers? Pull Z.1 out of purple in pages 87
to 88 of the current draft.
**Write it up first.** - Shall we accept debug.sxw? Annex D, from the
subcommittee.
**Resubmit next time.** - 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.