George V. Reilly

A Use for Octal: Calculating Modulo 36 from Modulo 9

(I posted an earlier version of this in December 2004 on my old technical blog. A discussion at work last week about 36-bit computers at the Living Computers Museum prompted me to write an updated post with improved ex­pla­na­tions and much better typography.)

I've been pro­gram­ming in C since 1985 and C++ since 1991, but I've never found a use for octal rep­re­sen­ta­tion until [2004], aside from the per­mis­sions argument for chmod. Octal has always seemed as vestigial as a human appendix, a leftover from the early days of computers, when word sizes were often a multiple of three: 6-, 12-, 24-, or 36-bits wide. All modern computers use word continue.

Rounding

I recently learned from a Stack­Over­flow question that the rounding behavior in Python 3.x is different from Python 2.x:

The round() function rounding strategy and return type have changed. Exact halfway cases are now rounded to the nearest even result instead of away from zero. (For example, round(2.5) now returns 2 rather than 3.)

The “away from zero” rounding strategy is the one that most of us learned at school. The “nearest even” strategy is also known as “banker’s rounding”.

There are actually five rounding strategies defined in IEEE 754:

Mode / Example Value +11.5 +12.5 −11.5 −12.5
to nearest, ties to even +12.0 +12.0 −12.0 −12.0
to nearest, ties away from zero +12.0 +13.0 −12.0 −13.0
toward 0 (truncation) +11.0 +12.0 −11.0 −12.0
toward +∞ (ceiling) +12.0 +13.0 −11.0 −12.0
toward −∞ (floor) +11.0 +12.0 −12.0 −13.0

Further continue.

Happy Pi Day

3/14 is considered to be Pi Day by many geeks, as π is ap­prox­i­mate­ly 3.14. I wish I could say that I had celebrated by eating pie, but I didn't.

π is surely the most important irrational number, which has been known since antiquity.

π shows up in so many different formulas. My own favorite is Euler's Identity, eiπ + 1 = 0. (This marks the first use of the re­Struc­tured­Text math role in my blog.)

I am also find of the ap­prox­i­mate fraction 355 ⁄ 113.

The Wikipedia article on π has much more on π.

Update: Wonkblog: 10 stunning images show the beauty hidden in pi