In an Old Notebook (Generating Random Sequences VI)

April 4, 2017

Looking for something else in old notebooks, I found a diagram with no other indication, but clearly a low-cost random generator.

So, why not test it?

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Size(_t) matters!

December 27, 2016

Sometime last week, a tweet from @nixCraft prompted the question, quite ironically, how do you get the maximum (largest positive) value for an integer?

max_int

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Pretty Printing a Tree in a Terminal

December 6, 2016

More often than I’d like, simple tasks turn out to be not that simple. For example, displaying (beautifully) a binary tree for debugging purpose in a terminal. Of course, one could still use lots of parentheses, but that does not lend itself to a very fast assessment of the tree. We could, however, use box drawing characters, as in DOS’s goode olde tymes, since they’re now part of the Unicode standard.

tree-01

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Padé Approximants

September 20, 2016

Sometimes, you need to compute a function that’s complex, cumbersome, or which your favorite language doesn’t quite provide for. We may be interested in an exact implementation, or in a sufficiently good approximation. For the later, I often turn to Abramovitz and Stegun’s Handbook of Mathematical Function, a treasure trove of tables and approximations to hard functions. But how do they get all these approximations? The rational function approximations seemed the most mysterious of them all. Indeed, how can one come up with

e^x \approx 1-0.9664x+0.3536x^2

for e^x, for 0\leqslant x\leqslant\ln 2?

Well, turns out, it’s hard work, but there’s a twist to it. Let’s see how it’s done!

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The protoshadok number system

September 13, 2016

We’re so used to our positional notation system that we can’t really figure out how to write numbers in other systems. Most of the ancient systems are either tedious, complicated, or both. Zero, of course, plays a central role within that positional system. But is it indispensable?

shadok

In one of my classes, I discuss a lot of different numeration systems (like Egyptian, Babylonian, Roman and Greek) to explain why the positional system solves all, or at least most, of these systems’ problems. I even give the example of Shadok counting (in french) to show that the basis used isn’t that important (it still has to be greater than one, and, while not strictly necessary, preferably a positive integer). But can we write numbers in a positional system without zero?

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Serializing Trees

September 6, 2016

Quite a while ago I discussed using flat arrays and address calculations to store a tree in a simple array. The trick wasn’t new (I think it’s due to Williams, 1964 [1]), but is only really practical when we consider heaps, or otherwise very well balanced trees. If you have a misshapen tree, that trick doesn’t help you. It doesn’t help you either if you try to serialize a misshapen tree to disk.

But what if we do want to serialize arbitrarily-shaped trees to disk? Is it painful? Fortunately, no! Let’s see how.

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Making a good random table

April 5, 2016

I am still experimenting with hash functions, and I was toying with the Zobrist hash function[1] that is best known for its use in chess engines. The hash function is conceptually simple: you need a large table of random numbers, indexed, in a chess application, by the position on the board of the piece and by the piece itself. To compute a hash for a whole board configuration, you simply xor all the random numbers together. The hard part is choosing the random numbers.

IMG_0405-small

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