Since we now have minimal ANSI support, we can use it. Of course, for cute things such as changing text color (red for error, green for OK, etc.), but that’s not very amusing. Let’s make some ANSI ART!!1!

## Whatever sums your floats (Part II)

September 26, 2017A while ago, Martin Capoušek drew my attention on Kahan’s summation algorithm and ask how it compared to the other methods I presented then.

Well, let’s find out.

## Halton Sequences (Generating Random Sequences VII)

September 7, 2017Quite a while ago, while discussing Monte Carlo Integration with my students, the topic of choosing sample locations came up, and we discussed low-discrepancy sequences (a.k.a. quasi-random sequences). In a low-discrepancy sequence, values generated look kind of uniform-random, but avoids clumping. A closer examination reveal that they are suspiciously well-spaced. That’s what we want in Monte Carlo integration.

But how do we generate such sequences? Well, there are many ways to do so. Some more amusing than other, some more structured than others. One of the early example, Halton sequences (c. 1964) is particularly well behaved: it generates 0, 0.5, then 0.25 and 0.75, then 0.125, 0.375, 0.625, and 0.875, etc. It does so with a rather simple binary trick.

## Much Ado About Nothing

March 7, 2017A rather long time ago, I wrote a blog entry on branchless equivalents of simple functions such as `sex`, `abs`, `min`, `max`. The **S**ing **EX**tension instruction propagates the sign bit in the upper bits, and is typically used in the promotion of, say, a 16 bits signed value into a 32 bits variable.

But this time, I needed something a bit different: I only wanted the sign-extended part. Could I do much better than last time? Turns out, the compiler has a mind of its own.

## 8-bit Audio Companding

February 7, 2017Computationally inexpensive sound compression is always difficult, at least if you want some quality. One could think, for example, that taking the 8 most significant bits of 16 bits will give us 2:1 (lossy) compression but without too much loss. However, cutting the 8 least significant bits leads to noticeable hissing. However, we do not have to compress linearly, we can apply some transformation, say, vaguely exponential to reconstruct the sound.

That’s the idea behind μ-law encoding, or “logarithmic companding”. Instead of quantizing uniformly, we have large (original) values widely spaced but small (original) value, the assumption being that the signal variation is small when the amplitude is small and large when the amplitude is great. ITU standard G.711 proposes the following table:

## Stretching samples

January 31, 2017So for an experiment I ended up needing conversions between 8 bits and 16 bits samples. To upscale an 8 bit sample to 16 bits, it is not enough to simply shift it by 8 bits (or multiply it by 256, same difference) because the largest value you get isn’t 65535 but merely 65280. Fortunately, stretching correctly from 8 bit to 16 bit isn’t too difficult, even quite straightforward.

## Strings in C++ Switch/Case statements

January 10, 2017Something that used to bug me—used to, because I am so accustomed to work around it that I rarely notice the problem—is that in neither C nor C++ you can use strings (`const char *` or `std::string`) in switch/case statement. Indeed, the switch/case statement works only on integral values (an `enum`, an integral type such as `char` and `int`, or an object type with implicit cast to an integral type). But strings aren’t of integral types!

In pure C, we’re pretty much done for. The C preprocessor is too weak to help us built compile-time expression out of strings (or, more exactly, `const char *`), and there’sn’t much else in the language to help us. However, things are a bit different in C++.