Linux and the Alpha
In this article, I will discuss techniques to optimize code for platforms running Linux on Alpha processors. It is based on four years of experience with the Alpha architecture. The primary lesson from this experience is that, for many applications, the memory system, and not the processor itself, is the primary bottleneck. For this reason, most techniques are targeted at avoiding the memory system bottleneck. Since the gap between processor and memory system speed is large, these techniques achieve performance improvements of up to 1700%. While the focus is on the Alpha architecture, many of the covered techniques are readily applicable to other RISC processors and even modern CISC CPUs.
The tricky part in discussing how the same techniques work on other architectures is that we want to do this without igniting a war over which CPU architecture is the “best” or the “fastest”. Such terms are, to a good degree, meaningless, since they can be applied usefully relative to a given problem only. For this reason, performance results are presented as follows: for the Alpha we present both absolute and relative results. The absolute numbers are useful to give a concrete feel for how fast the code is. The relative results (i.e., speed ups) are what tell us how well a given technique works. Where meaningful, we also list the speed up (but not the absolute performance) achieved on a Pentium Pro-based system. Only listing speed up for the Pentium Pro case makes it impossible to tell which system was faster on a given problem while still allowing us to compare the relative benefits. (To avoid any misconception: this arrangement was not chosen because the Alpha performed poorly; the author has been using Alphas for some time now and is generally pleased with the performance level they achieve.)
Since an architecture per se doesn't perform at all, let us be a bit more specific about the systems used for the measurements:
Alpha system: The Alpha system was an AlphaStation 600 5/333 (aka Alcor). It has a 333MHz 21164 processor with 4MB of third-level cache and 64MB of main-memory. While a nice (and very expensive) box, it is by no means the latest and greatest of the available Alpha systems. At the time of this writing, much faster and much cheaper 500MHz systems have already been around for a while.
Pentium Pro system: The x86 system was a Gateway 2000 with a Pentium Pro processor with 32MB of main memory and 256KB of second-level cache. For clarity, this system is referred to as “P6” during the remainder of this section.
Both the Alpha and the P6 systems were running Red Hat 4.0 with kernel version 2.0.18. The compiler used was gcc version 2.7.2. On the Alpha, option -O2 was used (with this version of gcc, using an option setting of -O3 or higher generally results in slower code.). On the P6, options -O6 and -m486 were used.
It is also illustrative to compare gcc to commercial Alpha compilers, such as Digital's GEM C compiler. The GEM C compiler usually generates somewhat better code but now and then it creates code much faster than gcc's code (this usually happens on floating-point intensive code). For this reason, some of the measurements also include the results obtained with GEM C. This compiler was invoked as:
cc -migrate -O4 -tune ev5 -std1 -non_shared
It's not clear which version of the compiler it was—it came with Digital UNIX version 3.2.
The Alpha architecture does not provide an integer division instruction. The rationale for this is:
Such operations are relatively rare.
Division is fundamentally of an iterative nature, so implementing it in hardware is not all that much faster than a good software implementation. (See Reference 1.)
Nevertheless, there are important routines that depend on integer division. Hash-tables are a good example as computing a hash-table index typically involves dividing by an integer prime constant.
There are basically two ways to avoid integer division. Either the integer division is replaced by a floating-point division or, if the division is by a constant, it is possible to replace the division by a multiplication with a constant, a shift and a correction by one (which isn't always necessary). Floating-point division may sound like a bad idea, but the Alpha has a very fast floating-point unit, and since a 32-bit integer easily fits into a double without a loss of precision, it works surprisingly well. Replacing a division by a constant with a multiplication by the inverse is certainly faster, although it's also a bit tricky since care must be taken that the result is always accurate (off-by-one errors are particularly common). Fortunately, for compile-time constants, gcc takes care of this without help.
To illustrate the effect this can have, we measured how long it takes to look up all symbols in the standard C library (libc.so) using the ELF hash-table look-up algorithm (which involves one integer division by a prime constant). With integer division, roughly 1.2 million look ups per second can be performed. Using a double multiplication by the inverse of the divisor instead brings this number up to 1.95 million look ups per second (62% improvement). Using integer multiplication instead gives the best performance of 2.05 million lookups per second (70% improvement). Since the performance difference between the double and the integer multiply-by-inverse version isn't all that big, it's usually better to use the floating-point version. This works perfectly well, as long as the operands fit in 52 bits, and avoids having to worry about off-by-one errors.