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Naoki Shibata, Google+, here. Did SLEEF – SIMD Library for Evaluating Elementary Functions, here. Nice work. We have talked with various intrinsic library folks about producing a restricted range vector exponential for FinQuant applications. The idea is that by reducing the range of the vector expontential to be an interest rate that you actually expect to see in an MC simulation you can reduce the number of approximation terms in the Chebyshev expansion without losing the desired error bounds. Such a code might save a couple of cycles per element ( a big deal) but would also need to catch exceptions ( and go slower) if the interest rate exceeded a max threshold. Interesting that Shibata uses the Taylor Series approximation in this code. I am not sure what the trade-offs are these days.
Most of today’s processors have capabilities to execute SIMD instructions, and we can expect significant speed-ups in various kinds of computation if these instructions are properly used. But, this is technically hard because many popular programming techniques like table look-ups, conditional branches, scattering/gathering operations can easily slow down the computation. With this library, the trigonometric functions(sin, cos, tan, sincos), inverse trigonometric functions(asin, acos, atan, atan2), exponential and logarithmic functions(exp, log, pow, exp2, exp10, expm1, log10, log1p), hyperbolic/inverse hyperbolic functions(sinh, cosh, tanh, asinh, acosh, atanh), and some other functions(cbrt, ilogb, ldexp) can be evaluated in both double precision and single precision without table look-ups, scattering from, or gathering into SIMD registers, or conditional branches using SSE2, AVX, AVX2, FMA4, or ARM NEON instruction sets.
You can download the library here.
You can see the javadoc here.
Many of the techniques used in SLEEF 2 are described in Elementary Functions: Algorithms And Implementation written by Jean-Michel Muller.
Markdown has arrived on WordPress.com! Some of you may respond with "Finally!" Others might be asking, "what's that?" Markdown is a quick way to add formatted text without writing out any HTML.
Let's take a closer look. Here is an example of how Markdown looks while editing a post:
This is how that same example looks in the Reddle theme after it's converted to HTML:
Making your way to the cutting edge of any field is a daunting challenge. But especially when the edge of the field is expanding; and even harder still when the rate of expansion is accelerating. John recently helped Physics World create a special 25th anniversary issue where they identified the five biggest breakthroughs in physics over the past 25 years, and also the five biggest open questions.
Performance Analysis and Optimization
Due to the rising complexity and scale of systems and applications, we require novel, sophisticated and easy-to-use approaches for performance analysis at scale. We are developing such techniques, which we are deploying in close collaboration with our code teams. Our projects include Open|SpeedShop and eGprof. We are also designing novel techniques to rebalance application load at scale based on Libra.
The best part about writing a dissertation is finding clever ways to procrastinate. The motivation for this blog comes from one of the more creative ways I've found to keep myself from writing. I've posted about data mining in the past and this post follows up on those ideas using a topic that is relevant to anyone that has ever considered getting, or has successfully completed, their PhD.
A scary question, a really scary question
Vincent Price was just featured last Thursday night with a series of his movies, scary horror ones shown on Turner Classic Movies. Price was known for his distinctive voice and special smirk, which was perfect for these movies. The series was in honor of Halloween. October 31 is the day of trick-or-treating, wearing costumes, going door-to-door to get candy, telling scary stories, and watching horror films.
Harvard has America's largest college or university endowment, but not nearly its best.
FORTUNE -- Harvard University has the nation's largest college or university endowment, valued at $32.7 billion through the end of June. It also has worse investment returns than any of its peers over the past five years, according to a Fortune analysis.
This may come as a surprise to Harvard employees and alums, who have been told that the endowment's investment arm -- Harvard Management Company -- regularly beats its benchmarks.
Yesterday we had a great discussion in our Alternative Banking Book Club about municipal financing, based on the sixth chapter in our book Occupy Finance called A Civics Lesson: Wall Street Feasts on the Commons. The conversation was kindly led by Tom Sgouros, a policy analyst and author from Rhode Island, which seems to be a hotbed of super terrible muni financing.
Cloudflare (a web security company) has a primer on elliptic curve cryptography and its uses for privacy and security online. Quick version: RSA cryptography relies on the fact that multiplying integers is easy but factoring them is hard. Elliptic curve cryptography relies on the fact that there's a group law for elliptic curves over the integers mod n, and applying that group law repeatedly (exponentiation) is easy but determining how many times that law was applied (taking the discrete logarithm) is hard.