# Cleve’s Corner: Cleve Moler on Mathematics and ComputingScientific computing, math & more

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# Benchmarking a GPU

Posted by Cleve Moler,

I recently acquired a GPU, a graphics processing unit. It's called a GPU because such processors were originally intended to speed up graphics. But MATLAB uses it to speed up computation. Let's see how the gpuArray object benchmarks on my machine.... read more >>

# How Far Apart Are Two Random Points in a Square?5

Posted by Cleve Moler,

How far apart can you expect two points chosen at random in the unit square to be? I found this problem on the YouTube channel maintained by Presh Talwalkar, Mind Your Decisions. He correctly calls it a very hard puzzle. At first, I guessed the answer might be $1/2$. But the correct answer is more interesting than that.... read more >>

# Ulps Plots Reveal Math Function Accuracy2

Posted by Cleve Moler,

"ULP" stands for "unit in the last place." An ulps plot samples a fundamental math function such as $\sin{x}$, or a more esoteric function like a Bessel function. The samples are compared with more accurate values obtained from a higher precision computation. A plot of the accuracy, measured in ulps, reveals valuable information about the underlying algorithms.... read more >>

# Season’s Greetings Fractal6

Posted by Cleve Moler,

I don't recall where I found this seasonal fractal. And I can't explain how it works. So please submit a comment if you can shed any light on either of these questions.... read more >>

# The Ziggurat Random Normal Generator

Posted by Cleve Moler,

This is the third in a multi-part series on the MATLAB random number generators. MATLAB has used variants of George Marsaglia's ziggurat algorithm to generate normally distributed random numbers for almost twenty years. ... read more >>