Saturday, March 03, 2012

Diversions in C Minor

Last year we saw the passing of Dennis Ritchie. I was one of the lucky students who used the K&R book as a text book in college. Actually it's pretty amazing that the text books for CS first years were K&R and The Mythical Man-Month. There was pretty much no excuse for me to F up after being taught from those two books. The untimely passing of Ritchie made me recollect that I never really finished K&R. My professor used many of the chapters as reference material, and of course at some point I figured that I already knew everything so well that I didn't need no stinkin' book. So I decided then that I would re-read the book including all of its problems.

Of course I didn't start re-reading K&R right then as I should have. But I did get around to it recently. The very first problem in chapter two asked the reader to calculate the minimum signed chars, shorts, ints, and longs, and the maximum of those plus their unsigned cousins. These are all very straightforward things to calculate for anyone with an understanding of modular arithmetic. The book then mentions a more challenging problem: calculating minimum and maximum floats. No problemo I thought: Obviously that doesn't work, or this would be a pretty boring blog post. Here's where the awesome comes in. On my MacBook Air, this prints 1.175494e-38 for FLT_MIN but the second line prints 1.401298e-45 for the "calculated" minimum float. That's right it calculates a value that is smaller than FLT_MIN.

Experienced C developers will surely recognize what is going on here but I was flummoxed. It was only upon looking at some of the other constants defined in float.h that I started to figure out what was going on. In particular I noticed that on my MBA, FLT_MIN * FLT_EPS = 1.401298e-45. FLT_EPS is "float epsilon" and is defined as the smallest x for which 1+x != x. This is sort of the standard error on the system, i.e. any calculation could be off by a factor of FLT_EPS. I decided to calculate this in my program and then to also use it to calculate FLT_MAX: The FLT_MAX calculation takes a long time, since it uses such a small increment. I'm sure a bigger increment could be used to speed it up.

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