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What Every Computer Scientist Should Know About Floating-Point Arithmetic

53 points by kqr2 16y ago

RiderOfGiraffes 16y ago
An old friend that we see time and time again. Here are a few, although there isn't much discussion: http://news.ycombinator.com/item?id=1937182 http://news.ycombinator.com/item?id=1937182 http://news.ycombinator.com/item?id=1746797 http://news.ycombinator.com/item?id=1746797 http://news.ycombinator.com/item?id=687604 http://news.ycombinator.com/item?id=687604 http://news.ycombinator.com/item?id=453396 http://news.ycombinator.com/item?id=453396
- T-zex 16y ago
  Repetitio Est Mater Studiorum
wladimir 16y ago
Great. This isn't just useful for computer scientists, though. Also for other sciences that do computer simulations of any kind. And hopefully programmers will read it too and stop making awful mistakes such as using floating point values for money amounts.
bobds 16y ago
Instead of the same old paper again, how about a comparison of the ways current language implementations handle floating point numbers?
- dfox 16y ago
  There is no meaningful difference, because it is dependent on how CPUs handle FP arithmetic. And only significant change in that from time when this paper was published is that IBM got their decimal FP formats as optional part into standard that everyone uses for FP arithmetics.
  - ced 16y ago
    Technically, that's true, but the more interesting question is "How do languages handle non-integers?" Quite a few languages (like Lisp) have a rational data type, such that 1/3 + 1/4 is done exactly. Others have a decimal data type, whose main purpose is for calculations involving money. 0.1 + 0.2 = 0.3 And finally, I'm no expert on Mathematica, but IIRC it computes error bounds on your results, and it only displays decimal digits if they are within those bounds. It's the proper way of doing things, and again, 0.1 + 0.2 = 0.3
- wladimir 16y ago
  Most current languages don't 'handle' floating point numbers themselves, they simply use the CPU instructions available to work with them. The only way around that is to use a library that supports higher-precision floating point through emulation. Then agian, that still doesn't change the theoretical background in any way.
  - tankenmate 16y ago
    The GNU Multiple Precision Arithmetic Library http://gmplib.org/ http://gmplib.org/
aidenn0 16y ago
Friends don't let friends use floating point numbers. Computers are so darn fast today that there is no excuse for not using an arbitrary precision library. Floating point should be thought of as an optimization, not as a default. Unless you are writing DSP code (in which case this article should be nothing new), don't use floating point!
nagnatron 16y ago
I remember seeing this article in the lecture notes of my Numerical Analysis class. Very cool read.
kondro 16y ago
I'm glad I work in a world where the performance overhead of decimal (both SQL and Ruby's BigDecimal) isn't too high. I still remember when every Rails-based example with an invoice in it stored dollar amounts in the DB as floats. Ahh bless.
jwr 16y ago
TL;DR summary in the spirit of times: when doing floating-point math, expect your results to float. There be dragons. Big ones.
- mgedmin 16y ago
  Actually, my takeaway from this paper was exactly the opposite: if you understand how floats work, you can trust the results of floating-point calculation.
brazzy 16y ago
And for those without a math or CS degree: http://floating-point-gui.de/ http://floating-point-gui.de/

53 points by kqr2 16y ago

An old friend that we see time and time again. Here are a few, although there isn't much discussion: http://news.ycombinator.com/item?id=1937182 http://news.ycombinator.com/item?id=1937182 http://news.ycombinator.com/item?id=1746797 http://news.ycombinator.com/item?id=1746797 http://news.ycombinator.com/item?id=687604 http://news.ycombinator.com/item?id=687604 http://news.ycombinator.com/item?id=453396 http://news.ycombinator.com/item?id=453396

T-zex 16y ago
Repetitio Est Mater Studiorum

wladimir 16y ago

Great. This isn't just useful for computer scientists, though. Also for other sciences that do computer simulations of any kind. And hopefully programmers will read it too and stop making awful mistakes such as using floating point values for money amounts.

bobds 16y ago

Instead of the same old paper again, how about a comparison of the ways current language implementations handle floating point numbers?

dfox 16y ago
There is no meaningful difference, because it is dependent on how CPUs handle FP arithmetic. And only significant change in that from time when this paper was published is that IBM got their decimal FP formats as optional part into standard that everyone uses for FP arithmetics.
- ced 16y ago
  Technically, that's true, but the more interesting question is "How do languages handle non-integers?" Quite a few languages (like Lisp) have a rational data type, such that 1/3 + 1/4 is done exactly. Others have a decimal data type, whose main purpose is for calculations involving money. 0.1 + 0.2 = 0.3 And finally, I'm no expert on Mathematica, but IIRC it computes error bounds on your results, and it only displays decimal digits if they are within those bounds. It's the proper way of doing things, and again, 0.1 + 0.2 = 0.3
wladimir 16y ago
Most current languages don't 'handle' floating point numbers themselves, they simply use the CPU instructions available to work with them. The only way around that is to use a library that supports higher-precision floating point through emulation. Then agian, that still doesn't change the theoretical background in any way.
- tankenmate 16y ago
  The GNU Multiple Precision Arithmetic Library http://gmplib.org/ http://gmplib.org/

aidenn0 16y ago

Friends don't let friends use floating point numbers. Computers are so darn fast today that there is no excuse for not using an arbitrary precision library. Floating point should be thought of as an optimization, not as a default. Unless you are writing DSP code (in which case this article should be nothing new), don't use floating point!

nagnatron 16y ago

I remember seeing this article in the lecture notes of my Numerical Analysis class. Very cool read.

kondro 16y ago

I'm glad I work in a world where the performance overhead of decimal (both SQL and Ruby's BigDecimal) isn't too high. I still remember when every Rails-based example with an invoice in it stored dollar amounts in the DB as floats. Ahh bless.

jwr 16y ago

TL;DR summary in the spirit of times: when doing floating-point math, expect your results to float. There be dragons. Big ones.

mgedmin 16y ago
Actually, my takeaway from this paper was exactly the opposite: if you understand how floats work, you can trust the results of floating-point calculation.

brazzy 16y ago

And for those without a math or CS degree: http://floating-point-gui.de/ http://floating-point-gui.de/