On Fri, 19 Dec 2008 14:51:29 -0500, Christophe M. wrote:
and just in case you need further convincing, this is the scariest
example i’ve ever seen. taken from Stefano T.'s
The example you give is pretty scary, but there’s much scarier. You
need a big complicated function to hit weird floating point anomalies.
x + y - y should always equal x, right?
irb(main):012:0> 1.0 + 3.0 - 3.0
Seems to work. Except when it doesn’t…
irb(main):017:0> x = 1.0/3
irb(main):018:0> x + 0.1 - 0.1 == x
Take into consideration the rather innocent looking function
(333.75-x2)* y6 + x2 * (11* x2 * y2-121 * y4 -2) +
5.5 * y**8 + x/(2*y)
You’ve obviously lived a depraved life if you think that looks
We can calculate it for some specific x and y,
f(77617.0,33096.0) # => 1.17260394005318
There is only one problem: this result is WRONG. The correct result can
be obtained by calculating separately the numerator and denominator of f
using integer arithmetic.
Out of curiosity, I tried this equation in Python, and got the same
result. Hardly surprising, as Python and Ruby will probably be using the
same floating point library.
I also tried in on my HP-48GX calculator, and got the same result too.
arithmetic truths could be voted on, that would be three votes for the
Does anyone have access to Mathematica? What does it give?
f_num(77617, 33096).to_f / f_den(77617, 33096).to_f
# => -0.827396059946821
Just to add more confusion to the story, here’s another mathematically
equivalent expression (unless I’ve made a silly mistake):
irb(main):026:0> def f2(x, y)
irb(main):027:1> a = x2
irb(main):028:1> b = y2
irb(main):029:1> f = x/(2y)
irb(main):030:1> 11ab(a - 11b)+(333.75 - a)b**3 + 5.5b**4 - 2a+f
irb(main):032:0> f2(77617, 33096)
The moral of the story? Floats are evil. They are just similar enough to
the real numbers you learn about in school to fool you into thinking
they behave just like reals, but they don’t.