Does ruby calculate floats wrong? [duplicate]

Question

This question already has an answer here:

• Addition error with ruby-1.9.2 [duplicate] 2 answers

Whats wrong here? (ruby version: 1.9.2p290 (2011-07-09 revision 32553) [x86_64-darwin11.0.0]

x = 523.8
w = 46.9
xm = x + w
assert_equal w, (xm - x) # FAILS with: <46.9> expected but was <46.89999999999998>

Answer 1

This is perfectly normal; it is a fact about the lower-level concept of floating point arithmetic rather than Ruby and therefore can occur in any language.

Floating point arithmetic is not exact. Equality should be replaced with closeness along the lines of assert((xm-x).abs < epsilon), where epsilon is some small number like 0.01.

Answer 2

From The Floating-Point Guide:

Why don’t my numbers, like 0.1 + 0.2 add up to a nice round 0.3, and instead I get a weird result like 0.30000000000000004?

Because internally, computers use a format (binary floating-point) that cannot accurately represent a number like 0.1, 0.2 or 0.3 at all.

When the code is compiled or interpreted, your “0.1” is already rounded to the nearest number in that format, which results in a small rounding error even before the calculation happens.

Read the linked-to site for details and ways to get around this.

Answer 3

Read this. It describes the way binary representation of floating point numbers work in every language, not just Ruby.

Answer 4

The answer to your question is: No.

(Other answers tell you why, but you didn't ask that. :p)