Why is cos(x) != cos(y) even though x == y? (Or sine or tangent or log or just about any other floating point computation), C++ FAQ

C++ FAQ

From Marshall Cline: Bjarne Stroustrup, Herb Sutter, Andrei Alexandrescu, Pearson / Addison-Wesley Publishers and I collaborated to create a new C++ Super-FAQ! It's a team effort, with huge contributions from each of us and with amazing support from dozens of brilliant editors. The result is "awesomer" than ever! I originally wrote/published the FAQ in 1991 and now look forward to this new phase - and to continue working with it for another 20 years!

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FAQ: Why is `cos(x) != cos(y)` even though `x == y`? (Or sine or tangent or log or just about any other floating point computation) ←(in the new Super-FAQ)

It's in Section: Newbie Questions / Answers:

FAQ: What is this "newbie section" all about?
FAQ: Where do I start? Why do I feel so confused, so stupid?
FAQ: Should I use void main() or int main()?
FAQ: Should I use f(void) or f()?
FAQ: What are the criteria for choosing between short / int / long data types?
FAQ: What the heck is a const variable? Isn't that a contradiction in terms?
FAQ: Why would I use a const variable / const identifier as opposed to #define?
FAQ: Are you saying that the preprocessor is evil?
FAQ: What is the "standard library"? What is included / excluded from it?
FAQ: How should I lay out my code? When should I use spaces, tabs, and/or newlines in my code?
FAQ: Is it okay if a lot of numbers appear in my code?
FAQ: What's the point of the L, U and f suffixes on numeric literals?
FAQ: I can understand the and (&&) and or (||) operators, but what's the purpose of the not (!) operator?
FAQ: Is !(a < b) logically the same as a >= b?
FAQ: What is this NaN thing?
FAQ: Why is floating point so inaccurate? Why doesn't this print 0.43?
FAQ: Why doesn't my floating-point comparison work?
FAQ: Why is cos(x) != cos(y) even though x == y? (Or sine or tangent or log or just about any other floating point computation) (this FAQ)
FAQ: What is the type of an enumeration such as enum Color? Is it of type int?
FAQ: If an enumeration type is distinct from any other type, what good is it? What can you do with it?
FAQ: What other "newbie" guides are there for me?