Machine Arithmetic Properties

In high school algebra classes we a taught some properties of real numbers: commutative [ab=ba], associative for addition [a+(b+c)=(a+b)+c], associative for multiplication [a(bc)=(ab)c], distributive [a(b+c)=ab+ac], and inverses [there exists a^-1 such that a(a^-1)=1]. In computer science classes we find that computer arithmetic does not always exactly obey those rules. This is a spreadsheet that uses random numbers to test those five properties of real numbers to determine the failure rate for machine arithmetic.

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(file size: 170KB)

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