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Floating Point and Undefined Behaviour

Two kinds of question catch strong C++ candidates out. One is about the number format: why a sum comes out different in another build, or why a sort crashed on data with a missing price. The other is about undefined behaviour: code that looks correct, passes its tests at -O0, and does something else at -O2. Both come from the gap between what the programmer means and what the standard promises.

What a double holds

A double is an IEEE 754 binary64 value: 1 sign bit, 11 exponent bits and 52 fraction bits. That gives 15 to 17 significant decimal digits and exact integers up to 253=9,007,199,254,740,9922^{53} = 9{,}007{,}199{,}254{,}740{,}992. Above that, not every integer can be represented, and 253+12^{53} + 1 rounds back to 2532^{53}.

Most decimal fractions have no exact binary form, so 0.1 + 0.2 == 0.3 is false. Precision also depends on magnitude, which makes addition non-associative:

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