Created on 2020-11-18.00:00:00 last changed 4 months ago
[ 2020-11-29; Reflector prioritization ]
Set priority to 3 during reflector discussions.
[time.duration.cast] p7 requires that the return value is "The least result t representable in ToDuration for which t >= d".This means that chrono::ceil<chrono::microseconds>(chrono::duration<float, milli>(m)).count() is required to be the smallest integer n such that (float)n == m*1000.0f, which might be less than the mathematically correct value of m x 1000. (The specific values below assume float uses the IEEE binary32 format and default rounding, but similar problems will exist for other formats, even if the specific values are different.) For example, if m == 13421772.0f then the naively expected result is n == 13421772000, but the standard requires n == 13421771265, a significantly lower value. This surprising result is a consequence of how the chrono::ceil spec interacts with floating-point arithmetic, due to the fact that for the integers in the range [13421770753, 13421772799], only one can be exactly represented as 32-bit float. All but that one will be rounded to a different value when converted to float. A straightforward implementation of chrono::ceil will produce (long long)(13421772.0f * 1000) which is 13421771776, which is less than the expected result, but compares equal using the t >= d expression. That expression converts both operands to their common_type, which is chrono::duration<float, micro>. That means we compare (float)13421771776 >= (13421772.0f * 1000) which is true. But the spec requires an even worse result. All integers in [13421771265, 13421771776) are also rounded to that value when converted to float. That means chrono::microseconds(13421771265) is "the least result representable in ToDuration for which t >= d". Meeting the "least result" requirement is impractical, and unhelpful. The straightforward result 13421771776 is already lower than the naively expected result (which is surprising for a "ceil" function). To meet the standard's requirements the implementation would have to do extra work, just to produce an even lower (and even more surprising) result. It might be impractical to require the naively expected value to be returned (the additional work might have unacceptable performance implications), but the standard should at least permit the straightforward result instead of requiring an even worse one. The same problem almost certainly exists for chrono::floor in reverse.
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