Math precision requirements of C and C++ standard

Question

Do the C and C++ standards require the math operations in math.h on floating points (i.e. sqrt, exp, log, sin

Answer 1

No, and for good reason. In general, you'd need an infinite precision (and infinite time) to determine the exact mathematical result. Now most of the times you need only a few extra iterations to determine sufficient bits for rounding, but this number of extra bits depend on the exact result (simply put: when the result is close to .5 ULP). Even determining the extra number of iterations required is highly non-trivial. As a result, requiring exact results is far, far slower than a pragmatic approach.