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* In debug mode, MPFR would check that the result is exact
(i.e. that the ternary value is 0).
-- new "rounding mode" MPFR_RNDF (faithful rounding)?
- This is not really a rounding mode since it is non-deterministic. The
- goal is to avoid the Table Maker's Dilemma in internal computations.
- The definition of faithful rounding of a real number x is: return either
- RNDD(x) or RNDU(x). This means that if x is exactly representable, one
- returns x exactly. In MPFR, the ternary value should be unspecified for
- efficiency reasons.
- Note: One typically implements faithful rounding by computing an
- approximation to the result with some adequately chosen error bound,
- then by rounding this approximation to nearest.
- Concerning the choice of the error bound, if the result x is equal to
- 1 + t, where t is a very small positive number, then the error bound
- needs to be at most ulp(x)/4 + t. Since t can be arbitrarily small,
- the error bound needs to be at most ulp(x)/4. And this error bound
- is sufficient in all cases. Note that with the even rounding rule or
- rounding away from zero, it is not needed to relax the condition when
- x is exactly representable.
-
- add tests of the ternary value for constants
- When doing Extensive Check (--enable-assert=full), since all the