On Tue, 23 Feb 2021 03:58:46 GMT, Joe Darcy <da...@openjdk.org> wrote:
> In floating-point, usually doing an operation to double precision and then > rounding to float gives the right result in float precision. One exception to > this is fused multiply add (fma) where "a * b + c" is computed with a single > rounding. This requires the equivalent of extra intermediate precision inside > the operation. If a float fma is implemented using a double fma rounded to > float, for some well-chosen arguments where the final result is near a > half-way result in *float*, an incorrect answer will be computed due to > double rounding. In more detail, the double result will round up and then the > cast to float will round up again whereas a single rounding of the exact > answer to float would only round-up once. > > The new float fma implementation does the exact arithmetic using BigDecimal > where possible, with guard to handle the non-finite and signed zero IEEE 754 > details. This pull request has now been integrated. Changeset: e5304b3a Author: Joe Darcy <da...@openjdk.org> URL: https://git.openjdk.java.net/jdk/commit/e5304b3a Stats: 32 lines in 2 files changed: 4 ins; 11 del; 17 mod 8253409: Double-rounding possibility in float fma Reviewed-by: bpb ------------- PR: https://git.openjdk.java.net/jdk/pull/2684
