IEEE decimal interchange

The shared Format descriptor includes decimal32, decimal64, decimal128, and custom layouts. Datums retain a coefficient and quantum exponent, including distinct cohort members with the same numerical value. BID and DPD codecs preserve complete datums, and arithmetic rounds exact expressions into the chosen decimal format with explicit exception outcomes.

Algebraic adds square, reciprocal square root, hypotenuse, integer powers, and integer-degree roots in all five rounding modes. Each rounds the complete expression once. Import DecimalInterchange.Transcendentals.Certified.Proof for the finite-result expMinus1 and logPlus1 certificates.

Environment threads the current rounding direction and sticky exception flags through pure computations. Neighbors, remainder, exponent operations, and external text conversion use the same datums and projection. Narrower imports separate execution from the accompanying numerical and representation proofs.

References

• IEEE, IEEE Standard for Floating-Point Arithmetic, IEEE Std 754-2019, https://doi.org/10.1109/IEEESTD.2019.8766229.
• Mike Cowlishaw, General Decimal Arithmetic, https://speleotrove.com/decimal/decarith.html.