ADR 0047: Numeric rounding semantics

Historical-evidence note: test paths named below record the evidence used when this ADR was accepted; they are not active architecture or release owners. Current ownership is the four-surface ASL tree, with per-ID AVS coverage projected into spec/evidence/release-traceability-readiness.json.

Decision scope

This decision completes the rounding decision and supersedes the result-open parts of ADR 0039. ADR 0049 separately closes subnormal handling for the named hardware profile; ADR 0087 and ADR 0088 through ADR 0095 remain outside this decision.

Affected domains

• cube-matrix
• scalar-binary
• scalar-fp-convert
• scalar-fp-to-integer
• scalar-fused
• scalar-integer-to-fp
• scalar-unary
• tile-binary
• tile-convert
• tile-dequantize
• tile-expand
• tile-fused
• tile-partial
• tile-quantize
• tile-reduction
• tile-unary

Context

ADR 0039 separated the scalar active-rounding field, fixed scalar conversion mnemonics, bundle RMode, public conversion controls, target controls, and backend-only controls. It deliberately left their meanings and every operation-domain rounding point open.

The remaining evidence contains two traps for an implementation:

• the scalar and bundle selectors are both three bits wide but do not share an encoding namespace; and
• FCVTA means nearest with ties away from zero, not directed rounding away from zero for every inexact value.

PTO defines the scalar field location, the four assigned directional codes, and an RNE fallback for reserved values in the owning ASL.

Decision

Semantic modes

The ASL type NumericRoundingMode is the common semantic vocabulary:

Name	Rule
RNE	nearest, ties to even
RTM	toward negative infinity
RTP	toward positive infinity
RTZ	toward zero
RNA	nearest, ties away from zero
RTO	if inexact, select the adjacent result whose least-significant retained integer bit is one
RHB	nearest; on an exact halfway case select the numerically greater candidate

Encoded selector namespaces must translate explicitly to this type. Equal bit widths or ordinals never imply equal meanings.

Scalar active rounding

CORE_STATE[39:37] has four assigned active-rounding encodings:

Raw value	Resolution
000	RNE
001	RTM
010	RTP
011	RTZ
100–111	reserved; resolve to RNE

The reserved fallback is deterministic and has no trap or other architectural effect. It does not import meanings from bundle RMode.

Scalar floating binary, unary, format-conversion, and integer-to-floating operations use the resolved active mode when encoding their destination. Fused multiply-add variants evaluate the exact fused expression and round once at the destination boundary.

Fixed scalar conversions

The conversion mnemonic, not CORE_STATE.FRM, selects the mode:

Mnemonic	Mode
FCVTA	RNA
FCVTM	RTM
FCVTN	RNE
FCVTP	RTP
FCVTZ	RTZ

The finite source is rounded once before ADR 0090 selects an out-of-range, indefinite, or saturation result. This decision fixes the order but leaves those ADR 0090 results open.

Bundle and public conversion selectors

B.DATR.RMode has the following complete mapping:

Raw value	Bundle name	Semantic mode
000	NONE	operation-defined default
001	RNE	RNE
010	RTZ	RTZ
011	RDN	RTM
100	RUP	RTP
101	RNA	RNA
110	RTO	RTO
111	RHB	RHB

The public conversion enumeration is a separate namespace and translates as follows:

Public value	Public name	Bundle selection
0	CAST_NONE	NONE
1	CAST_RINT	RNE
2	CAST_ROUND	RNA
3	CAST_FLOOR	RDN
4	CAST_CEIL	RUP
5	CAST_TRUNC	RTZ
6	CAST_ODD	RTO

Public value 7 is unassigned and rejects before effects. There is no public RHB ordinal in this version. Backend tokens with similar names remain non-normative unless another accepted profile decision maps them.

Only ACCCVT, TCVT, TQUANT, and TDEQUANT consume TileNumericSelection. NONE resolves to RNE except that floating-to-integer TCVT resolves NONE to RTZ. An explicit bundle code always overrides that default. These operations round at the destination-format boundary before saturation. Saturation-disabled range results remain ADR 0090 decisions.

Operation-fixed domains

All other tile operations ignore bundle RMode and use operation-fixed rules:

• floating elementwise, expansion, partial, and PReLU results use RNE at each operation-defined destination boundary; exact integer, bitwise, comparison, minimum, maximum, broadcast, and selection results do not round;
• reductions visit elements in increasing logical row-major order and round every floating sum or product step to the declared accumulator type using RNE; minimum, maximum, and argument selection do not round; and
• matrix operations visit K in increasing logical order, perform one RNE-rounded fused multiply-add into the declared accumulator per term, and apply any post-dot bias with RNE. ACCCVT owns the later accumulator conversion.

The generated domain ledger records the rule and saturation ordering for all 16 affected rounding domains and 100 affected operations.

Rejected alternatives

• Treating scalar raw values 4 through 7 as the bundle modes was rejected because it conflates distinct architectural namespaces.
• Rejecting reserved scalar values before effects was rejected because PTO defines a deterministic RNE fallback.
• Defining FCVTA as directed away from zero was rejected because it changes non-halfway values and conflicts with the mnemonic's ties-away contract.
• Passing public enumeration ordinals directly into B.DATR.RMode was rejected because CAST_ROUND, CAST_FLOOR, CAST_CEIL, and CAST_TRUNC have different ordinals from their bundle encodings.

Consequences

This decision is complete for selector encodings, tie rules, operation defaults, rounding points, and rounding-before-saturation order. The ASL carries semantic rounding values rather than ambiguous raw codes across profile hooks.

This decision does not claim complete numeric results. Format encodings and legality, special values, flags, overflow and indefinite results, approximation error, reduction tie behavior, quantization equations, matrix precision beyond the stated rounding points, and bounded target variation remain owned by ADR 0087 and ADR 0088 through ADR 0095. ADR 0049 separately owns subnormal handling for the named hardware profile. Stage 5 therefore remains in progress.

Evidence

• asl/types.asl
• asl/scalar/floating.asl
• asl/scalar/dispatch.asl
• asl/bundle/dispatch.asl
• asl/tile/conversion.asl
• asl/tile/cube.asl
• spec/catalog/tile-operations.json
• spec/hardware-conformance-profile.json
• spec/evidence/numeric-rounding-selector-contract.json
• scripts/generate-numeric-rounding-selector-contract
• tests/asl/arch/data-types/rounding/arch-static-rounding-contract-001.asl
• tests/asl/scalar/model/dispatch/fsu/scalar-exec-flag-and-rounding-helpers-001.asl
• tests/asl/tile/model/numeric/rounding/tile-static-rounding-contract-001.asl
• spec/evidence/release-traceability-readiness.json