ADR 0080: Tile elementwise and irregular operations

Context

ADR 0062 recorded a single repository-wide mnemonic audit. This record preserves the accepted decisions for this family as one decision-scoped owner. The former identifiers remain only in legacy_ids and the generated ADR index; current normative meaning is owned by the affected ASL/NDF clauses.

Decisions

Decision 056: TADD applies PadValue outside the valid destination rectangle

TADD accepts the B.DATR.PadValueOrByteId field in its PadValue interpretation. Within ValidRow x ValidCol, the destination element is the profile-defined sum of the corresponding left and right source elements. The two sources and destination MUST have matching physical rows, physical columns, valid rows, valid columns, row-major layout, and DataType.

After the valid-rectangle additions are computed, every physical destination element outside ValidRow x ValidCol is handled by the resolved PadValue. Zero, Max, and Min define those elements using the selected DataType's corresponding value. Null leaves those elements undefined. Omission resolves to Null. An explicitly present code 00 selects Zero, so omission and encoded zero remain architecturally distinct.

All source elements required by the valid rectangle MUST be defined before any destination effect. Both source payloads are snapshotted after complete preflight, so either source MAY alias the destination with read-old/write-new behavior. The destination update, including padding definedness, becomes visible as one complete commit.

Decision 057: TADD has a closed Local VEC block schema

TADD is the VEC elementwise addition operation selected by TEPL carrier Mode=0, Function=0. It reads two Local source Tiles in left-to-right binding order and writes one explicit new Local destination. B.IOS and B.IOR are illegal for this operation. All participating B.IOT bindings MUST carry the same PE_MASK; each selected PE executes independently, while PE_MASK=0000 is a strict no-op before source reads, destination allocation, or faults.

LB0 specifies ValidCol and MUST resolve to a nonzero 16-bit value. LB1 specifies ValidRow; omission defaults it to one. LB2 specifies physical Col; omission defaults it to ValidCol. The resolved physical row count is derived from destination capacity, Col, and DataType. ValidRow MUST NOT exceed physical rows and ValidCol MUST NOT exceed Col. Both sources and the destination MUST have matching physical rows, physical columns, valid rows, valid columns, row-major layout, and DataType.

The TADD DataType set is exactly FP64, FP32, TF32, HF32, FP16, BF16, E4M3, E5M2, S64, S32, S16, S8, U64, U32, U16, and U8. Every other DataType encoding is unsupported by TADD and MUST reject before effects. The selected numeric profile defines addition, exceptional values, overflow, and its fixed default rounding behavior for each supported type. TADD does not consume CMode, Sat, Canonicalize, secondary DataType, RMode, or Layout; any explicit nondefault value in those fields is illegal.

PadValueOrByteId is the only applicable B.DATR field and follows Decision 056 in ADR-0080. The valid source rectangles MUST be defined before any effect. Descriptor, schema, mask, field, dimension, allocation, and source-definedness checks all complete before source snapshots or destination publication.

Decision 058: TSUB is ordered Local VEC subtraction with the binary Tile schema

TSUB is selected by TEPL carrier Mode=0, Function=1. It reads an ordered left Local source and right Local source, and writes one explicit new Local destination. Within ValidRow x ValidCol, each destination element is the selected numeric profile's left - right result. Operand order MUST NOT be commuted. The numeric profile defines floating exceptional values, integer overflow and underflow, and the fixed default rounding behavior for each supported DataType.

The block schema, dimensions, allocation, Local-only restriction, equal PE_MASK rule, zero-mask strict no-op, source persistence, destination rename, preflight, snapshot, and atomic publication rules are the same as the closed binary VEC schema defined for TADD: LB0 is required nonzero ValidCol, omitted LB1 gives ValidRow=1, omitted LB2 gives Col=ValidCol, and physical rows are derived from capacity, Col, and DataType. Both sources and the destination MUST match in physical and valid shape, row-major layout, and DataType. All source elements required by the valid rectangle MUST be defined.

The TSUB DataType set is exactly FP64, FP32, TF32, HF32, FP16, BF16, E4M3, E5M2, S64, S32, S16, S8, U64, U32, U16, and U8. Every other DataType encoding is unsupported by TSUB and MUST reject before effects. PadValueOrByteId is the only applicable B.DATR field: omission selects Null, explicit 00 selects Zero, 01 selects Max, 10 selects Min, and 11 selects Null. The selected padding rule applies to every physical destination element outside the valid rectangle. CMode, Sat, Canonicalize, secondary DataType, RMode, and Layout are not consumed, and explicit nondefault values are illegal.

Both source payloads are snapshotted after complete preflight. Either source MAY alias the destination with read-old/write-new behavior, and both sources MAY name the same Tile. The complete valid result plus padding definedness is published as one destination commit; any rejection leaves all descriptors, payloads, and allocation state unchanged.

Decision 059: TMUL is Local VEC elementwise multiplication

TMUL is selected by TEPL carrier Mode=0, Function=2. It reads two Local source Tiles and writes one explicit new Local destination. Within ValidRow x ValidCol, each destination element is the selected numeric profile's product of the corresponding source elements. The profile defines floating exceptional values, integer overflow, and its fixed default rounding behavior.

TMUL uses the same closed Local binary VEC block schema, dimension defaults, descriptor matching, allocation, mask, source persistence, rename, preflight, snapshot, and atomic publication rules as TADD. LB0 is required nonzero ValidCol; omitted LB1 gives ValidRow=1; omitted LB2 gives Col=ValidCol; and physical rows are derived from capacity, Col, and DataType. Both sources and destination MUST match in physical and valid shape, row-major layout, and DataType, and every source element used by the valid rectangle MUST be defined.

The TMUL DataType set is exactly FP64, FP32, TF32, HF32, FP16, BF16, E4M3, E5M2, S64, S32, S16, S8, U64, U32, U16, and U8. Other DataType encodings are unsupported by TMUL and reject before effects. PadValueOrByteId is the only applicable B.DATR field and applies to every physical destination element outside the valid rectangle: omission selects Null, explicit 00 selects Zero, 01 selects Max, 10 selects Min, and 11 selects Null. Explicit nondefault CMode, Sat, Canonicalize, secondary DataType, RMode, or Layout is illegal.

Both source payloads are snapshotted after complete preflight. Either source MAY alias the destination with read-old/write-new behavior, and both sources MAY name the same Tile. PE_MASK=0000 is a strict no-op before reads, allocation, or faults. An executing block publishes the complete valid result and padding definedness as one destination commit; rejection has no architectural effect.

Decision 060: TDIV is SFU elementwise division with type-specific zero handling

TDIV retains the unchanged TEPL carrier Mode=0, Function=3, but its semantic engine is SFU because division requires complex execution hardware. Canonical block assembly uses BSTART.SFU TDIV, DataType; the raw encoding is unchanged and BSTART.TEPL remains only the carrier-compatible spelling.

TDIV reads an ordered Local numerator Tile and denominator Tile and writes one explicit new Local destination. Within ValidRow x ValidCol, each destination element is the selected numeric profile's quotient numerator / denominator. Signed integer DataTypes use signed division, unsigned integer DataTypes use unsigned division, and floating DataTypes use their floating division profile. Integer division by zero in any element of the valid denominator rectangle causes Illegal Block Exception before source snapshots, allocation publication, or destination effects. Floating division by positive or negative zero is not a block-legality failure; its result and numeric status follow the selected floating profile. Denominator elements outside the valid rectangle are not read and do not participate in zero checking.

TDIV uses the closed Local binary Tile schema: required nonzero LB0=ValidCol, omitted LB1 default ValidRow=1, omitted LB2 default Col=ValidCol, capacity-derived physical rows, equal source/destination physical and valid shape, row-major layout, DataType, equal PE_MASK, and zero-mask strict no-op. Both valid source rectangles MUST be defined before effects. The TDIV DataType set is exactly FP64, FP32, TF32, HF32, FP16, BF16, E4M3, E5M2, S64, S32, S16, S8, U64, U32, U16, and U8; every other type is unsupported and rejects before effects.

PadValueOrByteId is the only applicable B.DATR field. Omission selects Null; explicit 00 selects Zero, 01 selects Max, 10 selects Min, and 11 selects Null. Padding applies only outside the valid destination rectangle. CMode, Sat, Canonicalize, secondary DataType, RMode, and Layout are not consumed and explicit nondefault values are illegal; the numeric profile owns TDIV's fixed rounding and exceptional-value behavior.

All legality and integer zero checks complete before both source payloads are snapshotted. Either source MAY alias the destination with read-old/write-new behavior. The valid quotient results and padding definedness publish in one destination commit; any exception leaves descriptors, payloads, and allocation state unchanged.

Decision 061: TREM is SFU modulo with a divisor-signed result

TREM retains the unchanged TEPL carrier Mode=0, Function=4, but its semantic engine is SFU. Canonical block assembly uses BSTART.SFU TREM, DataType; no raw encoding changes.

TREM reads an ordered Local dividend Tile and divisor Tile and writes one explicit new Local destination. Within ValidRow x ValidCol, it computes modulo rather than a truncation-toward-zero language remainder. For signed integer DataTypes, q=floor(dividend/divisor) and result=dividend-q*divisor, so every nonzero result has the divisor's sign and its magnitude is smaller than the divisor's magnitude. Unsigned DataTypes use ordinary unsigned remainder. Floating DataTypes use the selected floating modulo profile with the same divisor-signed result rule.

An integer zero divisor in any valid element causes Illegal Block Exception before effects. Floating modulo by positive or negative zero is not a block-legality rejection; its result and numeric status follow the floating profile. Elements outside the valid divisor rectangle are not read or checked. The profile also defines signed overflow boundaries and floating exceptional values.

TREM uses the same closed Local binary Tile schema and defaults as TDIV: required nonzero LB0=ValidCol, omitted LB1 gives ValidRow=1, omitted LB2 gives Col=ValidCol, physical rows derive from capacity, and both sources and destination match in physical shape, valid shape, row-major layout, and DataType. Both source valid rectangles MUST be defined. The exact TREM DataType set is FP64, FP32, TF32, HF32, FP16, BF16, E4M3, E5M2, S64, S32, S16, S8, U64, U32, U16, and U8; other types reject before effects.

PadValueOrByteId is the only applicable B.DATR field, with omission Null, explicit 00 Zero, 01 Max, 10 Min, and 11 Null. Explicit nondefault CMode, Sat, Canonicalize, secondary DataType, RMode, or Layout is illegal. Equal masks, zero-mask no-op, source persistence, destination rename, complete preflight, source snapshots, read-old/write-new aliasing, padding definedness, atomic commit, and rollback follow the binary Tile contract.

Decision 062: TAND is integer-only Local VEC bitwise AND

TAND is selected by TEPL carrier Mode=0, Function=6. It reads two ordered Local source Tiles and writes one explicit renamed Local destination. Within ValidRow x ValidCol, every destination element is the raw bitwise AND of the corresponding left and right integer elements. Signedness does not change the bit operation.

The exact supported DataType set is S64, S32, S16, S8, U64, U32, U16, and U8. Floating, compact floating, exponent-only, and packed integer encodings are unsupported by TAND and reject before effects. TAND uses the closed Local binary VEC schema: nonzero LB0=ValidCol is required; omitted LB1 gives ValidRow=1; omitted LB2 gives Col=ValidCol; and physical rows derive from capacity, Col, and DataType. Both sources and destination MUST match in physical and valid shape, row-major layout, and DataType, and every source element read by the valid rectangle MUST be defined.

PadValueOrByteId is the only applicable B.DATR field. Omission selects Null; explicit 00 selects Zero, 01 selects Max, 10 selects Min, and 11 selects Null. Max and Min use the selected integer DataType's numeric maximum and minimum. The selector applies to every physical destination element outside the valid rectangle. Explicit nondefault CMode, Sat, Canonicalize, secondary DataType, RMode, or Layout is illegal.

TAND takes no B.IOR or B.IOS, requires equal source and destination PE_MASK values, and treats PE_MASK=0000 as a strict no-op before reads, allocation, or faults. Both source payloads are snapshotted only after complete preflight. Sources MAY be identical and either source MAY alias the destination with read-old/write-new behavior. The valid bitwise result plus padding definedness publishes as one destination commit; rejection leaves descriptors, payloads, and allocation state unchanged.

Decision 063: TOR is integer-only Local VEC bitwise OR

TOR is selected by TEPL carrier Mode=0, Function=7. It reads two ordered Local source Tiles and writes one explicit renamed Local destination. Within ValidRow x ValidCol, each destination element is the raw bitwise OR of the corresponding left and right integer elements. Signedness does not change the bit operation.

The exact supported DataType set is S64, S32, S16, S8, U64, U32, U16, and U8. Every floating, compact floating, exponent-only, and packed integer encoding is unsupported by TOR and rejects before effects. TOR uses the closed Local binary VEC schema: LB0=ValidCol is required and nonzero; omitted LB1 gives ValidRow=1; omitted LB2 gives Col=ValidCol; and physical rows derive from capacity, Col, and DataType. Both sources and the destination MUST match in physical and valid shape, row-major layout, and DataType, and all valid source elements MUST be defined.

PadValueOrByteId is the only applicable B.DATR field. Omission selects Null; explicit 00 selects Zero, 01 selects Max, 10 selects Min, and 11 selects Null. Max and Min use the selected integer DataType's numeric maximum and minimum. Padding applies outside the valid destination rectangle. Explicit nondefault CMode, Sat, Canonicalize, secondary DataType, RMode, or Layout is illegal.

TOR takes no B.IOR or B.IOS, requires equal source and destination PE_MASK values, and treats PE_MASK=0000 as a strict no-op before reads, allocation, or faults. Both source payloads are snapshotted after complete preflight. Sources MAY be identical and either source MAY alias the destination with read-old/write-new behavior. Valid results plus padding definedness publish as one destination commit; rejection leaves architectural state unchanged.

Decision 064: TXOR is integer-only Local VEC bitwise XOR

TXOR is selected by TEPL carrier Mode=0, Function=8. It reads two ordered Local source Tiles and writes one explicit renamed Local destination. Within ValidRow x ValidCol, each destination element is the raw bitwise XOR of the corresponding left and right integer elements. Signedness does not affect the bit operation.

TXOR supports exactly S64, S32, S16, S8, U64, U32, U16, and U8. Floating, compact floating, exponent-only, and packed integer encodings are unsupported and reject before effects. The closed Local binary VEC schema requires nonzero LB0=ValidCol; omitted LB1 gives ValidRow=1; omitted LB2 gives Col=ValidCol; and physical rows derive from capacity, Col, and DataType. Both sources and destination MUST match in physical and valid shape, row-major layout, and DataType, and every valid source element MUST be defined.

PadValueOrByteId is the only applicable B.DATR field. Omission selects Null; explicit 00 selects Zero, 01 selects Max, 10 selects Min, and 11 selects Null, using the selected integer DataType's numeric bounds. Explicit nondefault CMode, Sat, Canonicalize, secondary DataType, RMode, or Layout is illegal.

TXOR takes no B.IOR or B.IOS, requires equal source and destination PE_MASK values, and treats PE_MASK=0000 as a strict no-op before reads, allocation, or faults. Both sources persist and are snapshotted after complete preflight. They MAY be identical and either MAY alias the destination with read-old/write-new behavior. Valid XOR results plus padding definedness publish atomically; rejection leaves architectural state unchanged.

Decision 065: TSHL uses element-width-masked logical left shifts

TSHL is selected by TEPL carrier Mode=0, Function=9. It reads a Local value Tile as source0 and a Local shift-count Tile as source1, and writes one explicit renamed Local destination. For an element width W of 8, 16, 32, or 64 bits, the shift count is the unsigned value of the low log2(W) bits of the corresponding source1 element. The destination element is the low W bits of source0 << count; verification-carrier bits above W are zero. Signedness does not alter this raw left-shift rule.

TSHL supports exactly S64, S32, S16, S8, U64, U32, U16, and U8. Other DataTypes reject before effects. Its closed Local binary VEC schema requires nonzero LB0=ValidCol; omitted LB1 gives ValidRow=1; omitted LB2 gives Col=ValidCol; and physical rows derive from capacity, Col, and DataType. Sources and destination MUST match in physical and valid shape, row-major layout, and DataType, and all valid source elements MUST be defined.

PadValueOrByteId is the only applicable B.DATR field. Omission selects Null; explicit 00 selects Zero, 01 selects Max, 10 selects Min, and 11 selects Null, using the selected integer type's numeric bounds. Explicit nondefault CMode, Sat, Canonicalize, secondary DataType, RMode, or Layout is illegal.

TSHL takes no B.IOR or B.IOS, requires equal PE_MASK values, and mask zero is a strict no-op. Sources persist, may be identical, and may alias the destination. Both payloads are snapshotted after complete preflight; narrowed valid results plus padding definedness publish atomically, and rejection has no architectural effect.

Decision 066: TSHR follows integer signedness at the element width

TSHR is selected by TEPL carrier Mode=0, Function=10. It reads a Local value Tile as source0 and a Local shift-count Tile as source1, and writes one explicit renamed Local destination. For element width W, the unsigned shift count is selected by the low log2(W) bits of source1. Signed DataTypes use arithmetic right shift with sign fill; unsigned DataTypes use logical right shift with zero fill. The low W result bits are stored and verification- carrier bits above W are zero.

TSHR supports exactly S64, S32, S16, S8, U64, U32, U16, and U8. Other types reject before effects. The closed Local binary VEC schema requires nonzero LB0=ValidCol; omitted LB1 gives ValidRow=1; omitted LB2 gives Col=ValidCol; and physical rows derive from capacity, Col, and DataType. Sources and destination MUST match physical shape, valid shape, row-major layout, and DataType, and all valid source elements MUST be defined.

PadValueOrByteId is the only applicable B.DATR field. Omission selects Null; explicit 00 selects Zero, 01 selects Max, 10 selects Min, and 11 selects Null, using the selected integer type's numeric bounds. Explicit nondefault CMode, Sat, Canonicalize, secondary DataType, RMode, or Layout is illegal.

TSHR takes no B.IOR or B.IOS, requires equal PE_MASK values, and mask zero is a strict no-op. Both sources persist, may be identical, and may alias the destination. Payloads are snapshotted after complete preflight; the typed shift results plus padding definedness publish atomically, and rejection has no architectural effect.

Decision 067: TMAX is typed maximum with deterministic floating ties

TMAX is selected by TEPL carrier Mode=0, Function=11. It reads two ordered Local source Tiles and writes one explicit renamed Local destination. Signed integer DataTypes use signed numeric ordering, unsigned integer DataTypes use unsigned numeric ordering, and floating DataTypes use the selected numeric profile's maximum operation.

TMAX supports exactly FP64, FP32, TF32, HF32, FP16, BF16, E4M3, E5M2, S64, S32, S16, S8, U64, U32, U16, and U8. Other types reject before effects. For supported floating types, one NaN selects the non-NaN operand without changing its encoding; two NaNs produce the destination canonical NaN; signaling NaN reports the selected profile's invalid condition; equal-sign zero preserves that sign; and a mixed-sign zero tie produces positive zero. Operand order does not change these results. Source encodings invalid for the selected operation/profile reject before effects.

The closed Local binary VEC schema requires nonzero LB0=ValidCol; omitted LB1 gives ValidRow=1; omitted LB2 gives Col=ValidCol; and physical rows derive from capacity, Col, and DataType. Both sources and destination MUST match physical and valid shape, row-major layout, and DataType, and all valid source elements MUST be defined.

PadValueOrByteId is the only applicable B.DATR field. Omission selects Null; explicit 00 selects Zero, 01 selects Max, 10 selects Min, and 11 selects Null. Explicit nondefault CMode, Sat, Canonicalize, secondary DataType, RMode, or Layout is illegal.

TMAX takes no B.IOR or B.IOS, requires equal PE_MASK values, and mask zero is a strict no-op. Sources persist, may be identical, and may alias the destination. Payloads are snapshotted after all legality and value-encoding checks; the complete result plus padding definedness publishes atomically, and rejection has no architectural effect.

Decision 126: TEXTRACT uses two optional private-GPR offsets

TEXTRACT is selected by TEPL carrier Mode=3, Function=2 and executes on the SFU engine. It reads one Local source Tile and writes one explicit newly allocated Local destination. The row offset is the unsigned low sixteen bits of the selected PE's private B.IOR.RegSrc0; the column offset is the unsigned low sixteen bits of B.IOR.RegSrc1. An omitted B.IOR supplies zero for both offsets. When B.IOR is present, RegSrc2 and RegDst MUST be zero.

B.DIM never supplies the offsets. Required nonzero LB0 supplies destination ValidCol; omitted LB1 gives destination ValidRow=1; omitted LB2 gives destination physical Col=ValidCol; destination physical rows derive from capacity, Col, and DataType. Before effects, row_offset + ValidRow MUST be at most the source ValidRow and column_offset + ValidCol MUST be at most the source ValidCol.

For every destination valid element [r,c], the result is source element [row_offset+r,column_offset+c]. The source and destination use the same DataType. Every assigned Tile DataType except HiF4X2 is supported; globally reserved encodings and HiF4X2 reject before effects. The selected assigned Layout transformation governs destination placement. PadValueOrByteId applies to destination physical elements outside its valid rectangle; omission selects Null and explicit values select Zero, Max, Min, or Null.

TEXTRACT has no architectural ReLU, quantization, Fix-pipe, auxiliary Tile, or target-specific overload. It is Local-only; source and destination use the same PE_MASK, with mask zero a strict no-op. The source valid elements needed by the extraction window MUST be defined. Complete preflight precedes a source snapshot, and destination contents, padding definedness, and descriptor publish atomically. The source persists and rejection has no architectural effect.

Decision 127: TINSERT explicitly reads the old destination and writes a renamed result

TINSERT is selected by TEPL carrier Mode=3, Function=3 and executes on the SFU engine. Its architectural Tile operands are an old-destination source, an insertion source, and one explicit newly allocated destination result. The result begins as an exact snapshot of the old destination, after which the insertion source valid rectangle replaces the result window beginning at the selected row and column offsets. The old destination and insertion source both persist.

The row offset is the unsigned low sixteen bits of the selected PE's private B.IOR.RegSrc0; the column offset is the unsigned low sixteen bits of B.IOR.RegSrc1. An omitted B.IOR supplies zero for both. When B.IOR is present, RegSrc2 and RegDst MUST be zero. B.DIM describes the result geometry and MUST match the old-destination physical and valid shape; it never supplies the offsets.

The old destination, insertion source, and result use one DataType. Every assigned Tile DataType except HiF4X2 is supported. Before effects, row_offset + insertion.ValidRow MUST be at most result.ValidRow and column_offset + insertion.ValidCol MUST be at most result.ValidCol. Every insertion-source valid element MUST be defined. Every result element not covered by the inserted rectangle, including its definedness, is preserved from the old destination. PadValueOrByteId is not applicable because no uncovered region is synthesized. An assigned Layout value may select the defined source-to-result layout transformation; reserved values reject.

TINSERT has no architectural ReLU, quantization, Fix-pipe, auxiliary Tile, or target-specific mode overload. It is Local-only. All three bindings use the same PE_MASK; mask zero is a strict no-op. Complete preflight precedes both source snapshots. The copied old state, inserted window, definedness, and new destination descriptor publish atomically. Legal aliasing always observes old source values; rejection has no architectural effect.

Decision 128: TIMG2COL reads a feature-map descriptor and two logical matrix offsets

TIMG2COL is selected by TEPL carrier Mode=3, Function=4 and executes on the SFU engine. It reads one Local Matrix-location feature-map Tile and writes one explicit newly allocated Local Matrix-location destination in the standard Left-input representation. The source persists.

The source Tile carries a complete architectural feature-map descriptor. Its layout is either NC1HWC0, with dimensions N,C1,H,W,C0, or NDC1HWC0, with dimensions N,D,C1,H,W,C0. Every dimension is nonzero. The descriptor also carries nonzero filter height and width, nonzero row and column strides, nonzero row and column dilations, nonnegative left, right, top, and bottom padding, a logical channel count no greater than C1*C0, and one typed padding value. A descriptor requesting transposed IMG2COL is not assigned by this PTO form and is illegal. The descriptor MUST be valid before execution; TIMG2COL neither creates nor modifies it.

The destination row start posM is the unsigned low sixteen bits of the selected PE's private B.IOR.RegSrc0; the destination-column start posK is the unsigned low sixteen bits of B.IOR.RegSrc1. Omitted B.IOR supplies zero for both. When present, RegSrc2 and RegDst MUST be zero. Required nonzero B.DIM.LB0 supplies destination ValidCol; omitted LB1 supplies destination ValidRow=1; omitted LB2 supplies destination physical Col=ValidCol; physical rows derive from capacity, Col, and DataType. B.DIM never supplies filter, stride, dilation, padding, posM, or posK.

Let outH = floor((H + padTop + padBottom - dilationH*(filterH-1) - 1) / strideH) + 1 and define outW analogously. Both values MUST be positive. The logical im2col row extent is N*D*outH*outW, where D=1 for NC1HWC0; the packed column extent is C1*filterH*filterW*C0. The complete destination rectangle beginning at (posM,posK) MUST fit those extents.

For result element [r,c], m=posM+r selects n, d, outRow, and outCol in that order. k=posK+c selects c1, kernelRow, kernelCol, and c0 from the packed column order. The corresponding source coordinates are inputRow=outRow*strideH + kernelRow*dilationH - padTop and inputCol=outCol*strideW + kernelCol*dilationW - padLeft. An out-of-range input coordinate or a packed channel c1*C0+c0 outside the logical channel count yields the descriptor's padding value; otherwise the exact source element is copied. Only actually referenced in-range source elements must be defined.

Source and destination use the same DataType. This form supports exactly FP32, FP16, BF16, S32, S16, S8, U32, U16, and U8; every other assigned or reserved DataType rejects before effects. The feature-map layout and padding value come only from the source descriptor. B.DATR may be omitted; it supplies no secondary DataType, layout conversion, numeric mode, or padding override, and every nondefault contribution is illegal.

TIMG2COL is Local-only and takes no B.IOS. Source and destination use the same PE_MASK; nonzero partial masks are legal and mask zero is a strict no-op. Complete descriptor, range, type, capacity, definedness, and allocation preflight precedes a source snapshot. The complete destination payload, padding definedness, and descriptor publish atomically, and rejection has no architectural effect.

Decision 068: TMIN is typed minimum with deterministic floating ties

TMIN is selected by TEPL carrier Mode=0, Function=12. It reads two ordered Local source Tiles and writes one explicit renamed Local destination. Signed integer DataTypes use signed numeric ordering, unsigned integer DataTypes use unsigned numeric ordering, and floating DataTypes use the selected numeric profile's minimum operation.

TMIN supports exactly FP64, FP32, TF32, HF32, FP16, BF16, E4M3, E5M2, S64, S32, S16, S8, U64, U32, U16, and U8. Other types reject before effects. For supported floating types, one NaN selects the non-NaN operand without changing its encoding; two NaNs produce the destination canonical NaN; signaling NaN reports the selected profile's invalid condition; equal-sign zero preserves that sign; and a mixed-sign zero tie produces negative zero. Operand order does not change these results. Source encodings invalid for the selected operation/profile reject before effects.

The closed Local binary VEC schema requires nonzero LB0=ValidCol; omitted LB1 gives ValidRow=1; omitted LB2 gives Col=ValidCol; and physical rows derive from capacity, Col, and DataType. Both sources and destination MUST match physical and valid shape, row-major layout, and DataType, and all valid source elements MUST be defined.

PadValueOrByteId is the only applicable B.DATR field. Omission selects Null; explicit 00 selects Zero, 01 selects Max, 10 selects Min, and 11 selects Null. Explicit nondefault CMode, Sat, Canonicalize, secondary DataType, RMode, or Layout is illegal.

TMIN takes no B.IOR or B.IOS, requires equal PE_MASK values, and mask zero is a strict no-op. Sources persist, may be identical, and may alias the destination. Payloads are snapshotted after all legality and value-encoding checks; the complete result plus padding definedness publishes atomically, and rejection has no architectural effect.

Decision 069: TCMP produces a packed one-bit Local predicate Tile

TCMP is selected by TEPL carrier Mode=0, Function=13. It reads two ordered Local numeric source Tiles and writes one explicit renamed Local predicate destination. B.DATR.CMode maps 0=EQ, 1=NE, 2=LT, 3=GT, 4=LE, and 5=GE; encodings 6 and 7 are reserved. Omission retains encoded zero and therefore selects EQ.

Each logical comparison produces exactly one predicate bit. Logical element index i occupies bit i mod 8 of byte floor(i/8), so lower logical indices occupy lower bit positions. The destination is predicate-kind Tile storage, not a numeric DataType, and retains the sources' logical Row, Col, ValidRow, and ValidCol. Its allocated capacity MUST hold at least ceil(Row*Col/8) bytes.

TCMP supports input types FP64, FP32, TF32, HF32, FP16, BF16, E4M3, E5M2, S64, S32, S16, S8, U64, U32, U16, and U8. Signed and unsigned ordered comparisons use their respective numeric ordering; floating comparisons use the selected profile. With either floating operand NaN, EQ/LT/LE/GT/GE produce zero and NE produces one; signaling NaN also reports the selected profile's invalid condition. Positive and negative zero compare equal, LE and GE are true, and strict relations are false. Source encodings invalid for the selected operation/profile reject before effects.

Source dimensions use required nonzero LB0=ValidCol, omitted LB1 default ValidRow=1, omitted LB2 default Col=ValidCol, and capacity-derived rows. Both sources MUST match physical and valid shape, row-major layout, and DataType. CMode and PadValueOrByteId are the only applicable B.DATR fields. Pad omission is Null; Zero and Min write zero predicate bits outside the valid rectangle; Max writes one bits; and Null leaves those bits undefined. Explicit nondefault Sat, Canonicalize, secondary DataType, RMode, or Layout is illegal.

TCMP takes no B.IOR or B.IOS, requires equal source and destination PE_MASK values, and mask zero is a strict no-op. Sources persist and their valid regions MUST be defined. Complete preflight precedes source snapshots; the packed predicate payload, padding definedness, and destination descriptor publish atomically, and rejection has no architectural effect.

Decision 070: TABS is typed elementwise absolute value

TABS is selected by TEPL carrier Mode=0, Function=15. It reads one Local source Tile and writes one explicit renamed Local destination. For signed integer DataTypes, each result is the element-width two's-complement absolute value: a negative input is negated modulo its width, so the most-negative value retains its bit pattern. For unsigned integer DataTypes, the operation is the identity. For floating DataTypes, TABS clears only the sign bit; this maps negative zero to positive zero and preserves infinity, NaN class, and NaN payload without raising an invalid condition solely because the operand is a signaling NaN. Verification-carrier bits above the element width are zero.

TABS supports exactly FP64, FP32, TF32, HF32, FP16, BF16, E4M3, E5M2, S64, S32, S16, S8, U64, U32, U16, and U8. Other DataTypes reject before effects. Its closed Local unary VEC schema requires nonzero LB0=ValidCol; omitted LB1 gives ValidRow=1; omitted LB2 gives Col=ValidCol; and physical rows derive from capacity, Col, and DataType. Source and destination MUST match in physical and valid shape, row-major layout, and DataType, and every valid source element MUST be defined.

PadValueOrByteId is the only applicable B.DATR field. Omission selects Null; explicit 00 selects Zero, 01 selects Max, 10 selects Min, and 11 selects Null, using the selected DataType's values. Explicit nondefault CMode, Sat, Canonicalize, secondary DataType, RMode, or Layout is illegal.

TABS takes no B.IOR or B.IOS, requires equal source and destination PE_MASK values, and treats mask zero as a strict no-op before reads, allocation, or faults. The source persists and MAY alias the destination. After complete preflight, the source payload is snapshotted and the typed absolute-value result plus padding definedness publishes atomically. Rejection leaves descriptors, payloads, and allocation state unchanged.

Decision 071: TNOT complements only the selected integer element width

TNOT is selected by TEPL carrier Mode=0, Function=16. It reads one Local source Tile and writes one explicit renamed Local destination. For an element width W of 8, 16, 32, or 64 bits, each result is the low W bits of the bitwise complement of the corresponding source element. Signedness does not alter the operation. Verification-carrier bits above W are zero.

TNOT supports exactly S64, S32, S16, S8, U64, U32, U16, and U8. Every floating, compact floating, exponent-only, and packed integer DataType is unsupported and rejects before effects. Its closed Local unary VEC schema requires nonzero LB0=ValidCol; omitted LB1 gives ValidRow=1; omitted LB2 gives Col=ValidCol; and physical rows derive from capacity, Col, and DataType. Source and destination MUST match in physical and valid shape, row-major layout, and DataType, and every valid source element MUST be defined.

PadValueOrByteId is the only applicable B.DATR field. Omission selects Null; explicit 00 selects Zero, 01 selects Max, 10 selects Min, and 11 selects Null, using the selected integer DataType's numeric bounds. Explicit nondefault CMode, Sat, Canonicalize, secondary DataType, RMode, or Layout is illegal.

TNOT takes no B.IOR or B.IOS, requires equal source and destination PE_MASK values, and mask zero is a strict no-op. The source persists and MAY alias the destination. Complete preflight precedes the source snapshot; the width-limited result plus padding definedness publishes atomically, and rejection has no architectural effect.

Decision 072: TNEG negates at the selected numeric element width

TNEG is selected by TEPL carrier Mode=0, Function=17. It reads one Local source Tile and writes one explicit renamed Local destination. For signed and unsigned integer DataTypes, each result is 0 - source modulo the selected 8, 16, 32, or 64-bit element width; the most-negative signed value therefore retains its bit pattern. For floating DataTypes, TNEG toggles only the sign bit, preserving infinity, NaN class, and NaN payload without raising an invalid condition solely because the operand is a signaling NaN. Positive and negative zero exchange encodings. Verification-carrier bits above the element width are zero.

TNEG supports exactly FP64, FP32, TF32, HF32, FP16, BF16, E4M3, E5M2, S64, S32, S16, S8, U64, U32, U16, and U8. Other DataTypes reject before effects. Its closed Local unary VEC schema requires nonzero LB0=ValidCol; omitted LB1 gives ValidRow=1; omitted LB2 gives Col=ValidCol; and physical rows derive from capacity, Col, and DataType. Source and destination MUST match in physical and valid shape, row-major layout, and DataType, and every valid source element MUST be defined.

PadValueOrByteId is the only applicable B.DATR field. Omission selects Null; explicit 00 selects Zero, 01 selects Max, 10 selects Min, and 11 selects Null. Explicit nondefault CMode, Sat, Canonicalize, secondary DataType, RMode, or Layout is illegal.

TNEG takes no B.IOR or B.IOS, requires equal source and destination PE_MASK values, and mask zero is a strict no-op. The source persists and MAY alias the destination. Complete preflight precedes the source snapshot; the typed result plus padding definedness publishes atomically, and rejection has no architectural effect.

Decision 073: TEXP is floating-only same-type natural exponential

TEXP is selected by TEPL carrier Mode=0, Function=18 and executes on the SFU engine without changing the TEPL carrier encoding. It reads one Local floating source Tile and writes one explicit renamed Local destination of the same DataType. Each valid destination element is the selected numeric profile's same-type natural exponential exp(source). The profile owns finite approximation accuracy, rounding, overflow, underflow, inexact reporting, NaN propagation, and canonical result requirements.

Independently of profile approximation, exp(+0) and exp(-0) are positive one, exp(+infinity) is positive infinity, and exp(-infinity) is positive zero. A quiet NaN produces the profile's quiet-NaN result; a signaling NaN also reports the profile invalid condition and produces a quiet NaN.

TEXP supports exactly FP64, FP32, TF32, HF32, FP16, BF16, E4M3, and E5M2. Integer, exponent-only, other compact floating, and packed DataTypes reject before effects. Its closed Local unary SFU schema requires nonzero LB0=ValidCol; omitted LB1 gives ValidRow=1; omitted LB2 gives Col=ValidCol; and physical rows derive from capacity, Col, and DataType. Source and destination MUST match in physical and valid shape, row-major layout, and DataType, and every valid source element MUST be defined.

PadValueOrByteId is the only applicable B.DATR field. Omission selects Null; explicit 00 selects Zero, 01 selects Max, 10 selects Min, and 11 selects Null. Explicit nondefault CMode, Sat, Canonicalize, secondary DataType, RMode, or Layout is illegal; TEXP uses the selected profile's fixed/default rounding behavior.

TEXP takes no B.IOR or B.IOS, requires equal source and destination PE_MASK values, and mask zero is a strict no-op. The source persists and MAY alias the destination. Complete preflight precedes source snapshot and SFU evaluation; the result, numeric status, padding definedness, and destination descriptor publish atomically. Rejection has no architectural effect.

Decision 074: TLOG is floating-only same-type natural logarithm

TLOG is selected by TEPL carrier Mode=0, Function=19 and executes on the SFU engine without changing the TEPL carrier encoding. It reads one Local floating source Tile and writes one explicit renamed Local destination of the same DataType. Each valid destination element is the selected numeric profile's same-type natural logarithm log(source). The profile owns finite approximation accuracy, rounding, underflow, inexact reporting, NaN propagation, and canonical result requirements.

Independently of profile approximation, log(+1) is positive zero; log(+0) and log(-0) are negative infinity and report divide-by-zero; log(+infinity) is positive infinity; and every negative finite nonzero value and negative infinity produce a quiet NaN and report invalid. A quiet NaN produces the profile's quiet-NaN result; a signaling NaN additionally reports invalid and produces a quiet NaN.

E4M3 does not encode infinity. TLOG does not admit saturation, so an E4M3 positive or negative zero produces the canonical quiet NaN 0x7F and reports DZ without reporting OF.

TLOG supports exactly FP64, FP32, TF32, HF32, FP16, BF16, E4M3, and E5M2. Integer, exponent-only, other compact floating, and packed DataTypes reject before effects. Its closed Local unary SFU schema requires nonzero LB0=ValidCol; omitted LB1 gives ValidRow=1; omitted LB2 gives Col=ValidCol; and physical rows derive from capacity, Col, and DataType. Source and destination MUST match in physical and valid shape, row-major layout, and DataType, and every valid source element MUST be defined.

PadValueOrByteId is the only applicable B.DATR field. Omission selects Null; explicit 00 selects Zero, 01 selects Max, 10 selects Min, and 11 selects Null. Explicit nondefault CMode, Sat, Canonicalize, secondary DataType, RMode, or Layout is illegal; TLOG uses the selected profile's fixed/default rounding behavior.

TLOG takes no B.IOR or B.IOS, requires equal source and destination PE_MASK values, and mask zero is a strict no-op. The source persists and MAY alias the destination. Complete preflight precedes source snapshot and SFU evaluation; the result, numeric status, padding definedness, and destination descriptor publish atomically. Rejection has no architectural effect.

Decision 075: TRECIP is floating-only same-type reciprocal

TRECIP is selected by TEPL carrier Mode=0, Function=20 and executes on the SFU engine without changing the TEPL carrier encoding. It reads one Local floating source Tile and writes one explicit renamed Local destination of the same DataType. Each valid destination element is the selected numeric profile's same-type reciprocal 1.0/source. The profile owns finite approximation accuracy, rounding, overflow, underflow, inexact reporting, NaN propagation, and canonical result requirements.

Positive and negative zero produce positive and negative infinity respectively and report divide-by-zero; they do not make the instruction illegal. Positive and negative infinity produce positive and negative zero respectively. A quiet NaN produces the profile's quiet-NaN result; a signaling NaN additionally reports invalid and produces a quiet NaN.

E4M3 does not encode infinity. TRECIP does not admit saturation, so either E4M3 signed zero produces the canonical quiet NaN 0x7F and reports DZ without reporting OF.

TRECIP supports exactly FP64, FP32, TF32, HF32, FP16, BF16, E4M3, and E5M2. Integer, exponent-only, other compact floating, and packed DataTypes reject before effects. Its closed Local unary SFU schema requires nonzero LB0=ValidCol; omitted LB1 gives ValidRow=1; omitted LB2 gives Col=ValidCol; and physical rows derive from capacity, Col, and DataType. Source and destination MUST match in physical and valid shape, row-major layout, and DataType, and every valid source element MUST be defined.

PadValueOrByteId is the only applicable B.DATR field. Omission selects Null; explicit 00 selects Zero, 01 selects Max, 10 selects Min, and 11 selects Null. Explicit nondefault CMode, Sat, Canonicalize, secondary DataType, RMode, or Layout is illegal; TRECIP uses the selected profile's fixed/default rounding behavior.

TRECIP takes no B.IOR or B.IOS, requires equal source and destination PE_MASK values, and mask zero is a strict no-op. The source persists and MAY alias the destination. Complete preflight precedes source snapshot and SFU evaluation; the result, numeric status, padding definedness, and destination descriptor publish atomically. Rejection has no architectural effect.

Decision 076: TSQRT is floating-only same-type square root

TSQRT is selected by TEPL carrier Mode=0, Function=21 and executes on the SFU engine without changing the TEPL carrier encoding. It reads one Local floating source Tile and writes one explicit renamed Local destination of the same DataType. Each valid destination element is the selected numeric profile's same-type square root. The profile owns finite approximation accuracy, rounding, underflow, inexact reporting, NaN propagation, and canonical result requirements.

Square root preserves the sign of positive and negative zero, maps positive infinity to positive infinity, and maps every negative finite nonzero value and negative infinity to a quiet NaN while reporting invalid. A quiet NaN produces the profile's quiet-NaN result; a signaling NaN additionally reports invalid and produces a quiet NaN.

TSQRT supports exactly FP64, FP32, TF32, HF32, FP16, BF16, E4M3, and E5M2. Integer, exponent-only, other compact floating, and packed DataTypes reject before effects. Its closed Local unary SFU schema requires nonzero LB0=ValidCol; omitted LB1 gives ValidRow=1; omitted LB2 gives Col=ValidCol; and physical rows derive from capacity, Col, and DataType. Source and destination MUST match in physical and valid shape, row-major layout, and DataType, and every valid source element MUST be defined.

PadValueOrByteId is the only applicable B.DATR field. Omission selects Null; explicit 00 selects Zero, 01 selects Max, 10 selects Min, and 11 selects Null. Explicit nondefault CMode, Sat, Canonicalize, secondary DataType, RMode, or Layout is illegal; TSQRT uses the selected profile's fixed/default rounding behavior.

TSQRT takes no B.IOR or B.IOS, requires equal source and destination PE_MASK values, and mask zero is a strict no-op. The source persists and MAY alias the destination. Complete preflight precedes source snapshot and SFU evaluation; the result, numeric status, padding definedness, and destination descriptor publish atomically. Rejection has no architectural effect.

Decision 077: TRSQRT is floating-only same-type reciprocal square root

TRSQRT is selected by TEPL carrier Mode=0, Function=22 and executes on the SFU engine without changing the TEPL carrier encoding. It reads one Local floating source Tile and writes one explicit renamed Local destination of the same DataType. Each valid destination element is the selected numeric profile's same-type reciprocal square root 1.0/sqrt(source). The profile owns finite approximation accuracy, rounding, overflow, underflow, inexact reporting, NaN propagation, and canonical result requirements; the operation is one profile operation rather than two architecturally rounded instructions.

Positive and negative zero produce positive and negative infinity respectively and report divide-by-zero; they do not make the instruction illegal. Positive infinity produces positive zero. Every negative finite nonzero value and negative infinity produce a quiet NaN and report invalid. A quiet NaN produces the profile's quiet-NaN result; a signaling NaN additionally reports invalid and produces a quiet NaN.

E4M3 does not encode infinity. TRSQRT does not admit saturation, so either E4M3 signed zero produces the canonical quiet NaN 0x7F and reports DZ without reporting OF.

TRSQRT supports exactly FP64, FP32, TF32, HF32, FP16, BF16, E4M3, and E5M2. Integer, exponent-only, other compact floating, and packed DataTypes reject before effects. Its closed Local unary SFU schema requires nonzero LB0=ValidCol; omitted LB1 gives ValidRow=1; omitted LB2 gives Col=ValidCol; and physical rows derive from capacity, Col, and DataType. Source and destination MUST match in physical and valid shape, row-major layout, and DataType, and every valid source element MUST be defined.

PadValueOrByteId is the only applicable B.DATR field. Omission selects Null; explicit 00 selects Zero, 01 selects Max, 10 selects Min, and 11 selects Null. Explicit nondefault CMode, Sat, Canonicalize, secondary DataType, RMode, or Layout is illegal; TRSQRT uses the selected profile's fixed/default rounding behavior.

TRSQRT takes no B.IOR or B.IOS, requires equal source and destination PE_MASK values, and mask zero is a strict no-op. The source persists and MAY alias the destination. Complete preflight precedes source snapshot and SFU evaluation; the result, numeric status, padding definedness, and destination descriptor publish atomically. Rejection has no architectural effect.

Decision 078: TRELU is a same-type Local VEC rectifier

TRELU is selected by TEPL carrier Mode=0, Function=23 and executes on the VEC engine without changing the TEPL carrier encoding. It reads one Local source Tile and writes one explicit renamed Local destination of the same DataType. For a signed integer element, a negative value produces element-width zero and a nonnegative value is preserved. For an unsigned integer element, TRELU is the identity operation.

For a floating element, every negative finite value and negative infinity produce positive zero; positive finite values and positive infinity are preserved; and both positive and negative zero produce positive zero. A quiet NaN produces the selected numeric profile's quiet-NaN result. A signaling NaN also reports invalid and produces a quiet NaN. The selected profile owns NaN payload propagation or canonicalization details.

TRELU supports exactly FP64, FP32, TF32, HF32, FP16, BF16, E4M3, E5M2, S64, S32, S16, S8, U64, U32, U16, and U8. Exponent-only, other compact floating, packed, pointer, and every other DataType reject before effects. Its closed Local unary VEC schema requires nonzero LB0=ValidCol; omitted LB1 gives ValidRow=1; omitted LB2 gives Col=ValidCol; and physical rows derive from capacity, Col, and DataType. Source and destination MUST match in physical and valid shape, row-major layout, and DataType, and every valid source element MUST be defined.

PadValueOrByteId is the only applicable B.DATR field. Omission selects Null; explicit 00 selects Zero, 01 selects Max, 10 selects Min, and 11 selects Null. Explicit nondefault CMode, Sat, Canonicalize, secondary DataType, RMode, or Layout is illegal.

TRELU takes no B.IOR or B.IOS, requires equal source and destination PE_MASK values, and mask zero is a strict no-op. The source persists and MAY alias the destination. Complete preflight precedes source snapshot and VEC evaluation; the result, numeric status, padding definedness, and destination descriptor publish atomically. Rejection has no architectural effect.

Decision 079: TSEL consumes a packed one-bit predicate Tile

TSEL is selected by TEPL carrier Mode=0, Function=26 and executes on the VEC engine. It reads one Local predicate mask Tile and two Local numeric data Tiles, then writes one explicit renamed Local numeric destination. For logical element index i, mask bit i mod 8 of byte floor(i/8) selects the true source when one and the false source when zero. Lower logical indices occupy lower bit positions. The mask MUST use predicate-kind storage produced under the packed predicate contract; an ordinary numeric Tile is not a legal mask.

The two data sources and destination MUST have identical physical shape, logical shape, valid shape, row-major layout, and DataType. The mask has the same logical Row, Col, ValidRow, and ValidCol, uses packed predicate storage with capacity of at least ceil(Row*Col/8) bytes, and has every predicate bit in the valid region defined. Every valid element of both data sources MUST also be defined. Selection copies the chosen source element's encoding exactly; it performs no numeric conversion, rounding, saturation, NaN canonicalization, or floating-status update.

TSEL supports data sources and destination of exactly FP64, FP32, TF32, HF32, FP16, BF16, E4M3, E5M2, S64, S32, S16, S8, U64, U32, U16, and U8. Every other numeric DataType and every non-predicate mask reject before effects. Required nonzero LB0 supplies ValidCol; omitted LB1 gives ValidRow=1; omitted LB2 gives Col=ValidCol; and data Tile physical rows derive from capacity, Col, and DataType.

PadValueOrByteId is the only applicable B.DATR field. Omission selects Null; explicit 00 selects Zero, 01 selects Max, 10 selects Min, and 11 selects Null for destination elements outside the valid rectangle. Explicit nondefault CMode, Sat, Canonicalize, secondary DataType, RMode, or Layout is illegal.

TSEL takes no B.IOR or B.IOS. Every participating B.IOT binding MUST use the same PE_MASK, and mask zero is a strict no-op. All three sources persist; the two data sources MAY be identical and MAY alias the destination. Complete preflight precedes predicate and data-source snapshots. The selected payload, padding definedness, and destination descriptor publish atomically, and rejection has no architectural effect.

Decision 080: TCVT is the complete typed conversion and canonicalization boundary

TCVT is selected by TEPL carrier Mode=0, Function=27 and executes on the VEC engine. It reads one Local source Tile and writes one explicit renamed Local destination. The DataType selected by BSTART.VEC TCVT is the source type. An optional B.DATR.DataType is the destination type; when that field is omitted, the destination type inherits the source type. An explicitly encoded zero selects destination FP64 and never means inheritance.

Every assigned Tile DataType may be a TCVT source or destination: FP64, FP32, TF32, HF32, FP16, BF16, HiF8, E4M3, E5M2, E3M2, E2M3, E2M1X2, E1M2X2, E8M0, HiF4X2, S64, S32, S16, S8, S4X2, U64, U32, U16, U8, and U4X2. Globally reserved DataType codes reject before effects. HiF4X2 is supported only by TCVT; using it with another Tile operation is illegal unless a later architecture revision explicitly assigns that support.

The source and destination have equal logical Row, Col, ValidRow, and ValidCol, but their physical byte capacities and element packing follow their own DataTypes and layouts. Packed-X2 formats retain one logical element per nibble: even logical indices occupy the low nibble and odd logical indices occupy the high nibble of the same byte. Required nonzero LB0 supplies ValidCol; omitted LB1 gives ValidRow=1; omitted LB2 gives Col=ValidCol. Source and destination capacity MUST contain their complete physical representations, and every valid source element MUST be defined.

RMode code zero selects the operation default; code one explicitly selects RNE; codes two through seven select RTZ, RTM, RTP, RNA, RTO, and RHB respectively. The operation default is RTZ for floating-to-integer conversion and RNE for every other conversion that requires rounding. Sat omission or zero disables saturation; Sat=1 clamps an out-of-range finite result to the destination type's minimum or maximum before encoding. Without saturation, integer-to-integer narrowing is modulo the destination width; the selected numeric profile defines floating overflow, invalid, NaN, infinity, subnormal, inexact, and format-specific finite conversion results without leaving them implementation-defined.

Canonicalize=1 is legal only when the source carries the private CUBE output representation. It converts that representation into the standard public left-matrix Tile representation, including any DataType-dependent fractal merge or split, and requires Layout=NORM. A private CUBE source requires Canonicalize=1; an ordinary source requires Canonicalize=0.

With Canonicalize=0, Layout=NORM preserves logical row-major placement; each of the other twelve assigned Layout codes applies its assigned complete layout transformation. Every reserved Layout value rejects before effects. PadValueOrByteId is also applicable: omission selects Null, while explicit 00, 01, 10, and 11 select Zero, Max, Min, and Null for the destination region outside the valid rectangle. CMode is not applicable and every explicit nonzero CMode is illegal.

TCVT takes no B.IOR or B.IOS, requires equal source and destination PE_MASK values, and mask zero is a strict no-op. The source persists and MAY alias the destination. Complete type, encoding, geometry, capacity, layout, canonicalization, and source-definedness preflight precedes source snapshot and destination allocation. Converted payload, numeric status, padding definedness, representation state, and destination descriptor publish atomically; rejection has no architectural effect.

Decision 081: TFMA is one same-type fused elementwise multiply-add

TFMA is selected by TEPL carrier Mode=0, Function=28 and executes on the VEC engine. It reads Local multiplicand-left, multiplicand-right, and addend Tiles and writes one explicit renamed Local destination. Each floating result is one fused left * right + addend operation with no architecturally rounded intermediate product and exactly one selected-profile rounding at the final result. Each signed or unsigned integer result is the same expression modulo the element width. Verification-carrier bits above an integer element width are zero.

TFMA supports exactly FP64, FP32, TF32, HF32, FP16, BF16, E4M3, E5M2, S64, S32, S16, S8, U64, U32, U16, and U8. Every other DataType rejects before effects. All three sources and the destination MUST match physical shape, valid shape, row-major layout, and DataType, and every valid source element MUST be defined.

For floating DataTypes, the selected numeric profile owns final rounding, overflow, underflow, inexact, subnormal, NaN payload, and canonical-result details while preserving fused evaluation. Signaling NaNs report invalid and produce a quiet NaN. Zero multiplied by infinity, infinity multiplied by zero, and an infinite product combined with an opposite-signed infinite addend also report invalid and produce a quiet NaN. Other quiet NaNs propagate according to the profile. TFMA does not consume an encoded RMode, Sat, or Canonicalize; it uses the profile's fixed/default arithmetic rounding.

The closed Local ternary VEC schema requires nonzero LB0=ValidCol; omitted LB1 gives ValidRow=1; omitted LB2 gives Col=ValidCol; and physical rows derive from capacity, Col, and DataType. PadValueOrByteId is the only applicable B.DATR field. Omission selects Null; explicit 00, 01, 10, and 11 select Zero, Max, Min, and Null. Explicit nondefault CMode, Sat, Canonicalize, secondary DataType, RMode, or Layout is illegal.

TFMA takes no B.IOR or B.IOS. Every participating B.IOT binding MUST use the same PE_MASK, and mask zero is a strict no-op. Sources persist, may be identical, and any source MAY alias the destination. Complete preflight precedes snapshots of all three source payloads. The fused result, numeric status, padding definedness, and destination descriptor publish atomically; rejection has no architectural effect.