BFloat16 sum of outer products and accumulate

The BFloat16 floating-point sum of outer products and accumulate instruction works with a 32-bit element ZA tile.

This instruction multiplies the SVL_{S}×2 sub-matrix of BFloat16 values held in the first source vector by the 2×SVL_{S} sub-matrix of BFloat16 values in the second source vector.

Each source vector is independently predicated by a corresponding governing predicate. When a 16-bit source element is Inactive it is treated as having the value +0.0, but if both pairs of source vector elements that correspond to a 32-bit destination element contain Inactive elements, then the destination element remains unmodified.

The resulting SVL_{S}×SVL_{S} single-precision floating-point sum of outer products is then destructively added to the single-precision floating-point destination tile. This is equivalent to performing a 2-way dot product and accumulate to each of the destination tile elements.

Each 32-bit container of the first source vector holds 2 consecutive column elements of each row of a SVL_{S}×2 sub-matrix. Similarly, each 32-bit container of the second source vector holds 2 consecutive row elements of each column of a 2×SVL_{S} sub-matrix.

This instruction follows SME BFloat16 numerical behaviors.

(FEAT_SME)

31 | 30 | 29 | 28 | 27 | 26 | 25 | 24 | 23 | 22 | 21 | 20 | 19 | 18 | 17 | 16 | 15 | 14 | 13 | 12 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |

1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | Zm | Pm | Pn | Zn | 0 | 0 | 0 | ZAda | |||||||||||||

S |

if !IsFeatureImplemented(FEAT_SME) then UNDEFINED; constant integer a = UInt(Pn); constant integer b = UInt(Pm); constant integer n = UInt(Zn); constant integer m = UInt(Zm); constant integer da = UInt(ZAda);

<ZAda> |
Is the name of the ZA tile ZA0-ZA3, encoded in the "ZAda" field. |

<Pn> |
Is the name of the first governing scalable predicate register P0-P7, encoded in the "Pn" field. |

<Pm> |
Is the name of the second governing scalable predicate register P0-P7, encoded in the "Pm" field. |

<Zn> |
Is the name of the first source scalable vector register, encoded in the "Zn" field. |

<Zm> |
Is the name of the second source scalable vector register, encoded in the "Zm" field. |

CheckStreamingSVEAndZAEnabled(); constant integer VL = CurrentVL; constant integer PL = VL DIV 8; constant integer dim = VL DIV 32; constant bits(PL) mask1 = P[a, PL]; constant bits(PL) mask2 = P[b, PL]; constant bits(VL) operand1 = Z[n, VL]; constant bits(VL) operand2 = Z[m, VL]; constant bits(dim*dim*32) operand3 = ZAtile[da, 32, dim*dim*32]; bits(dim*dim*32) result; for row = 0 to dim-1 for col = 0 to dim-1 // determine row/col predicates constant boolean prow_0 = (ActivePredicateElement(mask1, 2*row + 0, 16)); constant boolean prow_1 = (ActivePredicateElement(mask1, 2*row + 1, 16)); constant boolean pcol_0 = (ActivePredicateElement(mask2, 2*col + 0, 16)); constant boolean pcol_1 = (ActivePredicateElement(mask2, 2*col + 1, 16)); bits(32) sum = Elem[operand3, row*dim+col, 32]; if (prow_0 && pcol_0) || (prow_1 && pcol_1) then constant bits(16) erow_0 = (if prow_0 then Elem[operand1, 2*row + 0, 16] else FPZero('0', 16)); constant bits(16) erow_1 = (if prow_1 then Elem[operand1, 2*row + 1, 16] else FPZero('0', 16)); constant bits(16) ecol_0 = (if pcol_0 then Elem[operand2, 2*col + 0, 16] else FPZero('0', 16)); constant bits(16) ecol_1 = (if pcol_1 then Elem[operand2, 2*col + 1, 16] else FPZero('0', 16)); sum = BFDotAdd(sum, erow_0, erow_1, ecol_0, ecol_1, FPCR); Elem[result, row*dim+col, 32] = sum; ZAtile[da, 32, dim*dim*32] = result;

Internal version only: aarchmrs v2024-03_relA, pseudocode v2024-03_rel, sve v2024-03_rel ; Build timestamp: 2024-03-26T09:45

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