BFMOPA (non-widening)

BFloat16 outer product and accumulate

This instruction works with a 16-bit element ZA tile.

This instruction generates an outer product of the first source vector and the second source vector. The first source is SVLH×1 vector and the second source is 1×SVLH vector.

Each source vector is independently predicated by a corresponding governing predicate. When either source vector element is Inactive the corresponding destination tile element remains unmodified.

The resulting outer product, SVLH×SVLH, is then destructively added to the destination tile. This is equivalent to performing a single multiply-accumulate to each of the destination tile elements.

This instruction follows SME2 ZA-targeting non-widening BFloat16 numerical behaviors.

ID_AA64SMFR0_EL1.B16B16 indicates whether this instruction is implemented.

Encoding: SME2

Variants: FEAT_SME_B16B16 (ARMv9.4)

313029282726252423222120191817161514131211109876543210
100000011010100
ZmPmPnZnSZAda

BFMOPA <ZAda>.H, <Pn>/M, <Pm>/M, <Zn>.H, <Zm>.H

Decoding algorithm

if !IsFeatureImplemented(FEAT_SME_B16B16) then EndOfDecode(Decode_UNDEF);
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);

Operation

CheckStreamingSVEAndZAEnabled();
constant integer VL = CurrentVL;
constant integer PL = VL DIV 8;
constant integer dim = VL DIV 16;
constant bits(PL) mask1 = P[a, PL];
constant bits(PL) mask2 = P[b, PL];
constant bits(VL) op1 = Z[n, VL];
constant bits(VL) op2 = Z[m, VL];
constant bits(dim*dim*16) op3 = ZAtile[da, 16, dim*dim*16];
bits(dim*dim*16) result;

for row = 0 to dim-1
    for col = 0 to dim-1
        constant bits(16) elem2 = Elem[op2, col, 16];
        constant bits(16) elem3 = Elem[op3, row*dim+col, 16];

        if ActivePredicateElement(mask1, row, 16) && ActivePredicateElement(mask2, col, 16) then
            constant bits(16) elem1 = Elem[op1, row, 16];
            Elem[result, row*dim+col, 16] = BFMulAdd_ZA(elem3, elem1, elem2, FPCR);
        else
            Elem[result, row*dim+col, 16] = elem3;

ZAtile[da, 16, dim*dim*16] = result;

Explanations

<ZAda>: Is the name of the ZA tile ZA0-ZA1, 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.