FMOP4A (widening, 2-way, FP16 to FP32)

Half-precision quarter-tile sums of two outer products, accumulating

This instruction generates four independent quarter-tile half-precision sums of outer products from the sub-matrices in the half-vectors of the one or two first and second source vectors and accumulates the results to the corresponding elements of a 32-bit element ZA tile.

Each of the quarter-tile sums of outer products is generated by multiplying the SVLS÷2 × 2 sub-matrix of half-precision values held in the half-vectors of the first source vectors by the 2 × SVLS÷2 sub-matrix of half-precision values held in the half-vectors of the second source vectors. Each 32-bit container of the first source vectors holds 2 elements of each row of a SVLS÷2 × 2 sub-matrix. Similarly, each 32-bit container of the second source vectors holds 2 elements of each column of a 2 × SVLS÷2 sub-matrix.

The instruction widens the sub-matrices of half-precision values held in the first source vectors to single-precision values and multiplies them by the corresponding widened sub-matrices of half-precision values in the second source vectors to single-precision values. The resulting quarter-tile SVLS÷2 × SVLS÷2 single-precision sums of outer products are then destructively added to the single-precision destination tile. This is equivalent to performing a 2-way dot product and accumulate to each of the destination tile elements.

This instruction follows SME ZA-targeting floating-point behaviors.

This instruction is unpredicated.

Encoding: Single and multiple vectors

Variants: FEAT_SME_MOP4 (ARMv9.6)

313029282726252423222120191817161514131211109876543210
100000010011000000000000
MZmNZnSZAda

FMOP4A <ZAda>.S, <Zn>.H, { <Zm1>.H-<Zm2>.H }

Decoding algorithm

if !IsFeatureImplemented(FEAT_SME_MOP4) then EndOfDecode(Decode_UNDEF);
constant integer n = UInt('0':Zn:'0');
constant integer m = UInt('1':Zm:'0');
constant integer nreg = 1;
constant integer mreg = 2;
constant integer da = UInt(ZAda);
constant boolean sub_op = FALSE;

Encoding: Single vectors

Variants: FEAT_SME_MOP4 (ARMv9.6)

313029282726252423222120191817161514131211109876543210
100000010010000000000000
MZmNZnSZAda

FMOP4A <ZAda>.S, <Zn>.H, <Zm>.H

Decoding algorithm

if !IsFeatureImplemented(FEAT_SME_MOP4) then EndOfDecode(Decode_UNDEF);
constant integer n = UInt('0':Zn:'0');
constant integer m = UInt('1':Zm:'0');
constant integer nreg = 1;
constant integer mreg = 1;
constant integer da = UInt(ZAda);
constant boolean sub_op = FALSE;

Encoding: Multiple and single vectors

Variants: FEAT_SME_MOP4 (ARMv9.6)

313029282726252423222120191817161514131211109876543210
100000010010000000010000
MZmNZnSZAda

FMOP4A <ZAda>.S, { <Zn1>.H-<Zn2>.H }, <Zm>.H

Decoding algorithm

if !IsFeatureImplemented(FEAT_SME_MOP4) then EndOfDecode(Decode_UNDEF);
constant integer n = UInt('0':Zn:'0');
constant integer m = UInt('1':Zm:'0');
constant integer nreg = 2;
constant integer mreg = 1;
constant integer da = UInt(ZAda);
constant boolean sub_op = FALSE;

Encoding: Multiple vectors

Variants: FEAT_SME_MOP4 (ARMv9.6)

313029282726252423222120191817161514131211109876543210
100000010011000000010000
MZmNZnSZAda

FMOP4A <ZAda>.S, { <Zn1>.H-<Zn2>.H }, { <Zm1>.H-<Zm2>.H }

Decoding algorithm

if !IsFeatureImplemented(FEAT_SME_MOP4) then EndOfDecode(Decode_UNDEF);
constant integer n = UInt('0':Zn:'0');
constant integer m = UInt('1':Zm:'0');
constant integer nreg = 2;
constant integer mreg = 2;
constant integer da = UInt(ZAda);
constant boolean sub_op = FALSE;

Operation

CheckStreamingSVEAndZAEnabled();
constant integer VL = CurrentVL;
constant integer hvsize = VL DIV 2;
constant integer dim = hvsize DIV 32;
constant integer tilesize = 4*dim*dim*32;
constant bits(tilesize) op3 = ZAtile[da, 32, tilesize];
bits(tilesize) result;

for outprod = 0 to 3
    constant integer row_hv = outprod DIV 2;
    constant integer col_hv = outprod MOD 2;
    constant integer row_base = row_hv * dim;
    constant integer col_base = col_hv * dim;

    constant bits(VL) op1 = Z[n + (nreg-1)*col_hv, VL];
    constant bits(VL) op2 = Z[m + (mreg-1)*row_hv, VL];

    for row = 0 to dim-1
        for col = 0 to dim-1
            constant integer row_idx = row_base + row;
            constant integer col_idx = col_base + col;
            constant integer tile_idx = row_idx * dim * 2 + col_idx;

            constant bits(32) sum = Elem[op3, tile_idx, 32];

            bits(16) erow_0 = Elem[op1, 2*row_idx + 0, 16];
            bits(16) erow_1 = Elem[op1, 2*row_idx + 1, 16];
            constant bits(16) ecol_0 = Elem[op2, 2*col_idx + 0, 16];
            constant bits(16) ecol_1 = Elem[op2, 2*col_idx + 1, 16];
            if sub_op then
                erow_0 = FPNeg(erow_0, FPCR);
                erow_1 = FPNeg(erow_1, FPCR);

            Elem[result, tile_idx, 32] = FPDotAdd_ZA(sum, erow_0, erow_1, ecol_0, ecol_1, FPCR);
ZAtile[da, 32, tilesize] = result;

Explanations

<ZAda>: Is the name of the ZA tile ZA0-ZA3, encoded in the "ZAda" field.
<Zn>: Is the name of the first source scalable vector register, registers in the range Z0-Z15, encoded as "Zn" times 2.
<Zm1>: Is the name of the first scalable vector register of the second source multi-vector group, in the range Z16-Z31, encoded as "Zm" times 2 plus 16.
<Zm2>: Is the name of the second scalable vector register of the second source multi-vector group, in the range Z16-Z31, encoded as "Zm" times 2 plus 17.
<Zm>: Is the name of the second source scalable vector register, registers in the range Z16-Z31, encoded as "Zm" times 2 plus 16.
<Zn1>: Is the name of the first scalable vector register of the first source multi-vector group, in the range Z0-Z15, encoded as "Zn" times 2.
<Zn2>: Is the name of the second scalable vector register of the first source multi-vector group, in the range Z0-Z15, encoded as "Zn" times 2 plus 1.