FMOPA (widening, 2-way, FP8 to FP16)
8-bit floating-point sum of outer products and accumulate
The 8-bit floating-point sum of outer products and accumulate instruction works with a 16-bit element ZA tile.
This instruction widens the SVLH×2 sub-matrix of 8-bit floating-point values held in the first source vector to half-precision floating-point values and multiplies it by the widened 2×SVLH sub-matrix of 8-bit floating-point values in the second source vector to half-precision floating-point values.
Each source vector is independently predicated by a corresponding governing predicate. When a 8-bit source element is Inactive it is treated as having the value +0.0, but if both groups of source vector elements that correspond to a 16-bit destination element contain Inactive elements, then the destination element remains unmodified.
The resulting SVLH×SVLH half-precision floating-point sum of outer products are scaled by 2-UInt(FPMR.LSCALE[3:0]), before being destructively added to the half-precision floating-point destination tile. This is equivalent to performing a downscaled 2-way dot product and accumulate to each of the destination tile elements.
Each 16-bit container of the first source vector holds 2 consecutive column elements of each row of a SVLH×2 sub-matrix. Similarly, each 16-bit container of the second source vector holds 2 consecutive row elements of each column of a 2×SVLH sub-matrix.
The 8-bit floating-point encoding format for the elements of the first source vector and the second source vector is selected by FPMR.F8S1 and FPMR.F8S2 respectively.
Green
True
SM_1_only
True
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
FMOPA <ZAda>.H, <Pn>/M, <Pm>/M, <Zn>.B, <Zm>.B
if !IsFeatureImplemented(FEAT_SME_F8F16) 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-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.
CheckFPMREnabled();
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) operand1 = Z[n, VL];
constant bits(VL) operand2 = Z[m, VL];
constant bits(dim*dim*16) operand3 = ZAtile[da, 16, dim*dim*16];
bits(dim*dim*16) result;
for row = 0 to dim-1
for col = 0 to dim-1
array [0..1] of boolean prow;
array [0..1] of boolean pcol;
boolean any_active = FALSE;
for i = 0 to 1
prow[i] = ActivePredicateElement(mask1, 2*row + i, 8);
pcol[i] = ActivePredicateElement(mask2, 2*col + i, 8);
any_active = any_active || (prow[i] && pcol[i]);
if any_active then
bits(16) sum = Elem[operand3, row*dim+col, 16];
bits(16) rowop = Zeros(16);
bits(16) colop = Zeros(16);
for i = 0 to 1
if prow[i] then
Elem[rowop, i, 8] = Elem[operand1, 2*row + i, 8];
if pcol[i] then
Elem[colop, i, 8] = Elem[operand2, 2*col + i, 8];
sum = FP8DotAddFP(sum, rowop, colop, FPCR, FPMR);
Elem[result, row*dim+col, 16] = sum;
else
Elem[result, row*dim+col, 16] = Elem[operand3, row*dim+col, 16];
ZAtile[da, 16, dim*dim*16] = result;