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BFDOT (indexed)

BFloat16 floating-point indexed dot product.

The BFloat16 floating-point (BF16) indexed dot product instruction computes the dot product of a pair of BF16 values held in each 32-bit element of the first source vector multiplied by a pair of BF16 values in an indexed 32-bit element of the second source vector, and then destructively adds the single-precision dot product to the corresponding single-precision element of the destination vector.

The BF16 pairs within the second source vector are specified using an immediate index which selects the same BF16 pair position within each 128-bit vector segment. The index range is from 0 to 3. This instruction is unpredicated.

All floating-point calculations performed by this instruction are performed with the following behaviors, irrespective of the value in FPCR:

* Uses the non-IEEE 754 Round-to-Odd mode, which forces bit 0 of an inexact result to 1, and rounds an overflow to an appropriately signed Infinity.

* The cumulative FPSR exception bits (IDC, IXC, UFC, OFC, DZC and IOC) are not modified.

* Trapped floating-point exceptions are disabled, as if the FPCR trap enable bits (IDE, IXE, UFE, OFE, DZE and IOE) are all zero.

* Denormalized inputs and results are flushed to zero, as if FPCR.FZ == 1.

* Only the Default NaN is generated, as if FPCR.DN == 1.

ID_AA64ZFR0_EL1.BF16 indicates whether this instruction is implemented.



BFDOT <Zda>.S, <Zn>.H, <Zm>.H[<imm>]

if !HaveSVE() || !HaveBF16Ext() then UNDEFINED;
integer n = UInt(Zn);
integer m = UInt(Zm);
integer da = UInt(Zda);
integer index = UInt(i2);

Assembler Symbols


Is the name of the third source and destination scalable vector register, encoded in the "Zda" field.


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


Is the name of the second source scalable vector register Z0-Z7, encoded in the "Zm" field.


Is the immediate index, in the range 0 to 3, encoded in the "i2" field.


integer elements = VL DIV 32;
integer eltspersegment = 128 DIV 32;
bits(VL) operand1 = Z[n];
bits(VL) operand2 = Z[m];
bits(VL) operand3 = Z[da];
bits(VL) result;

for e = 0 to elements-1
    integer segmentbase = e - e MOD eltspersegment;
    integer s = segmentbase + index;
    bits(16) elt1_a = Elem[operand1, 2 * e + 0, 16];
    bits(16) elt1_b = Elem[operand1, 2 * e + 1, 16];
    bits(16) elt2_a = Elem[operand2, 2 * s + 0, 16];
    bits(16) elt2_b = Elem[operand2, 2 * s + 1, 16];

    bits(32) sum = BFAdd(BFMul(elt1_a, elt2_a), BFMul(elt1_b, elt2_b));
    Elem[result, e, 32] = BFAdd(Elem[operand3, e, 32], sum);

Z[da] = result;

Operational information

This instruction might be immediately preceded in program order by a MOVPRFX instruction that conforms to all of the following requirements, otherwise the behavior of either or both instructions is unpredictable:

  • The MOVPRFX instruction must specify the same destination register as this instruction.
  • The destination register must not refer to architectural register state referenced by any other source operand register of this instruction.
The MOVPRFX instructions that can be used with this instruction are as follows:
  • An unpredicated MOVPRFX instruction.