FMLAL (multiple and single vector, FP16 to FP32)

Multi-vector floating-point multiply-add long by vector

This instruction widens all 16-bit half-precision elements in the one, two, or four first source vectors and the second source vector to single-precision format, then multiplies the corresponding elements and destructively adds these values without intermediate rounding to the overlapping 32-bit single-precision elements of the ZA double-vector groups.

The double-vector group within all of, each half of, or each quarter of the ZA array is selected by the sum of the vector select register and offset range, modulo all, half, or quarter the number of ZA array vectors.

The vector group symbol, VGx2 or VGx4, indicates that the ZA operand consists of two or four ZA double-vector groups respectively. The vector group symbol is preferred for disassembly, but optional in assembler source code.

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

This instruction is unpredicated.

Encoding: One ZA double-vector

Variants: FEAT_SME2 (ARMv9.3)

313029282726252423222120191817161514131211109876543210
110000010010001100
ZmRvZnopSoff3

FMLAL ZA.S[<Wv>, <offs1>:<offs2>], <Zn>.H, <Zm>.H

Decoding algorithm

if !IsFeatureImplemented(FEAT_SME2) then EndOfDecode(Decode_UNDEF);
constant integer v = UInt('010':Rv);
constant integer n = UInt(Zn);
constant integer m = UInt('0':Zm);
constant integer offset = UInt(off3:'0');
constant integer nreg = 1;

Encoding: Two ZA double-vectors

Variants: FEAT_SME2 (ARMv9.3)

313029282726252423222120191817161514131211109876543210
1100000100100010000
ZmRvZnopSo2off2

FMLAL ZA.S[<Wv>, <offs1>:<offs2>{, VGx2}], { <Zn1>.H-<Zn2>.H }, <Zm>.H

Decoding algorithm

if !IsFeatureImplemented(FEAT_SME2) then EndOfDecode(Decode_UNDEF);
constant integer v = UInt('010':Rv);
constant integer n = UInt(Zn);
constant integer m = UInt('0':Zm);
constant integer offset = UInt(off2:'0');
constant integer nreg = 2;

Encoding: Four ZA double-vectors

Variants: FEAT_SME2 (ARMv9.3)

313029282726252423222120191817161514131211109876543210
1100000100110010000
ZmRvZnopSo2off2

FMLAL ZA.S[<Wv>, <offs1>:<offs2>{, VGx4}], { <Zn1>.H-<Zn4>.H }, <Zm>.H

Decoding algorithm

if !IsFeatureImplemented(FEAT_SME2) then EndOfDecode(Decode_UNDEF);
constant integer v = UInt('010':Rv);
constant integer n = UInt(Zn);
constant integer m = UInt('0':Zm);
constant integer offset = UInt(off2:'0');
constant integer nreg = 4;

Operation

CheckStreamingSVEAndZAEnabled();
constant integer VL = CurrentVL;
constant integer elements = VL DIV 32;
constant integer vectors = VL DIV 8;
constant integer vstride = vectors DIV nreg;
constant bits(32) vbase = X[v, 32];
integer vec = (UInt(vbase) + offset) MOD vstride;
bits(VL) result;
vec = vec - (vec MOD 2);

for r = 0 to nreg-1
    constant bits(VL) op1 = Z[(n+r) MOD 32, VL];
    constant bits(VL) op2 = Z[m, VL];
    for i = 0 to 1
        constant bits(VL) op3 = ZAvector[vec + i, VL];
        for e = 0 to elements-1
            constant bits(16) elem1 = Elem[op1, 2 * e + i, 16];
            constant bits(16) elem2 = Elem[op2, 2 * e + i, 16];
            constant bits(32) elem3 = Elem[op3, e, 32];
            Elem[result, e, 32] = FPMulAddH_ZA(elem3, elem1, elem2,
                                                    FPCR);
        ZAvector[vec + i, VL] = result;
    vec = vec + vstride;

Explanations

<Wv>: Is the 32-bit name of the vector select register W8-W11, encoded in the "Rv" field.
<offs1>: For the "One ZA double-vector" variant: is the first vector select offset, encoded as "off3" field times 2.
<offs1>: For the "Four ZA double-vectors" and "Two ZA double-vectors" variants: is the first vector select offset, encoded as "off2" field times 2.
<offs2>: For the "One ZA double-vector" variant: is the second vector select offset, encoded as "off3" field times 2 plus 1.
<offs2>: For the "Four ZA double-vectors" and "Two ZA double-vectors" variants: is the second vector select offset, encoded as "off2" field times 2 plus 1.
<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 Z0-Z15, encoded in the "Zm" field.
<Zn1>: Is the name of the first scalable vector register of the first source multi-vector group, encoded as "Zn".
<Zn2>: Is the name of the second scalable vector register of the first source multi-vector group, encoded as "Zn" plus 1 modulo 32.
<Zn4>: Is the name of the fourth scalable vector register of the first source multi-vector group, encoded as "Zn" plus 3 modulo 32.