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## FCMLA (indexed)

Floating-point complex multiply-add by indexed values with rotate.

Multiply the duplicated real components for rotations 0 and 180, or imaginary components for rotations 90 and 270, of the floating-point complex numbers in each 128-bit segment of the first source vector by the specified complex number in the corresponding the second source vector segment rotated by 0, 90, 180 or 270 degrees in the direction from the positive real axis towards the positive imaginary axis, when considered in polar representation.

Then destructively add the products to the corresponding components of the complex numbers in the addend and destination vector, without intermediate rounding.

These transformations permit the creation of a variety of multiply-add and multiply-subtract operations on complex numbers by combining two of these instructions with the same vector operands but with rotations that are 90 degrees apart.

Each complex number is represented in a vector register as an even/odd pair of elements with the real part in the even-numbered element and the imaginary part in the odd-numbered element.

The complex numbers within the second source vector are specified using an immediate index which selects the same complex number position within each 128-bit vector segment. The index range is from 0 to one less than the number of complex numbers per 128-bit segment, encoded in 1 to 2 bits depending on the size of the complex number. This instruction is unpredicated.

It has encodings from 2 classes: Half-precision and Single-precision

### Half-precision

 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 0 1 1 0 0 1 0 0 1 0 1 i2 Zm 0 0 0 1 rot Zn Zda

#### Half-precision

FCMLA <Zda>.H, <Zn>.H, <Zm>.H[<imm>], <const>

```if !HaveSVE() then UNDEFINED;
integer esize = 16;
integer index = UInt(i2);
integer n = UInt(Zn);
integer m = UInt(Zm);
integer da = UInt(Zda);
integer sel_a = UInt(rot<0>);
integer sel_b = UInt(NOT(rot<0>));
boolean neg_i = (rot<1> == '1');
boolean neg_r = (rot<0> != rot<1>);```

### Single-precision

 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 0 1 1 0 0 1 0 0 1 1 1 i1 Zm 0 0 0 1 rot Zn Zda

#### Single-precision

FCMLA <Zda>.S, <Zn>.S, <Zm>.S[<imm>], <const>

```if !HaveSVE() then UNDEFINED;
integer esize = 32;
integer index = UInt(i1);
integer n = UInt(Zn);
integer m = UInt(Zm);
integer da = UInt(Zda);
integer sel_a = UInt(rot<0>);
integer sel_b = UInt(NOT(rot<0>));
boolean neg_i = (rot<1> == '1');
boolean neg_r = (rot<0> != rot<1>);```

### 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.
 For the half-precision variant: is the name of the second source scalable vector register Z0-Z7, encoded in the "Zm" field. For the single-precision variant: is the name of the second source scalable vector register Z0-Z15, encoded in the "Zm" field.
 For the half-precision variant: is the index of a Real and Imaginary pair, in the range 0 to 3, encoded in the "i2" field. For the single-precision variant: is the index of a Real and Imaginary pair, in the range 0 to 1, encoded in the "i1" field.
<const> Is the const specifier, encoded in rot:
rot <const>
00 #0
01 #90
10 #180
11 #270

### Operation

```CheckSVEEnabled();
integer pairs = VL DIV (2 * esize);
integer pairspersegment = 128 DIV (2 * esize);
bits(VL) operand1 = Z[n];
bits(VL) operand2 = Z[m];
bits(VL) operand3 = Z[da];
bits(VL) result;

for p = 0 to pairs-1
segmentbase = p - p MOD pairspersegment;
s = segmentbase + index;
addend_r = Elem[operand3, 2 * p + 0, esize];
addend_i = Elem[operand3, 2 * p + 1, esize];
elt1_a   = Elem[operand1, 2 * p + sel_a, esize];
elt2_a   = Elem[operand2, 2 * s + sel_a, esize];
elt2_b   = Elem[operand2, 2 * s + sel_b, esize];
if neg_r then elt2_a = FPNeg(elt2_a);
if neg_i then elt2_b = FPNeg(elt2_b);