PMULL, PMULL2

Polynomial multiply long

This instruction multiplies corresponding elements in the lower or upper half of the vectors of the two source SIMD&FP registers, places the results in a vector, and writes the vector to the destination SIMD&FP register. The destination vector elements are twice as long as the elements that are multiplied.

For information about multiplying polynomials, see Polynomial arithmetic over {0, 1}.

The PMULL instruction extracts each source vector from the lower half of each source register. The PMULL2 instruction extracts each source vector from the upper half of each source register.

The PMULL and PMULL2 variants that operate on 64-bit source elements are defined only when FEAT_PMULL is implemented.

Depending on the settings in the CPACR_EL1, CPTR_EL2, and CPTR_EL3 registers, and the current Security state and Exception level, an attempt to execute the instruction might be trapped.

Encoding: Three registers, not all the same type

Variants: FEAT_AdvSIMD (ARMv8.0)

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		0	0	1	1	1	0			1						1	1	1	0	0	0
	Q	U						size			Rm					opcode						Rn					Rd

PMULL{2} <Vd>.<Ta>, <Vn>.<Tb>, <Vm>.<Tb>

Decoding algorithm

if !IsFeatureImplemented(FEAT_AdvSIMD) then EndOfDecode(Decode_UNDEF);
if size == '01' || size == '10' then EndOfDecode(Decode_UNDEF);
if size == '11' && !IsFeatureImplemented(FEAT_PMULL) then EndOfDecode(Decode_UNDEF);
constant integer d = UInt(Rd);
constant integer n = UInt(Rn);
constant integer m = UInt(Rm);
constant integer esize = 8 << UInt(size);
constant integer datasize = 64;
constant integer part = UInt(Q);
constant integer elements = datasize DIV esize;

Operation

CheckFPAdvSIMDEnabled64();
constant bits(datasize) operand1 = Vpart[n, part, datasize];
constant bits(datasize) operand2 = Vpart[m, part, datasize];
bits(2*datasize) result;
bits(esize) element1;
bits(esize) element2;

for e = 0 to elements-1
    element1 = Elem[operand1, e, esize];
    element2 = Elem[operand2, e, esize];
    Elem[result, e, 2*esize] = PolynomialMult(element1, element2);

V[d, 2*datasize] = result;

Explanations

2: <Vd>: Is the name of the SIMD&FP destination register, encoded in the "Rd" field.
<Ta>: <Vn>: Is the name of the first SIMD&FP source register, encoded in the "Rn" field.
<Tb>: <Vm>: Is the name of the second SIMD&FP source register, encoded in the "Rm" field.

Operational Notes

If PSTATE.DIT is 1:

• The execution time of this instruction is independent of:
  • The values of the data supplied in any of its registers.
  • The values of the NZCV flags.
• The response of this instruction to asynchronous exceptions does not vary based on:
  • The values of the data supplied in any of its registers.
  • The values of the NZCV flags.