SQRDMULH (by element)

Signed saturating rounding doubling multiply returning high half (by element)

This instruction multiplies each vector element in the first source SIMD&FP register by the specified vector element of the second source SIMD&FP register, doubles the results, places the most significant half of the final results into a vector, and writes the vector to the destination SIMD&FP register.

The results are rounded. For truncated results, see SQDMULH.

If any of the results overflows, they are saturated. If saturation occurs, the cumulative saturation bit FPSR.QC is set.

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: Scalar

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	1	0	1	1	1	1	1									1	1	0	1		0
		U						size		L	M	Rm							op	H		Rn					Rd

SQRDMULH <V><d>, <V><n>, <Vm>.<Ts>[<index>]

Decoding algorithm

if !IsFeatureImplemented(FEAT_AdvSIMD) then EndOfDecode(Decode_UNDEF);
constant integer idxdsize = 64 << UInt(H);
integer index;
bit Rmhi;
case size of
    when '01' index = UInt(H:L:M); Rmhi = '0';
    when '10' index = UInt(H:L);   Rmhi = M;
    otherwise EndOfDecode(Decode_UNDEF);

constant integer d = UInt(Rd);
constant integer n = UInt(Rn);
constant integer m = UInt(Rmhi:Rm);

constant integer esize = 8 << UInt(size);
constant integer datasize = esize;
constant integer elements = 1;

constant boolean round = TRUE;

Encoding: Vector

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	1									1	1	0	1		0
	Q	U						size		L	M	Rm							op	H		Rn					Rd

SQRDMULH <Vd>.<T>, <Vn>.<T>, <Vm>.<Ts>[<index>]

Decoding algorithm

if !IsFeatureImplemented(FEAT_AdvSIMD) then EndOfDecode(Decode_UNDEF);
constant integer idxdsize = 64 << UInt(H);
integer index;
bit Rmhi;
case size of
    when '01' index = UInt(H:L:M); Rmhi = '0';
    when '10' index = UInt(H:L);   Rmhi = M;
    otherwise EndOfDecode(Decode_UNDEF);

constant integer d = UInt(Rd);
constant integer n = UInt(Rn);
constant integer m = UInt(Rmhi:Rm);

constant integer esize = 8 << UInt(size);
constant integer datasize = 64 << UInt(Q);
constant integer elements = datasize DIV esize;

constant boolean round = TRUE;

Operation

CheckFPAdvSIMDEnabled64();
constant bits(datasize) operand1 = V[n, datasize];
constant bits(idxdsize) operand2 = V[m, idxdsize];
bits(datasize) result;
integer element1;
integer element2;
integer product;
boolean sat;

element2 = SInt(Elem[operand2, index, esize]);
for e = 0 to elements-1
    element1 = SInt(Elem[operand1, e, esize]);
    product = 2 * element1 * element2;
    product = RShr(product, esize, round);
    // The following only saturates if element1 and element2 equal -(2^(esize-1))
    (Elem[result, e, esize], sat) = SignedSatQ(product, esize);
    if sat then FPSR.QC = '1';

V[d, datasize] = result;

Explanations

<V>: <d>: Is the number of the SIMD&FP destination register, encoded in the "Rd" field.
<n>: Is the number of the first SIMD&FP source register, encoded in the "Rn" field.
<Vm>: <Ts>: <index>: <Vd>: Is the name of the SIMD&FP destination register, encoded in the "Rd" field.
<T>: <Vn>: Is the name of the first SIMD&FP source register, encoded in the "Rn" 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.