VRSQRT28PD

Approximation to the Reciprocal Square Root of Packed Double Precision

stableVMJITAOTinstruction

Encodings

Operand encoding

Each mode is a value of the Op/En column above. It says which field of the encoded instruction carries each operand, in the order they are written, and whether the instruction reads it, writes it or both.

Measured cost

Description#

Computes the reciprocal square root of the float64 values in the source operand (the second operand) and store the results to the destination operand (the first operand). The approximate reciprocal is evaluated with less than 2^-28 of maximum relative error.

If any source element is NaN, the quietized NaN source value is returned for that element. Negative (non-zero) source numbers, as well as -, return the canonical NaN and set the Invalid Flag (#I). A value of -0 must return - and set the DivByZero flags (#Z). Negative numbers should return NaN and set the Invalid flag (#I). Note however that the instruction flush input denormals to zero of the same sign, so negative denormals return - and set the DivByZero flag.

The source operand is a ZMM register, a 512-bit memory location or a 512-bit vector broadcasted from a 64-bit memory location. The destination operand is a ZMM register, conditionally updated using writemask k1.

EVEX.vvvv is reserved and must be 1111b otherwise instructions will #UD.

A numerically exact implementation of VRSQRT28xx can be found at https://software.intel.com/en-us/articles/reference-implementations-for-IA-approximation-instructions-vrcp14-vrsqrt14-vrcp28-vrsqrt28-vexp2.

Operation#

VRSQRT28PD (EVEX Encoded Versions)

(KL, VL) = (8, 512)

FOR j := 0 TO KL-1

i := j * 64

IF k1[j] OR *no writemask* THEN

             IF (EVEX.b = 1) AND (SRC *is memory*)

                  THEN DEST[i+63:i] := (1.0/ SQRT(SRC[63:0]));

                  ELSE DEST[i+63:i] := (1.0/ SQRT(SRC[i+63:i]));

             FI;

ELSE

       IF *merging-masking*               ; merging-masking

             THEN *DEST[i+63:i] remains unchanged*

             ELSE                         ; zeroing-masking

                  DEST[i+63:i] := 0

       FI;

FI;

ENDFOR;



                                 Table 8-7. VRSQRT28PD Special Cases

Input Value                  Result Value              Comments
NAN
X = 2-2n                     QNAN(input)               If (SRC = SNaN) then #I
X<0
X = -0 or negative denormal  2n
X = +0 or positive denormal
X = +INF                     QNaN_Indefinite           Including -INF

                             -INF                      #Z

                             +INF                      #Z

                             +0

Intel C/C++ compiler intrinsics#

VRSQRT28PD __m512d _mm512_rsqrt28_round_pd(__m512d a, int sae);
VRSQRT28PD __m512d _mm512_mask_rsqrt28_round_pd(__m512d s, __mmask8 m,__m512d a, int sae);
VRSQRT28PD __m512d _mm512_maskz_rsqrt28_round_pd(__mmask8 m,__m512d a, int sae);

SIMD Floating-Point Exceptions#

Invalid (if SNaN input), Divide-by-zero.

Other Exceptions#

See Table 2-48, "Type E2 Class Exception Conditions."

Sources

• This instruction in the Intel manual
• Latency and throughput per microarchitecture