VRCP28PD—Approximation to the Reciprocal of Packed Double-Precision Floating-Point Values with Less Than 2^-28 Relative Error

Opcode/Instruction	Op /En	64/32 bit Mode Support	CPUID Feature Flag	Description
EVEX.512.66.0F38.W1 CA /r VRCP28PD zmm1 {k1}{z}, zmm2/m512/m64bcst {sae}	FV	V/V	AVX512ER	Computes the approximate reciprocals ( < 2^-28 relative error) of the packed double-precision floating-point values in zmm2/m512/m64bcst and stores the results in zmm1. Under writemask.

Opcode/Instruction

Op /En

64/32 bit Mode Support

CPUID Feature Flag

Description

EVEX.512.66.0F38.W1 CA /r

VRCP28PD zmm1 {k1}{z}, zmm2/m512/m64bcst {sae}

V/V

AVX512ER

Computes the approximate reciprocals ( < 2^-28 relative error) of the packed double-precision floating-point values in zmm2/m512/m64bcst and stores the results in zmm1. Under writemask.

Instruction Operand Encoding

Op/En	Operand 1	Operand 2	Operand 3	Operand 4
FV	ModRM:reg (w)	ModRM:r/m (r)	NA	NA

Description

Computes the reciprocal approximation 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.

Denormal input values are treated as zeros and do not signal #DE, irrespective of MXCSR.DAZ. Denormal results are flushed to zeros and do not signal #UE, irrespective of MXCSR.FZ.

If any source element is NaN, the quietized NaN source value is returned for that element. If any source element is ±∞, ±0.0 is returned for that element. Also, if any source element is ±0.0, ±∞ is returned for that element.

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 VRCP28xx can be found at https://software.intel.com/en-us/articles/refer-ence-implementations-for-IA-approximation-instructions-vrcp14-vrsqrt14-vrcp28-vrsqrt28-vexp2.

Operation

VRCP28PD (EVEX encoded versions)

(KL, VL) = (8, 512)
FOR j (cid:197) 0 TO KL-1
    i (cid:197) j * 64
    IF k1[j] OR *no writemask* THEN
        IF (EVEX.b = 1) AND (SRC *is memory*)
            THEN DEST[i+63:i] (cid:197) RCP_28_DP(1.0/SRC[63:0]);
            ELSE DEST[i+63:i] (cid:197) RCP_28_DP(1.0/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] (cid:197) 0
        FI;
    FI;
ENDFOR;
Table 5-17. VRCP28PD Special Cases


Input value
Result value
Comments

NAN
QNAN(input)
If (SRC = SNaN) then #I

0 ≤ X < 2^-1022
INF
Positive input denormal or zero; #Z

-2^-1022< X ≤ -0
-INF
Negative input denormal or zero; #Z

X > 2¹⁰²²
+0.0f


X < -2¹⁰²²
-0.0f


X = +∞
+0.0f


X = -∞
-0.0f


X = 2^-n
2ⁿ
Exact result (unless input/output is a denormal)

X = -2^-n
-2ⁿ
Exact result (unless input/output is a denormal)

Input value	Result value	Comments
NAN	QNAN(input)	If (SRC = SNaN) then #I
0 ≤ X < 2^-1022	INF	Positive input denormal or zero; #Z
-2^-1022< X ≤ -0	-INF	Negative input denormal or zero; #Z
X > 2¹⁰²²	+0.0f
X < -2¹⁰²²	-0.0f
X = +∞	+0.0f
X = -∞	-0.0f
X = 2^-n	2ⁿ	Exact result (unless input/output is a denormal)
X = -2^-n	-2ⁿ	Exact result (unless input/output is a denormal)

Intel C/C++ Compiler Intrinsic Equivalent

VRCP28PD __m512d _mm512_rcp28_round_pd ( __m512d a, int sae);
VRCP28PD __m512d _mm512_mask_rcp28_round_pd(__m512d a, __mmask8 m, __m512d b, int sae);
VRCP28PD __m512d _mm512_maskz_rcp28_round_pd( __mmask8 m, __m512d b, int sae);

SIMD Floating-Point Exceptions

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

Other Exceptions

See Exceptions Type E2.