VRSQRT14PD — Compute Approximate Reciprocals of Square Roots of Packed Float64 Values

Opcode/Instruction	Op/En	64/32 bit Mode Support	CPUID Feature Flag	Description
EVEX.128.66.0F38.W1 4E /r VRSQRT14PD xmm1 {k1}{z}, xmm2/m128/m64bcst	A	V/V	AVX512VL AVX512F	Computes the approximate reciprocal square roots of the packed double precision floating-point values in xmm2/m128/m64bcst and stores the results in xmm1. Under writemask.
EVEX.256.66.0F38.W1 4E /r VRSQRT14PD ymm1 {k1}{z}, ymm2/m256/m64bcst	A	V/V	AVX512VL AVX512F	Computes the approximate reciprocal square roots of the packed double precision floating-point values in ymm2/m256/m64bcst and stores the results in ymm1. Under writemask.
EVEX.512.66.0F38.W1 4E /r VRSQRT14PD zmm1 {k1}{z}, zmm2/m512/m64bcst	A	V/V	AVX512F	Computes the approximate reciprocal square roots 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	Tuple Type	Operand 1	Operand 2	Operand 3	Operand 4
A	Full	ModRM:reg (w)	ModRM:r/m (r)	N/A	N/A

Description ¶

This instruction performs a SIMD computation of the approximate reciprocals of the square roots of the eight packed double precision floating-point values in the source operand (the second operand) and stores the packed double precision floating-point results in the destination operand (the first operand) according to the writemask. The maximum relative error for this approximation is less than 2^-14.

EVEX.512 encoded version: The source operand can be 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.256 encoded version: The source operand is a YMM register, a 256-bit memory location, or a 256-bit vector broadcasted from a 64-bit memory location. The destination operand is a YMM register, conditionally updated using writemask k1.

EVEX.128 encoded version: The source operand is a XMM register, a 128-bit memory location, or a 128-bit vector broadcasted from a 64-bit memory location. The destination operand is a XMM register, conditionally updated using writemask k1.

The VRSQRT14PD instruction is not affected by the rounding control bits in the MXCSR register. When a source value is a 0.0, an ∞ with the sign of the source value is returned. When the source operand is an +∞ then +ZERO value is returned. A denormal source value is treated as zero only if DAZ bit is set in MXCSR. Otherwise it is treated correctly and performs the approximation with the specified masked response. When a source value is a negative value (other than 0.0) a floating-point QNaN_indefinite is returned. When a source value is an SNaN or QNaN, the SNaN is converted to a QNaN or the source QNaN is returned.

MXCSR exception flags are not affected by this instruction and floating-point exceptions are not reported.

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

A numerically exact implementation of VRSQRT14xx can be found at https://software.intel.com/en-us/arti- ¶

cles/reference-implementations-for-IA-approximation-instructions-vrcp14-vrsqrt14-vrcp28-vrsqrt28-vexp2. ¶

Operation ¶

VRSQRT14PD (EVEX encoded versions) ¶

(KL, VL) = (2, 128), (4, 256), (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] := APPROXIMATE(1.0/ SQRT(SRC[63:0]));
                ELSE DEST[i+63:i] := APPROXIMATE(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;
DEST[MAXVL-1:VL] := 0

Input value	Result value	Comments
Any denormal	Normal	Cannot generate overflow
X = 2^-2n	₂ⁿ
X<0	QNaN_Indefinite	Including -INF
X = -0	-INF
X = +0	+INF
X = +INF	+0

Table 5-34. VRSQRT14PD Special Cases

Intel C/C++ Compiler Intrinsic Equivalent ¶

VRSQRT14PD __m512d _mm512_rsqrt14_pd( __m512d a);

VRSQRT14PD __m512d _mm512_mask_rsqrt14_pd(__m512d s, __mmask8 k, __m512d a);

VRSQRT14PD __m512d _mm512_maskz_rsqrt14_pd( __mmask8 k, __m512d a);

VRSQRT14PD __m256d _mm256_rsqrt14_pd( __m256d a);

VRSQRT14PD __m256d _mm512_mask_rsqrt14_pd(__m256d s, __mmask8 k, __m256d a);

VRSQRT14PD __m256d _mm512_maskz_rsqrt14_pd( __mmask8 k, __m256d a);

VRSQRT14PD __m128d _mm_rsqrt14_pd( __m128d a);

VRSQRT14PD __m128d _mm_mask_rsqrt14_pd(__m128d s, __mmask8 k, __m128d a);

VRSQRT14PD __m128d _mm_maskz_rsqrt14_pd( __mmask8 k, __m128d a);

SIMD Floating-Point Exceptions ¶

None.

Other Exceptions ¶

See Table 2-49, “Type E4 Class Exception Conditions.”