# 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.”