# VRSQRT14PS — Compute Approximate Reciprocals of Square Roots of Packed Float32 Values

Opcode/Instruction | Op/En | 64/32 bit Mode Support | CPUID Feature Flag | Description
--- | --- | --- | --- | ---
EVEX.128.66.0F38.W0 4E /r VRSQRT14PS xmm1 {k1}{z}, xmm2/m128/m32bcst | A | V/V | AVX512VL AVX512F | Computes the approximate reciprocal square roots of the packed single-precision floating-point values in xmm2/m128/m32bcst and stores the results in xmm1. Under writemask.
EVEX.256.66.0F38.W0 4E /r VRSQRT14PS ymm1 {k1}{z}, ymm2/m256/m32bcst | A | V/V | AVX512VL AVX512F | Computes the approximate reciprocal square roots of the packed single-precision floating-point values in ymm2/m256/m32bcst and stores the results in ymm1. Under writemask.
EVEX.512.66.0F38.W0 4E /r VRSQRT14PS zmm1 {k1}{z}, zmm2/m512/m32bcst | A | V/V | AVX512F | Computes the approximate reciprocal square roots of the packed single-precision floating-point values in zmm2/m512/m32bcst 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 16 packed single-precision floating-point values in the source operand (the second operand) and stores the packed single-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 32-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 32-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 32-bit memory location. The destination operand is a XMM register, conditionally updated using writemask k1.

The VRSQRT14PS 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 ¶

#### VRSQRT14PS (EVEX encoded versions) ¶

    (KL, VL) = (4, 128), (8, 256), (16, 512)
    FOR j := 0 TO KL-1
        i := j * 32
        IF k1[j] OR *no writemask* THEN
                IF (EVEX.b = 1) AND (SRC *is memory*)
                    THEN DEST[i+31:i] := APPROXIMATE(1.0/ SQRT(SRC[31:0]));
                    ELSE DEST[i+31:i] := APPROXIMATE(1.0/ SQRT(SRC[i+31:i]));
                FI;
        ELSE
            IF *merging-masking* ; merging-masking
                THEN *DEST[i+31:i] remains unchanged*
                ELSE
                        ; zeroing-masking
                    DEST[i+31: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 5-36. VRSQRT14PS Special Cases

### Intel C/C++ Compiler Intrinsic Equivalent ¶

    VRSQRT14PS __m512 _mm512_rsqrt14_ps( __m512 a);

    VRSQRT14PS __m512 _mm512_mask_rsqrt14_ps(__m512 s, __mmask16 k, __m512 a);

    VRSQRT14PS __m512 _mm512_maskz_rsqrt14_ps( __mmask16 k, __m512 a);

    VRSQRT14PS __m256 _mm256_rsqrt14_ps( __m256 a);

    VRSQRT14PS __m256 _mm256_mask_rsqrt14_ps(__m256 s, __mmask8 k, __m256 a);

    VRSQRT14PS __m256 _mm256_maskz_rsqrt14_ps( __mmask8 k, __m256 a);

    VRSQRT14PS __m128 _mm_rsqrt14_ps( __m128 a);

    VRSQRT14PS __m128 _mm_mask_rsqrt14_ps(__m128 s, __mmask8 k, __m128 a);

    VRSQRT14PS __m128 _mm_maskz_rsqrt14_ps( __mmask8 k, __m128 a);

### SIMD Floating-Point Exceptions ¶

None.

### Other Exceptions ¶

See Table 2-21, “Type 4 Class Exception Conditions.”