# VRSQRTSH — Compute Approximate Reciprocal of Square Root of Scalar FP16 Value

Instruction En bit Mode Flag Support Instruction En bit Mode Flag Support 64/32 CPUID Feature Instruction En bit Mode Flag CPUID Feature Instruction En bit Mode Flag Op/ 64/32 CPUID Feature Instruction En bit Mode Flag 64/32 CPUID Feature Instruction En bit Mode Flag CPUID Feature Instruction En bit Mode Flag Op/ 64/32 CPUID Feature |  | Support |  | Description
--- | --- | --- | --- | ---
EVEX.LLIG.66.MAP6.W0 4F /r VRSQRTSH xmm1{k1}{z}, xmm2, xmm3/m16 | A | V/V | AVX512-FP16 | Compute the approximate reciprocal square root of the FP16 value in xmm3/m16 and store the result in the low word element of xmm1 subject to writemask k1. Bits 127:16 of xmm2 are copied to xmm1[127:16].

## Instruction Operand Encoding ¶

Op/En | Tuple | Operand 1 | Operand 2 | Operand 3 | Operand 4
--- | --- | --- | --- | --- | ---
A | Scalar | ModRM:reg (w) | VEX.vvvv (r) | ModRM:r/m (r) | N/A

### Description ¶

This instruction performs the computation of the approximate reciprocal square-root of the low FP16 value in the second source operand (the third operand) and stores the result in the low word element of the destination operand (the first operand) according to the writemask k1.

The maximum relative error for this approximation is less than 2−11 + 2−14.

Bits 127:16 of the destination operand are copied from the corresponding bits of the first source operand. Bits MAXVL−1:128 of the destination operand are zeroed.

For special cases, see Table 5-38.

### Operation ¶

#### VRSQRTSH dest{k1}, src1, src2 ¶

    VL = 128, 256 or 512
    KL := VL/16
    IF k1[0] or *no writemask*:
        DEST.fp16[0] := APPROXIMATE(1.0 / SQRT(src2.fp16[0]))
    ELSE IF *zeroing*:
        DEST.fp16[0] := 0
    //else DEST.fp16[0] remains unchanged
    DEST[127:16] := src1[127:16]
    DEST[MAXVL-1:128] := 0

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

    VRSQRTSH __m128h _mm_mask_rsqrt_sh (__m128h src, __mmask8 k, __m128h a, __m128h b);

    VRSQRTSH __m128h _mm_maskz_rsqrt_sh (__mmask8 k, __m128h a, __m128h b);

    VRSQRTSH __m128h _mm_rsqrt_sh (__m128h a, __m128h b);

### SIMD Floating-Point Exceptions ¶

None.

### Other Exceptions ¶

EVEX-encoded instruction, see Table 2-58, “Type E10 Class Exception Conditions.”