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VRSQRT14PD

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Henk-Jan Lebbink edited this page Jun 5, 2018 · 12 revisions

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) NA NA

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

Table 5-26. VRSQRT14PD Special Cases

<table>
	<tr>
		<td><b>Input value</b></td>
		<td><b>Result value</b></td>
		<td><b>Comments</b></td>
	</tr>
	<tr>
		<td>Any denormal</td>
		<td>Normal</td>
		<td>Cannot generate overflow</td>
	</tr>
	<tr>
		<td>X = 2-2n</td>
		<td>2n</td>
		<td></td>
	</tr>
	<tr>
		<td>X < 0</td>
		<td>QNaN_Indefinite</td>
		<td>Including -INF</td>
	</tr>
	<tr>
		<td>X = -0</td>
		<td>-INF</td>
		<td></td>
	</tr>
	<tr>
		<td>X = +0</td>
		<td>+INF</td>
		<td></td>
	</tr>
	<tr>
		<td>X = +INF</td>
		<td>+0</td>
		<td></td>
	</tr>
</table>

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 Exceptions Type E4.

Source: Intel® Architecture Software Developer's Manual (May 2018)
Generated: 5-6-2018

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