VRSQRT14SD — Compute Approximate Reciprocal of Square Root of Scalar Float64 Value

Opcode/Instruction	Op/En	64/32 bit Mode Support	CPUID Feature Flag	Description
EVEX.LLIG.66.0F38.W1 4F /r VRSQRT14SD xmm1 {k1}{z}, xmm2, xmm3/m64	A	V/V	AVX512F	Computes the approximate reciprocal square root of the scalar double precision floating-point value in xmm3/m64 and stores the result in the low quadword element of xmm1 using writemask k1. Bits[127:64] of xmm2 is copied to xmm1[127:64].

Instruction Operand Encoding ¶

Op/En	Tuple Type	Operand 1	Operand 2	Operand 3	Operand 4
A	Tuple1 Scalar	ModRM:reg (w)	EVEX.vvvv (r)	ModRM:r/m (r)	N/A

Description ¶

Computes the approximate reciprocal of the square roots of the scalar double precision floating-point value in the low quadword element of the source operand (the second operand) and stores the result in the low quadword element of the destination operand (the first operand) according to the writemask. The maximum relative error for this approximation is less than 2^-14. The source operand can be an XMM register or a 32-bit memory location. The destination operand is an XMM register.

Bits (127:64) of the XMM register destination are copied from corresponding bits in the first source operand. Bits (MAXVL-1:128) of the destination register are zeroed.

The VRSQRT14SD 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.

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 ¶

VRSQRT14SD (EVEX version) ¶

IF k1[0] or *no writemask*
    THEN DEST[63:0] := APPROXIMATE(1.0/ SQRT(SRC2[63:0]))
    ELSE
        IF *merging-masking* ; merging-masking
            THEN *DEST[63:0] remains unchanged*
            ELSE
                    ; zeroing-masking
                THEN DEST[63:0] := 0
        FI;
FI;
DEST[127:64] := SRC1[127:64]
DEST[MAXVL-1:128] := 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 5-35. VRSQRT14SD Special Cases

Intel C/C++ Compiler Intrinsic Equivalent ¶

VRSQRT14SD __m128d _mm_rsqrt14_sd( __m128d a, __m128d b);

VRSQRT14SD __m128d _mm_mask_rsqrt14_sd(__m128d s, __mmask8 k, __m128d a, __m128d b);

VRSQRT14SD __m128d _mm_maskz_rsqrt14_sd( __mmask8d m, __m128d a, __m128d b);

SIMD Floating-Point Exceptions ¶

None.

Other Exceptions ¶

See Table 2-51, “Type E5 Class Exception Conditions.”