# RSQRTSS (Compute Reciprocal of Square Root of Scalar Single-Precision Floating-Point Value)

## Opcodes

Opcode*/Instruction | Op/En | 64/32 bit Mode Support | CPUID Feature Flag | Description |
---|---|---|---|---|

F3 0F 52 /r
RSQRTSS xmm1, xmm2/m32 |
RM | V/V | SSE | Computes the approximate reciprocal of the square root of the low single-precision floating-point value in xmm2/m32 and stores the results in xmm1. |

VEX.NDS.LIG.F3.0F.WIG 52 /r VRSQRTSS xmm1, xmm2, xmm3/m32 |
RVM | V/V | AVX | Computes the approximate reciprocal of the square root of the low single precision floating-point value in xmm3/m32 and stores the results in xmm1. Also, upper single precision floating-point values (bits[127:32]) from xmm2 are copied to xmm1[127:32]. |

## Instruction Operand Encoding

Op/En | Operand 1 | Operand 2 | Operand 3 | Operand 4 |
---|---|---|---|---|

RM | ModRM:reg (w) | ModRM:r/m (r) | NA | NA |

RVM | ModRM:reg (w) | VEX.vvvv (r) | ModRM:r/m (r) | NA |

## Description

Computes an approximate reciprocal of the square root of the low single-precision floating-point value in the source operand (second operand) stores the single-precision floating-point result in the destination operand. The source operand can be an XMM register or a 32-bit memory location. The destination operand is an XMM register. The three high-order doublewords of the destination operand remain unchanged. See Figure 10-6 in the *Intel® 64 and IA-32 Architectures Software Developer’s Manual, Volume 1*, for an illustration of a scalar single-precision floating-point operation.

The relative error for this approximation is:

|Relative Error| ≤ 1.5 ∗ 2^{−12}

The RSQRTSS instruction is not affected by the rounding control bits in the MXCSR register. When a source value is a 0.0, an ∞ of the sign of the source value is returned. A denormal source value is treated as a 0.0 (of the same sign). When a source value is a negative value (other than −0.0), a floating-point 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.

In 64-bit mode, using a REX prefix in the form of REX.R permits this instruction to access additional registers (XMM8-XMM15).

128-bit Legacy SSE version: The first source operand and the destination operand are the same. Bits (VLMAX-1:32) of the corresponding YMM destination register remain unchanged.

VEX.128 encoded version: Bits (VLMAX-1:128) of the destination YMM register are zeroed.

## Operation

**RSQRTSS (128-bit Legacy SSE version)**

DEST[31:0] ← APPROXIMATE(1/SQRT(SRC2[31:0])) DEST[VLMAX-1:32] (Unmodified)

**VRSQRTSS (VEX.128 encoded version)**

DEST[31:0] ← APPROXIMATE(1/SQRT(SRC2[31:0])) DEST[127:32] ← SRC1[127:32] DEST[VLMAX-1:128] ← 0

## Intel C/C++ Compiler Intrinsic Equivalent

RSQRTSS:

__m128 _mm_rsqrt_ss(__m128 a)

## SIMD Floating-Point Exceptions

None.

## Other Exceptions

See Exceptions Type 5.