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

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

## 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 (MAXVL-1:32) of the corresponding YMM destination register remain unchanged.

VEX.128 encoded version: Bits (MAXVL-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[MAXVL-1:32] (Unmodified)

### VRSQRTSS (VEX.128 Encoded Version) ¶

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

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

    RSQRTSS __m128 _mm_rsqrt_ss(__m128 a)

## SIMD Floating-Point Exceptions ¶

None.

## Other Exceptions ¶

See Table 2-22, “Type 5 Class Exception Conditions.”