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].

Opcode*/Instruction

Op/En

64/32 bit Mode Support

CPUID Feature Flag

Description

F3 0F 52 /r

RSQRTSS xmm1, xmm2/m32

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.”