# RSQRTPS (Compute Reciprocals of Square Roots of Packed Single-Precision Floating-Point Values)

## Opcodes

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

0F 52 /r
RSQRTPS xmm1, xmm2/m128 |
RM | V/V | SSE | Computes the approximate reciprocals of the square roots of the packed single-precision floating-point values in xmm2/m128 and stores the results in xmm1. |

VEX.128.0F.WIG 52 /r
VRSQRTPS xmm1, xmm2/m128 |
RM | V/V | AVX | Computes the approximate reciprocals of the square roots of packed single-precision values in xmm2/mem and stores the results in xmm1. |

VEX.256.0F.WIG 52 /r
VRSQRTPS ymm1, ymm2/m256 |
RM | V/V | AVX | Computes the approximate reciprocals of the square roots of packed single-precision values in ymm2/mem and stores the results in ymm1. |

## Instruction Operand Encoding

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

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

## Description

Performs a SIMD computation of the approximate reciprocals of the square roots of the four packed single-preci-sion floating-point values in the source operand (second operand) and stores the packed single-precision floating-point results in the destination operand. The source operand can be an XMM register or a 128-bit memory location. The destination operand is an XMM register. See Figure 10-5 in the *Intel® 64 and IA-32 Architectures Software Developer’s Manual, Volume 1*, for an illustration of a SIMD single-precision floating-point operation.

The relative error for this approximation is:

|Relative Error| ≤ 1.5 ∗ 2^{−12}

The RSQRTPS 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 second source can be an XMM register or an 128-bit memory location. The desti-nation is not distinct from the first source XMM register and the upper bits (VLMAX-1:128) of the corresponding YMM register destination are unmodified.

VEX.128 encoded version: the first source operand is an XMM register or 128-bit memory location. The destination operand is an XMM register. The upper bits (VLMAX-1:128) of the corresponding YMM register destination are zeroed.

VEX.256 encoded version: The first source operand is a YMM register. The second source operand can be a YMM register or a 256-bit memory location. The destination operand is a YMM register.

Note: In VEX-encoded versions, VEX.vvvv is reserved and must be 1111b, otherwise instructions will #UD.

## Operation

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

DEST[31:0] ← APPROXIMATE(1/SQRT(SRC[31:0])) DEST[63:32] ← APPROXIMATE(1/SQRT(SRC1[63:32])) DEST[95:64] ← APPROXIMATE(1/SQRT(SRC1[95:64])) DEST[127:96] ← APPROXIMATE(1/SQRT(SRC2[127:96])) DEST[VLMAX-1:128] (Unmodified)

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

DEST[31:0] ← APPROXIMATE(1/SQRT(SRC[31:0])) DEST[63:32] ← APPROXIMATE(1/SQRT(SRC1[63:32])) DEST[95:64] ← APPROXIMATE(1/SQRT(SRC1[95:64])) DEST[127:96] ← APPROXIMATE(1/SQRT(SRC2[127:96])) DEST[VLMAX-1:128] ← 0

**VRSQRTPS (VEX.256 encoded version)**

DEST[31:0] ← APPROXIMATE(1/SQRT(SRC[31:0])) DEST[63:32] ← APPROXIMATE(1/SQRT(SRC1[63:32])) DEST[95:64] ← APPROXIMATE(1/SQRT(SRC1[95:64])) DEST[127:96] ← APPROXIMATE(1/SQRT(SRC2[127:96])) DEST[159:128] ← APPROXIMATE(1/SQRT(SRC2[159:128])) DEST[191:160] ← APPROXIMATE(1/SQRT(SRC2[191:160])) DEST[223:192] ← APPROXIMATE(1/SQRT(SRC2[223:192])) DEST[255:224] ← APPROXIMATE(1/SQRT(SRC2[255:224]))

## Intel C/C++ Compiler Intrinsic Equivalent

RSQRTPS:

__m128 _mm_rsqrt_ps(__m128 a)

RSQRTPS:

__m256 _mm256_rsqrt_ps (__m256 a);

## SIMD Floating-Point Exceptions

None.

## Other Exceptions

See Exceptions Type 4; additionally

#UD | If VEX.vvvv ≠ 1111B. |
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