# RCPPS — Compute Reciprocals of Packed Single Precision Floating-Point Values

Opcode*/Instruction | Op/En | 64/32 bit Mode Support | CPUID Feature Flag | Description
--- | --- | --- | --- | ---
NP 0F 53 /r RCPPS xmm1, xmm2/m128 | RM | V/V | SSE | Computes the approximate reciprocals of the packed single precision floating-point values in xmm2/m128 and stores the results in xmm1.
VEX.128.0F.WIG 53 /r VRCPPS xmm1, xmm2/m128 | RM | V/V | AVX | Computes the approximate reciprocals of packed single precision values in xmm2/mem and stores the results in xmm1.
VEX.256.0F.WIG 53 /r VRCPPS ymm1, ymm2/m256 | RM | V/V | AVX | Computes the approximate reciprocals 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) | N/A | N/A

## Description ¶

Performs a SIMD computation of the approximate reciprocals of the four packed single precision floating-point values in the source operand (second operand) 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 RCPPS 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). Tiny results (see Section 4.9.1.5, “Numeric Underflow Exception (#U)” in Intel® 64 and IA-32 Architectures Software Developer’s Manual, Volume 1) are always flushed to 0.0, with the sign of the operand. (Input values greater than or equal to |1.11111111110100000000000B∗2125| are guaranteed to not produce tiny results; input values less than or equal to |1.00000000000110000000001B*2126| are guaranteed to produce tiny results, which are in turn flushed to 0.0; and input values in between this range may or may not produce tiny results, depending on the implementation.) 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 destination is not distinct from the first source XMM register and the upper bits (MAXVL-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 (MAXVL-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 ¶

### RCPPS (128-bit Legacy SSE Version) ¶

    DEST[31:0] := APPROXIMATE(1/SRC[31:0])
    DEST[63:32] := APPROXIMATE(1/SRC[63:32])
    DEST[95:64] := APPROXIMATE(1/SRC[95:64])
    DEST[127:96] := APPROXIMATE(1/SRC[127:96])
    DEST[MAXVL-1:128] (Unmodified)

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

    DEST[31:0] := APPROXIMATE(1/SRC[31:0])
    DEST[63:32] := APPROXIMATE(1/SRC[63:32])
    DEST[95:64] := APPROXIMATE(1/SRC[95:64])
    DEST[127:96] := APPROXIMATE(1/SRC[127:96])
    DEST[MAXVL-1:128] := 0

### VRCPPS (VEX.256 Encoded Version) ¶

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

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

    RCCPS __m128 _mm_rcp_ps(__m128 a)

    RCPPS __m256 _mm256_rcp_ps (__m256 a);

## SIMD Floating-Point Exceptions ¶

None.

## Other Exceptions ¶

See Table 2-21, “Type 4 Class Exception Conditions,” additionally:

#UD | If VEX.vvvv ≠ 1111B.