RCPSS — Compute Reciprocal of Scalar Single Precision Floating-Point Values

Opcode*/Instruction	Op/En	64/32 bit Mode Support	CPUID Feature Flag	Description
F3 0F 53 /r RCPSS xmm1, xmm2/m32	RM	V/V	SSE	Computes the approximate reciprocal of the scalar single precision floating-point value in xmm2/m32 and stores the result in xmm1.
VEX.LIG.F3.0F.WIG 53 /r VRCPSS xmm1, xmm2, xmm3/m32	RVM	V/V	AVX	Computes the approximate reciprocal of the scalar single precision floating-point value in xmm3/m32 and stores the result 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 of an approximate reciprocal of the low single precision floating-point value in the source operand (second operand) and 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 RCPSS 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 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 ¶

RCPSS (128-bit Legacy SSE Version) ¶

DEST[31:0] := APPROXIMATE(1/SRC[31:0])
DEST[MAXVL-1:32] (Unmodified)

VRCPSS (VEX.128 Encoded Version) ¶

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

Intel C/C++ Compiler Intrinsic Equivalent ¶

RCPSS __m128 _mm_rcp_ss(__m128 a)

SIMD Floating-Point Exceptions ¶

None.

Other Exceptions ¶

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