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SSE Reciprocal instructions
 A basic building block operation in geometry
involves computing divisions and square roots. For instance, transformation
often involves dividing each x, y, z coordinate by the W perspective coordinate;
normalization is another common geometry operation, which requires the
computation of 1/square-root. In order to optimize these cases, SSE introduces
two approximation instructions: RCP and RSQRT. These instructions are implemented
via hardware lookup tables and are inherently less precise (12 bits of
mantissa) than the full IEEE-compliant DIV and SQRT (24 bits of mantissa),
but have the advantage of being much faster than the full precision versions.
When greater precision is needed, the approximation instructions can be
used with a single Newton-Raphson iteration to achieve almost the same
precision as the IEEE instructions (~22 bits of mantissa). For a basic
geometry pipeline, these instructions can improve overall performance on
the order of 15%.
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RCPSS xmm1, xmm2/m32 |
| Computes of an approximate reciprocal 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.
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| DEST[31-0] ← APPROX (1.0/(SRC[31-0])); |
| RCPSS __m128 _mm_rcp_ss(__m128 a) |
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RCPPS xmm1, xmm2/m128 |
| 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.
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DEST[31-0] ←
APPROXIMATE(1.0/(SRC[31-0]));
DEST[63-32] ← APPROXIMATE(1.0/(SRC[63-32]));
DEST[95-64] ← APPROXIMATE(1.0/(SRC[95-64]));
DEST[127-96] ← APPROXIMATE(1.0/(SRC[127-96])); |
| RCCPS __m128 _mm_rcp_ps(__m128 a) |
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RSQRTSS xmm1, xmm2/m32 |
| 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.
 |
| DEST[31-0] ←
APPROXIMATE(1.0/SQRT(SRC[31-0])); |
| RSQRTSS __m128 _mm_rsqrt_ss(__m128 a) |
|
RSQRTPS xmm1, xmm2/m128 |
| Performs a SIMD computation of the
approximate reciprocals of the square roots of the four packed
single-precision 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.
 |
DEST[31-0] ←
APPROXIMATE(1.0/SQRT(SRC[31-0]));
DEST[63-32] ← APPROXIMATE(1.0/SQRT(SRC[63-32]));
DEST[95-64] ← APPROXIMATE(1.0/SQRT(SRC[95-64]));
DEST[127-96] ← APPROXIMATE(1.0/SQRT(SRC[127-96])); |
| RSQRTPS __m128 _mm_rsqrt_ps(__m128 a) |
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