
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/squareroot. 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 IEEEcompliant 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 NewtonRaphson 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%.
RCPSS xmm1, xmm2/m32 
Computes of an approximate reciprocal of
the low singleprecision floatingpoint value in the source operand (second
operand) stores the singleprecision floatingpoint result in the
destination operand. The source operand can be an XMM register or a 32bit
memory location. The destination operand is an XMM register. The three
highorder doublewords of the destination operand remain unchanged.

DEST[310] ← APPROX (1.0/(SRC[310])); 
RCPSS __m128 _mm_rcp_ss(__m128 a) 
RCPPS xmm1, xmm2/m128 
Performs a SIMD computation of the
approximate reciprocals of the four packed singleprecision floatingpoint
values in the source operand (second operand) stores the packed
singleprecision floatingpoint results in the destination operand. The
source operand can be an XMM register or a 128bit memory location. The
destination operand is an XMM register.

DEST[310] ←
APPROXIMATE(1.0/(SRC[310]));
DEST[6332] ← APPROXIMATE(1.0/(SRC[6332]));
DEST[9564] ← APPROXIMATE(1.0/(SRC[9564]));
DEST[12796] ← APPROXIMATE(1.0/(SRC[12796])); 
RCCPS __m128 _mm_rcp_ps(__m128 a) 
RSQRTSS xmm1, xmm2/m32 
Computes an approximate reciprocal of
the square root of the low singleprecision floating point value in the
source operand (second operand) stores the singleprecision floatingpoint
result in the destination operand. The source operand can be an XMM register
or a 32bit memory location. The destination operand is an XMM register. The
three highorder doublewords of the destination operand remain unchanged.

DEST[310] ←
APPROXIMATE(1.0/SQRT(SRC[310])); 
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
singleprecision floatingpoint values in the source operand (second
operand) and stores the packed singleprecision floatingpoint results in
the destination operand. The source operand can be an XMM register or a
128bit memory location. The destination operand is an XMM register.

DEST[310] ←
APPROXIMATE(1.0/SQRT(SRC[310]));
DEST[6332] ← APPROXIMATE(1.0/SQRT(SRC[6332]));
DEST[9564] ← APPROXIMATE(1.0/SQRT(SRC[9564]));
DEST[12796] ← APPROXIMATE(1.0/SQRT(SRC[12796])); 
RSQRTPS __m128 _mm_rsqrt_ps(__m128 a) 

