that depending on the task the other uses memory cache more efficiently.
This block of four three dimensional vectors will be called mat4x3 data type in the code. To see its usefulness we will normalize these
four vectors in it. To achieve that first 3 multiplications followed by 3 additions are needed vertically as follows:
Continuing from that we can execute a special SSE square root instruction to the result and multiple each three of the original
components with its reciprocal to get the final result (also mat4x3, of course):
This normalization can be seen in the first code example.
5.0 Mask operations
With width four SIMD at least four bits are needed to represent a mask:
SSE uses the same 128-bit type for representing masks returned by floating point comparisons. Single float's byte sequence 0x00000000
in hexadecimals represents false and 0xFFFFFFFF represents true. SSE has comparison instructions for all the basic arithmetic
comparisons like greater or equal than.
Mask are then produced by using standard C++ comparison operators between two vec4 types:
or listing all the elements:
The resulting mask can then be used to conditionally only write to parts of vec4 or deciding a path based on whether all the bits are set,
none of them are set, or some of them are set.
Examples of different kinds of control logic turned into mask operations can be found in the algorithm examples.
6.0 C++ SSE header
In February 2009 Krzysztof Jakubowski posted a full implementation of C++ wrapping over the 32-bit floating point and the 32-bit
integer SSE C intrinsics on a ray tracing Internet forum called ompf. It is called veclib and it s licensed with very permissive zlib license.
From my experiments with that implementation this guide was born.
Generally, when writing vector code in vector notation in C++, one can in my experience do so without any overhead to worry about by
using expression templates. Basically expression templates help avoid unnecessary temporaries over naive C++ operator overloaded
implementations. An implementation of this is a BSD-type licensed piece of code called cvalarray.
What I advocate is to use these two implementations together to get, as far as I know, the fastest and neatest freely available C++
implementation of basic 3D vectors and SSE types. Of course, for some specific higher level tasks there are better options, like Eigen for
linear algebra. To get better notation compared to what veclib uses I took example of GLSL specifications to come up with this for
writing SSE code:
C++ vector types with SSE for single precision (32-bit)
vec2,vec3,vec4 floating point vector
vec2b,vec3b,vec4b mask type for floating point vector
ivec2,ivec3,ivec4 signed integer vector
ivec2b,ivec3b,ivec4b mask type for signed integer vector
mat4x2,mat4x3,mat4x4 4 column floating point matrix (SSE)
Also any of these can be prefixed with "p" for double precision. And this is then a full header file, that implements part of these types:
#include "cvalarray.hpp"
#include "veclib.h"
typedef veclib::f32x4 vec4;
typedef veclib::f32x4b vec4b;
typedef veclib::i32x4 ivec4;
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