OpenCLで複素数を処理する関数が必要になったので、私はそれらのセットを実装しました。具体的には、和と減算(簡単な、標準的なベクトル演算で行うことができます)、乗算、除算、複素数の係数、引数(または角度)と平方根の取得が必要でした。
関連するWikipediaの記事:
http://en.wikipedia.org/wiki/Complex_number#Absolute_value_and_argument
http://en.wikipedia.org/wiki/Square_root#Principal_square_root_of_a_complex_number
これは、ほとんど自明で、誰かにこの時間を節約するかもしれないで期待してて、それは、ある程度の時間がかかるん、ここに行く:
//2 component vector to hold the real and imaginary parts of a complex number:
typedef float2 cfloat;
#define I ((cfloat)(0.0, 1.0))
/*
* Return Real (Imaginary) component of complex number:
*/
inline float real(cfloat a){
return a.x;
}
inline float imag(cfloat a){
return a.y;
}
/*
* Get the modulus of a complex number (its length):
*/
inline float cmod(cfloat a){
return (sqrt(a.x*a.x + a.y*a.y));
}
/*
* Get the argument of a complex number (its angle):
* http://en.wikipedia.org/wiki/Complex_number#Absolute_value_and_argument
*/
inline float carg(cfloat a){
if(a.x > 0){
return atan(a.y/a.x);
}else if(a.x < 0 && a.y >= 0){
return atan(a.y/a.x) + M_PI;
}else if(a.x < 0 && a.y < 0){
return atan(a.y/a.x) - M_PI;
}else if(a.x == 0 && a.y > 0){
return M_PI/2;
}else if(a.x == 0 && a.y < 0){
return -M_PI/2;
}else{
return 0;
}
}
/*
* Multiply two complex numbers:
*
* a = (aReal + I*aImag)
* b = (bReal + I*bImag)
* a * b = (aReal + I*aImag) * (bReal + I*bImag)
* = aReal*bReal +I*aReal*bImag +I*aImag*bReal +I^2*aImag*bImag
* = (aReal*bReal - aImag*bImag) + I*(aReal*bImag + aImag*bReal)
*/
inline cfloat cmult(cfloat a, cfloat b){
return (cfloat)(a.x*b.x - a.y*b.y, a.x*b.y + a.y*b.x);
}
/*
* Divide two complex numbers:
*
* aReal + I*aImag (aReal + I*aImag) * (bReal - I*bImag)
* ----------------- = ---------------------------------------
* bReal + I*bImag (bReal + I*bImag) * (bReal - I*bImag)
*
* aReal*bReal - I*aReal*bImag + I*aImag*bReal - I^2*aImag*bImag
* = ---------------------------------------------------------------
* bReal^2 - I*bReal*bImag + I*bImag*bReal -I^2*bImag^2
*
* aReal*bReal + aImag*bImag aImag*bReal - Real*bImag
* = ---------------------------- + I* --------------------------
* bReal^2 + bImag^2 bReal^2 + bImag^2
*
*/
inline cfloat cdiv(cfloat a, cfloat b){
return (cfloat)((a.x*b.x + a.y*b.y)/(b.x*b.x + b.y*b.y), (a.y*b.x - a.x*b.y)/(b.x*b.x + b.y*b.y));
}
/*
* Square root of complex number.
* Although a complex number has two square roots, numerically we will
* only determine one of them -the principal square root, see wikipedia
* for more info:
* http://en.wikipedia.org/wiki/Square_root#Principal_square_root_of_a_complex_number
*/
inline cfloat csqrt(cfloat a){
return (cfloat)(sqrt(cmod(a)) * cos(carg(a)/2), sqrt(cmod(a)) * sin(carg(a)/2));
}
記事ここで私それを行う方法をllustrates:http://developer.amd.com/resources/documentation-articles/articles-whitepapers/opencl-optimization-case-study-fast-fourier-transform-part-1/ – ChrisF