C-and-CUDA.md

-TODO
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+Programming language:
+* static codes `st-wslda`:  [C99](https://en.wikipedia.org/wiki/C99) standard
+* time dependent codes `td-wslda`: mixture of [C99](https://en.wikipedia.org/wiki/C99) and [CUDA](https://en.wikipedia.org/wiki/CUDA).  
+
+In general CUDA is compatible with C99. Thus, in practice when editing files (*predefines.h*, *problem-definition.h* or *logger.h*) you can use C language irrespectively to code variants (`st` or `td`). There is only one exception related to function `delta_ext` in *problem-definition.h* file. It declaration is 
+* static codes `st-wslda`: 
+```c
+double complex delta_ext(int ix, int iy, int iz, int it, double complex delta, double *params, size_t extra_data_size, void *extra_data)
+```
+* time dependent codes `td-wslda`:
+```cuda
+__device__ Complex delta_ext(int ix, int iy, int iz, int it, Complex delta, double *params, size_t extra_data_size, void *extra_data)
+```
+
+The change arises from incompatibility of complex type in C99 and CUDA. Namely:
+* `st-wslda`: return type must be C99 [double complex](https://en.cppreference.com/w/c/numeric/complex)
+* `td-wslda`: return type must be compatible with [CUDA Complex](https://thrust.github.io/doc/group__complex__numbers.html)  
+
+Below we provide example of the same code written in both standards:
+* C99  
+```c
+double complex delta_ext(int ix, int iy, int iz, int it, double complex delta, double *params, size_t extra_data_size, void *extra_data)
+{
+    double complex D = 1.0 + I*2.0; // assign value
+    double complex Dc = conj(D); // complex conjugate
+    double absolute_value = cabs(D);
+    double phase = carg(D);
+    double real_part = creal(D);
+    double imginary_part = cimag(D);
+    double complex exponentiation = cexp(D);
+    double complex power = cpow(D, 2);
+    // ...
+    
+    return D; 
+}
+```
+* CUDA  
+```cuda
+__device__ Complex delta_ext(int ix, int iy, int iz, int it, Complex delta, double *params, size_t extra_data_size, void *extra_data)
+{
+    Complex D = Complex(1.0,2.0); // assign value
+    Complex Dc = thrust::conj(D); // complex conjugate
+    double absolute_value = thrust::abs(D);
+    double phase = thrust::arg(D);
+    double real_part = D.real();
+    double imginary_part = D.imag();
+    Complex exponentiation = thrust::exp(D);
+    Complex power = thrust::pow(D, 2);
+    // ...
+    
+    return D; 
+}
+```