# Using the syntax in C++/Cuda code

The expressions and variables presented in the common documentation all
correspond to specific C++ types of variables defined by the KeOps
library. The C++ keyword `auto`

allows us to define them without
having to worry about explicit type naming:

```
auto p = Pm(0,1);
auto a = Vj(1,1);
auto x = Vi(2,3);
auto y = Vj(3,3);
auto f = Square(p-y)*Exp(x+y);
```

Here, the `f`

variable represents a symbolic computation; as a C++ object, it is completely useless.

The list of available operations to build a formula is given in the following table: Math operators.

Next we define the type of reduction that we want to perform, as follows:

```
auto Sum_f = Sum_Reduction(f,0);
```

This means that we want to perform a sum reduction over the “j” indices, resulting in an “i”-indexed output.
We would use `Sum_Reduction(f,1)`

for a reduction over the “i” indices.

The list of available reductions is given in the following table: Reductions. The code name of the reduction must be followed by `_Reduction`

in C++ code.

The convolution operation is then performed using one of these three calls:

```
EvalRed<CpuConv>(Sum_f,Nx, Ny, pres, params, px, py, pu, pv, pb);
EvalRed<GpuConv1D_FromHost>(Sum_f,Nx, Ny, pres, params, px, py, pu, pv, pb);
EvalRed<GpuConv2D_FromHost>(Sum_f,Nx, Ny, pres, params, px, py, pu, pv, pb);
```

where `pc`

, `pp`

, `pa`

, `px`

, and `py`

are pointers to their respective arrays in (Cpu) memory, `pc`

denoting the output. These three functions correspond to computations performed respectively on the Cpu, on the Gpu with a “1D” tiling algorithm, and with a “2D” tiling algorithm.

For a minimal working example code, see the files `./keops/examples/test_simple.cpp`_ and `./keops/examples/test_simple.cu`_

If data arrays are already located in the GPU memory, these functions should be favored:

```
EvalRed<GpuConv1D_FromDevice>(Sum_f,Nx, Ny, pres, params, px, py, pu, pv, pb);
EvalRed<GpuConv2D_FromDevice>(Sum_f,Nx, Ny, pres, params, px, py, pu, pv, pb);
```