Fatal error: cuda.h: No such file or directory

I have never compiled a cuda project myself but I think you will need to link the library to the compiler.

Some quick googling says Nvidia has compiler for this which will handle everything. So you just need to install that and you should be good to go. It's called NVVC. Once installed just run:

nvcc helloworld.cu -o hello.out

With external libraries like these, you almost always need to link them. You don't have to do it for the standard library because the linker already knows where to find it.

The proper include header file for this is not cuda.h but cuda_runtime.h, assuming you want to use gcc as the compiler for this code. As the other answer points out, you could just use nvcc (which is already installed on your machine) which wouldn't require any include headers for this code at all.

If you want to use nvcc you probably should make sure that the appropriate PATH environment variable is set. This and other useful information is contained in the linux install guide.

So if you modify your code like this:

#include <cuda_runtime.h>

int main ()
{
    int deviceCount;
    cudaError_t e = cudaGetDeviceCount(&deviceCount);
    return e == cudaSuccess ? deviceCount : -1;
}

You should be able to compile it successfully using a command something like this:

gcc -I/usr/local/cuda/include -L/usr/local/cuda/lib64 has_cuda.c -lcudart -o has_cuda

The path after the -I switch should contain the path to cuda_runtime.h on your machine. Normally that would be set up as above, but I'm not sure if the cuda symlink is set up on your machine, and also it looks like your include directory may be at an unusual place, i.e.

/usr/local/cuda-8.0/targets/x86_64-linux/include

but you can use find just as you have been doing to locate it.

Likewise, the path after the -L switch needs to be the path to your cuda lib64 directory, which will contain libcudart.so and and its cousins. Again, that would normally be symlinked on the path I have shown, but your machine install may not conform to my expectations. You should be able to use find to locate the correct path.

And as indicated in the other answer, if you use nvcc (which you have already located), you won't need to explicitly select the -I and -L path. The easiest way to make this work is to rename your file from has_cuda.c to has_cuda.cu, then you should be able to compile like this:

nvcc has_cuda.cu -o has_cuda

Finally, Ubuntu 16.10 is not an officially supported distribution for CUDA at this time, so there may be some things unexpected about the way it got installed on your machine. I'd encourage you to read the previously linked install guide, as it contains useful information about post-installation setup steps, such as setting environment variables, and also how to "verify" the CUDA installation.

Any time you are running CUDA codes, and having any sort of trouble, make sure to use proper cuda error checking and run your codes with cuda-memcheck, like so:

cuda-memcheck ./has_cuda

Even if you don't understand the error information reported, it may be useful for those trying to help you.