Want to add to @Stephen Kitt answer's and emphasize that the settings of the ARCH and CROSS_COMPILE variables (but mainly the ARCH) is curical EVEN before the configuration phase.

In this example, I would assume the OTHER WAY AROUND (i.e. corss compile Linux kernel from Mac which is aarch64 to Intel which is x86_64), but the idea is the same and relevant also in your "cross compilation dicrection":

Let's say your target machine's kernel config has this setting:

CONFIG_DRM_I915=y
CONFIG_DRM_I915_GVT=y

Without ARCH=x86_64 set, what happens (during kernel configuration phase on the host machine which is aarch64):

1. Kernel sees host ARCH = aarch64
2. Checks if CONFIG_DRM_I915 is valid for aarch64
3. Intel graphics driver is x86_64-only
4. CONFIG_DRM_I915=y gets SILENTLY DROPPED

(see how this driver's compilation/configuration is dependent on the X86 compilation flag here)

5. Your .config (in the kernel's source folder on your host machine) loses Intel graphics support.

With ARCH=x86_64 set the relevant configuration for the CONFIG_DRM_I915 will be set correctly as you probably desired.

looks like a PATH issue. what happens when you just type "aarch64-linux-gnu-gcc "in your shell? does it find the compiler?

64-bit ARM

For 64-bit ARM, the toolchain prefix is aarch64 and usage is:

sudo apt install gcc-aarch64-linux-gnu
aarch64-linux-gnu-gcc -o main.out main.c

You can try it out on this C hello world with QEMU:

main.c

#include <stdio.h>

int main(void) {
    puts("hello");
}

and then:

sudo apt install qemu-user
qemu-aarch64 main.out

will output:

hello

Then a few fun things you can do to quickly see that ARM is actually running under the hood:

• GDB step debug it: https://stackoverflow.com/questions/20590155/how-to-single-step-arm-assembly-in-gdb-on-qemu/51310791#51310791
• log the executed ARM instructions with: qemu-aarch64 -d in_asm,out_asm main.out https://stackoverflow.com/questions/13005303/how-does-native-android-code-written-for-arm-run-on-x86/44505097#44505097

Tested in Ubuntu 19.10.

For reliability in serious applications, the disk image provider must also provide a compatible cross compiler

Although you can install a cross compiler with apt conveniently, I must warn you that this is not necessarily reliable unless explicitly supported by the image provider.

If you pick the cross compiler wrongly, the following may happen:

• the dynamic linker is at the wrong path: https://stackoverflow.com/questions/31929092/trying-to-run-a-cross-compiled-executable-on-target-device-fails-with-no-such-f/49993116#49993116
• binary incompatibility with the glibc and any other libraries you link against: https://stackoverflow.com/questions/11107263/how-compatible-are-different-versions-of-glibc

Raspberry PI cross compilation

For RPI in particular, the provided cross compilers are available at: https://github.com/raspberrypi/tools and can be used as explained at: https://raspberrypi.stackexchange.com/questions/64273/installing-raspberry-pi-cross-compiler/83215#83215

git clone https://github.com/raspberrypi/tools
export PATH="$(pwd)/tools/arm-bcm2708/gcc-linaro-arm-linux-gnueabihf-raspbian-x64/bin:${PATH}"
printf '#include <stdio.h>\nint main() { puts("hello world"); }\n' > hello_world.c
printf '#include <iostream>\nint main() { std::cout << "hello world" << std::endl; }\n' > hello_world.cpp
arm-linux-gnueabihf-gcc -std=c99 -o hello_world_c hello_world.c
arm-linux-gnueabihf-g++ -std=c++11 -o hello_world_cpp hello_world.cpp

Ubuntu cross compilation

If you want to cross compile for Ubuntu arm64, I have never been able to find a clear reference on which cross compilers support which distro version: What are the officially supported cross compilers for Ubuntu server alternative architectures like ARM?

Buildroot

My favorite alternative is to build your own image with Buildroot: https://stackoverflow.com/questions/47557262/how-to-download-the-torvalds-linux-kernel-master-recompile-it-and-boot-it-wi/49349237#49349237

This builds everything from source, including the toolchain and the image, and ensures that everything is compatible.