The command
swift build --destination /tmp/cross-toolchain/arm64v8-ubuntu-bionic-destination.json
Results in:

ld: unknown option: -rpath=$ORIGIN
<unknown>:0: error: link command failed with exit code 1 (use -v to see invocation)

Using the -v option, the result is:

xcrun --sdk macosx --find xctest
xcrun --sdk macosx --show-sdk-path
xcrun --sdk macosx --show-sdk-platform-path
xcrun --sdk macosx --find xctest
/private/tmp/cross-toolchain/swift.xctoolchain/usr/bin/swiftc -sdk /private/tmp/cross-toolchain/arm64v8-ubuntu-bionic.sdk -use-ld=gold -tools-directory /private/tmp/cross-toolchain/swift.xctoolchain/usr/bin -g -L /Users/freeksanders/helloworld/.build/aarch64-unknown-linux/debug -o /Users/freeksanders/helloworld/.build/aarch64-unknown-linux/debug/helloworld -module-name helloworld -emit-executable -Xlinker '-rpath=$ORIGIN' @/Users/freeksanders/helloworld/.build/aarch64-unknown-linux/debug/helloworld.product/Objects.LinkFileList
ld: unknown option: -rpath=$ORIGIN
<unknown>:0: error: link command failed with exit code 1 (use -v to see invocation)

This can be 'solved' by changing the '-rpath=$ORIGIN' to -rpath $ORIGIN, i.o.w.:
/private/tmp/cross-toolchain/swift.xctoolchain/usr/bin/swiftc -sdk /private/tmp/cross-toolchain/arm64v8-ubuntu-bionic.sdk -use-ld=gold -tools-directory /private/tmp/cross-toolchain/swift.xctoolchain/usr/bin -g -L /Users/freeksanders/helloworld/.build/aarch64-unknown-linux/debug -o /Users/freeksanders/helloworld/.build/aarch64-unknown-linux/debug/helloworld -module-name helloworld -emit-executable -Xlinker -rpath $ORIGIN @/Users/freeksanders/helloworld/.build/aarch64-unknown-linux/debug/helloworld.product/Objects.LinkFileList

However, that creates the following error:
ld: library not found for -lobjc

Seems the issue might be related to this:
https://stackoverflow.com/a/7388525/2500428

Not sure how to proceed here, but any pointers would be nice.

The script runs the build of binutils fine but just stops at:
Configuring gold (~11s)..
.. building gold (~1m)..

The xt-gold-make.log shows as first error:
gold-threads.cc:288:13: error: expected expression
: once_(PTHREAD_ONCE_INIT)
^
/Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.14.sdk/usr/include/pthread.h:216:27: note: expanded from macro 'PTHREAD_ONCE_INIT'
#define PTHREAD_ONCE_INIT {_PTHREAD_ONCE_SIG_init, {0}}

Any insights in how to get past this ?

UPDATE: I just realized my supposedly 64-bit Raspberry Pi is actually 32-bit (I think). Seems the Raspbian releases are still 32-bit. Lame.

$ arch
armv7l
$ cat /proc/cpuinfo
processor	: 0
model name	: ARMv7 Processor rev 3 (v7l)
BogoMIPS	: 108.00
Features	: half thumb fastmult vfp edsp neon vfpv3 tls vfpv4 idiva idivt vfpd32 lpae evtstrm crc32 
CPU implementer	: 0x41
CPU architecture: 7
CPU variant	: 0x0
CPU part	: 0xd08
CPU revision	: 3
.
.
.

I followed your link to the pre-built toolchain. I'd open an issue at that fork, but they haven't enabled Github Issues for the repo (https://github.com/CSCIX65G/SwiftCrossCompilers).

I ran through the steps to build the helloworld example, but it won't run on RPi 4 with Debian Buster:

$ ./helloworld 
-bash: ./helloworld: cannot execute binary file: Exec format error
$ file ./helloworld 
./helloworld: ELF 64-bit LSB pie executable, ARM aarch64, version 1 (SYSV), dynamically linked, interpreter /lib/ld-linux-aarch64.so.1, for GNU/Linux 3.7.0, with debug_info, not stripped

As you can see, the file format is slightly different from the LSB shared object type your README mentions. I built it using:

$ swift build --destination /Library/Developer/Destinations/arm64-5.0-RELEASE.json

which contains

{
    "version": 1,
    "sdk": "/Library/Developer/SDKs/arm64-5.0-RELEASE.sdk",
    "sysroot-flag": "/Library/Developer/Toolchains/arm64-5.0-RELEASE.xctoolchain",
    "toolchain-bin-dir": "/Library/Developer/Toolchains/arm64-5.0-RELEASE.xctoolchain/usr/bin",
    "target": "aarch64-unknown-linux",
    "dynamic-library-extension": "so",
    "extra-cc-flags": [
        "-I", "/Library/Developer/SDKs/arm64-5.0-RELEASE.sdk/usr/include/aarch64-linux-gnu",
        "-I", "/Library/Developer/SDKs/arm64-5.0-RELEASE.sdk/usr/include",
        "-fPIC"
    ],
    "extra-swiftc-flags": [
        "-target", "aarch64-unknown-linux",
        "-use-ld=gold", "-tools-directory", "/Library/Developer/Toolchains/arm64-5.0-RELEASE.xctoolchain/usr/bin"
    ],
    "extra-cpp-flags": [
        "-I", "/Library/Developer/SDKs/arm64-5.0-RELEASE.sdk/usr/include/aarch64-linux-gnu",
        "-I", "/Library/Developer/SDKs/arm64-5.0-RELEASE.sdk/usr/include"
    ]
}

I am not using Docker because there are no obvious instructions on how to do that with the pre-built toolchain (or even if it’s necessary).

I realize this is probably not directly your responsibility, but I’d sure appreciate any help. Thanks!

After patching gold-threads.cc line 288, I was able to build the complete toolchain.
I checked everything including the file format which my Mac with Mojave said was:

"ELF 64-bit LSB pie executable ARM aarch64, version 1 (SYSV), dynamically linked, interpreter /lib/ld-linux-aarch64.so.1, for GNU/Linux 3.7.0, with debug_info, not stripped"

Copied it to an RPi 3B+ with Ubuntu Bionic but ./helloworld would not start with bash error:
"./helloworld: cannot execute binary file: Exec format error"

Any idea why that might be the case ?
(RPi running Linux 4.14.34-hypriotos-v7+ armv71 GNU/Linux)

When I run swift build --destination /tmp/cross-toolchain/arm64v8-ubuntu-bionic-destination.json

I get the following error message:

<unknown>:0: error: unknown argument: '-color-diagnostics'

Does anyone know how to fix this issue?

If I just run swift build then everything works correctly, so it's only an issue when trying to use the cross-toolchain.

I've tried this on two macs, one using Xcode 12 and the other using Xcode 11.