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As per the issue I created at numpy's GitHub:

the differences you are experiencing seem to be all within a single "ULP" (unit in the last place), maybe 2? For special math functions, like exp, or sin, small errors are unfortunately expected and can be system dependend (both hardware and OS/math libraries).

One thing that could be would might have a slightly larger effect could be use of SVML that NumPy has on newer machines (i.e. only on the intel one). That can be disabled at build time using NPY_DISABLE_SVML=1 as an environment variable, but I don't think you can disable its use without building NumPy. (However, right now, it may well be that the M1 machine is the less precise one, or that they are both roughly the same, just different)

I haven't tried compiling numpy using NPY_DISABLE_SVML=1 and my plan now is to use a docker container that can run on all my platforms and use a single "truth" for my tests.

In order to make installing of Ruby versions 2.6.x or 2.7.x successful on M1 MacBook using either rbenv or asdf (asdf is used in this example) follow these steps:

Upgrade to the latest version of rbenv or asdf-ruby plugin using your prefered installation method. In my case it's asdf-ruby installed over homebrew:

I found the answer (https://github.com/Homebrew/discussions/discussions/2482)

Currently (2022-02-05), CRAN builds R binaries for Apple silicon using Apple clang (from Command Line Tools for Xcode 12.4) and an experimental build of gfortran.

If you obtain R from CRAN (i.e., here), then you need to replicate CRAN's compiler setup on your system before building R packages that contain C/C++/Fortran code from their sources (and before using Rcpp, etc.). This requirement ensures that your package builds are compatible with R itself.

A further complication is the fact that Apple clang doesn't support OpenMP, so you need to do even more work to compile programs that make use of multithreading. You could circumvent the issue by building R itself and all R packages from sources with LLVM clang, which does support OpenMP, but this approach is onerous and "for experts only". There is another approach that has been tested by a few people, including Simon Urbanek, the maintainer of R for macOS. It is experimental and also "for experts only", but seems to work on my machine and is simpler than trying to build R yourself.

Warning: These instructions come with no warranty and could break at any time. They assume some level of familiarity with C/C++/Fortran program compilation, Makefile syntax, and Unix shells. As usual, sudo at your own risk.

I will try to address compilers and OpenMP support at the same time. I am going to assume that you are starting from nothing. Feel free to skip steps you've already taken, though you might find a fresh start helpful.

I've tested these instructions on a machine running Big Sur, and at least one person has tested them on a machine running Monterey. I would be glad to hear from others.

1. Download an R binary from CRAN here and install. Be sure to select the binary built for Apple silicon.

2. Run

Try using the new arm version of python!

Seems a bug of openssl itself. https://github.com/openssl/openssl/issues/16487

~~What about export SDKROOT="/Library/Developer/CommandLineTools/SDKs/MacOSX.sdk "?~~

Homebrew pre-build packages for some versions of macOS. But it keep dropping this pre-building support for old macOS. On macOS 10.12, you're building openssl from the source code and Xcode command line tool is needed.

I found a solution myself in reinstalling apr-util:

brew reinstall apr-util

Install llvm with debug mode enabled:

I got the same problem. Open your terminal and write this: