[LinearAlgebra] Support more env variables to set OpenBLAS threads (#46118)

Author: giordano

stdlib/LinearAlgebra/src/LinearAlgebra.jl

@@ -555,14 +555,29 @@ function versioninfo(io::IO=stdout)
         "JULIA_NUM_THREADS",
         "MKL_DYNAMIC",
         "MKL_NUM_THREADS",
-        "OPENBLAS_NUM_THREADS",
+         # OpenBLAS has a hierarchy of environment variables for setting the
+         # number of threads, see
+         # https://github.com/xianyi/OpenBLAS/blob/c43ec53bdd00d9423fc609d7b7ecb35e7bf41b85/README.md#setting-the-number-of-threads-using-environment-variables
+        ("OPENBLAS_NUM_THREADS", "GOTO_NUM_THREADS", "OMP_NUM_THREADS"),
     ]
     printed_at_least_one_env_var = false
+    print_var(io, indent, name) = println(io, indent, name, " = ", ENV[name])
     for name in env_var_names
-        if haskey(ENV, name)
-            value = ENV[name]
-            println(io, indent, name, " = ", value)
-            printed_at_least_one_env_var = true
+        if name isa Tuple
+            # If `name` is a Tuple, then find the first environment which is
+            # defined, and disregard the following ones.
+            for nm in name
+                if haskey(ENV, nm)
+                    print_var(io, indent, nm)
+                    printed_at_least_one_env_var = true
+                    break
+                end
+            end
+        else
+            if haskey(ENV, name)
+                print_var(io, indent, name)
+                printed_at_least_one_env_var = true
+            end
         end
     end
     if !printed_at_least_one_env_var
@@ -581,7 +596,8 @@ function __init__()
     # register a hook to disable BLAS threading
     Base.at_disable_library_threading(() -> BLAS.set_num_threads(1))
 
-    if !haskey(ENV, "OPENBLAS_NUM_THREADS")
+    # https://github.com/xianyi/OpenBLAS/blob/c43ec53bdd00d9423fc609d7b7ecb35e7bf41b85/README.md#setting-the-number-of-threads-using-environment-variables
+    if !haskey(ENV, "OPENBLAS_NUM_THREADS") && !haskey(ENV, "GOTO_NUM_THREADS") && !haskey(ENV, "OMP_NUM_THREADS")
         @static if Sys.isapple() && Base.BinaryPlatforms.arch(Base.BinaryPlatforms.HostPlatform()) == "aarch64"
             BLAS.set_num_threads(max(1, Sys.CPU_THREADS))
         else