diff --git a/test/codegen/README b/test/codegen/README
index d6b8cf5b32..b803fe585f 100644
--- a/test/codegen/README
+++ b/test/codegen/README
@@ -16,8 +16,10 @@ step of the top-level test/run.go suite, called "asmcheck".
 
 The codegen harness is part of the all.bash test suite, but for
 performance reasons only the codegen tests for the host machine's
-GOARCH are enabled by default. To perform comprehensive tests for all
-the supported architectures, one can run the following command
+GOARCH are enabled by default, and only on GOOS=linux.
+
+To perform comprehensive tests for all the supported architectures
+(even on a non-Linux system), one can run the following command
 
   $ ../bin/go run run.go -all_codegen -v codegen