diff --git a/numpy/core/setup.py b/numpy/core/setup.py
index fcc4225459d6..0c20bfd2f419 100644
--- a/numpy/core/setup.py
+++ b/numpy/core/setup.py
@@ -105,7 +105,7 @@ def win32_checks(deflist):
     if a == "Intel" or a == "AMD64":
         deflist.append('FORCE_NO_LONG_DOUBLE_FORMATTING')
 
-def check_math_capabilities(config, moredefs, mathlibs):
+def check_math_capabilities(config, ext, moredefs, mathlibs):
     def check_func(func_name):
         return config.check_func(func_name, libraries=mathlibs,
                                  decl=True, call=True)
@@ -170,6 +170,14 @@ def check_funcs(funcs_name):
     for dec, fn in OPTIONAL_FUNCTION_ATTRIBUTES:
         if config.check_gcc_function_attribute(dec, fn):
             moredefs.append((fname2def(fn), 1))
+            if fn == 'attribute_target_avx512f':
+                # GH-14787: Work around GCC<8.4 bug when compiling with AVX512
+                # support on Windows-based platforms
+                if (sys.platform in ('win32', 'cygwin') and
+                        config.check_compiler_gcc() and
+                        not config.check_gcc_version_at_least(8, 4)):
+                    ext.extra_compile_args.extend(
+                            ['-ffixed-xmm%s' % n for n in range(16, 32)])
 
     for dec, fn, code, header in OPTIONAL_FUNCTION_ATTRIBUTES_WITH_INTRINSICS:
         if config.check_gcc_function_attribute_with_intrinsics(dec, fn, code,
@@ -431,7 +439,7 @@ def generate_config_h(ext, build_dir):
             mathlibs = check_mathlib(config_cmd)
             moredefs.append(('MATHLIB', ','.join(mathlibs)))
 
-            check_math_capabilities(config_cmd, moredefs, mathlibs)
+            check_math_capabilities(config_cmd, ext, moredefs, mathlibs)
             moredefs.extend(cocache.check_ieee_macros(config_cmd)[0])
             moredefs.extend(cocache.check_complex(config_cmd, mathlibs)[0])
 
diff --git a/numpy/distutils/command/autodist.py b/numpy/distutils/command/autodist.py
index 8f6436004a0a..b72d0cab1a7d 100644
--- a/numpy/distutils/command/autodist.py
+++ b/numpy/distutils/command/autodist.py
@@ -46,15 +46,16 @@ def check_restrict(cmd):
     return ''
 
 
-def check_compiler_gcc4(cmd):
-    """Return True if the C compiler is GCC 4.x."""
+def check_compiler_gcc(cmd):
+    """Check if the compiler is GCC."""
+
     cmd._check_compiler()
     body = textwrap.dedent("""
         int
         main()
         {
-        #if (! defined __GNUC__) || (__GNUC__ < 4)
-        #error gcc >= 4 required
+        #if (! defined __GNUC__)
+        #error gcc required
         #endif
             return 0;
         }
@@ -62,6 +63,30 @@ def check_compiler_gcc4(cmd):
     return cmd.try_compile(body, None, None)
 
 
+def check_gcc_version_at_least(cmd, major, minor=0, patchlevel=0):
+    """
+    Check that the gcc version is at least the specified version."""
+
+    cmd._check_compiler()
+    version = '.'.join([str(major), str(minor), str(patchlevel)])
+    body = textwrap.dedent("""
+        int
+        main()
+        {
+        #if (! defined __GNUC__) || (__GNUC__ < %(major)d) || \\
+                (__GNUC_MINOR__ < %(minor)d) || \\
+                (__GNUC_PATCHLEVEL__ < %(patchlevel)d)
+        #error gcc >= %(version)s required
+        #endif
+            return 0;
+        }
+        """)
+    kw = {'version': version, 'major': major, 'minor': minor,
+          'patchlevel': patchlevel}
+
+    return cmd.try_compile(body % kw, None, None)
+
+
 def check_gcc_function_attribute(cmd, attribute, name):
     """Return True if the given function attribute is supported."""
     cmd._check_compiler()
diff --git a/numpy/distutils/command/config.py b/numpy/distutils/command/config.py
index e54a5444995b..60881f4a3a4a 100644
--- a/numpy/distutils/command/config.py
+++ b/numpy/distutils/command/config.py
@@ -20,9 +20,10 @@
 from numpy.distutils.command.autodist import (check_gcc_function_attribute,
                                               check_gcc_function_attribute_with_intrinsics,
                                               check_gcc_variable_attribute,
+                                              check_gcc_version_at_least,
                                               check_inline,
                                               check_restrict,
-                                              check_compiler_gcc4)
+                                              check_compiler_gcc)
 
 LANG_EXT['f77'] = '.f'
 LANG_EXT['f90'] = '.f90'
@@ -416,9 +417,9 @@ def check_restrict(self):
         otherwise."""
         return check_restrict(self)
 
-    def check_compiler_gcc4(self):
-        """Return True if the C compiler is gcc >= 4."""
-        return check_compiler_gcc4(self)
+    def check_compiler_gcc(self):
+        """Return True if the C compiler is gcc"""
+        return check_compiler_gcc(self)
 
     def check_gcc_function_attribute(self, attribute, name):
         return check_gcc_function_attribute(self, attribute, name)
@@ -431,6 +432,11 @@ def check_gcc_function_attribute_with_intrinsics(self, attribute, name,
     def check_gcc_variable_attribute(self, attribute):
         return check_gcc_variable_attribute(self, attribute)
 
+    def check_gcc_version_at_least(self, major, minor=0, patchlevel=0):
+        """Return True if the GCC version is greater than or equal to the
+        specified version."""
+        return check_gcc_version_at_least(self, major, minor, patchlevel)
+
     def get_output(self, body, headers=None, include_dirs=None,
                    libraries=None, library_dirs=None,
                    lang="c", use_tee=None):