Merge pull request #10915 from mattip/implement-nep-0015

ENH: implement nep 0015: merge multiarray and umath

49 files changed, 231 insertions, 221 deletions

diff --git a/numpy/core/code_generators/generate_numpy_api.py b/numpy/core/code_generators/generate_numpy_api.py
index b4aeaa277..7f2541667 100644
--- a/numpy/core/code_generators/generate_numpy_api.py
+++ b/numpy/core/code_generators/generate_numpy_api.py
@@ -46,11 +46,11 @@ static int
 _import_array(void)
 {
   int st;
-  PyObject *numpy = PyImport_ImportModule("numpy.core.multiarray");
+  PyObject *numpy = PyImport_ImportModule("numpy.core._multiarray_umath");
   PyObject *c_api = NULL;
 
   if (numpy == NULL) {
-      PyErr_SetString(PyExc_ImportError, "numpy.core.multiarray failed to import");
+      PyErr_SetString(PyExc_ImportError, "numpy.core._multiarray_umath failed to import");
       return -1;
   }
   c_api = PyObject_GetAttrString(numpy, "_ARRAY_API");
diff --git a/numpy/core/code_generators/generate_ufunc_api.py b/numpy/core/code_generators/generate_ufunc_api.py
index 3bcf137f7..1b0143e88 100644
--- a/numpy/core/code_generators/generate_ufunc_api.py
+++ b/numpy/core/code_generators/generate_ufunc_api.py
@@ -36,11 +36,12 @@ static void **PyUFunc_API=NULL;
 static NPY_INLINE int
 _import_umath(void)
 {
-  PyObject *numpy = PyImport_ImportModule("numpy.core.umath");
+  PyObject *numpy = PyImport_ImportModule("numpy.core._multiarray_umath");
   PyObject *c_api = NULL;
 
   if (numpy == NULL) {
-      PyErr_SetString(PyExc_ImportError, "numpy.core.umath failed to import");
+      PyErr_SetString(PyExc_ImportError,
+                      "numpy.core._multiarray_umath failed to import");
       return -1;
   }
   c_api = PyObject_GetAttrString(numpy, "_UFUNC_API");
diff --git a/numpy/core/code_generators/generate_umath.py b/numpy/core/code_generators/generate_umath.py
index 632bcb41f..6dc01877b 100644
--- a/numpy/core/code_generators/generate_umath.py
+++ b/numpy/core/code_generators/generate_umath.py
@@ -1080,6 +1080,8 @@ def make_code(funcdict, filename):
         Please make changes to the code generator program (%s)
     **/
     #include "cpuid.h"
+    #include "ufunc_object.h"
+    #include "ufunc_type_resolution.h"
     %s
 
     static int
diff --git a/numpy/core/multiarray.py b/numpy/core/multiarray.py
new file mode 100644
index 000000000..8b07bccf2
--- /dev/null
+++ b/numpy/core/multiarray.py
@@ -0,0 +1,34 @@
+"""
+Create the numpy.core.multiarray namespace for backward compatibility. In v1.16
+the multiarray and umath c-extension modules were merged into a single
+_multiarray_umath extension module. So we replicate the old namespace
+by importing from the extension module.
+"""
+
+from . import _multiarray_umath
+from numpy.core._multiarray_umath import *
+from numpy.core._multiarray_umath import (_fastCopyAndTranspose, _flagdict, _insert,
+     _reconstruct, _vec_string, _ARRAY_API, _monotonicity)
+
+__all__ = ['_ARRAY_API', 'ALLOW_THREADS', 'BUFSIZE', 'CLIP', 'DATETIMEUNITS',
+    'ITEM_HASOBJECT', 'ITEM_IS_POINTER', 'LIST_PICKLE', 'MAXDIMS',
+    'MAY_SHARE_BOUNDS', 'MAY_SHARE_EXACT', 'NEEDS_INIT', 'NEEDS_PYAPI',
+    'RAISE', 'USE_GETITEM', 'USE_SETITEM', 'WRAP',
+    '_fastCopyAndTranspose', '_flagdict', '_insert', '_reconstruct',
+    '_vec_string', '_monotonicity',
+    'add_docstring', 'arange', 'array', 'bincount', 'broadcast', 'busday_count',
+    'busday_offset', 'busdaycalendar', 'can_cast', 'compare_chararrays',
+    'concatenate', 'copyto', 'correlate', 'correlate2', 'count_nonzero',
+    'c_einsum', 'datetime_as_string', 'datetime_data', 'digitize', 'dot',
+    'dragon4_positional', 'dragon4_scientific', 'dtype', 'empty', 'empty_like',
+    'error', 'flagsobj', 'flatiter', 'format_longfloat', 'frombuffer',
+    'fromfile', 'fromiter', 'fromstring', 'getbuffer', 'inner', 'int_asbuffer',
+    'interp', 'interp_complex', 'is_busday', 'lexsort', 'matmul',
+    'may_share_memory', 'min_scalar_type', 'ndarray', 'nditer', 'nested_iters',
+    'newbuffer', 'normalize_axis_index', 'packbits', 'promote_types',
+    'putmask', 'ravel_multi_index', 'result_type', 'scalar',
+    'set_datetimeparse_function', 'set_legacy_print_mode', 'set_numeric_ops',
+    'set_string_function', 'set_typeDict', 'shares_memory', 'test_interrupt',
+    'tracemalloc_domain', 'typeinfo', 'unpackbits', 'unravel_index', 'vdot',
+    'where', 'zeros']
+
diff --git a/numpy/core/numeric.py b/numpy/core/numeric.py
index 6c9baef0a..1b4818b76 100644
--- a/numpy/core/numeric.py
+++ b/numpy/core/numeric.py
@@ -2914,10 +2914,7 @@ True_ = bool_(True)
 
 def extend_all(module):
     existing = set(__all__)
-    try:
-        mall = getattr(module, '__all__')
-    except AttributeError:
-        mall = [k for k in module.__dict__.keys() if not k.startswith('_')]
+    mall = getattr(module, '__all__')
     for a in mall:
         if a not in existing:
             __all__.append(a)
diff --git a/numpy/core/setup.py b/numpy/core/setup.py
index f826b278f..b306aa4e8 100644
--- a/numpy/core/setup.py
+++ b/numpy/core/setup.py
@@ -514,9 +514,9 @@ def configuration(parent_package='',top_path=None):
 
     def generate_numpyconfig_h(ext, build_dir):
         """Depends on config.h: generate_config_h has to be called before !"""
-        # put private include directory in build_dir on search path
+        # put common include directory in build_dir on search path
         # allows using code generation in headers headers
-        config.add_include_dirs(join(build_dir, "src", "private"))
+        config.add_include_dirs(join(build_dir, "src", "common"))
         config.add_include_dirs(join(build_dir, "src", "npymath"))
 
         target = join(build_dir, header_dir, '_numpyconfig.h')
@@ -603,7 +603,7 @@ def configuration(parent_package='',top_path=None):
     generate_numpy_api = generate_api_func('generate_numpy_api')
     generate_ufunc_api = generate_api_func('generate_ufunc_api')
 
-    config.add_include_dirs(join(local_dir, "src", "private"))
+    config.add_include_dirs(join(local_dir, "src", "common"))
     config.add_include_dirs(join(local_dir, "src"))
     config.add_include_dirs(join(local_dir))
 
@@ -700,9 +700,9 @@ def configuration(parent_package='',top_path=None):
     npysort_sources = [join('src', 'npysort', 'quicksort.c.src'),
                        join('src', 'npysort', 'mergesort.c.src'),
                        join('src', 'npysort', 'heapsort.c.src'),
-                       join('src', 'private', 'npy_partition.h.src'),
+                       join('src', 'common', 'npy_partition.h.src'),
                        join('src', 'npysort', 'selection.c.src'),
-                       join('src', 'private', 'npy_binsearch.h.src'),
+                       join('src', 'common', 'npy_binsearch.h.src'),
                        join('src', 'npysort', 'binsearch.c.src'),
                        ]
     config.add_library('npysort',
@@ -710,16 +710,55 @@ def configuration(parent_package='',top_path=None):
                        include_dirs=[])
 
     #######################################################################
-    #                        multiarray module                            #
+    #             _multiarray_umath module - common part                  #
+    #######################################################################
+
+    common_deps = [
+            join('src', 'common', 'array_assign.h'),
+            join('src', 'common', 'binop_override.h'),
+            join('src', 'common', 'cblasfuncs.h'),
+            join('src', 'common', 'lowlevel_strided_loops.h'),
+            join('src', 'common', 'mem_overlap.h'),
+            join('src', 'common', 'npy_config.h'),
+            join('src', 'common', 'npy_extint128.h'),
+            join('src', 'common', 'npy_longdouble.h'),
+            join('src', 'common', 'templ_common.h.src'),
+            join('src', 'common', 'ucsnarrow.h'),
+            join('src', 'common', 'ufunc_override.h'),
+            join('src', 'common', 'umathmodule.h'),
+            ]
+
+    common_src = [
+            join('src', 'common', 'array_assign.c'),
+            join('src', 'common', 'mem_overlap.c'),
+            join('src', 'common', 'npy_longdouble.c'),
+            join('src', 'common', 'templ_common.h.src'),
+            join('src', 'common', 'ucsnarrow.c'),
+            join('src', 'common', 'ufunc_override.c'),
+            ]
+
+    blas_info = get_info('blas_opt', 0)
+    if blas_info and ('HAVE_CBLAS', None) in blas_info.get('define_macros', []):
+        extra_info = blas_info
+        # These files are also in MANIFEST.in so that they are always in
+        # the source distribution independently of HAVE_CBLAS.
+        common_src.extend([join('src', 'common', 'cblasfuncs.c'),
+                           join('src', 'common', 'python_xerbla.c'),
+                          ])
+        if uses_accelerate_framework(blas_info):
+            common_src.extend(get_sgemv_fix())
+    else:
+        extra_info = {}
+
+    #######################################################################
+    #             _multiarray_umath module - multiarray part              #
     #######################################################################
 
     multiarray_deps = [
             join('src', 'multiarray', 'arrayobject.h'),
             join('src', 'multiarray', 'arraytypes.h'),
-            join('src', 'multiarray', 'array_assign.h'),
             join('src', 'multiarray', 'buffer.h'),
             join('src', 'multiarray', 'calculation.h'),
-            join('src', 'multiarray', 'cblasfuncs.h'),
             join('src', 'multiarray', 'common.h'),
             join('src', 'multiarray', 'convert_datatype.h'),
             join('src', 'multiarray', 'convert.h'),
@@ -742,17 +781,8 @@ def configuration(parent_package='',top_path=None):
             join('src', 'multiarray', 'shape.h'),
             join('src', 'multiarray', 'strfuncs.h'),
             join('src', 'multiarray', 'typeinfo.h'),
-            join('src', 'multiarray', 'ucsnarrow.h'),
             join('src', 'multiarray', 'usertypes.h'),
             join('src', 'multiarray', 'vdot.h'),
-            join('src', 'private', 'npy_config.h'),
-            join('src', 'private', 'templ_common.h.src'),
-            join('src', 'private', 'lowlevel_strided_loops.h'),
-            join('src', 'private', 'mem_overlap.h'),
-            join('src', 'private', 'npy_longdouble.h'),
-            join('src', 'private', 'ufunc_override.h'),
-            join('src', 'private', 'binop_override.h'),
-            join('src', 'private', 'npy_extint128.h'),
             join('include', 'numpy', 'arrayobject.h'),
             join('include', 'numpy', '_neighborhood_iterator_imp.h'),
             join('include', 'numpy', 'npy_endian.h'),
@@ -778,7 +808,6 @@ def configuration(parent_package='',top_path=None):
             join('src', 'multiarray', 'alloc.c'),
             join('src', 'multiarray', 'arrayobject.c'),
             join('src', 'multiarray', 'arraytypes.c.src'),
-            join('src', 'multiarray', 'array_assign.c'),
             join('src', 'multiarray', 'array_assign_scalar.c'),
             join('src', 'multiarray', 'array_assign_array.c'),
             join('src', 'multiarray', 'buffer.c'),
@@ -821,40 +850,11 @@ def configuration(parent_package='',top_path=None):
             join('src', 'multiarray', 'temp_elide.c'),
             join('src', 'multiarray', 'typeinfo.c'),
             join('src', 'multiarray', 'usertypes.c'),
-            join('src', 'multiarray', 'ucsnarrow.c'),
             join('src', 'multiarray', 'vdot.c'),
-            join('src', 'private', 'templ_common.h.src'),
-            join('src', 'private', 'mem_overlap.c'),
-            join('src', 'private', 'npy_longdouble.c'),
-            join('src', 'private', 'ufunc_override.c'),
             ]
 
-    blas_info = get_info('blas_opt', 0)
-    if blas_info and ('HAVE_CBLAS', None) in blas_info.get('define_macros', []):
-        extra_info = blas_info
-        # These files are also in MANIFEST.in so that they are always in
-        # the source distribution independently of HAVE_CBLAS.
-        multiarray_src.extend([join('src', 'multiarray', 'cblasfuncs.c'),
-                               join('src', 'multiarray', 'python_xerbla.c'),
-                               ])
-        if uses_accelerate_framework(blas_info):
-            multiarray_src.extend(get_sgemv_fix())
-    else:
-        extra_info = {}
-
-    config.add_extension('multiarray',
-                         sources=multiarray_src +
-                                 [generate_config_h,
-                                  generate_numpyconfig_h,
-                                  generate_numpy_api,
-                                  join(codegen_dir, 'generate_numpy_api.py'),
-                                  join('*.py')],
-                         depends=deps + multiarray_deps,
-                         libraries=['npymath', 'npysort'],
-                         extra_info=extra_info)
-
     #######################################################################
-    #                           umath module                              #
+    #             _multiarray_umath module - umath part                   #
     #######################################################################
 
     def generate_umath_c(ext, build_dir):
@@ -883,34 +883,34 @@ def configuration(parent_package='',top_path=None):
             join('src', 'umath', 'scalarmath.c.src'),
             join('src', 'umath', 'ufunc_type_resolution.c'),
             join('src', 'umath', 'override.c'),
-            join('src', 'private', 'mem_overlap.c'),
-            join('src', 'private', 'npy_longdouble.c'),
-            join('src', 'private', 'ufunc_override.c')]
+            ]
 
     umath_deps = [
             generate_umath_py,
             join('include', 'numpy', 'npy_math.h'),
             join('include', 'numpy', 'halffloat.h'),
             join('src', 'multiarray', 'common.h'),
-            join('src', 'private', 'templ_common.h.src'),
+            join('src', 'common', 'templ_common.h.src'),
             join('src', 'umath', 'simd.inc.src'),
             join('src', 'umath', 'override.h'),
             join(codegen_dir, 'generate_ufunc_api.py'),
-            join('src', 'private', 'lowlevel_strided_loops.h'),
-            join('src', 'private', 'mem_overlap.h'),
-            join('src', 'private', 'npy_longdouble.h'),
-            join('src', 'private', 'ufunc_override.h'),
-            join('src', 'private', 'binop_override.h')] + npymath_sources
-
-    config.add_extension('umath',
-                         sources=umath_src +
+            ] 
+
+    config.add_extension('_multiarray_umath',
+                         sources=multiarray_src + umath_src + 
+                                 npymath_sources + common_src +
                                  [generate_config_h,
-                                 generate_numpyconfig_h,
-                                 generate_umath_c,
-                                 generate_ufunc_api],
-                         depends=deps + umath_deps,
-                         libraries=['npymath'],
-                         )
+                                  generate_numpyconfig_h,
+                                  generate_numpy_api,
+                                  join(codegen_dir, 'generate_numpy_api.py'),
+                                  join('*.py'),
+                                  generate_umath_c,
+                                  generate_ufunc_api,
+                                 ],
+                         depends=deps + multiarray_deps + umath_deps + 
+                                common_deps,
+                         libraries=['npymath', 'npysort'],
+                         extra_info=extra_info)
 
     #######################################################################
     #                        umath_tests module                           #
@@ -939,9 +939,9 @@ def configuration(parent_package='',top_path=None):
 
     config.add_extension('_multiarray_tests',
                     sources=[join('src', 'multiarray', '_multiarray_tests.c.src'),
-                             join('src', 'private', 'mem_overlap.c')],
-                    depends=[join('src', 'private', 'mem_overlap.h'),
-                             join('src', 'private', 'npy_extint128.h')],
+                             join('src', 'common', 'mem_overlap.c')],
+                    depends=[join('src', 'common', 'mem_overlap.h'),
+                             join('src', 'common', 'npy_extint128.h')],
                     libraries=['npymath'])
 
     #######################################################################
diff --git a/numpy/core/src/multiarray/array_assign.c b/numpy/core/src/common/array_assign.c
index a48e245d8..a48e245d8 100644
--- a/numpy/core/src/multiarray/array_assign.c
+++ b/numpy/core/src/common/array_assign.c
diff --git a/numpy/core/src/multiarray/array_assign.h b/numpy/core/src/common/array_assign.h
index 3fecff007..3fecff007 100644
--- a/numpy/core/src/multiarray/array_assign.h
+++ b/numpy/core/src/common/array_assign.h
diff --git a/numpy/core/src/private/binop_override.h b/numpy/core/src/common/binop_override.h
index 47df63e38..47df63e38 100644
--- a/numpy/core/src/private/binop_override.h
+++ b/numpy/core/src/common/binop_override.h
diff --git a/numpy/core/src/multiarray/cblasfuncs.c b/numpy/core/src/common/cblasfuncs.c
index 6460c5db1..6460c5db1 100644
--- a/numpy/core/src/multiarray/cblasfuncs.c
+++ b/numpy/core/src/common/cblasfuncs.c
diff --git a/numpy/core/src/multiarray/cblasfuncs.h b/numpy/core/src/common/cblasfuncs.h
index 66ce4ca5b..66ce4ca5b 100644
--- a/numpy/core/src/multiarray/cblasfuncs.h
+++ b/numpy/core/src/common/cblasfuncs.h
diff --git a/numpy/core/src/private/get_attr_string.h b/numpy/core/src/common/get_attr_string.h
index bec87c5ed..bec87c5ed 100644
--- a/numpy/core/src/private/get_attr_string.h
+++ b/numpy/core/src/common/get_attr_string.h
diff --git a/numpy/core/src/private/lowlevel_strided_loops.h b/numpy/core/src/common/lowlevel_strided_loops.h
index f9c671f77..f9c671f77 100644
--- a/numpy/core/src/private/lowlevel_strided_loops.h
+++ b/numpy/core/src/common/lowlevel_strided_loops.h
diff --git a/numpy/core/src/private/mem_overlap.c b/numpy/core/src/common/mem_overlap.c
index 21db1893b..21db1893b 100644
--- a/numpy/core/src/private/mem_overlap.c
+++ b/numpy/core/src/common/mem_overlap.c
diff --git a/numpy/core/src/private/mem_overlap.h b/numpy/core/src/common/mem_overlap.h
index 8044f1663..8044f1663 100644
--- a/numpy/core/src/private/mem_overlap.h
+++ b/numpy/core/src/common/mem_overlap.h
diff --git a/numpy/core/src/private/npy_binsearch.h.src b/numpy/core/src/common/npy_binsearch.h.src
index ce3b34b0e..ce3b34b0e 100644
--- a/numpy/core/src/private/npy_binsearch.h.src
+++ b/numpy/core/src/common/npy_binsearch.h.src
diff --git a/numpy/core/src/private/npy_cblas.h b/numpy/core/src/common/npy_cblas.h
index a083f3bcc..a083f3bcc 100644
--- a/numpy/core/src/private/npy_cblas.h
+++ b/numpy/core/src/common/npy_cblas.h
diff --git a/numpy/core/src/private/npy_config.h b/numpy/core/src/common/npy_config.h
index 8143e7719..8143e7719 100644
--- a/numpy/core/src/private/npy_config.h
+++ b/numpy/core/src/common/npy_config.h
diff --git a/numpy/core/src/private/npy_extint128.h b/numpy/core/src/common/npy_extint128.h
index a887ff317..a887ff317 100644
--- a/numpy/core/src/private/npy_extint128.h
+++ b/numpy/core/src/common/npy_extint128.h
diff --git a/numpy/core/src/private/npy_fpmath.h b/numpy/core/src/common/npy_fpmath.h
index dbb3fb23d..dbb3fb23d 100644
--- a/numpy/core/src/private/npy_fpmath.h
+++ b/numpy/core/src/common/npy_fpmath.h
diff --git a/numpy/core/src/private/npy_import.h b/numpy/core/src/common/npy_import.h
index 221e1e645..221e1e645 100644
--- a/numpy/core/src/private/npy_import.h
+++ b/numpy/core/src/common/npy_import.h
diff --git a/numpy/core/src/private/npy_longdouble.c b/numpy/core/src/common/npy_longdouble.c
index 508fbceac..508fbceac 100644
--- a/numpy/core/src/private/npy_longdouble.c
+++ b/numpy/core/src/common/npy_longdouble.c
diff --git a/numpy/core/src/private/npy_longdouble.h b/numpy/core/src/common/npy_longdouble.h
index 036b53070..036b53070 100644
--- a/numpy/core/src/private/npy_longdouble.h
+++ b/numpy/core/src/common/npy_longdouble.h
diff --git a/numpy/core/src/private/npy_partition.h.src b/numpy/core/src/common/npy_partition.h.src
index a22cf911c..a22cf911c 100644
--- a/numpy/core/src/private/npy_partition.h.src
+++ b/numpy/core/src/common/npy_partition.h.src
diff --git a/numpy/core/src/private/npy_pycompat.h b/numpy/core/src/common/npy_pycompat.h
index aa0b5c122..aa0b5c122 100644
--- a/numpy/core/src/private/npy_pycompat.h
+++ b/numpy/core/src/common/npy_pycompat.h
diff --git a/numpy/core/src/private/npy_sort.h b/numpy/core/src/common/npy_sort.h
index 8c6f05623..8c6f05623 100644
--- a/numpy/core/src/private/npy_sort.h
+++ b/numpy/core/src/common/npy_sort.h
diff --git a/numpy/core/src/multiarray/python_xerbla.c b/numpy/core/src/common/python_xerbla.c
index bdf0b9058..bdf0b9058 100644
--- a/numpy/core/src/multiarray/python_xerbla.c
+++ b/numpy/core/src/common/python_xerbla.c
diff --git a/numpy/core/src/private/templ_common.h.src b/numpy/core/src/common/templ_common.h.src
index a65a00758..a65a00758 100644
--- a/numpy/core/src/private/templ_common.h.src
+++ b/numpy/core/src/common/templ_common.h.src
diff --git a/numpy/core/src/multiarray/ucsnarrow.c b/numpy/core/src/common/ucsnarrow.c
index 8e293e9f2..8e293e9f2 100644
--- a/numpy/core/src/multiarray/ucsnarrow.c
+++ b/numpy/core/src/common/ucsnarrow.c
diff --git a/numpy/core/src/multiarray/ucsnarrow.h b/numpy/core/src/common/ucsnarrow.h
index fe31a5e25..fe31a5e25 100644
--- a/numpy/core/src/multiarray/ucsnarrow.h
+++ b/numpy/core/src/common/ucsnarrow.h
diff --git a/numpy/core/src/private/ufunc_override.c b/numpy/core/src/common/ufunc_override.c
index 33b54c665..33b54c665 100644
--- a/numpy/core/src/private/ufunc_override.c
+++ b/numpy/core/src/common/ufunc_override.c
diff --git a/numpy/core/src/private/ufunc_override.h b/numpy/core/src/common/ufunc_override.h
index 5b269d270..5b269d270 100644
--- a/numpy/core/src/private/ufunc_override.h
+++ b/numpy/core/src/common/ufunc_override.h
diff --git a/numpy/core/src/common/umathmodule.h b/numpy/core/src/common/umathmodule.h
new file mode 100644
index 000000000..6998596ee
--- /dev/null
+++ b/numpy/core/src/common/umathmodule.h
@@ -0,0 +1,8 @@
+#include "__umath_generated.c"
+#include "__ufunc_api.c"
+
+PyObject * add_newdoc_ufunc(PyObject *NPY_UNUSED(dummy), PyObject *args);
+PyObject * ufunc_frompyfunc(PyObject *NPY_UNUSED(dummy), PyObject *args, PyObject *NPY_UNUSED(kwds));
+int initumath(PyObject *m);
+
+
diff --git a/numpy/core/src/multiarray/descriptor.c b/numpy/core/src/multiarray/descriptor.c
index a0dc98f0e..1d44cf8be 100644
--- a/numpy/core/src/multiarray/descriptor.c
+++ b/numpy/core/src/multiarray/descriptor.c
@@ -2401,7 +2401,7 @@ arraydescr_reduce(PyArray_Descr *self, PyObject *NPY_UNUSED(args))
     if (ret == NULL) {
         return NULL;
     }
-    mod = PyImport_ImportModule("numpy.core.multiarray");
+    mod = PyImport_ImportModule("numpy.core._multiarray_umath");
     if (mod == NULL) {
         Py_DECREF(ret);
         return NULL;
diff --git a/numpy/core/src/multiarray/methods.c b/numpy/core/src/multiarray/methods.c
index 2e836d1d0..3d2cce5e1 100644
--- a/numpy/core/src/multiarray/methods.c
+++ b/numpy/core/src/multiarray/methods.c
@@ -1566,7 +1566,7 @@ array_reduce(PyArrayObject *self, PyObject *NPY_UNUSED(args))
     if (ret == NULL) {
         return NULL;
     }
-    mod = PyImport_ImportModule("numpy.core.multiarray");
+    mod = PyImport_ImportModule("numpy.core._multiarray_umath");
     if (mod == NULL) {
         Py_DECREF(ret);
         return NULL;
diff --git a/numpy/core/src/multiarray/multiarraymodule.c b/numpy/core/src/multiarray/multiarraymodule.c
index dc571dfcb..8f782cff6 100644
--- a/numpy/core/src/multiarray/multiarraymodule.c
+++ b/numpy/core/src/multiarray/multiarraymodule.c
@@ -19,6 +19,7 @@
 #include "structmember.h"
 
 #define NPY_NO_DEPRECATED_API NPY_API_VERSION
+#define _UMATHMODULE
 #define _MULTIARRAYMODULE
 #include <numpy/npy_common.h>
 #include "numpy/arrayobject.h"
@@ -54,7 +55,6 @@ NPY_NO_EXPORT int NPY_NUMUSERTYPES = 0;
 #include "ctors.h"
 #include "array_assign.h"
 #include "common.h"
-#include "ufunc_override.h"
 #include "multiarraymodule.h"
 #include "cblasfuncs.h"
 #include "vdot.h"
@@ -67,6 +67,17 @@ NPY_NO_EXPORT int NPY_NUMUSERTYPES = 0;
 #include "get_attr_string.h"
 
 /*
+ *****************************************************************************
+ **                    INCLUDE GENERATED CODE                               **
+ *****************************************************************************
+ */
+#include "funcs.inc"
+#include "loops.h"
+#include "umathmodule.h"
+
+NPY_NO_EXPORT int initscalarmath(PyObject *);
+
+/*
  * global variable to determine if legacy printing is enabled, accessible from
  * C. For simplicity the mode is encoded as an integer where '0' means no
  * legacy mode, and '113' means 1.13 legacy mode. We can upgrade this if we
@@ -4365,6 +4376,18 @@ static struct PyMethodDef array_module_methods[] = {
         METH_VARARGS | METH_KEYWORDS, NULL},
     {"set_legacy_print_mode", (PyCFunction)set_legacy_print_mode,
         METH_VARARGS, NULL},
+    /* from umath */
+    {"frompyfunc",
+        (PyCFunction) ufunc_frompyfunc,
+        METH_VARARGS | METH_KEYWORDS, NULL},
+    {"seterrobj",
+        (PyCFunction) ufunc_seterr,
+        METH_VARARGS, NULL},
+    {"geterrobj",
+        (PyCFunction) ufunc_geterr,
+        METH_VARARGS, NULL},
+    {"_add_newdoc_ufunc", (PyCFunction)add_newdoc_ufunc,
+        METH_VARARGS, NULL},
     {NULL, NULL, 0, NULL}                /* sentinel */
 };
 
@@ -4382,9 +4405,6 @@ static struct PyMethodDef array_module_methods[] = {
 static int
 setup_scalartypes(PyObject *NPY_UNUSED(dict))
 {
-    initialize_casting_tables();
-    initialize_numeric_types();
-
     if (PyType_Ready(&PyBool_Type) < 0) {
         return -1;
     }
@@ -4624,7 +4644,7 @@ intern_strings(void)
 #if defined(NPY_PY3K)
 static struct PyModuleDef moduledef = {
         PyModuleDef_HEAD_INIT,
-        "multiarray",
+        "_multiarray_umath",
         NULL,
         -1,
         array_module_methods,
@@ -4638,10 +4658,10 @@ static struct PyModuleDef moduledef = {
 /* Initialization function for the module */
 #if defined(NPY_PY3K)
 #define RETVAL(x) x
-PyMODINIT_FUNC PyInit_multiarray(void) {
+PyMODINIT_FUNC PyInit__multiarray_umath(void) {
 #else
 #define RETVAL(x)
-PyMODINIT_FUNC initmultiarray(void) {
+PyMODINIT_FUNC init_multiarray_umath(void) {
 #endif
     PyObject *m, *d, *s;
     PyObject *c_api;
@@ -4650,7 +4670,7 @@ PyMODINIT_FUNC initmultiarray(void) {
 #if defined(NPY_PY3K)
     m = PyModule_Create(&moduledef);
 #else
-    m = Py_InitModule("multiarray", array_module_methods);
+    m = Py_InitModule("_multiarray_umath", array_module_methods);
 #endif
     if (!m) {
         goto err;
@@ -4684,6 +4704,17 @@ PyMODINIT_FUNC initmultiarray(void) {
      * static structure slots with functions from the Python C_API.
      */
     PyArray_Type.tp_hash = PyObject_HashNotImplemented;
+
+    /* Load the ufunc operators into the array module's namespace */
+    if (InitOperators(d) < 0) {
+        goto err;
+    }
+
+    initialize_casting_tables();
+    initialize_numeric_types();
+    if(initscalarmath(m) < 0)
+        goto err;
+
     if (PyType_Ready(&PyArray_Type) < 0) {
         goto err;
     }
@@ -4730,6 +4761,16 @@ PyMODINIT_FUNC initmultiarray(void) {
     PyDict_SetItemString(d, "_ARRAY_API", c_api);
     Py_DECREF(c_api);
 
+    c_api = NpyCapsule_FromVoidPtr((void *)PyUFunc_API, NULL);
+    if (c_api == NULL) {
+        goto err;
+    }
+    PyDict_SetItemString(d, "_UFUNC_API", c_api);
+    Py_DECREF(c_api);
+    if (PyErr_Occurred()) {
+        goto err;
+    }
+
     /*
      * PyExc_Exception should catch all the standard errors that are
      * now raised instead of the string exception "multiarray.error"
@@ -4806,7 +4847,9 @@ PyMODINIT_FUNC initmultiarray(void) {
     if (set_typeinfo(d) != 0) {
         goto err;
     }
-
+    if (initumath(m) != 0) {
+        goto err;
+    }
     return RETVAL(m);
 
  err:
diff --git a/numpy/core/src/multiarray/scalartypes.c.src b/numpy/core/src/multiarray/scalartypes.c.src
index b36c98d9c..fdd4d7878 100644
--- a/numpy/core/src/multiarray/scalartypes.c.src
+++ b/numpy/core/src/multiarray/scalartypes.c.src
@@ -1870,7 +1870,7 @@ gentype_reduce(PyObject *self, PyObject *NPY_UNUSED(args))
     }
 #endif
 
-    mod = PyImport_ImportModule("numpy.core.multiarray");
+    mod = PyImport_ImportModule("numpy.core._multiarray_umath");
     if (mod == NULL) {
         return NULL;
     }
diff --git a/numpy/core/src/umath/cpuid.c b/numpy/core/src/umath/cpuid.c
index 912d51eeb..6744ceb05 100644
--- a/numpy/core/src/umath/cpuid.c
+++ b/numpy/core/src/umath/cpuid.c
@@ -1,13 +1,11 @@
 #define _UMATHMODULE
+#define _MULTIARRAYMODULE
 #define NPY_NO_DEPRECATED_API NPY_API_VERSION
 
 #include <Python.h>
 
 #include "npy_config.h"
 
-#define PY_ARRAY_UNIQUE_SYMBOL _npy_umathmodule_ARRAY_API
-#define NO_IMPORT_ARRAY
-
 #include "cpuid.h"
 
 #define XCR_XFEATURE_ENABLED_MASK 0x0
diff --git a/numpy/core/src/umath/extobj.c b/numpy/core/src/umath/extobj.c
index 188054e22..aea1815e8 100644
--- a/numpy/core/src/umath/extobj.c
+++ b/numpy/core/src/umath/extobj.c
@@ -1,13 +1,11 @@
 #define _UMATHMODULE
+#define _MULTIARRAYMODULE
 #define NPY_NO_DEPRECATED_API NPY_API_VERSION
 
 #include <Python.h>
 
 #include "npy_config.h"
 
-#define PY_ARRAY_UNIQUE_SYMBOL _npy_umathmodule_ARRAY_API
-#define NO_IMPORT_ARRAY
-
 #include "npy_pycompat.h"
 
 #include "extobj.h"
diff --git a/numpy/core/src/umath/loops.c.src b/numpy/core/src/umath/loops.c.src
index 0b02031a7..e3e011190 100644
--- a/numpy/core/src/umath/loops.c.src
+++ b/numpy/core/src/umath/loops.c.src
@@ -1,14 +1,12 @@
 /* -*- c -*- */
 
 #define _UMATHMODULE
+#define _MULTIARRAYMODULE
 #define NPY_NO_DEPRECATED_API NPY_API_VERSION
 
 #include "Python.h"
 
 #include "npy_config.h"
-#define PY_ARRAY_UNIQUE_SYMBOL _npy_umathmodule_ARRAY_API
-#define NO_IMPORT_ARRAY
-
 #include "numpy/npy_common.h"
 #include "numpy/arrayobject.h"
 #include "numpy/ufuncobject.h"
diff --git a/numpy/core/src/umath/reduction.c b/numpy/core/src/umath/reduction.c
index 8136d7b3f..6d04ce372 100644
--- a/numpy/core/src/umath/reduction.c
+++ b/numpy/core/src/umath/reduction.c
@@ -7,15 +7,13 @@
  * See LICENSE.txt for the license.
  */
 #define _UMATHMODULE
+#define _MULTIARRAYMODULE
 #define NPY_NO_DEPRECATED_API NPY_API_VERSION
 
 #define PY_SSIZE_T_CLEAN
 #include <Python.h>
 
 #include "npy_config.h"
-#define PY_ARRAY_UNIQUE_SYMBOL _npy_umathmodule_ARRAY_API
-#define NO_IMPORT_ARRAY
-
 #include <numpy/arrayobject.h>
 
 #include "npy_config.h"
diff --git a/numpy/core/src/umath/scalarmath.c.src b/numpy/core/src/umath/scalarmath.c.src
index 3e29c4b4e..e98d9f865 100644
--- a/numpy/core/src/umath/scalarmath.c.src
+++ b/numpy/core/src/umath/scalarmath.c.src
@@ -7,13 +7,11 @@
 */
 
 #define _UMATHMODULE
+#define _MULTIARRAYMODULE
 #define NPY_NO_DEPRECATED_API NPY_API_VERSION
 
 #include "Python.h"
 #include "npy_config.h"
-#define PY_ARRAY_UNIQUE_SYMBOL _npy_umathmodule_ARRAY_API
-#define NO_IMPORT_ARRAY
-
 #include "numpy/arrayobject.h"
 #include "numpy/ufuncobject.h"
 #include "numpy/arrayscalars.h"
diff --git a/numpy/core/src/umath/ufunc_object.c b/numpy/core/src/umath/ufunc_object.c
index 20c448d8b..459b0a594 100644
--- a/numpy/core/src/umath/ufunc_object.c
+++ b/numpy/core/src/umath/ufunc_object.c
@@ -24,15 +24,13 @@
  *
  */
 #define _UMATHMODULE
+#define _MULTIARRAYMODULE
 #define NPY_NO_DEPRECATED_API NPY_API_VERSION
 
 #include "Python.h"
 
 #include "npy_config.h"
 
-#define PY_ARRAY_UNIQUE_SYMBOL _npy_umathmodule_ARRAY_API
-#define NO_IMPORT_ARRAY
-
 #include "npy_pycompat.h"
 
 #include "numpy/arrayobject.h"
diff --git a/numpy/core/src/umath/ufunc_object.h b/numpy/core/src/umath/ufunc_object.h
index 5438270f1..f5de9f9b7 100644
--- a/numpy/core/src/umath/ufunc_object.h
+++ b/numpy/core/src/umath/ufunc_object.h
@@ -1,6 +1,8 @@
 #ifndef _NPY_UMATH_UFUNC_OBJECT_H_
 #define _NPY_UMATH_UFUNC_OBJECT_H_
 
+#include <numpy/ufuncobject.h>
+
 NPY_NO_EXPORT PyObject *
 ufunc_geterr(PyObject *NPY_UNUSED(dummy), PyObject *args);
 
diff --git a/numpy/core/src/umath/ufunc_type_resolution.c b/numpy/core/src/umath/ufunc_type_resolution.c
index 1766ba564..807b03512 100644
--- a/numpy/core/src/umath/ufunc_type_resolution.c
+++ b/numpy/core/src/umath/ufunc_type_resolution.c
@@ -9,14 +9,12 @@
  * See LICENSE.txt for the license.
  */
 #define _UMATHMODULE
+#define _MULTIARRAYMODULE
 #define NPY_NO_DEPRECATED_API NPY_API_VERSION
 
 #include "Python.h"
 
 #include "npy_config.h"
-#define PY_ARRAY_UNIQUE_SYMBOL _npy_umathmodule_ARRAY_API
-#define NO_IMPORT_ARRAY
-
 #include "npy_pycompat.h"
 
 #include "numpy/ufuncobject.h"
diff --git a/numpy/core/src/umath/umathmodule.c b/numpy/core/src/umath/umathmodule.c
index 9291a5138..20bd2b0a8 100644
--- a/numpy/core/src/umath/umathmodule.c
+++ b/numpy/core/src/umath/umathmodule.c
@@ -16,12 +16,12 @@
  * __ufunc_api.c
  */
 #define _UMATHMODULE
+#define _MULTIARRAYMODULE
 #define NPY_NO_DEPRECATED_API NPY_API_VERSION
 
 #include "Python.h"
 
 #include "npy_config.h"
-#define PY_ARRAY_UNIQUE_SYMBOL _npy_umathmodule_ARRAY_API
 
 #include "numpy/arrayobject.h"
 #include "numpy/ufuncobject.h"
@@ -30,20 +30,6 @@
 
 #include "numpy/npy_math.h"
 
-/*
- *****************************************************************************
- **                    INCLUDE GENERATED CODE                               **
- *****************************************************************************
- */
-#include "funcs.inc"
-#include "loops.h"
-#include "ufunc_object.h"
-#include "ufunc_type_resolution.h"
-#include "__umath_generated.c"
-#include "__ufunc_api.c"
-
-NPY_NO_EXPORT int initscalarmath(PyObject *);
-
 static PyUFuncGenericFunction pyfunc_functions[] = {PyUFunc_On_Om};
 
 static int
@@ -82,7 +68,7 @@ object_ufunc_loop_selector(PyUFuncObject *ufunc,
     return 0;
 }
 
-static PyObject *
+PyObject *
 ufunc_frompyfunc(PyObject *NPY_UNUSED(dummy), PyObject *args, PyObject *NPY_UNUSED(kwds)) {
     /* Keywords are ignored for now */
 
@@ -179,7 +165,7 @@ ufunc_frompyfunc(PyObject *NPY_UNUSED(dummy), PyObject *args, PyObject *NPY_UNUS
 }
 
 /* docstring in numpy.add_newdocs.py */
-static PyObject *
+PyObject *
 add_newdoc_ufunc(PyObject *NPY_UNUSED(dummy), PyObject *args)
 {
     PyUFuncObject *ufunc;
@@ -270,97 +256,24 @@ intern_strings(void)
         npy_um_str_array_wrap && npy_um_str_array_finalize && npy_um_str_ufunc;
 }
 
-/* Setup the umath module */
-/* Remove for time being, it is declared in __ufunc_api.h */
-/*static PyTypeObject PyUFunc_Type;*/
-
-static struct PyMethodDef methods[] = {
-    {"frompyfunc",
-        (PyCFunction) ufunc_frompyfunc,
-        METH_VARARGS | METH_KEYWORDS, NULL},
-    {"seterrobj",
-        (PyCFunction) ufunc_seterr,
-        METH_VARARGS, NULL},
-    {"geterrobj",
-        (PyCFunction) ufunc_geterr,
-        METH_VARARGS, NULL},
-    {"_add_newdoc_ufunc", (PyCFunction)add_newdoc_ufunc,
-        METH_VARARGS, NULL},
-    {NULL, NULL, 0, NULL}                /* sentinel */
-};
-
-
-#if defined(NPY_PY3K)
-static struct PyModuleDef moduledef = {
-        PyModuleDef_HEAD_INIT,
-        "umath",
-        NULL,
-        -1,
-        methods,
-        NULL,
-        NULL,
-        NULL,
-        NULL
-};
-#endif
-
-#include <stdio.h>
+/* Setup the umath part of the module */
 
-#if defined(NPY_PY3K)
-#define RETVAL(x) x
-PyMODINIT_FUNC PyInit_umath(void)
-#else
-#define RETVAL(x)
-PyMODINIT_FUNC initumath(void)
-#endif
+int initumath(PyObject *m)
 {
-    PyObject *m, *d, *s, *s2, *c_api;
+    PyObject *d, *s, *s2;
     int UFUNC_FLOATING_POINT_SUPPORT = 1;
 
 #ifdef NO_UFUNC_FLOATING_POINT_SUPPORT
     UFUNC_FLOATING_POINT_SUPPORT = 0;
 #endif
-    /* Create the module and add the functions */
-#if defined(NPY_PY3K)
-    m = PyModule_Create(&moduledef);
-#else
-    m = Py_InitModule("umath", methods);
-#endif
-    if (!m) {
-        goto err;
-    }
-
-    /* Import the array */
-    if (_import_array() < 0) {
-        if (!PyErr_Occurred()) {
-            PyErr_SetString(PyExc_ImportError,
-                            "umath failed: Could not import array core.");
-        }
-        goto err;
-    }
 
     /* Initialize the types */
     if (PyType_Ready(&PyUFunc_Type) < 0)
-        goto err;
+        return -1;
 
     /* Add some symbolic constants to the module */
     d = PyModule_GetDict(m);
 
-    c_api = NpyCapsule_FromVoidPtr((void *)PyUFunc_API, NULL);
-    if (PyErr_Occurred()) {
-        goto err;
-    }
-    PyDict_SetItemString(d, "_UFUNC_API", c_api);
-    Py_DECREF(c_api);
-    if (PyErr_Occurred()) {
-        goto err;
-    }
-
-    /* Load the ufunc operators into the array module's namespace */
-    if (InitOperators(d) < 0) {
-        goto err;
-    }
-
     PyDict_SetItemString(d, "pi", s = PyFloat_FromDouble(NPY_PI));
     Py_DECREF(s);
     PyDict_SetItemString(d, "e", s = PyFloat_FromDouble(NPY_E));
@@ -417,19 +330,11 @@ PyMODINIT_FUNC initumath(void)
     PyDict_SetItemString(d, "conj", s);
     PyDict_SetItemString(d, "mod", s2);
 
-    initscalarmath(m);
-
     if (!intern_strings()) {
-        goto err;
-    }
-
-    return RETVAL(m);
-
- err:
-    /* Check for errors */
-    if (!PyErr_Occurred()) {
         PyErr_SetString(PyExc_RuntimeError,
-                        "cannot load umath module.");
+           "cannot intern umath strings while initializing _multiarray_umath.");
+        return -1;
     }
-    return RETVAL(NULL);
+
+    return 0;
 }
diff --git a/numpy/core/umath.py b/numpy/core/umath.py
new file mode 100644
index 000000000..efa213b1a
--- /dev/null
+++ b/numpy/core/umath.py
@@ -0,0 +1,32 @@
+"""
+Create the numpy.core.umath namespace for backward compatibility. In v1.16
+the multiarray and umath c-extension modules were merged into a single
+_multiarray_umath extension module. So we replicate the old namespace
+by importing from the extension module.
+"""
+
+from . import _multiarray_umath
+from numpy.core._multiarray_umath import *
+from numpy.core._multiarray_umath import _add_newdoc_ufunc, _arg
+
+__all__ = ['ERR_CALL', 'ERR_DEFAULT', 'ERR_IGNORE', 'ERR_LOG', 'ERR_PRINT',
+    'ERR_RAISE', 'ERR_WARN', 'FLOATING_POINT_SUPPORT', 'FPE_DIVIDEBYZERO',
+    'FPE_INVALID', 'FPE_OVERFLOW', 'FPE_UNDERFLOW', 'NAN', 'NINF', 'NZERO',
+    'PINF', 'PZERO', 'SHIFT_DIVIDEBYZERO', 'SHIFT_INVALID', 'SHIFT_OVERFLOW',
+    'SHIFT_UNDERFLOW', 'UFUNC_BUFSIZE_DEFAULT', 'UFUNC_PYVALS_NAME',
+    '_add_newdoc_ufunc', '_arg',
+    'absolute', 'add', 'arccos', 'arccosh', 'arcsin', 'arcsinh', 'arctan',
+    'arctan2', 'arctanh', 'bitwise_and', 'bitwise_or', 'bitwise_xor', 'cbrt',
+    'ceil', 'conj', 'conjugate', 'copysign', 'cos', 'cosh', 'deg2rad',
+    'degrees', 'divide', 'divmod', 'e', 'equal', 'euler_gamma', 'exp', 'exp2',
+    'expm1', 'fabs', 'floor', 'floor_divide', 'float_power', 'fmax', 'fmin',
+    'fmod', 'frexp', 'frompyfunc', 'gcd', 'geterrobj', 'greater',
+    'greater_equal', 'heaviside', 'hypot', 'invert', 'isfinite', 'isinf',
+    'isnan', 'isnat', 'lcm', 'ldexp', 'left_shift', 'less', 'less_equal',
+    'log', 'log10', 'log1p', 'log2', 'logaddexp', 'logaddexp2', 'logical_and',
+    'logical_not', 'logical_or', 'logical_xor', 'maximum', 'minimum', 'mod',
+    'modf', 'multiply', 'negative', 'nextafter', 'not_equal', 'pi', 'positive',
+    'power', 'rad2deg', 'radians', 'reciprocal', 'remainder', 'right_shift',
+    'rint', 'seterrobj', 'sign', 'signbit', 'sin', 'sinh', 'spacing', 'sqrt',
+    'square', 'subtract', 'tan', 'tanh', 'true_divide', 'trunc']
+
diff --git a/numpy/lib/__init__.py b/numpy/lib/__init__.py
index dc40ac67b..c1757150e 100644
--- a/numpy/lib/__init__.py
+++ b/numpy/lib/__init__.py
@@ -26,7 +26,7 @@ from .financial import *
 from .arrayterator import Arrayterator
 from .arraypad import *
 from ._version import *
-from numpy.core.multiarray import tracemalloc_domain
+from numpy.core._multiarray_umath import tracemalloc_domain
 
 __all__ = ['emath', 'math', 'tracemalloc_domain']
 __all__ += type_check.__all__
diff --git a/numpy/tests/test_ctypeslib.py b/numpy/tests/test_ctypeslib.py
index 62793a9d6..675f8d242 100644
--- a/numpy/tests/test_ctypeslib.py
+++ b/numpy/tests/test_ctypeslib.py
@@ -12,11 +12,11 @@ try:
     cdll = None
     if hasattr(sys, 'gettotalrefcount'):
         try:
-            cdll = load_library('multiarray_d', np.core.multiarray.__file__)
+            cdll = load_library('_multiarray_umath_d', np.core._multiarray_umath.__file__)
         except OSError:
             pass
     if cdll is None:
-        cdll = load_library('multiarray', np.core.multiarray.__file__)
+        cdll = load_library('_multiarray_umath', np.core._multiarray_umath.__file__)
     _HAS_CTYPE = True
 except ImportError:
     _HAS_CTYPE = False
@@ -30,7 +30,7 @@ class TestLoadLibrary(object):
     def test_basic(self):
         try:
             # Should succeed
-            load_library('multiarray', np.core.multiarray.__file__)
+            load_library('_multiarray_umath', np.core._multiarray_umath.__file__)
         except ImportError as e:
             msg = ("ctypes is not available on this python: skipping the test"
                    " (import error was: %s)" % str(e))
@@ -43,7 +43,7 @@ class TestLoadLibrary(object):
             try:
                 so = get_shared_lib_extension(is_python_ext=True)
                 # Should succeed
-                load_library('multiarray%s' % so, np.core.multiarray.__file__)
+                load_library('_multiarray_umath%s' % so, np.core._multiarray_umath.__file__)
             except ImportError:
                 print("No distutils available, skipping test.")
         except ImportError as e: