numpy · eric-wieser · May 29, 2018 · May 9, 2018 · Apr 30, 2018 · May 28, 2018
diff --git a/doc/source/reference/c-api.generalized-ufuncs.rst b/doc/source/reference/c-api.generalized-ufuncs.rst
@@ -101,6 +101,7 @@ Dimension Index
     enumerates the dimension names according to the order of the first
     occurrence of each name in the signature.
 
+.. _details-of-signature:
 
 Details of Signature
 --------------------
@@ -126,9 +127,9 @@ The formal syntax of signatures is as follows::
     <Output arguments>     ::= <Argument list>
     <Argument list>        ::= nil | <Argument> | <Argument> "," <Argument list>
     <Argument>             ::= "(" <Core dimension list> ")"
-    <Core dimension list>  ::= nil | <Dimension name> |
-                               <Dimension name> "," <Core dimension list>
-    <Dimension name>       ::= valid Python variable name
+    <Core dimension list>  ::= nil | <Core dimension name> |
+                               <Core dimension name> "," <Core dimension list>
+    <Core dimension name>  ::= valid Python variable name
 
 
 Notes:

diff --git a/doc/source/reference/c-api.ufunc.rst b/doc/source/reference/c-api.ufunc.rst
@@ -93,12 +93,23 @@ Functions
         the corresponding 1-d loop function in the func array.
 
     :param types:
-        Must be of length (*nin* + *nout*) \* *ntypes*, and it
-        contains the data-types (built-in only) that the corresponding
-        function in the *func* array can deal with.
+       Length ``(nin + nout) * ntypes`` array of ``char`` encoding the
+       :ref:`PyArray_Descr.type_num` (built-in only) that the corresponding
+       function in the ``func`` array accepts. For instance, for a comparison
+       ufunc with three ``ntypes``, two ``nin`` and one ``nout``, where the
+       first function accepts :ref:`npy_int32` and the the second
+       :ref:`npy_int64`, with both returning :ref:`npy_bool`, ``types`` would
+       be ``(char[]) {5, 5, 0, 7, 7, 0}`` since ``NPY_INT32`` is 5,
+       ``NPY_INT64`` is 7, and ``NPY_BOOL`` is 0 (on the python side, these
+       are exposed via :ref:`dtype.num`, i.e., for the example here,
+       ``dtype(np.int32).num``, ``dtype(np.int64).num``, and
+       ``dtype(np.bool_).num``, resp.).
+
+        :ref:`casting-rules` will be used at runtime to find the first
+        ``func`` callable by the input/output provided.
 
     :param ntypes:
-        How many different data-type "signatures" the ufunc has implemented.
+        How many different data-type-specific functions the ufunc has implemented.
 
     :param nin:
         The number of inputs to this operation.
@@ -129,10 +140,11 @@ Functions
         int nin, int nout, int identity, char* name, char* doc, int unused, char *signature)
 
    This function is very similar to PyUFunc_FromFuncAndData above, but has
-   an extra *signature* argument, to define generalized universal functions.
+   an extra *signature* argument, to define a
+   :ref:`generalized universal functions <c-api.generalized-ufuncs>`.
    Similarly to how ufuncs are built around an element-by-element operation,
-   gufuncs are around subarray-by-subarray operations, the signature defining
-   the subarrays to operate on.
+   gufuncs are around subarray-by-subarray operations, the
+   :ref:`signature <details-of-signature>` defining the subarrays to operate on.
 
    :param signature:
         The signature for the new gufunc. Setting it to NULL is equivalent

diff --git a/doc/source/reference/ufuncs.rst b/doc/source/reference/ufuncs.rst
@@ -424,8 +424,8 @@ advanced usage and will not typically be used.
     provided by the **types** attribute of the ufunc object. For backwards
     compatibility this argument can also be provided as *sig*, although
     the long form is preferred. Note that this should not be confused with
-    the generalized ufunc signature that is stored in the **signature**
-    attribute of the of the ufunc object.
+    the generalized ufunc :ref:`signature <details-of-signature>` that is
+    stored in the **signature** attribute of the of the ufunc object.
 
 *extobj*
 

diff --git a/doc/source/user/c-info.ufunc-tutorial.rst b/doc/source/user/c-info.ufunc-tutorial.rst
@@ -1057,6 +1057,7 @@ PyUFunc_FromFuncAndData Specification
 What follows is the full specification of PyUFunc_FromFuncAndData, which
 automatically generates a ufunc from a C function with the correct signature.
 
+.. seealso:: :c:func:`PyUFunc_FromFuncAndDataAndSignature`
 
 .. c:function:: PyObject *PyUFunc_FromFuncAndData( \
         PyUFuncGenericFunction* func, void** data, char* types, int ntypes, \

diff --git a/numpy/core/include/numpy/ufuncobject.h b/numpy/core/include/numpy/ufuncobject.h
@@ -167,7 +167,7 @@ typedef struct _tagPyUFuncObject {
         int *core_dim_ixs;
         /*
          * positions of 1st core dimensions of each
-         * argument in core_dim_ixs
+         * argument in core_dim_ixs, equivalent to cumsum(core_num_dims)
          */
         int *core_offsets;
         /* signature string for printing purpose */