# UFunc API

## Constants

`UFUNC_ERR_{HANDLER}`
  UFUNC_ERR_IGNORE
  UFUNC_ERR_WARN
  UFUNC_ERR_RAISE
  UFUNC_ERR_CALL
`UFUNC_{THING}_{ERR}`
  UFUNC_MASK_DIVIDEBYZERO
  UFUNC_MASK_OVERFLOW
  UFUNC_MASK_UNDERFLOW
  UFUNC_MASK_INVALID
  UFUNC_SHIFT_DIVIDEBYZERO
  UFUNC_SHIFT_OVERFLOW
  UFUNC_SHIFT_UNDERFLOW
  UFUNC_SHIFT_INVALID
  UFUNC_FPE_DIVIDEBYZERO
  UFUNC_FPE_OVERFLOW
  UFUNC_FPE_UNDERFLOW
  UFUNC_FPE_INVALID
`PyUFunc_{VALUE}`
  PyUFunc_One
  PyUFunc_Zero
  PyUFunc_MinusOne
  PyUFunc_ReorderableNone
  PyUFunc_None
  PyUFunc_IdentityValue

## Macros

NPY_LOOP_BEGIN_THREADS

  Used in universal function code to only release the Python GIL if loop->obj is not true (i.e. this is not an OBJECT array loop). Requires use of `NPY_BEGIN_THREADS_DEF` in variable declaration area.

NPY_LOOP_END_THREADS

  Used in universal function code to re-acquire the Python GIL if it was released (because loop->obj was not true).

## Types

type PyUFuncGenericFunction

  pointers to functions that actually implement the underlying (element-by-element) function \(N\) times with the following signature:

  void loopfunc(char **args, npy_intp const *dimensions, npy_intp const *steps, void *data)

    args

    > An array of pointers to the actual data for the input and output arrays. The input arguments are given first followed by the output arguments.

    dimensions

    > A pointer to the size of the dimension over which this function is looping.

    steps

    > A pointer to the number of bytes to jump to get to the next element in this dimension for each of the input and output arguments.

    data

    > Arbitrary data (extra arguments, function names, etc. ) that can be stored with the ufunc and will be passed in when it is called.

    This is an example of a func specialized for addition of doubles returning doubles.

        static void
        double_add(char **args,
                   npy_intp const *dimensions,
                   npy_intp const *steps,
                   void *extra)
        {
            npy_intp i;
            npy_intp is1 = steps[0], is2 = steps[1];
            npy_intp os = steps[2], n = dimensions[0];
            char *i1 = args[0], *i2 = args[1], *op = args[2];
            for (i = 0; i < n; i++) {
                *((double *)op) = *((double *)i1) +
                                  *((double *)i2);
                i1 += is1;
                i2 += is2;
                op += os;
             }
        }

## Functions

PyObject *PyUFunc_FromFuncAndData(PyUFuncGenericFunction *func, void **data, char *types, int ntypes, int nin, int nout, int identity, char *name, char *doc, int unused)

  Create a new broadcasting universal function from required variables. Each ufunc builds around the notion of an element-by-element operation. Each ufunc object contains pointers to 1-d loops implementing the basic functionality for each supported type.

  Note

  The func, data, types, name, and doc arguments are not copied by `PyUFunc_FromFuncAndData`. The caller must ensure that the memory used by these arrays is not freed as long as the ufunc object is alive.

  Parameters

    - func – Must to an array of length ntypes containing `PyUFuncGenericFunction` items.

    - data – Should be `NULL` or a pointer to an array of size ntypes . This array may contain arbitrary extra-data to be passed to the corresponding loop function in the func array.

    - types –

      Length `(nin + nout) * ntypes` array of `char` encoding the `numpy.dtype.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 `numpy.int32` and the the second `numpy.int64`, with both returning `numpy.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.

      The bit-width names can also be used (e.g. `NPY_INT32`, `NPY_COMPLEX128` ) if desired.

      Type casting rules will be used at runtime to find the first `func` callable by the input/output provided.

    - ntypes – How many different data-type-specific functions the ufunc has implemented.

    - nin – The number of inputs to this operation.

    - nout – The number of outputs

    - identity – Either `PyUFunc_One`, `PyUFunc_Zero`, `PyUFunc_MinusOne`, or `PyUFunc_None`. This specifies what should be returned when an empty array is passed to the reduce method of the ufunc. The special value `PyUFunc_IdentityValue` may only be used with the `PyUFunc_FromFuncAndDataAndSignatureAndIdentity` method, to allow an arbitrary python object to be used as the identity.

    - name – The name for the ufunc as a `NULL` terminated string. Specifying a name of ‘add’ or ‘multiply’ enables a special behavior for integer-typed reductions when no dtype is given. If the input type is an integer (or boolean) data type smaller than the size of the `numpy.int_` data type, it will be internally upcast to the `numpy.int_` (or `numpy.uint`) data type.

    - doc – Allows passing in a documentation string to be stored with the ufunc. The documentation string should not contain the name of the function or the calling signature as that will be dynamically determined from the object and available when accessing the __doc__ attribute of the ufunc.

    - unused – Unused and present for backwards compatibility of the C-API.

PyObject *PyUFunc_FromFuncAndDataAndSignature(PyUFuncGenericFunction *func, void **data, char *types, int ntypes, 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 a generalized universal functions. 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.

  Parameters

    - signature – The signature for the new gufunc. Setting it to NULL is equivalent to calling PyUFunc_FromFuncAndData. A copy of the string is made, so the passed in buffer can be freed.

PyObject *PyUFunc_FromFuncAndDataAndSignatureAndIdentity(PyUFuncGenericFunction *func, void **data, char *types, int ntypes, int nin, int nout, int identity, char *name, char *doc, int unused, char *signature, PyObject *identity_value)

  This function is very similar to PyUFunc_FromFuncAndDataAndSignature above, but has an extra identity_value argument, to define an arbitrary identity for the ufunc when `identity` is passed as `PyUFunc_IdentityValue`.

  Parameters

    - identity_value – The identity for the new gufunc. Must be passed as `NULL` unless the `identity` argument is `PyUFunc_IdentityValue`. Setting it to NULL is equivalent to calling PyUFunc_FromFuncAndDataAndSignature.

int PyUFunc_RegisterLoopForType(PyUFuncObject *ufunc, int usertype, PyUFuncGenericFunction function, int *arg_types, void *data)

  This function allows the user to register a 1-d loop with an already- created ufunc to be used whenever the ufunc is called with any of its input arguments as the user-defined data-type. This is needed in order to make ufuncs work with built-in data-types. The data-type must have been previously registered with the numpy system. The loop is passed in as function. This loop can take arbitrary data which should be passed in as data. The data-types the loop requires are passed in as arg_types which must be a pointer to memory at least as large as ufunc->nargs.

int PyUFunc_RegisterLoopForDescr(PyUFuncObject *ufunc, PyArray_Descr *userdtype, PyUFuncGenericFunction function, PyArray_Descr **arg_dtypes, void *data)

  This function behaves like PyUFunc_RegisterLoopForType above, except that it allows the user to register a 1-d loop using PyArray_Descr objects instead of dtype type num values. This allows a 1-d loop to be registered for structured array data-dtypes and custom data-types instead of scalar data-types.

int PyUFunc_ReplaceLoopBySignature(PyUFuncObject *ufunc, PyUFuncGenericFunction newfunc, int *signature, PyUFuncGenericFunction *oldfunc)

  Replace a 1-d loop matching the given signature in the already-created ufunc with the new 1-d loop newfunc. Return the old 1-d loop function in oldfunc. Return 0 on success and -1 on failure. This function works only with built-in types (use `PyUFunc_RegisterLoopForType` for user-defined types). A signature is an array of data-type numbers indicating the inputs followed by the outputs assumed by the 1-d loop.

int PyUFunc_checkfperr(int errmask, PyObject *errobj)

  A simple interface to the IEEE error-flag checking support. The errmask argument is a mask of `UFUNC_MASK_{ERR}` bitmasks indicating which errors to check for (and how to check for them). The errobj must be a Python tuple with two elements: a string containing the name which will be used in any communication of error and either a callable Python object (call-back function) or `Py_None`. The callable object will only be used if `UFUNC_ERR_CALL` is set as the desired error checking method. This routine manages the GIL and is safe to call even after releasing the GIL. If an error in the IEEE-compatible hardware is determined a -1 is returned, otherwise a 0 is returned.

void PyUFunc_clearfperr()

  Clear the IEEE error flags.

void PyUFunc_GetPyValues(char *name, int *bufsize, int *errmask, PyObject **errobj)

  Get the Python values used for ufunc processing from the thread-local storage area unless the defaults have been set in which case the name lookup is bypassed. The name is placed as a string in the first element of *errobj. The second element is the looked-up function to call on error callback. The value of the looked-up buffer-size to use is passed into bufsize, and the value of the error mask is placed into errmask.

## Generic functions

At the core of every ufunc is a collection of type-specific functions that defines the basic functionality for each of the supported types. These functions must evaluate the underlying function \(N\geq1\) times. Extra-data may be passed in that may be used during the calculation. This feature allows some general functions to be used as these basic looping functions. The general function has all the code needed to point variables to the right place and set up a function call. The general function assumes that the actual function to call is passed in as the extra data and calls it with the correct values. All of these functions are suitable for placing directly in the array of functions stored in the functions member of the PyUFuncObject structure.

void PyUFunc_f_f_As_d_d(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

void PyUFunc_d_d(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

void PyUFunc_f_f(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

void PyUFunc_g_g(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

void PyUFunc_F_F_As_D_D(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

void PyUFunc_F_F(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

void PyUFunc_D_D(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

void PyUFunc_G_G(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

void PyUFunc_e_e(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

void PyUFunc_e_e_As_f_f(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

void PyUFunc_e_e_As_d_d(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

  Type specific, core 1-d functions for ufuncs where each calculation is obtained by calling a function taking one input argument and returning one output. This function is passed in `func`. The letters correspond to dtypechar’s of the supported data types ( `e` - half, `f` - float, `d` - double, `g` - long double, `F` - cfloat, `D` - cdouble, `G` - clongdouble). The argument func must support the same signature. The _As_X_X variants assume ndarray’s of one data type but cast the values to use an underlying function that takes a different data type. Thus, `PyUFunc_f_f_As_d_d` uses ndarrays of data type `NPY_FLOAT` but calls out to a C-function that takes double and returns double.

void PyUFunc_ff_f_As_dd_d(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

void PyUFunc_ff_f(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

void PyUFunc_dd_d(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

void PyUFunc_gg_g(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

void PyUFunc_FF_F_As_DD_D(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

void PyUFunc_DD_D(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

void PyUFunc_FF_F(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

void PyUFunc_GG_G(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

void PyUFunc_ee_e(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

void PyUFunc_ee_e_As_ff_f(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

void PyUFunc_ee_e_As_dd_d(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

  Type specific, core 1-d functions for ufuncs where each calculation is obtained by calling a function taking two input arguments and returning one output. The underlying function to call is passed in as func. The letters correspond to dtypechar’s of the specific data type supported by the general-purpose function. The argument `func` must support the corresponding signature. The `_As_XX_X` variants assume ndarrays of one data type but cast the values at each iteration of the loop to use the underlying function that takes a different data type.

void PyUFunc_O_O(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

void PyUFunc_OO_O(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

  One-input, one-output, and two-input, one-output core 1-d functions for the `NPY_OBJECT` data type. These functions handle reference count issues and return early on error. The actual function to call is func and it must accept calls with the signature `(PyObject*) (PyObject*)` for `PyUFunc_O_O` or `(PyObject*)(PyObject *, PyObject *)` for `PyUFunc_OO_O`.

void PyUFunc_O_O_method(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

  This general purpose 1-d core function assumes that func is a string representing a method of the input object. For each iteration of the loop, the Python object is extracted from the array and its func method is called returning the result to the output array.

void PyUFunc_OO_O_method(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

  This general purpose 1-d core function assumes that func is a string representing a method of the input object that takes one argument. The first argument in args is the method whose function is called, the second argument in args is the argument passed to the function. The output of the function is stored in the third entry of args.

void PyUFunc_On_Om(char **args, npy_intp const *dimensions, npy_intp const *steps, void *func)

  This is the 1-d core function used by the dynamic ufuncs created by umath.frompyfunc(function, nin, nout). In this case func is a pointer to a `PyUFunc_PyFuncData` structure which has definition

  type PyUFunc_PyFuncData

        typedef struct {
            int nin;
            int nout;
            PyObject *callable;
        } PyUFunc_PyFuncData;

  At each iteration of the loop, the nin input objects are extracted from their object arrays and placed into an argument tuple, the Python callable is called with the input arguments, and the nout outputs are placed into their object arrays.

## Importing the API

PY_UFUNC_UNIQUE_SYMBOL

NO_IMPORT_UFUNC

void import_ufunc(void)

  These are the constants and functions for accessing the ufunc C-API from extension modules in precisely the same way as the array C-API can be accessed. The `import_ufunc` () function must always be called (in the initialization subroutine of the extension module). If your extension module is in one file then that is all that is required. The other two constants are useful if your extension module makes use of multiple files. In that case, define `PY_UFUNC_UNIQUE_SYMBOL` to something unique to your code and then in source files that do not contain the module initialization function but still need access to the UFUNC API, define `PY_UFUNC_UNIQUE_SYMBOL` to the same name used previously and also define `NO_IMPORT_UFUNC`.

  The C-API is actually an array of function pointers. This array is created (and pointed to by a global variable) by import_ufunc. The global variable is either statically defined or allowed to be seen by other files depending on the state of `PY_UFUNC_UNIQUE_SYMBOL` and `NO_IMPORT_UFUNC`.

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