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+UFunc API
+=========
+
+.. sectionauthor:: Travis E. Oliphant
+
+.. index::
+ pair: ufunc; C-API
+
+
+Constants
+---------
+
+.. cvar:: UFUNC_ERR_{HANDLER}
+
+ ``{HANDLER}`` can be **IGNORE**, **WARN**, **RAISE**, or **CALL**
+
+.. cvar:: UFUNC_{THING}_{ERR}
+
+ ``{THING}`` can be **MASK**, **SHIFT**, or **FPE**, and ``{ERR}`` can
+ be **DIVIDEBYZERO**, **OVERFLOW**, **UNDERFLOW**, and **INVALID**.
+
+.. cvar:: PyUFunc_{VALUE}
+
+ ``{VALUE}`` can be **One** (1), **Zero** (0), or **None** (-1)
+
+
+Macros
+------
+
+.. cmacro:: 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 :cmacro:`NPY_BEGIN_THREADS_DEF` in variable
+ declaration area.
+
+.. cmacro:: 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).
+
+.. cfunction:: UFUNC_CHECK_ERROR(loop)
+
+ A macro used internally to check for errors and goto fail if
+ found. This macro requires a fail label in the current code
+ block. The *loop* variable must have at least members (obj,
+ errormask, and errorobj). If *loop* ->obj is nonzero, then
+ :cfunc:`PyErr_Occurred` () is called (meaning the GIL must be held). If
+ *loop* ->obj is zero, then if *loop* ->errormask is nonzero,
+ :cfunc:`PyUFunc_checkfperr` is called with arguments *loop* ->errormask
+ and *loop* ->errobj. If the result of this check of the IEEE
+ floating point registers is true then the code redirects to the
+ fail label which must be defined.
+
+.. cfunction:: UFUNC_CHECK_STATUS(ret)
+
+ A macro that expands to platform-dependent code. The *ret*
+ variable can can be any integer. The :cdata:`UFUNC_FPE_{ERR}` bits are
+ set in *ret* according to the status of the corresponding error
+ flags of the floating point processor.
+
+
+Functions
+---------
+
+.. cfunction:: PyObject* PyUFunc_FromFuncAndData(PyUFuncGenericFunction* func, void** data, char* types, int ntypes, int nin, int nout, int identity, char* name, char* doc, int check_return)
+
+ 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.
+
+ :param nin:
+
+ The number of inputs to this operation.
+
+ :param nout:
+
+ The number of outputs
+
+ :param ntypes:
+
+ How many different data-type "signatures" the ufunc has implemented.
+
+ :param func:
+
+ Must to an array of length *ntypes* containing
+ :ctype:`PyUFuncGenericFunction` items. These items are pointers to
+ functions that acutally implement the underlying
+ (element-by-element) function :math:`N` times. T
+
+ :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.
+
+ :param 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 1-d loop function in the func array.
+
+ :param name:
+
+ The name for the ufunc.
+
+ :param 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.
+
+ :param check_return:
+
+ Unused and present for backwards compatibility of the C-API. A
+ corresponding *check_return* integer does exist in the ufunc
+ structure and it does get set with this value when the ufunc
+ object is created.
+
+.. cfunction:: 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.
+
+.. cfunction:: 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
+ :cfunc:`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.
+
+.. cfunction:: int PyUFunc_GenericFunction(PyUFuncObject* self, PyObject* args, PyArrayObject** mps)
+
+ A generic ufunc call. The ufunc is passed in as *self*, the
+ arguments to the ufunc as *args*. The *mps* argument is an array
+ of :ctype:`PyArrayObject` pointers containing the converted input
+ arguments as well as the ufunc outputs on return. The user is
+ responsible for managing this array and receives a new reference
+ for each array in *mps*. The total number of arrays in *mps* is
+ given by *self* ->nin + *self* ->nout.
+
+.. cfunction:: int PyUFunc_checkfperr(int errmask, PyObject* errobj)
+
+ A simple interface to the IEEE error-flag checking support. The
+ *errmask* argument is a mask of :cdata:`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 :cdata:`Py_None`. The callable object will only be used if
+ :cdata:`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-compatibile
+ hardware is determined a -1 is returned, otherwise a 0 is
+ returned.
+
+.. cfunction:: void PyUFunc_clearfperr()
+
+ Clear the IEEE error flags.
+
+.. cfunction:: 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 :math:`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.
+
+.. cfunction:: void PyUFunc_f_f_As_d_d(char** args, npy_intp* dimensions, npy_intp* steps, void* func)
+
+.. cfunction:: void PyUFunc_d_d(char** args, npy_intp* dimensions, npy_intp* steps, void* func)
+
+.. cfunction:: void PyUFunc_f_f(char** args, npy_intp* dimensions, npy_intp* steps, void* func)
+
+.. cfunction:: void PyUFunc_g_g(char** args, npy_intp* dimensions, npy_intp* steps, void* func)
+
+.. cfunction:: void PyUFunc_F_F_As_D_D(char** args, npy_intp* dimensions, npy_intp* steps, void* func)
+
+.. cfunction:: void PyUFunc_F_F(char** args, npy_intp* dimensions, npy_intp* steps, void* func)
+
+.. cfunction:: void PyUFunc_D_D(char** args, npy_intp* dimensions, npy_intp* steps, void* func)
+
+.. cfunction:: void PyUFunc_G_G(char** args, npy_intp* dimensions, npy_intp* 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 ( ``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,
+ :cfunc:`PyUFunc_f_f_As_d_d` uses ndarrays of data type :cdata:`NPY_FLOAT`
+ but calls out to a C-function that takes double and returns
+ double.
+
+.. cfunction:: void PyUFunc_ff_f_As_dd_d(char** args, npy_intp* dimensions, npy_intp* steps, void* func)
+
+.. cfunction:: void PyUFunc_ff_f(char** args, npy_intp* dimensions, npy_intp* steps, void* func)
+
+.. cfunction:: void PyUFunc_dd_d(char** args, npy_intp* dimensions, npy_intp* steps, void* func)
+
+.. cfunction:: void PyUFunc_gg_g(char** args, npy_intp* dimensions, npy_intp* steps, void* func)
+
+.. cfunction:: void PyUFunc_FF_F_As_DD_D(char** args, npy_intp* dimensions, npy_intp* steps, void* func)
+
+.. cfunction:: void PyUFunc_DD_D(char** args, npy_intp* dimensions, npy_intp* steps, void* func)
+
+.. cfunction:: void PyUFunc_FF_F(char** args, npy_intp* dimensions, npy_intp* steps, void* func)
+
+.. cfunction:: void PyUFunc_GG_G(char** args, npy_intp* dimensions, npy_intp* 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.
+
+.. cfunction:: void PyUFunc_O_O(char** args, npy_intp* dimensions, npy_intp* steps, void* func)
+
+.. cfunction:: void PyUFunc_OO_O(char** args, npy_intp* dimensions, npy_intp* steps, void* func)
+
+ One-input, one-output, and two-input, one-output core 1-d functions
+ for the :cdata:`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 :cfunc:`PyUFunc_O_O` or ``(PyObject*)(PyObject *, PyObject *)``
+ for :cfunc:`PyUFunc_OO_O`.
+
+.. cfunction:: void PyUFunc_O_O_method(char** args, npy_intp* dimensions, npy_intp* 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 obejct is extracted from the array
+ and its *func* method is called returning the result to the output array.
+
+.. cfunction:: void PyUFunc_OO_O_method(char** args, npy_intp* dimensions, npy_intp* 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*.
+
+.. cfunction:: void PyUFunc_On_Om(char** args, npy_intp* dimensions, npy_intp* 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 :ctype:`PyUFunc_PyFuncData` structure which has definition
+
+ .. ctype:: PyUFunc_PyFuncData
+
+ .. code-block:: c
+
+ typedef struct {
+ int nin;
+ int nout;
+ PyObject *callable;
+ } PyUFunc_PyFuncData;
+
+ At each iteration of the loop, the *nin* input objects are exctracted
+ 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
+-----------------
+
+.. cvar:: PY_UFUNC_UNIQUE_SYMBOL
+
+.. cvar:: NO_IMPORT_UFUNC
+
+.. cfunction:: 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 :cdata:`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 :cdata:`PY_UFUNC_UNIQUE_SYMBOL` to the same name used previously
+ and also define :cdata:`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
+ :cdata:`Py_UFUNC_UNIQUE_SYMBOL` and :cdata:`NO_IMPORT_UFUNC`.
+
+.. index::
+ pair: ufunc; C-API