"""
python _generate_pyx.py

Generate Ufunc definition source files for scipy.special.  Produces
files '_ufuncs.c' and '_ufuncs_cxx.c' by first producing Cython.

This will generate both calls to PyUFunc_FromFuncAndData and the
required ufunc inner loops.

The functions signatures are contained in 'functions.json', the syntax
for a function signature is

    <function>:       <name> ':' <input> '*' <output>
                        '->' <retval> '*' <ignored_retval>
    <input>:          <typecode>*
    <output>:         <typecode>*
    <retval>:         <typecode>?
    <ignored_retval>: <typecode>?
    <headers>:        <header_name> [',' <header_name>]*

The input parameter types are denoted by single character type
codes, according to

   'f': 'float'
   'd': 'double'
   'g': 'long double'
   'F': 'float complex'
   'D': 'double complex'
   'G': 'long double complex'
   'i': 'int'
   'l': 'long'
   'v': 'void'

If multiple kernel functions are given for a single ufunc, the one
which is used is determined by the standard ufunc mechanism. Kernel
functions that are listed first are also matched first against the
ufunc input types, so functions listed earlier take precedence.

In addition, versions with casted variables, such as d->f,D->F and
i->d are automatically generated.

There should be either a single header that contains all of the kernel
functions listed, or there should be one header for each kernel
function. Cython pxd files are allowed in addition to .h files.

Cython functions may use fused types, but the names in the list
should be the specialized ones, such as 'somefunc[float]'.

Function coming from C++ should have ``++`` appended to the name of
the header.

Floating-point exceptions inside these Ufuncs are converted to
special function errors --- which are separately controlled by the
user, and off by default, as they are usually not especially useful
for the user.


The C++ module
--------------
In addition to ``_ufuncs`` module, a second module ``_ufuncs_cxx`` is
generated. This module only exports function pointers that are to be
used when constructing some of the ufuncs in ``_ufuncs``. The function
pointers are exported via Cython's standard mechanism.

This mainly avoids build issues --- Python distutils has no way to
figure out what to do if you want to link both C++ and Fortran code in
the same shared library.

"""

from __future__ import division, print_function, absolute_import

#---------------------------------------------------------------------------------
# Extra code
#---------------------------------------------------------------------------------

UFUNCS_EXTRA_CODE_COMMON = """\
# This file is automatically generated by _generate_pyx.py.
# Do not edit manually!
from __future__ import absolute_import

include "_ufuncs_extra_code_common.pxi"
"""

UFUNCS_EXTRA_CODE = """\
include "_ufuncs_extra_code.pxi"
"""

UFUNCS_EXTRA_CODE_BOTTOM = """\
#
# Aliases
#
jn = jv
"""

CYTHON_SPECIAL_PXD = """\
# This file is automatically generated by _generate_pyx.py.
# Do not edit manually!
"""

CYTHON_SPECIAL_PYX = """\
# This file is automatically generated by _generate_pyx.py.
# Do not edit manually!
\"\"\"
.. highlight:: cython

Cython API for Special Functions
================================

Scalar, typed versions of many of the functions in ``scipy.special``
can be accessed directly from Cython; the complete list is given
below. Functions are overloaded using Cython fused types so their
names match their ufunc counterpart. The module follows the following
conventions:

- If a function's ufunc counterpart returns multiple values, then the
  function returns its outputs via pointers in the final arguments
- If a function's ufunc counterpart returns a single value, then the
  function's output is returned directly.

The module is usable from Cython via::

    cimport scipy.special.cython_special

Error Handling
--------------

Functions can indicate an error by returning ``nan``; however they
cannot emit warnings like their counterparts in ``scipy.special``.

Available Functions
-------------------

FUNCLIST
\"\"\"

from __future__ import absolute_import
include "_cython_special.pxi"
"""


#---------------------------------------------------------------------------------
# Code generation
#---------------------------------------------------------------------------------

import os
import optparse
import re
import textwrap
import itertools
import numpy
import json


BASE_DIR = os.path.abspath(os.path.dirname(__file__))

add_newdocs = __import__('add_newdocs')

CY_TYPES = {
    'f': 'float',
    'd': 'double',
    'g': 'long double',
    'F': 'float complex',
    'D': 'double complex',
    'G': 'long double complex',
    'i': 'int',
    'l': 'long',
    'v': 'void',
}

C_TYPES = {
    'f': 'npy_float',
    'd': 'npy_double',
    'g': 'npy_longdouble',
    'F': 'npy_cfloat',
    'D': 'npy_cdouble',
    'G': 'npy_clongdouble',
    'i': 'npy_int',
    'l': 'npy_long',
    'v': 'void',
}

TYPE_NAMES = {
    'f': 'NPY_FLOAT',
    'd': 'NPY_DOUBLE',
    'g': 'NPY_LONGDOUBLE',
    'F': 'NPY_CFLOAT',
    'D': 'NPY_CDOUBLE',
    'G': 'NPY_CLONGDOUBLE',
    'i': 'NPY_INT',
    'l': 'NPY_LONG',
}

CYTHON_SPECIAL_BENCHFUNCS = {
    'airy': ['d*dddd', 'D*DDDD'],
    'beta': ['dd'],
    'erf': ['d', 'D'],
    'exprel': ['d'],
    'gamma': ['d', 'D'],
    'jv': ['dd', 'dD'],
    'loggamma': ['D'],
    'logit': ['d'],
    'psi': ['d', 'D'],
}


def underscore(arg):
    return arg.replace(" ", "_")


def cast_order(c):
    return ['ilfdgFDG'.index(x) for x in c]


# These downcasts will cause the function to return NaNs, unless the
# values happen to coincide exactly.
DANGEROUS_DOWNCAST = set([
    ('F', 'i'), ('F', 'l'), ('F', 'f'), ('F', 'd'), ('F', 'g'),
    ('D', 'i'), ('D', 'l'), ('D', 'f'), ('D', 'd'), ('D', 'g'),
    ('G', 'i'), ('G', 'l'), ('G', 'f'), ('G', 'd'), ('G', 'g'),
    ('f', 'i'), ('f', 'l'),
    ('d', 'i'), ('d', 'l'),
    ('g', 'i'), ('g', 'l'),
    ('l', 'i'),
])

NAN_VALUE = {
    'f': 'NPY_NAN',
    'd': 'NPY_NAN',
    'g': 'NPY_NAN',
    'F': 'NPY_NAN',
    'D': 'NPY_NAN',
    'G': 'NPY_NAN',
    'i': '0xbad0bad0',
    'l': '0xbad0bad0',
}


def generate_loop(func_inputs, func_outputs, func_retval,
                  ufunc_inputs, ufunc_outputs):
    """
    Generate a UFunc loop function that calls a function given as its
    data parameter with the specified input and output arguments and
    return value.

    This function can be passed to PyUFunc_FromFuncAndData.

    Parameters
    ----------
    func_inputs, func_outputs, func_retval : str
        Signature of the function to call, given as type codes of the
        input, output and return value arguments. These 1-character
        codes are given according to the CY_TYPES and TYPE_NAMES
        lists above.

        The corresponding C function signature to be called is:

            retval func(intype1 iv1, intype2 iv2, ..., outtype1 *ov1, ...);

        If len(ufunc_outputs) == len(func_outputs)+1, the return value
        is treated as the first output argument. Otherwise, the return
        value is ignored.

    ufunc_inputs, ufunc_outputs : str
        Ufunc input and output signature.

        This does not have to exactly match the function signature,
        as long as the type casts work out on the C level.

    Returns
    -------
    loop_name
        Name of the generated loop function.
    loop_body
        Generated C code for the loop.

    """
    if len(func_inputs) != len(ufunc_inputs):
        raise ValueError("Function and ufunc have different number of inputs")

    if len(func_outputs) != len(ufunc_outputs) and not (
            func_retval != "v" and len(func_outputs)+1 == len(ufunc_outputs)):
        raise ValueError("Function retval and ufunc outputs don't match")

    name = "loop_%s_%s_%s_As_%s_%s" % (
        func_retval, func_inputs, func_outputs, ufunc_inputs, ufunc_outputs
        )
    body = "cdef void %s(char **args, np.npy_intp *dims, np.npy_intp *steps, void *data) nogil:\n" % name
    body += "    cdef np.npy_intp i, n = dims[0]\n"
    body += "    cdef void *func = (<void**>data)[0]\n"
    body += "    cdef char *func_name = <char*>(<void**>data)[1]\n"

    for j in range(len(ufunc_inputs)):
        body += "    cdef char *ip%d = args[%d]\n" % (j, j)
    for j in range(len(ufunc_outputs)):
        body += "    cdef char *op%d = args[%d]\n" % (j, j + len(ufunc_inputs))

    ftypes = []
    fvars = []
    outtypecodes = []
    for j in range(len(func_inputs)):
        ftypes.append(CY_TYPES[func_inputs[j]])
        fvars.append("<%s>(<%s*>ip%d)[0]" % (
            CY_TYPES[func_inputs[j]],
            CY_TYPES[ufunc_inputs[j]], j))

    if len(func_outputs)+1 == len(ufunc_outputs):
        func_joff = 1
        outtypecodes.append(func_retval)
        body += "    cdef %s ov0\n" % (CY_TYPES[func_retval],)
    else:
        func_joff = 0

    for j, outtype in enumerate(func_outputs):
        body += "    cdef %s ov%d\n" % (CY_TYPES[outtype], j+func_joff)
        ftypes.append("%s *" % CY_TYPES[outtype])
        fvars.append("&ov%d" % (j+func_joff))
        outtypecodes.append(outtype)

    body += "    for i in range(n):\n"
    if len(func_outputs)+1 == len(ufunc_outputs):
        rv = "ov0 = "
    else:
        rv = ""

    funcall = "        %s(<%s(*)(%s) nogil>func)(%s)\n" % (
        rv, CY_TYPES[func_retval], ", ".join(ftypes), ", ".join(fvars))

    # Cast-check inputs and call function
    input_checks = []
    for j in range(len(func_inputs)):
        if (ufunc_inputs[j], func_inputs[j]) in DANGEROUS_DOWNCAST:
            chk = "<%s>(<%s*>ip%d)[0] == (<%s*>ip%d)[0]" % (
                CY_TYPES[func_inputs[j]], CY_TYPES[ufunc_inputs[j]], j,
                CY_TYPES[ufunc_inputs[j]], j)
            input_checks.append(chk)

    if input_checks:
        body += "        if %s:\n" % (" and ".join(input_checks))
        body += "    " + funcall
        body += "        else:\n"
        body += "            sf_error.error(func_name, sf_error.DOMAIN, \"invalid input argument\")\n"
        for j, outtype in enumerate(outtypecodes):
            body += "            ov%d = <%s>%s\n" % (
                j, CY_TYPES[outtype], NAN_VALUE[outtype])
    else:
        body += funcall

    # Assign and cast-check output values
    for j, (outtype, fouttype) in enumerate(zip(ufunc_outputs, outtypecodes)):
        if (fouttype, outtype) in DANGEROUS_DOWNCAST:
            body += "        if ov%d == <%s>ov%d:\n" % (j, CY_TYPES[outtype], j)
            body += "            (<%s *>op%d)[0] = <%s>ov%d\n" % (
                CY_TYPES[outtype], j, CY_TYPES[outtype], j)
            body += "        else:\n"
            body += "            sf_error.error(func_name, sf_error.DOMAIN, \"invalid output\")\n"
            body += "            (<%s *>op%d)[0] = <%s>%s\n" % (
                CY_TYPES[outtype], j, CY_TYPES[outtype], NAN_VALUE[outtype])
        else:
            body += "        (<%s *>op%d)[0] = <%s>ov%d\n" % (
                CY_TYPES[outtype], j, CY_TYPES[outtype], j)
    for j in range(len(ufunc_inputs)):
        body += "        ip%d += steps[%d]\n" % (j, j)
    for j in range(len(ufunc_outputs)):
        body += "        op%d += steps[%d]\n" % (j, j + len(ufunc_inputs))

    body += "    sf_error.check_fpe(func_name)\n"

    return name, body


def generate_fused_type(codes):
    """
    Generate name of and cython code for a fused type.

    Parameters
    ----------
    typecodes : str
        Valid inputs to CY_TYPES (i.e. f, d, g, ...).

    """
    cytypes = map(lambda x: CY_TYPES[x], codes)
    name = codes + "_number_t"
    declaration = ["ctypedef fused " + name + ":"]
    for cytype in cytypes:
        declaration.append("    " + cytype)
    declaration = "\n".join(declaration)
    return name, declaration


def generate_bench(name, codes):
    tab = " "*4
    top, middle, end = [], [], []

    tmp = codes.split("*")
    if len(tmp) > 1:
        incodes = tmp[0]
        outcodes = tmp[1]
    else:
        incodes = tmp[0]
        outcodes = ""

    inargs, inargs_and_types = [], []
    for n, code in enumerate(incodes):
        arg = "x{}".format(n)
        inargs.append(arg)
        inargs_and_types.append("{} {}".format(CY_TYPES[code], arg))
    line = "def {{}}(int N, {}):".format(", ".join(inargs_and_types))
    top.append(line)
    top.append(tab + "cdef int n")

    outargs = []
    for n, code in enumerate(outcodes):
        arg = "y{}".format(n)
        outargs.append("&{}".format(arg))
        line = "cdef {} {}".format(CY_TYPES[code], arg)
        middle.append(tab + line)

    end.append(tab + "for n in range(N):")
    end.append(2*tab + "{}({})")
    pyfunc = "_bench_{}_{}_{}".format(name, incodes, "py")
    cyfunc = "_bench_{}_{}_{}".format(name, incodes, "cy")
    pytemplate = "\n".join(top + end)
    cytemplate = "\n".join(top + middle + end)
    pybench = pytemplate.format(pyfunc, "_ufuncs." + name, ", ".join(inargs))
    cybench = cytemplate.format(cyfunc, name, ", ".join(inargs + outargs))
    return pybench, cybench


def generate_doc(name, specs):
    tab = " "*4
    doc = ["- :py:func:`~scipy.special.{}`::\n".format(name)]
    for spec in specs:
        incodes, outcodes = spec.split("->")
        incodes = incodes.split("*")
        intypes = list(map(lambda x: CY_TYPES[x], incodes[0]))
        if len(incodes) > 1:
            types = map(lambda x: "{} *".format(CY_TYPES[x]), incodes[1])
            intypes.extend(types)
        outtype = CY_TYPES[outcodes]
        line = "{} {}({})".format(outtype, name, ", ".join(intypes))
        doc.append(2*tab + line)
    doc[-1] = "{}\n".format(doc[-1])
    doc = "\n".join(doc)
    return doc


def npy_cdouble_from_double_complex(var):
    """Cast a cython double complex to a numpy cdouble."""
    res = "_complexstuff.npy_cdouble_from_double_complex({})".format(var)
    return res


def double_complex_from_npy_cdouble(var):
    """Cast a numpy cdouble to a cython double complex."""
    res = "_complexstuff.double_complex_from_npy_cdouble({})".format(var)
    return res


def iter_variants(inputs, outputs):
    """
    Generate variants of UFunc signatures, by changing variable types,
    within the limitation that the corresponding C types casts still
    work out.

    This does not generate all possibilities, just the ones required
    for the ufunc to work properly with the most common data types.

    Parameters
    ----------
    inputs, outputs : str
        UFunc input and output signature strings

    Yields
    ------
    new_input, new_output : str
        Modified input and output strings.
        Also the original input/output pair is yielded.

    """
    maps = [
        # always use long instead of int (more common type on 64-bit)
        ('i', 'l'),
    ]

    # float32-preserving signatures
    if not ('i' in inputs or 'l' in inputs):
        # Don't add float32 versions of ufuncs with integer arguments, as this
        # can lead to incorrect dtype selection if the integer arguments are
        # arrays, but float arguments are scalars.
        # For instance sph_harm(0,[0],0,0).dtype == complex64
        # This may be a NumPy bug, but we need to work around it.
        # cf. gh-4895, https://github.com/numpy/numpy/issues/5895
        maps = maps + [(a + 'dD', b + 'fF') for a, b in maps]

    # do the replacements
    for src, dst in maps:
        new_inputs = inputs
        new_outputs = outputs
        for a, b in zip(src, dst):
            new_inputs = new_inputs.replace(a, b)
            new_outputs = new_outputs.replace(a, b)
        yield new_inputs, new_outputs


class Func(object):
    """
    Base class for Ufunc and FusedFunc.

    """
    def __init__(self, name, signatures):
        self.name = name
        self.signatures = []
        self.function_name_overrides = {}

        for header in signatures.keys():
            for name, sig in signatures[header].items():
                inarg, outarg, ret = self._parse_signature(sig)
                self.signatures.append((name, inarg, outarg, ret, header))

    def _parse_signature(self, sig):
        m = re.match(r"\s*([fdgFDGil]*)\s*\*\s*([fdgFDGil]*)\s*->\s*([*fdgFDGil]*)\s*$", sig)
        if m:
            inarg, outarg, ret = [x.strip() for x in m.groups()]
            if ret.count('*') > 1:
                raise ValueError("{}: Invalid signature: {}".format(self.name, sig))
            return inarg, outarg, ret
        m = re.match(r"\s*([fdgFDGil]*)\s*->\s*([fdgFDGil]?)\s*$", sig)
        if m:
            inarg, ret = [x.strip() for x in m.groups()]
            return inarg, "", ret
        raise ValueError("{}: Invalid signature: {}".format(self.name, sig))

    def get_prototypes(self, nptypes_for_h=False):
        prototypes = []
        for func_name, inarg, outarg, ret, header in self.signatures:
            ret = ret.replace('*', '')
            c_args = ([C_TYPES[x] for x in inarg]
                      + [C_TYPES[x] + ' *' for x in outarg])
            cy_args = ([CY_TYPES[x] for x in inarg]
                       + [CY_TYPES[x] + ' *' for x in outarg])
            c_proto = "%s (*)(%s)" % (C_TYPES[ret], ", ".join(c_args))
            if header.endswith("h") and nptypes_for_h:
                cy_proto = c_proto + "nogil"
            else:
                cy_proto = "%s (*)(%s) nogil" % (CY_TYPES[ret], ", ".join(cy_args))
            prototypes.append((func_name, c_proto, cy_proto, header))
        return prototypes

    def cython_func_name(self, c_name, specialized=False, prefix="_func_",
                         override=True):
        # act on function name overrides
        if override and c_name in self.function_name_overrides:
            c_name = self.function_name_overrides[c_name]
            prefix = ""

        # support fused types
        m = re.match(r'^(.*?)(\[.*\])$', c_name)
        if m:
            c_base_name, fused_part = m.groups()
        else:
            c_base_name, fused_part = c_name, ""
        if specialized:
            return "%s%s%s" % (prefix, c_base_name, fused_part.replace(' ', '_'))
        else:
            return "%s%s" % (prefix, c_base_name,)


class Ufunc(Func):
    """
    Ufunc signature, restricted format suitable for special functions.

    Parameters
    ----------
    name
        Name of the ufunc to create
    signature
        String of form 'func: fff*ff->f, func2: ddd->*i' describing
        the C-level functions and types of their input arguments
        and return values.

        The syntax is 'function_name: inputparams*outputparams->output_retval*ignored_retval'

    Attributes
    ----------
    name : str
        Python name for the Ufunc
    signatures : list of (func_name, inarg_spec, outarg_spec, ret_spec, header_name)
        List of parsed signatures
    doc : str
        Docstring, obtained from add_newdocs
    function_name_overrides : dict of str->str
        Overrides for the function names in signatures

    """
    def __init__(self, name, signatures):
        super(Ufunc, self).__init__(name, signatures)
        self.doc = add_newdocs.get("scipy.special." + name)
        if self.doc is None:
            raise ValueError("No docstring for ufunc %r" % name)
        self.doc = textwrap.dedent(self.doc).strip()

    def _get_signatures_and_loops(self, all_loops):
        inarg_num = None
        outarg_num = None

        seen = set()
        variants = []

        def add_variant(func_name, inarg, outarg, ret, inp, outp):
            if inp in seen:
                return
            seen.add(inp)

            sig = (func_name, inp, outp)
            if "v" in outp:
                raise ValueError("%s: void signature %r" % (self.name, sig))
            if len(inp) != inarg_num or len(outp) != outarg_num:
                raise ValueError("%s: signature %r does not have %d/%d input/output args" % (
                    self.name, sig,
                    inarg_num, outarg_num))

            loop_name, loop = generate_loop(inarg, outarg, ret, inp, outp)
            all_loops[loop_name] = loop
            variants.append((func_name, loop_name, inp, outp))

        # First add base variants
        for func_name, inarg, outarg, ret, header in self.signatures:
            outp = re.sub(r'\*.*', '', ret) + outarg
            ret = ret.replace('*', '')
            if inarg_num is None:
                inarg_num = len(inarg)
                outarg_num = len(outp)

            inp, outp = list(iter_variants(inarg, outp))[0]
            add_variant(func_name, inarg, outarg, ret, inp, outp)

        # Then the supplementary ones
        for func_name, inarg, outarg, ret, header in self.signatures:
            outp = re.sub(r'\*.*', '', ret) + outarg
            ret = ret.replace('*', '')
            for inp, outp in iter_variants(inarg, outp):
                add_variant(func_name, inarg, outarg, ret, inp, outp)

        # Then sort variants to input argument cast order
        # -- the sort is stable, so functions earlier in the signature list
        #    are still preferred
        variants.sort(key=lambda v: cast_order(v[2]))

        return variants, inarg_num, outarg_num

    def generate(self, all_loops):
        toplevel = ""

        variants, inarg_num, outarg_num = self._get_signatures_and_loops(all_loops)

        loops = []
        funcs = []
        types = []

        for func_name, loop_name, inputs, outputs in variants:
            for x in inputs:
                types.append(TYPE_NAMES[x])
            for x in outputs:
                types.append(TYPE_NAMES[x])
            loops.append(loop_name)
            funcs.append(func_name)

        toplevel += "cdef np.PyUFuncGenericFunction ufunc_%s_loops[%d]\n" % (self.name, len(loops))
        toplevel += "cdef void *ufunc_%s_ptr[%d]\n" % (self.name, 2*len(funcs))
        toplevel += "cdef void *ufunc_%s_data[%d]\n" % (self.name, len(funcs))
        toplevel += "cdef char ufunc_%s_types[%d]\n" % (self.name, len(types))
        toplevel += 'cdef char *ufunc_%s_doc = (\n    "%s")\n' % (
            self.name,
            self.doc.replace("\\", "\\\\").replace('"', '\\"').replace('\n', '\\n\"\n    "')
            )

        for j, function in enumerate(loops):
            toplevel += "ufunc_%s_loops[%d] = <np.PyUFuncGenericFunction>%s\n" % (self.name, j, function)
        for j, type in enumerate(types):
            toplevel += "ufunc_%s_types[%d] = <char>%s\n" % (self.name, j, type)
        for j, func in enumerate(funcs):
            toplevel += "ufunc_%s_ptr[2*%d] = <void*>%s\n" % (self.name, j,
                                                              self.cython_func_name(func, specialized=True))
            toplevel += "ufunc_%s_ptr[2*%d+1] = <void*>(<char*>\"%s\")\n" % (self.name, j,
                                                                             self.name)
        for j, func in enumerate(funcs):
            toplevel += "ufunc_%s_data[%d] = &ufunc_%s_ptr[2*%d]\n" % (
                self.name, j, self.name, j)

        toplevel += ('@ = np.PyUFunc_FromFuncAndData(ufunc_@_loops, '
                     'ufunc_@_data, ufunc_@_types, %d, %d, %d, 0, '
                     '"@", ufunc_@_doc, 0)\n' % (len(types)/(inarg_num+outarg_num),
                                                 inarg_num, outarg_num)
                     ).replace('@', self.name)

        return toplevel


class FusedFunc(Func):
    """
    Generate code for a fused-type special function that can be
    cimported in cython.

    """
    def __init__(self, name, signatures):
        super(FusedFunc, self).__init__(name, signatures)
        self.doc = "See the documentation for scipy.special." + self.name
        # "codes" are the keys for CY_TYPES
        self.incodes, self.outcodes = self._get_codes()
        self.fused_types = set()
        self.intypes, infused_types = self._get_types(self.incodes)
        self.fused_types.update(infused_types)
        self.outtypes, outfused_types = self._get_types(self.outcodes)
        self.fused_types.update(outfused_types)
        self.invars, self.outvars = self._get_vars()

    def _get_codes(self):
        inarg_num, outarg_num = None, None
        all_inp, all_outp = [], []
        for _, inarg, outarg, ret, _ in self.signatures:
            outp = re.sub(r'\*.*', '', ret) + outarg
            if inarg_num is None:
                inarg_num = len(inarg)
                outarg_num = len(outp)
            inp, outp = list(iter_variants(inarg, outp))[0]
            all_inp.append(inp)
            all_outp.append(outp)

        incodes = []
        for n in range(inarg_num):
            codes = unique(map(lambda x: x[n], all_inp))
            codes.sort()
            incodes.append(''.join(codes))
        outcodes = []
        for n in range(outarg_num):
            codes = unique(map(lambda x: x[n], all_outp))
            codes.sort()
            outcodes.append(''.join(codes))

        return tuple(incodes), tuple(outcodes)

    def _get_types(self, codes):
        all_types = []
        fused_types = set()
        for code in codes:
            if len(code) == 1:
                # It's not a fused type
                all_types.append((CY_TYPES[code], code))
            else:
                # It's a fused type
                fused_type, dec = generate_fused_type(code)
                fused_types.add(dec)
                all_types.append((fused_type, code))
        return all_types, fused_types

    def _get_vars(self):
        invars = ["x{}".format(n) for n in range(len(self.intypes))]
        outvars = ["y{}".format(n) for n in range(len(self.outtypes))]
        return invars, outvars

    def _get_conditional(self, types, codes, adverb):
        """Generate an if/elif/else clause that selects a specialization of
        fused types.

        """
        clauses = []
        seen = set()
        for (typ, typcode), code in zip(types, codes):
            if len(typcode) == 1:
                continue
            if typ not in seen:
                clauses.append("{} is {}".format(typ, underscore(CY_TYPES[code])))
                seen.add(typ)
        if clauses and adverb != "else":
            line = "{} {}:".format(adverb, " and ".join(clauses))
        elif clauses and adverb == "else":
            line = "else:"
        else:
            line = None
        return line

    def _get_incallvars(self, intypes, c):
        """Generate pure input variables to a specialization,
        i.e. variables that aren't used to return a value.

        """
        incallvars = []
        for n, intype in enumerate(intypes):
            var = self.invars[n]
            if c and intype == "double complex":
                var = npy_cdouble_from_double_complex(var)
            incallvars.append(var)
        return incallvars

    def _get_outcallvars(self, outtypes, c):
        """Generate output variables to a specialization,
        i.e. pointers that are used to return values.

        """
        outcallvars, tmpvars, casts = [], [], []
        # If there are more out variables than out types, we want the
        # tail of the out variables
        start = len(self.outvars) - len(outtypes)
        outvars = self.outvars[start:]
        for n, (var, outtype) in enumerate(zip(outvars, outtypes)):
            if c and outtype == "double complex":
                tmp = "tmp{}".format(n)
                tmpvars.append(tmp)
                outcallvars.append("&{}".format(tmp))
                tmpcast = double_complex_from_npy_cdouble(tmp)
                casts.append("{}[0] = {}".format(var, tmpcast))
            else:
                outcallvars.append("{}".format(var))
        return outcallvars, tmpvars, casts

    def _get_nan_decs(self):
        """Set all variables to nan for specializations of fused types for
        which don't have signatures.

        """
        # Set non fused-type variables to nan
        tab = " "*4
        fused_types, lines = [], [tab + "else:"]
        seen = set()
        for outvar, outtype, code in zip(self.outvars, self.outtypes, self.outcodes):
            if len(code) == 1:
                line = "{}[0] = {}".format(outvar, NAN_VALUE[code])
                lines.append(2*tab + line)
            else:
                fused_type = outtype
                name, _ = fused_type
                if name not in seen:
                    fused_types.append(fused_type)
                    seen.add(name)
        if not fused_types:
            return lines

        # Set fused-type variables to nan
        all_codes = tuple([codes for _unused, codes in fused_types])

        codelens = list(map(lambda x: len(x), all_codes))
        last = numpy.prod(codelens) - 1
        for m, codes in enumerate(itertools.product(*all_codes)):
            fused_codes, decs = [], []
            for n, fused_type in enumerate(fused_types):
                code = codes[n]
                fused_codes.append(underscore(CY_TYPES[code]))
                for nn, outvar in enumerate(self.outvars):
                    if self.outtypes[nn] == fused_type:
                        line = "{}[0] = {}".format(outvar, NAN_VALUE[code])
                        decs.append(line)
            if m == 0:
                adverb = "if"
            elif m == last:
                adverb = "else"
            else:
                adverb = "elif"
            cond = self._get_conditional(fused_types, codes, adverb)
            lines.append(2*tab + cond)
            lines.extend(map(lambda x: 3*tab + x, decs))
        return lines

    def _get_tmp_decs(self, all_tmpvars):
        """Generate the declarations of any necessary temporary
        variables.

        """
        tab = " "*4
        tmpvars = list(all_tmpvars)
        tmpvars.sort()
        tmpdecs = [tab + "cdef npy_cdouble {}".format(tmpvar)
                   for tmpvar in tmpvars]
        return tmpdecs

    def _get_python_wrap(self):
        """Generate a python wrapper for functions which pass their
        arguments as pointers.

        """
        tab = " "*4
        body, callvars = [], []
        for (intype, _), invar in zip(self.intypes, self.invars):
            callvars.append("{} {}".format(intype, invar))
        line = "def _{}_pywrap({}):".format(self.name, ", ".join(callvars))
        body.append(line)
        for (outtype, _), outvar in zip(self.outtypes, self.outvars):
            line = "cdef {} {}".format(outtype, outvar)
            body.append(tab + line)
        addr_outvars = map(lambda x: "&{}".format(x), self.outvars)
        line = "{}({}, {})".format(self.name, ", ".join(self.invars),
                                   ", ".join(addr_outvars))
        body.append(tab + line)
        line = "return {}".format(", ".join(self.outvars))
        body.append(tab + line)
        body = "\n".join(body)
        return body

    def _get_common(self, signum, sig):
        """Generate code common to all the _generate_* methods."""
        tab = " "*4
        func_name, incodes, outcodes, retcode, header = sig
        # Convert ints to longs; cf. iter_variants()
        incodes = incodes.replace('i', 'l')
        outcodes = outcodes.replace('i', 'l')
        retcode = retcode.replace('i', 'l')

        if header.endswith("h"):
            c = True
        else:
            c = False
        if header.endswith("++"):
            cpp = True
        else:
            cpp = False

        intypes = list(map(lambda x: CY_TYPES[x], incodes))
        outtypes = list(map(lambda x: CY_TYPES[x], outcodes))
        retcode = re.sub(r'\*.*', '', retcode)
        if not retcode:
            retcode = 'v'
        rettype = CY_TYPES[retcode]

        if cpp:
            # Functions from _ufuncs_cxx are exported as a void*
            # pointers; cast them to the correct types
            func_name = "scipy.special._ufuncs_cxx._export_{}".format(func_name)
            func_name = "(<{}(*)({}) nogil>{})"\
                    .format(rettype, ", ".join(intypes + outtypes), func_name)
        else:
            func_name = self.cython_func_name(func_name, specialized=True)

        if signum == 0:
            adverb = "if"
        else:
            adverb = "elif"
        cond = self._get_conditional(self.intypes, incodes, adverb)
        if cond:
            lines = [tab + cond]
            sp = 2*tab
        else:
            lines = []
            sp = tab

        return func_name, incodes, outcodes, retcode, \
            intypes, outtypes, rettype, c, lines, sp

    def _generate_from_return_and_no_outargs(self):
        tab = " "*4
        specs, body = [], []
        for signum, sig in enumerate(self.signatures):
            func_name, incodes, outcodes, retcode, intypes, outtypes, \
                rettype, c, lines, sp = self._get_common(signum, sig)
            body.extend(lines)

            # Generate the call to the specialized function
            callvars = self._get_incallvars(intypes, c)
            call = "{}({})".format(func_name, ", ".join(callvars))
            if c and rettype == "double complex":
                call = double_complex_from_npy_cdouble(call)
            line = sp + "return {}".format(call)
            body.append(line)
            sig = "{}->{}".format(incodes, retcode)
            specs.append(sig)

        if len(specs) > 1:
            # Return nan for signatures without a specialization
            body.append(tab + "else:")
            outtype, outcodes = self.outtypes[0]
            last = len(outcodes) - 1
            if len(outcodes) == 1:
                line = "return {}".format(NAN_VALUE[outcodes])
                body.append(2*tab + line)
            else:
                for n, code in enumerate(outcodes):
                    if n == 0:
                        adverb = "if"
                    elif n == last:
                        adverb = "else"
                    else:
                        adverb = "elif"
                    cond = self._get_conditional(self.outtypes, code, adverb)
                    body.append(2*tab + cond)
                    line = "return {}".format(NAN_VALUE[code])
                    body.append(3*tab + line)

        # Generate the head of the function
        callvars, head = [], []
        for n, (intype, _) in enumerate(self.intypes):
            callvars.append("{} {}".format(intype, self.invars[n]))
        (outtype, _) = self.outtypes[0]
        dec = "cpdef {} {}({}) nogil".format(outtype, self.name, ", ".join(callvars))
        head.append(dec + ":")
        head.append(tab + '"""{}"""'.format(self.doc))

        src = "\n".join(head + body)
        return dec, src, specs

    def _generate_from_outargs_and_no_return(self):
        tab = " "*4
        all_tmpvars = set()
        specs, body = [], []
        for signum, sig in enumerate(self.signatures):
            func_name, incodes, outcodes, retcode, intypes, outtypes, \
                rettype, c, lines, sp = self._get_common(signum, sig)
            body.extend(lines)

            # Generate the call to the specialized function
            callvars = self._get_incallvars(intypes, c)
            outcallvars, tmpvars, casts = self._get_outcallvars(outtypes, c)
            callvars.extend(outcallvars)
            all_tmpvars.update(tmpvars)

            call = "{}({})".format(func_name, ", ".join(callvars))
            body.append(sp + call)
            body.extend(map(lambda x: sp + x, casts))
            if len(outcodes) == 1:
                sig = "{}->{}".format(incodes, outcodes)
                specs.append(sig)
            else:
                sig = "{}*{}->v".format(incodes, outcodes)
                specs.append(sig)

        if len(specs) > 1:
            lines = self._get_nan_decs()
            body.extend(lines)

        if len(self.outvars) == 1:
            line = "return {}[0]".format(self.outvars[0])
            body.append(tab + line)

        # Generate the head of the function
        callvars, head = [], []
        for invar, (intype, _) in zip(self.invars, self.intypes):
            callvars.append("{} {}".format(intype, invar))
        if len(self.outvars) > 1:
            for outvar, (outtype, _) in zip(self.outvars, self.outtypes):
                callvars.append("{} *{}".format(outtype, outvar))
        if len(self.outvars) == 1:
            outtype, _ = self.outtypes[0]
            dec = "cpdef {} {}({}) nogil".format(outtype, self.name, ", ".join(callvars))
        else:
            dec = "cdef void {}({}) nogil".format(self.name, ", ".join(callvars))
        head.append(dec + ":")
        head.append(tab + '"""{}"""'.format(self.doc))
        if len(self.outvars) == 1:
            outvar = self.outvars[0]
            outtype, _ = self.outtypes[0]
            line = "cdef {} {}".format(outtype, outvar)
            head.append(tab + line)
        head.extend(self._get_tmp_decs(all_tmpvars))

        src = "\n".join(head + body)
        return dec, src, specs

    def _generate_from_outargs_and_return(self):
        tab = " "*4
        all_tmpvars = set()
        specs, body = [], []
        for signum, sig in enumerate(self.signatures):
            func_name, incodes, outcodes, retcode, intypes, outtypes, \
                rettype, c, lines, sp = self._get_common(signum, sig)
            body.extend(lines)

            # Generate the call to the specialized function
            callvars = self._get_incallvars(intypes, c)
            outcallvars, tmpvars, casts = self._get_outcallvars(outtypes, c)
            callvars.extend(outcallvars)
            all_tmpvars.update(tmpvars)
            call = "{}({})".format(func_name, ", ".join(callvars))
            if c and rettype == "double complex":
                call = double_complex_from_npy_cdouble(call)
            call = "{}[0] = {}".format(self.outvars[0], call)
            body.append(sp + call)
            body.extend(map(lambda x: sp + x, casts))
            sig = "{}*{}->v".format(incodes, outcodes + retcode)
            specs.append(sig)

        if len(specs) > 1:
            lines = self._get_nan_decs()
            body.extend(lines)

        # Generate the head of the function
        callvars, head = [], []
        for invar, (intype, _) in zip(self.invars, self.intypes):
            callvars.append("{} {}".format(intype, invar))
        for outvar, (outtype, _) in zip(self.outvars, self.outtypes):
            callvars.append("{} *{}".format(outtype, outvar))
        dec = "cdef void {}({}) nogil".format(self.name, ", ".join(callvars))
        head.append(dec + ":")
        head.append(tab + '"""{}"""'.format(self.doc))
        head.extend(self._get_tmp_decs(all_tmpvars))

        src = "\n".join(head + body)
        return dec, src, specs

    def generate(self):
        _, _, outcodes, retcode, _ = self.signatures[0]
        retcode = re.sub(r'\*.*', '', retcode)
        if not retcode:
            retcode = 'v'

        if len(outcodes) == 0 and retcode != 'v':
            dec, src, specs = self._generate_from_return_and_no_outargs()
        elif len(outcodes) > 0 and retcode == 'v':
            dec, src, specs = self._generate_from_outargs_and_no_return()
        elif len(outcodes) > 0 and retcode != 'v':
            dec, src, specs = self._generate_from_outargs_and_return()
        else:
            raise ValueError("Invalid signature")

        if len(self.outvars) > 1:
            wrap = self._get_python_wrap()
        else:
            wrap = None

        return dec, src, specs, self.fused_types, wrap


def get_declaration(ufunc, c_name, c_proto, cy_proto, header, proto_h_filename):
    """
    Construct a Cython declaration of a function coming either from a
    pxd or a header file. Do sufficient tricks to enable compile-time
    type checking against the signature expected by the ufunc.
    """

    defs = []
    defs_h = []

    var_name = c_name.replace('[', '_').replace(']', '_').replace(' ', '_')

    if header.endswith('.pxd'):
        defs.append("from .%s cimport %s as %s" % (
            header[:-4], ufunc.cython_func_name(c_name, prefix=""),
            ufunc.cython_func_name(c_name)))

        # check function signature at compile time
        proto_name = '_proto_%s_t' % var_name
        defs.append("ctypedef %s" % (cy_proto.replace('(*)', proto_name)))
        defs.append("cdef %s *%s_var = &%s" % (
            proto_name, proto_name, ufunc.cython_func_name(c_name, specialized=True)))
    else:
        # redeclare the function, so that the assumed
        # signature is checked at compile time
        new_name = "%s \"%s\"" % (ufunc.cython_func_name(c_name), c_name)
        defs.append("cdef extern from \"%s\":" % proto_h_filename)
        defs.append("    cdef %s" % (cy_proto.replace('(*)', new_name)))
        defs_h.append("#include \"%s\"" % header)
        defs_h.append("%s;" % (c_proto.replace('(*)', c_name)))

    return defs, defs_h, var_name


def generate_ufuncs(fn_prefix, cxx_fn_prefix, ufuncs):
    filename = fn_prefix + ".pyx"
    proto_h_filename = fn_prefix + '_defs.h'

    cxx_proto_h_filename = cxx_fn_prefix + '_defs.h'
    cxx_pyx_filename = cxx_fn_prefix + ".pyx"
    cxx_pxd_filename = cxx_fn_prefix + ".pxd"

    toplevel = ""

    # for _ufuncs*
    defs = []
    defs_h = []
    all_loops = {}

    # for _ufuncs_cxx*
    cxx_defs = []
    cxx_pxd_defs = [
        "from . cimport sf_error",
        "cdef void _set_action(sf_error.sf_error_t, sf_error.sf_action_t) nogil"
    ]
    cxx_defs_h = []

    ufuncs.sort(key=lambda u: u.name)

    for ufunc in ufuncs:
        # generate function declaration and type checking snippets
        cfuncs = ufunc.get_prototypes()
        for c_name, c_proto, cy_proto, header in cfuncs:
            if header.endswith('++'):
                header = header[:-2]

                # for the CXX module
                item_defs, item_defs_h, var_name = get_declaration(ufunc, c_name, c_proto, cy_proto,
                                                                   header, cxx_proto_h_filename)
                cxx_defs.extend(item_defs)
                cxx_defs_h.extend(item_defs_h)

                cxx_defs.append("cdef void *_export_%s = <void*>%s" % (
                    var_name, ufunc.cython_func_name(c_name, specialized=True, override=False)))
                cxx_pxd_defs.append("cdef void *_export_%s" % (var_name,))

                # let cython grab the function pointer from the c++ shared library
                ufunc.function_name_overrides[c_name] = "scipy.special._ufuncs_cxx._export_" + var_name
            else:
                # usual case
                item_defs, item_defs_h, _ = get_declaration(ufunc, c_name, c_proto, cy_proto, header,
                                                            proto_h_filename)
                defs.extend(item_defs)
                defs_h.extend(item_defs_h)

        # ufunc creation code snippet
        t = ufunc.generate(all_loops)
        toplevel += t + "\n"

    # Produce output
    toplevel = "\n".join(sorted(all_loops.values()) + defs + [toplevel])

    with open(filename, 'w') as f:
        f.write(UFUNCS_EXTRA_CODE_COMMON)
        f.write(UFUNCS_EXTRA_CODE)
        f.write("\n")
        f.write(toplevel)
        f.write(UFUNCS_EXTRA_CODE_BOTTOM)

    defs_h = unique(defs_h)
    with open(proto_h_filename, 'w') as f:
        f.write("#ifndef UFUNCS_PROTO_H\n#define UFUNCS_PROTO_H 1\n")
        f.write("\n".join(defs_h))
        f.write("\n#endif\n")

    cxx_defs_h = unique(cxx_defs_h)
    with open(cxx_proto_h_filename, 'w') as f:
        f.write("#ifndef UFUNCS_PROTO_H\n#define UFUNCS_PROTO_H 1\n")
        f.write("\n".join(cxx_defs_h))
        f.write("\n#endif\n")

    with open(cxx_pyx_filename, 'w') as f:
        f.write(UFUNCS_EXTRA_CODE_COMMON)
        f.write("\n")
        f.write("\n".join(cxx_defs))
        f.write("\n# distutils: language = c++\n")

    with open(cxx_pxd_filename, 'w') as f:
        f.write("\n".join(cxx_pxd_defs))


def generate_fused_funcs(modname, ufunc_fn_prefix, fused_funcs):
    pxdfile = modname + ".pxd"
    pyxfile = modname + ".pyx"
    proto_h_filename = ufunc_fn_prefix + '_defs.h'

    sources = []
    declarations = []
    # Code for benchmarks
    bench_aux = []
    fused_types = set()
    # Parameters for the tests
    doc = []
    defs = []

    for func in fused_funcs:
        if func.name.startswith("_"):
            # Don't try to deal with functions that have extra layers
            # of wrappers.
            continue

        # Get the function declaration for the .pxd and the source
        # code for the .pyx
        dec, src, specs, func_fused_types, wrap = func.generate()
        declarations.append(dec)
        sources.append(src)
        if wrap:
            sources.append(wrap)
        fused_types.update(func_fused_types)

        # Declare the specializations
        cfuncs = func.get_prototypes(nptypes_for_h=True)
        for c_name, c_proto, cy_proto, header in cfuncs:
            if header.endswith('++'):
                # We grab the c++ functions from the c++ module
                continue
            item_defs, _, _ = get_declaration(func, c_name, c_proto,
                                              cy_proto, header,
                                              proto_h_filename)
            defs.extend(item_defs)

        # Add a line to the documentation
        doc.append(generate_doc(func.name, specs))

        # Generate code for benchmarks
        if func.name in CYTHON_SPECIAL_BENCHFUNCS:
            for codes in CYTHON_SPECIAL_BENCHFUNCS[func.name]:
                pybench, cybench = generate_bench(func.name, codes)
                bench_aux.extend([pybench, cybench])

    fused_types = list(fused_types)
    fused_types.sort()

    with open(pxdfile, 'w') as f:
        f.write(CYTHON_SPECIAL_PXD)
        f.write("\n")
        f.write("\n\n".join(fused_types))
        f.write("\n\n")
        f.write("\n".join(declarations))
    with open(pyxfile, 'w') as f:
        header = CYTHON_SPECIAL_PYX
        header = header.replace("FUNCLIST", "\n".join(doc))
        f.write(header)
        f.write("\n")
        f.write("\n".join(defs))
        f.write("\n\n")
        f.write("\n\n".join(sources))
        f.write("\n\n")
        f.write("\n\n".join(bench_aux))


def unique(lst):
    """
    Return a list without repeated entries (first occurrence is kept),
    preserving order.
    """
    seen = set()
    new_lst = []
    for item in lst:
        if item in seen:
            continue
        seen.add(item)
        new_lst.append(item)
    return new_lst


def all_newer(src_files, dst_files):
    from distutils.dep_util import newer
    return all(os.path.exists(dst) and newer(dst, src)
               for dst in dst_files for src in src_files)


def main():
    p = optparse.OptionParser(usage=(__doc__ or '').strip())
    options, args = p.parse_args()
    if len(args) != 0:
        p.error('invalid number of arguments')

    pwd = os.path.dirname(__file__)
    src_files = (os.path.abspath(__file__),
                 os.path.abspath(os.path.join(pwd, 'functions.json')),
                 os.path.abspath(os.path.join(pwd, 'add_newdocs.py')))
    dst_files = ('_ufuncs.pyx',
                 '_ufuncs_defs.h',
                 '_ufuncs_cxx.pyx',
                 '_ufuncs_cxx.pxd',
                 '_ufuncs_cxx_defs.h',
                 'cython_special.pyx',
                 'cython_special.pxd')

    os.chdir(BASE_DIR)

    if all_newer(src_files, dst_files):
        print("scipy/special/_generate_pyx.py: all files up-to-date")
        return

    ufuncs, fused_funcs = [], []
    with open('functions.json') as data:
        functions = json.load(data)
    for f, sig in functions.items():
        ufuncs.append(Ufunc(f, sig))
        fused_funcs.append(FusedFunc(f, sig))
    generate_ufuncs("_ufuncs", "_ufuncs_cxx", ufuncs)
    generate_fused_funcs("cython_special", "_ufuncs", fused_funcs)


if __name__ == "__main__":
    main()
