ufunc_type_resolution.c

/*
 * NOTE: The type resolution defined in this file is considered legacy.
 *
 * The new mechanism separates type resolution and promotion into two
 * distinct steps, as per NEP 43.
 * Further, the functions in this file rely on the operands rather than
 * only the DTypes/descriptors.  They are still called and at this point
 * vital (NumPy ~1.21), but should hopefully become largely irrelevant very
 * quickly.
 *
 * At that point, this file should be deletable in its entirety.
 *
 *
 * This file implements type resolution for NumPy element-wise ufuncs.
 * This mechanism is still backwards-compatible with the pre-existing
 * legacy mechanism, so performs much slower than is necessary.
 *
 * Written by Mark Wiebe (mwwiebe@gmail.com)
 * Copyright (c) 2011 by Enthought, Inc.
 *
 * See LICENSE.txt for the license.
 */
#define NPY_NO_DEPRECATED_API NPY_API_VERSION
#define _MULTIARRAYMODULE
#define _UMATHMODULE

#define PY_SSIZE_T_CLEAN
#include <Python.h>

// printif debug tracing
#ifndef NPY_UF_DBG_TRACING
    #define NPY_UF_DBG_TRACING 0
#endif

#include "npy_config.h"
#include "npy_pycompat.h"
#include "npy_import.h"

#include "numpy/ufuncobject.h"
#include "ufunc_type_resolution.h"
#include "ufunc_object.h"
#include "common.h"
#include "convert_datatype.h"
#include "dtypemeta.h"

#include "mem_overlap.h"
#if defined(HAVE_CBLAS)
#include "cblasfuncs.h"
#endif

#include <stdbool.h>
#include <arrayobject.h>

static PyObject *
npy_casting_to_py_object(NPY_CASTING casting)
{
    switch (casting) {
        case NPY_NO_CASTING:
            return PyUnicode_FromString("no");
        case NPY_EQUIV_CASTING:
            return PyUnicode_FromString("equiv");
        case NPY_SAFE_CASTING:
            return PyUnicode_FromString("safe");
        case NPY_SAME_KIND_CASTING:
            return PyUnicode_FromString("same_kind");
        case NPY_UNSAFE_CASTING:
            return PyUnicode_FromString("unsafe");
        default:
            return PyLong_FromLong(casting);
    }
}


/**
 * Always returns -1 to indicate the exception was raised, for convenience
 */
static int
raise_binary_type_reso_error(PyUFuncObject *ufunc, PyArrayObject **operands) {
    static PyObject *exc_type = NULL;
    PyObject *exc_value;

    npy_cache_import(
        "numpy._core._exceptions", "_UFuncBinaryResolutionError",
        &exc_type);
    if (exc_type == NULL) {
        return -1;
    }

    /* produce an error object */
    exc_value = Py_BuildValue(
        "O(OO)", ufunc,
        (PyObject *)PyArray_DESCR(operands[0]),
        (PyObject *)PyArray_DESCR(operands[1])
    );
    if (exc_value == NULL){
        return -1;
    }
    PyErr_SetObject(exc_type, exc_value);
    Py_DECREF(exc_value);

    return -1;
}

/** Helper function to raise UFuncNoLoopError
 * Always returns -1 to indicate the exception was raised, for convenience
 */
NPY_NO_EXPORT int
raise_no_loop_found_error(
        PyUFuncObject *ufunc, PyObject **dtypes, int ambiguous_promoter)
{
    static PyObject *exc_type = NULL;

    npy_cache_import(
        "numpy._core._exceptions", "_UFuncNoLoopError",
        &exc_type);
    if (exc_type == NULL) {
        return -1;
    }

    PyObject *dtypes_tup = PyArray_TupleFromItems(ufunc->nargs, dtypes, 1);
    if (dtypes_tup == NULL) {
        return -1;
    }
    /* produce an error object */
    PyObject *exc_value = PyTuple_Pack(3, ufunc, dtypes_tup,
                                       ambiguous_promoter ? Py_True : Py_False);
    Py_DECREF(dtypes_tup);
    if (exc_value == NULL) {
        return -1;
    }
    PyErr_SetObject(exc_type, exc_value);
    Py_DECREF(exc_value);

    return -1;
}


static int
raise_casting_error(
        PyObject *exc_type,
        PyUFuncObject *ufunc,
        NPY_CASTING casting,
        PyArray_Descr *from,
        PyArray_Descr *to,
        npy_intp i)
{
    PyObject *exc_value;
    PyObject *casting_value;

    casting_value = npy_casting_to_py_object(casting);
    if (casting_value == NULL) {
        return -1;
    }

    exc_value = Py_BuildValue(
        "ONOOi",
        ufunc,
        casting_value,
        (PyObject *)from,
        (PyObject *)to,
        i
    );
    if (exc_value == NULL){
        return -1;
    }
    PyErr_SetObject(exc_type, exc_value);
    Py_DECREF(exc_value);

    return -1;
}

/** Helper function to raise UFuncInputCastingError
 * Always returns -1 to indicate the exception was raised, for convenience
 */
static int
raise_input_casting_error(
        PyUFuncObject *ufunc,
        NPY_CASTING casting,
        PyArray_Descr *from,
        PyArray_Descr *to,
        npy_intp i)
{
    static PyObject *exc_type = NULL;
    npy_cache_import(
        "numpy._core._exceptions", "_UFuncInputCastingError",
        &exc_type);
    if (exc_type == NULL) {
        return -1;
    }

    return raise_casting_error(exc_type, ufunc, casting, from, to, i);
}


/** Helper function to raise UFuncOutputCastingError
 * Always returns -1 to indicate the exception was raised, for convenience
 */
static int
raise_output_casting_error(
        PyUFuncObject *ufunc,
        NPY_CASTING casting,
        PyArray_Descr *from,
        PyArray_Descr *to,
        npy_intp i)
{
    static PyObject *exc_type = NULL;
    npy_cache_import(
        "numpy._core._exceptions", "_UFuncOutputCastingError",
        &exc_type);
    if (exc_type == NULL) {
        return -1;
    }

    return raise_casting_error(exc_type, ufunc, casting, from, to, i);
}


/*UFUNC_API
 *
 * Validates that the input operands can be cast to
 * the input types, and the output types can be cast to
 * the output operands where provided.
 *
 * Returns 0 on success, -1 (with exception raised) on validation failure.
 */
NPY_NO_EXPORT int
PyUFunc_ValidateCasting(PyUFuncObject *ufunc,
                            NPY_CASTING casting,
                            PyArrayObject **operands,
                            PyArray_Descr **dtypes)
{
    int i, nin = ufunc->nin, nop = nin + ufunc->nout;

    for (i = 0; i < nop; ++i) {
        if (i < nin) {
            if (!PyArray_CanCastArrayTo(operands[i], dtypes[i], casting)) {
                return raise_input_casting_error(
                    ufunc, casting, PyArray_DESCR(operands[i]), dtypes[i], i);
            }
        } else if (operands[i] != NULL) {
            if (!PyArray_CanCastTypeTo(dtypes[i],
                                    PyArray_DESCR(operands[i]), casting)) {
                return raise_output_casting_error(
                    ufunc, casting, dtypes[i], PyArray_DESCR(operands[i]), i);
            }
        }
    }

    return 0;
}


/*
 * Same as `PyUFunc_ValidateCasting` but only checks output casting.
 */
NPY_NO_EXPORT int
PyUFunc_ValidateOutCasting(PyUFuncObject *ufunc,
        NPY_CASTING casting, PyArrayObject **operands, PyArray_Descr **dtypes)
{
    int i, nin = ufunc->nin, nop = nin + ufunc->nout;

    for (i = nin; i < nop; ++i) {
        if (operands[i] == NULL) {
            continue;
        }
        if (!PyArray_CanCastTypeTo(dtypes[i],
                PyArray_DESCR(operands[i]), casting)) {
            return raise_output_casting_error(
                    ufunc, casting, dtypes[i], PyArray_DESCR(operands[i]), i);
        }
    }
    return 0;
}

/*UFUNC_API
 *
 * This function applies the default type resolution rules
 * for the provided ufunc.
 *
 * Returns 0 on success, -1 on error.
 */
NPY_NO_EXPORT int
PyUFunc_DefaultTypeResolver(PyUFuncObject *ufunc,
                                NPY_CASTING casting,
                                PyArrayObject **operands,
                                PyObject *type_tup,
                                PyArray_Descr **out_dtypes)
{
    int i, nop = ufunc->nin + ufunc->nout;
    int retval = 0, any_object = 0;
    NPY_CASTING input_casting;

    for (i = 0; i < nop; ++i) {
        if (operands[i] != NULL &&
                PyTypeNum_ISOBJECT(PyArray_DESCR(operands[i])->type_num)) {
            any_object = 1;
            break;
        }
    }

    /*
     * Decide the casting rules for inputs and outputs.  We want
     * NPY_SAFE_CASTING or stricter, so that the loop selection code
     * doesn't choose an integer loop for float inputs, or a float32
     * loop for float64 inputs.
     */
    input_casting = (casting > NPY_SAFE_CASTING) ? NPY_SAFE_CASTING : casting;

    if (type_tup == NULL) {
        /* Find the best ufunc inner loop, and fill in the dtypes */
        retval = linear_search_type_resolver(ufunc, operands,
                        input_casting, casting, any_object,
                        out_dtypes);
    } else {
        /* Find the specified ufunc inner loop, and fill in the dtypes */
        retval = type_tuple_type_resolver(ufunc, type_tup,
                        operands, input_casting, casting, any_object, out_dtypes);
    }

    return retval;
}

/*
 * This function applies special type resolution rules for the case
 * where all the functions have the pattern XX->bool, using
 * PyArray_ResultType instead of a linear search to get the best
 * loop.
 *
 * Returns 0 on success, -1 on error.
 */
NPY_NO_EXPORT int
PyUFunc_SimpleBinaryComparisonTypeResolver(PyUFuncObject *ufunc,
                                NPY_CASTING casting,
                                PyArrayObject **operands,
                                PyObject *type_tup,
                                PyArray_Descr **out_dtypes)
{
    int i, type_num1, type_num2;
    const char *ufunc_name = ufunc_get_name_cstr(ufunc);

    if (ufunc->nin != 2 || ufunc->nout != 1) {
        PyErr_Format(PyExc_RuntimeError, "ufunc %s is configured "
                "to use binary comparison type resolution but has "
                "the wrong number of inputs or outputs",
                ufunc_name);
        return -1;
    }

    /*
     * Use the default type resolution if there's a custom data type
     * or object arrays.
     */
    type_num1 = PyArray_DESCR(operands[0])->type_num;
    type_num2 = PyArray_DESCR(operands[1])->type_num;
    if (type_num1 >= NPY_NTYPES_LEGACY || type_num2 >= NPY_NTYPES_LEGACY ||
            type_num1 == NPY_OBJECT || type_num2 == NPY_OBJECT) {
        return PyUFunc_DefaultTypeResolver(ufunc, casting, operands,
                type_tup, out_dtypes);
    }

    if (type_tup == NULL) {
        if (PyArray_ISDATETIME(operands[0])
                && PyArray_ISDATETIME(operands[1])
                && type_num1 != type_num2) {
            /*
             * Reject mixed datetime and timedelta explicitly, this was always
             * implicitly rejected because casting fails (except with
             * `casting="unsafe"` admittedly).
             * This is required to ensure that `==` and `!=` can correctly
             * detect that they should return a result array of False/True.
             */
            return raise_binary_type_reso_error(ufunc, operands);
        }
        /*
         * This check is required to avoid a potential FutureWarning that
         * ResultType would give for number->string promotions.
         * (We never supported flexible dtypes here.)
         */
        else if (!PyArray_ISFLEXIBLE(operands[0]) &&
                !PyArray_ISFLEXIBLE(operands[1])) {
            out_dtypes[0] = PyArray_ResultType(2, operands, 0, NULL);
            if (out_dtypes[0] == NULL) {
                return -1;
            }
            if (PyArray_ISINTEGER(operands[0])
                    && PyArray_ISINTEGER(operands[1])
                    && !PyDataType_ISINTEGER(out_dtypes[0])) {
                /*
                 * NumPy promotion allows uint+int to go to float, avoid it
                 * (input must have been a mix of signed and unsigned)
                 */
                if (PyArray_ISSIGNED(operands[0])) {
                    Py_SETREF(out_dtypes[0], PyArray_DescrFromType(NPY_LONGLONG));
                    out_dtypes[1] = PyArray_DescrFromType(NPY_ULONGLONG);
                    Py_INCREF(out_dtypes[1]);
                }
                else {
                    Py_SETREF(out_dtypes[0], PyArray_DescrFromType(NPY_ULONGLONG));
                    out_dtypes[1] = PyArray_DescrFromType(NPY_LONGLONG);
                    Py_INCREF(out_dtypes[1]);
                }
            }
            else {
                out_dtypes[1] = out_dtypes[0];
                Py_INCREF(out_dtypes[1]);
            }
        }
        else {
            /* Not doing anything will lead to a loop no found error. */
            out_dtypes[0] = PyArray_DESCR(operands[0]);
            Py_INCREF(out_dtypes[0]);
            out_dtypes[1] = PyArray_DESCR(operands[1]);
            Py_INCREF(out_dtypes[1]);
        }
    }
    else {
        /* Usually a failure, but let the default version handle it */
        return PyUFunc_DefaultTypeResolver(ufunc, casting,
                operands, type_tup, out_dtypes);
    }

    /* Output type is always boolean (cannot fail for builtins) */
    out_dtypes[2] = PyArray_DescrFromType(NPY_BOOL);

    /* Check against the casting rules */
    if (PyUFunc_ValidateCasting(ufunc, casting, operands, out_dtypes) < 0) {
        for (i = 0; i < 3; ++i) {
            Py_DECREF(out_dtypes[i]);
            out_dtypes[i] = NULL;
        }
        return -1;
    }

    return 0;
}

NPY_NO_EXPORT int
PyUFunc_NegativeTypeResolver(PyUFuncObject *ufunc,
                             NPY_CASTING casting,
                             PyArrayObject **operands,
                             PyObject *type_tup,
                             PyArray_Descr **out_dtypes)
{
    int ret;
    ret = PyUFunc_SimpleUniformOperationTypeResolver(ufunc, casting, operands,
                                                   type_tup, out_dtypes);
    if (ret < 0) {
        return ret;
    }

    /* The type resolver would have upcast already */
    if (out_dtypes[0]->type_num == NPY_BOOL) {
        PyErr_Format(PyExc_TypeError,
            "The numpy boolean negative, the `-` operator, is not supported, "
            "use the `~` operator or the logical_not function instead.");
        return -1;
    }

    return ret;
}


/*
 * The ones_like function shouldn't really be a ufunc, but while it
 * still is, this provides type resolution that always forces UNSAFE
 * casting.
 */
NPY_NO_EXPORT int
PyUFunc_OnesLikeTypeResolver(PyUFuncObject *ufunc,
                                NPY_CASTING NPY_UNUSED(casting),
                                PyArrayObject **operands,
                                PyObject *type_tup,
                                PyArray_Descr **out_dtypes)
{
    return PyUFunc_SimpleUniformOperationTypeResolver(ufunc,
                        NPY_UNSAFE_CASTING,
                        operands, type_tup, out_dtypes);
}

/*
 * This function applies special type resolution rules for the case
 * where all of the types in the signature are the same, eg XX->X or XX->XX.
 * It uses PyArray_ResultType instead of a linear search to get the best
 * loop.
 *
 * Note that a simpler linear search through the functions loop
 * is still done, but switching to a simple array lookup for
 * built-in types would be better at some point.
 *
 * Returns 0 on success, -1 on error.
 */
NPY_NO_EXPORT int
PyUFunc_SimpleUniformOperationTypeResolver(
        PyUFuncObject *ufunc,
        NPY_CASTING casting,
        PyArrayObject **operands,
        PyObject *type_tup,
        PyArray_Descr **out_dtypes)
{
    const char *ufunc_name = ufunc_get_name_cstr(ufunc);

    if (ufunc->nin < 1) {
        PyErr_Format(PyExc_RuntimeError, "ufunc %s is configured "
                "to use uniform operation type resolution but has "
                "no inputs",
                ufunc_name);
        return -1;
    }
    int nop = ufunc->nin + ufunc->nout;

    /*
     * There's a custom data type or an object array
     */
    bool has_custom_or_object = false;
    for (int iop = 0; iop < ufunc->nin; iop++) {
        int type_num = PyArray_DESCR(operands[iop])->type_num;
        if (type_num >= NPY_NTYPES_LEGACY || type_num == NPY_OBJECT) {
            has_custom_or_object = true;
            break;
        }
    }

    if (has_custom_or_object) {
        return PyUFunc_DefaultTypeResolver(ufunc, casting, operands,
                type_tup, out_dtypes);
    }

    if (type_tup == NULL) {
        /* PyArray_ResultType forgets to force a byte order when n == 1 */
        if (ufunc->nin == 1){
            out_dtypes[0] = NPY_DT_CALL_ensure_canonical(
                    PyArray_DESCR(operands[0]));
        }
        else {
            int iop;
            npy_bool has_flexible = 0;
            npy_bool has_object = 0;
            for (iop = 0; iop < ufunc->nin; iop++) {
                if (PyArray_ISOBJECT(operands[iop])) {
                    has_object = 1;
                }
                if (PyArray_ISFLEXIBLE(operands[iop])) {
                    has_flexible = 1;
                }
            }
            if (NPY_UNLIKELY(has_flexible && !has_object)) {
                /*
                 * DEPRECATED NumPy 1.20, 2020-12.
                 * This check is required to avoid the FutureWarning that
                 * ResultType will give for number->string promotions.
                 * (We never supported flexible dtypes here.)
                 */
                for (iop = 0; iop < ufunc->nin; iop++) {
                    out_dtypes[iop] = PyArray_DESCR(operands[iop]);
                    Py_INCREF(out_dtypes[iop]);
                }
                raise_no_loop_found_error(ufunc, (PyObject **)out_dtypes, 0);
                for (iop = 0; iop < ufunc->nin; iop++) {
                    Py_DECREF(out_dtypes[iop]);
                    out_dtypes[iop] = NULL;
                }
                return -1;
            }
            out_dtypes[0] = PyArray_ResultType(ufunc->nin, operands, 0, NULL);
        }
        if (out_dtypes[0] == NULL) {
            return -1;
        }
    }
    else {
        /*
         * This is a fast-path, since all descriptors will be identical, mainly
         * when only a single descriptor was passed (which would set the out
         * one in the tuple), there is no need to check all loops.
         * Note that this also allows (None, None, float64) to resolve to
         * (float64, float64, float64), even when the inputs do not match,
         * i.e. fixing the output part of the signature can fix all of them.
         * This is necessary to support `nextafter(1., inf, dtype=float32)`,
         * where it is "clear" we want to cast 1. and inf to float32.
         */
        PyArray_Descr *descr = NULL;
        if (PyTuple_CheckExact(type_tup) &&
                PyTuple_GET_SIZE(type_tup) == nop) {
            for (int i = 0; i < nop; i++) {
                PyObject *item = PyTuple_GET_ITEM(type_tup, i);
                if (item == Py_None) {
                    if (i < ufunc->nin) {
                        continue;
                    }
                    /* All outputs must be set (this could be relaxed) */
                    descr = NULL;
                    break;
                }
                if (!PyArray_DescrCheck(item)) {
                    /* Defer to default resolver (will raise an error there) */
                    descr = NULL;
                    break;
                }
                if (descr != NULL && descr != (PyArray_Descr *)item) {
                    /* Descriptor mismatch: try with default (probable error) */
                    descr = NULL;
                    break;
                }
                descr = (PyArray_Descr *)item;
            }
        }
        if (descr == NULL) {
            /* in all bad/unlikely cases, use the default type resolver: */
            return PyUFunc_DefaultTypeResolver(ufunc, casting,
                    operands, type_tup, out_dtypes);
        }
        else if (descr->type_num == PyArray_DESCR(operands[0])->type_num) {
            /* Prefer the input descriptor if it matches (preserve metadata) */
            descr = PyArray_DESCR(operands[0]);
        }
        out_dtypes[0] = NPY_DT_CALL_ensure_canonical(descr);
    }

    /* All types are the same - copy the first one to the rest */
    for (int iop = 1; iop < nop; iop++) {
        out_dtypes[iop] = out_dtypes[0];
        Py_INCREF(out_dtypes[iop]);
    }

    /* Check against the casting rules */
    if (PyUFunc_ValidateCasting(ufunc, casting, operands, out_dtypes) < 0) {
        for (int iop = 0; iop < nop; iop++) {
            Py_DECREF(out_dtypes[iop]);
            out_dtypes[iop] = NULL;
        }
        return -1;
    }

    return 0;
}

/*
 * This function applies special type resolution rules for the absolute
 * ufunc. This ufunc converts complex -> float, so isn't covered
 * by the simple unary type resolution.
 *
 * Returns 0 on success, -1 on error.
 */
NPY_NO_EXPORT int
PyUFunc_AbsoluteTypeResolver(PyUFuncObject *ufunc,
                                NPY_CASTING casting,
                                PyArrayObject **operands,
                                PyObject *type_tup,
                                PyArray_Descr **out_dtypes)
{
    /* Use the default for complex types, to find the loop producing float */
    if (PyTypeNum_ISCOMPLEX(PyArray_DESCR(operands[0])->type_num)) {
        return PyUFunc_DefaultTypeResolver(ufunc, casting, operands,
                    type_tup, out_dtypes);
    }
    else {
        return PyUFunc_SimpleUniformOperationTypeResolver(ufunc, casting,
                    operands, type_tup, out_dtypes);
    }
}

/*
 * This function applies special type resolution rules for the isnat
 * ufunc. This ufunc converts datetime/timedelta -> bool, and is not covered
 * by the simple unary type resolution.
 *
 * Returns 0 on success, -1 on error.
 */
NPY_NO_EXPORT int
PyUFunc_IsNaTTypeResolver(PyUFuncObject *ufunc,
                          NPY_CASTING casting,
                          PyArrayObject **operands,
                          PyObject *type_tup,
                          PyArray_Descr **out_dtypes)
{
    if (!PyTypeNum_ISDATETIME(PyArray_DESCR(operands[0])->type_num)) {
        PyErr_SetString(PyExc_TypeError,
                "ufunc 'isnat' is only defined for np.datetime64 and np.timedelta64.");
        return -1;
    }

    out_dtypes[0] = NPY_DT_CALL_ensure_canonical(PyArray_DESCR(operands[0]));
    out_dtypes[1] = PyArray_DescrFromType(NPY_BOOL);

    return 0;
}


NPY_NO_EXPORT int
PyUFunc_IsFiniteTypeResolver(PyUFuncObject *ufunc,
                          NPY_CASTING casting,
                          PyArrayObject **operands,
                          PyObject *type_tup,
                          PyArray_Descr **out_dtypes)
{
    if (!PyTypeNum_ISDATETIME(PyArray_DESCR(operands[0])->type_num)) {
        return PyUFunc_DefaultTypeResolver(ufunc, casting, operands,
                                    type_tup, out_dtypes);
    }

    out_dtypes[0] = NPY_DT_CALL_ensure_canonical(PyArray_DESCR(operands[0]));
    out_dtypes[1] = PyArray_DescrFromType(NPY_BOOL);

    return 0;
}


/*
 * Creates a new NPY_TIMEDELTA dtype, copying the datetime metadata
 * from the given dtype.
 *
 * NOTE: This function is copied from datetime.c in multiarray,
 *       because umath and multiarray are not linked together.
 */
static PyArray_Descr *
timedelta_dtype_with_copied_meta(PyArray_Descr *dtype)
{
    PyArray_Descr *ret;
    PyArray_DatetimeMetaData *dst, *src;
    PyArray_DatetimeDTypeMetaData *dst_dtmd, *src_dtmd;

    ret = PyArray_DescrNewFromType(NPY_TIMEDELTA);
    if (ret == NULL) {
        return NULL;
    }

    src_dtmd = (PyArray_DatetimeDTypeMetaData *)((_PyArray_LegacyDescr *)dtype)->c_metadata;
    dst_dtmd = (PyArray_DatetimeDTypeMetaData *)((_PyArray_LegacyDescr *)ret)->c_metadata;
    src = &(src_dtmd->meta);
    dst = &(dst_dtmd->meta);

    *dst = *src;

    return ret;
}

/*
 * This function applies the type resolution rules for addition.
 * In particular, there's special cases for string and unicodes, as
 * well as a number of special cases with datetime:
 *    m8[<A>] + m8[<B>] => m8[gcd(<A>,<B>)] + m8[gcd(<A>,<B>)]
 *    m8[<A>] + int     => m8[<A>] + m8[<A>]
 *    int     + m8[<A>] => m8[<A>] + m8[<A>]
 *    M8[<A>] + int     => M8[<A>] + m8[<A>]
 *    int     + M8[<A>] => m8[<A>] + M8[<A>]
 *    M8[<A>] + m8[<B>] => M8[gcd(<A>,<B>)] + m8[gcd(<A>,<B>)]
 *    m8[<A>] + M8[<B>] => m8[gcd(<A>,<B>)] + M8[gcd(<A>,<B>)]
 * TODO: Non-linear time unit cases require highly special-cased loops
 *    M8[<A>] + m8[Y|M|B]
 *    m8[Y|M|B] + M8[<A>]
 */
NPY_NO_EXPORT int
PyUFunc_AdditionTypeResolver(PyUFuncObject *ufunc,
                                NPY_CASTING casting,
                                PyArrayObject **operands,
                                PyObject *type_tup,
                                PyArray_Descr **out_dtypes)
{
    int type_num1, type_num2;
    int i;

    type_num1 = PyArray_DESCR(operands[0])->type_num;
    type_num2 = PyArray_DESCR(operands[1])->type_num;

    /* Use the default when datetime, timedelta, string and unicode are not involved */
    if (!PyTypeNum_ISDATETIME(type_num1) && !PyTypeNum_ISDATETIME(type_num2)
        && !(PyTypeNum_ISSTRING(type_num1) && PyTypeNum_ISSTRING(type_num2))) {
        return PyUFunc_SimpleUniformOperationTypeResolver(ufunc, casting,
                    operands, type_tup, out_dtypes);
    }

    if ((type_num1 == NPY_STRING && type_num2 == NPY_STRING)
            || (type_num1 == NPY_UNICODE && type_num2 == NPY_UNICODE)) {
        // This is wrong, but only the DType matters here (String or Unicode) and
        // the loop has the correct implementation itself.
        out_dtypes[0] = PyArray_DescrFromType(type_num1);
        out_dtypes[1] = out_dtypes[0];
        Py_INCREF(out_dtypes[1]);
        out_dtypes[2] = out_dtypes[0];
        Py_INCREF(out_dtypes[2]);
    } else if (type_num1 == NPY_TIMEDELTA) {
        /* m8[<A>] + m8[<B>] => m8[gcd(<A>,<B>)] + m8[gcd(<A>,<B>)] */
        if (type_num2 == NPY_TIMEDELTA) {
            out_dtypes[0] = PyArray_PromoteTypes(PyArray_DESCR(operands[0]),
                                                PyArray_DESCR(operands[1]));
            if (out_dtypes[0] == NULL) {
                return -1;
            }
            out_dtypes[1] = out_dtypes[0];
            Py_INCREF(out_dtypes[1]);
            out_dtypes[2] = out_dtypes[0];
            Py_INCREF(out_dtypes[2]);
        }
        /* m8[<A>] + M8[<B>] => m8[gcd(<A>,<B>)] + M8[gcd(<A>,<B>)] */
        else if (type_num2 == NPY_DATETIME) {
            out_dtypes[1] = PyArray_PromoteTypes(PyArray_DESCR(operands[0]),
                                                PyArray_DESCR(operands[1]));
            if (out_dtypes[1] == NULL) {
                return -1;
            }
            /* Make a new NPY_TIMEDELTA, and copy the datetime's metadata */
            out_dtypes[0] = timedelta_dtype_with_copied_meta(out_dtypes[1]);
            if (out_dtypes[0] == NULL) {
                Py_DECREF(out_dtypes[1]);
                out_dtypes[1] = NULL;
                return -1;
            }
            out_dtypes[2] = out_dtypes[1];
            Py_INCREF(out_dtypes[2]);
        }
        /* m8[<A>] + int => m8[<A>] + m8[<A>] */
        else if (PyTypeNum_ISINTEGER(type_num2) ||
                                    PyTypeNum_ISBOOL(type_num2)) {
            out_dtypes[0] = NPY_DT_CALL_ensure_canonical(
                    PyArray_DESCR(operands[0]));
            if (out_dtypes[0] == NULL) {
                return -1;
            }
            out_dtypes[1] = out_dtypes[0];
            Py_INCREF(out_dtypes[1]);
            out_dtypes[2] = out_dtypes[0];
            Py_INCREF(out_dtypes[2]);

            type_num2 = NPY_TIMEDELTA;
        }
        else {
            return raise_binary_type_reso_error(ufunc, operands);
        }
    }
    else if (type_num1 == NPY_DATETIME) {
        /* M8[<A>] + m8[<B>] => M8[gcd(<A>,<B>)] + m8[gcd(<A>,<B>)] */
        if (type_num2 == NPY_TIMEDELTA) {
            out_dtypes[0] = PyArray_PromoteTypes(PyArray_DESCR(operands[0]),
                                                PyArray_DESCR(operands[1]));
            if (out_dtypes[0] == NULL) {
                return -1;
            }
            /* Make a new NPY_TIMEDELTA, and copy the datetime's metadata */
            out_dtypes[1] = timedelta_dtype_with_copied_meta(out_dtypes[0]);
            if (out_dtypes[1] == NULL) {
                Py_DECREF(out_dtypes[0]);
                out_dtypes[0] = NULL;
                return -1;
            }
            out_dtypes[2] = out_dtypes[0];
            Py_INCREF(out_dtypes[2]);
        }
        /* M8[<A>] + int => M8[<A>] + m8[<A>] */
        else if (PyTypeNum_ISINTEGER(type_num2) ||
                    PyTypeNum_ISBOOL(type_num2)) {
            out_dtypes[0] = NPY_DT_CALL_ensure_canonical(
                    PyArray_DESCR(operands[0]));
            if (out_dtypes[0] == NULL) {
                return -1;
            }
            /* Make a new NPY_TIMEDELTA, and copy type1's metadata */
            out_dtypes[1] = timedelta_dtype_with_copied_meta(
                                            PyArray_DESCR(operands[0]));
            if (out_dtypes[1] == NULL) {
                Py_DECREF(out_dtypes[0]);
                out_dtypes[0] = NULL;
                return -1;
            }
            out_dtypes[2] = out_dtypes[0];
            Py_INCREF(out_dtypes[2]);

            type_num2 = NPY_TIMEDELTA;
        }
        else {
            return raise_binary_type_reso_error(ufunc, operands);
        }
    }
    else if (PyTypeNum_ISINTEGER(type_num1) || PyTypeNum_ISBOOL(type_num1)) {
        /* int + m8[<A>] => m8[<A>] + m8[<A>] */
        if (type_num2 == NPY_TIMEDELTA) {
            out_dtypes[0] = NPY_DT_CALL_ensure_canonical(
                    PyArray_DESCR(operands[1]));
            if (out_dtypes[0] == NULL) {
                return -1;
            }
            out_dtypes[1] = out_dtypes[0];
            Py_INCREF(out_dtypes[1]);
            out_dtypes[2] = out_dtypes[0];
            Py_INCREF(out_dtypes[2]);

            type_num1 = NPY_TIMEDELTA;
        }
        else if (type_num2 == NPY_DATETIME) {
            /* Make a new NPY_TIMEDELTA, and copy type2's metadata */
            out_dtypes[0] = timedelta_dtype_with_copied_meta(
                                            PyArray_DESCR(operands[1]));
            if (out_dtypes[0] == NULL) {
                return -1;
            }
            out_dtypes[1] = NPY_DT_CALL_ensure_canonical(
                    PyArray_DESCR(operands[1]));
            if (out_dtypes[1] == NULL) {
                Py_DECREF(out_dtypes[0]);
                out_dtypes[0] = NULL;
                return -1;
            }
            out_dtypes[2] = out_dtypes[1];
            Py_INCREF(out_dtypes[2]);

            type_num1 = NPY_TIMEDELTA;
        }
        else {
            return raise_binary_type_reso_error(ufunc, operands);
        }
    }
    else {
        return raise_binary_type_reso_error(ufunc, operands);
    }

    /* Check against the casting rules */
    if (PyUFunc_ValidateCasting(ufunc, casting, operands, out_dtypes) < 0) {
        for (i = 0; i < 3; ++i) {
            Py_DECREF(out_dtypes[i]);
            out_dtypes[i] = NULL;
        }
        return -1;
    }

    return 0;
}

/*
 * This function applies the type resolution rules for subtraction.
 * In particular, there are a number of special cases with datetime:
 *    m8[<A>] - m8[<B>] => m8[gcd(<A>,<B>)] - m8[gcd(<A>,<B>)]
 *    m8[<A>] - int     => m8[<A>] - m8[<A>]
 *    int     - m8[<A>] => m8[<A>] - m8[<A>]
 *    M8[<A>] - int     => M8[<A>] - m8[<A>]
 *    M8[<A>] - m8[<B>] => M8[gcd(<A>,<B>)] - m8[gcd(<A>,<B>)]
 * TODO: Non-linear time unit cases require highly special-cased loops
 *    M8[<A>] - m8[Y|M|B]
 */
NPY_NO_EXPORT int
PyUFunc_SubtractionTypeResolver(PyUFuncObject *ufunc,
                                NPY_CASTING casting,
                                PyArrayObject **operands,
                                PyObject *type_tup,
                                PyArray_Descr **out_dtypes)
{
    int type_num1, type_num2;
    int i;

    type_num1 = PyArray_DESCR(operands[0])->type_num;
    type_num2 = PyArray_DESCR(operands[1])->type_num;

    /* Use the default when datetime and timedelta are not involved */
    if (!PyTypeNum_ISDATETIME(type_num1) && !PyTypeNum_ISDATETIME(type_num2)) {
        int ret;
        ret = PyUFunc_SimpleUniformOperationTypeResolver(ufunc, casting,
                                                operands, type_tup, out_dtypes);
        if (ret < 0) {
            return ret;
        }

        /* The type resolver would have upcast already */
        if (out_dtypes[0]->type_num == NPY_BOOL) {
            PyErr_Format(PyExc_TypeError,
                "numpy boolean subtract, the `-` operator, is not supported, "
                "use the bitwise_xor, the `^` operator, or the logical_xor "
                "function instead.");
            return -1;
        }
        return ret;
    }

    if (type_num1 == NPY_TIMEDELTA) {
        /* m8[<A>] - m8[<B>] => m8[gcd(<A>,<B>)] - m8[gcd(<A>,<B>)] */
        if (type_num2 == NPY_TIMEDELTA) {
            out_dtypes[0] = PyArray_PromoteTypes(PyArray_DESCR(operands[0]),
                                                PyArray_DESCR(operands[1]));
            if (out_dtypes[0] == NULL) {
                return -1;
            }
            out_dtypes[1] = out_dtypes[0];
            Py_INCREF(out_dtypes[1]);
            out_dtypes[2] = out_dtypes[0];
            Py_INCREF(out_dtypes[2]);
        }
        /* m8[<A>] - int => m8[<A>] - m8[<A>] */
        else if (PyTypeNum_ISINTEGER(type_num2) ||
                                        PyTypeNum_ISBOOL(type_num2)) {
            out_dtypes[0] = NPY_DT_CALL_ensure_canonical(
                    PyArray_DESCR(operands[0]));
            if (out_dtypes[0] == NULL) {
                return -1;
            }
            out_dtypes[1] = out_dtypes[0];
            Py_INCREF(out_dtypes[1]);
            out_dtypes[2] = out_dtypes[0];
            Py_INCREF(out_dtypes[2]);

            type_num2 = NPY_TIMEDELTA;
        }
        else {
            return raise_binary_type_reso_error(ufunc, operands);
        }
    }
    else if (type_num1 == NPY_DATETIME) {
        /* M8[<A>] - m8[<B>] => M8[gcd(<A>,<B>)] - m8[gcd(<A>,<B>)] */
        if (type_num2 == NPY_TIMEDELTA) {
            out_dtypes[0] = PyArray_PromoteTypes(PyArray_DESCR(operands[0]),
                                                PyArray_DESCR(operands[1]));
            if (out_dtypes[0] == NULL) {
                return -1;
            }
            /* Make a new NPY_TIMEDELTA, and copy the datetime's metadata */
            out_dtypes[1] = timedelta_dtype_with_copied_meta(out_dtypes[0]);
            if (out_dtypes[1] == NULL) {
                Py_DECREF(out_dtypes[0]);
                out_dtypes[0] = NULL;
                return -1;
            }
            out_dtypes[2] = out_dtypes[0];
            Py_INCREF(out_dtypes[2]);
        }
        /* M8[<A>] - int => M8[<A>] - m8[<A>] */
        else if (PyTypeNum_ISINTEGER(type_num2) ||
                    PyTypeNum_ISBOOL(type_num2)) {
            out_dtypes[0] = NPY_DT_CALL_ensure_canonical(
                    PyArray_DESCR(operands[0]));
            if (out_dtypes[0] == NULL) {
                return -1;
            }
            /* Make a new NPY_TIMEDELTA, and copy type1's metadata */
            out_dtypes[1] = timedelta_dtype_with_copied_meta(
                                            PyArray_DESCR(operands[0]));
            if (out_dtypes[1] == NULL) {
                Py_DECREF(out_dtypes[0]);
                out_dtypes[0] = NULL;
                return -1;
            }
            out_dtypes[2] = out_dtypes[0];
            Py_INCREF(out_dtypes[2]);

            type_num2 = NPY_TIMEDELTA;
        }
        /* M8[<A>] - M8[<B>] => M8[gcd(<A>,<B>)] - M8[gcd(<A>,<B>)] */
        else if (type_num2 == NPY_DATETIME) {
            out_dtypes[0] = PyArray_PromoteTypes(PyArray_DESCR(operands[0]),
                                                PyArray_DESCR(operands[1]));
            if (out_dtypes[0] == NULL) {
                return -1;
            }
            /* Make a new NPY_TIMEDELTA, and copy type1's metadata */
            out_dtypes[2] = timedelta_dtype_with_copied_meta(out_dtypes[0]);
            if (out_dtypes[2] == NULL) {
                Py_DECREF(out_dtypes[0]);
                return -1;
            }
            out_dtypes[1] = out_dtypes[0];
            Py_INCREF(out_dtypes[1]);
        }
        else {
            return raise_binary_type_reso_error(ufunc, operands);
        }
    }
    else if (PyTypeNum_ISINTEGER(type_num1) || PyTypeNum_ISBOOL(type_num1)) {
        /* int - m8[<A>] => m8[<A>] - m8[<A>] */
        if (type_num2 == NPY_TIMEDELTA) {
            out_dtypes[0] = NPY_DT_CALL_ensure_canonical(
                    PyArray_DESCR(operands[1]));
            if (out_dtypes[0] == NULL) {
                return -1;
            }
            out_dtypes[1] = out_dtypes[0];
            Py_INCREF(out_dtypes[1]);
            out_dtypes[2] = out_dtypes[0];
            Py_INCREF(out_dtypes[2]);

            type_num1 = NPY_TIMEDELTA;
        }
        else {
            return raise_binary_type_reso_error(ufunc, operands);
        }
    }
    else {
        return raise_binary_type_reso_error(ufunc, operands);
    }

    /* Check against the casting rules */
    if (PyUFunc_ValidateCasting(ufunc, casting, operands, out_dtypes) < 0) {
        for (i = 0; i < 3; ++i) {
            Py_DECREF(out_dtypes[i]);
            out_dtypes[i] = NULL;
        }
        return -1;
    }

    return 0;
}

/*
 * This function applies the type resolution rules for multiplication.
 * In particular, there are a number of special cases with datetime:
 *    int## * m8[<A>] => int64 * m8[<A>]
 *    m8[<A>] * int## => m8[<A>] * int64
 *    float## * m8[<A>] => float64 * m8[<A>]
 *    m8[<A>] * float## => m8[<A>] * float64
 */
NPY_NO_EXPORT int
PyUFunc_MultiplicationTypeResolver(PyUFuncObject *ufunc,
                                NPY_CASTING casting,
                                PyArrayObject **operands,
                                PyObject *type_tup,
                                PyArray_Descr **out_dtypes)
{
    int type_num1, type_num2;
    int i;

    type_num1 = PyArray_DESCR(operands[0])->type_num;
    type_num2 = PyArray_DESCR(operands[1])->type_num;

    /* Use the default when datetime and timedelta are not involved */
    if (!PyTypeNum_ISDATETIME(type_num1) && !PyTypeNum_ISDATETIME(type_num2)
        && !((PyTypeNum_ISSTRING(type_num1) && PyTypeNum_ISINTEGER(type_num2))
             || (PyTypeNum_ISINTEGER(type_num1) && PyTypeNum_ISSTRING(type_num2)))) {
        return PyUFunc_SimpleUniformOperationTypeResolver(ufunc, casting,
                    operands, type_tup, out_dtypes);
    }

    if (PyTypeNum_ISSTRING(type_num1) || PyTypeNum_ISSTRING(type_num2)) {
        if (PyTypeNum_ISSTRING(type_num1)) {
            out_dtypes[0] = NPY_DT_CALL_ensure_canonical(PyArray_DESCR(operands[0]));
            if (out_dtypes[0] == NULL) {
                return -1;
            }

            out_dtypes[1] = PyArray_DescrNewFromType(NPY_INT64);
            if (out_dtypes[1] == NULL) {
                return -1;
            }

            // This is wrong cause of elsize, but only the DType matters
            // here (String or Unicode). The loop has the correct implementation itself.
            out_dtypes[2] = out_dtypes[0];
            Py_INCREF(out_dtypes[0]);
        }
        else {
            out_dtypes[0] = PyArray_DescrNewFromType(NPY_INT64);
            if (out_dtypes[0] == NULL) {
                return -1;
            }

            out_dtypes[1] = NPY_DT_CALL_ensure_canonical(PyArray_DESCR(operands[1]));
            if (out_dtypes[1] == NULL) {
                return -1;
            }

            // This is wrong agaian cause of elsize, but only the DType matters
            // here (String or Unicode).
            out_dtypes[2] = out_dtypes[1];
            Py_INCREF(out_dtypes[1]);
        }
    }
    else if (type_num1 == NPY_TIMEDELTA) {
        /* m8[<A>] * int## => m8[<A>] * int64 */
        if (PyTypeNum_ISINTEGER(type_num2) || PyTypeNum_ISBOOL(type_num2)) {
            out_dtypes[0] = NPY_DT_CALL_ensure_canonical(
                    PyArray_DESCR(operands[0]));
            if (out_dtypes[0] == NULL) {
                return -1;
            }
            out_dtypes[1] = PyArray_DescrNewFromType(NPY_LONGLONG);
            if (out_dtypes[1] == NULL) {
                Py_DECREF(out_dtypes[0]);
                out_dtypes[0] = NULL;
                return -1;
            }
            out_dtypes[2] = out_dtypes[0];
            Py_INCREF(out_dtypes[2]);

            type_num2 = NPY_LONGLONG;
        }
        /* m8[<A>] * float## => m8[<A>] * float64 */
        else if (PyTypeNum_ISFLOAT(type_num2)) {
            out_dtypes[0] = NPY_DT_CALL_ensure_canonical(
                    PyArray_DESCR(operands[0]));
            if (out_dtypes[0] == NULL) {
                return -1;
            }
            out_dtypes[1] = PyArray_DescrNewFromType(NPY_DOUBLE);
            if (out_dtypes[1] == NULL) {
                Py_DECREF(out_dtypes[0]);
                out_dtypes[0] = NULL;
                return -1;
            }
            out_dtypes[2] = out_dtypes[0];
            Py_INCREF(out_dtypes[2]);

            type_num2 = NPY_DOUBLE;
        }
        else {
            return raise_binary_type_reso_error(ufunc, operands);
        }
    }
    else if (PyTypeNum_ISINTEGER(type_num1) || PyTypeNum_ISBOOL(type_num1)) {
        /* int## * m8[<A>] => int64 * m8[<A>] */
        if (type_num2 == NPY_TIMEDELTA) {
            out_dtypes[0] = PyArray_DescrNewFromType(NPY_LONGLONG);
            if (out_dtypes[0] == NULL) {
                return -1;
            }
            out_dtypes[1] = NPY_DT_CALL_ensure_canonical(
                    PyArray_DESCR(operands[1]));
            if (out_dtypes[1] == NULL) {
                Py_DECREF(out_dtypes[0]);
                out_dtypes[0] = NULL;
                return -1;
            }
            out_dtypes[2] = out_dtypes[1];
            Py_INCREF(out_dtypes[2]);

            type_num1 = NPY_LONGLONG;
        }
        else {
            return raise_binary_type_reso_error(ufunc, operands);
        }
    }
    else if (PyTypeNum_ISFLOAT(type_num1)) {
        /* float## * m8[<A>] => float64 * m8[<A>] */
        if (type_num2 == NPY_TIMEDELTA) {
            out_dtypes[0] = PyArray_DescrNewFromType(NPY_DOUBLE);
            if (out_dtypes[0] == NULL) {
                return -1;
            }
            out_dtypes[1] = NPY_DT_CALL_ensure_canonical(
                    PyArray_DESCR(operands[1]));
            if (out_dtypes[1] == NULL) {
                Py_DECREF(out_dtypes[0]);
                out_dtypes[0] = NULL;
                return -1;
            }
            out_dtypes[2] = out_dtypes[1];
            Py_INCREF(out_dtypes[2]);

            type_num1 = NPY_DOUBLE;
        }
        else {
            return raise_binary_type_reso_error(ufunc, operands);
        }
    }
    else {
        return raise_binary_type_reso_error(ufunc, operands);
    }

    /* Check against the casting rules */
    if (PyUFunc_ValidateCasting(ufunc, casting, operands, out_dtypes) < 0) {
        for (i = 0; i < 3; ++i) {
            Py_DECREF(out_dtypes[i]);
            out_dtypes[i] = NULL;
        }
        return -1;
    }

    return 0;
}


/*
 * This function applies the type resolution rules for division.
 * In particular, there are a number of special cases with datetime:
 *    m8[<A>] / m8[<B>] to  m8[gcd(<A>,<B>)] / m8[gcd(<A>,<B>)]  -> float64
 *    m8[<A>] / int##   to m8[<A>] / int64 -> m8[<A>]
 *    m8[<A>] / float## to m8[<A>] / float64 -> m8[<A>]
 */
NPY_NO_EXPORT int
PyUFunc_DivisionTypeResolver(PyUFuncObject *ufunc,
                                NPY_CASTING casting,
                                PyArrayObject **operands,
                                PyObject *type_tup,
                                PyArray_Descr **out_dtypes)
{
    int type_num1, type_num2;
    int i;

    type_num1 = PyArray_DESCR(operands[0])->type_num;
    type_num2 = PyArray_DESCR(operands[1])->type_num;

    /* Use the default when datetime and timedelta are not involved */
    if (!PyTypeNum_ISDATETIME(type_num1) && !PyTypeNum_ISDATETIME(type_num2)) {
        return PyUFunc_DefaultTypeResolver(ufunc, casting, operands,
                    type_tup, out_dtypes);
    }

    if (type_num1 == NPY_TIMEDELTA) {
        /*
         * m8[<A>] / m8[<B>] to
         * m8[gcd(<A>,<B>)] / m8[gcd(<A>,<B>)]  -> float64
         */
        if (type_num2 == NPY_TIMEDELTA) {
            out_dtypes[0] = PyArray_PromoteTypes(PyArray_DESCR(operands[0]),
                                                PyArray_DESCR(operands[1]));
            if (out_dtypes[0] == NULL) {
                return -1;
            }
            out_dtypes[1] = out_dtypes[0];
            Py_INCREF(out_dtypes[1]);

            /*
             * TODO: split function into truediv and floordiv resolvers
             */
            if (strcmp(ufunc->name, "floor_divide") == 0) {
                out_dtypes[2] = PyArray_DescrFromType(NPY_LONGLONG);
            }
            else {
            out_dtypes[2] = PyArray_DescrFromType(NPY_DOUBLE);
            }
            if (out_dtypes[2] == NULL) {
                Py_DECREF(out_dtypes[0]);
                out_dtypes[0] = NULL;
                Py_DECREF(out_dtypes[1]);
                out_dtypes[1] = NULL;
                return -1;
            }
        }
        /* m8[<A>] / int## => m8[<A>] / int64 */
        else if (PyTypeNum_ISINTEGER(type_num2)) {
            out_dtypes[0] = NPY_DT_CALL_ensure_canonical(
                    PyArray_DESCR(operands[0]));
            if (out_dtypes[0] == NULL) {
                return -1;
            }
            out_dtypes[1] = PyArray_DescrFromType(NPY_LONGLONG);
            if (out_dtypes[1] == NULL) {
                Py_DECREF(out_dtypes[0]);
                out_dtypes[0] = NULL;
                return -1;
            }
            out_dtypes[2] = out_dtypes[0];
            Py_INCREF(out_dtypes[2]);

            type_num2 = NPY_LONGLONG;
        }
        /* m8[<A>] / float## => m8[<A>] / float64 */
        else if (PyTypeNum_ISFLOAT(type_num2)) {
            out_dtypes[0] = NPY_DT_CALL_ensure_canonical(
                    PyArray_DESCR(operands[0]));
            if (out_dtypes[0] == NULL) {
                return -1;
            }
            out_dtypes[1] = PyArray_DescrNewFromType(NPY_DOUBLE);
            if (out_dtypes[1] == NULL) {
                Py_DECREF(out_dtypes[0]);
                out_dtypes[0] = NULL;
                return -1;
            }
            out_dtypes[2] = out_dtypes[0];
            Py_INCREF(out_dtypes[2]);

            type_num2 = NPY_DOUBLE;
        }
        else {
            return raise_binary_type_reso_error(ufunc, operands);
        }
    }
    else {
        return raise_binary_type_reso_error(ufunc, operands);
    }

    /* Check against the casting rules */
    if (PyUFunc_ValidateCasting(ufunc, casting, operands, out_dtypes) < 0) {
        for (i = 0; i < 3; ++i) {
            Py_DECREF(out_dtypes[i]);
            out_dtypes[i] = NULL;
        }
        return -1;
    }

    return 0;
}


NPY_NO_EXPORT int
PyUFunc_RemainderTypeResolver(PyUFuncObject *ufunc,
                                NPY_CASTING casting,
                                PyArrayObject **operands,
                                PyObject *type_tup,
                                PyArray_Descr **out_dtypes)
{
    int type_num1, type_num2;
    int i;

    type_num1 = PyArray_DESCR(operands[0])->type_num;
    type_num2 = PyArray_DESCR(operands[1])->type_num;

    /* Use the default when datetime and timedelta are not involved */
    if (!PyTypeNum_ISDATETIME(type_num1) && !PyTypeNum_ISDATETIME(type_num2)) {
        return PyUFunc_DefaultTypeResolver(ufunc, casting, operands,
                    type_tup, out_dtypes);
    }
    if (type_num1 == NPY_TIMEDELTA) {
        if (type_num2 == NPY_TIMEDELTA) {
            out_dtypes[0] = PyArray_PromoteTypes(PyArray_DESCR(operands[0]),
                                                PyArray_DESCR(operands[1]));
            if (out_dtypes[0] == NULL) {
                return -1;
            }
            out_dtypes[1] = out_dtypes[0];
            Py_INCREF(out_dtypes[1]);
            out_dtypes[2] = out_dtypes[0];
            Py_INCREF(out_dtypes[2]);
        }
        else {
            return raise_binary_type_reso_error(ufunc, operands);
        }
    }
    else {
        return raise_binary_type_reso_error(ufunc, operands);
    }

    /* Check against the casting rules */
    if (PyUFunc_ValidateCasting(ufunc, casting, operands, out_dtypes) < 0) {
        for (i = 0; i < 3; ++i) {
            Py_DECREF(out_dtypes[i]);
            out_dtypes[i] = NULL;
        }
        return -1;
    }

    return 0;
}


/*
 * True division should return float64 results when both inputs are integer
 * types. The PyUFunc_DefaultTypeResolver promotes 8 bit integers to float16
 * and 16 bit integers to float32, so that is overridden here by specifying a
 * 'dd->d' signature. Returns -1 on failure.
*/
NPY_NO_EXPORT int
PyUFunc_TrueDivisionTypeResolver(PyUFuncObject *ufunc,
                                 NPY_CASTING casting,
                                 PyArrayObject **operands,
                                 PyObject *type_tup,
                                 PyArray_Descr **out_dtypes)
{
    int type_num1, type_num2;
    static PyObject *default_type_tup = NULL;

    /* Set default type for integer inputs to NPY_DOUBLE */
    if (default_type_tup == NULL) {
        PyArray_Descr *tmp = PyArray_DescrFromType(NPY_DOUBLE);

        if (tmp == NULL) {
            return -1;
        }
        default_type_tup = PyTuple_Pack(3, tmp, tmp, tmp);
        if (default_type_tup == NULL) {
            Py_DECREF(tmp);
            return -1;
        }
        Py_DECREF(tmp);
    }

    type_num1 = PyArray_DESCR(operands[0])->type_num;
    type_num2 = PyArray_DESCR(operands[1])->type_num;

    if (type_tup == NULL &&
            (PyTypeNum_ISINTEGER(type_num1) || PyTypeNum_ISBOOL(type_num1)) &&
            (PyTypeNum_ISINTEGER(type_num2) || PyTypeNum_ISBOOL(type_num2))) {
        return PyUFunc_DefaultTypeResolver(ufunc, casting, operands,
                                           default_type_tup, out_dtypes);
    }
    return PyUFunc_DivisionTypeResolver(ufunc, casting, operands,
                                        type_tup, out_dtypes);
}

static int
find_userloop(PyUFuncObject *ufunc,
                PyArray_Descr **dtypes,
                PyUFuncGenericFunction *out_innerloop,
                void **out_innerloopdata)
{
    npy_intp i, nin = ufunc->nin, j, nargs = nin + ufunc->nout;

    /* Use this to try to avoid repeating the same userdef loop search */
    int last_userdef = -1;

    for (i = 0; i < nargs; ++i) {
        int type_num;

        /* no more ufunc arguments to check */
        if (dtypes[i] == NULL) {
            break;
        }

        type_num = dtypes[i]->type_num;
        if (type_num != last_userdef &&
                (PyTypeNum_ISUSERDEF(type_num) || type_num == NPY_VOID)) {
            PyObject *key, *obj;

            last_userdef = type_num;

            key = PyLong_FromLong(type_num);
            if (key == NULL) {
                return -1;
            }
            obj = PyDict_GetItemWithError(ufunc->userloops, key);
            Py_DECREF(key);
            if (obj == NULL && PyErr_Occurred()){
                return -1;
            }
            else if (obj == NULL) {
                continue;
            }
            PyUFunc_Loop1d *funcdata = PyCapsule_GetPointer(obj, NULL);
            if (funcdata == NULL) {
                return -1;
            }
            for (; funcdata != NULL; funcdata = funcdata->next) {
                int *types = funcdata->arg_types;

                for (j = 0; j < nargs; ++j) {
                    if (types[j] != dtypes[j]->type_num) {
                        break;
                    }
                }
                /* It matched */
                if (j == nargs) {
                    *out_innerloop = funcdata->func;
                    *out_innerloopdata = funcdata->data;
                    return 1;
                }
            }
        }
    }

    /* Didn't find a match */
    return 0;
}

NPY_NO_EXPORT int
PyUFunc_DefaultLegacyInnerLoopSelector(PyUFuncObject *ufunc,
                                PyArray_Descr **dtypes,
                                PyUFuncGenericFunction *out_innerloop,
                                void **out_innerloopdata,
                                int *out_needs_api)
{
    int nargs = ufunc->nargs;
    const char *types;
    int i, j;

    /*
     * If there are user-loops search them first.
     * TODO: There needs to be a loop selection acceleration structure,
     *       like a hash table.
     */
    if (ufunc->userloops) {
        switch (find_userloop(ufunc, dtypes,
                    out_innerloop, out_innerloopdata)) {
            /* Error */
            case -1:
                return -1;
            /* Found a loop */
            case 1:
                return 0;
        }
    }

    types = ufunc->types;
    for (i = 0; i < ufunc->ntypes; ++i) {
        /* Copy the types into an int array for matching */
        for (j = 0; j < nargs; ++j) {
            if (types[j] != dtypes[j]->type_num) {
                break;
            }
        }
        if (j == nargs) {
            *out_innerloop = ufunc->functions[i];
            *out_innerloopdata = (ufunc->data == NULL) ? NULL : ufunc->data[i];
            return 0;
        }

        types += nargs;
    }

    return raise_no_loop_found_error(ufunc, (PyObject **)dtypes, 0);
}


static int
ufunc_loop_matches(PyUFuncObject *self,
                    PyArrayObject **op,
                    NPY_CASTING input_casting,
                    NPY_CASTING output_casting,
                    int any_object,
                    int use_min_scalar,
                    int *types, PyArray_Descr **dtypes,
                    int *out_no_castable_output,
                    char *out_err_src_typecode,
                    char *out_err_dst_typecode)
{
    npy_intp i, nin = self->nin, nop = nin + self->nout;

    /*
     * First check if all the inputs can be safely cast
     * to the types for this function
     */
    for (i = 0; i < nin; ++i) {
        PyArray_Descr *tmp;

        /*
         * If no inputs are objects and there are more than one
         * loop, don't allow conversion to object.  The rationale
         * behind this is mostly performance.  Except for custom
         * ufuncs built with just one object-parametered inner loop,
         * only the types that are supported are implemented.  Trying
         * the object version of logical_or on float arguments doesn't
         * seem right.
         */
        if (types[i] == NPY_OBJECT && !any_object && self->ntypes > 1) {
            return 0;
        }
        if (types[i] == NPY_NOTYPE) {
            continue;  /* Matched by being explicitly specified. */
        }

        /*
         * If type num is NPY_VOID and struct dtypes have been passed in,
         * use struct dtype object. Otherwise create new dtype object
         * from type num.
         */
        if (types[i] == NPY_VOID && dtypes != NULL) {
            tmp = dtypes[i];
            Py_INCREF(tmp);
        }
        else {
            tmp = PyArray_DescrFromType(types[i]);
        }
        if (tmp == NULL) {
            return -1;
        }

#if NPY_UF_DBG_TRACING
        printf("Checking type for op %d, type %d: ", (int)i, (int)types[i]);
        PyObject_Print((PyObject *)tmp, stdout, 0);
        printf(", operand type: ");
        PyObject_Print((PyObject *)PyArray_DESCR(op[i]), stdout, 0);
        printf("\n");
#endif
        /*
         * If all the inputs are scalars, use the regular
         * promotion rules, not the special value-checking ones.
         */
        if (!use_min_scalar) {
            if (!PyArray_CanCastTypeTo(PyArray_DESCR(op[i]), tmp,
                                                    input_casting)) {
                Py_DECREF(tmp);
                return 0;
            }
        }
        else {
            if (!PyArray_CanCastArrayTo(op[i], tmp, input_casting)) {
                Py_DECREF(tmp);
                return 0;
            }
        }
        Py_DECREF(tmp);
    }

    /*
     * If all the inputs were ok, then check casting back to the
     * outputs.
     */
    for (i = nin; i < nop; ++i) {
        if (types[i] == NPY_NOTYPE) {
            continue;  /* Matched by being explicitly specified. */
        }
        if (op[i] != NULL) {
            PyArray_Descr *tmp = PyArray_DescrFromType(types[i]);
            if (tmp == NULL) {
                return -1;
            }
            if (!PyArray_CanCastTypeTo(tmp, PyArray_DESCR(op[i]),
                                                        output_casting)) {
                if (!(*out_no_castable_output)) {
                    *out_no_castable_output = 1;
                    *out_err_src_typecode = tmp->type;
                    *out_err_dst_typecode = PyArray_DESCR(op[i])->type;
                }
                Py_DECREF(tmp);
                return 0;
            }
            Py_DECREF(tmp);
        }
    }
    return 1;
}

static int
set_ufunc_loop_data_types(PyUFuncObject *self, PyArrayObject **op,
                    PyArray_Descr **out_dtypes,
                    int *type_nums, PyArray_Descr **dtypes)
{
    int i, nin = self->nin, nop = nin + self->nout;

    /*
     * Fill the dtypes array.
     * For outputs,
     * also search the inputs for a matching type_num to copy
     * instead of creating a new one, similarly to preserve metadata.
     **/
    for (i = 0; i < nop; ++i) {
        if (dtypes != NULL) {
            out_dtypes[i] = dtypes[i];
            Py_XINCREF(out_dtypes[i]);
        /*
         * Copy the dtype from 'op' if the type_num matches,
         * to preserve metadata.
         */
        }
        else if (op[i] != NULL &&
                 PyArray_DESCR(op[i])->type_num == type_nums[i]) {
            out_dtypes[i] = NPY_DT_CALL_ensure_canonical(
                    PyArray_DESCR(op[i]));
        }
        /*
         * For outputs, copy the dtype from op[0] if the type_num
         * matches, similarly to preserve metadata.
         */
        else if (i >= nin && op[0] != NULL &&
                            PyArray_DESCR(op[0])->type_num == type_nums[i]) {
            out_dtypes[i] = NPY_DT_CALL_ensure_canonical(
                    PyArray_DESCR(op[0]));
        }
        /* Otherwise create a plain descr from the type number */
        else {
            out_dtypes[i] = PyArray_DescrFromType(type_nums[i]);
        }

        if (out_dtypes[i] == NULL) {
            goto fail;
        }
    }

    return 0;

fail:
    while (--i >= 0) {
        Py_DECREF(out_dtypes[i]);
        out_dtypes[i] = NULL;
    }
    return -1;
}

/*
 * Does a search through the arguments and the loops
 */
static int
linear_search_userloop_type_resolver(PyUFuncObject *self,
                        PyArrayObject **op,
                        NPY_CASTING input_casting,
                        NPY_CASTING output_casting,
                        int any_object,
                        int use_min_scalar,
                        PyArray_Descr **out_dtype,
                        int *out_no_castable_output,
                        char *out_err_src_typecode,
                        char *out_err_dst_typecode)
{
    npy_intp i, nop = self->nin + self->nout;

    /* Use this to try to avoid repeating the same userdef loop search */
    int last_userdef = -1;

    for (i = 0; i < nop; ++i) {
        int type_num;

        /* no more ufunc arguments to check */
        if (op[i] == NULL) {
            break;
        }

        type_num = PyArray_DESCR(op[i])->type_num;
        if (type_num != last_userdef &&
                (PyTypeNum_ISUSERDEF(type_num) || type_num == NPY_VOID)) {
            PyObject *key, *obj;

            last_userdef = type_num;

            key = PyLong_FromLong(type_num);
            if (key == NULL) {
                return -1;
            }
            obj = PyDict_GetItemWithError(self->userloops, key);
            Py_DECREF(key);
            if (obj == NULL && PyErr_Occurred()){
                return -1;
            }
            else if (obj == NULL) {
                continue;
            }
            PyUFunc_Loop1d *funcdata = PyCapsule_GetPointer(obj, NULL);
            if (funcdata == NULL) {
                return -1;
            }
            for (; funcdata != NULL; funcdata = funcdata->next) {
                int *types = funcdata->arg_types;
                switch (ufunc_loop_matches(self, op,
                            input_casting, output_casting,
                            any_object, use_min_scalar,
                            types, funcdata->arg_dtypes,
                            out_no_castable_output, out_err_src_typecode,
                            out_err_dst_typecode)) {
                    /* Error */
                    case -1:
                        return -1;
                    /* Found a match */
                    case 1:
                        set_ufunc_loop_data_types(self, op, out_dtype, types, funcdata->arg_dtypes);
                        return 1;
                }
            }
        }
    }

    /* Didn't find a match */
    return 0;
}

/*
 * Does a search through the arguments and the loops
 */
static int
type_tuple_userloop_type_resolver(PyUFuncObject *self,
                        int n_specified,
                        int *specified_types,
                        PyArrayObject **op,
                        NPY_CASTING input_casting,
                        NPY_CASTING casting,
                        int any_object,
                        int use_min_scalar,
                        PyArray_Descr **out_dtype)
{
    int i, j, nin = self->nin, nop = nin + self->nout;
    assert(n_specified == nop);
    int types[NPY_MAXARGS];

    /* Use this to try to avoid repeating the same userdef loop search */
    int last_userdef = -1;

    int no_castable_output = 0;
    char err_src_typecode = '-', err_dst_typecode = '-';

    for (i = 0; i < nin; ++i) {
        int type_num = PyArray_DESCR(op[i])->type_num;
        if (type_num != last_userdef && PyTypeNum_ISUSERDEF(type_num)) {
            PyObject *key, *obj;

            last_userdef = type_num;

            key = PyLong_FromLong(type_num);
            if (key == NULL) {
                return -1;
            }
            obj = PyDict_GetItemWithError(self->userloops, key);
            Py_DECREF(key);
            if (obj == NULL && PyErr_Occurred()){
                return -1;
            }
            else if (obj == NULL) {
                continue;
            }

            PyUFunc_Loop1d *funcdata = PyCapsule_GetPointer(obj, NULL);
            if (funcdata == NULL) {
                return -1;
            }
            for (; funcdata != NULL; funcdata = funcdata->next) {
                int *orig_types = funcdata->arg_types;

                /*
                 * Copy the types into an int array for matching
                 * (Mostly duplicated in `type_tuple_type_resolver`)
                 */
                for (j = 0; j < nop; ++j) {
                    if (specified_types[j] == NPY_NOTYPE) {
                        types[j] = orig_types[j];
                        continue;
                    }
                    if (orig_types[j] != specified_types[j]) {
                        break;
                    }
                    /* indicate that we do not have to check this type anymore. */
                    types[j] = NPY_NOTYPE;
                }

                if (j != nop) {
                    /* no match */
                    continue;
                }

                switch (ufunc_loop_matches(self, op,
                            input_casting, casting,
                            any_object, use_min_scalar,
                            types, NULL,
                            &no_castable_output, &err_src_typecode,
                            &err_dst_typecode)) {
                    /* It works */
                    case 1:
                        set_ufunc_loop_data_types(self, op,
                            out_dtype, orig_types, NULL);
                        /*
                         * In principle, we only need to validate the
                         * NPY_NOTYPE ones
                         */
                        if (PyUFunc_ValidateCasting(self,
                                casting, op, out_dtype) < 0) {
                            for (j = 0; j < self->nargs; j++) {
                                Py_DECREF(out_dtype[j]);
                                out_dtype[j] = NULL;
                            }
                            return -1;
                        }
                        return 1;
                    /* Didn't match */
                    case 0:
                        PyErr_Format(PyExc_TypeError,
                             "found a user loop for ufunc '%s' "
                             "matching the type-tuple, "
                             "but the inputs and/or outputs could not be "
                             "cast according to the casting rule",
                             ufunc_get_name_cstr(self));
                        return -1;
                    /* Error */
                    case -1:
                        return -1;
                }
            }
        }
    }

    /* Didn't find a match */
    return 0;
}


/*
 * Does a linear search for the best inner loop of the ufunc.
 *
 * Note that if an error is returned, the caller must free the non-zero
 * references in out_dtype.  This function does not do its own clean-up.
 */
NPY_NO_EXPORT int
linear_search_type_resolver(PyUFuncObject *self,
                        PyArrayObject **op,
                        NPY_CASTING input_casting,
                        NPY_CASTING output_casting,
                        int any_object,
                        PyArray_Descr **out_dtype)
{
    npy_intp i, j, nin = self->nin, nop = nin + self->nout;
    int types[NPY_MAXARGS];
    const char *ufunc_name;
    int no_castable_output = 0;

    /* For making a better error message on coercion error */
    char err_dst_typecode = '-', err_src_typecode = '-';

    ufunc_name = ufunc_get_name_cstr(self);

    assert(npy_promotion_state != NPY_USE_WEAK_PROMOTION_AND_WARN);
    /* Always "use" with new promotion in case of Python int/float/complex */
    int use_min_scalar;
    if (npy_promotion_state == NPY_USE_LEGACY_PROMOTION) {
        use_min_scalar = should_use_min_scalar(nin, op, 0, NULL);
    }
    else {
        use_min_scalar = should_use_min_scalar_weak_literals(nin, op);
    }

    /* If the ufunc has userloops, search for them. */
    if (self->userloops) {
        switch (linear_search_userloop_type_resolver(self, op,
                                input_casting, output_casting,
                                any_object, use_min_scalar, out_dtype,
                                &no_castable_output, &err_src_typecode,
                                &err_dst_typecode)) {
            /* Error */
            case -1:
                return -1;
            /* A loop was found */
            case 1:
                return 0;
        }
    }

    /*
     * Determine the UFunc loop.  This could in general be *much* faster,
     * and a better way to implement it might be for the ufunc to
     * provide a function which gives back the result type and inner
     * loop function.
     *
     * A default fast mechanism could be provided for functions which
     * follow the most typical pattern, when all functions have signatures
     * "xx...x -> x" for some built-in data type x, as follows.
     *  - Use PyArray_ResultType to get the output type
     *  - Look up the inner loop in a table based on the output type_num
     *
     * The method for finding the loop in the previous code did not
     * appear consistent (as noted by some asymmetry in the generated
     * coercion tables for np.add).
     */
    no_castable_output = 0;
    for (i = 0; i < self->ntypes; ++i) {
        const char *orig_types = self->types + i*self->nargs;

        /* Copy the types into an int array for matching */
        for (j = 0; j < nop; ++j) {
            types[j] = orig_types[j];
        }

        switch (ufunc_loop_matches(self, op,
                    input_casting, output_casting,
                    any_object, use_min_scalar,
                    types, NULL,
                    &no_castable_output, &err_src_typecode,
                    &err_dst_typecode)) {
            /* Error */
            case -1:
                return -1;
            /* Found a match */
            case 1:
                set_ufunc_loop_data_types(self, op, out_dtype, types, NULL);
                return 0;
        }
    }

    /* If no function was found, throw an error */
    if (no_castable_output) {
        PyErr_Format(PyExc_TypeError,
                "ufunc '%s' output (typecode '%c') could not be coerced to "
                "provided output parameter (typecode '%c') according "
                "to the casting rule '%s'",
                ufunc_name, err_src_typecode, err_dst_typecode,
                npy_casting_to_string(output_casting));
    }
    else {
        /*
         * TODO: We should try again if the casting rule is same_kind
         *       or unsafe, and look for a function more liberally.
         */
        PyErr_Format(PyExc_TypeError,
                "ufunc '%s' not supported for the input types, and the "
                "inputs could not be safely coerced to any supported "
                "types according to the casting rule '%s'",
                ufunc_name,
                npy_casting_to_string(input_casting));
    }

    return -1;
}


static int
type_tuple_type_resolver_core(PyUFuncObject *self,
        PyArrayObject **op,
        NPY_CASTING input_casting, NPY_CASTING casting,
        int specified_types[],
        int any_object,
        int no_castable_output, int use_min_scalar,
        PyArray_Descr **out_dtype)
{
    int i, j;
    int nop = self->nargs;
    int types[NPY_MAXARGS];

    /* For making a better error message on coercion error */
    char err_dst_typecode = '-', err_src_typecode = '-';

    /* If the ufunc has userloops, search for them. */
    if (self->userloops) {
        switch (type_tuple_userloop_type_resolver(self,
                nop, specified_types,
                op, input_casting, casting,
                any_object, use_min_scalar,
                out_dtype)) {
            /* Error */
            case -1:
                return -1;
            /* Found matching loop */
            case 1:
                return 0;
        }
    }

    for (i = 0; i < self->ntypes; ++i) {
        const char *orig_types = self->types + i*self->nargs;

        /*
         * Check specified types and copy into an int array for matching
         * (Mostly duplicated in `type_tuple_userloop_type_resolver`)
         */
        for (j = 0; j < nop; ++j) {
            if (specified_types[j] == NPY_NOTYPE) {
                types[j] = orig_types[j];
                continue;
            }
            if (orig_types[j] != specified_types[j]) {
                break;
            }
            /* indicate that we do not have to check this type anymore. */
            types[j] = NPY_NOTYPE;
        }
        if (j < nop) {
            /* no match */
            continue;
        }

        switch (ufunc_loop_matches(self, op,
                input_casting, casting,
                any_object, use_min_scalar,
                types, NULL,
                &no_castable_output, &err_src_typecode,
                &err_dst_typecode)) {
            case -1:
                /* Error */
                return -1;
            case 0:
                /* Cannot cast inputs */
                continue;
            case 1:
                /* Success, fill also the NPY_NOTYPE (cast from char to int) */
                for (j = 0; j < nop; j++) {
                    types[j] = orig_types[j];
                }
                set_ufunc_loop_data_types(self, op, out_dtype, types, NULL);
                /* In principle, we only need to validate the NPY_NOTYPE ones */
                if (PyUFunc_ValidateCasting(self, casting, op, out_dtype) < 0) {
                    for (j = 0; j < self->nargs; j++) {
                        Py_DECREF(out_dtype[j]);
                        out_dtype[j] = NULL;
                    }
                    return -1;
                }
                return 0;
        }
    }
    return -2;
}

/*
 * Does a linear search for the inner loop of the ufunc specified by type_tup.
 *
 * Note that if an error is returned, the caller must free the non-zero
 * references in out_dtype.  This function does not do its own clean-up.
 */
NPY_NO_EXPORT int
type_tuple_type_resolver(PyUFuncObject *self,
                        PyObject *type_tup,
                        PyArrayObject **op,
                        NPY_CASTING input_casting,
                        NPY_CASTING casting,
                        int any_object,
                        PyArray_Descr **out_dtype)
{
    int nin = self->nin, nop = nin + self->nout;
    int specified_types[NPY_MAXARGS];
    const char *ufunc_name;
    int no_castable_output = 0;

    ufunc_name = ufunc_get_name_cstr(self);

    assert(npy_promotion_state != NPY_USE_WEAK_PROMOTION_AND_WARN);
    /* Always "use" with new promotion in case of Python int/float/complex */
    int use_min_scalar;
    if (npy_promotion_state == NPY_USE_LEGACY_PROMOTION) {
        use_min_scalar = should_use_min_scalar(nin, op, 0, NULL);
    }
    else {
        use_min_scalar = should_use_min_scalar_weak_literals(nin, op);
    }

    /* Fill in specified_types from the tuple or string */
    const char *bad_type_tup_msg = (
            "Only NumPy must call `ufunc->type_resolver()` explicitly. "
            "NumPy ensures that a type-tuple is normalized now to be a tuple "
            "only containing None or descriptors.  If anything else is passed "
            "(you are seeing this message), the `type_resolver()` was called "
            "directly by a third party. "
            "This is unexpected, please inform the NumPy developers about it. "
            "Also note that `type_resolver` will be phased out, since it must "
            "be replaced.");

    if (PyTuple_CheckExact(type_tup)) {
        Py_ssize_t n = PyTuple_GET_SIZE(type_tup);
        if (n != nop) {
            PyErr_SetString(PyExc_RuntimeError, bad_type_tup_msg);
            return -1;
        }
        for (int i = 0; i < nop; ++i) {
            PyObject *item = PyTuple_GET_ITEM(type_tup, i);
            if (item == Py_None) {
                specified_types[i] = NPY_NOTYPE;
            }
            else {
                if (!PyArray_DescrCheck(item)) {
                    PyErr_SetString(PyExc_RuntimeError, bad_type_tup_msg);
                    return -1;
                }
                specified_types[i] = ((PyArray_Descr *)item)->type_num;
            }
        }
    }
    else {
        PyErr_SetString(PyExc_RuntimeError, bad_type_tup_msg);
        return -1;
    }

    int res = type_tuple_type_resolver_core(self,
            op, input_casting, casting, specified_types, any_object,
            no_castable_output, use_min_scalar, out_dtype);

    if (res != -2) {
        return res;
    }

    /*
     * When the user passes `dtype=dtype`, it gets translated to
     * `signature=(None,)*nin + (dtype,)*nout`.  If the signature matches that
     * exactly (could be relaxed but that is not necessary for backcompat),
     * we also try `signature=(dtype,)*(nin+nout)`.
     * Since reduction pass in `(dtype, None, dtype)` we broaden this to
     * replacing all unspecified dtypes with the homogeneous output one.
     * Note that this can (and often will) lead to unsafe casting.  This is
     * normally rejected (but not currently for reductions!).
     * This used to be the main meaning for `dtype=dtype`, but some calls broke
     * the expectation, and changing it allows for `dtype=dtype` to be useful
     * for ufuncs like `np.ldexp` in the future while also normalizing it to
     * a `signature` early on.
     */
    int homogeneous_type = NPY_NOTYPE;
    if (self->nout > 0) {
        homogeneous_type = specified_types[nin];
        for (int i = nin+1; i < nop; i++) {
            if (specified_types[i] != homogeneous_type) {
                homogeneous_type = NPY_NOTYPE;
                break;
            }
        }
    }
    if (homogeneous_type != NPY_NOTYPE) {
        for (int i = 0; i < nin; i++) {
            if (specified_types[i] != NPY_NOTYPE) {
                /* Never replace a specified type! */
                continue;
            }
            specified_types[i] = homogeneous_type;
        }

        /* Try again with the homogeneous specified types. */
        res = type_tuple_type_resolver_core(self,
                op, input_casting, casting, specified_types, any_object,
                no_castable_output, use_min_scalar, out_dtype);

        if (res != -2) {
            return res;
        }
    }

    /* If no function was found, throw an error */
    PyErr_Format(PyExc_TypeError,
            "No loop matching the specified signature and casting "
            "was found for ufunc %s", ufunc_name);

    return -1;
}

NPY_NO_EXPORT int
PyUFunc_DivmodTypeResolver(PyUFuncObject *ufunc,
                                NPY_CASTING casting,
                                PyArrayObject **operands,
                                PyObject *type_tup,
                                PyArray_Descr **out_dtypes)
{
    int type_num1, type_num2;
    int i;

    type_num1 = PyArray_DESCR(operands[0])->type_num;
    type_num2 = PyArray_DESCR(operands[1])->type_num;

    /* Use the default when datetime and timedelta are not involved */
    if (!PyTypeNum_ISDATETIME(type_num1) && !PyTypeNum_ISDATETIME(type_num2)) {
        return PyUFunc_DefaultTypeResolver(ufunc, casting, operands,
                    type_tup, out_dtypes);
    }
    if (type_num1 == NPY_TIMEDELTA) {
        if (type_num2 == NPY_TIMEDELTA) {
            out_dtypes[0] = PyArray_PromoteTypes(PyArray_DESCR(operands[0]),
                                                PyArray_DESCR(operands[1]));
            out_dtypes[1] = out_dtypes[0];
            Py_INCREF(out_dtypes[1]);
            out_dtypes[2] = PyArray_DescrFromType(NPY_LONGLONG);
            out_dtypes[3] = out_dtypes[0];
            Py_INCREF(out_dtypes[3]);
        }
        else {
            return raise_binary_type_reso_error(ufunc, operands);
        }
    }
    else {
        return raise_binary_type_reso_error(ufunc, operands);
    }

    /* Check against the casting rules */
    if (PyUFunc_ValidateCasting(ufunc, casting, operands, out_dtypes) < 0) {
        for (i = 0; i < 4; ++i) {
            Py_DECREF(out_dtypes[i]);
            out_dtypes[i] = NULL;
        }
        return -1;
    }

    return 0;
}