Modules/_datetimemodule.c

/*  C implementation for the date/time type documented at
 *  http://www.zope.org/Members/fdrake/DateTimeWiki/FrontPage
 */

#include "Python.h"
#include "structmember.h"

#include <time.h>

#ifdef MS_WINDOWS
#  include <winsock2.h>         /* struct timeval */
#endif

/* Differentiate between building the core module and building extension
 * modules.
 */
#ifndef Py_BUILD_CORE
#define Py_BUILD_CORE
#endif
#include "datetime.h"
#undef Py_BUILD_CORE

/*[clinic input]
module datetime
class datetime.datetime "PyDateTime_DateTime *" "&PyDateTime_DateTimeType"
[clinic start generated code]*/
/*[clinic end generated code: output=da39a3ee5e6b4b0d input=78142cb64b9e98bc]*/

#include "clinic/_datetimemodule.c.h"

/* We require that C int be at least 32 bits, and use int virtually
 * everywhere.  In just a few cases we use a temp long, where a Python
 * API returns a C long.  In such cases, we have to ensure that the
 * final result fits in a C int (this can be an issue on 64-bit boxes).
 */
#if SIZEOF_INT < 4
#       error "_datetime.c requires that C int have at least 32 bits"
#endif

#define MINYEAR 1
#define MAXYEAR 9999
#define MAXORDINAL 3652059 /* date(9999,12,31).toordinal() */

/* Nine decimal digits is easy to communicate, and leaves enough room
 * so that two delta days can be added w/o fear of overflowing a signed
 * 32-bit int, and with plenty of room left over to absorb any possible
 * carries from adding seconds.
 */
#define MAX_DELTA_DAYS 999999999

/* Rename the long macros in datetime.h to more reasonable short names. */
#define GET_YEAR                PyDateTime_GET_YEAR
#define GET_MONTH               PyDateTime_GET_MONTH
#define GET_DAY                 PyDateTime_GET_DAY
#define DATE_GET_HOUR           PyDateTime_DATE_GET_HOUR
#define DATE_GET_MINUTE         PyDateTime_DATE_GET_MINUTE
#define DATE_GET_SECOND         PyDateTime_DATE_GET_SECOND
#define DATE_GET_MICROSECOND    PyDateTime_DATE_GET_MICROSECOND
#define DATE_GET_FOLD           PyDateTime_DATE_GET_FOLD

/* Date accessors for date and datetime. */
#define SET_YEAR(o, v)          (((o)->data[0] = ((v) & 0xff00) >> 8), \
                 ((o)->data[1] = ((v) & 0x00ff)))
#define SET_MONTH(o, v)         (PyDateTime_GET_MONTH(o) = (v))
#define SET_DAY(o, v)           (PyDateTime_GET_DAY(o) = (v))

/* Date/Time accessors for datetime. */
#define DATE_SET_HOUR(o, v)     (PyDateTime_DATE_GET_HOUR(o) = (v))
#define DATE_SET_MINUTE(o, v)   (PyDateTime_DATE_GET_MINUTE(o) = (v))
#define DATE_SET_SECOND(o, v)   (PyDateTime_DATE_GET_SECOND(o) = (v))
#define DATE_SET_MICROSECOND(o, v)      \
    (((o)->data[7] = ((v) & 0xff0000) >> 16), \
     ((o)->data[8] = ((v) & 0x00ff00) >> 8), \
     ((o)->data[9] = ((v) & 0x0000ff)))
#define DATE_SET_FOLD(o, v)   (PyDateTime_DATE_GET_FOLD(o) = (v))

/* Time accessors for time. */
#define TIME_GET_HOUR           PyDateTime_TIME_GET_HOUR
#define TIME_GET_MINUTE         PyDateTime_TIME_GET_MINUTE
#define TIME_GET_SECOND         PyDateTime_TIME_GET_SECOND
#define TIME_GET_MICROSECOND    PyDateTime_TIME_GET_MICROSECOND
#define TIME_GET_FOLD           PyDateTime_TIME_GET_FOLD
#define TIME_SET_HOUR(o, v)     (PyDateTime_TIME_GET_HOUR(o) = (v))
#define TIME_SET_MINUTE(o, v)   (PyDateTime_TIME_GET_MINUTE(o) = (v))
#define TIME_SET_SECOND(o, v)   (PyDateTime_TIME_GET_SECOND(o) = (v))
#define TIME_SET_MICROSECOND(o, v)      \
    (((o)->data[3] = ((v) & 0xff0000) >> 16), \
     ((o)->data[4] = ((v) & 0x00ff00) >> 8), \
     ((o)->data[5] = ((v) & 0x0000ff)))
#define TIME_SET_FOLD(o, v)   (PyDateTime_TIME_GET_FOLD(o) = (v))

/* Delta accessors for timedelta. */
#define GET_TD_DAYS(o)          (((PyDateTime_Delta *)(o))->days)
#define GET_TD_SECONDS(o)       (((PyDateTime_Delta *)(o))->seconds)
#define GET_TD_MICROSECONDS(o)  (((PyDateTime_Delta *)(o))->microseconds)

#define SET_TD_DAYS(o, v)       ((o)->days = (v))
#define SET_TD_SECONDS(o, v)    ((o)->seconds = (v))
#define SET_TD_MICROSECONDS(o, v) ((o)->microseconds = (v))

/* p is a pointer to a time or a datetime object; HASTZINFO(p) returns
 * p->hastzinfo.
 */
#define HASTZINFO(p) (((_PyDateTime_BaseTZInfo *)(p))->hastzinfo)
#define GET_TIME_TZINFO(p) (HASTZINFO(p) ? \
                            ((PyDateTime_Time *)(p))->tzinfo : Py_None)
#define GET_DT_TZINFO(p) (HASTZINFO(p) ? \
                          ((PyDateTime_DateTime *)(p))->tzinfo : Py_None)
/* M is a char or int claiming to be a valid month.  The macro is equivalent
 * to the two-sided Python test
 *      1 <= M <= 12
 */
#define MONTH_IS_SANE(M) ((unsigned int)(M) - 1 < 12)

/* Forward declarations. */
static PyTypeObject PyDateTime_DateType;
static PyTypeObject PyDateTime_DateTimeType;
static PyTypeObject PyDateTime_DeltaType;
static PyTypeObject PyDateTime_TimeType;
static PyTypeObject PyDateTime_TZInfoType;
static PyTypeObject PyDateTime_TimeZoneType;

static int check_tzinfo_subclass(PyObject *p);

_Py_IDENTIFIER(as_integer_ratio);
_Py_IDENTIFIER(fromutc);
_Py_IDENTIFIER(isoformat);
_Py_IDENTIFIER(strftime);

/* ---------------------------------------------------------------------------
 * Math utilities.
 */

/* k = i+j overflows iff k differs in sign from both inputs,
 * iff k^i has sign bit set and k^j has sign bit set,
 * iff (k^i)&(k^j) has sign bit set.
 */
#define SIGNED_ADD_OVERFLOWED(RESULT, I, J) \
    ((((RESULT) ^ (I)) & ((RESULT) ^ (J))) < 0)

/* Compute Python divmod(x, y), returning the quotient and storing the
 * remainder into *r.  The quotient is the floor of x/y, and that's
 * the real point of this.  C will probably truncate instead (C99
 * requires truncation; C89 left it implementation-defined).
 * Simplification:  we *require* that y > 0 here.  That's appropriate
 * for all the uses made of it.  This simplifies the code and makes
 * the overflow case impossible (divmod(LONG_MIN, -1) is the only
 * overflow case).
 */
static int
divmod(int x, int y, int *r)
{
    int quo;

    assert(y > 0);
    quo = x / y;
    *r = x - quo * y;
    if (*r < 0) {
        --quo;
        *r += y;
    }
    assert(0 <= *r && *r < y);
    return quo;
}

/* Nearest integer to m / n for integers m and n. Half-integer results
 * are rounded to even.
 */
static PyObject *
divide_nearest(PyObject *m, PyObject *n)
{
    PyObject *result;
    PyObject *temp;

    temp = _PyLong_DivmodNear(m, n);
    if (temp == NULL)
        return NULL;
    result = PyTuple_GET_ITEM(temp, 0);
    Py_INCREF(result);
    Py_DECREF(temp);

    return result;
}

/* ---------------------------------------------------------------------------
 * General calendrical helper functions
 */

/* For each month ordinal in 1..12, the number of days in that month,
 * and the number of days before that month in the same year.  These
 * are correct for non-leap years only.
 */
static const int _days_in_month[] = {
    0, /* unused; this vector uses 1-based indexing */
    31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31
};

static const int _days_before_month[] = {
    0, /* unused; this vector uses 1-based indexing */
    0, 31, 59, 90, 120, 151, 181, 212, 243, 273, 304, 334
};

/* year -> 1 if leap year, else 0. */
static int
is_leap(int year)
{
    /* Cast year to unsigned.  The result is the same either way, but
     * C can generate faster code for unsigned mod than for signed
     * mod (especially for % 4 -- a good compiler should just grab
     * the last 2 bits when the LHS is unsigned).
     */
    const unsigned int ayear = (unsigned int)year;
    return ayear % 4 == 0 && (ayear % 100 != 0 || ayear % 400 == 0);
}

/* year, month -> number of days in that month in that year */
static int
days_in_month(int year, int month)
{
    assert(month >= 1);
    assert(month <= 12);
    if (month == 2 && is_leap(year))
        return 29;
    else
        return _days_in_month[month];
}

/* year, month -> number of days in year preceding first day of month */
static int
days_before_month(int year, int month)
{
    int days;

    assert(month >= 1);
    assert(month <= 12);
    days = _days_before_month[month];
    if (month > 2 && is_leap(year))
        ++days;
    return days;
}

/* year -> number of days before January 1st of year.  Remember that we
 * start with year 1, so days_before_year(1) == 0.
 */
static int
days_before_year(int year)
{
    int y = year - 1;
    /* This is incorrect if year <= 0; we really want the floor
     * here.  But so long as MINYEAR is 1, the smallest year this
     * can see is 1.
     */
    assert (year >= 1);
    return y*365 + y/4 - y/100 + y/400;
}

/* Number of days in 4, 100, and 400 year cycles.  That these have
 * the correct values is asserted in the module init function.
 */
#define DI4Y    1461    /* days_before_year(5); days in 4 years */
#define DI100Y  36524   /* days_before_year(101); days in 100 years */
#define DI400Y  146097  /* days_before_year(401); days in 400 years  */

/* ordinal -> year, month, day, considering 01-Jan-0001 as day 1. */
static void
ord_to_ymd(int ordinal, int *year, int *month, int *day)
{
    int n, n1, n4, n100, n400, leapyear, preceding;

    /* ordinal is a 1-based index, starting at 1-Jan-1.  The pattern of
     * leap years repeats exactly every 400 years.  The basic strategy is
     * to find the closest 400-year boundary at or before ordinal, then
     * work with the offset from that boundary to ordinal.  Life is much
     * clearer if we subtract 1 from ordinal first -- then the values
     * of ordinal at 400-year boundaries are exactly those divisible
     * by DI400Y:
     *
     *    D  M   Y            n              n-1
     *    -- --- ----        ----------     ----------------
     *    31 Dec -400        -DI400Y       -DI400Y -1
     *     1 Jan -399         -DI400Y +1   -DI400Y      400-year boundary
     *    ...
     *    30 Dec  000        -1             -2
     *    31 Dec  000         0             -1
     *     1 Jan  001         1              0          400-year boundary
     *     2 Jan  001         2              1
     *     3 Jan  001         3              2
     *    ...
     *    31 Dec  400         DI400Y        DI400Y -1
     *     1 Jan  401         DI400Y +1     DI400Y      400-year boundary
     */
    assert(ordinal >= 1);
    --ordinal;
    n400 = ordinal / DI400Y;
    n = ordinal % DI400Y;
    *year = n400 * 400 + 1;

    /* Now n is the (non-negative) offset, in days, from January 1 of
     * year, to the desired date.  Now compute how many 100-year cycles
     * precede n.
     * Note that it's possible for n100 to equal 4!  In that case 4 full
     * 100-year cycles precede the desired day, which implies the
     * desired day is December 31 at the end of a 400-year cycle.
     */
    n100 = n / DI100Y;
    n = n % DI100Y;

    /* Now compute how many 4-year cycles precede it. */
    n4 = n / DI4Y;
    n = n % DI4Y;

    /* And now how many single years.  Again n1 can be 4, and again
     * meaning that the desired day is December 31 at the end of the
     * 4-year cycle.
     */
    n1 = n / 365;
    n = n % 365;

    *year += n100 * 100 + n4 * 4 + n1;
    if (n1 == 4 || n100 == 4) {
        assert(n == 0);
        *year -= 1;
        *month = 12;
        *day = 31;
        return;
    }

    /* Now the year is correct, and n is the offset from January 1.  We
     * find the month via an estimate that's either exact or one too
     * large.
     */
    leapyear = n1 == 3 && (n4 != 24 || n100 == 3);
    assert(leapyear == is_leap(*year));
    *month = (n + 50) >> 5;
    preceding = (_days_before_month[*month] + (*month > 2 && leapyear));
    if (preceding > n) {
        /* estimate is too large */
        *month -= 1;
        preceding -= days_in_month(*year, *month);
    }
    n -= preceding;
    assert(0 <= n);
    assert(n < days_in_month(*year, *month));

    *day = n + 1;
}

/* year, month, day -> ordinal, considering 01-Jan-0001 as day 1. */
static int
ymd_to_ord(int year, int month, int day)
{
    return days_before_year(year) + days_before_month(year, month) + day;
}

/* Day of week, where Monday==0, ..., Sunday==6.  1/1/1 was a Monday. */
static int
weekday(int year, int month, int day)
{
    return (ymd_to_ord(year, month, day) + 6) % 7;
}

/* Ordinal of the Monday starting week 1 of the ISO year.  Week 1 is the
 * first calendar week containing a Thursday.
 */
static int
iso_week1_monday(int year)
{
    int first_day = ymd_to_ord(year, 1, 1);     /* ord of 1/1 */
    /* 0 if 1/1 is a Monday, 1 if a Tue, etc. */
    int first_weekday = (first_day + 6) % 7;
    /* ordinal of closest Monday at or before 1/1 */
    int week1_monday  = first_day - first_weekday;

    if (first_weekday > 3)      /* if 1/1 was Fri, Sat, Sun */
        week1_monday += 7;
    return week1_monday;
}

/* ---------------------------------------------------------------------------
 * Range checkers.
 */

/* Check that -MAX_DELTA_DAYS <= days <= MAX_DELTA_DAYS.  If so, return 0.
 * If not, raise OverflowError and return -1.
 */
static int
check_delta_day_range(int days)
{
    if (-MAX_DELTA_DAYS <= days && days <= MAX_DELTA_DAYS)
        return 0;
    PyErr_Format(PyExc_OverflowError,
                 "days=%d; must have magnitude <= %d",
                 days, MAX_DELTA_DAYS);
    return -1;
}

/* Check that date arguments are in range.  Return 0 if they are.  If they
 * aren't, raise ValueError and return -1.
 */
static int
check_date_args(int year, int month, int day)
{

    if (year < MINYEAR || year > MAXYEAR) {
        PyErr_Format(PyExc_ValueError, "year %i is out of range", year);
        return -1;
    }
    if (month < 1 || month > 12) {
        PyErr_SetString(PyExc_ValueError,
                        "month must be in 1..12");
        return -1;
    }
    if (day < 1 || day > days_in_month(year, month)) {
        PyErr_SetString(PyExc_ValueError,
                        "day is out of range for month");
        return -1;
    }
    return 0;
}

/* Check that time arguments are in range.  Return 0 if they are.  If they
 * aren't, raise ValueError and return -1.
 */
static int
check_time_args(int h, int m, int s, int us, int fold)
{
    if (h < 0 || h > 23) {
        PyErr_SetString(PyExc_ValueError,
                        "hour must be in 0..23");
        return -1;
    }
    if (m < 0 || m > 59) {
        PyErr_SetString(PyExc_ValueError,
                        "minute must be in 0..59");
        return -1;
    }
    if (s < 0 || s > 59) {
        PyErr_SetString(PyExc_ValueError,
                        "second must be in 0..59");
        return -1;
    }
    if (us < 0 || us > 999999) {
        PyErr_SetString(PyExc_ValueError,
                        "microsecond must be in 0..999999");
        return -1;
    }
    if (fold != 0 && fold != 1) {
        PyErr_SetString(PyExc_ValueError,
                        "fold must be either 0 or 1");
        return -1;
    }
    return 0;
}

/* ---------------------------------------------------------------------------
 * Normalization utilities.
 */

/* One step of a mixed-radix conversion.  A "hi" unit is equivalent to
 * factor "lo" units.  factor must be > 0.  If *lo is less than 0, or
 * at least factor, enough of *lo is converted into "hi" units so that
 * 0 <= *lo < factor.  The input values must be such that int overflow
 * is impossible.
 */
static void
normalize_pair(int *hi, int *lo, int factor)
{
    assert(factor > 0);
    assert(lo != hi);
    if (*lo < 0 || *lo >= factor) {
        const int num_hi = divmod(*lo, factor, lo);
        const int new_hi = *hi + num_hi;
        assert(! SIGNED_ADD_OVERFLOWED(new_hi, *hi, num_hi));
        *hi = new_hi;
    }
    assert(0 <= *lo && *lo < factor);
}

/* Fiddle days (d), seconds (s), and microseconds (us) so that
 *      0 <= *s < 24*3600
 *      0 <= *us < 1000000
 * The input values must be such that the internals don't overflow.
 * The way this routine is used, we don't get close.
 */
static void
normalize_d_s_us(int *d, int *s, int *us)
{
    if (*us < 0 || *us >= 1000000) {
        normalize_pair(s, us, 1000000);
        /* |s| can't be bigger than about
         * |original s| + |original us|/1000000 now.
         */

    }
    if (*s < 0 || *s >= 24*3600) {
        normalize_pair(d, s, 24*3600);
        /* |d| can't be bigger than about
         * |original d| +
         * (|original s| + |original us|/1000000) / (24*3600) now.
         */
    }
    assert(0 <= *s && *s < 24*3600);
    assert(0 <= *us && *us < 1000000);
}

/* Fiddle years (y), months (m), and days (d) so that
 *      1 <= *m <= 12
 *      1 <= *d <= days_in_month(*y, *m)
 * The input values must be such that the internals don't overflow.
 * The way this routine is used, we don't get close.
 */
static int
normalize_y_m_d(int *y, int *m, int *d)
{
    int dim;            /* # of days in month */

    /* In actual use, m is always the month component extracted from a
     * date/datetime object.  Therefore it is always in [1, 12] range.
     */

    assert(1 <= *m && *m <= 12);

    /* Now only day can be out of bounds (year may also be out of bounds
     * for a datetime object, but we don't care about that here).
     * If day is out of bounds, what to do is arguable, but at least the
     * method here is principled and explainable.
     */
    dim = days_in_month(*y, *m);
    if (*d < 1 || *d > dim) {
        /* Move day-1 days from the first of the month.  First try to
         * get off cheap if we're only one day out of range
         * (adjustments for timezone alone can't be worse than that).
         */
        if (*d == 0) {
            --*m;
            if (*m > 0)
                *d = days_in_month(*y, *m);
            else {
                --*y;
                *m = 12;
                *d = 31;
            }
        }
        else if (*d == dim + 1) {
            /* move forward a day */
            ++*m;
            *d = 1;
            if (*m > 12) {
                *m = 1;
                ++*y;
            }
        }
        else {
            int ordinal = ymd_to_ord(*y, *m, 1) +
                                      *d - 1;
            if (ordinal < 1 || ordinal > MAXORDINAL) {
                goto error;
            } else {
                ord_to_ymd(ordinal, y, m, d);
                return 0;
            }
        }
    }
    assert(*m > 0);
    assert(*d > 0);
    if (MINYEAR <= *y && *y <= MAXYEAR)
        return 0;
 error:
    PyErr_SetString(PyExc_OverflowError,
            "date value out of range");
    return -1;

}

/* Fiddle out-of-bounds months and days so that the result makes some kind
 * of sense.  The parameters are both inputs and outputs.  Returns < 0 on
 * failure, where failure means the adjusted year is out of bounds.
 */
static int
normalize_date(int *year, int *month, int *day)
{
    return normalize_y_m_d(year, month, day);
}

/* Force all the datetime fields into range.  The parameters are both
 * inputs and outputs.  Returns < 0 on error.
 */
static int
normalize_datetime(int *year, int *month, int *day,
                   int *hour, int *minute, int *second,
                   int *microsecond)
{
    normalize_pair(second, microsecond, 1000000);
    normalize_pair(minute, second, 60);
    normalize_pair(hour, minute, 60);
    normalize_pair(day, hour, 24);
    return normalize_date(year, month, day);
}

/* ---------------------------------------------------------------------------
 * Basic object allocation:  tp_alloc implementations.  These allocate
 * Python objects of the right size and type, and do the Python object-
 * initialization bit.  If there's not enough memory, they return NULL after
 * setting MemoryError.  All data members remain uninitialized trash.
 *
 * We abuse the tp_alloc "nitems" argument to communicate whether a tzinfo
 * member is needed.  This is ugly, imprecise, and possibly insecure.
 * tp_basicsize for the time and datetime types is set to the size of the
 * struct that has room for the tzinfo member, so subclasses in Python will
 * allocate enough space for a tzinfo member whether or not one is actually
 * needed.  That's the "ugly and imprecise" parts.  The "possibly insecure"
 * part is that PyType_GenericAlloc() (which subclasses in Python end up
 * using) just happens today to effectively ignore the nitems argument
 * when tp_itemsize is 0, which it is for these type objects.  If that
 * changes, perhaps the callers of tp_alloc slots in this file should
 * be changed to force a 0 nitems argument unless the type being allocated
 * is a base type implemented in this file (so that tp_alloc is time_alloc
 * or datetime_alloc below, which know about the nitems abuse).
 */

static PyObject *
time_alloc(PyTypeObject *type, Py_ssize_t aware)
{
    PyObject *self;

    self = (PyObject *)
        PyObject_MALLOC(aware ?
                        sizeof(PyDateTime_Time) :
                sizeof(_PyDateTime_BaseTime));
    if (self == NULL)
        return (PyObject *)PyErr_NoMemory();
    (void)PyObject_INIT(self, type);
    return self;
}

static PyObject *
datetime_alloc(PyTypeObject *type, Py_ssize_t aware)
{
    PyObject *self;

    self = (PyObject *)
        PyObject_MALLOC(aware ?
                        sizeof(PyDateTime_DateTime) :
                sizeof(_PyDateTime_BaseDateTime));
    if (self == NULL)
        return (PyObject *)PyErr_NoMemory();
    (void)PyObject_INIT(self, type);
    return self;
}

/* ---------------------------------------------------------------------------
 * Helpers for setting object fields.  These work on pointers to the
 * appropriate base class.
 */

/* For date and datetime. */
static void
set_date_fields(PyDateTime_Date *self, int y, int m, int d)
{
    self->hashcode = -1;
    SET_YEAR(self, y);
    SET_MONTH(self, m);
    SET_DAY(self, d);
}

/* ---------------------------------------------------------------------------
 * Create various objects, mostly without range checking.
 */

/* Create a date instance with no range checking. */
static PyObject *
new_date_ex(int year, int month, int day, PyTypeObject *type)
{
    PyDateTime_Date *self;

    if (check_date_args(year, month, day) < 0) {
        return NULL;
    }

    self = (PyDateTime_Date *) (type->tp_alloc(type, 0));
    if (self != NULL)
        set_date_fields(self, year, month, day);
    return (PyObject *) self;
}

#define new_date(year, month, day) \
    new_date_ex(year, month, day, &PyDateTime_DateType)

/* Create a datetime instance with no range checking. */
static PyObject *
new_datetime_ex2(int year, int month, int day, int hour, int minute,
                 int second, int usecond, PyObject *tzinfo, int fold, PyTypeObject *type)
{
    PyDateTime_DateTime *self;
    char aware = tzinfo != Py_None;

    if (check_date_args(year, month, day) < 0) {
        return NULL;
    }
    if (check_time_args(hour, minute, second, usecond, fold) < 0) {
        return NULL;
    }
    if (check_tzinfo_subclass(tzinfo) < 0) {
        return NULL;
    }

    self = (PyDateTime_DateTime *) (type->tp_alloc(type, aware));
    if (self != NULL) {
        self->hastzinfo = aware;
        set_date_fields((PyDateTime_Date *)self, year, month, day);
        DATE_SET_HOUR(self, hour);
        DATE_SET_MINUTE(self, minute);
        DATE_SET_SECOND(self, second);
        DATE_SET_MICROSECOND(self, usecond);
        if (aware) {
            Py_INCREF(tzinfo);
            self->tzinfo = tzinfo;
        }
        DATE_SET_FOLD(self, fold);
    }
    return (PyObject *)self;
}

static PyObject *
new_datetime_ex(int year, int month, int day, int hour, int minute,
                int second, int usecond, PyObject *tzinfo, PyTypeObject *type)
{
    return new_datetime_ex2(year, month, day, hour, minute, second, usecond,
                            tzinfo, 0, type);
}

#define new_datetime(y, m, d, hh, mm, ss, us, tzinfo, fold) \
    new_datetime_ex2(y, m, d, hh, mm, ss, us, tzinfo, fold, \
                    &PyDateTime_DateTimeType)

/* Create a time instance with no range checking. */
static PyObject *
new_time_ex2(int hour, int minute, int second, int usecond,
             PyObject *tzinfo, int fold, PyTypeObject *type)
{
    PyDateTime_Time *self;
    char aware = tzinfo != Py_None;

    if (check_time_args(hour, minute, second, usecond, fold) < 0) {
        return NULL;
    }
    if (check_tzinfo_subclass(tzinfo) < 0) {
        return NULL;
    }

    self = (PyDateTime_Time *) (type->tp_alloc(type, aware));
    if (self != NULL) {
        self->hastzinfo = aware;
        self->hashcode = -1;
        TIME_SET_HOUR(self, hour);
        TIME_SET_MINUTE(self, minute);
        TIME_SET_SECOND(self, second);
        TIME_SET_MICROSECOND(self, usecond);
        if (aware) {
            Py_INCREF(tzinfo);
            self->tzinfo = tzinfo;
        }
        TIME_SET_FOLD(self, fold);
    }
    return (PyObject *)self;
}

static PyObject *
new_time_ex(int hour, int minute, int second, int usecond,
            PyObject *tzinfo, PyTypeObject *type)
{
    return new_time_ex2(hour, minute, second, usecond, tzinfo, 0, type);
}

#define new_time(hh, mm, ss, us, tzinfo, fold)                       \
    new_time_ex2(hh, mm, ss, us, tzinfo, fold, &PyDateTime_TimeType)

/* Create a timedelta instance.  Normalize the members iff normalize is
 * true.  Passing false is a speed optimization, if you know for sure
 * that seconds and microseconds are already in their proper ranges.  In any
 * case, raises OverflowError and returns NULL if the normalized days is out
 * of range).
 */
static PyObject *
new_delta_ex(int days, int seconds, int microseconds, int normalize,
             PyTypeObject *type)
{
    PyDateTime_Delta *self;

    if (normalize)
        normalize_d_s_us(&days, &seconds, &microseconds);
    assert(0 <= seconds && seconds < 24*3600);
    assert(0 <= microseconds && microseconds < 1000000);

    if (check_delta_day_range(days) < 0)
        return NULL;

    self = (PyDateTime_Delta *) (type->tp_alloc(type, 0));
    if (self != NULL) {
        self->hashcode = -1;
        SET_TD_DAYS(self, days);
        SET_TD_SECONDS(self, seconds);
        SET_TD_MICROSECONDS(self, microseconds);
    }
    return (PyObject *) self;
}

#define new_delta(d, s, us, normalize)  \
    new_delta_ex(d, s, us, normalize, &PyDateTime_DeltaType)


typedef struct
{
    PyObject_HEAD
    PyObject *offset;
    PyObject *name;
} PyDateTime_TimeZone;

/* The interned UTC timezone instance */
static PyObject *PyDateTime_TimeZone_UTC;
/* The interned Epoch datetime instance */
static PyObject *PyDateTime_Epoch;

/* Create new timezone instance checking offset range.  This
   function does not check the name argument.  Caller must assure
   that offset is a timedelta instance and name is either NULL
   or a unicode object. */
static PyObject *
create_timezone(PyObject *offset, PyObject *name)
{
    PyDateTime_TimeZone *self;
    PyTypeObject *type = &PyDateTime_TimeZoneType;

    assert(offset != NULL);
    assert(PyDelta_Check(offset));
    assert(name == NULL || PyUnicode_Check(name));

    self = (PyDateTime_TimeZone *)(type->tp_alloc(type, 0));
    if (self == NULL) {
        return NULL;
    }
    Py_INCREF(offset);
    self->offset = offset;
    Py_XINCREF(name);
    self->name = name;
    return (PyObject *)self;
}

static int delta_bool(PyDateTime_Delta *self);

static PyObject *
new_timezone(PyObject *offset, PyObject *name)
{
    assert(offset != NULL);
    assert(PyDelta_Check(offset));
    assert(name == NULL || PyUnicode_Check(name));

    if (name == NULL && delta_bool((PyDateTime_Delta *)offset) == 0) {
        Py_INCREF(PyDateTime_TimeZone_UTC);
        return PyDateTime_TimeZone_UTC;
    }
    if (GET_TD_MICROSECONDS(offset) != 0 || GET_TD_SECONDS(offset) % 60 != 0) {
        PyErr_Format(PyExc_ValueError, "offset must be a timedelta"
                     " representing a whole number of minutes,"
                     " not %R.", offset);
        return NULL;
    }
    if ((GET_TD_DAYS(offset) == -1 && GET_TD_SECONDS(offset) == 0) ||
        GET_TD_DAYS(offset) < -1 || GET_TD_DAYS(offset) >= 1) {
        PyErr_Format(PyExc_ValueError, "offset must be a timedelta"
                     " strictly between -timedelta(hours=24) and"
                     " timedelta(hours=24),"
                     " not %R.", offset);
        return NULL;
    }

    return create_timezone(offset, name);
}

/* ---------------------------------------------------------------------------
 * tzinfo helpers.
 */

/* Ensure that p is None or of a tzinfo subclass.  Return 0 if OK; if not
 * raise TypeError and return -1.
 */
static int
check_tzinfo_subclass(PyObject *p)
{
    if (p == Py_None || PyTZInfo_Check(p))
        return 0;
    PyErr_Format(PyExc_TypeError,
                 "tzinfo argument must be None or of a tzinfo subclass, "
                 "not type '%s'",
                 Py_TYPE(p)->tp_name);
    return -1;
}

/* If self has a tzinfo member, return a BORROWED reference to it.  Else
 * return NULL, which is NOT AN ERROR.  There are no error returns here,
 * and the caller must not decref the result.
 */
static PyObject *
get_tzinfo_member(PyObject *self)
{
    PyObject *tzinfo = NULL;

    if (PyDateTime_Check(self) && HASTZINFO(self))
        tzinfo = ((PyDateTime_DateTime *)self)->tzinfo;
    else if (PyTime_Check(self) && HASTZINFO(self))
        tzinfo = ((PyDateTime_Time *)self)->tzinfo;

    return tzinfo;
}

/* Call getattr(tzinfo, name)(tzinfoarg), and check the result.  tzinfo must
 * be an instance of the tzinfo class.  If the method returns None, this
 * returns None.  If the method doesn't return None or timedelta, TypeError is
 * raised and this returns NULL.  If it returns a timedelta and the value is
 * out of range or isn't a whole number of minutes, ValueError is raised and
 * this returns NULL.  Else result is returned.
 */
static PyObject *
call_tzinfo_method(PyObject *tzinfo, const char *name, PyObject *tzinfoarg)
{
    PyObject *offset;

    assert(tzinfo != NULL);
    assert(PyTZInfo_Check(tzinfo) || tzinfo == Py_None);
    assert(tzinfoarg != NULL);

    if (tzinfo == Py_None)
        Py_RETURN_NONE;
    offset = PyObject_CallMethod(tzinfo, name, "O", tzinfoarg);
    if (offset == Py_None || offset == NULL)
        return offset;
    if (PyDelta_Check(offset)) {
        if (GET_TD_MICROSECONDS(offset) != 0) {
            Py_DECREF(offset);
            PyErr_Format(PyExc_ValueError, "offset must be a timedelta"
                         " representing a whole number of seconds");
            return NULL;
        }
        if ((GET_TD_DAYS(offset) == -1 && GET_TD_SECONDS(offset) == 0) ||
            GET_TD_DAYS(offset) < -1 || GET_TD_DAYS(offset) >= 1) {
            Py_DECREF(offset);
            PyErr_Format(PyExc_ValueError, "offset must be a timedelta"
                         " strictly between -timedelta(hours=24) and"
                         " timedelta(hours=24).");
            return NULL;
        }
    }
    else {
        PyErr_Format(PyExc_TypeError,
                     "tzinfo.%s() must return None or "
                     "timedelta, not '%.200s'",
                     name, Py_TYPE(offset)->tp_name);
        Py_DECREF(offset);
        return NULL;
    }

    return offset;
}

/* Call tzinfo.utcoffset(tzinfoarg), and extract an integer from the
 * result.  tzinfo must be an instance of the tzinfo class.  If utcoffset()
 * returns None, call_utcoffset returns 0 and sets *none to 1.  If uctoffset()
 * doesn't return None or timedelta, TypeError is raised and this returns -1.
 * If utcoffset() returns an invalid timedelta (out of range, or not a whole
 * # of minutes), ValueError is raised and this returns -1.  Else *none is
 * set to 0 and the offset is returned (as int # of minutes east of UTC).
 */
static PyObject *
call_utcoffset(PyObject *tzinfo, PyObject *tzinfoarg)
{
    return call_tzinfo_method(tzinfo, "utcoffset", tzinfoarg);
}

/* Call tzinfo.dst(tzinfoarg), and extract an integer from the
 * result.  tzinfo must be an instance of the tzinfo class.  If dst()
 * returns None, call_dst returns 0 and sets *none to 1.  If dst()
 & doesn't return None or timedelta, TypeError is raised and this
 * returns -1.  If dst() returns an invalid timedelta for a UTC offset,
 * ValueError is raised and this returns -1.  Else *none is set to 0 and
 * the offset is returned (as an int # of minutes east of UTC).
 */
static PyObject *
call_dst(PyObject *tzinfo, PyObject *tzinfoarg)
{
    return call_tzinfo_method(tzinfo, "dst", tzinfoarg);
}

/* Call tzinfo.tzname(tzinfoarg), and return the result.  tzinfo must be
 * an instance of the tzinfo class or None.  If tzinfo isn't None, and
 * tzname() doesn't return None or a string, TypeError is raised and this
 * returns NULL.  If the result is a string, we ensure it is a Unicode
 * string.
 */
static PyObject *
call_tzname(PyObject *tzinfo, PyObject *tzinfoarg)
{
    PyObject *result;
    _Py_IDENTIFIER(tzname);

    assert(tzinfo != NULL);
    assert(check_tzinfo_subclass(tzinfo) >= 0);
    assert(tzinfoarg != NULL);

    if (tzinfo == Py_None)
        Py_RETURN_NONE;

    result = _PyObject_CallMethodIdObjArgs(tzinfo, &PyId_tzname,
                                           tzinfoarg, NULL);

    if (result == NULL || result == Py_None)
        return result;

    if (!PyUnicode_Check(result)) {
        PyErr_Format(PyExc_TypeError, "tzinfo.tzname() must "
                     "return None or a string, not '%s'",
                     Py_TYPE(result)->tp_name);
        Py_DECREF(result);
        result = NULL;
    }

    return result;
}

/* repr is like "someclass(arg1, arg2)".  If tzinfo isn't None,
 * stuff
 *     ", tzinfo=" + repr(tzinfo)
 * before the closing ")".
 */
static PyObject *
append_keyword_tzinfo(PyObject *repr, PyObject *tzinfo)
{
    PyObject *temp;

    assert(PyUnicode_Check(repr));
    assert(tzinfo);
    if (tzinfo == Py_None)
        return repr;
    /* Get rid of the trailing ')'. */
    assert(PyUnicode_READ_CHAR(repr, PyUnicode_GET_LENGTH(repr)-1) == ')');
    temp = PyUnicode_Substring(repr, 0, PyUnicode_GET_LENGTH(repr) - 1);
    Py_DECREF(repr);
    if (temp == NULL)
        return NULL;
    repr = PyUnicode_FromFormat("%U, tzinfo=%R)", temp, tzinfo);
    Py_DECREF(temp);
    return repr;
}

/* repr is like "someclass(arg1, arg2)".  If fold isn't 0,
 * stuff
 *     ", fold=" + repr(tzinfo)
 * before the closing ")".
 */
static PyObject *
append_keyword_fold(PyObject *repr, int fold)
{
    PyObject *temp;

    assert(PyUnicode_Check(repr));
    if (fold == 0)
        return repr;
    /* Get rid of the trailing ')'. */
    assert(PyUnicode_READ_CHAR(repr, PyUnicode_GET_LENGTH(repr)-1) == ')');
    temp = PyUnicode_Substring(repr, 0, PyUnicode_GET_LENGTH(repr) - 1);
    Py_DECREF(repr);
    if (temp == NULL)
        return NULL;
    repr = PyUnicode_FromFormat("%U, fold=%d)", temp, fold);
    Py_DECREF(temp);
    return repr;
}

/* ---------------------------------------------------------------------------
 * String format helpers.
 */

static PyObject *
format_ctime(PyDateTime_Date *date, int hours, int minutes, int seconds)
{
    static const char * const DayNames[] = {
        "Mon", "Tue", "Wed", "Thu", "Fri", "Sat", "Sun"
    };
    static const char * const MonthNames[] = {
        "Jan", "Feb", "Mar", "Apr", "May", "Jun",
        "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"
    };

    int wday = weekday(GET_YEAR(date), GET_MONTH(date), GET_DAY(date));

    return PyUnicode_FromFormat("%s %s %2d %02d:%02d:%02d %04d",
                                DayNames[wday], MonthNames[GET_MONTH(date)-1],
                                GET_DAY(date), hours, minutes, seconds,
                                GET_YEAR(date));
}

static PyObject *delta_negative(PyDateTime_Delta *self);

/* Add an hours & minutes UTC offset string to buf.  buf has no more than
 * buflen bytes remaining.  The UTC offset is gotten by calling
 * tzinfo.uctoffset(tzinfoarg).  If that returns None, \0 is stored into
 * *buf, and that's all.  Else the returned value is checked for sanity (an
 * integer in range), and if that's OK it's converted to an hours & minutes
 * string of the form
 *   sign HH sep MM
 * Returns 0 if everything is OK.  If the return value from utcoffset() is
 * bogus, an appropriate exception is set and -1 is returned.
 */
static int
format_utcoffset(char *buf, size_t buflen, const char *sep,
                PyObject *tzinfo, PyObject *tzinfoarg)
{
    PyObject *offset;
    int hours, minutes, seconds;
    char sign;

    assert(buflen >= 1);

    offset = call_utcoffset(tzinfo, tzinfoarg);
    if (offset == NULL)
        return -1;
    if (offset == Py_None) {
        Py_DECREF(offset);
        *buf = '\0';
        return 0;
    }
    /* Offset is normalized, so it is negative if days < 0 */
    if (GET_TD_DAYS(offset) < 0) {
        sign = '-';
        Py_SETREF(offset, delta_negative((PyDateTime_Delta *)offset));
        if (offset == NULL)
            return -1;
    }
    else {
        sign = '+';
    }
    /* Offset is not negative here. */
    seconds = GET_TD_SECONDS(offset);
    Py_DECREF(offset);
    minutes = divmod(seconds, 60, &seconds);
    hours = divmod(minutes, 60, &minutes);
    if (seconds == 0)
        PyOS_snprintf(buf, buflen, "%c%02d%s%02d", sign, hours, sep, minutes);
    else
        PyOS_snprintf(buf, buflen, "%c%02d%s%02d%s%02d", sign, hours,
                      sep, minutes, sep, seconds);
    return 0;
}

static PyObject *
make_Zreplacement(PyObject *object, PyObject *tzinfoarg)
{
    PyObject *temp;
    PyObject *tzinfo = get_tzinfo_member(object);
    PyObject *Zreplacement = PyUnicode_FromStringAndSize(NULL, 0);
    _Py_IDENTIFIER(replace);

    if (Zreplacement == NULL)
        return NULL;
    if (tzinfo == Py_None || tzinfo == NULL)
        return Zreplacement;

    assert(tzinfoarg != NULL);
    temp = call_tzname(tzinfo, tzinfoarg);
    if (temp == NULL)
        goto Error;
    if (temp == Py_None) {
        Py_DECREF(temp);
        return Zreplacement;
    }

    assert(PyUnicode_Check(temp));
    /* Since the tzname is getting stuffed into the
     * format, we have to double any % signs so that
     * strftime doesn't treat them as format codes.
     */
    Py_DECREF(Zreplacement);
    Zreplacement = _PyObject_CallMethodId(temp, &PyId_replace, "ss", "%", "%%");
    Py_DECREF(temp);
    if (Zreplacement == NULL)
        return NULL;
    if (!PyUnicode_Check(Zreplacement)) {
        PyErr_SetString(PyExc_TypeError,
                        "tzname.replace() did not return a string");
        goto Error;
    }
    return Zreplacement;

  Error:
    Py_DECREF(Zreplacement);
    return NULL;
}

static PyObject *
make_freplacement(PyObject *object)
{
    char freplacement[64];
    if (PyTime_Check(object))
        sprintf(freplacement, "%06d", TIME_GET_MICROSECOND(object));
    else if (PyDateTime_Check(object))
        sprintf(freplacement, "%06d", DATE_GET_MICROSECOND(object));
    else
        sprintf(freplacement, "%06d", 0);

    return PyBytes_FromStringAndSize(freplacement, strlen(freplacement));
}

/* I sure don't want to reproduce the strftime code from the time module,
 * so this imports the module and calls it.  All the hair is due to
 * giving special meanings to the %z, %Z and %f format codes via a
 * preprocessing step on the format string.
 * tzinfoarg is the argument to pass to the object's tzinfo method, if
 * needed.
 */
static PyObject *
wrap_strftime(PyObject *object, PyObject *format, PyObject *timetuple,
              PyObject *tzinfoarg)
{
    PyObject *result = NULL;            /* guilty until proved innocent */

    PyObject *zreplacement = NULL;      /* py string, replacement for %z */
    PyObject *Zreplacement = NULL;      /* py string, replacement for %Z */
    PyObject *freplacement = NULL;      /* py string, replacement for %f */

    const char *pin;            /* pointer to next char in input format */
    Py_ssize_t flen;            /* length of input format */
    char ch;                    /* next char in input format */

    PyObject *newfmt = NULL;            /* py string, the output format */
    char *pnew;         /* pointer to available byte in output format */
    size_t totalnew;            /* number bytes total in output format buffer,
                               exclusive of trailing \0 */
    size_t usednew;     /* number bytes used so far in output format buffer */

    const char *ptoappend;      /* ptr to string to append to output buffer */
    Py_ssize_t ntoappend;       /* # of bytes to append to output buffer */

    assert(object && format && timetuple);
    assert(PyUnicode_Check(format));
    /* Convert the input format to a C string and size */
    pin = PyUnicode_AsUTF8AndSize(format, &flen);
    if (!pin)
        return NULL;

    /* Scan the input format, looking for %z/%Z/%f escapes, building
     * a new format.  Since computing the replacements for those codes
     * is expensive, don't unless they're actually used.
     */
    if (flen > INT_MAX - 1) {
        PyErr_NoMemory();
        goto Done;
    }

    totalnew = flen + 1;        /* realistic if no %z/%Z */
    newfmt = PyBytes_FromStringAndSize(NULL, totalnew);
    if (newfmt == NULL) goto Done;
    pnew = PyBytes_AsString(newfmt);
    usednew = 0;

    while ((ch = *pin++) != '\0') {
        if (ch != '%') {
            ptoappend = pin - 1;
            ntoappend = 1;
        }
        else if ((ch = *pin++) == '\0') {
            /* There's a lone trailing %; doesn't make sense. */
            PyErr_SetString(PyExc_ValueError, "strftime format "
                            "ends with raw %");
            goto Done;
        }
        /* A % has been seen and ch is the character after it. */
        else if (ch == 'z') {
            if (zreplacement == NULL) {
                /* format utcoffset */
                char buf[100];
                PyObject *tzinfo = get_tzinfo_member(object);
                zreplacement = PyBytes_FromStringAndSize("", 0);
                if (zreplacement == NULL) goto Done;
                if (tzinfo != Py_None && tzinfo != NULL) {
                    assert(tzinfoarg != NULL);
                    if (format_utcoffset(buf,
                                         sizeof(buf),
                                         "",
                                         tzinfo,
                                         tzinfoarg) < 0)
                        goto Done;
                    Py_DECREF(zreplacement);
                    zreplacement =
                      PyBytes_FromStringAndSize(buf,
                                               strlen(buf));
                    if (zreplacement == NULL)
                        goto Done;
                }
            }
            assert(zreplacement != NULL);
            ptoappend = PyBytes_AS_STRING(zreplacement);
            ntoappend = PyBytes_GET_SIZE(zreplacement);
        }
        else if (ch == 'Z') {
            /* format tzname */
            if (Zreplacement == NULL) {
                Zreplacement = make_Zreplacement(object,
                                                 tzinfoarg);
                if (Zreplacement == NULL)
                    goto Done;
            }
            assert(Zreplacement != NULL);
            assert(PyUnicode_Check(Zreplacement));
            ptoappend = PyUnicode_AsUTF8AndSize(Zreplacement,
                                                  &ntoappend);
            if (ptoappend == NULL)
                goto Done;
        }
        else if (ch == 'f') {
            /* format microseconds */
            if (freplacement == NULL) {
                freplacement = make_freplacement(object);
                if (freplacement == NULL)
                    goto Done;
            }
            assert(freplacement != NULL);
            assert(PyBytes_Check(freplacement));
            ptoappend = PyBytes_AS_STRING(freplacement);
            ntoappend = PyBytes_GET_SIZE(freplacement);
        }
        else {
            /* percent followed by neither z nor Z */
            ptoappend = pin - 2;
            ntoappend = 2;
        }

        /* Append the ntoappend chars starting at ptoappend to
         * the new format.
         */
        if (ntoappend == 0)
            continue;
        assert(ptoappend != NULL);
        assert(ntoappend > 0);
        while (usednew + ntoappend > totalnew) {
            if (totalnew > (PY_SSIZE_T_MAX >> 1)) { /* overflow */
                PyErr_NoMemory();
                goto Done;
            }
            totalnew <<= 1;
            if (_PyBytes_Resize(&newfmt, totalnew) < 0)
                goto Done;
            pnew = PyBytes_AsString(newfmt) + usednew;
        }
        memcpy(pnew, ptoappend, ntoappend);
        pnew += ntoappend;
        usednew += ntoappend;
        assert(usednew <= totalnew);
    }  /* end while() */

    if (_PyBytes_Resize(&newfmt, usednew) < 0)
        goto Done;
    {
        PyObject *format;
        PyObject *time = PyImport_ImportModuleNoBlock("time");

        if (time == NULL)
            goto Done;
        format = PyUnicode_FromString(PyBytes_AS_STRING(newfmt));
        if (format != NULL) {
            result = _PyObject_CallMethodIdObjArgs(time, &PyId_strftime,
                                                   format, timetuple, NULL);
            Py_DECREF(format);
        }
        Py_DECREF(time);
    }
 Done:
    Py_XDECREF(freplacement);
    Py_XDECREF(zreplacement);
    Py_XDECREF(Zreplacement);
    Py_XDECREF(newfmt);
    return result;
}

/* ---------------------------------------------------------------------------
 * Wrap functions from the time module.  These aren't directly available
 * from C.  Perhaps they should be.
 */

/* Call time.time() and return its result (a Python float). */
static PyObject *
time_time(void)
{
    PyObject *result = NULL;
    PyObject *time = PyImport_ImportModuleNoBlock("time");

    if (time != NULL) {
        _Py_IDENTIFIER(time);

        result = _PyObject_CallMethodId(time, &PyId_time, NULL);
        Py_DECREF(time);
    }
    return result;
}

/* Build a time.struct_time.  The weekday and day number are automatically
 * computed from the y,m,d args.
 */
static PyObject *
build_struct_time(int y, int m, int d, int hh, int mm, int ss, int dstflag)
{
    PyObject *time;
    PyObject *result;
    _Py_IDENTIFIER(struct_time);
    PyObject *args;


    time = PyImport_ImportModuleNoBlock("time");
    if (time == NULL) {
        return NULL;
    }

    args = Py_BuildValue("iiiiiiiii",
                         y, m, d,
                         hh, mm, ss,
                         weekday(y, m, d),
                         days_before_month(y, m) + d,
                         dstflag);
    if (args == NULL) {
        Py_DECREF(time);
        return NULL;
    }

    result = _PyObject_CallMethodIdObjArgs(time, &PyId_struct_time,
                                           args, NULL);
    Py_DECREF(time);
    Py_DECREF(args);
    return result;
}

/* ---------------------------------------------------------------------------
 * Miscellaneous helpers.
 */

/* For various reasons, we need to use tp_richcompare instead of tp_reserved.
 * The comparisons here all most naturally compute a cmp()-like result.
 * This little helper turns that into a bool result for rich comparisons.
 */
static PyObject *
diff_to_bool(int diff, int op)
{
    PyObject *result;
    int istrue;

    switch (op) {
        case Py_EQ: istrue = diff == 0; break;
        case Py_NE: istrue = diff != 0; break;
        case Py_LE: istrue = diff <= 0; break;
        case Py_GE: istrue = diff >= 0; break;
        case Py_LT: istrue = diff < 0; break;
        case Py_GT: istrue = diff > 0; break;
        default:
            assert(! "op unknown");
            istrue = 0; /* To shut up compiler */
    }
    result = istrue ? Py_True : Py_False;
    Py_INCREF(result);
    return result;
}

/* Raises a "can't compare" TypeError and returns NULL. */
static PyObject *
cmperror(PyObject *a, PyObject *b)
{
    PyErr_Format(PyExc_TypeError,
                 "can't compare %s to %s",
                 Py_TYPE(a)->tp_name, Py_TYPE(b)->tp_name);
    return NULL;
}

/* ---------------------------------------------------------------------------
 * Cached Python objects; these are set by the module init function.
 */

/* Conversion factors. */
static PyObject *one = NULL;      /* 1 */
static PyObject *us_per_ms = NULL;      /* 1000 */
static PyObject *us_per_second = NULL;  /* 1000000 */
static PyObject *us_per_minute = NULL;  /* 1e6 * 60 as Python int */
static PyObject *us_per_hour = NULL;    /* 1e6 * 3600 as Python int */
static PyObject *us_per_day = NULL;     /* 1e6 * 3600 * 24 as Python int */
static PyObject *us_per_week = NULL;    /* 1e6*3600*24*7 as Python int */
static PyObject *seconds_per_day = NULL; /* 3600*24 as Python int */

/* ---------------------------------------------------------------------------
 * Class implementations.
 */

/*
 * PyDateTime_Delta implementation.
 */

/* Convert a timedelta to a number of us,
 *      (24*3600*self.days + self.seconds)*1000000 + self.microseconds
 * as a Python int.
 * Doing mixed-radix arithmetic by hand instead is excruciating in C,
 * due to ubiquitous overflow possibilities.
 */
static PyObject *
delta_to_microseconds(PyDateTime_Delta *self)
{
    PyObject *x1 = NULL;
    PyObject *x2 = NULL;
    PyObject *x3 = NULL;
    PyObject *result = NULL;

    x1 = PyLong_FromLong(GET_TD_DAYS(self));
    if (x1 == NULL)
        goto Done;
    x2 = PyNumber_Multiply(x1, seconds_per_day);        /* days in seconds */
    if (x2 == NULL)
        goto Done;
    Py_DECREF(x1);
    x1 = NULL;

    /* x2 has days in seconds */
    x1 = PyLong_FromLong(GET_TD_SECONDS(self));         /* seconds */
    if (x1 == NULL)
        goto Done;
    x3 = PyNumber_Add(x1, x2);          /* days and seconds in seconds */
    if (x3 == NULL)
        goto Done;
    Py_DECREF(x1);
    Py_DECREF(x2);
    /* x1 = */ x2 = NULL;

    /* x3 has days+seconds in seconds */
    x1 = PyNumber_Multiply(x3, us_per_second);          /* us */
    if (x1 == NULL)
        goto Done;
    Py_DECREF(x3);
    x3 = NULL;

    /* x1 has days+seconds in us */
    x2 = PyLong_FromLong(GET_TD_MICROSECONDS(self));
    if (x2 == NULL)
        goto Done;
    result = PyNumber_Add(x1, x2);

Done:
    Py_XDECREF(x1);
    Py_XDECREF(x2);
    Py_XDECREF(x3);
    return result;
}

/* Convert a number of us (as a Python int) to a timedelta.
 */
static PyObject *
microseconds_to_delta_ex(PyObject *pyus, PyTypeObject *type)
{
    int us;
    int s;
    int d;
    long temp;

    PyObject *tuple = NULL;
    PyObject *num = NULL;
    PyObject *result = NULL;

    tuple = PyNumber_Divmod(pyus, us_per_second);
    if (tuple == NULL)
        goto Done;

    num = PyTuple_GetItem(tuple, 1);            /* us */
    if (num == NULL)
        goto Done;
    temp = PyLong_AsLong(num);
    num = NULL;
    if (temp == -1 && PyErr_Occurred())
        goto Done;
    assert(0 <= temp && temp < 1000000);
    us = (int)temp;
    if (us < 0) {
        /* The divisor was positive, so this must be an error. */
        assert(PyErr_Occurred());
        goto Done;
    }

    num = PyTuple_GetItem(tuple, 0);            /* leftover seconds */
    if (num == NULL)
        goto Done;
    Py_INCREF(num);
    Py_DECREF(tuple);

    tuple = PyNumber_Divmod(num, seconds_per_day);
    if (tuple == NULL)
        goto Done;
    Py_DECREF(num);

    num = PyTuple_GetItem(tuple, 1);            /* seconds */
    if (num == NULL)
        goto Done;
    temp = PyLong_AsLong(num);
    num = NULL;
    if (temp == -1 && PyErr_Occurred())
        goto Done;
    assert(0 <= temp && temp < 24*3600);
    s = (int)temp;

    if (s < 0) {
        /* The divisor was positive, so this must be an error. */
        assert(PyErr_Occurred());
        goto Done;
    }

    num = PyTuple_GetItem(tuple, 0);            /* leftover days */
    if (num == NULL)
        goto Done;
    Py_INCREF(num);
    temp = PyLong_AsLong(num);
    if (temp == -1 && PyErr_Occurred())
        goto Done;
    d = (int)temp;
    if ((long)d != temp) {
        PyErr_SetString(PyExc_OverflowError, "normalized days too "
                        "large to fit in a C int");
        goto Done;
    }
    result = new_delta_ex(d, s, us, 0, type);

Done:
    Py_XDECREF(tuple);
    Py_XDECREF(num);
    return result;
}

#define microseconds_to_delta(pymicros) \
    microseconds_to_delta_ex(pymicros, &PyDateTime_DeltaType)

static PyObject *
multiply_int_timedelta(PyObject *intobj, PyDateTime_Delta *delta)
{
    PyObject *pyus_in;
    PyObject *pyus_out;
    PyObject *result;

    pyus_in = delta_to_microseconds(delta);
    if (pyus_in == NULL)
        return NULL;

    pyus_out = PyNumber_Multiply(pyus_in, intobj);
    Py_DECREF(pyus_in);
    if (pyus_out == NULL)
        return NULL;

    result = microseconds_to_delta(pyus_out);
    Py_DECREF(pyus_out);
    return result;
}

static PyObject *
multiply_float_timedelta(PyObject *floatobj, PyDateTime_Delta *delta)
{
    PyObject *result = NULL;
    PyObject *pyus_in = NULL, *temp, *pyus_out;
    PyObject *ratio = NULL;

    pyus_in = delta_to_microseconds(delta);
    if (pyus_in == NULL)
        return NULL;
    ratio = _PyObject_CallMethodId(floatobj, &PyId_as_integer_ratio, NULL);
    if (ratio == NULL)
        goto error;
    temp = PyNumber_Multiply(pyus_in, PyTuple_GET_ITEM(ratio, 0));
    Py_DECREF(pyus_in);
    pyus_in = NULL;
    if (temp == NULL)
        goto error;
    pyus_out = divide_nearest(temp, PyTuple_GET_ITEM(ratio, 1));
    Py_DECREF(temp);
    if (pyus_out == NULL)
        goto error;
    result = microseconds_to_delta(pyus_out);
    Py_DECREF(pyus_out);
 error:
    Py_XDECREF(pyus_in);
    Py_XDECREF(ratio);

    return result;
}

static PyObject *
divide_timedelta_int(PyDateTime_Delta *delta, PyObject *intobj)
{
    PyObject *pyus_in;
    PyObject *pyus_out;
    PyObject *result;

    pyus_in = delta_to_microseconds(delta);
    if (pyus_in == NULL)
        return NULL;

    pyus_out = PyNumber_FloorDivide(pyus_in, intobj);
    Py_DECREF(pyus_in);
    if (pyus_out == NULL)
        return NULL;

    result = microseconds_to_delta(pyus_out);
    Py_DECREF(pyus_out);
    return result;
}

static PyObject *
divide_timedelta_timedelta(PyDateTime_Delta *left, PyDateTime_Delta *right)
{
    PyObject *pyus_left;
    PyObject *pyus_right;
    PyObject *result;

    pyus_left = delta_to_microseconds(left);
    if (pyus_left == NULL)
        return NULL;

    pyus_right = delta_to_microseconds(right);
    if (pyus_right == NULL)     {
        Py_DECREF(pyus_left);
        return NULL;
    }

    result = PyNumber_FloorDivide(pyus_left, pyus_right);
    Py_DECREF(pyus_left);
    Py_DECREF(pyus_right);
    return result;
}

static PyObject *
truedivide_timedelta_timedelta(PyDateTime_Delta *left, PyDateTime_Delta *right)
{
    PyObject *pyus_left;
    PyObject *pyus_right;
    PyObject *result;

    pyus_left = delta_to_microseconds(left);
    if (pyus_left == NULL)
        return NULL;

    pyus_right = delta_to_microseconds(right);
    if (pyus_right == NULL)     {
        Py_DECREF(pyus_left);
        return NULL;
    }

    result = PyNumber_TrueDivide(pyus_left, pyus_right);
    Py_DECREF(pyus_left);
    Py_DECREF(pyus_right);
    return result;
}

static PyObject *
truedivide_timedelta_float(PyDateTime_Delta *delta, PyObject *f)
{
    PyObject *result = NULL;
    PyObject *pyus_in = NULL, *temp, *pyus_out;
    PyObject *ratio = NULL;

    pyus_in = delta_to_microseconds(delta);
    if (pyus_in == NULL)
        return NULL;
    ratio = _PyObject_CallMethodId(f, &PyId_as_integer_ratio, NULL);
    if (ratio == NULL)
        goto error;
    temp = PyNumber_Multiply(pyus_in, PyTuple_GET_ITEM(ratio, 1));
    Py_DECREF(pyus_in);
    pyus_in = NULL;
    if (temp == NULL)
        goto error;
    pyus_out = divide_nearest(temp, PyTuple_GET_ITEM(ratio, 0));
    Py_DECREF(temp);
    if (pyus_out == NULL)
        goto error;
    result = microseconds_to_delta(pyus_out);
    Py_DECREF(pyus_out);
 error:
    Py_XDECREF(pyus_in);
    Py_XDECREF(ratio);

    return result;
}

static PyObject *
truedivide_timedelta_int(PyDateTime_Delta *delta, PyObject *i)
{
    PyObject *result;
    PyObject *pyus_in, *pyus_out;
    pyus_in = delta_to_microseconds(delta);
    if (pyus_in == NULL)
        return NULL;
    pyus_out = divide_nearest(pyus_in, i);
    Py_DECREF(pyus_in);
    if (pyus_out == NULL)
        return NULL;
    result = microseconds_to_delta(pyus_out);
    Py_DECREF(pyus_out);

    return result;
}

static PyObject *
delta_add(PyObject *left, PyObject *right)
{
    PyObject *result = Py_NotImplemented;

    if (PyDelta_Check(left) && PyDelta_Check(right)) {
        /* delta + delta */
        /* The C-level additions can't overflow because of the
         * invariant bounds.
         */
        int days = GET_TD_DAYS(left) + GET_TD_DAYS(right);
        int seconds = GET_TD_SECONDS(left) + GET_TD_SECONDS(right);
        int microseconds = GET_TD_MICROSECONDS(left) +
                           GET_TD_MICROSECONDS(right);
        result = new_delta(days, seconds, microseconds, 1);
    }

    if (result == Py_NotImplemented)
        Py_INCREF(result);
    return result;
}

static PyObject *
delta_negative(PyDateTime_Delta *self)
{
    return new_delta(-GET_TD_DAYS(self),
                     -GET_TD_SECONDS(self),
                     -GET_TD_MICROSECONDS(self),
                     1);
}

static PyObject *
delta_positive(PyDateTime_Delta *self)
{
    /* Could optimize this (by returning self) if this isn't a
     * subclass -- but who uses unary + ?  Approximately nobody.
     */
    return new_delta(GET_TD_DAYS(self),
                     GET_TD_SECONDS(self),
                     GET_TD_MICROSECONDS(self),
                     0);
}

static PyObject *
delta_abs(PyDateTime_Delta *self)
{
    PyObject *result;

    assert(GET_TD_MICROSECONDS(self) >= 0);
    assert(GET_TD_SECONDS(self) >= 0);

    if (GET_TD_DAYS(self) < 0)
        result = delta_negative(self);
    else
        result = delta_positive(self);

    return result;
}

static PyObject *
delta_subtract(PyObject *left, PyObject *right)
{
    PyObject *result = Py_NotImplemented;

    if (PyDelta_Check(left) && PyDelta_Check(right)) {
        /* delta - delta */
        /* The C-level additions can't overflow because of the
         * invariant bounds.
         */
        int days = GET_TD_DAYS(left) - GET_TD_DAYS(right);
        int seconds = GET_TD_SECONDS(left) - GET_TD_SECONDS(right);
        int microseconds = GET_TD_MICROSECONDS(left) -
                           GET_TD_MICROSECONDS(right);
        result = new_delta(days, seconds, microseconds, 1);
    }

    if (result == Py_NotImplemented)
        Py_INCREF(result);
    return result;
}

static int
delta_cmp(PyObject *self, PyObject *other)
{
    int diff = GET_TD_DAYS(self) - GET_TD_DAYS(other);
    if (diff == 0) {
        diff = GET_TD_SECONDS(self) - GET_TD_SECONDS(other);
        if (diff == 0)
            diff = GET_TD_MICROSECONDS(self) -
                GET_TD_MICROSECONDS(other);
    }
    return diff;
}

static PyObject *
delta_richcompare(PyObject *self, PyObject *other, int op)
{
    if (PyDelta_Check(other)) {
        int diff = delta_cmp(self, other);
        return diff_to_bool(diff, op);
    }
    else {
        Py_RETURN_NOTIMPLEMENTED;
    }
}

static PyObject *delta_getstate(PyDateTime_Delta *self);

static Py_hash_t
delta_hash(PyDateTime_Delta *self)
{
    if (self->hashcode == -1) {
        PyObject *temp = delta_getstate(self);
        if (temp != NULL) {
            self->hashcode = PyObject_Hash(temp);
            Py_DECREF(temp);
        }
    }
    return self->hashcode;
}

static PyObject *
delta_multiply(PyObject *left, PyObject *right)
{
    PyObject *result = Py_NotImplemented;

    if (PyDelta_Check(left)) {
        /* delta * ??? */
        if (PyLong_Check(right))
            result = multiply_int_timedelta(right,
                            (PyDateTime_Delta *) left);
        else if (PyFloat_Check(right))
            result = multiply_float_timedelta(right,
                            (PyDateTime_Delta *) left);
    }
    else if (PyLong_Check(left))
        result = multiply_int_timedelta(left,
                        (PyDateTime_Delta *) right);
    else if (PyFloat_Check(left))
        result = multiply_float_timedelta(left,
                        (PyDateTime_Delta *) right);

    if (result == Py_NotImplemented)
        Py_INCREF(result);
    return result;
}

static PyObject *
delta_divide(PyObject *left, PyObject *right)
{
    PyObject *result = Py_NotImplemented;

    if (PyDelta_Check(left)) {
        /* delta * ??? */
        if (PyLong_Check(right))
            result = divide_timedelta_int(
                            (PyDateTime_Delta *)left,
                            right);
        else if (PyDelta_Check(right))
            result = divide_timedelta_timedelta(
                            (PyDateTime_Delta *)left,
                            (PyDateTime_Delta *)right);
    }

    if (result == Py_NotImplemented)
        Py_INCREF(result);
    return result;
}

static PyObject *
delta_truedivide(PyObject *left, PyObject *right)
{
    PyObject *result = Py_NotImplemented;

    if (PyDelta_Check(left)) {
        if (PyDelta_Check(right))
            result = truedivide_timedelta_timedelta(
                            (PyDateTime_Delta *)left,
                            (PyDateTime_Delta *)right);
        else if (PyFloat_Check(right))
            result = truedivide_timedelta_float(
                            (PyDateTime_Delta *)left, right);
        else if (PyLong_Check(right))
            result = truedivide_timedelta_int(
                            (PyDateTime_Delta *)left, right);
    }

    if (result == Py_NotImplemented)
        Py_INCREF(result);
    return result;
}

static PyObject *
delta_remainder(PyObject *left, PyObject *right)
{
    PyObject *pyus_left;
    PyObject *pyus_right;
    PyObject *pyus_remainder;
    PyObject *remainder;

    if (!PyDelta_Check(left) || !PyDelta_Check(right))
        Py_RETURN_NOTIMPLEMENTED;

    pyus_left = delta_to_microseconds((PyDateTime_Delta *)left);
    if (pyus_left == NULL)
        return NULL;

    pyus_right = delta_to_microseconds((PyDateTime_Delta *)right);
    if (pyus_right == NULL) {
        Py_DECREF(pyus_left);
        return NULL;
    }

    pyus_remainder = PyNumber_Remainder(pyus_left, pyus_right);
    Py_DECREF(pyus_left);
    Py_DECREF(pyus_right);
    if (pyus_remainder == NULL)
        return NULL;

    remainder = microseconds_to_delta(pyus_remainder);
    Py_DECREF(pyus_remainder);
    if (remainder == NULL)
        return NULL;

    return remainder;
}

static PyObject *
delta_divmod(PyObject *left, PyObject *right)
{
    PyObject *pyus_left;
    PyObject *pyus_right;
    PyObject *divmod;
    PyObject *delta;
    PyObject *result;

    if (!PyDelta_Check(left) || !PyDelta_Check(right))
        Py_RETURN_NOTIMPLEMENTED;

    pyus_left = delta_to_microseconds((PyDateTime_Delta *)left);
    if (pyus_left == NULL)
        return NULL;

    pyus_right = delta_to_microseconds((PyDateTime_Delta *)right);
    if (pyus_right == NULL) {
        Py_DECREF(pyus_left);
        return NULL;
    }

    divmod = PyNumber_Divmod(pyus_left, pyus_right);
    Py_DECREF(pyus_left);
    Py_DECREF(pyus_right);
    if (divmod == NULL)
        return NULL;

    assert(PyTuple_Size(divmod) == 2);
    delta = microseconds_to_delta(PyTuple_GET_ITEM(divmod, 1));
    if (delta == NULL) {
        Py_DECREF(divmod);
        return NULL;
    }
    result = PyTuple_Pack(2, PyTuple_GET_ITEM(divmod, 0), delta);
    Py_DECREF(delta);
    Py_DECREF(divmod);
    return result;
}

/* Fold in the value of the tag ("seconds", "weeks", etc) component of a
 * timedelta constructor.  sofar is the # of microseconds accounted for
 * so far, and there are factor microseconds per current unit, the number
 * of which is given by num.  num * factor is added to sofar in a
 * numerically careful way, and that's the result.  Any fractional
 * microseconds left over (this can happen if num is a float type) are
 * added into *leftover.
 * Note that there are many ways this can give an error (NULL) return.
 */
static PyObject *
accum(const char* tag, PyObject *sofar, PyObject *num, PyObject *factor,
      double *leftover)
{
    PyObject *prod;
    PyObject *sum;

    assert(num != NULL);

    if (PyLong_Check(num)) {
        prod = PyNumber_Multiply(num, factor);
        if (prod == NULL)
            return NULL;
        sum = PyNumber_Add(sofar, prod);
        Py_DECREF(prod);
        return sum;
    }

    if (PyFloat_Check(num)) {
        double dnum;
        double fracpart;
        double intpart;
        PyObject *x;
        PyObject *y;

        /* The Plan:  decompose num into an integer part and a
         * fractional part, num = intpart + fracpart.
         * Then num * factor ==
         *      intpart * factor + fracpart * factor
         * and the LHS can be computed exactly in long arithmetic.
         * The RHS is again broken into an int part and frac part.
         * and the frac part is added into *leftover.
         */
        dnum = PyFloat_AsDouble(num);
        if (dnum == -1.0 && PyErr_Occurred())
            return NULL;
        fracpart = modf(dnum, &intpart);
        x = PyLong_FromDouble(intpart);
        if (x == NULL)
            return NULL;

        prod = PyNumber_Multiply(x, factor);
        Py_DECREF(x);
        if (prod == NULL)
            return NULL;

        sum = PyNumber_Add(sofar, prod);
        Py_DECREF(prod);
        if (sum == NULL)
            return NULL;

        if (fracpart == 0.0)
            return sum;
        /* So far we've lost no information.  Dealing with the
         * fractional part requires float arithmetic, and may
         * lose a little info.
         */
        assert(PyLong_Check(factor));
        dnum = PyLong_AsDouble(factor);

        dnum *= fracpart;
        fracpart = modf(dnum, &intpart);
        x = PyLong_FromDouble(intpart);
        if (x == NULL) {
            Py_DECREF(sum);
            return NULL;
        }

        y = PyNumber_Add(sum, x);
        Py_DECREF(sum);
        Py_DECREF(x);
        *leftover += fracpart;
        return y;
    }

    PyErr_Format(PyExc_TypeError,
                 "unsupported type for timedelta %s component: %s",
                 tag, Py_TYPE(num)->tp_name);
    return NULL;
}

static PyObject *
delta_new(PyTypeObject *type, PyObject *args, PyObject *kw)
{
    PyObject *self = NULL;

    /* Argument objects. */
    PyObject *day = NULL;
    PyObject *second = NULL;
    PyObject *us = NULL;
    PyObject *ms = NULL;
    PyObject *minute = NULL;
    PyObject *hour = NULL;
    PyObject *week = NULL;

    PyObject *x = NULL;         /* running sum of microseconds */
    PyObject *y = NULL;         /* temp sum of microseconds */
    double leftover_us = 0.0;

    static char *keywords[] = {
        "days", "seconds", "microseconds", "milliseconds",
        "minutes", "hours", "weeks", NULL
    };

    if (PyArg_ParseTupleAndKeywords(args, kw, "|OOOOOOO:__new__",
                                    keywords,
                                    &day, &second, &us,
                                    &ms, &minute, &hour, &week) == 0)
        goto Done;

    x = PyLong_FromLong(0);
    if (x == NULL)
        goto Done;

#define CLEANUP         \
    Py_DECREF(x);       \
    x = y;              \
    if (x == NULL)      \
        goto Done

    if (us) {
        y = accum("microseconds", x, us, one, &leftover_us);
        CLEANUP;
    }
    if (ms) {
        y = accum("milliseconds", x, ms, us_per_ms, &leftover_us);
        CLEANUP;
    }
    if (second) {
        y = accum("seconds", x, second, us_per_second, &leftover_us);
        CLEANUP;
    }
    if (minute) {
        y = accum("minutes", x, minute, us_per_minute, &leftover_us);
        CLEANUP;
    }
    if (hour) {
        y = accum("hours", x, hour, us_per_hour, &leftover_us);
        CLEANUP;
    }
    if (day) {
        y = accum("days", x, day, us_per_day, &leftover_us);
        CLEANUP;
    }
    if (week) {
        y = accum("weeks", x, week, us_per_week, &leftover_us);
        CLEANUP;
    }
    if (leftover_us) {
        /* Round to nearest whole # of us, and add into x. */
        double whole_us = round(leftover_us);
        int x_is_odd;
        PyObject *temp;

        whole_us = round(leftover_us);
        if (fabs(whole_us - leftover_us) == 0.5) {
            /* We're exactly halfway between two integers.  In order
             * to do round-half-to-even, we must determine whether x
             * is odd. Note that x is odd when it's last bit is 1. The
             * code below uses bitwise and operation to check the last
             * bit. */
            temp = PyNumber_And(x, one);  /* temp <- x & 1 */
            if (temp == NULL) {
                Py_DECREF(x);
                goto Done;
            }
            x_is_odd = PyObject_IsTrue(temp);
            Py_DECREF(temp);
            if (x_is_odd == -1) {
                Py_DECREF(x);
                goto Done;
            }
            whole_us = 2.0 * round((leftover_us + x_is_odd) * 0.5) - x_is_odd;
        }

        temp = PyLong_FromLong((long)whole_us);

        if (temp == NULL) {
            Py_DECREF(x);
            goto Done;
        }
        y = PyNumber_Add(x, temp);
        Py_DECREF(temp);
        CLEANUP;
    }

    self = microseconds_to_delta_ex(x, type);
    Py_DECREF(x);
Done:
    return self;

#undef CLEANUP
}

static int
delta_bool(PyDateTime_Delta *self)
{
    return (GET_TD_DAYS(self) != 0
        || GET_TD_SECONDS(self) != 0
        || GET_TD_MICROSECONDS(self) != 0);
}

static PyObject *
delta_repr(PyDateTime_Delta *self)
{
    if (GET_TD_MICROSECONDS(self) != 0)
        return PyUnicode_FromFormat("%s(%d, %d, %d)",
                                    Py_TYPE(self)->tp_name,
                                    GET_TD_DAYS(self),
                                    GET_TD_SECONDS(self),
                                    GET_TD_MICROSECONDS(self));
    if (GET_TD_SECONDS(self) != 0)
        return PyUnicode_FromFormat("%s(%d, %d)",
                                    Py_TYPE(self)->tp_name,
                                    GET_TD_DAYS(self),
                                    GET_TD_SECONDS(self));

    return PyUnicode_FromFormat("%s(%d)",
                                Py_TYPE(self)->tp_name,
                                GET_TD_DAYS(self));
}

static PyObject *
delta_str(PyDateTime_Delta *self)
{
    int us = GET_TD_MICROSECONDS(self);
    int seconds = GET_TD_SECONDS(self);
    int minutes = divmod(seconds, 60, &seconds);
    int hours = divmod(minutes, 60, &minutes);
    int days = GET_TD_DAYS(self);

    if (days) {
        if (us)
            return PyUnicode_FromFormat("%d day%s, %d:%02d:%02d.%06d",
                                        days, (days == 1 || days == -1) ? "" : "s",
                                        hours, minutes, seconds, us);
        else
            return PyUnicode_FromFormat("%d day%s, %d:%02d:%02d",
                                        days, (days == 1 || days == -1) ? "" : "s",
                                        hours, minutes, seconds);
    } else {
        if (us)
            return PyUnicode_FromFormat("%d:%02d:%02d.%06d",
                                        hours, minutes, seconds, us);
        else
            return PyUnicode_FromFormat("%d:%02d:%02d",
                                        hours, minutes, seconds);
    }

}

/* Pickle support, a simple use of __reduce__. */

/* __getstate__ isn't exposed */
static PyObject *
delta_getstate(PyDateTime_Delta *self)
{
    return Py_BuildValue("iii", GET_TD_DAYS(self),
                                GET_TD_SECONDS(self),
                                GET_TD_MICROSECONDS(self));
}

static PyObject *
delta_total_seconds(PyObject *self)
{
    PyObject *total_seconds;
    PyObject *total_microseconds;

    total_microseconds = delta_to_microseconds((PyDateTime_Delta *)self);
    if (total_microseconds == NULL)
        return NULL;

    total_seconds = PyNumber_TrueDivide(total_microseconds, us_per_second);

    Py_DECREF(total_microseconds);
    return total_seconds;
}

static PyObject *
delta_reduce(PyDateTime_Delta* self)
{
    return Py_BuildValue("ON", Py_TYPE(self), delta_getstate(self));
}

#define OFFSET(field)  offsetof(PyDateTime_Delta, field)

static PyMemberDef delta_members[] = {

    {"days",         T_INT, OFFSET(days),         READONLY,
     PyDoc_STR("Number of days.")},

    {"seconds",      T_INT, OFFSET(seconds),      READONLY,
     PyDoc_STR("Number of seconds (>= 0 and less than 1 day).")},

    {"microseconds", T_INT, OFFSET(microseconds), READONLY,
     PyDoc_STR("Number of microseconds (>= 0 and less than 1 second).")},
    {NULL}
};

static PyMethodDef delta_methods[] = {
    {"total_seconds", (PyCFunction)delta_total_seconds, METH_NOARGS,
     PyDoc_STR("Total seconds in the duration.")},

    {"__reduce__", (PyCFunction)delta_reduce, METH_NOARGS,
     PyDoc_STR("__reduce__() -> (cls, state)")},

    {NULL,      NULL},
};

static const char delta_doc[] =
PyDoc_STR("Difference between two datetime values.");

static PyNumberMethods delta_as_number = {
    delta_add,                                  /* nb_add */
    delta_subtract,                             /* nb_subtract */
    delta_multiply,                             /* nb_multiply */
    delta_remainder,                            /* nb_remainder */
    delta_divmod,                               /* nb_divmod */
    0,                                          /* nb_power */
    (unaryfunc)delta_negative,                  /* nb_negative */
    (unaryfunc)delta_positive,                  /* nb_positive */
    (unaryfunc)delta_abs,                       /* nb_absolute */
    (inquiry)delta_bool,                        /* nb_bool */
    0,                                          /*nb_invert*/
    0,                                          /*nb_lshift*/
    0,                                          /*nb_rshift*/
    0,                                          /*nb_and*/
    0,                                          /*nb_xor*/
    0,                                          /*nb_or*/
    0,                                          /*nb_int*/
    0,                                          /*nb_reserved*/
    0,                                          /*nb_float*/
    0,                                          /*nb_inplace_add*/
    0,                                          /*nb_inplace_subtract*/
    0,                                          /*nb_inplace_multiply*/
    0,                                          /*nb_inplace_remainder*/
    0,                                          /*nb_inplace_power*/
    0,                                          /*nb_inplace_lshift*/
    0,                                          /*nb_inplace_rshift*/
    0,                                          /*nb_inplace_and*/
    0,                                          /*nb_inplace_xor*/
    0,                                          /*nb_inplace_or*/
    delta_divide,                               /* nb_floor_divide */
    delta_truedivide,                           /* nb_true_divide */
    0,                                          /* nb_inplace_floor_divide */
    0,                                          /* nb_inplace_true_divide */
};

static PyTypeObject PyDateTime_DeltaType = {
    PyVarObject_HEAD_INIT(NULL, 0)
    "datetime.timedelta",                               /* tp_name */
    sizeof(PyDateTime_Delta),                           /* tp_basicsize */
    0,                                                  /* tp_itemsize */
    0,                                                  /* tp_dealloc */
    0,                                                  /* tp_print */
    0,                                                  /* tp_getattr */
    0,                                                  /* tp_setattr */
    0,                                                  /* tp_reserved */
    (reprfunc)delta_repr,                               /* tp_repr */
    &delta_as_number,                                   /* tp_as_number */
    0,                                                  /* tp_as_sequence */
    0,                                                  /* tp_as_mapping */
    (hashfunc)delta_hash,                               /* tp_hash */
    0,                                                  /* tp_call */
    (reprfunc)delta_str,                                /* tp_str */
    PyObject_GenericGetAttr,                            /* tp_getattro */
    0,                                                  /* tp_setattro */
    0,                                                  /* tp_as_buffer */
    Py_TPFLAGS_DEFAULT | Py_TPFLAGS_BASETYPE,           /* tp_flags */
    delta_doc,                                          /* tp_doc */
    0,                                                  /* tp_traverse */
    0,                                                  /* tp_clear */
    delta_richcompare,                                  /* tp_richcompare */
    0,                                                  /* tp_weaklistoffset */
    0,                                                  /* tp_iter */
    0,                                                  /* tp_iternext */
    delta_methods,                                      /* tp_methods */
    delta_members,                                      /* tp_members */
    0,                                                  /* tp_getset */
    0,                                                  /* tp_base */
    0,                                                  /* tp_dict */
    0,                                                  /* tp_descr_get */
    0,                                                  /* tp_descr_set */
    0,                                                  /* tp_dictoffset */
    0,                                                  /* tp_init */
    0,                                                  /* tp_alloc */
    delta_new,                                          /* tp_new */
    0,                                                  /* tp_free */
};

/*
 * PyDateTime_Date implementation.
 */

/* Accessor properties. */

static PyObject *
date_year(PyDateTime_Date *self, void *unused)
{
    return PyLong_FromLong(GET_YEAR(self));
}

static PyObject *
date_month(PyDateTime_Date *self, void *unused)
{
    return PyLong_FromLong(GET_MONTH(self));
}

static PyObject *
date_day(PyDateTime_Date *self, void *unused)
{
    return PyLong_FromLong(GET_DAY(self));
}

static PyGetSetDef date_getset[] = {
    {"year",        (getter)date_year},
    {"month",       (getter)date_month},
    {"day",         (getter)date_day},
    {NULL}
};

/* Constructors. */

static char *date_kws[] = {"year", "month", "day", NULL};

static PyObject *
date_new(PyTypeObject *type, PyObject *args, PyObject *kw)
{
    PyObject *self = NULL;
    PyObject *state;
    int year;
    int month;
    int day;

    /* Check for invocation from pickle with __getstate__ state */
    if (PyTuple_GET_SIZE(args) == 1 &&
        PyBytes_Check(state = PyTuple_GET_ITEM(args, 0)) &&
        PyBytes_GET_SIZE(state) == _PyDateTime_DATE_DATASIZE &&
        MONTH_IS_SANE(PyBytes_AS_STRING(state)[2]))
    {
        PyDateTime_Date *me;

        me = (PyDateTime_Date *) (type->tp_alloc(type, 0));
        if (me != NULL) {
            char *pdata = PyBytes_AS_STRING(state);
            memcpy(me->data, pdata, _PyDateTime_DATE_DATASIZE);
            me->hashcode = -1;
        }
        return (PyObject *)me;
    }

    if (PyArg_ParseTupleAndKeywords(args, kw, "iii", date_kws,
                                    &year, &month, &day)) {
        self = new_date_ex(year, month, day, type);
    }
    return self;
}

/* Return new date from localtime(t). */
static PyObject *
date_local_from_object(PyObject *cls, PyObject *obj)
{
    struct tm tm;
    time_t t;

    if (_PyTime_ObjectToTime_t(obj, &t, _PyTime_ROUND_FLOOR) == -1)
        return NULL;

    if (_PyTime_localtime(t, &tm) != 0)
        return NULL;

    return PyObject_CallFunction(cls, "iii",
                                 tm.tm_year + 1900,
                                 tm.tm_mon + 1,
                                 tm.tm_mday);
}

/* Return new date from current time.
 * We say this is equivalent to fromtimestamp(time.time()), and the
 * only way to be sure of that is to *call* time.time().  That's not
 * generally the same as calling C's time.
 */
static PyObject *
date_today(PyObject *cls, PyObject *dummy)
{
    PyObject *time;
    PyObject *result;
    _Py_IDENTIFIER(fromtimestamp);

    time = time_time();
    if (time == NULL)
        return NULL;

    /* Note well:  today() is a class method, so this may not call
     * date.fromtimestamp.  For example, it may call
     * datetime.fromtimestamp.  That's why we need all the accuracy
     * time.time() delivers; if someone were gonzo about optimization,
     * date.today() could get away with plain C time().
     */
    result = _PyObject_CallMethodIdObjArgs(cls, &PyId_fromtimestamp,
                                           time, NULL);
    Py_DECREF(time);
    return result;
}

/* Return new date from given timestamp (Python timestamp -- a double). */
static PyObject *
date_fromtimestamp(PyObject *cls, PyObject *args)
{
    PyObject *timestamp;
    PyObject *result = NULL;

    if (PyArg_ParseTuple(args, "O:fromtimestamp", &timestamp))
        result = date_local_from_object(cls, timestamp);
    return result;
}

/* Return new date from proleptic Gregorian ordinal.  Raises ValueError if
 * the ordinal is out of range.
 */
static PyObject *
date_fromordinal(PyObject *cls, PyObject *args)
{
    PyObject *result = NULL;
    int ordinal;

    if (PyArg_ParseTuple(args, "i:fromordinal", &ordinal)) {
        int year;
        int month;
        int day;

        if (ordinal < 1)
            PyErr_SetString(PyExc_ValueError, "ordinal must be "
                                              ">= 1");
        else {
            ord_to_ymd(ordinal, &year, &month, &day);
            result = PyObject_CallFunction(cls, "iii",
                                           year, month, day);
        }
    }
    return result;
}

/*
 * Date arithmetic.
 */

/* date + timedelta -> date.  If arg negate is true, subtract the timedelta
 * instead.
 */
static PyObject *
add_date_timedelta(PyDateTime_Date *date, PyDateTime_Delta *delta, int negate)
{
    PyObject *result = NULL;
    int year = GET_YEAR(date);
    int month = GET_MONTH(date);
    int deltadays = GET_TD_DAYS(delta);
    /* C-level overflow is impossible because |deltadays| < 1e9. */
    int day = GET_DAY(date) + (negate ? -deltadays : deltadays);

    if (normalize_date(&year, &month, &day) >= 0)
        result = new_date(year, month, day);
    return result;
}

static PyObject *
date_add(PyObject *left, PyObject *right)
{
    if (PyDateTime_Check(left) || PyDateTime_Check(right))
        Py_RETURN_NOTIMPLEMENTED;

    if (PyDate_Check(left)) {
        /* date + ??? */
        if (PyDelta_Check(right))
            /* date + delta */
            return add_date_timedelta((PyDateTime_Date *) left,
                                      (PyDateTime_Delta *) right,
                                      0);
    }
    else {
        /* ??? + date
         * 'right' must be one of us, or we wouldn't have been called
         */
        if (PyDelta_Check(left))
            /* delta + date */
            return add_date_timedelta((PyDateTime_Date *) right,
                                      (PyDateTime_Delta *) left,
                                      0);
    }
    Py_RETURN_NOTIMPLEMENTED;
}

static PyObject *
date_subtract(PyObject *left, PyObject *right)
{
    if (PyDateTime_Check(left) || PyDateTime_Check(right))
        Py_RETURN_NOTIMPLEMENTED;

    if (PyDate_Check(left)) {
        if (PyDate_Check(right)) {
            /* date - date */
            int left_ord = ymd_to_ord(GET_YEAR(left),
                                      GET_MONTH(left),
                                      GET_DAY(left));
            int right_ord = ymd_to_ord(GET_YEAR(right),
                                       GET_MONTH(right),
                                       GET_DAY(right));
            return new_delta(left_ord - right_ord, 0, 0, 0);
        }
        if (PyDelta_Check(right)) {
            /* date - delta */
            return add_date_timedelta((PyDateTime_Date *) left,
                                      (PyDateTime_Delta *) right,
                                      1);
        }
    }
    Py_RETURN_NOTIMPLEMENTED;
}


/* Various ways to turn a date into a string. */

static PyObject *
date_repr(PyDateTime_Date *self)
{
    return PyUnicode_FromFormat("%s(%d, %d, %d)",
                                Py_TYPE(self)->tp_name,
                                GET_YEAR(self), GET_MONTH(self), GET_DAY(self));
}

static PyObject *
date_isoformat(PyDateTime_Date *self)
{
    return PyUnicode_FromFormat("%04d-%02d-%02d",
                                GET_YEAR(self), GET_MONTH(self), GET_DAY(self));
}

/* str() calls the appropriate isoformat() method. */
static PyObject *
date_str(PyDateTime_Date *self)
{
    return _PyObject_CallMethodId((PyObject *)self, &PyId_isoformat, NULL);
}


static PyObject *
date_ctime(PyDateTime_Date *self)
{
    return format_ctime(self, 0, 0, 0);
}

static PyObject *
date_strftime(PyDateTime_Date *self, PyObject *args, PyObject *kw)
{
    /* This method can be inherited, and needs to call the
     * timetuple() method appropriate to self's class.
     */
    PyObject *result;
    PyObject *tuple;
    PyObject *format;
    _Py_IDENTIFIER(timetuple);
    static char *keywords[] = {"format", NULL};

    if (! PyArg_ParseTupleAndKeywords(args, kw, "U:strftime", keywords,
                                      &format))
        return NULL;

    tuple = _PyObject_CallMethodId((PyObject *)self, &PyId_timetuple, NULL);
    if (tuple == NULL)
        return NULL;
    result = wrap_strftime((PyObject *)self, format, tuple,
                           (PyObject *)self);
    Py_DECREF(tuple);
    return result;
}

static PyObject *
date_format(PyDateTime_Date *self, PyObject *args)
{
    PyObject *format;

    if (!PyArg_ParseTuple(args, "U:__format__", &format))
        return NULL;

    /* if the format is zero length, return str(self) */
    if (PyUnicode_GetLength(format) == 0)
        return PyObject_Str((PyObject *)self);

    return _PyObject_CallMethodIdObjArgs((PyObject *)self, &PyId_strftime,
                                         format, NULL);
}

/* ISO methods. */

static PyObject *
date_isoweekday(PyDateTime_Date *self)
{
    int dow = weekday(GET_YEAR(self), GET_MONTH(self), GET_DAY(self));

    return PyLong_FromLong(dow + 1);
}

static PyObject *
date_isocalendar(PyDateTime_Date *self)
{
    int  year         = GET_YEAR(self);
    int  week1_monday = iso_week1_monday(year);
    int today         = ymd_to_ord(year, GET_MONTH(self), GET_DAY(self));
    int  week;
    int  day;

    week = divmod(today - week1_monday, 7, &day);
    if (week < 0) {
        --year;
        week1_monday = iso_week1_monday(year);
        week = divmod(today - week1_monday, 7, &day);
    }
    else if (week >= 52 && today >= iso_week1_monday(year + 1)) {
        ++year;
        week = 0;
    }
    return Py_BuildValue("iii", year, week + 1, day + 1);
}

/* Miscellaneous methods. */

static PyObject *
date_richcompare(PyObject *self, PyObject *other, int op)
{
    if (PyDate_Check(other)) {
        int diff = memcmp(((PyDateTime_Date *)self)->data,
                          ((PyDateTime_Date *)other)->data,
                          _PyDateTime_DATE_DATASIZE);
        return diff_to_bool(diff, op);
    }
    else
        Py_RETURN_NOTIMPLEMENTED;
}

static PyObject *
date_timetuple(PyDateTime_Date *self)
{
    return build_struct_time(GET_YEAR(self),
                             GET_MONTH(self),
                             GET_DAY(self),
                             0, 0, 0, -1);
}

static PyObject *
date_replace(PyDateTime_Date *self, PyObject *args, PyObject *kw)
{
    PyObject *clone;
    PyObject *tuple;
    int year = GET_YEAR(self);
    int month = GET_MONTH(self);
    int day = GET_DAY(self);

    if (! PyArg_ParseTupleAndKeywords(args, kw, "|iii:replace", date_kws,
                                      &year, &month, &day))
        return NULL;
    tuple = Py_BuildValue("iii", year, month, day);
    if (tuple == NULL)
        return NULL;
    clone = date_new(Py_TYPE(self), tuple, NULL);
    Py_DECREF(tuple);
    return clone;
}

static Py_hash_t
generic_hash(unsigned char *data, int len)
{
    return _Py_HashBytes(data, len);
}


static PyObject *date_getstate(PyDateTime_Date *self);

static Py_hash_t
date_hash(PyDateTime_Date *self)
{
    if (self->hashcode == -1) {
        self->hashcode = generic_hash(
            (unsigned char *)self->data, _PyDateTime_DATE_DATASIZE);
    }

    return self->hashcode;
}

static PyObject *
date_toordinal(PyDateTime_Date *self)
{
    return PyLong_FromLong(ymd_to_ord(GET_YEAR(self), GET_MONTH(self),
                                     GET_DAY(self)));
}

static PyObject *
date_weekday(PyDateTime_Date *self)
{
    int dow = weekday(GET_YEAR(self), GET_MONTH(self), GET_DAY(self));

    return PyLong_FromLong(dow);
}

/* Pickle support, a simple use of __reduce__. */

/* __getstate__ isn't exposed */
static PyObject *
date_getstate(PyDateTime_Date *self)
{
    PyObject* field;
    field = PyBytes_FromStringAndSize((char*)self->data,
                                       _PyDateTime_DATE_DATASIZE);
    return Py_BuildValue("(N)", field);
}

static PyObject *
date_reduce(PyDateTime_Date *self, PyObject *arg)
{
    return Py_BuildValue("(ON)", Py_TYPE(self), date_getstate(self));
}

static PyMethodDef date_methods[] = {

    /* Class methods: */

    {"fromtimestamp", (PyCFunction)date_fromtimestamp, METH_VARARGS |
                                                       METH_CLASS,
     PyDoc_STR("timestamp -> local date from a POSIX timestamp (like "
               "time.time()).")},

    {"fromordinal", (PyCFunction)date_fromordinal,      METH_VARARGS |
                                                    METH_CLASS,
     PyDoc_STR("int -> date corresponding to a proleptic Gregorian "
               "ordinal.")},

    {"today",         (PyCFunction)date_today,   METH_NOARGS | METH_CLASS,
     PyDoc_STR("Current date or datetime:  same as "
               "self.__class__.fromtimestamp(time.time()).")},

    /* Instance methods: */

    {"ctime",       (PyCFunction)date_ctime,        METH_NOARGS,
     PyDoc_STR("Return ctime() style string.")},

    {"strftime",        (PyCFunction)date_strftime,     METH_VARARGS | METH_KEYWORDS,
     PyDoc_STR("format -> strftime() style string.")},

    {"__format__",      (PyCFunction)date_format,       METH_VARARGS,
     PyDoc_STR("Formats self with strftime.")},

    {"timetuple",   (PyCFunction)date_timetuple,    METH_NOARGS,
     PyDoc_STR("Return time tuple, compatible with time.localtime().")},

    {"isocalendar", (PyCFunction)date_isocalendar,  METH_NOARGS,
     PyDoc_STR("Return a 3-tuple containing ISO year, week number, and "
               "weekday.")},

    {"isoformat",   (PyCFunction)date_isoformat,        METH_NOARGS,
     PyDoc_STR("Return string in ISO 8601 format, YYYY-MM-DD.")},

    {"isoweekday",  (PyCFunction)date_isoweekday,   METH_NOARGS,
     PyDoc_STR("Return the day of the week represented by the date.\n"
               "Monday == 1 ... Sunday == 7")},

    {"toordinal",   (PyCFunction)date_toordinal,    METH_NOARGS,
     PyDoc_STR("Return proleptic Gregorian ordinal.  January 1 of year "
               "1 is day 1.")},

    {"weekday",     (PyCFunction)date_weekday,      METH_NOARGS,
     PyDoc_STR("Return the day of the week represented by the date.\n"
               "Monday == 0 ... Sunday == 6")},

    {"replace",     (PyCFunction)date_replace,      METH_VARARGS | METH_KEYWORDS,
     PyDoc_STR("Return date with new specified fields.")},

    {"__reduce__", (PyCFunction)date_reduce,        METH_NOARGS,
     PyDoc_STR("__reduce__() -> (cls, state)")},

    {NULL,      NULL}
};

static const char date_doc[] =
PyDoc_STR("date(year, month, day) --> date object");

static PyNumberMethods date_as_number = {
    date_add,                                           /* nb_add */
    date_subtract,                                      /* nb_subtract */
    0,                                                  /* nb_multiply */
    0,                                                  /* nb_remainder */
    0,                                                  /* nb_divmod */
    0,                                                  /* nb_power */
    0,                                                  /* nb_negative */
    0,                                                  /* nb_positive */
    0,                                                  /* nb_absolute */
    0,                                                  /* nb_bool */
};

static PyTypeObject PyDateTime_DateType = {
    PyVarObject_HEAD_INIT(NULL, 0)
    "datetime.date",                                    /* tp_name */
    sizeof(PyDateTime_Date),                            /* tp_basicsize */
    0,                                                  /* tp_itemsize */
    0,                                                  /* tp_dealloc */
    0,                                                  /* tp_print */
    0,                                                  /* tp_getattr */
    0,                                                  /* tp_setattr */
    0,                                                  /* tp_reserved */
    (reprfunc)date_repr,                                /* tp_repr */
    &date_as_number,                                    /* tp_as_number */
    0,                                                  /* tp_as_sequence */
    0,                                                  /* tp_as_mapping */
    (hashfunc)date_hash,                                /* tp_hash */
    0,                                                  /* tp_call */
    (reprfunc)date_str,                                 /* tp_str */
    PyObject_GenericGetAttr,                            /* tp_getattro */
    0,                                                  /* tp_setattro */
    0,                                                  /* tp_as_buffer */
    Py_TPFLAGS_DEFAULT | Py_TPFLAGS_BASETYPE,           /* tp_flags */
    date_doc,                                           /* tp_doc */
    0,                                                  /* tp_traverse */
    0,                                                  /* tp_clear */
    date_richcompare,                                   /* tp_richcompare */
    0,                                                  /* tp_weaklistoffset */
    0,                                                  /* tp_iter */
    0,                                                  /* tp_iternext */
    date_methods,                                       /* tp_methods */
    0,                                                  /* tp_members */
    date_getset,                                        /* tp_getset */
    0,                                                  /* tp_base */
    0,                                                  /* tp_dict */
    0,                                                  /* tp_descr_get */
    0,                                                  /* tp_descr_set */
    0,                                                  /* tp_dictoffset */
    0,                                                  /* tp_init */
    0,                                                  /* tp_alloc */
    date_new,                                           /* tp_new */
    0,                                                  /* tp_free */
};

/*
 * PyDateTime_TZInfo implementation.
 */

/* This is a pure abstract base class, so doesn't do anything beyond
 * raising NotImplemented exceptions.  Real tzinfo classes need
 * to derive from this.  This is mostly for clarity, and for efficiency in
 * datetime and time constructors (their tzinfo arguments need to
 * be subclasses of this tzinfo class, which is easy and quick to check).
 *
 * Note:  For reasons having to do with pickling of subclasses, we have
 * to allow tzinfo objects to be instantiated.  This wasn't an issue
 * in the Python implementation (__init__() could raise NotImplementedError
 * there without ill effect), but doing so in the C implementation hit a
 * brick wall.
 */

static PyObject *
tzinfo_nogo(const char* methodname)
{
    PyErr_Format(PyExc_NotImplementedError,
                 "a tzinfo subclass must implement %s()",
                 methodname);
    return NULL;
}

/* Methods.  A subclass must implement these. */

static PyObject *
tzinfo_tzname(PyDateTime_TZInfo *self, PyObject *dt)
{
    return tzinfo_nogo("tzname");
}

static PyObject *
tzinfo_utcoffset(PyDateTime_TZInfo *self, PyObject *dt)
{
    return tzinfo_nogo("utcoffset");
}

static PyObject *
tzinfo_dst(PyDateTime_TZInfo *self, PyObject *dt)
{
    return tzinfo_nogo("dst");
}


static PyObject *add_datetime_timedelta(PyDateTime_DateTime *date,
                                        PyDateTime_Delta *delta,
                                        int factor);
static PyObject *datetime_utcoffset(PyObject *self, PyObject *);
static PyObject *datetime_dst(PyObject *self, PyObject *);

static PyObject *
tzinfo_fromutc(PyDateTime_TZInfo *self, PyObject *dt)
{
    PyObject *result = NULL;
    PyObject *off = NULL, *dst = NULL;
    PyDateTime_Delta *delta = NULL;

    if (!PyDateTime_Check(dt)) {
        PyErr_SetString(PyExc_TypeError,
                        "fromutc: argument must be a datetime");
        return NULL;
    }
    if (GET_DT_TZINFO(dt) != (PyObject *)self) {
        PyErr_SetString(PyExc_ValueError, "fromutc: dt.tzinfo "
                        "is not self");
        return NULL;
    }

    off = datetime_utcoffset(dt, NULL);
    if (off == NULL)
        return NULL;
    if (off == Py_None) {
        PyErr_SetString(PyExc_ValueError, "fromutc: non-None "
                        "utcoffset() result required");
        goto Fail;
    }

    dst = datetime_dst(dt, NULL);
    if (dst == NULL)
        goto Fail;
    if (dst == Py_None) {
        PyErr_SetString(PyExc_ValueError, "fromutc: non-None "
                        "dst() result required");
        goto Fail;
    }

    delta = (PyDateTime_Delta *)delta_subtract(off, dst);
    if (delta == NULL)
        goto Fail;
    result = add_datetime_timedelta((PyDateTime_DateTime *)dt, delta, 1);
    if (result == NULL)
        goto Fail;

    Py_DECREF(dst);
    dst = call_dst(GET_DT_TZINFO(dt), result);
    if (dst == NULL)
        goto Fail;
    if (dst == Py_None)
        goto Inconsistent;
    if (delta_bool((PyDateTime_Delta *)dst) != 0) {
        Py_SETREF(result, add_datetime_timedelta((PyDateTime_DateTime *)result,
                                                 (PyDateTime_Delta *)dst, 1));
        if (result == NULL)
            goto Fail;
    }
    Py_DECREF(delta);
    Py_DECREF(dst);
    Py_DECREF(off);
    return result;

Inconsistent:
    PyErr_SetString(PyExc_ValueError, "fromutc: tz.dst() gave"
                    "inconsistent results; cannot convert");

    /* fall thru to failure */
Fail:
    Py_XDECREF(off);
    Py_XDECREF(dst);
    Py_XDECREF(delta);
    Py_XDECREF(result);
    return NULL;
}

/*
 * Pickle support.  This is solely so that tzinfo subclasses can use
 * pickling -- tzinfo itself is supposed to be uninstantiable.
 */

static PyObject *
tzinfo_reduce(PyObject *self)
{
    PyObject *args, *state;
    PyObject *getinitargs, *getstate;
    _Py_IDENTIFIER(__getinitargs__);
    _Py_IDENTIFIER(__getstate__);

    getinitargs = _PyObject_GetAttrId(self, &PyId___getinitargs__);
    if (getinitargs != NULL) {
        args = _PyObject_CallNoArg(getinitargs);
        Py_DECREF(getinitargs);
        if (args == NULL) {
            return NULL;
        }
    }
    else {
        PyErr_Clear();

        args = PyTuple_New(0);
        if (args == NULL) {
            return NULL;
        }
    }

    getstate = _PyObject_GetAttrId(self, &PyId___getstate__);
    if (getstate != NULL) {
        state = _PyObject_CallNoArg(getstate);
        Py_DECREF(getstate);
        if (state == NULL) {
            Py_DECREF(args);
            return NULL;
        }
    }
    else {
        PyObject **dictptr;
        PyErr_Clear();
        state = Py_None;
        dictptr = _PyObject_GetDictPtr(self);
        if (dictptr && *dictptr && PyDict_GET_SIZE(*dictptr)) {
            state = *dictptr;
        }
        Py_INCREF(state);
    }

    if (state == Py_None) {
        Py_DECREF(state);
        return Py_BuildValue("(ON)", Py_TYPE(self), args);
    }
    else
        return Py_BuildValue("(ONN)", Py_TYPE(self), args, state);
}

static PyMethodDef tzinfo_methods[] = {

    {"tzname",          (PyCFunction)tzinfo_tzname,             METH_O,
     PyDoc_STR("datetime -> string name of time zone.")},

    {"utcoffset",       (PyCFunction)tzinfo_utcoffset,          METH_O,
     PyDoc_STR("datetime -> timedelta showing offset from UTC, negative "
           "values indicating West of UTC")},

    {"dst",             (PyCFunction)tzinfo_dst,                METH_O,
     PyDoc_STR("datetime -> DST offset in minutes east of UTC.")},

    {"fromutc",         (PyCFunction)tzinfo_fromutc,            METH_O,
     PyDoc_STR("datetime in UTC -> datetime in local time.")},

    {"__reduce__",  (PyCFunction)tzinfo_reduce,             METH_NOARGS,
     PyDoc_STR("-> (cls, state)")},

    {NULL, NULL}
};

static const char tzinfo_doc[] =
PyDoc_STR("Abstract base class for time zone info objects.");

static PyTypeObject PyDateTime_TZInfoType = {
    PyVarObject_HEAD_INIT(NULL, 0)
    "datetime.tzinfo",                          /* tp_name */
    sizeof(PyDateTime_TZInfo),                  /* tp_basicsize */
    0,                                          /* tp_itemsize */
    0,                                          /* tp_dealloc */
    0,                                          /* tp_print */
    0,                                          /* tp_getattr */
    0,                                          /* tp_setattr */
    0,                                          /* tp_reserved */
    0,                                          /* tp_repr */
    0,                                          /* tp_as_number */
    0,                                          /* tp_as_sequence */
    0,                                          /* tp_as_mapping */
    0,                                          /* tp_hash */
    0,                                          /* tp_call */
    0,                                          /* tp_str */
    PyObject_GenericGetAttr,                    /* tp_getattro */
    0,                                          /* tp_setattro */
    0,                                          /* tp_as_buffer */
    Py_TPFLAGS_DEFAULT | Py_TPFLAGS_BASETYPE,   /* tp_flags */
    tzinfo_doc,                                 /* tp_doc */
    0,                                          /* tp_traverse */
    0,                                          /* tp_clear */
    0,                                          /* tp_richcompare */
    0,                                          /* tp_weaklistoffset */
    0,                                          /* tp_iter */
    0,                                          /* tp_iternext */
    tzinfo_methods,                             /* tp_methods */
    0,                                          /* tp_members */
    0,                                          /* tp_getset */
    0,                                          /* tp_base */
    0,                                          /* tp_dict */
    0,                                          /* tp_descr_get */
    0,                                          /* tp_descr_set */
    0,                                          /* tp_dictoffset */
    0,                                          /* tp_init */
    0,                                          /* tp_alloc */
    PyType_GenericNew,                          /* tp_new */
    0,                                          /* tp_free */
};

static char *timezone_kws[] = {"offset", "name", NULL};

static PyObject *
timezone_new(PyTypeObject *type, PyObject *args, PyObject *kw)
{
    PyObject *offset;
    PyObject *name = NULL;
    if (PyArg_ParseTupleAndKeywords(args, kw, "O!|U:timezone", timezone_kws,
                                    &PyDateTime_DeltaType, &offset, &name))
        return new_timezone(offset, name);

    return NULL;
}

static void
timezone_dealloc(PyDateTime_TimeZone *self)
{
    Py_CLEAR(self->offset);
    Py_CLEAR(self->name);
    Py_TYPE(self)->tp_free((PyObject *)self);
}

static PyObject *
timezone_richcompare(PyDateTime_TimeZone *self,
                     PyDateTime_TimeZone *other, int op)
{
    if (op != Py_EQ && op != Py_NE)
        Py_RETURN_NOTIMPLEMENTED;
    if (Py_TYPE(other) != &PyDateTime_TimeZoneType) {
        if (op == Py_EQ)
            Py_RETURN_FALSE;
        else
            Py_RETURN_TRUE;
    }
    return delta_richcompare(self->offset, other->offset, op);
}

static Py_hash_t
timezone_hash(PyDateTime_TimeZone *self)
{
    return delta_hash((PyDateTime_Delta *)self->offset);
}

/* Check argument type passed to tzname, utcoffset, or dst methods.
   Returns 0 for good argument.  Returns -1 and sets exception info
   otherwise.
 */
static int
_timezone_check_argument(PyObject *dt, const char *meth)
{
    if (dt == Py_None || PyDateTime_Check(dt))
        return 0;
    PyErr_Format(PyExc_TypeError, "%s(dt) argument must be a datetime instance"
                 " or None, not %.200s", meth, Py_TYPE(dt)->tp_name);
    return -1;
}

static PyObject *
timezone_repr(PyDateTime_TimeZone *self)
{
    /* Note that although timezone is not subclassable, it is convenient
       to use Py_TYPE(self)->tp_name here. */
    const char *type_name = Py_TYPE(self)->tp_name;

    if (((PyObject *)self) == PyDateTime_TimeZone_UTC)
        return PyUnicode_FromFormat("%s.utc", type_name);

    if (self->name == NULL)
        return PyUnicode_FromFormat("%s(%R)", type_name, self->offset);

    return PyUnicode_FromFormat("%s(%R, %R)", type_name, self->offset,
                                self->name);
}


static PyObject *
timezone_str(PyDateTime_TimeZone *self)
{
    int hours, minutes, seconds;
    PyObject *offset;
    char sign;

    if (self->name != NULL) {
        Py_INCREF(self->name);
        return self->name;
    }
    if ((PyObject *)self == PyDateTime_TimeZone_UTC ||
           (GET_TD_DAYS(self->offset) == 0 &&
            GET_TD_SECONDS(self->offset) == 0 &&
            GET_TD_MICROSECONDS(self->offset) == 0))
        return PyUnicode_FromString("UTC");
    /* Offset is normalized, so it is negative if days < 0 */
    if (GET_TD_DAYS(self->offset) < 0) {
        sign = '-';
        offset = delta_negative((PyDateTime_Delta *)self->offset);
        if (offset == NULL)
            return NULL;
    }
    else {
        sign = '+';
        offset = self->offset;
        Py_INCREF(offset);
    }
    /* Offset is not negative here. */
    seconds = GET_TD_SECONDS(offset);
    Py_DECREF(offset);
    minutes = divmod(seconds, 60, &seconds);
    hours = divmod(minutes, 60, &minutes);
    /* XXX ignore sub-minute data, currently not allowed. */
    assert(seconds == 0);
    return PyUnicode_FromFormat("UTC%c%02d:%02d", sign, hours, minutes);
}

static PyObject *
timezone_tzname(PyDateTime_TimeZone *self, PyObject *dt)
{
    if (_timezone_check_argument(dt, "tzname") == -1)
        return NULL;

    return timezone_str(self);
}

static PyObject *
timezone_utcoffset(PyDateTime_TimeZone *self, PyObject *dt)
{
    if (_timezone_check_argument(dt, "utcoffset") == -1)
        return NULL;

    Py_INCREF(self->offset);
    return self->offset;
}

static PyObject *
timezone_dst(PyObject *self, PyObject *dt)
{
    if (_timezone_check_argument(dt, "dst") == -1)
        return NULL;

    Py_RETURN_NONE;
}

static PyObject *
timezone_fromutc(PyDateTime_TimeZone *self, PyDateTime_DateTime *dt)
{
    if (!PyDateTime_Check(dt)) {
        PyErr_SetString(PyExc_TypeError,
                        "fromutc: argument must be a datetime");
        return NULL;
    }
    if (!HASTZINFO(dt) || dt->tzinfo != (PyObject *)self) {
        PyErr_SetString(PyExc_ValueError, "fromutc: dt.tzinfo "
                        "is not self");
        return NULL;
    }

    return add_datetime_timedelta(dt, (PyDateTime_Delta *)self->offset, 1);
}

static PyObject *
timezone_getinitargs(PyDateTime_TimeZone *self)
{
    if (self->name == NULL)
        return Py_BuildValue("(O)", self->offset);
    return Py_BuildValue("(OO)", self->offset, self->name);
}

static PyMethodDef timezone_methods[] = {
    {"tzname", (PyCFunction)timezone_tzname, METH_O,
     PyDoc_STR("If name is specified when timezone is created, returns the name."
               "  Otherwise returns offset as 'UTC(+|-)HH:MM'.")},

    {"utcoffset", (PyCFunction)timezone_utcoffset, METH_O,
     PyDoc_STR("Return fixed offset.")},

    {"dst", (PyCFunction)timezone_dst, METH_O,
     PyDoc_STR("Return None.")},

    {"fromutc", (PyCFunction)timezone_fromutc, METH_O,
     PyDoc_STR("datetime in UTC -> datetime in local time.")},

    {"__getinitargs__", (PyCFunction)timezone_getinitargs, METH_NOARGS,
     PyDoc_STR("pickle support")},

    {NULL, NULL}
};

static const char timezone_doc[] =
PyDoc_STR("Fixed offset from UTC implementation of tzinfo.");

static PyTypeObject PyDateTime_TimeZoneType = {
    PyVarObject_HEAD_INIT(NULL, 0)
    "datetime.timezone",              /* tp_name */
    sizeof(PyDateTime_TimeZone),      /* tp_basicsize */
    0,                                /* tp_itemsize */
    (destructor)timezone_dealloc,     /* tp_dealloc */
    0,                                /* tp_print */
    0,                                /* tp_getattr */
    0,                                /* tp_setattr */
    0,                                /* tp_reserved */
    (reprfunc)timezone_repr,          /* tp_repr */
    0,                                /* tp_as_number */
    0,                                /* tp_as_sequence */
    0,                                /* tp_as_mapping */
    (hashfunc)timezone_hash,          /* tp_hash */
    0,                                /* tp_call */
    (reprfunc)timezone_str,           /* tp_str */
    0,                                /* tp_getattro */
    0,                                /* tp_setattro */
    0,                                /* tp_as_buffer */
    Py_TPFLAGS_DEFAULT,               /* tp_flags */
    timezone_doc,                     /* tp_doc */
    0,                                /* tp_traverse */
    0,                                /* tp_clear */
    (richcmpfunc)timezone_richcompare,/* tp_richcompare */
    0,                                /* tp_weaklistoffset */
    0,                                /* tp_iter */
    0,                                /* tp_iternext */
    timezone_methods,                 /* tp_methods */
    0,                                /* tp_members */
    0,                                /* tp_getset */
    &PyDateTime_TZInfoType,           /* tp_base */
    0,                                /* tp_dict */
    0,                                /* tp_descr_get */
    0,                                /* tp_descr_set */
    0,                                /* tp_dictoffset */
    0,                                /* tp_init */
    0,                                /* tp_alloc */
    timezone_new,                     /* tp_new */
};

/*
 * PyDateTime_Time implementation.
 */

/* Accessor properties.
 */

static PyObject *
time_hour(PyDateTime_Time *self, void *unused)
{
    return PyLong_FromLong(TIME_GET_HOUR(self));
}

static PyObject *
time_minute(PyDateTime_Time *self, void *unused)
{
    return PyLong_FromLong(TIME_GET_MINUTE(self));
}

/* The name time_second conflicted with some platform header file. */
static PyObject *
py_time_second(PyDateTime_Time *self, void *unused)
{
    return PyLong_FromLong(TIME_GET_SECOND(self));
}

static PyObject *
time_microsecond(PyDateTime_Time *self, void *unused)
{
    return PyLong_FromLong(TIME_GET_MICROSECOND(self));
}

static PyObject *
time_tzinfo(PyDateTime_Time *self, void *unused)
{
    PyObject *result = HASTZINFO(self) ? self->tzinfo : Py_None;
    Py_INCREF(result);
    return result;
}

static PyObject *
time_fold(PyDateTime_Time *self, void *unused)
{
    return PyLong_FromLong(TIME_GET_FOLD(self));
}

static PyGetSetDef time_getset[] = {
    {"hour",        (getter)time_hour},
    {"minute",      (getter)time_minute},
    {"second",      (getter)py_time_second},
    {"microsecond", (getter)time_microsecond},
    {"tzinfo",      (getter)time_tzinfo},
    {"fold",        (getter)time_fold},
    {NULL}
};

/*
 * Constructors.
 */

static char *time_kws[] = {"hour", "minute", "second", "microsecond",
                           "tzinfo", "fold", NULL};

static PyObject *
time_new(PyTypeObject *type, PyObject *args, PyObject *kw)
{
    PyObject *self = NULL;
    PyObject *state;
    int hour = 0;
    int minute = 0;
    int second = 0;
    int usecond = 0;
    PyObject *tzinfo = Py_None;
    int fold = 0;

    /* Check for invocation from pickle with __getstate__ state */
    if (PyTuple_GET_SIZE(args) >= 1 &&
        PyTuple_GET_SIZE(args) <= 2 &&
        PyBytes_Check(state = PyTuple_GET_ITEM(args, 0)) &&
        PyBytes_GET_SIZE(state) == _PyDateTime_TIME_DATASIZE &&
        (0x7F & ((unsigned char) (PyBytes_AS_STRING(state)[0]))) < 24)
    {
        PyDateTime_Time *me;
        char aware;

        if (PyTuple_GET_SIZE(args) == 2) {
            tzinfo = PyTuple_GET_ITEM(args, 1);
            if (check_tzinfo_subclass(tzinfo) < 0) {
                PyErr_SetString(PyExc_TypeError, "bad "
                    "tzinfo state arg");
                return NULL;
            }
        }
        aware = (char)(tzinfo != Py_None);
        me = (PyDateTime_Time *) (type->tp_alloc(type, aware));
        if (me != NULL) {
            char *pdata = PyBytes_AS_STRING(state);

            memcpy(me->data, pdata, _PyDateTime_TIME_DATASIZE);
            me->hashcode = -1;
            me->hastzinfo = aware;
            if (aware) {
                Py_INCREF(tzinfo);
                me->tzinfo = tzinfo;
            }
            if (pdata[0] & (1 << 7)) {
                me->data[0] -= 128;
                me->fold = 1;
            }
            else {
                me->fold = 0;
            }
        }
        return (PyObject *)me;
    }

    if (PyArg_ParseTupleAndKeywords(args, kw, "|iiiiO$i", time_kws,
                                    &hour, &minute, &second, &usecond,
                                    &tzinfo, &fold)) {
        self = new_time_ex2(hour, minute, second, usecond, tzinfo, fold,
                            type);
    }
    return self;
}

/*
 * Destructor.
 */

static void
time_dealloc(PyDateTime_Time *self)
{
    if (HASTZINFO(self)) {
        Py_XDECREF(self->tzinfo);
    }
    Py_TYPE(self)->tp_free((PyObject *)self);
}

/*
 * Indirect access to tzinfo methods.
 */

/* These are all METH_NOARGS, so don't need to check the arglist. */
static PyObject *
time_utcoffset(PyObject *self, PyObject *unused) {
    return call_utcoffset(GET_TIME_TZINFO(self), Py_None);
}

static PyObject *
time_dst(PyObject *self, PyObject *unused) {
    return call_dst(GET_TIME_TZINFO(self), Py_None);
}

static PyObject *
time_tzname(PyDateTime_Time *self, PyObject *unused) {
    return call_tzname(GET_TIME_TZINFO(self), Py_None);
}

/*
 * Various ways to turn a time into a string.
 */

static PyObject *
time_repr(PyDateTime_Time *self)
{
    const char *type_name = Py_TYPE(self)->tp_name;
    int h = TIME_GET_HOUR(self);
    int m = TIME_GET_MINUTE(self);
    int s = TIME_GET_SECOND(self);
    int us = TIME_GET_MICROSECOND(self);
    int fold = TIME_GET_FOLD(self);
    PyObject *result = NULL;

    if (us)
        result = PyUnicode_FromFormat("%s(%d, %d, %d, %d)",
                                      type_name, h, m, s, us);
    else if (s)
        result = PyUnicode_FromFormat("%s(%d, %d, %d)",
                                      type_name, h, m, s);
    else
        result = PyUnicode_FromFormat("%s(%d, %d)", type_name, h, m);
    if (result != NULL && HASTZINFO(self))
        result = append_keyword_tzinfo(result, self->tzinfo);
    if (result != NULL && fold)
        result = append_keyword_fold(result, fold);
    return result;
}

static PyObject *
time_str(PyDateTime_Time *self)
{
    return _PyObject_CallMethodId((PyObject *)self, &PyId_isoformat, NULL);
}

static PyObject *
time_isoformat(PyDateTime_Time *self, PyObject *args, PyObject *kw)
{
    char buf[100];
    char *timespec = NULL;
    static char *keywords[] = {"timespec", NULL};
    PyObject *result;
    int us = TIME_GET_MICROSECOND(self);
    static char *specs[][2] = {
        {"hours", "%02d"},
        {"minutes", "%02d:%02d"},
        {"seconds", "%02d:%02d:%02d"},
        {"milliseconds", "%02d:%02d:%02d.%03d"},
        {"microseconds", "%02d:%02d:%02d.%06d"},
    };
    size_t given_spec;

    if (!PyArg_ParseTupleAndKeywords(args, kw, "|s:isoformat", keywords, &timespec))
        return NULL;

    if (timespec == NULL || strcmp(timespec, "auto") == 0) {
        if (us == 0) {
            /* seconds */
            given_spec = 2;
        }
        else {
            /* microseconds */
            given_spec = 4;
        }
    }
    else {
        for (given_spec = 0; given_spec < Py_ARRAY_LENGTH(specs); given_spec++) {
            if (strcmp(timespec, specs[given_spec][0]) == 0) {
                if (given_spec == 3) {
                    /* milliseconds */
                    us = us / 1000;
                }
                break;
            }
        }
    }

    if (given_spec == Py_ARRAY_LENGTH(specs)) {
        PyErr_Format(PyExc_ValueError, "Unknown timespec value");
        return NULL;
    }
    else {
        result = PyUnicode_FromFormat(specs[given_spec][1],
                                      TIME_GET_HOUR(self), TIME_GET_MINUTE(self),
                                      TIME_GET_SECOND(self), us);
    }

    if (result == NULL || !HASTZINFO(self) || self->tzinfo == Py_None)
        return result;

    /* We need to append the UTC offset. */
    if (format_utcoffset(buf, sizeof(buf), ":", self->tzinfo,
                         Py_None) < 0) {
        Py_DECREF(result);
        return NULL;
    }
    PyUnicode_AppendAndDel(&result, PyUnicode_FromString(buf));
    return result;
}

static PyObject *
time_strftime(PyDateTime_Time *self, PyObject *args, PyObject *kw)
{
    PyObject *result;
    PyObject *tuple;
    PyObject *format;
    static char *keywords[] = {"format", NULL};

    if (! PyArg_ParseTupleAndKeywords(args, kw, "U:strftime", keywords,
                                      &format))
        return NULL;

    /* Python's strftime does insane things with the year part of the
     * timetuple.  The year is forced to (the otherwise nonsensical)
     * 1900 to work around that.
     */
    tuple = Py_BuildValue("iiiiiiiii",
                          1900, 1, 1, /* year, month, day */
                  TIME_GET_HOUR(self),
                  TIME_GET_MINUTE(self),
                  TIME_GET_SECOND(self),
                  0, 1, -1); /* weekday, daynum, dst */
    if (tuple == NULL)
        return NULL;
    assert(PyTuple_Size(tuple) == 9);
    result = wrap_strftime((PyObject *)self, format, tuple,
                           Py_None);
    Py_DECREF(tuple);
    return result;
}

/*
 * Miscellaneous methods.
 */

static PyObject *
time_richcompare(PyObject *self, PyObject *other, int op)
{
    PyObject *result = NULL;
    PyObject *offset1, *offset2;
    int diff;

    if (! PyTime_Check(other))
        Py_RETURN_NOTIMPLEMENTED;

    if (GET_TIME_TZINFO(self) == GET_TIME_TZINFO(other)) {
        diff = memcmp(((PyDateTime_Time *)self)->data,
                      ((PyDateTime_Time *)other)->data,
                      _PyDateTime_TIME_DATASIZE);
        return diff_to_bool(diff, op);
    }
    offset1 = time_utcoffset(self, NULL);
    if (offset1 == NULL)
        return NULL;
    offset2 = time_utcoffset(other, NULL);
    if (offset2 == NULL)
        goto done;
    /* If they're both naive, or both aware and have the same offsets,
     * we get off cheap.  Note that if they're both naive, offset1 ==
     * offset2 == Py_None at this point.
     */
    if ((offset1 == offset2) ||
        (PyDelta_Check(offset1) && PyDelta_Check(offset2) &&
         delta_cmp(offset1, offset2) == 0)) {
        diff = memcmp(((PyDateTime_Time *)self)->data,
                      ((PyDateTime_Time *)other)->data,
                      _PyDateTime_TIME_DATASIZE);
        result = diff_to_bool(diff, op);
    }
    /* The hard case: both aware with different UTC offsets */
    else if (offset1 != Py_None && offset2 != Py_None) {
        int offsecs1, offsecs2;
        assert(offset1 != offset2); /* else last "if" handled it */
        offsecs1 = TIME_GET_HOUR(self) * 3600 +
                   TIME_GET_MINUTE(self) * 60 +
                   TIME_GET_SECOND(self) -
                   GET_TD_DAYS(offset1) * 86400 -
                   GET_TD_SECONDS(offset1);
        offsecs2 = TIME_GET_HOUR(other) * 3600 +
                   TIME_GET_MINUTE(other) * 60 +
                   TIME_GET_SECOND(other) -
                   GET_TD_DAYS(offset2) * 86400 -
                   GET_TD_SECONDS(offset2);
        diff = offsecs1 - offsecs2;
        if (diff == 0)
            diff = TIME_GET_MICROSECOND(self) -
                   TIME_GET_MICROSECOND(other);
        result = diff_to_bool(diff, op);
    }
    else if (op == Py_EQ) {
        result = Py_False;
        Py_INCREF(result);
    }
    else if (op == Py_NE) {
        result = Py_True;
        Py_INCREF(result);
    }
    else {
        PyErr_SetString(PyExc_TypeError,
                        "can't compare offset-naive and "
                        "offset-aware times");
    }
 done:
    Py_DECREF(offset1);
    Py_XDECREF(offset2);
    return result;
}

static Py_hash_t
time_hash(PyDateTime_Time *self)
{
    if (self->hashcode == -1) {
        PyObject *offset, *self0;
        if (TIME_GET_FOLD(self)) {
            self0 = new_time_ex2(TIME_GET_HOUR(self),
                                 TIME_GET_MINUTE(self),
                                 TIME_GET_SECOND(self),
                                 TIME_GET_MICROSECOND(self),
                                 HASTZINFO(self) ? self->tzinfo : Py_None,
                                 0, Py_TYPE(self));
            if (self0 == NULL)
                return -1;
        }
        else {
            self0 = (PyObject *)self;
            Py_INCREF(self0);
        }
        offset = time_utcoffset(self0, NULL);
        Py_DECREF(self0);

        if (offset == NULL)
            return -1;

        /* Reduce this to a hash of another object. */
        if (offset == Py_None)
            self->hashcode = generic_hash(
                (unsigned char *)self->data, _PyDateTime_TIME_DATASIZE);
        else {
            PyObject *temp1, *temp2;
            int seconds, microseconds;
            assert(HASTZINFO(self));
            seconds = TIME_GET_HOUR(self) * 3600 +
                      TIME_GET_MINUTE(self) * 60 +
                      TIME_GET_SECOND(self);
            microseconds = TIME_GET_MICROSECOND(self);
            temp1 = new_delta(0, seconds, microseconds, 1);
            if (temp1 == NULL) {
                Py_DECREF(offset);
                return -1;
            }
            temp2 = delta_subtract(temp1, offset);
            Py_DECREF(temp1);
            if (temp2 == NULL) {
                Py_DECREF(offset);
                return -1;
            }
            self->hashcode = PyObject_Hash(temp2);
            Py_DECREF(temp2);
        }
        Py_DECREF(offset);
    }
    return self->hashcode;
}

static PyObject *
time_replace(PyDateTime_Time *self, PyObject *args, PyObject *kw)
{
    PyObject *clone;
    PyObject *tuple;
    int hh = TIME_GET_HOUR(self);
    int mm = TIME_GET_MINUTE(self);
    int ss = TIME_GET_SECOND(self);
    int us = TIME_GET_MICROSECOND(self);
    PyObject *tzinfo = HASTZINFO(self) ? self->tzinfo : Py_None;
    int fold = TIME_GET_FOLD(self);

    if (! PyArg_ParseTupleAndKeywords(args, kw, "|iiiiO$i:replace",
                                      time_kws,
                                      &hh, &mm, &ss, &us, &tzinfo, &fold))
        return NULL;
    tuple = Py_BuildValue("iiiiO", hh, mm, ss, us, tzinfo);
    if (tuple == NULL)
        return NULL;
    clone = time_new(Py_TYPE(self), tuple, NULL);
    if (clone != NULL) {
        if (fold != 0 && fold != 1) {
            PyErr_SetString(PyExc_ValueError,
                            "fold must be either 0 or 1");
            return NULL;
        }
        TIME_SET_FOLD(clone, fold);
    }
    Py_DECREF(tuple);
    return clone;
}

/* Pickle support, a simple use of __reduce__. */

/* Let basestate be the non-tzinfo data string.
 * If tzinfo is None, this returns (basestate,), else (basestate, tzinfo).
 * So it's a tuple in any (non-error) case.
 * __getstate__ isn't exposed.
 */
static PyObject *
time_getstate(PyDateTime_Time *self, int proto)
{
    PyObject *basestate;
    PyObject *result = NULL;

    basestate =  PyBytes_FromStringAndSize((char *)self->data,
                                            _PyDateTime_TIME_DATASIZE);
    if (basestate != NULL) {
        if (proto > 3 && TIME_GET_FOLD(self))
            /* Set the first bit of the first byte */
            PyBytes_AS_STRING(basestate)[0] |= (1 << 7);
        if (! HASTZINFO(self) || self->tzinfo == Py_None)
            result = PyTuple_Pack(1, basestate);
        else
            result = PyTuple_Pack(2, basestate, self->tzinfo);
        Py_DECREF(basestate);
    }
    return result;
}

static PyObject *
time_reduce_ex(PyDateTime_Time *self, PyObject *args)
{
    int proto;
    if (!PyArg_ParseTuple(args, "i:__reduce_ex__", &proto))
        return NULL;

    return Py_BuildValue("(ON)", Py_TYPE(self), time_getstate(self, proto));
}

static PyObject *
time_reduce(PyDateTime_Time *self, PyObject *arg)
{
    return Py_BuildValue("(ON)", Py_TYPE(self), time_getstate(self, 2));
}

static PyMethodDef time_methods[] = {

    {"isoformat",   (PyCFunction)time_isoformat,        METH_VARARGS | METH_KEYWORDS,
     PyDoc_STR("Return string in ISO 8601 format, [HH[:MM[:SS[.mmm[uuu]]]]]"
               "[+HH:MM].\n\n"
               "timespec specifies what components of the time to include.\n")},

    {"strftime",        (PyCFunction)time_strftime,     METH_VARARGS | METH_KEYWORDS,
     PyDoc_STR("format -> strftime() style string.")},

    {"__format__",      (PyCFunction)date_format,       METH_VARARGS,
     PyDoc_STR("Formats self with strftime.")},

    {"utcoffset",       (PyCFunction)time_utcoffset,    METH_NOARGS,
     PyDoc_STR("Return self.tzinfo.utcoffset(self).")},

    {"tzname",          (PyCFunction)time_tzname,       METH_NOARGS,
     PyDoc_STR("Return self.tzinfo.tzname(self).")},

    {"dst",             (PyCFunction)time_dst,          METH_NOARGS,
     PyDoc_STR("Return self.tzinfo.dst(self).")},

    {"replace",     (PyCFunction)time_replace,          METH_VARARGS | METH_KEYWORDS,
     PyDoc_STR("Return time with new specified fields.")},

    {"__reduce_ex__", (PyCFunction)time_reduce_ex,        METH_VARARGS,
     PyDoc_STR("__reduce_ex__(proto) -> (cls, state)")},

    {"__reduce__", (PyCFunction)time_reduce,        METH_NOARGS,
     PyDoc_STR("__reduce__() -> (cls, state)")},

    {NULL,      NULL}
};

static const char time_doc[] =
PyDoc_STR("time([hour[, minute[, second[, microsecond[, tzinfo]]]]]) --> a time object\n\
\n\
All arguments are optional. tzinfo may be None, or an instance of\n\
a tzinfo subclass. The remaining arguments may be ints.\n");

static PyTypeObject PyDateTime_TimeType = {
    PyVarObject_HEAD_INIT(NULL, 0)
    "datetime.time",                            /* tp_name */
    sizeof(PyDateTime_Time),                    /* tp_basicsize */
    0,                                          /* tp_itemsize */
    (destructor)time_dealloc,                   /* tp_dealloc */
    0,                                          /* tp_print */
    0,                                          /* tp_getattr */
    0,                                          /* tp_setattr */
    0,                                          /* tp_reserved */
    (reprfunc)time_repr,                        /* tp_repr */
    0,                                          /* tp_as_number */
    0,                                          /* tp_as_sequence */
    0,                                          /* tp_as_mapping */
    (hashfunc)time_hash,                        /* tp_hash */
    0,                                          /* tp_call */
    (reprfunc)time_str,                         /* tp_str */
    PyObject_GenericGetAttr,                    /* tp_getattro */
    0,                                          /* tp_setattro */
    0,                                          /* tp_as_buffer */
    Py_TPFLAGS_DEFAULT | Py_TPFLAGS_BASETYPE, /* tp_flags */
    time_doc,                                   /* tp_doc */
    0,                                          /* tp_traverse */
    0,                                          /* tp_clear */
    time_richcompare,                           /* tp_richcompare */
    0,                                          /* tp_weaklistoffset */
    0,                                          /* tp_iter */
    0,                                          /* tp_iternext */
    time_methods,                               /* tp_methods */
    0,                                          /* tp_members */
    time_getset,                                /* tp_getset */
    0,                                          /* tp_base */
    0,                                          /* tp_dict */
    0,                                          /* tp_descr_get */
    0,                                          /* tp_descr_set */
    0,                                          /* tp_dictoffset */
    0,                                          /* tp_init */
    time_alloc,                                 /* tp_alloc */
    time_new,                                   /* tp_new */
    0,                                          /* tp_free */
};

/*
 * PyDateTime_DateTime implementation.
 */

/* Accessor properties.  Properties for day, month, and year are inherited
 * from date.
 */

static PyObject *
datetime_hour(PyDateTime_DateTime *self, void *unused)
{
    return PyLong_FromLong(DATE_GET_HOUR(self));
}

static PyObject *
datetime_minute(PyDateTime_DateTime *self, void *unused)
{
    return PyLong_FromLong(DATE_GET_MINUTE(self));
}

static PyObject *
datetime_second(PyDateTime_DateTime *self, void *unused)
{
    return PyLong_FromLong(DATE_GET_SECOND(self));
}

static PyObject *
datetime_microsecond(PyDateTime_DateTime *self, void *unused)
{
    return PyLong_FromLong(DATE_GET_MICROSECOND(self));
}

static PyObject *
datetime_tzinfo(PyDateTime_DateTime *self, void *unused)
{
    PyObject *result = HASTZINFO(self) ? self->tzinfo : Py_None;
    Py_INCREF(result);
    return result;
}

static PyObject *
datetime_fold(PyDateTime_DateTime *self, void *unused)
{
    return PyLong_FromLong(DATE_GET_FOLD(self));
}

static PyGetSetDef datetime_getset[] = {
    {"hour",        (getter)datetime_hour},
    {"minute",      (getter)datetime_minute},
    {"second",      (getter)datetime_second},
    {"microsecond", (getter)datetime_microsecond},
    {"tzinfo",      (getter)datetime_tzinfo},
    {"fold",        (getter)datetime_fold},
    {NULL}
};

/*
 * Constructors.
 */

static char *datetime_kws[] = {
    "year", "month", "day", "hour", "minute", "second",
    "microsecond", "tzinfo", "fold", NULL
};

static PyObject *
datetime_new(PyTypeObject *type, PyObject *args, PyObject *kw)
{
    PyObject *self = NULL;
    PyObject *state;
    int year;
    int month;
    int day;
    int hour = 0;
    int minute = 0;
    int second = 0;
    int usecond = 0;
    int fold = 0;
    PyObject *tzinfo = Py_None;

    /* Check for invocation from pickle with __getstate__ state */
    if (PyTuple_GET_SIZE(args) >= 1 &&
        PyTuple_GET_SIZE(args) <= 2 &&
        PyBytes_Check(state = PyTuple_GET_ITEM(args, 0)) &&
        PyBytes_GET_SIZE(state) == _PyDateTime_DATETIME_DATASIZE &&
        MONTH_IS_SANE(PyBytes_AS_STRING(state)[2] & 0x7F))
    {
        PyDateTime_DateTime *me;
        char aware;

        if (PyTuple_GET_SIZE(args) == 2) {
            tzinfo = PyTuple_GET_ITEM(args, 1);
            if (check_tzinfo_subclass(tzinfo) < 0) {
                PyErr_SetString(PyExc_TypeError, "bad "
                    "tzinfo state arg");
                return NULL;
            }
        }
        aware = (char)(tzinfo != Py_None);
        me = (PyDateTime_DateTime *) (type->tp_alloc(type , aware));
        if (me != NULL) {
            char *pdata = PyBytes_AS_STRING(state);

            memcpy(me->data, pdata, _PyDateTime_DATETIME_DATASIZE);
            me->hashcode = -1;
            me->hastzinfo = aware;
            if (aware) {
                Py_INCREF(tzinfo);
                me->tzinfo = tzinfo;
            }
            if (pdata[2] & (1 << 7)) {
                me->data[2] -= 128;
                me->fold = 1;
            }
            else {
                me->fold = 0;
            }
        }
        return (PyObject *)me;
    }

    if (PyArg_ParseTupleAndKeywords(args, kw, "iii|iiiiO$i", datetime_kws,
                                    &year, &month, &day, &hour, &minute,
                                    &second, &usecond, &tzinfo, &fold)) {
        self = new_datetime_ex2(year, month, day,
                                hour, minute, second, usecond,
                                tzinfo, fold, type);
    }
    return self;
}

/* TM_FUNC is the shared type of _PyTime_localtime() and
 * _PyTime_gmtime(). */
typedef int (*TM_FUNC)(time_t timer, struct tm*);

/* As of version 2015f max fold in IANA database is
 * 23 hours at 1969-09-30 13:00:00 in Kwajalein. */
static long long max_fold_seconds = 24 * 3600;
/* NB: date(1970,1,1).toordinal() == 719163 */
static long long epoch = 719163LL * 24 * 60 * 60;

static long long
utc_to_seconds(int year, int month, int day,
               int hour, int minute, int second)
{
    long long ordinal;

    /* ymd_to_ord() doesn't support year <= 0 */
    if (year < MINYEAR || year > MAXYEAR) {
        PyErr_Format(PyExc_ValueError, "year %i is out of range", year);
        return -1;
    }

    ordinal = ymd_to_ord(year, month, day);
    return ((ordinal * 24 + hour) * 60 + minute) * 60 + second;
}

static long long
local(long long u)
{
    struct tm local_time;
    time_t t;
    u -= epoch;
    t = u;
    if (t != u) {
        PyErr_SetString(PyExc_OverflowError,
        "timestamp out of range for platform time_t");
        return -1;
    }
    if (_PyTime_localtime(t, &local_time) != 0)
        return -1;
    return utc_to_seconds(local_time.tm_year + 1900,
                          local_time.tm_mon + 1,
                          local_time.tm_mday,
                          local_time.tm_hour,
                          local_time.tm_min,
                          local_time.tm_sec);
}

/* Internal helper.
 * Build datetime from a time_t and a distinct count of microseconds.
 * Pass localtime or gmtime for f, to control the interpretation of timet.
 */
static PyObject *
datetime_from_timet_and_us(PyObject *cls, TM_FUNC f, time_t timet, int us,
                           PyObject *tzinfo)
{
    struct tm tm;
    int year, month, day, hour, minute, second, fold = 0;

    if (f(timet, &tm) != 0)
        return NULL;

    year = tm.tm_year + 1900;
    month = tm.tm_mon + 1;
    day = tm.tm_mday;
    hour = tm.tm_hour;
    minute = tm.tm_min;
    /* The platform localtime/gmtime may insert leap seconds,
     * indicated by tm.tm_sec > 59.  We don't care about them,
     * except to the extent that passing them on to the datetime
     * constructor would raise ValueError for a reason that
     * made no sense to the user.
     */
    second = Py_MIN(59, tm.tm_sec);

    /* local timezone requires to compute fold */
    if (tzinfo == Py_None && f == _PyTime_localtime) {
        long long probe_seconds, result_seconds, transition;

        result_seconds = utc_to_seconds(year, month, day,
                                        hour, minute, second);
        /* Probe max_fold_seconds to detect a fold. */
        probe_seconds = local(epoch + timet - max_fold_seconds);
        if (probe_seconds == -1)
            return NULL;
        transition = result_seconds - probe_seconds - max_fold_seconds;
        if (transition < 0) {
            probe_seconds = local(epoch + timet + transition);
            if (probe_seconds == -1)
                return NULL;
            if (probe_seconds == result_seconds)
                fold = 1;
        }
    }
    return new_datetime_ex2(year, month, day, hour,
                            minute, second, us, tzinfo, fold,
                            (PyTypeObject *)cls);
}

/* Internal helper.
 * Build datetime from a Python timestamp.  Pass localtime or gmtime for f,
 * to control the interpretation of the timestamp.  Since a double doesn't
 * have enough bits to cover a datetime's full range of precision, it's
 * better to call datetime_from_timet_and_us provided you have a way
 * to get that much precision (e.g., C time() isn't good enough).
 */
static PyObject *
datetime_from_timestamp(PyObject *cls, TM_FUNC f, PyObject *timestamp,
                        PyObject *tzinfo)
{
    time_t timet;
    long us;

    if (_PyTime_ObjectToTimeval(timestamp,
                                &timet, &us, _PyTime_ROUND_HALF_EVEN) == -1)
        return NULL;

    return datetime_from_timet_and_us(cls, f, timet, (int)us, tzinfo);
}

/* Internal helper.
 * Build most accurate possible datetime for current time.  Pass localtime or
 * gmtime for f as appropriate.
 */
static PyObject *
datetime_best_possible(PyObject *cls, TM_FUNC f, PyObject *tzinfo)
{
    _PyTime_t ts = _PyTime_GetSystemClock();
    time_t secs;
    int us;

    if (_PyTime_AsTimevalTime_t(ts, &secs, &us, _PyTime_ROUND_FLOOR) < 0)
        return NULL;
    assert(0 <= us && us <= 999999);

    return datetime_from_timet_and_us(cls, f, secs, us, tzinfo);
}

/*[clinic input]

@classmethod
datetime.datetime.now

    tz: object = None
        Timezone object.

Returns new datetime object representing current time local to tz.

If no tz is specified, uses local timezone.
[clinic start generated code]*/

static PyObject *
datetime_datetime_now_impl(PyTypeObject *type, PyObject *tz)
/*[clinic end generated code: output=b3386e5345e2b47a input=80d09869c5267d00]*/
{
    PyObject *self;

    /* Return best possible local time -- this isn't constrained by the
     * precision of a timestamp.
     */
    if (check_tzinfo_subclass(tz) < 0)
        return NULL;

    self = datetime_best_possible((PyObject *)type,
                                  tz == Py_None ? _PyTime_localtime :
                                  _PyTime_gmtime,
                                  tz);
    if (self != NULL && tz != Py_None) {
        /* Convert UTC to tzinfo's zone. */
        self = _PyObject_CallMethodId(tz, &PyId_fromutc, "N", self);
    }
    return self;
}

/* Return best possible UTC time -- this isn't constrained by the
 * precision of a timestamp.
 */
static PyObject *
datetime_utcnow(PyObject *cls, PyObject *dummy)
{
    return datetime_best_possible(cls, _PyTime_gmtime, Py_None);
}

/* Return new local datetime from timestamp (Python timestamp -- a double). */
static PyObject *
datetime_fromtimestamp(PyObject *cls, PyObject *args, PyObject *kw)
{
    PyObject *self;
    PyObject *timestamp;
    PyObject *tzinfo = Py_None;
    static char *keywords[] = {"timestamp", "tz", NULL};

    if (! PyArg_ParseTupleAndKeywords(args, kw, "O|O:fromtimestamp",
                                      keywords, &timestamp, &tzinfo))
        return NULL;
    if (check_tzinfo_subclass(tzinfo) < 0)
        return NULL;

    self = datetime_from_timestamp(cls,
                                   tzinfo == Py_None ? _PyTime_localtime :
                                   _PyTime_gmtime,
                                   timestamp,
                                   tzinfo);
    if (self != NULL && tzinfo != Py_None) {
        /* Convert UTC to tzinfo's zone. */
        self = _PyObject_CallMethodId(tzinfo, &PyId_fromutc, "N", self);
    }
    return self;
}

/* Return new UTC datetime from timestamp (Python timestamp -- a double). */
static PyObject *
datetime_utcfromtimestamp(PyObject *cls, PyObject *args)
{
    PyObject *timestamp;
    PyObject *result = NULL;

    if (PyArg_ParseTuple(args, "O:utcfromtimestamp", &timestamp))
        result = datetime_from_timestamp(cls, _PyTime_gmtime, timestamp,
                                         Py_None);
    return result;
}

/* Return new datetime from _strptime.strptime_datetime(). */
static PyObject *
datetime_strptime(PyObject *cls, PyObject *args)
{
    static PyObject *module = NULL;
    PyObject *string, *format;
    _Py_IDENTIFIER(_strptime_datetime);

    if (!PyArg_ParseTuple(args, "UU:strptime", &string, &format))
        return NULL;

    if (module == NULL) {
        module = PyImport_ImportModuleNoBlock("_strptime");
        if (module == NULL)
            return NULL;
    }
    return _PyObject_CallMethodIdObjArgs(module, &PyId__strptime_datetime,
                                         cls, string, format, NULL);
}

/* Return new datetime from date/datetime and time arguments. */
static PyObject *
datetime_combine(PyObject *cls, PyObject *args, PyObject *kw)
{
    static char *keywords[] = {"date", "time", "tzinfo", NULL};
    PyObject *date;
    PyObject *time;
    PyObject *tzinfo = NULL;
    PyObject *result = NULL;

    if (PyArg_ParseTupleAndKeywords(args, kw, "O!O!|O:combine", keywords,
                                    &PyDateTime_DateType, &date,
                                    &PyDateTime_TimeType, &time, &tzinfo)) {
        if (tzinfo == NULL) {
            if (HASTZINFO(time))
                tzinfo = ((PyDateTime_Time *)time)->tzinfo;
            else
                tzinfo = Py_None;
        }
        result = PyObject_CallFunction(cls, "iiiiiiiO",
                                       GET_YEAR(date),
                                       GET_MONTH(date),
                                       GET_DAY(date),
                                       TIME_GET_HOUR(time),
                                       TIME_GET_MINUTE(time),
                                       TIME_GET_SECOND(time),
                                       TIME_GET_MICROSECOND(time),
                                       tzinfo);
        if (result)
            DATE_SET_FOLD(result, TIME_GET_FOLD(time));
    }
    return result;
}

/*
 * Destructor.
 */

static void
datetime_dealloc(PyDateTime_DateTime *self)
{
    if (HASTZINFO(self)) {
        Py_XDECREF(self->tzinfo);
    }
    Py_TYPE(self)->tp_free((PyObject *)self);
}

/*
 * Indirect access to tzinfo methods.
 */

/* These are all METH_NOARGS, so don't need to check the arglist. */
static PyObject *
datetime_utcoffset(PyObject *self, PyObject *unused) {
    return call_utcoffset(GET_DT_TZINFO(self), self);
}

static PyObject *
datetime_dst(PyObject *self, PyObject *unused) {
    return call_dst(GET_DT_TZINFO(self), self);
}

static PyObject *
datetime_tzname(PyObject *self, PyObject *unused) {
    return call_tzname(GET_DT_TZINFO(self), self);
}

/*
 * datetime arithmetic.
 */

/* factor must be 1 (to add) or -1 (to subtract).  The result inherits
 * the tzinfo state of date.
 */
static PyObject *
add_datetime_timedelta(PyDateTime_DateTime *date, PyDateTime_Delta *delta,
                       int factor)
{
    /* Note that the C-level additions can't overflow, because of
     * invariant bounds on the member values.
     */
    int year = GET_YEAR(date);
    int month = GET_MONTH(date);
    int day = GET_DAY(date) + GET_TD_DAYS(delta) * factor;
    int hour = DATE_GET_HOUR(date);
    int minute = DATE_GET_MINUTE(date);
    int second = DATE_GET_SECOND(date) + GET_TD_SECONDS(delta) * factor;
    int microsecond = DATE_GET_MICROSECOND(date) +
                      GET_TD_MICROSECONDS(delta) * factor;

    assert(factor == 1 || factor == -1);
    if (normalize_datetime(&year, &month, &day,
                           &hour, &minute, &second, &microsecond) < 0) {
        return NULL;
    }

    return new_datetime(year, month, day,
                        hour, minute, second, microsecond,
                        HASTZINFO(date) ? date->tzinfo : Py_None, 0);
}

static PyObject *
datetime_add(PyObject *left, PyObject *right)
{
    if (PyDateTime_Check(left)) {
        /* datetime + ??? */
        if (PyDelta_Check(right))
            /* datetime + delta */
            return add_datetime_timedelta(
                            (PyDateTime_DateTime *)left,
                            (PyDateTime_Delta *)right,
                            1);
    }
    else if (PyDelta_Check(left)) {
        /* delta + datetime */
        return add_datetime_timedelta((PyDateTime_DateTime *) right,
                                      (PyDateTime_Delta *) left,
                                      1);
    }
    Py_RETURN_NOTIMPLEMENTED;
}

static PyObject *
datetime_subtract(PyObject *left, PyObject *right)
{
    PyObject *result = Py_NotImplemented;

    if (PyDateTime_Check(left)) {
        /* datetime - ??? */
        if (PyDateTime_Check(right)) {
            /* datetime - datetime */
            PyObject *offset1, *offset2, *offdiff = NULL;
            int delta_d, delta_s, delta_us;

            if (GET_DT_TZINFO(left) == GET_DT_TZINFO(right)) {
                offset2 = offset1 = Py_None;
                Py_INCREF(offset1);
                Py_INCREF(offset2);
            }
            else {
                offset1 = datetime_utcoffset(left, NULL);
                if (offset1 == NULL)
                    return NULL;
                offset2 = datetime_utcoffset(right, NULL);
                if (offset2 == NULL) {
                    Py_DECREF(offset1);
                    return NULL;
                }
                if ((offset1 != Py_None) != (offset2 != Py_None)) {
                    PyErr_SetString(PyExc_TypeError,
                                    "can't subtract offset-naive and "
                                    "offset-aware datetimes");
                    Py_DECREF(offset1);
                    Py_DECREF(offset2);
                    return NULL;
                }
            }
            if ((offset1 != offset2) &&
                delta_cmp(offset1, offset2) != 0) {
                offdiff = delta_subtract(offset1, offset2);
                if (offdiff == NULL) {
                    Py_DECREF(offset1);
                    Py_DECREF(offset2);
                    return NULL;
                }
            }
            Py_DECREF(offset1);
            Py_DECREF(offset2);
            delta_d = ymd_to_ord(GET_YEAR(left),
                                 GET_MONTH(left),
                                 GET_DAY(left)) -
                      ymd_to_ord(GET_YEAR(right),
                                 GET_MONTH(right),
                                 GET_DAY(right));
            /* These can't overflow, since the values are
             * normalized.  At most this gives the number of
             * seconds in one day.
             */
            delta_s = (DATE_GET_HOUR(left) -
                       DATE_GET_HOUR(right)) * 3600 +
                      (DATE_GET_MINUTE(left) -
                       DATE_GET_MINUTE(right)) * 60 +
                      (DATE_GET_SECOND(left) -
                       DATE_GET_SECOND(right));
            delta_us = DATE_GET_MICROSECOND(left) -
                       DATE_GET_MICROSECOND(right);
            result = new_delta(delta_d, delta_s, delta_us, 1);
            if (result == NULL)
                return NULL;

            if (offdiff != NULL) {
                Py_SETREF(result, delta_subtract(result, offdiff));
                Py_DECREF(offdiff);
            }
        }
        else if (PyDelta_Check(right)) {
            /* datetime - delta */
            result = add_datetime_timedelta(
                            (PyDateTime_DateTime *)left,
                            (PyDateTime_Delta *)right,
                            -1);
        }
    }

    if (result == Py_NotImplemented)
        Py_INCREF(result);
    return result;
}

/* Various ways to turn a datetime into a string. */

static PyObject *
datetime_repr(PyDateTime_DateTime *self)
{
    const char *type_name = Py_TYPE(self)->tp_name;
    PyObject *baserepr;

    if (DATE_GET_MICROSECOND(self)) {
        baserepr = PyUnicode_FromFormat(
                      "%s(%d, %d, %d, %d, %d, %d, %d)",
                      type_name,
                      GET_YEAR(self), GET_MONTH(self), GET_DAY(self),
                      DATE_GET_HOUR(self), DATE_GET_MINUTE(self),
                      DATE_GET_SECOND(self),
                      DATE_GET_MICROSECOND(self));
    }
    else if (DATE_GET_SECOND(self)) {
        baserepr = PyUnicode_FromFormat(
                      "%s(%d, %d, %d, %d, %d, %d)",
                      type_name,
                      GET_YEAR(self), GET_MONTH(self), GET_DAY(self),
                      DATE_GET_HOUR(self), DATE_GET_MINUTE(self),
                      DATE_GET_SECOND(self));
    }
    else {
        baserepr = PyUnicode_FromFormat(
                      "%s(%d, %d, %d, %d, %d)",
                      type_name,
                      GET_YEAR(self), GET_MONTH(self), GET_DAY(self),
                      DATE_GET_HOUR(self), DATE_GET_MINUTE(self));
    }
    if (baserepr != NULL && DATE_GET_FOLD(self) != 0)
        baserepr = append_keyword_fold(baserepr, DATE_GET_FOLD(self));
    if (baserepr == NULL || ! HASTZINFO(self))
        return baserepr;
    return append_keyword_tzinfo(baserepr, self->tzinfo);
}

static PyObject *
datetime_str(PyDateTime_DateTime *self)
{
    return _PyObject_CallMethodId((PyObject *)self, &PyId_isoformat, "s", " ");
}

static PyObject *
datetime_isoformat(PyDateTime_DateTime *self, PyObject *args, PyObject *kw)
{
    int sep = 'T';
    char *timespec = NULL;
    static char *keywords[] = {"sep", "timespec", NULL};
    char buffer[100];
    PyObject *result = NULL;
    int us = DATE_GET_MICROSECOND(self);
    static char *specs[][2] = {
        {"hours", "%04d-%02d-%02d%c%02d"},
        {"minutes", "%04d-%02d-%02d%c%02d:%02d"},
        {"seconds", "%04d-%02d-%02d%c%02d:%02d:%02d"},
        {"milliseconds", "%04d-%02d-%02d%c%02d:%02d:%02d.%03d"},
        {"microseconds", "%04d-%02d-%02d%c%02d:%02d:%02d.%06d"},
    };
    size_t given_spec;

    if (!PyArg_ParseTupleAndKeywords(args, kw, "|Cs:isoformat", keywords, &sep, &timespec))
        return NULL;

    if (timespec == NULL || strcmp(timespec, "auto") == 0) {
        if (us == 0) {
            /* seconds */
            given_spec = 2;
        }
        else {
            /* microseconds */
            given_spec = 4;
        }
    }
    else {
        for (given_spec = 0; given_spec < Py_ARRAY_LENGTH(specs); given_spec++) {
            if (strcmp(timespec, specs[given_spec][0]) == 0) {
                if (given_spec == 3) {
                    us = us / 1000;
                }
                break;
            }
        }
    }

    if (given_spec == Py_ARRAY_LENGTH(specs)) {
        PyErr_Format(PyExc_ValueError, "Unknown timespec value");
        return NULL;
    }
    else {
        result = PyUnicode_FromFormat(specs[given_spec][1],
                                      GET_YEAR(self), GET_MONTH(self),
                                      GET_DAY(self), (int)sep,
                                      DATE_GET_HOUR(self), DATE_GET_MINUTE(self),
                                      DATE_GET_SECOND(self), us);
    }

    if (!result || !HASTZINFO(self))
        return result;

    /* We need to append the UTC offset. */
    if (format_utcoffset(buffer, sizeof(buffer), ":", self->tzinfo,
                         (PyObject *)self) < 0) {
        Py_DECREF(result);
        return NULL;
    }
    PyUnicode_AppendAndDel(&result, PyUnicode_FromString(buffer));
    return result;
}

static PyObject *
datetime_ctime(PyDateTime_DateTime *self)
{
    return format_ctime((PyDateTime_Date *)self,
                        DATE_GET_HOUR(self),
                        DATE_GET_MINUTE(self),
                        DATE_GET_SECOND(self));
}

/* Miscellaneous methods. */

static PyObject *
flip_fold(PyObject *dt)
{
    return new_datetime_ex2(GET_YEAR(dt),
                            GET_MONTH(dt),
                            GET_DAY(dt),
                            DATE_GET_HOUR(dt),
                            DATE_GET_MINUTE(dt),
                            DATE_GET_SECOND(dt),
                            DATE_GET_MICROSECOND(dt),
                            HASTZINFO(dt) ?
                             ((PyDateTime_DateTime *)dt)->tzinfo : Py_None,
                            !DATE_GET_FOLD(dt),
                            Py_TYPE(dt));
}

static PyObject *
get_flip_fold_offset(PyObject *dt)
{
    PyObject *result, *flip_dt;

    flip_dt = flip_fold(dt);
    if (flip_dt == NULL)
        return NULL;
    result = datetime_utcoffset(flip_dt, NULL);
    Py_DECREF(flip_dt);
    return result;
}

/* PEP 495 exception: Whenever one or both of the operands in
 * inter-zone comparison is such that its utcoffset() depends
 * on the value of its fold fold attribute, the result is False.
 *
 * Return 1 if exception applies, 0 if not,  and -1 on error.
 */
static int
pep495_eq_exception(PyObject *self, PyObject *other,
                    PyObject *offset_self, PyObject *offset_other)
{
    int result = 0;
    PyObject *flip_offset;

    flip_offset = get_flip_fold_offset(self);
    if (flip_offset == NULL)
        return -1;
    if (flip_offset != offset_self &&
        delta_cmp(flip_offset, offset_self))
    {
        result = 1;
        goto done;
    }
    Py_DECREF(flip_offset);

    flip_offset = get_flip_fold_offset(other);
    if (flip_offset == NULL)
        return -1;
    if (flip_offset != offset_other &&
        delta_cmp(flip_offset, offset_other))
        result = 1;
 done:
    Py_DECREF(flip_offset);
    return result;
}

static PyObject *
datetime_richcompare(PyObject *self, PyObject *other, int op)
{
    PyObject *result = NULL;
    PyObject *offset1, *offset2;
    int diff;

    if (! PyDateTime_Check(other)) {
        if (PyDate_Check(other)) {
            /* Prevent invocation of date_richcompare.  We want to
               return NotImplemented here to give the other object
               a chance.  But since DateTime is a subclass of
               Date, if the other object is a Date, it would
               compute an ordering based on the date part alone,
               and we don't want that.  So force unequal or
               uncomparable here in that case. */
            if (op == Py_EQ)
                Py_RETURN_FALSE;
            if (op == Py_NE)
                Py_RETURN_TRUE;
            return cmperror(self, other);
        }
        Py_RETURN_NOTIMPLEMENTED;
    }

    if (GET_DT_TZINFO(self) == GET_DT_TZINFO(other)) {
        diff = memcmp(((PyDateTime_DateTime *)self)->data,
                      ((PyDateTime_DateTime *)other)->data,
                      _PyDateTime_DATETIME_DATASIZE);
        return diff_to_bool(diff, op);
    }
    offset1 = datetime_utcoffset(self, NULL);
    if (offset1 == NULL)
        return NULL;
    offset2 = datetime_utcoffset(other, NULL);
    if (offset2 == NULL)
        goto done;
    /* If they're both naive, or both aware and have the same offsets,
     * we get off cheap.  Note that if they're both naive, offset1 ==
     * offset2 == Py_None at this point.
     */
    if ((offset1 == offset2) ||
        (PyDelta_Check(offset1) && PyDelta_Check(offset2) &&
         delta_cmp(offset1, offset2) == 0)) {
        diff = memcmp(((PyDateTime_DateTime *)self)->data,
                      ((PyDateTime_DateTime *)other)->data,
                      _PyDateTime_DATETIME_DATASIZE);
        if ((op == Py_EQ || op == Py_NE) && diff == 0) {
            int ex = pep495_eq_exception(self, other, offset1, offset2);
            if (ex == -1)
                goto done;
            if (ex)
                diff = 1;
        }
        result = diff_to_bool(diff, op);
    }
    else if (offset1 != Py_None && offset2 != Py_None) {
        PyDateTime_Delta *delta;

        assert(offset1 != offset2); /* else last "if" handled it */
        delta = (PyDateTime_Delta *)datetime_subtract((PyObject *)self,
                                                       other);
        if (delta == NULL)
            goto done;
        diff = GET_TD_DAYS(delta);
        if (diff == 0)
            diff = GET_TD_SECONDS(delta) |
                   GET_TD_MICROSECONDS(delta);
        Py_DECREF(delta);
        if ((op == Py_EQ || op == Py_NE) && diff == 0) {
            int ex = pep495_eq_exception(self, other, offset1, offset2);
            if (ex == -1)
                goto done;
            if (ex)
                diff = 1;
        }
        result = diff_to_bool(diff, op);
    }
    else if (op == Py_EQ) {
        result = Py_False;
        Py_INCREF(result);
    }
    else if (op == Py_NE) {
        result = Py_True;
        Py_INCREF(result);
    }
    else {
        PyErr_SetString(PyExc_TypeError,
                        "can't compare offset-naive and "
                        "offset-aware datetimes");
    }
 done:
    Py_DECREF(offset1);
    Py_XDECREF(offset2);
    return result;
}

static Py_hash_t
datetime_hash(PyDateTime_DateTime *self)
{
    if (self->hashcode == -1) {
        PyObject *offset, *self0;
        if (DATE_GET_FOLD(self)) {
            self0 = new_datetime_ex2(GET_YEAR(self),
                                     GET_MONTH(self),
                                     GET_DAY(self),
                                     DATE_GET_HOUR(self),
                                     DATE_GET_MINUTE(self),
                                     DATE_GET_SECOND(self),
                                     DATE_GET_MICROSECOND(self),
                                     HASTZINFO(self) ? self->tzinfo : Py_None,
                                     0, Py_TYPE(self));
            if (self0 == NULL)
                return -1;
        }
        else {
            self0 = (PyObject *)self;
            Py_INCREF(self0);
        }
        offset = datetime_utcoffset(self0, NULL);
        Py_DECREF(self0);

        if (offset == NULL)
            return -1;

        /* Reduce this to a hash of another object. */
        if (offset == Py_None)
            self->hashcode = generic_hash(
                (unsigned char *)self->data, _PyDateTime_DATETIME_DATASIZE);
        else {
            PyObject *temp1, *temp2;
            int days, seconds;

            assert(HASTZINFO(self));
            days = ymd_to_ord(GET_YEAR(self),
                              GET_MONTH(self),
                              GET_DAY(self));
            seconds = DATE_GET_HOUR(self) * 3600 +
                      DATE_GET_MINUTE(self) * 60 +
                      DATE_GET_SECOND(self);
            temp1 = new_delta(days, seconds,
                              DATE_GET_MICROSECOND(self),
                              1);
            if (temp1 == NULL) {
                Py_DECREF(offset);
                return -1;
            }
            temp2 = delta_subtract(temp1, offset);
            Py_DECREF(temp1);
            if (temp2 == NULL) {
                Py_DECREF(offset);
                return -1;
            }
            self->hashcode = PyObject_Hash(temp2);
            Py_DECREF(temp2);
        }
        Py_DECREF(offset);
    }
    return self->hashcode;
}

static PyObject *
datetime_replace(PyDateTime_DateTime *self, PyObject *args, PyObject *kw)
{
    PyObject *clone;
    PyObject *tuple;
    int y = GET_YEAR(self);
    int m = GET_MONTH(self);
    int d = GET_DAY(self);
    int hh = DATE_GET_HOUR(self);
    int mm = DATE_GET_MINUTE(self);
    int ss = DATE_GET_SECOND(self);
    int us = DATE_GET_MICROSECOND(self);
    PyObject *tzinfo = HASTZINFO(self) ? self->tzinfo : Py_None;
    int fold = DATE_GET_FOLD(self);

    if (! PyArg_ParseTupleAndKeywords(args, kw, "|iiiiiiiO$i:replace",
                                      datetime_kws,
                                      &y, &m, &d, &hh, &mm, &ss, &us,
                                      &tzinfo, &fold))
        return NULL;
    tuple = Py_BuildValue("iiiiiiiO", y, m, d, hh, mm, ss, us, tzinfo);
    if (tuple == NULL)
        return NULL;
    clone = datetime_new(Py_TYPE(self), tuple, NULL);

    if (clone != NULL) {
        if (fold != 0 && fold != 1) {
            PyErr_SetString(PyExc_ValueError,
                            "fold must be either 0 or 1");
            return NULL;
        }
        DATE_SET_FOLD(clone, fold);
    }
    Py_DECREF(tuple);
    return clone;
}

static PyObject *
local_timezone_from_timestamp(time_t timestamp)
{
    PyObject *result = NULL;
    PyObject *delta;
    struct tm local_time_tm;
    PyObject *nameo = NULL;
    const char *zone = NULL;

    if (_PyTime_localtime(timestamp, &local_time_tm) != 0)
        return NULL;
#ifdef HAVE_STRUCT_TM_TM_ZONE
    zone = local_time_tm.tm_zone;
    delta = new_delta(0, local_time_tm.tm_gmtoff, 0, 1);
#else /* HAVE_STRUCT_TM_TM_ZONE */
    {
        PyObject *local_time, *utc_time;
        struct tm utc_time_tm;
        char buf[100];
        strftime(buf, sizeof(buf), "%Z", &local_time_tm);
        zone = buf;
        local_time = new_datetime(local_time_tm.tm_year + 1900,
                                  local_time_tm.tm_mon + 1,
                                  local_time_tm.tm_mday,
                                  local_time_tm.tm_hour,
                                  local_time_tm.tm_min,
                                  local_time_tm.tm_sec, 0, Py_None, 0);
        if (local_time == NULL) {
            return NULL;
        }
        if (_PyTime_gmtime(timestamp, &utc_time_tm) != 0)
            return NULL;
        utc_time = new_datetime(utc_time_tm.tm_year + 1900,
                                utc_time_tm.tm_mon + 1,
                                utc_time_tm.tm_mday,
                                utc_time_tm.tm_hour,
                                utc_time_tm.tm_min,
                                utc_time_tm.tm_sec, 0, Py_None, 0);
        if (utc_time == NULL) {
            Py_DECREF(local_time);
            return NULL;
        }
        delta = datetime_subtract(local_time, utc_time);
        Py_DECREF(local_time);
        Py_DECREF(utc_time);
    }
#endif /* HAVE_STRUCT_TM_TM_ZONE */
    if (delta == NULL) {
            return NULL;
    }
    if (zone != NULL) {
        nameo = PyUnicode_DecodeLocale(zone, "surrogateescape");
        if (nameo == NULL)
            goto error;
    }
    result = new_timezone(delta, nameo);
    Py_XDECREF(nameo);
  error:
    Py_DECREF(delta);
    return result;
}

static PyObject *
local_timezone(PyDateTime_DateTime *utc_time)
{
    time_t timestamp;
    PyObject *delta;
    PyObject *one_second;
    PyObject *seconds;

    delta = datetime_subtract((PyObject *)utc_time, PyDateTime_Epoch);
    if (delta == NULL)
        return NULL;
    one_second = new_delta(0, 1, 0, 0);
    if (one_second == NULL) {
        Py_DECREF(delta);
        return NULL;
    }
    seconds = divide_timedelta_timedelta((PyDateTime_Delta *)delta,
                                         (PyDateTime_Delta *)one_second);
    Py_DECREF(one_second);
    Py_DECREF(delta);
    if (seconds == NULL)
        return NULL;
    timestamp = _PyLong_AsTime_t(seconds);
    Py_DECREF(seconds);
    if (timestamp == -1 && PyErr_Occurred())
        return NULL;
    return local_timezone_from_timestamp(timestamp);
}

static long long
local_to_seconds(int year, int month, int day,
                 int hour, int minute, int second, int fold);

static PyObject *
local_timezone_from_local(PyDateTime_DateTime *local_dt)
{
    long long seconds;
    time_t timestamp;
    seconds = local_to_seconds(GET_YEAR(local_dt),
                               GET_MONTH(local_dt),
                               GET_DAY(local_dt),
                               DATE_GET_HOUR(local_dt),
                               DATE_GET_MINUTE(local_dt),
                               DATE_GET_SECOND(local_dt),
                               DATE_GET_FOLD(local_dt));
    if (seconds == -1)
        return NULL;
    /* XXX: add bounds check */
    timestamp = seconds - epoch;
    return local_timezone_from_timestamp(timestamp);
}

static PyDateTime_DateTime *
datetime_astimezone(PyDateTime_DateTime *self, PyObject *args, PyObject *kw)
{
    PyDateTime_DateTime *result;
    PyObject *offset;
    PyObject *temp;
    PyObject *self_tzinfo;
    PyObject *tzinfo = Py_None;
    static char *keywords[] = {"tz", NULL};

    if (! PyArg_ParseTupleAndKeywords(args, kw, "|O:astimezone", keywords,
                                      &tzinfo))
        return NULL;

    if (check_tzinfo_subclass(tzinfo) == -1)
        return NULL;

    if (!HASTZINFO(self) || self->tzinfo == Py_None) {
        self_tzinfo = local_timezone_from_local(self);
        if (self_tzinfo == NULL)
            return NULL;
    } else {
        self_tzinfo = self->tzinfo;
        Py_INCREF(self_tzinfo);
    }

    /* Conversion to self's own time zone is a NOP. */
    if (self_tzinfo == tzinfo) {
        Py_DECREF(self_tzinfo);
        Py_INCREF(self);
        return self;
    }

    /* Convert self to UTC. */
    offset = call_utcoffset(self_tzinfo, (PyObject *)self);
    Py_DECREF(self_tzinfo);
    if (offset == NULL)
        return NULL;
    /* result = self - offset */
    result = (PyDateTime_DateTime *)add_datetime_timedelta(self,
                                       (PyDateTime_Delta *)offset, -1);
    Py_DECREF(offset);
    if (result == NULL)
        return NULL;

    /* Make sure result is aware and UTC. */
    if (!HASTZINFO(result)) {
        temp = (PyObject *)result;
        result = (PyDateTime_DateTime *)
                   new_datetime_ex2(GET_YEAR(result),
                                    GET_MONTH(result),
                                    GET_DAY(result),
                                    DATE_GET_HOUR(result),
                                    DATE_GET_MINUTE(result),
                                    DATE_GET_SECOND(result),
                                    DATE_GET_MICROSECOND(result),
                                    PyDateTime_TimeZone_UTC,
                                    DATE_GET_FOLD(result),
                                    Py_TYPE(result));
        Py_DECREF(temp);
        if (result == NULL)
            return NULL;
    }
    else {
        /* Result is already aware - just replace tzinfo. */
        temp = result->tzinfo;
        result->tzinfo = PyDateTime_TimeZone_UTC;
        Py_INCREF(result->tzinfo);
        Py_DECREF(temp);
    }

    /* Attach new tzinfo and let fromutc() do the rest. */
    temp = result->tzinfo;
    if (tzinfo == Py_None) {
        tzinfo = local_timezone(result);
        if (tzinfo == NULL) {
            Py_DECREF(result);
            return NULL;
        }
    }
    else
      Py_INCREF(tzinfo);
    result->tzinfo = tzinfo;
    Py_DECREF(temp);

    temp = (PyObject *)result;
    result = (PyDateTime_DateTime *)
        _PyObject_CallMethodIdObjArgs(tzinfo, &PyId_fromutc, temp, NULL);
    Py_DECREF(temp);

    return result;
}

static PyObject *
datetime_timetuple(PyDateTime_DateTime *self)
{
    int dstflag = -1;

    if (HASTZINFO(self) && self->tzinfo != Py_None) {
        PyObject * dst;

        dst = call_dst(self->tzinfo, (PyObject *)self);
        if (dst == NULL)
            return NULL;

        if (dst != Py_None)
            dstflag = delta_bool((PyDateTime_Delta *)dst);
        Py_DECREF(dst);
    }
    return build_struct_time(GET_YEAR(self),
                             GET_MONTH(self),
                             GET_DAY(self),
                             DATE_GET_HOUR(self),
                             DATE_GET_MINUTE(self),
                             DATE_GET_SECOND(self),
                             dstflag);
}

static long long
local_to_seconds(int year, int month, int day,
                 int hour, int minute, int second, int fold)
{
    long long t, a, b, u1, u2, t1, t2, lt;
    t = utc_to_seconds(year, month, day, hour, minute, second);
    /* Our goal is to solve t = local(u) for u. */
    lt = local(t);
    if (lt == -1)
        return -1;
    a = lt - t;
    u1 = t - a;
    t1 = local(u1);
    if (t1 == -1)
        return -1;
    if (t1 == t) {
        /* We found one solution, but it may not be the one we need.
         * Look for an earlier solution (if `fold` is 0), or a
         * later one (if `fold` is 1). */
        if (fold)
            u2 = u1 + max_fold_seconds;
        else
            u2 = u1 - max_fold_seconds;
        lt = local(u2);
        if (lt == -1)
            return -1;
        b = lt - u2;
        if (a == b)
            return u1;
    }
    else {
        b = t1 - u1;
        assert(a != b);
    }
    u2 = t - b;
    t2 = local(u2);
    if (t2 == -1)
        return -1;
    if (t2 == t)
        return u2;
    if (t1 == t)
        return u1;
    /* We have found both offsets a and b, but neither t - a nor t - b is
     * a solution.  This means t is in the gap. */
    return fold?Py_MIN(u1, u2):Py_MAX(u1, u2);
}

/* date(1970,1,1).toordinal() == 719163 */
#define EPOCH_SECONDS (719163LL * 24 * 60 * 60)

static PyObject *
datetime_timestamp(PyDateTime_DateTime *self)
{
    PyObject *result;

    if (HASTZINFO(self) && self->tzinfo != Py_None) {
        PyObject *delta;
        delta = datetime_subtract((PyObject *)self, PyDateTime_Epoch);
        if (delta == NULL)
            return NULL;
        result = delta_total_seconds(delta);
        Py_DECREF(delta);
    }
    else {
        long long seconds;
        seconds = local_to_seconds(GET_YEAR(self),
                                   GET_MONTH(self),
                                   GET_DAY(self),
                                   DATE_GET_HOUR(self),
                                   DATE_GET_MINUTE(self),
                                   DATE_GET_SECOND(self),
                                   DATE_GET_FOLD(self));
        if (seconds == -1)
            return NULL;
        result = PyFloat_FromDouble(seconds - EPOCH_SECONDS +
                                    DATE_GET_MICROSECOND(self) / 1e6);
    }
    return result;
}

static PyObject *
datetime_getdate(PyDateTime_DateTime *self)
{
    return new_date(GET_YEAR(self),
                    GET_MONTH(self),
                    GET_DAY(self));
}

static PyObject *
datetime_gettime(PyDateTime_DateTime *self)
{
    return new_time(DATE_GET_HOUR(self),
                    DATE_GET_MINUTE(self),
                    DATE_GET_SECOND(self),
                    DATE_GET_MICROSECOND(self),
                    Py_None,
                    DATE_GET_FOLD(self));
}

static PyObject *
datetime_gettimetz(PyDateTime_DateTime *self)
{
    return new_time(DATE_GET_HOUR(self),
                    DATE_GET_MINUTE(self),
                    DATE_GET_SECOND(self),
                    DATE_GET_MICROSECOND(self),
                    GET_DT_TZINFO(self),
                    DATE_GET_FOLD(self));
}

static PyObject *
datetime_utctimetuple(PyDateTime_DateTime *self)
{
    int y, m, d, hh, mm, ss;
    PyObject *tzinfo;
    PyDateTime_DateTime *utcself;

    tzinfo = GET_DT_TZINFO(self);
    if (tzinfo == Py_None) {
        utcself = self;
        Py_INCREF(utcself);
    }
    else {
        PyObject *offset;
        offset = call_utcoffset(tzinfo, (PyObject *)self);
        if (offset == NULL)
            return NULL;
        if (offset == Py_None) {
            Py_DECREF(offset);
            utcself = self;
            Py_INCREF(utcself);
        }
        else {
            utcself = (PyDateTime_DateTime *)add_datetime_timedelta(self,
                                                (PyDateTime_Delta *)offset, -1);
            Py_DECREF(offset);
            if (utcself == NULL)
                return NULL;
        }
    }
    y = GET_YEAR(utcself);
    m = GET_MONTH(utcself);
    d = GET_DAY(utcself);
    hh = DATE_GET_HOUR(utcself);
    mm = DATE_GET_MINUTE(utcself);
    ss = DATE_GET_SECOND(utcself);

    Py_DECREF(utcself);
    return build_struct_time(y, m, d, hh, mm, ss, 0);
}

/* Pickle support, a simple use of __reduce__. */

/* Let basestate be the non-tzinfo data string.
 * If tzinfo is None, this returns (basestate,), else (basestate, tzinfo).
 * So it's a tuple in any (non-error) case.
 * __getstate__ isn't exposed.
 */
static PyObject *
datetime_getstate(PyDateTime_DateTime *self, int proto)
{
    PyObject *basestate;
    PyObject *result = NULL;

    basestate = PyBytes_FromStringAndSize((char *)self->data,
                                           _PyDateTime_DATETIME_DATASIZE);
    if (basestate != NULL) {
        if (proto > 3 && DATE_GET_FOLD(self))
            /* Set the first bit of the third byte */
            PyBytes_AS_STRING(basestate)[2] |= (1 << 7);
        if (! HASTZINFO(self) || self->tzinfo == Py_None)
            result = PyTuple_Pack(1, basestate);
        else
            result = PyTuple_Pack(2, basestate, self->tzinfo);
        Py_DECREF(basestate);
    }
    return result;
}

static PyObject *
datetime_reduce_ex(PyDateTime_DateTime *self, PyObject *args)
{
    int proto;
    if (!PyArg_ParseTuple(args, "i:__reduce_ex__", &proto))
        return NULL;

    return Py_BuildValue("(ON)", Py_TYPE(self), datetime_getstate(self, proto));
}

static PyObject *
datetime_reduce(PyDateTime_DateTime *self, PyObject *arg)
{
    return Py_BuildValue("(ON)", Py_TYPE(self), datetime_getstate(self, 2));
}

static PyMethodDef datetime_methods[] = {

    /* Class methods: */

    DATETIME_DATETIME_NOW_METHODDEF

    {"utcnow",         (PyCFunction)datetime_utcnow,
     METH_NOARGS | METH_CLASS,
     PyDoc_STR("Return a new datetime representing UTC day and time.")},

    {"fromtimestamp", (PyCFunction)datetime_fromtimestamp,
     METH_VARARGS | METH_KEYWORDS | METH_CLASS,
     PyDoc_STR("timestamp[, tz] -> tz's local time from POSIX timestamp.")},

    {"utcfromtimestamp", (PyCFunction)datetime_utcfromtimestamp,
     METH_VARARGS | METH_CLASS,
     PyDoc_STR("Construct a naive UTC datetime from a POSIX timestamp.")},

    {"strptime", (PyCFunction)datetime_strptime,
     METH_VARARGS | METH_CLASS,
     PyDoc_STR("string, format -> new datetime parsed from a string "
               "(like time.strptime()).")},

    {"combine", (PyCFunction)datetime_combine,
     METH_VARARGS | METH_KEYWORDS | METH_CLASS,
     PyDoc_STR("date, time -> datetime with same date and time fields")},

    /* Instance methods: */

    {"date",   (PyCFunction)datetime_getdate, METH_NOARGS,
     PyDoc_STR("Return date object with same year, month and day.")},

    {"time",   (PyCFunction)datetime_gettime, METH_NOARGS,
     PyDoc_STR("Return time object with same time but with tzinfo=None.")},

    {"timetz",   (PyCFunction)datetime_gettimetz, METH_NOARGS,
     PyDoc_STR("Return time object with same time and tzinfo.")},

    {"ctime",       (PyCFunction)datetime_ctime,        METH_NOARGS,
     PyDoc_STR("Return ctime() style string.")},

    {"timetuple",   (PyCFunction)datetime_timetuple, METH_NOARGS,
     PyDoc_STR("Return time tuple, compatible with time.localtime().")},

    {"timestamp",   (PyCFunction)datetime_timestamp, METH_NOARGS,
     PyDoc_STR("Return POSIX timestamp as float.")},

    {"utctimetuple",   (PyCFunction)datetime_utctimetuple, METH_NOARGS,
     PyDoc_STR("Return UTC time tuple, compatible with time.localtime().")},

    {"isoformat",   (PyCFunction)datetime_isoformat, METH_VARARGS | METH_KEYWORDS,
     PyDoc_STR("[sep] -> string in ISO 8601 format, "
               "YYYY-MM-DDT[HH[:MM[:SS[.mmm[uuu]]]]][+HH:MM].\n"
               "sep is used to separate the year from the time, and "
               "defaults to 'T'.\n"
               "timespec specifies what components of the time to include"
               " (allowed values are 'auto', 'hours', 'minutes', 'seconds',"
               " 'milliseconds', and 'microseconds').\n")},

    {"utcoffset",       (PyCFunction)datetime_utcoffset, METH_NOARGS,
     PyDoc_STR("Return self.tzinfo.utcoffset(self).")},

    {"tzname",          (PyCFunction)datetime_tzname,   METH_NOARGS,
     PyDoc_STR("Return self.tzinfo.tzname(self).")},

    {"dst",             (PyCFunction)datetime_dst, METH_NOARGS,
     PyDoc_STR("Return self.tzinfo.dst(self).")},

    {"replace",     (PyCFunction)datetime_replace,      METH_VARARGS | METH_KEYWORDS,
     PyDoc_STR("Return datetime with new specified fields.")},

    {"astimezone",  (PyCFunction)datetime_astimezone, METH_VARARGS | METH_KEYWORDS,
     PyDoc_STR("tz -> convert to local time in new timezone tz\n")},

    {"__reduce_ex__", (PyCFunction)datetime_reduce_ex,     METH_VARARGS,
     PyDoc_STR("__reduce_ex__(proto) -> (cls, state)")},

    {"__reduce__", (PyCFunction)datetime_reduce,     METH_NOARGS,
     PyDoc_STR("__reduce__() -> (cls, state)")},

    {NULL,      NULL}
};

static const char datetime_doc[] =
PyDoc_STR("datetime(year, month, day[, hour[, minute[, second[, microsecond[,tzinfo]]]]])\n\
\n\
The year, month and day arguments are required. tzinfo may be None, or an\n\
instance of a tzinfo subclass. The remaining arguments may be ints.\n");

static PyNumberMethods datetime_as_number = {
    datetime_add,                               /* nb_add */
    datetime_subtract,                          /* nb_subtract */
    0,                                          /* nb_multiply */
    0,                                          /* nb_remainder */
    0,                                          /* nb_divmod */
    0,                                          /* nb_power */
    0,                                          /* nb_negative */
    0,                                          /* nb_positive */
    0,                                          /* nb_absolute */
    0,                                          /* nb_bool */
};

static PyTypeObject PyDateTime_DateTimeType = {
    PyVarObject_HEAD_INIT(NULL, 0)
    "datetime.datetime",                        /* tp_name */
    sizeof(PyDateTime_DateTime),                /* tp_basicsize */
    0,                                          /* tp_itemsize */
    (destructor)datetime_dealloc,               /* tp_dealloc */
    0,                                          /* tp_print */
    0,                                          /* tp_getattr */
    0,                                          /* tp_setattr */
    0,                                          /* tp_reserved */
    (reprfunc)datetime_repr,                    /* tp_repr */
    &datetime_as_number,                        /* tp_as_number */
    0,                                          /* tp_as_sequence */
    0,                                          /* tp_as_mapping */
    (hashfunc)datetime_hash,                    /* tp_hash */
    0,                                          /* tp_call */
    (reprfunc)datetime_str,                     /* tp_str */
    PyObject_GenericGetAttr,                    /* tp_getattro */
    0,                                          /* tp_setattro */
    0,                                          /* tp_as_buffer */
    Py_TPFLAGS_DEFAULT | Py_TPFLAGS_BASETYPE, /* tp_flags */
    datetime_doc,                               /* tp_doc */
    0,                                          /* tp_traverse */
    0,                                          /* tp_clear */
    datetime_richcompare,                       /* tp_richcompare */
    0,                                          /* tp_weaklistoffset */
    0,                                          /* tp_iter */
    0,                                          /* tp_iternext */
    datetime_methods,                           /* tp_methods */
    0,                                          /* tp_members */
    datetime_getset,                            /* tp_getset */
    &PyDateTime_DateType,                       /* tp_base */
    0,                                          /* tp_dict */
    0,                                          /* tp_descr_get */
    0,                                          /* tp_descr_set */
    0,                                          /* tp_dictoffset */
    0,                                          /* tp_init */
    datetime_alloc,                             /* tp_alloc */
    datetime_new,                               /* tp_new */
    0,                                          /* tp_free */
};

/* ---------------------------------------------------------------------------
 * Module methods and initialization.
 */

static PyMethodDef module_methods[] = {
    {NULL, NULL}
};

/* C API.  Clients get at this via PyDateTime_IMPORT, defined in
 * datetime.h.
 */
static PyDateTime_CAPI CAPI = {
    &PyDateTime_DateType,
    &PyDateTime_DateTimeType,
    &PyDateTime_TimeType,
    &PyDateTime_DeltaType,
    &PyDateTime_TZInfoType,
    new_date_ex,
    new_datetime_ex,
    new_time_ex,
    new_delta_ex,
    datetime_fromtimestamp,
    date_fromtimestamp,
    new_datetime_ex2,
    new_time_ex2
};



static struct PyModuleDef datetimemodule = {
    PyModuleDef_HEAD_INIT,
    "_datetime",
    "Fast implementation of the datetime type.",
    -1,
    module_methods,
    NULL,
    NULL,
    NULL,
    NULL
};

PyMODINIT_FUNC
PyInit__datetime(void)
{
    PyObject *m;        /* a module object */
    PyObject *d;        /* its dict */
    PyObject *x;
    PyObject *delta;

    m = PyModule_Create(&datetimemodule);
    if (m == NULL)
        return NULL;

    if (PyType_Ready(&PyDateTime_DateType) < 0)
        return NULL;
    if (PyType_Ready(&PyDateTime_DateTimeType) < 0)
        return NULL;
    if (PyType_Ready(&PyDateTime_DeltaType) < 0)
        return NULL;
    if (PyType_Ready(&PyDateTime_TimeType) < 0)
        return NULL;
    if (PyType_Ready(&PyDateTime_TZInfoType) < 0)
        return NULL;
    if (PyType_Ready(&PyDateTime_TimeZoneType) < 0)
        return NULL;

    /* timedelta values */
    d = PyDateTime_DeltaType.tp_dict;

    x = new_delta(0, 0, 1, 0);
    if (x == NULL || PyDict_SetItemString(d, "resolution", x) < 0)
        return NULL;
    Py_DECREF(x);

    x = new_delta(-MAX_DELTA_DAYS, 0, 0, 0);
    if (x == NULL || PyDict_SetItemString(d, "min", x) < 0)
        return NULL;
    Py_DECREF(x);

    x = new_delta(MAX_DELTA_DAYS, 24*3600-1, 1000000-1, 0);
    if (x == NULL || PyDict_SetItemString(d, "max", x) < 0)
        return NULL;
    Py_DECREF(x);

    /* date values */
    d = PyDateTime_DateType.tp_dict;

    x = new_date(1, 1, 1);
    if (x == NULL || PyDict_SetItemString(d, "min", x) < 0)
        return NULL;
    Py_DECREF(x);

    x = new_date(MAXYEAR, 12, 31);
    if (x == NULL || PyDict_SetItemString(d, "max", x) < 0)
        return NULL;
    Py_DECREF(x);

    x = new_delta(1, 0, 0, 0);
    if (x == NULL || PyDict_SetItemString(d, "resolution", x) < 0)
        return NULL;
    Py_DECREF(x);

    /* time values */
    d = PyDateTime_TimeType.tp_dict;

    x = new_time(0, 0, 0, 0, Py_None, 0);
    if (x == NULL || PyDict_SetItemString(d, "min", x) < 0)
        return NULL;
    Py_DECREF(x);

    x = new_time(23, 59, 59, 999999, Py_None, 0);
    if (x == NULL || PyDict_SetItemString(d, "max", x) < 0)
        return NULL;
    Py_DECREF(x);

    x = new_delta(0, 0, 1, 0);
    if (x == NULL || PyDict_SetItemString(d, "resolution", x) < 0)
        return NULL;
    Py_DECREF(x);

    /* datetime values */
    d = PyDateTime_DateTimeType.tp_dict;

    x = new_datetime(1, 1, 1, 0, 0, 0, 0, Py_None, 0);
    if (x == NULL || PyDict_SetItemString(d, "min", x) < 0)
        return NULL;
    Py_DECREF(x);

    x = new_datetime(MAXYEAR, 12, 31, 23, 59, 59, 999999, Py_None, 0);
    if (x == NULL || PyDict_SetItemString(d, "max", x) < 0)
        return NULL;
    Py_DECREF(x);

    x = new_delta(0, 0, 1, 0);
    if (x == NULL || PyDict_SetItemString(d, "resolution", x) < 0)
        return NULL;
    Py_DECREF(x);

    /* timezone values */
    d = PyDateTime_TimeZoneType.tp_dict;

    delta = new_delta(0, 0, 0, 0);
    if (delta == NULL)
        return NULL;
    x = create_timezone(delta, NULL);
    Py_DECREF(delta);
    if (x == NULL || PyDict_SetItemString(d, "utc", x) < 0)
        return NULL;
    PyDateTime_TimeZone_UTC = x;

    delta = new_delta(-1, 60, 0, 1); /* -23:59 */
    if (delta == NULL)
        return NULL;
    x = create_timezone(delta, NULL);
    Py_DECREF(delta);
    if (x == NULL || PyDict_SetItemString(d, "min", x) < 0)
        return NULL;
    Py_DECREF(x);

    delta = new_delta(0, (23 * 60 + 59) * 60, 0, 0); /* +23:59 */
    if (delta == NULL)
        return NULL;
    x = create_timezone(delta, NULL);
    Py_DECREF(delta);
    if (x == NULL || PyDict_SetItemString(d, "max", x) < 0)
        return NULL;
    Py_DECREF(x);

    /* Epoch */
    PyDateTime_Epoch = new_datetime(1970, 1, 1, 0, 0, 0, 0,
                                    PyDateTime_TimeZone_UTC, 0);
    if (PyDateTime_Epoch == NULL)
      return NULL;

    /* module initialization */
    PyModule_AddIntMacro(m, MINYEAR);
    PyModule_AddIntMacro(m, MAXYEAR);

    Py_INCREF(&PyDateTime_DateType);
    PyModule_AddObject(m, "date", (PyObject *) &PyDateTime_DateType);

    Py_INCREF(&PyDateTime_DateTimeType);
    PyModule_AddObject(m, "datetime",
                       (PyObject *)&PyDateTime_DateTimeType);

    Py_INCREF(&PyDateTime_TimeType);
    PyModule_AddObject(m, "time", (PyObject *) &PyDateTime_TimeType);

    Py_INCREF(&PyDateTime_DeltaType);
    PyModule_AddObject(m, "timedelta", (PyObject *) &PyDateTime_DeltaType);

    Py_INCREF(&PyDateTime_TZInfoType);
    PyModule_AddObject(m, "tzinfo", (PyObject *) &PyDateTime_TZInfoType);

    Py_INCREF(&PyDateTime_TimeZoneType);
    PyModule_AddObject(m, "timezone", (PyObject *) &PyDateTime_TimeZoneType);

    x = PyCapsule_New(&CAPI, PyDateTime_CAPSULE_NAME, NULL);
    if (x == NULL)
        return NULL;
    PyModule_AddObject(m, "datetime_CAPI", x);

    /* A 4-year cycle has an extra leap day over what we'd get from
     * pasting together 4 single years.
     */
    Py_BUILD_ASSERT(DI4Y == 4 * 365 + 1);
    assert(DI4Y == days_before_year(4+1));

    /* Similarly, a 400-year cycle has an extra leap day over what we'd
     * get from pasting together 4 100-year cycles.
     */
    Py_BUILD_ASSERT(DI400Y == 4 * DI100Y + 1);
    assert(DI400Y == days_before_year(400+1));

    /* OTOH, a 100-year cycle has one fewer leap day than we'd get from
     * pasting together 25 4-year cycles.
     */
    Py_BUILD_ASSERT(DI100Y == 25 * DI4Y - 1);
    assert(DI100Y == days_before_year(100+1));

    one = PyLong_FromLong(1);
    us_per_ms = PyLong_FromLong(1000);
    us_per_second = PyLong_FromLong(1000000);
    us_per_minute = PyLong_FromLong(60000000);
    seconds_per_day = PyLong_FromLong(24 * 3600);
    if (one == NULL || us_per_ms == NULL || us_per_second == NULL ||
        us_per_minute == NULL || seconds_per_day == NULL)
        return NULL;

    /* The rest are too big for 32-bit ints, but even
     * us_per_week fits in 40 bits, so doubles should be exact.
     */
    us_per_hour = PyLong_FromDouble(3600000000.0);
    us_per_day = PyLong_FromDouble(86400000000.0);
    us_per_week = PyLong_FromDouble(604800000000.0);
    if (us_per_hour == NULL || us_per_day == NULL || us_per_week == NULL)
        return NULL;
    return m;
}

/* ---------------------------------------------------------------------------
Some time zone algebra.  For a datetime x, let
    x.n = x stripped of its timezone -- its naive time.
    x.o = x.utcoffset(), and assuming that doesn't raise an exception or
      return None
    x.d = x.dst(), and assuming that doesn't raise an exception or
      return None
    x.s = x's standard offset, x.o - x.d

Now some derived rules, where k is a duration (timedelta).

1. x.o = x.s + x.d
   This follows from the definition of x.s.

2. If x and y have the same tzinfo member, x.s = y.s.
   This is actually a requirement, an assumption we need to make about
   sane tzinfo classes.

3. The naive UTC time corresponding to x is x.n - x.o.
   This is again a requirement for a sane tzinfo class.

4. (x+k).s = x.s
   This follows from #2, and that datimetimetz+timedelta preserves tzinfo.

5. (x+k).n = x.n + k
   Again follows from how arithmetic is defined.

Now we can explain tz.fromutc(x).  Let's assume it's an interesting case
(meaning that the various tzinfo methods exist, and don't blow up or return
None when called).

The function wants to return a datetime y with timezone tz, equivalent to x.
x is already in UTC.

By #3, we want

    y.n - y.o = x.n                             [1]

The algorithm starts by attaching tz to x.n, and calling that y.  So
x.n = y.n at the start.  Then it wants to add a duration k to y, so that [1]
becomes true; in effect, we want to solve [2] for k:

   (y+k).n - (y+k).o = x.n                      [2]

By #1, this is the same as

   (y+k).n - ((y+k).s + (y+k).d) = x.n          [3]

By #5, (y+k).n = y.n + k, which equals x.n + k because x.n=y.n at the start.
Substituting that into [3],

   x.n + k - (y+k).s - (y+k).d = x.n; the x.n terms cancel, leaving
   k - (y+k).s - (y+k).d = 0; rearranging,
   k = (y+k).s - (y+k).d; by #4, (y+k).s == y.s, so
   k = y.s - (y+k).d

On the RHS, (y+k).d can't be computed directly, but y.s can be, and we
approximate k by ignoring the (y+k).d term at first.  Note that k can't be
very large, since all offset-returning methods return a duration of magnitude
less than 24 hours.  For that reason, if y is firmly in std time, (y+k).d must
be 0, so ignoring it has no consequence then.

In any case, the new value is

    z = y + y.s                                 [4]

It's helpful to step back at look at [4] from a higher level:  it's simply
mapping from UTC to tz's standard time.

At this point, if

    z.n - z.o = x.n                             [5]

we have an equivalent time, and are almost done.  The insecurity here is
at the start of daylight time.  Picture US Eastern for concreteness.  The wall
time jumps from 1:59 to 3:00, and wall hours of the form 2:MM don't make good
sense then.  The docs ask that an Eastern tzinfo class consider such a time to
be EDT (because it's "after 2"), which is a redundant spelling of 1:MM EST
on the day DST starts.  We want to return the 1:MM EST spelling because that's
the only spelling that makes sense on the local wall clock.

In fact, if [5] holds at this point, we do have the standard-time spelling,
but that takes a bit of proof.  We first prove a stronger result.  What's the
difference between the LHS and RHS of [5]?  Let

    diff = x.n - (z.n - z.o)                    [6]

Now
    z.n =                       by [4]
    (y + y.s).n =               by #5
    y.n + y.s =                 since y.n = x.n
    x.n + y.s =                 since z and y are have the same tzinfo member,
                                    y.s = z.s by #2
    x.n + z.s

Plugging that back into [6] gives

    diff =
    x.n - ((x.n + z.s) - z.o) =     expanding
    x.n - x.n - z.s + z.o =         cancelling
    - z.s + z.o =                   by #2
    z.d

So diff = z.d.

If [5] is true now, diff = 0, so z.d = 0 too, and we have the standard-time
spelling we wanted in the endcase described above.  We're done.  Contrarily,
if z.d = 0, then we have a UTC equivalent, and are also done.

If [5] is not true now, diff = z.d != 0, and z.d is the offset we need to
add to z (in effect, z is in tz's standard time, and we need to shift the
local clock into tz's daylight time).

Let

    z' = z + z.d = z + diff                     [7]

and we can again ask whether

    z'.n - z'.o = x.n                           [8]

If so, we're done.  If not, the tzinfo class is insane, according to the
assumptions we've made.  This also requires a bit of proof.  As before, let's
compute the difference between the LHS and RHS of [8] (and skipping some of
the justifications for the kinds of substitutions we've done several times
already):

    diff' = x.n - (z'.n - z'.o) =           replacing z'.n via [7]
        x.n  - (z.n + diff - z'.o) =    replacing diff via [6]
        x.n - (z.n + x.n - (z.n - z.o) - z'.o) =
        x.n - z.n - x.n + z.n - z.o + z'.o =    cancel x.n
        - z.n + z.n - z.o + z'.o =              cancel z.n
        - z.o + z'.o =                      #1 twice
        -z.s - z.d + z'.s + z'.d =          z and z' have same tzinfo
        z'.d - z.d

So z' is UTC-equivalent to x iff z'.d = z.d at this point.  If they are equal,
we've found the UTC-equivalent so are done.  In fact, we stop with [7] and
return z', not bothering to compute z'.d.

How could z.d and z'd differ?  z' = z + z.d [7], so merely moving z' by
a dst() offset, and starting *from* a time already in DST (we know z.d != 0),
would have to change the result dst() returns:  we start in DST, and moving
a little further into it takes us out of DST.

There isn't a sane case where this can happen.  The closest it gets is at
the end of DST, where there's an hour in UTC with no spelling in a hybrid
tzinfo class.  In US Eastern, that's 5:MM UTC = 0:MM EST = 1:MM EDT.  During
that hour, on an Eastern clock 1:MM is taken as being in standard time (6:MM
UTC) because the docs insist on that, but 0:MM is taken as being in daylight
time (4:MM UTC).  There is no local time mapping to 5:MM UTC.  The local
clock jumps from 1:59 back to 1:00 again, and repeats the 1:MM hour in
standard time.  Since that's what the local clock *does*, we want to map both
UTC hours 5:MM and 6:MM to 1:MM Eastern.  The result is ambiguous
in local time, but so it goes -- it's the way the local clock works.

When x = 5:MM UTC is the input to this algorithm, x.o=0, y.o=-5 and y.d=0,
so z=0:MM.  z.d=60 (minutes) then, so [5] doesn't hold and we keep going.
z' = z + z.d = 1:MM then, and z'.d=0, and z'.d - z.d = -60 != 0 so [8]
(correctly) concludes that z' is not UTC-equivalent to x.

Because we know z.d said z was in daylight time (else [5] would have held and
we would have stopped then), and we know z.d != z'.d (else [8] would have held
and we would have stopped then), and there are only 2 possible values dst() can
return in Eastern, it follows that z'.d must be 0 (which it is in the example,
but the reasoning doesn't depend on the example -- it depends on there being
two possible dst() outcomes, one zero and the other non-zero).  Therefore
z' must be in standard time, and is the spelling we want in this case.

Note again that z' is not UTC-equivalent as far as the hybrid tzinfo class is
concerned (because it takes z' as being in standard time rather than the
daylight time we intend here), but returning it gives the real-life "local
clock repeats an hour" behavior when mapping the "unspellable" UTC hour into
tz.

When the input is 6:MM, z=1:MM and z.d=0, and we stop at once, again with
the 1:MM standard time spelling we want.

So how can this break?  One of the assumptions must be violated.  Two
possibilities:

1) [2] effectively says that y.s is invariant across all y belong to a given
   time zone.  This isn't true if, for political reasons or continental drift,
   a region decides to change its base offset from UTC.

2) There may be versions of "double daylight" time where the tail end of
   the analysis gives up a step too early.  I haven't thought about that
   enough to say.

In any case, it's clear that the default fromutc() is strong enough to handle
"almost all" time zones:  so long as the standard offset is invariant, it
doesn't matter if daylight time transition points change from year to year, or
if daylight time is skipped in some years; it doesn't matter how large or
small dst() may get within its bounds; and it doesn't even matter if some
perverse time zone returns a negative dst()).  So a breaking case must be
pretty bizarre, and a tzinfo subclass can override fromutc() if it is.
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