--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/cos/python/Objects/longobject.c	Tue Dec 27 18:59:02 2011 +0100
@@ -0,0 +1,4836 @@
+/* Long (arbitrary precision) integer object implementation */
+
+/* XXX The functional organization of this file is terrible */
+
+#include "Python.h"
+#include "longintrepr.h"
+
+
+/* convert a PyLong of size 1, 0 or -1 to an sdigit */
+#define MEDIUM_VALUE(x) (Py_SIZE(x) < 0 ? -(sdigit)(x)->ob_digit[0] :   \
+             (Py_SIZE(x) == 0 ? (sdigit)0 :                             \
+              (sdigit)(x)->ob_digit[0]))
+#define ABS(x) ((x) < 0 ? -(x) : (x))
+
+/* If a freshly-allocated long is already shared, it must
+   be a small integer, so negating it must go to PyLong_FromLong */
+#define NEGATE(x) \
+    do if (Py_REFCNT(x) == 1) Py_SIZE(x) = -Py_SIZE(x);  \
+       else { PyObject* tmp=PyLong_FromLong(-MEDIUM_VALUE(x));  \
+           Py_DECREF(x); (x) = (PyLongObject*)tmp; }               \
+    while(0)
+/* For long multiplication, use the O(N**2) school algorithm unless
+ * both operands contain more than KARATSUBA_CUTOFF digits (this
+ * being an internal Python long digit, in base BASE).
+ */
+#define KARATSUBA_CUTOFF 70
+#define KARATSUBA_SQUARE_CUTOFF (2 * KARATSUBA_CUTOFF)
+
+/* For exponentiation, use the binary left-to-right algorithm
+ * unless the exponent contains more than FIVEARY_CUTOFF digits.
+ * In that case, do 5 bits at a time.  The potential drawback is that
+ * a table of 2**5 intermediate results is computed.
+ */
+#define FIVEARY_CUTOFF 8
+
+#undef MIN
+#undef MAX
+#define MAX(x, y) ((x) < (y) ? (y) : (x))
+#define MIN(x, y) ((x) > (y) ? (y) : (x))
+
+#define SIGCHECK(PyTryBlock)                    \
+    do {                                        \
+        if (PyErr_CheckSignals()) PyTryBlock    \
+    } while(0)
+
+/* Normalize (remove leading zeros from) a long int object.
+   Doesn't attempt to free the storage--in most cases, due to the nature
+   of the algorithms used, this could save at most be one word anyway. */
+
+static PyLongObject *
+long_normalize(register PyLongObject *v)
+{
+    Py_ssize_t j = ABS(Py_SIZE(v));
+    Py_ssize_t i = j;
+
+    while (i > 0 && v->ob_digit[i-1] == 0)
+        --i;
+    if (i != j)
+        Py_SIZE(v) = (Py_SIZE(v) < 0) ? -(i) : i;
+    return v;
+}
+
+/* Allocate a new long int object with size digits.
+   Return NULL and set exception if we run out of memory. */
+
+#define MAX_LONG_DIGITS \
+    ((PY_SSIZE_T_MAX - offsetof(PyLongObject, ob_digit))/sizeof(digit))
+
+PyLongObject *
+_PyLong_New(Py_ssize_t size)
+{
+    PyLongObject *result;
+    /* Number of bytes needed is: offsetof(PyLongObject, ob_digit) +
+       sizeof(digit)*size.  Previous incarnations of this code used
+       sizeof(PyVarObject) instead of the offsetof, but this risks being
+       incorrect in the presence of padding between the PyVarObject header
+       and the digits. */
+    if (size > (Py_ssize_t)MAX_LONG_DIGITS) {
+        PyErr_SetString(PyExc_OverflowError,
+                        "too many digits in integer");
+        return NULL;
+    }
+    result = PyObject_MALLOC(offsetof(PyLongObject, ob_digit) +
+                             size*sizeof(digit));
+    if (!result) {
+        PyErr_NoMemory();
+        return NULL;
+    }
+    return (PyLongObject*)PyObject_INIT_VAR(result, &PyLong_Type, size);
+}
+
+PyObject *
+_PyLong_Copy(PyLongObject *src)
+{
+    PyLongObject *result;
+    Py_ssize_t i;
+
+    assert(src != NULL);
+    i = Py_SIZE(src);
+    if (i < 0)
+        i = -(i);
+    if (i < 2) {
+        sdigit ival = src->ob_digit[0];
+        if (Py_SIZE(src) < 0)
+            ival = -ival;
+        CHECK_SMALL_INT(ival);
+    }
+    result = _PyLong_New(i);
+    if (result != NULL) {
+        Py_SIZE(result) = Py_SIZE(src);
+        while (--i >= 0)
+            result->ob_digit[i] = src->ob_digit[i];
+    }
+    return (PyObject *)result;
+}
+
+/* Create a new long int object from a C long int */
+
+PyObject *
+PyLong_FromLong(long ival)
+{
+    PyLongObject *v;
+    unsigned long abs_ival;
+    unsigned long t;  /* unsigned so >> doesn't propagate sign bit */
+    int ndigits = 0;
+    int sign = 1;
+
+    if (ival < 0) {
+        /* negate: can't write this as abs_ival = -ival since that
+           invokes undefined behaviour when ival is LONG_MIN */
+        abs_ival = 0U-(unsigned long)ival;
+        sign = -1;
+    }
+    else {
+        abs_ival = (unsigned long)ival;
+    }
+
+    /* Fast path for single-digit ints */
+    if (!(abs_ival >> PyLong_SHIFT)) {
+        v = _PyLong_New(1);
+        if (v) {
+            Py_SIZE(v) = sign;
+            v->ob_digit[0] = Py_SAFE_DOWNCAST(
+                abs_ival, unsigned long, digit);
+        }
+        return (PyObject*)v;
+    }
+
+#if PyLong_SHIFT==15
+    /* 2 digits */
+    if (!(abs_ival >> 2*PyLong_SHIFT)) {
+        v = _PyLong_New(2);
+        if (v) {
+            Py_SIZE(v) = 2*sign;
+            v->ob_digit[0] = Py_SAFE_DOWNCAST(
+                abs_ival & PyLong_MASK, unsigned long, digit);
+            v->ob_digit[1] = Py_SAFE_DOWNCAST(
+                  abs_ival >> PyLong_SHIFT, unsigned long, digit);
+        }
+        return (PyObject*)v;
+    }
+#endif
+
+    /* Larger numbers: loop to determine number of digits */
+    t = abs_ival;
+    while (t) {
+        ++ndigits;
+        t >>= PyLong_SHIFT;
+    }
+    v = _PyLong_New(ndigits);
+    if (v != NULL) {
+        digit *p = v->ob_digit;
+        Py_SIZE(v) = ndigits*sign;
+        t = abs_ival;
+        while (t) {
+            *p++ = Py_SAFE_DOWNCAST(
+                t & PyLong_MASK, unsigned long, digit);
+            t >>= PyLong_SHIFT;
+        }
+    }
+    return (PyObject *)v;
+}
+
+/* Create a new long int object from a C unsigned long int */
+
+PyObject *
+PyLong_FromUnsignedLong(unsigned long ival)
+{
+    PyLongObject *v;
+    unsigned long t;
+    int ndigits = 0;
+
+    if (ival < PyLong_BASE)
+        return PyLong_FromLong(ival);
+    /* Count the number of Python digits. */
+    t = (unsigned long)ival;
+    while (t) {
+        ++ndigits;
+        t >>= PyLong_SHIFT;
+    }
+    v = _PyLong_New(ndigits);
+    if (v != NULL) {
+        digit *p = v->ob_digit;
+        Py_SIZE(v) = ndigits;
+        while (ival) {
+            *p++ = (digit)(ival & PyLong_MASK);
+            ival >>= PyLong_SHIFT;
+        }
+    }
+    return (PyObject *)v;
+}
+
+/* Create a new long int object from a C double */
+
+PyObject *
+PyLong_FromDouble(double dval)
+{
+    PyLongObject *v;
+    double frac;
+    int i, ndig, expo, neg;
+    neg = 0;
+    if (Py_IS_INFINITY(dval)) {
+        PyErr_SetString(PyExc_OverflowError,
+                        "cannot convert float infinity to integer");
+        return NULL;
+    }
+    if (Py_IS_NAN(dval)) {
+        PyErr_SetString(PyExc_ValueError,
+                        "cannot convert float NaN to integer");
+        return NULL;
+    }
+    if (dval < 0.0) {
+        neg = 1;
+        dval = -dval;
+    }
+    frac = frexp(dval, &expo); /* dval = frac*2**expo; 0.0 <= frac < 1.0 */
+    if (expo <= 0)
+        return PyLong_FromLong(0L);
+    ndig = (expo-1) / PyLong_SHIFT + 1; /* Number of 'digits' in result */
+    v = _PyLong_New(ndig);
+    if (v == NULL)
+        return NULL;
+    frac = ldexp(frac, (expo-1) % PyLong_SHIFT + 1);
+    for (i = ndig; --i >= 0; ) {
+        digit bits = (digit)frac;
+        v->ob_digit[i] = bits;
+        frac = frac - (double)bits;
+        frac = ldexp(frac, PyLong_SHIFT);
+    }
+    if (neg)
+        Py_SIZE(v) = -(Py_SIZE(v));
+    return (PyObject *)v;
+}
+
+/* Checking for overflow in PyLong_AsLong is a PITA since C doesn't define
+ * anything about what happens when a signed integer operation overflows,
+ * and some compilers think they're doing you a favor by being "clever"
+ * then.  The bit pattern for the largest postive signed long is
+ * (unsigned long)LONG_MAX, and for the smallest negative signed long
+ * it is abs(LONG_MIN), which we could write -(unsigned long)LONG_MIN.
+ * However, some other compilers warn about applying unary minus to an
+ * unsigned operand.  Hence the weird "0-".
+ */
+#define PY_ABS_LONG_MIN         (0-(unsigned long)LONG_MIN)
+#define PY_ABS_SSIZE_T_MIN      (0-(size_t)PY_SSIZE_T_MIN)
+
+/* Get a C long int from a long int object or any object that has an __int__
+   method.
+
+   On overflow, return -1 and set *overflow to 1 or -1 depending on the sign of
+   the result.  Otherwise *overflow is 0.
+
+   For other errors (e.g., TypeError), return -1 and set an error condition.
+   In this case *overflow will be 0.
+*/
+
+long
+PyLong_AsLongAndOverflow(PyObject *vv, int *overflow)
+{
+    /* This version by Tim Peters */
+    register PyLongObject *v;
+    unsigned long x, prev;
+    long res;
+    Py_ssize_t i;
+    int sign;
+    int do_decref = 0; /* if nb_int was called */
+
+    *overflow = 0;
+    if (vv == NULL) {
+        PyErr_BadInternalCall();
+        return -1;
+    }
+
+    if (!PyLong_Check(vv)) {
+        PyNumberMethods *nb;
+        nb = vv->ob_type->tp_as_number;
+        if (nb == NULL || nb->nb_int == NULL) {
+            PyErr_SetString(PyExc_TypeError,
+                            "an integer is required");
+            return -1;
+        }
+        vv = (*nb->nb_int) (vv);
+        if (vv == NULL)
+            return -1;
+        do_decref = 1;
+        if (!PyLong_Check(vv)) {
+            Py_DECREF(vv);
+            PyErr_SetString(PyExc_TypeError,
+                            "nb_int should return int object");
+            return -1;
+        }
+    }
+
+    res = -1;
+    v = (PyLongObject *)vv;
+    i = Py_SIZE(v);
+
+    switch (i) {
+    case -1:
+        res = -(sdigit)v->ob_digit[0];
+        break;
+    case 0:
+        res = 0;
+        break;
+    case 1:
+        res = v->ob_digit[0];
+        break;
+    default:
+        sign = 1;
+        x = 0;
+        if (i < 0) {
+            sign = -1;
+            i = -(i);
+        }
+        while (--i >= 0) {
+            prev = x;
+            x = (x << PyLong_SHIFT) | v->ob_digit[i];
+            if ((x >> PyLong_SHIFT) != prev) {
+                *overflow = sign;
+                goto exit;
+            }
+        }
+        /* Haven't lost any bits, but casting to long requires extra
+         * care (see comment above).
+         */
+        if (x <= (unsigned long)LONG_MAX) {
+            res = (long)x * sign;
+        }
+        else if (sign < 0 && x == PY_ABS_LONG_MIN) {
+            res = LONG_MIN;
+        }
+        else {
+            *overflow = sign;
+            /* res is already set to -1 */
+        }
+    }
+  exit:
+    if (do_decref) {
+        Py_DECREF(vv);
+    }
+    return res;
+}
+
+/* Get a C long int from a long int object or any object that has an __int__
+   method.  Return -1 and set an error if overflow occurs. */
+
+long
+PyLong_AsLong(PyObject *obj)
+{
+    int overflow;
+    long result = PyLong_AsLongAndOverflow(obj, &overflow);
+    if (overflow) {
+        /* XXX: could be cute and give a different
+           message for overflow == -1 */
+        PyErr_SetString(PyExc_OverflowError,
+                        "Python int too large to convert to C long");
+    }
+    return result;
+}
+
+/* Get a Py_ssize_t from a long int object.
+   Returns -1 and sets an error condition if overflow occurs. */
+
+Py_ssize_t
+PyLong_AsSsize_t(PyObject *vv) {
+    register PyLongObject *v;
+    size_t x, prev;
+    Py_ssize_t i;
+    int sign;
+
+    if (vv == NULL) {
+        PyErr_BadInternalCall();
+        return -1;
+    }
+    if (!PyLong_Check(vv)) {
+        PyErr_SetString(PyExc_TypeError, "an integer is required");
+        return -1;
+    }
+
+    v = (PyLongObject *)vv;
+    i = Py_SIZE(v);
+    switch (i) {
+    case -1: return -(sdigit)v->ob_digit[0];
+    case 0: return 0;
+    case 1: return v->ob_digit[0];
+    }
+    sign = 1;
+    x = 0;
+    if (i < 0) {
+        sign = -1;
+        i = -(i);
+    }
+    while (--i >= 0) {
+        prev = x;
+        x = (x << PyLong_SHIFT) | v->ob_digit[i];
+        if ((x >> PyLong_SHIFT) != prev)
+            goto overflow;
+    }
+    /* Haven't lost any bits, but casting to a signed type requires
+     * extra care (see comment above).
+     */
+    if (x <= (size_t)PY_SSIZE_T_MAX) {
+        return (Py_ssize_t)x * sign;
+    }
+    else if (sign < 0 && x == PY_ABS_SSIZE_T_MIN) {
+        return PY_SSIZE_T_MIN;
+    }
+    /* else overflow */
+
+  overflow:
+    PyErr_SetString(PyExc_OverflowError,
+                    "Python int too large to convert to C ssize_t");
+    return -1;
+}
+
+/* Get a C unsigned long int from a long int object.
+   Returns -1 and sets an error condition if overflow occurs. */
+
+unsigned long
+PyLong_AsUnsignedLong(PyObject *vv)
+{
+    register PyLongObject *v;
+    unsigned long x, prev;
+    Py_ssize_t i;
+
+    if (vv == NULL) {
+        PyErr_BadInternalCall();
+        return (unsigned long)-1;
+    }
+    if (!PyLong_Check(vv)) {
+        PyErr_SetString(PyExc_TypeError, "an integer is required");
+        return (unsigned long)-1;
+    }
+
+    v = (PyLongObject *)vv;
+    i = Py_SIZE(v);
+    x = 0;
+    if (i < 0) {
+        PyErr_SetString(PyExc_OverflowError,
+                        "can't convert negative value to unsigned int");
+        return (unsigned long) -1;
+    }
+    switch (i) {
+    case 0: return 0;
+    case 1: return v->ob_digit[0];
+    }
+    while (--i >= 0) {
+        prev = x;
+        x = (x << PyLong_SHIFT) | v->ob_digit[i];
+        if ((x >> PyLong_SHIFT) != prev) {
+            PyErr_SetString(PyExc_OverflowError,
+                            "python int too large to convert "
+                            "to C unsigned long");
+            return (unsigned long) -1;
+        }
+    }
+    return x;
+}
+
+/* Get a C size_t from a long int object. Returns (size_t)-1 and sets
+   an error condition if overflow occurs. */
+
+size_t
+PyLong_AsSize_t(PyObject *vv)
+{
+    register PyLongObject *v;
+    size_t x, prev;
+    Py_ssize_t i;
+
+    if (vv == NULL) {
+        PyErr_BadInternalCall();
+        return (size_t) -1;
+    }
+    if (!PyLong_Check(vv)) {
+        PyErr_SetString(PyExc_TypeError, "an integer is required");
+        return (size_t)-1;
+    }
+
+    v = (PyLongObject *)vv;
+    i = Py_SIZE(v);
+    x = 0;
+    if (i < 0) {
+        PyErr_SetString(PyExc_OverflowError,
+                   "can't convert negative value to size_t");
+        return (size_t) -1;
+    }
+    switch (i) {
+    case 0: return 0;
+    case 1: return v->ob_digit[0];
+    }
+    while (--i >= 0) {
+        prev = x;
+        x = (x << PyLong_SHIFT) | v->ob_digit[i];
+        if ((x >> PyLong_SHIFT) != prev) {
+            PyErr_SetString(PyExc_OverflowError,
+                "Python int too large to convert to C size_t");
+            return (size_t) -1;
+        }
+    }
+    return x;
+}
+
+/* Get a C unsigned long int from a long int object, ignoring the high bits.
+   Returns -1 and sets an error condition if an error occurs. */
+
+static unsigned long
+_PyLong_AsUnsignedLongMask(PyObject *vv)
+{
+    register PyLongObject *v;
+    unsigned long x;
+    Py_ssize_t i;
+    int sign;
+
+    if (vv == NULL || !PyLong_Check(vv)) {
+        PyErr_BadInternalCall();
+        return (unsigned long) -1;
+    }
+    v = (PyLongObject *)vv;
+    i = Py_SIZE(v);
+    switch (i) {
+    case 0: return 0;
+    case 1: return v->ob_digit[0];
+    }
+    sign = 1;
+    x = 0;
+    if (i < 0) {
+        sign = -1;
+        i = -i;
+    }
+    while (--i >= 0) {
+        x = (x << PyLong_SHIFT) | v->ob_digit[i];
+    }
+    return x * sign;
+}
+
+unsigned long
+PyLong_AsUnsignedLongMask(register PyObject *op)
+{
+    PyNumberMethods *nb;
+    PyLongObject *lo;
+    unsigned long val;
+
+    if (op && PyLong_Check(op))
+        return _PyLong_AsUnsignedLongMask(op);
+
+    if (op == NULL || (nb = op->ob_type->tp_as_number) == NULL ||
+        nb->nb_int == NULL) {
+        PyErr_SetString(PyExc_TypeError, "an integer is required");
+        return (unsigned long)-1;
+    }
+
+    lo = (PyLongObject*) (*nb->nb_int) (op);
+    if (lo == NULL)
+        return (unsigned long)-1;
+    if (PyLong_Check(lo)) {
+        val = _PyLong_AsUnsignedLongMask((PyObject *)lo);
+        Py_DECREF(lo);
+        if (PyErr_Occurred())
+            return (unsigned long)-1;
+        return val;
+    }
+    else
+    {
+        Py_DECREF(lo);
+        PyErr_SetString(PyExc_TypeError,
+                        "nb_int should return int object");
+        return (unsigned long)-1;
+    }
+}
+
+int
+_PyLong_Sign(PyObject *vv)
+{
+    PyLongObject *v = (PyLongObject *)vv;
+
+    assert(v != NULL);
+    assert(PyLong_Check(v));
+
+    return Py_SIZE(v) == 0 ? 0 : (Py_SIZE(v) < 0 ? -1 : 1);
+}
+
+size_t
+_PyLong_NumBits(PyObject *vv)
+{
+    PyLongObject *v = (PyLongObject *)vv;
+    size_t result = 0;
+    Py_ssize_t ndigits;
+
+    assert(v != NULL);
+    assert(PyLong_Check(v));
+    ndigits = ABS(Py_SIZE(v));
+    assert(ndigits == 0 || v->ob_digit[ndigits - 1] != 0);
+    if (ndigits > 0) {
+        digit msd = v->ob_digit[ndigits - 1];
+
+        result = (ndigits - 1) * PyLong_SHIFT;
+        if (result / PyLong_SHIFT != (size_t)(ndigits - 1))
+            goto Overflow;
+        do {
+            ++result;
+            if (result == 0)
+                goto Overflow;
+            msd >>= 1;
+        } while (msd);
+    }
+    return result;
+
+  Overflow:
+    PyErr_SetString(PyExc_OverflowError, "int has too many bits "
+                    "to express in a platform size_t");
+    return (size_t)-1;
+}
+
+PyObject *
+_PyLong_FromByteArray(const unsigned char* bytes, size_t n,
+                      int little_endian, int is_signed)
+{
+    const unsigned char* pstartbyte;    /* LSB of bytes */
+    int incr;                           /* direction to move pstartbyte */
+    const unsigned char* pendbyte;      /* MSB of bytes */
+    size_t numsignificantbytes;         /* number of bytes that matter */
+    Py_ssize_t ndigits;                 /* number of Python long digits */
+    PyLongObject* v;                    /* result */
+    Py_ssize_t idigit = 0;              /* next free index in v->ob_digit */
+
+    if (n == 0)
+        return PyLong_FromLong(0L);
+
+    if (little_endian) {
+        pstartbyte = bytes;
+        pendbyte = bytes + n - 1;
+        incr = 1;
+    }
+    else {
+        pstartbyte = bytes + n - 1;
+        pendbyte = bytes;
+        incr = -1;
+    }
+
+    if (is_signed)
+        is_signed = *pendbyte >= 0x80;
+
+    /* Compute numsignificantbytes.  This consists of finding the most
+       significant byte.  Leading 0 bytes are insignificant if the number
+       is positive, and leading 0xff bytes if negative. */
+    {
+        size_t i;
+        const unsigned char* p = pendbyte;
+        const int pincr = -incr;  /* search MSB to LSB */
+        const unsigned char insignficant = is_signed ? 0xff : 0x00;
+
+        for (i = 0; i < n; ++i, p += pincr) {
+            if (*p != insignficant)
+                break;
+        }
+        numsignificantbytes = n - i;
+        /* 2's-comp is a bit tricky here, e.g. 0xff00 == -0x0100, so
+           actually has 2 significant bytes.  OTOH, 0xff0001 ==
+           -0x00ffff, so we wouldn't *need* to bump it there; but we
+           do for 0xffff = -0x0001.  To be safe without bothering to
+           check every case, bump it regardless. */
+        if (is_signed && numsignificantbytes < n)
+            ++numsignificantbytes;
+    }
+
+    /* How many Python long digits do we need?  We have
+       8*numsignificantbytes bits, and each Python long digit has
+       PyLong_SHIFT bits, so it's the ceiling of the quotient. */
+    /* catch overflow before it happens */
+    if (numsignificantbytes > (PY_SSIZE_T_MAX - PyLong_SHIFT) / 8) {
+        PyErr_SetString(PyExc_OverflowError,
+                        "byte array too long to convert to int");
+        return NULL;
+    }
+    ndigits = (numsignificantbytes * 8 + PyLong_SHIFT - 1) / PyLong_SHIFT;
+    v = _PyLong_New(ndigits);
+    if (v == NULL)
+        return NULL;
+
+    /* Copy the bits over.  The tricky parts are computing 2's-comp on
+       the fly for signed numbers, and dealing with the mismatch between
+       8-bit bytes and (probably) 15-bit Python digits.*/
+    {
+        size_t i;
+        twodigits carry = 1;                    /* for 2's-comp calculation */
+        twodigits accum = 0;                    /* sliding register */
+        unsigned int accumbits = 0;             /* number of bits in accum */
+        const unsigned char* p = pstartbyte;
+
+        for (i = 0; i < numsignificantbytes; ++i, p += incr) {
+            twodigits thisbyte = *p;
+            /* Compute correction for 2's comp, if needed. */
+            if (is_signed) {
+                thisbyte = (0xff ^ thisbyte) + carry;
+                carry = thisbyte >> 8;
+                thisbyte &= 0xff;
+            }
+            /* Because we're going LSB to MSB, thisbyte is
+               more significant than what's already in accum,
+               so needs to be prepended to accum. */
+            accum |= (twodigits)thisbyte << accumbits;
+            accumbits += 8;
+            if (accumbits >= PyLong_SHIFT) {
+                /* There's enough to fill a Python digit. */
+                assert(idigit < ndigits);
+                v->ob_digit[idigit] = (digit)(accum & PyLong_MASK);
+                ++idigit;
+                accum >>= PyLong_SHIFT;
+                accumbits -= PyLong_SHIFT;
+                assert(accumbits < PyLong_SHIFT);
+            }
+        }
+        assert(accumbits < PyLong_SHIFT);
+        if (accumbits) {
+            assert(idigit < ndigits);
+            v->ob_digit[idigit] = (digit)accum;
+            ++idigit;
+        }
+    }
+
+    Py_SIZE(v) = is_signed ? -idigit : idigit;
+    return (PyObject *)long_normalize(v);
+}
+
+int
+_PyLong_AsByteArray(PyLongObject* v,
+                    unsigned char* bytes, size_t n,
+                    int little_endian, int is_signed)
+{
+    Py_ssize_t i;               /* index into v->ob_digit */
+    Py_ssize_t ndigits;         /* |v->ob_size| */
+    twodigits accum;            /* sliding register */
+    unsigned int accumbits;     /* # bits in accum */
+    int do_twos_comp;           /* store 2's-comp?  is_signed and v < 0 */
+    digit carry;                /* for computing 2's-comp */
+    size_t j;                   /* # bytes filled */
+    unsigned char* p;           /* pointer to next byte in bytes */
+    int pincr;                  /* direction to move p */
+
+    assert(v != NULL && PyLong_Check(v));
+
+    if (Py_SIZE(v) < 0) {
+        ndigits = -(Py_SIZE(v));
+        if (!is_signed) {
+            PyErr_SetString(PyExc_OverflowError,
+                            "can't convert negative int to unsigned");
+            return -1;
+        }
+        do_twos_comp = 1;
+    }
+    else {
+        ndigits = Py_SIZE(v);
+        do_twos_comp = 0;
+    }
+
+    if (little_endian) {
+        p = bytes;
+        pincr = 1;
+    }
+    else {
+        p = bytes + n - 1;
+        pincr = -1;
+    }
+
+    /* Copy over all the Python digits.
+       It's crucial that every Python digit except for the MSD contribute
+       exactly PyLong_SHIFT bits to the total, so first assert that the long is
+       normalized. */
+    assert(ndigits == 0 || v->ob_digit[ndigits - 1] != 0);
+    j = 0;
+    accum = 0;
+    accumbits = 0;
+    carry = do_twos_comp ? 1 : 0;
+    for (i = 0; i < ndigits; ++i) {
+        digit thisdigit = v->ob_digit[i];
+        if (do_twos_comp) {
+            thisdigit = (thisdigit ^ PyLong_MASK) + carry;
+            carry = thisdigit >> PyLong_SHIFT;
+            thisdigit &= PyLong_MASK;
+        }
+        /* Because we're going LSB to MSB, thisdigit is more
+           significant than what's already in accum, so needs to be
+           prepended to accum. */
+        accum |= (twodigits)thisdigit << accumbits;
+
+        /* The most-significant digit may be (probably is) at least
+           partly empty. */
+        if (i == ndigits - 1) {
+            /* Count # of sign bits -- they needn't be stored,
+             * although for signed conversion we need later to
+             * make sure at least one sign bit gets stored. */
+            digit s = do_twos_comp ? thisdigit ^ PyLong_MASK : thisdigit;
+            while (s != 0) {
+                s >>= 1;
+                accumbits++;
+            }
+        }
+        else
+            accumbits += PyLong_SHIFT;
+
+        /* Store as many bytes as possible. */
+        while (accumbits >= 8) {
+            if (j >= n)
+                goto Overflow;
+            ++j;
+            *p = (unsigned char)(accum & 0xff);
+            p += pincr;
+            accumbits -= 8;
+            accum >>= 8;
+        }
+    }
+
+    /* Store the straggler (if any). */
+    assert(accumbits < 8);
+    assert(carry == 0);  /* else do_twos_comp and *every* digit was 0 */
+    if (accumbits > 0) {
+        if (j >= n)
+            goto Overflow;
+        ++j;
+        if (do_twos_comp) {
+            /* Fill leading bits of the byte with sign bits
+               (appropriately pretending that the long had an
+               infinite supply of sign bits). */
+            accum |= (~(twodigits)0) << accumbits;
+        }
+        *p = (unsigned char)(accum & 0xff);
+        p += pincr;
+    }
+    else if (j == n && n > 0 && is_signed) {
+        /* The main loop filled the byte array exactly, so the code
+           just above didn't get to ensure there's a sign bit, and the
+           loop below wouldn't add one either.  Make sure a sign bit
+           exists. */
+        unsigned char msb = *(p - pincr);
+        int sign_bit_set = msb >= 0x80;
+        assert(accumbits == 0);
+        if (sign_bit_set == do_twos_comp)
+            return 0;
+        else
+            goto Overflow;
+    }
+
+    /* Fill remaining bytes with copies of the sign bit. */
+    {
+        unsigned char signbyte = do_twos_comp ? 0xffU : 0U;
+        for ( ; j < n; ++j, p += pincr)
+            *p = signbyte;
+    }
+
+    return 0;
+
+  Overflow:
+    PyErr_SetString(PyExc_OverflowError, "int too big to convert");
+    return -1;
+
+}
+
+/* Create a new long int object from a C pointer */
+
+PyObject *
+PyLong_FromVoidPtr(void *p)
+{
+#ifndef HAVE_LONG_LONG
+#   error "PyLong_FromVoidPtr: sizeof(void*) > sizeof(long), but no long long"
+#endif
+#if SIZEOF_LONG_LONG < SIZEOF_VOID_P
+#   error "PyLong_FromVoidPtr: sizeof(PY_LONG_LONG) < sizeof(void*)"
+#endif
+    /* special-case null pointer */
+    if (!p)
+        return PyLong_FromLong(0);
+    return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG)(Py_uintptr_t)p);
+
+}
+
+/* Get a C pointer from a long int object. */
+
+void *
+PyLong_AsVoidPtr(PyObject *vv)
+{
+#if SIZEOF_VOID_P <= SIZEOF_LONG
+    long x;
+
+    if (PyLong_Check(vv) && _PyLong_Sign(vv) < 0)
+        x = PyLong_AsLong(vv);
+    else
+        x = PyLong_AsUnsignedLong(vv);
+#else
+
+#ifndef HAVE_LONG_LONG
+#   error "PyLong_AsVoidPtr: sizeof(void*) > sizeof(long), but no long long"
+#endif
+#if SIZEOF_LONG_LONG < SIZEOF_VOID_P
+#   error "PyLong_AsVoidPtr: sizeof(PY_LONG_LONG) < sizeof(void*)"
+#endif
+    PY_LONG_LONG x;
+
+    if (PyLong_Check(vv) && _PyLong_Sign(vv) < 0)
+        x = PyLong_AsLongLong(vv);
+    else
+        x = PyLong_AsUnsignedLongLong(vv);
+
+#endif /* SIZEOF_VOID_P <= SIZEOF_LONG */
+
+    if (x == -1 && PyErr_Occurred())
+        return NULL;
+    return (void *)x;
+}
+
+#ifdef HAVE_LONG_LONG
+
+/* Initial PY_LONG_LONG support by Chris Herborth (chrish@qnx.com), later
+ * rewritten to use the newer PyLong_{As,From}ByteArray API.
+ */
+
+#define IS_LITTLE_ENDIAN (int)*(unsigned char*)&one
+#define PY_ABS_LLONG_MIN (0-(unsigned PY_LONG_LONG)PY_LLONG_MIN)
+
+/* Create a new long int object from a C PY_LONG_LONG int. */
+
+PyObject *
+PyLong_FromLongLong(PY_LONG_LONG ival)
+{
+    PyLongObject *v;
+    unsigned PY_LONG_LONG abs_ival;
+    unsigned PY_LONG_LONG t;  /* unsigned so >> doesn't propagate sign bit */
+    int ndigits = 0;
+    int negative = 0;
+
+    if (ival < 0) {
+        /* avoid signed overflow on negation;  see comments
+           in PyLong_FromLong above. */
+        abs_ival = (unsigned PY_LONG_LONG)(-1-ival) + 1;
+        negative = 1;
+    }
+    else {
+        abs_ival = (unsigned PY_LONG_LONG)ival;
+    }
+
+    /* Count the number of Python digits.
+       We used to pick 5 ("big enough for anything"), but that's a
+       waste of time and space given that 5*15 = 75 bits are rarely
+       needed. */
+    t = abs_ival;
+    while (t) {
+        ++ndigits;
+        t >>= PyLong_SHIFT;
+    }
+    v = _PyLong_New(ndigits);
+    if (v != NULL) {
+        digit *p = v->ob_digit;
+        Py_SIZE(v) = negative ? -ndigits : ndigits;
+        t = abs_ival;
+        while (t) {
+            *p++ = (digit)(t & PyLong_MASK);
+            t >>= PyLong_SHIFT;
+        }
+    }
+    return (PyObject *)v;
+}
+
+/* Create a new long int object from a C unsigned PY_LONG_LONG int. */
+
+PyObject *
+PyLong_FromUnsignedLongLong(unsigned PY_LONG_LONG ival)
+{
+    PyLongObject *v;
+    unsigned PY_LONG_LONG t;
+    int ndigits = 0;
+
+    if (ival < PyLong_BASE)
+        return PyLong_FromLong((long)ival);
+    /* Count the number of Python digits. */
+    t = (unsigned PY_LONG_LONG)ival;
+    while (t) {
+        ++ndigits;
+        t >>= PyLong_SHIFT;
+    }
+    v = _PyLong_New(ndigits);
+    if (v != NULL) {
+        digit *p = v->ob_digit;
+        Py_SIZE(v) = ndigits;
+        while (ival) {
+            *p++ = (digit)(ival & PyLong_MASK);
+            ival >>= PyLong_SHIFT;
+        }
+    }
+    return (PyObject *)v;
+}
+
+/* Create a new long int object from a C Py_ssize_t. */
+
+PyObject *
+PyLong_FromSsize_t(Py_ssize_t ival)
+{
+    PyLongObject *v;
+    size_t abs_ival;
+    size_t t;  /* unsigned so >> doesn't propagate sign bit */
+    int ndigits = 0;
+    int negative = 0;
+
+    CHECK_SMALL_INT(ival);
+    if (ival < 0) {
+        /* avoid signed overflow when ival = SIZE_T_MIN */
+        abs_ival = (size_t)(-1-ival)+1;
+        negative = 1;
+    }
+    else {
+        abs_ival = (size_t)ival;
+    }
+
+    /* Count the number of Python digits. */
+    t = abs_ival;
+    while (t) {
+        ++ndigits;
+        t >>= PyLong_SHIFT;
+    }
+    v = _PyLong_New(ndigits);
+    if (v != NULL) {
+        digit *p = v->ob_digit;
+        Py_SIZE(v) = negative ? -ndigits : ndigits;
+        t = abs_ival;
+        while (t) {
+            *p++ = (digit)(t & PyLong_MASK);
+            t >>= PyLong_SHIFT;
+        }
+    }
+    return (PyObject *)v;
+}
+
+/* Create a new long int object from a C size_t. */
+
+PyObject *
+PyLong_FromSize_t(size_t ival)
+{
+    PyLongObject *v;
+    size_t t;
+    int ndigits = 0;
+
+    if (ival < PyLong_BASE)
+        return PyLong_FromLong((long)ival);
+    /* Count the number of Python digits. */
+    t = ival;
+    while (t) {
+        ++ndigits;
+        t >>= PyLong_SHIFT;
+    }
+    v = _PyLong_New(ndigits);
+    if (v != NULL) {
+        digit *p = v->ob_digit;
+        Py_SIZE(v) = ndigits;
+        while (ival) {
+            *p++ = (digit)(ival & PyLong_MASK);
+            ival >>= PyLong_SHIFT;
+        }
+    }
+    return (PyObject *)v;
+}
+
+/* Get a C long long int from a long int object or any object that has an
+   __int__ method.  Return -1 and set an error if overflow occurs. */
+
+PY_LONG_LONG
+PyLong_AsLongLong(PyObject *vv)
+{
+    PyLongObject *v;
+    PY_LONG_LONG bytes;
+    int one = 1;
+    int res;
+
+    if (vv == NULL) {
+        PyErr_BadInternalCall();
+        return -1;
+    }
+    if (!PyLong_Check(vv)) {
+        PyNumberMethods *nb;
+        PyObject *io;
+        if ((nb = vv->ob_type->tp_as_number) == NULL ||
+            nb->nb_int == NULL) {
+            PyErr_SetString(PyExc_TypeError, "an integer is required");
+            return -1;
+        }
+        io = (*nb->nb_int) (vv);
+        if (io == NULL)
+            return -1;
+        if (PyLong_Check(io)) {
+            bytes = PyLong_AsLongLong(io);
+            Py_DECREF(io);
+            return bytes;
+        }
+        Py_DECREF(io);
+        PyErr_SetString(PyExc_TypeError, "integer conversion failed");
+        return -1;
+    }
+
+    v = (PyLongObject*)vv;
+    switch(Py_SIZE(v)) {
+    case -1: return -(sdigit)v->ob_digit[0];
+    case 0: return 0;
+    case 1: return v->ob_digit[0];
+    }
+    res = _PyLong_AsByteArray((PyLongObject *)vv, (unsigned char *)&bytes,
+                              SIZEOF_LONG_LONG, IS_LITTLE_ENDIAN, 1);
+
+    /* Plan 9 can't handle PY_LONG_LONG in ? : expressions */
+    if (res < 0)
+        return (PY_LONG_LONG)-1;
+    else
+        return bytes;
+}
+
+/* Get a C unsigned PY_LONG_LONG int from a long int object.
+   Return -1 and set an error if overflow occurs. */
+
+unsigned PY_LONG_LONG
+PyLong_AsUnsignedLongLong(PyObject *vv)
+{
+    PyLongObject *v;
+    unsigned PY_LONG_LONG bytes;
+    int one = 1;
+    int res;
+
+    if (vv == NULL) {
+        PyErr_BadInternalCall();
+        return (unsigned PY_LONG_LONG)-1;
+    }
+    if (!PyLong_Check(vv)) {
+        PyErr_SetString(PyExc_TypeError, "an integer is required");
+        return (unsigned PY_LONG_LONG)-1;
+    }
+
+    v = (PyLongObject*)vv;
+    switch(Py_SIZE(v)) {
+    case 0: return 0;
+    case 1: return v->ob_digit[0];
+    }
+
+    res = _PyLong_AsByteArray((PyLongObject *)vv, (unsigned char *)&bytes,
+                              SIZEOF_LONG_LONG, IS_LITTLE_ENDIAN, 0);
+
+    /* Plan 9 can't handle PY_LONG_LONG in ? : expressions */
+    if (res < 0)
+        return (unsigned PY_LONG_LONG)res;
+    else
+        return bytes;
+}
+
+/* Get a C unsigned long int from a long int object, ignoring the high bits.
+   Returns -1 and sets an error condition if an error occurs. */
+
+static unsigned PY_LONG_LONG
+_PyLong_AsUnsignedLongLongMask(PyObject *vv)
+{
+    register PyLongObject *v;
+    unsigned PY_LONG_LONG x;
+    Py_ssize_t i;
+    int sign;
+
+    if (vv == NULL || !PyLong_Check(vv)) {
+        PyErr_BadInternalCall();
+        return (unsigned long) -1;
+    }
+    v = (PyLongObject *)vv;
+    switch(Py_SIZE(v)) {
+    case 0: return 0;
+    case 1: return v->ob_digit[0];
+    }
+    i = Py_SIZE(v);
+    sign = 1;
+    x = 0;
+    if (i < 0) {
+        sign = -1;
+        i = -i;
+    }
+    while (--i >= 0) {
+        x = (x << PyLong_SHIFT) | v->ob_digit[i];
+    }
+    return x * sign;
+}
+
+unsigned PY_LONG_LONG
+PyLong_AsUnsignedLongLongMask(register PyObject *op)
+{
+    PyNumberMethods *nb;
+    PyLongObject *lo;
+    unsigned PY_LONG_LONG val;
+
+    if (op && PyLong_Check(op))
+        return _PyLong_AsUnsignedLongLongMask(op);
+
+    if (op == NULL || (nb = op->ob_type->tp_as_number) == NULL ||
+        nb->nb_int == NULL) {
+        PyErr_SetString(PyExc_TypeError, "an integer is required");
+        return (unsigned PY_LONG_LONG)-1;
+    }
+
+    lo = (PyLongObject*) (*nb->nb_int) (op);
+    if (lo == NULL)
+        return (unsigned PY_LONG_LONG)-1;
+    if (PyLong_Check(lo)) {
+        val = _PyLong_AsUnsignedLongLongMask((PyObject *)lo);
+        Py_DECREF(lo);
+        if (PyErr_Occurred())
+            return (unsigned PY_LONG_LONG)-1;
+        return val;
+    }
+    else
+    {
+        Py_DECREF(lo);
+        PyErr_SetString(PyExc_TypeError,
+                        "nb_int should return int object");
+        return (unsigned PY_LONG_LONG)-1;
+    }
+}
+#undef IS_LITTLE_ENDIAN
+
+/* Get a C long long int from a long int object or any object that has an
+   __int__ method.
+
+   On overflow, return -1 and set *overflow to 1 or -1 depending on the sign of
+   the result.  Otherwise *overflow is 0.
+
+   For other errors (e.g., TypeError), return -1 and set an error condition.
+   In this case *overflow will be 0.
+*/
+
+PY_LONG_LONG
+PyLong_AsLongLongAndOverflow(PyObject *vv, int *overflow)
+{
+    /* This version by Tim Peters */
+    register PyLongObject *v;
+    unsigned PY_LONG_LONG x, prev;
+    PY_LONG_LONG res;
+    Py_ssize_t i;
+    int sign;
+    int do_decref = 0; /* if nb_int was called */
+
+    *overflow = 0;
+    if (vv == NULL) {
+        PyErr_BadInternalCall();
+        return -1;
+    }
+
+    if (!PyLong_Check(vv)) {
+        PyNumberMethods *nb;
+        nb = vv->ob_type->tp_as_number;
+        if (nb == NULL || nb->nb_int == NULL) {
+            PyErr_SetString(PyExc_TypeError,
+                            "an integer is required");
+            return -1;
+        }
+        vv = (*nb->nb_int) (vv);
+        if (vv == NULL)
+            return -1;
+        do_decref = 1;
+        if (!PyLong_Check(vv)) {
+            Py_DECREF(vv);
+            PyErr_SetString(PyExc_TypeError,
+                            "nb_int should return int object");
+            return -1;
+        }
+    }
+
+    res = -1;
+    v = (PyLongObject *)vv;
+    i = Py_SIZE(v);
+
+    switch (i) {
+    case -1:
+        res = -(sdigit)v->ob_digit[0];
+        break;
+    case 0:
+        res = 0;
+        break;
+    case 1:
+        res = v->ob_digit[0];
+        break;
+    default:
+        sign = 1;
+        x = 0;
+        if (i < 0) {
+            sign = -1;
+            i = -(i);
+        }
+        while (--i >= 0) {
+            prev = x;
+            x = (x << PyLong_SHIFT) + v->ob_digit[i];
+            if ((x >> PyLong_SHIFT) != prev) {
+                *overflow = sign;
+                goto exit;
+            }
+        }
+        /* Haven't lost any bits, but casting to long requires extra
+         * care (see comment above).
+         */
+        if (x <= (unsigned PY_LONG_LONG)PY_LLONG_MAX) {
+            res = (PY_LONG_LONG)x * sign;
+        }
+        else if (sign < 0 && x == PY_ABS_LLONG_MIN) {
+            res = PY_LLONG_MIN;
+        }
+        else {
+            *overflow = sign;
+            /* res is already set to -1 */
+        }
+    }
+  exit:
+    if (do_decref) {
+        Py_DECREF(vv);
+    }
+    return res;
+}
+
+#endif /* HAVE_LONG_LONG */
+
+#define CHECK_BINOP(v,w)                                \
+    do {                                                \
+        if (!PyLong_Check(v) || !PyLong_Check(w))       \
+            Py_RETURN_NOTIMPLEMENTED;                   \
+    } while(0)
+
+/* bits_in_digit(d) returns the unique integer k such that 2**(k-1) <= d <
+   2**k if d is nonzero, else 0. */
+
+static const unsigned char BitLengthTable[32] = {
+    0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4,
+    5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5
+};
+
+static int
+bits_in_digit(digit d)
+{
+    int d_bits = 0;
+    while (d >= 32) {
+        d_bits += 6;
+        d >>= 6;
+    }
+    d_bits += (int)BitLengthTable[d];
+    return d_bits;
+}
+
+/* x[0:m] and y[0:n] are digit vectors, LSD first, m >= n required.  x[0:n]
+ * is modified in place, by adding y to it.  Carries are propagated as far as
+ * x[m-1], and the remaining carry (0 or 1) is returned.
+ */
+static digit
+v_iadd(digit *x, Py_ssize_t m, digit *y, Py_ssize_t n)
+{
+    Py_ssize_t i;
+    digit carry = 0;
+
+    assert(m >= n);
+    for (i = 0; i < n; ++i) {
+        carry += x[i] + y[i];
+        x[i] = carry & PyLong_MASK;
+        carry >>= PyLong_SHIFT;
+        assert((carry & 1) == carry);
+    }
+    for (; carry && i < m; ++i) {
+        carry += x[i];
+        x[i] = carry & PyLong_MASK;
+        carry >>= PyLong_SHIFT;
+        assert((carry & 1) == carry);
+    }
+    return carry;
+}
+
+/* x[0:m] and y[0:n] are digit vectors, LSD first, m >= n required.  x[0:n]
+ * is modified in place, by subtracting y from it.  Borrows are propagated as
+ * far as x[m-1], and the remaining borrow (0 or 1) is returned.
+ */
+static digit
+v_isub(digit *x, Py_ssize_t m, digit *y, Py_ssize_t n)
+{
+    Py_ssize_t i;
+    digit borrow = 0;
+
+    assert(m >= n);
+    for (i = 0; i < n; ++i) {
+        borrow = x[i] - y[i] - borrow;
+        x[i] = borrow & PyLong_MASK;
+        borrow >>= PyLong_SHIFT;
+        borrow &= 1;            /* keep only 1 sign bit */
+    }
+    for (; borrow && i < m; ++i) {
+        borrow = x[i] - borrow;
+        x[i] = borrow & PyLong_MASK;
+        borrow >>= PyLong_SHIFT;
+        borrow &= 1;
+    }
+    return borrow;
+}
+
+/* Shift digit vector a[0:m] d bits left, with 0 <= d < PyLong_SHIFT.  Put
+ * result in z[0:m], and return the d bits shifted out of the top.
+ */
+static digit
+v_lshift(digit *z, digit *a, Py_ssize_t m, int d)
+{
+    Py_ssize_t i;
+    digit carry = 0;
+
+    assert(0 <= d && d < PyLong_SHIFT);
+    for (i=0; i < m; i++) {
+        twodigits acc = (twodigits)a[i] << d | carry;
+        z[i] = (digit)acc & PyLong_MASK;
+        carry = (digit)(acc >> PyLong_SHIFT);
+    }
+    return carry;
+}
+
+/* Shift digit vector a[0:m] d bits right, with 0 <= d < PyLong_SHIFT.  Put
+ * result in z[0:m], and return the d bits shifted out of the bottom.
+ */
+static digit
+v_rshift(digit *z, digit *a, Py_ssize_t m, int d)
+{
+    Py_ssize_t i;
+    digit carry = 0;
+    digit mask = ((digit)1 << d) - 1U;
+
+    assert(0 <= d && d < PyLong_SHIFT);
+    for (i=m; i-- > 0;) {
+        twodigits acc = (twodigits)carry << PyLong_SHIFT | a[i];
+        carry = (digit)acc & mask;
+        z[i] = (digit)(acc >> d);
+    }
+    return carry;
+}
+
+/* Divide long pin, w/ size digits, by non-zero digit n, storing quotient
+   in pout, and returning the remainder.  pin and pout point at the LSD.
+   It's OK for pin == pout on entry, which saves oodles of mallocs/frees in
+   _PyLong_Format, but that should be done with great care since longs are
+   immutable. */
+
+static digit
+inplace_divrem1(digit *pout, digit *pin, Py_ssize_t size, digit n)
+{
+    twodigits rem = 0;
+
+    assert(n > 0 && n <= PyLong_MASK);
+    pin += size;
+    pout += size;
+    while (--size >= 0) {
+        digit hi;
+        rem = (rem << PyLong_SHIFT) | *--pin;
+        *--pout = hi = (digit)(rem / n);
+        rem -= (twodigits)hi * n;
+    }
+    return (digit)rem;
+}
+
+/* Divide a long integer by a digit, returning both the quotient
+   (as function result) and the remainder (through *prem).
+   The sign of a is ignored; n should not be zero. */
+
+static PyLongObject *
+divrem1(PyLongObject *a, digit n, digit *prem)
+{
+    const Py_ssize_t size = ABS(Py_SIZE(a));
+    PyLongObject *z;
+
+    assert(n > 0 && n <= PyLong_MASK);
+    z = _PyLong_New(size);
+    if (z == NULL)
+        return NULL;
+    *prem = inplace_divrem1(z->ob_digit, a->ob_digit, size, n);
+    return long_normalize(z);
+}
+
+/* Convert a long integer to a base 10 string.  Returns a new non-shared
+   string.  (Return value is non-shared so that callers can modify the
+   returned value if necessary.) */
+
+static PyObject *
+long_to_decimal_string(PyObject *aa)
+{
+    PyLongObject *scratch, *a;
+    PyObject *str;
+    Py_ssize_t size, strlen, size_a, i, j;
+    digit *pout, *pin, rem, tenpow;
+    unsigned char *p;
+    int negative;
+
+    a = (PyLongObject *)aa;
+    if (a == NULL || !PyLong_Check(a)) {
+        PyErr_BadInternalCall();
+        return NULL;
+    }
+    size_a = ABS(Py_SIZE(a));
+    negative = Py_SIZE(a) < 0;
+
+    /* quick and dirty upper bound for the number of digits
+       required to express a in base _PyLong_DECIMAL_BASE:
+
+         #digits = 1 + floor(log2(a) / log2(_PyLong_DECIMAL_BASE))
+
+       But log2(a) < size_a * PyLong_SHIFT, and
+       log2(_PyLong_DECIMAL_BASE) = log2(10) * _PyLong_DECIMAL_SHIFT
+                                  > 3 * _PyLong_DECIMAL_SHIFT
+    */
+    if (size_a > PY_SSIZE_T_MAX / PyLong_SHIFT) {
+        PyErr_SetString(PyExc_OverflowError,
+                        "long is too large to format");
+        return NULL;
+    }
+    /* the expression size_a * PyLong_SHIFT is now safe from overflow */
+    size = 1 + size_a * PyLong_SHIFT / (3 * _PyLong_DECIMAL_SHIFT);
+    scratch = _PyLong_New(size);
+    if (scratch == NULL)
+        return NULL;
+
+    /* convert array of base _PyLong_BASE digits in pin to an array of
+       base _PyLong_DECIMAL_BASE digits in pout, following Knuth (TAOCP,
+       Volume 2 (3rd edn), section 4.4, Method 1b). */
+    pin = a->ob_digit;
+    pout = scratch->ob_digit;
+    size = 0;
+    for (i = size_a; --i >= 0; ) {
+        digit hi = pin[i];
+        for (j = 0; j < size; j++) {
+            twodigits z = (twodigits)pout[j] << PyLong_SHIFT | hi;
+            hi = (digit)(z / _PyLong_DECIMAL_BASE);
+            pout[j] = (digit)(z - (twodigits)hi *
+                              _PyLong_DECIMAL_BASE);
+        }
+        while (hi) {
+            pout[size++] = hi % _PyLong_DECIMAL_BASE;
+            hi /= _PyLong_DECIMAL_BASE;
+        }
+        /* check for keyboard interrupt */
+        SIGCHECK({
+                Py_DECREF(scratch);
+                return NULL;
+            });
+    }
+    /* pout should have at least one digit, so that the case when a = 0
+       works correctly */
+    if (size == 0)
+        pout[size++] = 0;
+
+    /* calculate exact length of output string, and allocate */
+    strlen = negative + 1 + (size - 1) * _PyLong_DECIMAL_SHIFT;
+    tenpow = 10;
+    rem = pout[size-1];
+    while (rem >= tenpow) {
+        tenpow *= 10;
+        strlen++;
+    }
+    str = PyUnicode_New(strlen, '9');
+    if (str == NULL) {
+        Py_DECREF(scratch);
+        return NULL;
+    }
+
+    /* fill the string right-to-left */
+    assert(PyUnicode_KIND(str) == PyUnicode_1BYTE_KIND);
+    p = PyUnicode_1BYTE_DATA(str) + strlen;
+    *p = '\0';
+    /* pout[0] through pout[size-2] contribute exactly
+       _PyLong_DECIMAL_SHIFT digits each */
+    for (i=0; i < size - 1; i++) {
+        rem = pout[i];
+        for (j = 0; j < _PyLong_DECIMAL_SHIFT; j++) {
+            *--p = '0' + rem % 10;
+            rem /= 10;
+        }
+    }
+    /* pout[size-1]: always produce at least one decimal digit */
+    rem = pout[i];
+    do {
+        *--p = '0' + rem % 10;
+        rem /= 10;
+    } while (rem != 0);
+
+    /* and sign */
+    if (negative)
+        *--p = '-';
+
+    /* check we've counted correctly */
+    assert(p == PyUnicode_1BYTE_DATA(str));
+    Py_DECREF(scratch);
+    return (PyObject *)str;
+}
+
+/* Convert a long int object to a string, using a given conversion base,
+   which should be one of 2, 8, 10 or 16.  Return a string object.
+   If base is 2, 8 or 16, add the proper prefix '0b', '0o' or '0x'. */
+
+PyObject *
+_PyLong_Format(PyObject *aa, int base)
+{
+    register PyLongObject *a = (PyLongObject *)aa;
+    PyObject *v;
+    Py_ssize_t i, sz;
+    Py_ssize_t size_a;
+    char *p;
+    char sign = '\0';
+    char *buffer;
+    int bits;
+
+    assert(base == 2 || base == 8 || base == 10 || base == 16);
+    if (base == 10)
+        return long_to_decimal_string((PyObject *)a);
+
+    if (a == NULL || !PyLong_Check(a)) {
+        PyErr_BadInternalCall();
+        return NULL;
+    }
+    size_a = ABS(Py_SIZE(a));
+
+    /* Compute a rough upper bound for the length of the string */
+    switch (base) {
+    case 16:
+        bits = 4;
+        break;
+    case 8:
+        bits = 3;
+        break;
+    case 2:
+        bits = 1;
+        break;
+    default:
+        assert(0); /* shouldn't ever get here */
+        bits = 0; /* to silence gcc warning */
+    }
+    /* compute length of output string: allow 2 characters for prefix and
+       1 for possible '-' sign. */
+    if (size_a > (PY_SSIZE_T_MAX - 3) / PyLong_SHIFT / sizeof(Py_UCS4)) {
+        PyErr_SetString(PyExc_OverflowError,
+                        "int is too large to format");
+        return NULL;
+    }
+    /* now size_a * PyLong_SHIFT + 3 <= PY_SSIZE_T_MAX, so the RHS below
+       is safe from overflow */
+    sz = 3 + (size_a * PyLong_SHIFT + (bits - 1)) / bits;
+    assert(sz >= 0);
+    buffer = PyMem_Malloc(sz);
+    if (buffer == NULL) {
+        PyErr_NoMemory();
+        return NULL;
+    }
+    p = &buffer[sz];
+    if (Py_SIZE(a) < 0)
+        sign = '-';
+
+    if (Py_SIZE(a) == 0) {
+        *--p = '0';
+    }
+    else {
+        /* JRH: special case for power-of-2 bases */
+        twodigits accum = 0;
+        int accumbits = 0;              /* # of bits in accum */
+        for (i = 0; i < size_a; ++i) {
+            accum |= (twodigits)a->ob_digit[i] << accumbits;
+            accumbits += PyLong_SHIFT;
+            assert(accumbits >= bits);
+            do {
+                char cdigit;
+                cdigit = (char)(accum & (base - 1));
+                cdigit += (cdigit < 10) ? '0' : 'a'-10;
+                assert(p > buffer);
+                *--p = cdigit;
+                accumbits -= bits;
+                accum >>= bits;
+            } while (i < size_a-1 ? accumbits >= bits : accum > 0);
+        }
+    }
+
+    if (base == 16)
+        *--p = 'x';
+    else if (base == 8)
+        *--p = 'o';
+    else /* (base == 2) */
+        *--p = 'b';
+    *--p = '0';
+    if (sign)
+        *--p = sign;
+    v = PyUnicode_DecodeASCII(p, &buffer[sz] - p, NULL);
+    PyMem_Free(buffer);
+    return v;
+}
+
+/* Table of digit values for 8-bit string -> integer conversion.
+ * '0' maps to 0, ..., '9' maps to 9.
+ * 'a' and 'A' map to 10, ..., 'z' and 'Z' map to 35.
+ * All other indices map to 37.
+ * Note that when converting a base B string, a char c is a legitimate
+ * base B digit iff _PyLong_DigitValue[Py_CHARPyLong_MASK(c)] < B.
+ */
+unsigned char _PyLong_DigitValue[256] = {
+    37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
+    37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
+    37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
+    0,  1,  2,  3,  4,  5,  6,  7,  8,  9,  37, 37, 37, 37, 37, 37,
+    37, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24,
+    25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 37, 37, 37, 37,
+    37, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24,
+    25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 37, 37, 37, 37,
+    37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
+    37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
+    37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
+    37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
+    37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
+    37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
+    37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
+    37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
+};
+
+/* *str points to the first digit in a string of base `base` digits.  base
+ * is a power of 2 (2, 4, 8, 16, or 32).  *str is set to point to the first
+ * non-digit (which may be *str!).  A normalized long is returned.
+ * The point to this routine is that it takes time linear in the number of
+ * string characters.
+ */
+static PyLongObject *
+long_from_binary_base(char **str, int base)
+{
+    char *p = *str;
+    char *start = p;
+    int bits_per_char;
+    Py_ssize_t n;
+    PyLongObject *z;
+    twodigits accum;
+    int bits_in_accum;
+    digit *pdigit;
+
+    assert(base >= 2 && base <= 32 && (base & (base - 1)) == 0);
+    n = base;
+    for (bits_per_char = -1; n; ++bits_per_char)
+        n >>= 1;
+    /* n <- total # of bits needed, while setting p to end-of-string */
+    while (_PyLong_DigitValue[Py_CHARMASK(*p)] < base)
+        ++p;
+    *str = p;
+    /* n <- # of Python digits needed, = ceiling(n/PyLong_SHIFT). */
+    n = (p - start) * bits_per_char + PyLong_SHIFT - 1;
+    if (n / bits_per_char < p - start) {
+        PyErr_SetString(PyExc_ValueError,
+                        "int string too large to convert");
+        return NULL;
+    }
+    n = n / PyLong_SHIFT;
+    z = _PyLong_New(n);
+    if (z == NULL)
+        return NULL;
+    /* Read string from right, and fill in long from left; i.e.,
+     * from least to most significant in both.
+     */
+    accum = 0;
+    bits_in_accum = 0;
+    pdigit = z->ob_digit;
+    while (--p >= start) {
+        int k = (int)_PyLong_DigitValue[Py_CHARMASK(*p)];
+        assert(k >= 0 && k < base);
+        accum |= (twodigits)k << bits_in_accum;
+        bits_in_accum += bits_per_char;
+        if (bits_in_accum >= PyLong_SHIFT) {
+            *pdigit++ = (digit)(accum & PyLong_MASK);
+            assert(pdigit - z->ob_digit <= n);
+            accum >>= PyLong_SHIFT;
+            bits_in_accum -= PyLong_SHIFT;
+            assert(bits_in_accum < PyLong_SHIFT);
+        }
+    }
+    if (bits_in_accum) {
+        assert(bits_in_accum <= PyLong_SHIFT);
+        *pdigit++ = (digit)accum;
+        assert(pdigit - z->ob_digit <= n);
+    }
+    while (pdigit - z->ob_digit < n)
+        *pdigit++ = 0;
+    return long_normalize(z);
+}
+
+PyObject *
+PyLong_FromString(char *str, char **pend, int base)
+{
+    int sign = 1, error_if_nonzero = 0;
+    char *start, *orig_str = str;
+    PyLongObject *z = NULL;
+    PyObject *strobj;
+    Py_ssize_t slen;
+
+    if ((base != 0 && base < 2) || base > 36) {
+        PyErr_SetString(PyExc_ValueError,
+                        "int() arg 2 must be >= 2 and <= 36");
+        return NULL;
+    }
+    while (*str != '\0' && isspace(Py_CHARMASK(*str)))
+        str++;
+    if (*str == '+')
+        ++str;
+    else if (*str == '-') {
+        ++str;
+        sign = -1;
+    }
+    if (base == 0) {
+        if (str[0] != '0')
+            base = 10;
+        else if (str[1] == 'x' || str[1] == 'X')
+            base = 16;
+        else if (str[1] == 'o' || str[1] == 'O')
+            base = 8;
+        else if (str[1] == 'b' || str[1] == 'B')
+            base = 2;
+        else {
+            /* "old" (C-style) octal literal, now invalid.
+               it might still be zero though */
+            error_if_nonzero = 1;
+            base = 10;
+        }
+    }
+    if (str[0] == '0' &&
+        ((base == 16 && (str[1] == 'x' || str[1] == 'X')) ||
+         (base == 8  && (str[1] == 'o' || str[1] == 'O')) ||
+         (base == 2  && (str[1] == 'b' || str[1] == 'B'))))
+        str += 2;
+
+    start = str;
+    if ((base & (base - 1)) == 0)
+        z = long_from_binary_base(&str, base);
+    else {
+/***
+Binary bases can be converted in time linear in the number of digits, because
+Python's representation base is binary.  Other bases (including decimal!) use
+the simple quadratic-time algorithm below, complicated by some speed tricks.
+
+First some math:  the largest integer that can be expressed in N base-B digits
+is B**N-1.  Consequently, if we have an N-digit input in base B, the worst-
+case number of Python digits needed to hold it is the smallest integer n s.t.
+
+    BASE**n-1 >= B**N-1  [or, adding 1 to both sides]
+    BASE**n >= B**N      [taking logs to base BASE]
+    n >= log(B**N)/log(BASE) = N * log(B)/log(BASE)
+
+The static array log_base_BASE[base] == log(base)/log(BASE) so we can compute
+this quickly.  A Python long with that much space is reserved near the start,
+and the result is computed into it.
+
+The input string is actually treated as being in base base**i (i.e., i digits
+are processed at a time), where two more static arrays hold:
+
+    convwidth_base[base] = the largest integer i such that base**i <= BASE
+    convmultmax_base[base] = base ** convwidth_base[base]
+
+The first of these is the largest i such that i consecutive input digits
+must fit in a single Python digit.  The second is effectively the input
+base we're really using.
+
+Viewing the input as a sequence <c0, c1, ..., c_n-1> of digits in base
+convmultmax_base[base], the result is "simply"
+
+   (((c0*B + c1)*B + c2)*B + c3)*B + ... ))) + c_n-1
+
+where B = convmultmax_base[base].
+
+Error analysis:  as above, the number of Python digits `n` needed is worst-
+case
+
+    n >= N * log(B)/log(BASE)
+
+where `N` is the number of input digits in base `B`.  This is computed via
+
+    size_z = (Py_ssize_t)((scan - str) * log_base_BASE[base]) + 1;
+
+below.  Two numeric concerns are how much space this can waste, and whether
+the computed result can be too small.  To be concrete, assume BASE = 2**15,
+which is the default (and it's unlikely anyone changes that).
+
+Waste isn't a problem:  provided the first input digit isn't 0, the difference
+between the worst-case input with N digits and the smallest input with N
+digits is about a factor of B, but B is small compared to BASE so at most
+one allocated Python digit can remain unused on that count.  If
+N*log(B)/log(BASE) is mathematically an exact integer, then truncating that
+and adding 1 returns a result 1 larger than necessary.  However, that can't
+happen:  whenever B is a power of 2, long_from_binary_base() is called
+instead, and it's impossible for B**i to be an integer power of 2**15 when
+B is not a power of 2 (i.e., it's impossible for N*log(B)/log(BASE) to be
+an exact integer when B is not a power of 2, since B**i has a prime factor
+other than 2 in that case, but (2**15)**j's only prime factor is 2).
+
+The computed result can be too small if the true value of N*log(B)/log(BASE)
+is a little bit larger than an exact integer, but due to roundoff errors (in
+computing log(B), log(BASE), their quotient, and/or multiplying that by N)
+yields a numeric result a little less than that integer.  Unfortunately, "how
+close can a transcendental function get to an integer over some range?"
+questions are generally theoretically intractable.  Computer analysis via
+continued fractions is practical:  expand log(B)/log(BASE) via continued
+fractions, giving a sequence i/j of "the best" rational approximations.  Then
+j*log(B)/log(BASE) is approximately equal to (the integer) i.  This shows that
+we can get very close to being in trouble, but very rarely.  For example,
+76573 is a denominator in one of the continued-fraction approximations to
+log(10)/log(2**15), and indeed:
+
+    >>> log(10)/log(2**15)*76573
+    16958.000000654003
+
+is very close to an integer.  If we were working with IEEE single-precision,
+rounding errors could kill us.  Finding worst cases in IEEE double-precision
+requires better-than-double-precision log() functions, and Tim didn't bother.
+Instead the code checks to see whether the allocated space is enough as each
+new Python digit is added, and copies the whole thing to a larger long if not.
+This should happen extremely rarely, and in fact I don't have a test case
+that triggers it(!).  Instead the code was tested by artificially allocating
+just 1 digit at the start, so that the copying code was exercised for every
+digit beyond the first.
+***/
+        register twodigits c;           /* current input character */
+        Py_ssize_t size_z;
+        int i;
+        int convwidth;
+        twodigits convmultmax, convmult;
+        digit *pz, *pzstop;
+        char* scan;
+
+        static double log_base_BASE[37] = {0.0e0,};
+        static int convwidth_base[37] = {0,};
+        static twodigits convmultmax_base[37] = {0,};
+
+        if (log_base_BASE[base] == 0.0) {
+            twodigits convmax = base;
+            int i = 1;
+
+            log_base_BASE[base] = (log((double)base) /
+                                   log((double)PyLong_BASE));
+            for (;;) {
+                twodigits next = convmax * base;
+                if (next > PyLong_BASE)
+                    break;
+                convmax = next;
+                ++i;
+            }
+            convmultmax_base[base] = convmax;
+            assert(i > 0);
+            convwidth_base[base] = i;
+        }
+
+        /* Find length of the string of numeric characters. */
+        scan = str;
+        while (_PyLong_DigitValue[Py_CHARMASK(*scan)] < base)
+            ++scan;
+
+        /* Create a long object that can contain the largest possible
+         * integer with this base and length.  Note that there's no
+         * need to initialize z->ob_digit -- no slot is read up before
+         * being stored into.
+         */
+        size_z = (Py_ssize_t)((scan - str) * log_base_BASE[base]) + 1;
+        /* Uncomment next line to test exceedingly rare copy code */
+        /* size_z = 1; */
+        assert(size_z > 0);
+        z = _PyLong_New(size_z);
+        if (z == NULL)
+            return NULL;
+        Py_SIZE(z) = 0;
+
+        /* `convwidth` consecutive input digits are treated as a single
+         * digit in base `convmultmax`.
+         */
+        convwidth = convwidth_base[base];
+        convmultmax = convmultmax_base[base];
+
+        /* Work ;-) */
+        while (str < scan) {
+            /* grab up to convwidth digits from the input string */
+            c = (digit)_PyLong_DigitValue[Py_CHARMASK(*str++)];
+            for (i = 1; i < convwidth && str != scan; ++i, ++str) {
+                c = (twodigits)(c *  base +
+                                (int)_PyLong_DigitValue[Py_CHARMASK(*str)]);
+                assert(c < PyLong_BASE);
+            }
+
+            convmult = convmultmax;
+            /* Calculate the shift only if we couldn't get
+             * convwidth digits.
+             */
+            if (i != convwidth) {
+                convmult = base;
+                for ( ; i > 1; --i)
+                    convmult *= base;
+            }
+
+            /* Multiply z by convmult, and add c. */
+            pz = z->ob_digit;
+            pzstop = pz + Py_SIZE(z);
+            for (; pz < pzstop; ++pz) {
+                c += (twodigits)*pz * convmult;
+                *pz = (digit)(c & PyLong_MASK);
+                c >>= PyLong_SHIFT;
+            }
+            /* carry off the current end? */
+            if (c) {
+                assert(c < PyLong_BASE);
+                if (Py_SIZE(z) < size_z) {
+                    *pz = (digit)c;
+                    ++Py_SIZE(z);
+                }
+                else {
+                    PyLongObject *tmp;
+                    /* Extremely rare.  Get more space. */
+                    assert(Py_SIZE(z) == size_z);
+                    tmp = _PyLong_New(size_z + 1);
+                    if (tmp == NULL) {
+                        Py_DECREF(z);
+                        return NULL;
+                    }
+                    memcpy(tmp->ob_digit,
+                           z->ob_digit,
+                           sizeof(digit) * size_z);
+                    Py_DECREF(z);
+                    z = tmp;
+                    z->ob_digit[size_z] = (digit)c;
+                    ++size_z;
+                }
+            }
+        }
+    }
+    if (z == NULL)
+        return NULL;
+    if (error_if_nonzero) {
+        /* reset the base to 0, else the exception message
+           doesn't make too much sense */
+        base = 0;
+        if (Py_SIZE(z) != 0)
+            goto onError;
+        /* there might still be other problems, therefore base
+           remains zero here for the same reason */
+    }
+    if (str == start)
+        goto onError;
+    if (sign < 0)
+        Py_SIZE(z) = -(Py_SIZE(z));
+    while (*str && isspace(Py_CHARMASK(*str)))
+        str++;
+    if (*str != '\0')
+        goto onError;
+    if (pend)
+        *pend = str;
+    long_normalize(z);
+    return (PyObject *) maybe_small_long(z);
+
+  onError:
+    Py_XDECREF(z);
+    slen = strlen(orig_str) < 200 ? strlen(orig_str) : 200;
+    strobj = PyUnicode_FromStringAndSize(orig_str, slen);
+    if (strobj == NULL)
+        return NULL;
+    PyErr_Format(PyExc_ValueError,
+                 "invalid literal for int() with base %d: %R",
+                 base, strobj);
+    Py_DECREF(strobj);
+    return NULL;
+}
+
+PyObject *
+PyLong_FromUnicode(Py_UNICODE *u, Py_ssize_t length, int base)
+{
+    PyObject *v, *unicode = PyUnicode_FromUnicode(u, length);
+    if (unicode == NULL)
+        return NULL;
+    v = PyLong_FromUnicodeObject(unicode, base);
+    Py_DECREF(unicode);
+    return v;
+}
+
+PyObject *
+PyLong_FromUnicodeObject(PyObject *u, int base)
+{
+    PyObject *result;
+    PyObject *asciidig;
+    char *buffer, *end;
+    Py_ssize_t buflen;
+
+    asciidig = _PyUnicode_TransformDecimalAndSpaceToASCII(u);
+    if (asciidig == NULL)
+        return NULL;
+    buffer = PyUnicode_AsUTF8AndSize(asciidig, &buflen);
+    if (buffer == NULL) {
+        Py_DECREF(asciidig);
+        return NULL;
+    }
+    result = PyLong_FromString(buffer, &end, base);
+    if (result != NULL && end != buffer + buflen) {
+        PyErr_SetString(PyExc_ValueError,
+                        "null byte in argument for int()");
+        Py_DECREF(result);
+        result = NULL;
+    }
+    Py_DECREF(asciidig);
+    return result;
+}
+
+/* forward */
+static PyLongObject *x_divrem
+    (PyLongObject *, PyLongObject *, PyLongObject **);
+static PyObject *long_long(PyObject *v);
+
+/* Long division with remainder, top-level routine */
+
+static int
+long_divrem(PyLongObject *a, PyLongObject *b,
+            PyLongObject **pdiv, PyLongObject **prem)
+{
+    Py_ssize_t size_a = ABS(Py_SIZE(a)), size_b = ABS(Py_SIZE(b));
+    PyLongObject *z;
+
+    if (size_b == 0) {
+        PyErr_SetString(PyExc_ZeroDivisionError,
+                        "integer division or modulo by zero");
+        return -1;
+    }
+    if (size_a < size_b ||
+        (size_a == size_b &&
+         a->ob_digit[size_a-1] < b->ob_digit[size_b-1])) {
+        /* |a| < |b|. */
+        *pdiv = (PyLongObject*)PyLong_FromLong(0);
+        if (*pdiv == NULL)
+            return -1;
+        Py_INCREF(a);
+        *prem = (PyLongObject *) a;
+        return 0;
+    }
+    if (size_b == 1) {
+        digit rem = 0;
+        z = divrem1(a, b->ob_digit[0], &rem);
+        if (z == NULL)
+            return -1;
+        *prem = (PyLongObject *) PyLong_FromLong((long)rem);
+        if (*prem == NULL) {
+            Py_DECREF(z);
+            return -1;
+        }
+    }
+    else {
+        z = x_divrem(a, b, prem);
+        if (z == NULL)
+            return -1;
+    }
+    /* Set the signs.
+       The quotient z has the sign of a*b;
+       the remainder r has the sign of a,
+       so a = b*z + r. */
+    if ((Py_SIZE(a) < 0) != (Py_SIZE(b) < 0))
+        NEGATE(z);
+    if (Py_SIZE(a) < 0 && Py_SIZE(*prem) != 0)
+        NEGATE(*prem);
+    *pdiv = maybe_small_long(z);
+    return 0;
+}
+
+/* Unsigned long division with remainder -- the algorithm.  The arguments v1
+   and w1 should satisfy 2 <= ABS(Py_SIZE(w1)) <= ABS(Py_SIZE(v1)). */
+
+static PyLongObject *
+x_divrem(PyLongObject *v1, PyLongObject *w1, PyLongObject **prem)
+{
+    PyLongObject *v, *w, *a;
+    Py_ssize_t i, k, size_v, size_w;
+    int d;
+    digit wm1, wm2, carry, q, r, vtop, *v0, *vk, *w0, *ak;
+    twodigits vv;
+    sdigit zhi;
+    stwodigits z;
+
+    /* We follow Knuth [The Art of Computer Programming, Vol. 2 (3rd
+       edn.), section 4.3.1, Algorithm D], except that we don't explicitly
+       handle the special case when the initial estimate q for a quotient
+       digit is >= PyLong_BASE: the max value for q is PyLong_BASE+1, and
+       that won't overflow a digit. */
+
+    /* allocate space; w will also be used to hold the final remainder */
+    size_v = ABS(Py_SIZE(v1));
+    size_w = ABS(Py_SIZE(w1));
+    assert(size_v >= size_w && size_w >= 2); /* Assert checks by div() */
+    v = _PyLong_New(size_v+1);
+    if (v == NULL) {
+        *prem = NULL;
+        return NULL;
+    }
+    w = _PyLong_New(size_w);
+    if (w == NULL) {
+        Py_DECREF(v);
+        *prem = NULL;
+        return NULL;
+    }
+
+    /* normalize: shift w1 left so that its top digit is >= PyLong_BASE/2.
+       shift v1 left by the same amount.  Results go into w and v. */
+    d = PyLong_SHIFT - bits_in_digit(w1->ob_digit[size_w-1]);
+    carry = v_lshift(w->ob_digit, w1->ob_digit, size_w, d);
+    assert(carry == 0);
+    carry = v_lshift(v->ob_digit, v1->ob_digit, size_v, d);
+    if (carry != 0 || v->ob_digit[size_v-1] >= w->ob_digit[size_w-1]) {
+        v->ob_digit[size_v] = carry;
+        size_v++;
+    }
+
+    /* Now v->ob_digit[size_v-1] < w->ob_digit[size_w-1], so quotient has
+       at most (and usually exactly) k = size_v - size_w digits. */
+    k = size_v - size_w;
+    assert(k >= 0);
+    a = _PyLong_New(k);
+    if (a == NULL) {
+        Py_DECREF(w);
+        Py_DECREF(v);
+        *prem = NULL;
+        return NULL;
+    }
+    v0 = v->ob_digit;
+    w0 = w->ob_digit;
+    wm1 = w0[size_w-1];
+    wm2 = w0[size_w-2];
+    for (vk = v0+k, ak = a->ob_digit + k; vk-- > v0;) {
+        /* inner loop: divide vk[0:size_w+1] by w0[0:size_w], giving
+           single-digit quotient q, remainder in vk[0:size_w]. */
+
+        SIGCHECK({
+                Py_DECREF(a);
+                Py_DECREF(w);
+                Py_DECREF(v);
+                *prem = NULL;
+                return NULL;
+            });
+
+        /* estimate quotient digit q; may overestimate by 1 (rare) */
+        vtop = vk[size_w];
+        assert(vtop <= wm1);
+        vv = ((twodigits)vtop << PyLong_SHIFT) | vk[size_w-1];
+        q = (digit)(vv / wm1);
+        r = (digit)(vv - (twodigits)wm1 * q); /* r = vv % wm1 */
+        while ((twodigits)wm2 * q > (((twodigits)r << PyLong_SHIFT)
+                                     | vk[size_w-2])) {
+            --q;
+            r += wm1;
+            if (r >= PyLong_BASE)
+                break;
+        }
+        assert(q <= PyLong_BASE);
+
+        /* subtract q*w0[0:size_w] from vk[0:size_w+1] */
+        zhi = 0;
+        for (i = 0; i < size_w; ++i) {
+            /* invariants: -PyLong_BASE <= -q <= zhi <= 0;
+               -PyLong_BASE * q <= z < PyLong_BASE */
+            z = (sdigit)vk[i] + zhi -
+                (stwodigits)q * (stwodigits)w0[i];
+            vk[i] = (digit)z & PyLong_MASK;
+            zhi = (sdigit)Py_ARITHMETIC_RIGHT_SHIFT(stwodigits,
+                                                    z, PyLong_SHIFT);
+        }
+
+        /* add w back if q was too large (this branch taken rarely) */
+        assert((sdigit)vtop + zhi == -1 || (sdigit)vtop + zhi == 0);
+        if ((sdigit)vtop + zhi < 0) {
+            carry = 0;
+            for (i = 0; i < size_w; ++i) {
+                carry += vk[i] + w0[i];
+                vk[i] = carry & PyLong_MASK;
+                carry >>= PyLong_SHIFT;
+            }
+            --q;
+        }
+
+        /* store quotient digit */
+        assert(q < PyLong_BASE);
+        *--ak = q;
+    }
+
+    /* unshift remainder; we reuse w to store the result */
+    carry = v_rshift(w0, v0, size_w, d);
+    assert(carry==0);
+    Py_DECREF(v);
+
+    *prem = long_normalize(w);
+    return long_normalize(a);
+}
+
+/* For a nonzero PyLong a, express a in the form x * 2**e, with 0.5 <=
+   abs(x) < 1.0 and e >= 0; return x and put e in *e.  Here x is
+   rounded to DBL_MANT_DIG significant bits using round-half-to-even.
+   If a == 0, return 0.0 and set *e = 0.  If the resulting exponent
+   e is larger than PY_SSIZE_T_MAX, raise OverflowError and return
+   -1.0. */
+
+/* attempt to define 2.0**DBL_MANT_DIG as a compile-time constant */
+#if DBL_MANT_DIG == 53
+#define EXP2_DBL_MANT_DIG 9007199254740992.0
+#else
+#define EXP2_DBL_MANT_DIG (ldexp(1.0, DBL_MANT_DIG))
+#endif
+
+double
+_PyLong_Frexp(PyLongObject *a, Py_ssize_t *e)
+{
+    Py_ssize_t a_size, a_bits, shift_digits, shift_bits, x_size;
+    /* See below for why x_digits is always large enough. */
+    digit rem, x_digits[2 + (DBL_MANT_DIG + 1) / PyLong_SHIFT];
+    double dx;
+    /* Correction term for round-half-to-even rounding.  For a digit x,
+       "x + half_even_correction[x & 7]" gives x rounded to the nearest
+       multiple of 4, rounding ties to a multiple of 8. */
+    static const int half_even_correction[8] = {0, -1, -2, 1, 0, -1, 2, 1};
+
+    a_size = ABS(Py_SIZE(a));
+    if (a_size == 0) {
+        /* Special case for 0: significand 0.0, exponent 0. */
+        *e = 0;
+        return 0.0;
+    }
+    a_bits = bits_in_digit(a->ob_digit[a_size-1]);
+    /* The following is an overflow-free version of the check
+       "if ((a_size - 1) * PyLong_SHIFT + a_bits > PY_SSIZE_T_MAX) ..." */
+    if (a_size >= (PY_SSIZE_T_MAX - 1) / PyLong_SHIFT + 1 &&
+        (a_size > (PY_SSIZE_T_MAX - 1) / PyLong_SHIFT + 1 ||
+         a_bits > (PY_SSIZE_T_MAX - 1) % PyLong_SHIFT + 1))
+        goto overflow;
+    a_bits = (a_size - 1) * PyLong_SHIFT + a_bits;
+
+    /* Shift the first DBL_MANT_DIG + 2 bits of a into x_digits[0:x_size]
+       (shifting left if a_bits <= DBL_MANT_DIG + 2).
+
+       Number of digits needed for result: write // for floor division.
+       Then if shifting left, we end up using
+
+         1 + a_size + (DBL_MANT_DIG + 2 - a_bits) // PyLong_SHIFT
+
+       digits.  If shifting right, we use
+
+         a_size - (a_bits - DBL_MANT_DIG - 2) // PyLong_SHIFT
+
+       digits.  Using a_size = 1 + (a_bits - 1) // PyLong_SHIFT along with
+       the inequalities
+
+         m // PyLong_SHIFT + n // PyLong_SHIFT <= (m + n) // PyLong_SHIFT
+         m // PyLong_SHIFT - n // PyLong_SHIFT <=
+                                          1 + (m - n - 1) // PyLong_SHIFT,
+
+       valid for any integers m and n, we find that x_size satisfies
+
+         x_size <= 2 + (DBL_MANT_DIG + 1) // PyLong_SHIFT
+
+       in both cases.
+    */
+    if (a_bits <= DBL_MANT_DIG + 2) {
+        shift_digits = (DBL_MANT_DIG + 2 - a_bits) / PyLong_SHIFT;
+        shift_bits = (DBL_MANT_DIG + 2 - a_bits) % PyLong_SHIFT;
+        x_size = 0;
+        while (x_size < shift_digits)
+            x_digits[x_size++] = 0;
+        rem = v_lshift(x_digits + x_size, a->ob_digit, a_size,
+                       (int)shift_bits);
+        x_size += a_size;
+        x_digits[x_size++] = rem;
+    }
+    else {
+        shift_digits = (a_bits - DBL_MANT_DIG - 2) / PyLong_SHIFT;
+        shift_bits = (a_bits - DBL_MANT_DIG - 2) % PyLong_SHIFT;
+        rem = v_rshift(x_digits, a->ob_digit + shift_digits,
+                       a_size - shift_digits, (int)shift_bits);
+        x_size = a_size - shift_digits;
+        /* For correct rounding below, we need the least significant
+           bit of x to be 'sticky' for this shift: if any of the bits
+           shifted out was nonzero, we set the least significant bit
+           of x. */
+        if (rem)
+            x_digits[0] |= 1;
+        else
+            while (shift_digits > 0)
+                if (a->ob_digit[--shift_digits]) {
+                    x_digits[0] |= 1;
+                    break;
+                }
+    }
+    assert(1 <= x_size && x_size <= (Py_ssize_t)Py_ARRAY_LENGTH(x_digits));
+
+    /* Round, and convert to double. */
+    x_digits[0] += half_even_correction[x_digits[0] & 7];
+    dx = x_digits[--x_size];
+    while (x_size > 0)
+        dx = dx * PyLong_BASE + x_digits[--x_size];
+
+    /* Rescale;  make correction if result is 1.0. */
+    dx /= 4.0 * EXP2_DBL_MANT_DIG;
+    if (dx == 1.0) {
+        if (a_bits == PY_SSIZE_T_MAX)
+            goto overflow;
+        dx = 0.5;
+        a_bits += 1;
+    }
+
+    *e = a_bits;
+    return Py_SIZE(a) < 0 ? -dx : dx;
+
+  overflow:
+    /* exponent > PY_SSIZE_T_MAX */
+    PyErr_SetString(PyExc_OverflowError,
+                    "huge integer: number of bits overflows a Py_ssize_t");
+    *e = 0;
+    return -1.0;
+}
+
+/* Get a C double from a long int object.  Rounds to the nearest double,
+   using the round-half-to-even rule in the case of a tie. */
+
+double
+PyLong_AsDouble(PyObject *v)
+{
+    Py_ssize_t exponent;
+    double x;
+
+    if (v == NULL) {
+        PyErr_BadInternalCall();
+        return -1.0;
+    }
+    if (!PyLong_Check(v)) {
+        PyErr_SetString(PyExc_TypeError, "an integer is required");
+        return -1.0;
+    }
+    x = _PyLong_Frexp((PyLongObject *)v, &exponent);
+    if ((x == -1.0 && PyErr_Occurred()) || exponent > DBL_MAX_EXP) {
+        PyErr_SetString(PyExc_OverflowError,
+                        "long int too large to convert to float");
+        return -1.0;
+    }
+    return ldexp(x, (int)exponent);
+}
+
+/* Methods */
+
+static void
+long_dealloc(PyObject *v)
+{
+    Py_TYPE(v)->tp_free(v);
+}
+
+static int
+long_compare(PyLongObject *a, PyLongObject *b)
+{
+    Py_ssize_t sign;
+
+    if (Py_SIZE(a) != Py_SIZE(b)) {
+        sign = Py_SIZE(a) - Py_SIZE(b);
+    }
+    else {
+        Py_ssize_t i = ABS(Py_SIZE(a));
+        while (--i >= 0 && a->ob_digit[i] == b->ob_digit[i])
+            ;
+        if (i < 0)
+            sign = 0;
+        else {
+            sign = (sdigit)a->ob_digit[i] - (sdigit)b->ob_digit[i];
+            if (Py_SIZE(a) < 0)
+                sign = -sign;
+        }
+    }
+    return sign < 0 ? -1 : sign > 0 ? 1 : 0;
+}
+
+#define TEST_COND(cond) \
+    ((cond) ? Py_True : Py_False)
+
+static PyObject *
+long_richcompare(PyObject *self, PyObject *other, int op)
+{
+    int result;
+    PyObject *v;
+    CHECK_BINOP(self, other);
+    if (self == other)
+        result = 0;
+    else
+        result = long_compare((PyLongObject*)self, (PyLongObject*)other);
+    /* Convert the return value to a Boolean */
+    switch (op) {
+    case Py_EQ:
+        v = TEST_COND(result == 0);
+        break;
+    case Py_NE:
+        v = TEST_COND(result != 0);
+        break;
+    case Py_LE:
+        v = TEST_COND(result <= 0);
+        break;
+    case Py_GE:
+        v = TEST_COND(result >= 0);
+        break;
+    case Py_LT:
+        v = TEST_COND(result == -1);
+        break;
+    case Py_GT:
+        v = TEST_COND(result == 1);
+        break;
+    default:
+        PyErr_BadArgument();
+        return NULL;
+    }
+    Py_INCREF(v);
+    return v;
+}
+
+static Py_hash_t
+long_hash(PyLongObject *v)
+{
+    Py_uhash_t x;
+    Py_ssize_t i;
+    int sign;
+
+    i = Py_SIZE(v);
+    switch(i) {
+    case -1: return v->ob_digit[0]==1 ? -2 : -(sdigit)v->ob_digit[0];
+    case 0: return 0;
+    case 1: return v->ob_digit[0];
+    }
+    sign = 1;
+    x = 0;
+    if (i < 0) {
+        sign = -1;
+        i = -(i);
+    }
+    while (--i >= 0) {
+        /* Here x is a quantity in the range [0, _PyHASH_MODULUS); we
+           want to compute x * 2**PyLong_SHIFT + v->ob_digit[i] modulo
+           _PyHASH_MODULUS.
+
+           The computation of x * 2**PyLong_SHIFT % _PyHASH_MODULUS
+           amounts to a rotation of the bits of x.  To see this, write
+
+             x * 2**PyLong_SHIFT = y * 2**_PyHASH_BITS + z
+
+           where y = x >> (_PyHASH_BITS - PyLong_SHIFT) gives the top
+           PyLong_SHIFT bits of x (those that are shifted out of the
+           original _PyHASH_BITS bits, and z = (x << PyLong_SHIFT) &
+           _PyHASH_MODULUS gives the bottom _PyHASH_BITS - PyLong_SHIFT
+           bits of x, shifted up.  Then since 2**_PyHASH_BITS is
+           congruent to 1 modulo _PyHASH_MODULUS, y*2**_PyHASH_BITS is
+           congruent to y modulo _PyHASH_MODULUS.  So
+
+             x * 2**PyLong_SHIFT = y + z (mod _PyHASH_MODULUS).
+
+           The right-hand side is just the result of rotating the
+           _PyHASH_BITS bits of x left by PyLong_SHIFT places; since
+           not all _PyHASH_BITS bits of x are 1s, the same is true
+           after rotation, so 0 <= y+z < _PyHASH_MODULUS and y + z is
+           the reduction of x*2**PyLong_SHIFT modulo
+           _PyHASH_MODULUS. */
+        x = ((x << PyLong_SHIFT) & _PyHASH_MODULUS) |
+            (x >> (_PyHASH_BITS - PyLong_SHIFT));
+        x += v->ob_digit[i];
+        if (x >= _PyHASH_MODULUS)
+            x -= _PyHASH_MODULUS;
+    }
+    x = x * sign;
+    if (x == (Py_uhash_t)-1)
+        x = (Py_uhash_t)-2;
+    return (Py_hash_t)x;
+}
+
+
+/* Add the absolute values of two long integers. */
+
+static PyLongObject *
+x_add(PyLongObject *a, PyLongObject *b)
+{
+    Py_ssize_t size_a = ABS(Py_SIZE(a)), size_b = ABS(Py_SIZE(b));
+    PyLongObject *z;
+    Py_ssize_t i;
+    digit carry = 0;
+
+    /* Ensure a is the larger of the two: */
+    if (size_a < size_b) {
+        { PyLongObject *temp = a; a = b; b = temp; }
+        { Py_ssize_t size_temp = size_a;
+            size_a = size_b;
+            size_b = size_temp; }
+    }
+    z = _PyLong_New(size_a+1);
+    if (z == NULL)
+        return NULL;
+    for (i = 0; i < size_b; ++i) {
+        carry += a->ob_digit[i] + b->ob_digit[i];
+        z->ob_digit[i] = carry & PyLong_MASK;
+        carry >>= PyLong_SHIFT;
+    }
+    for (; i < size_a; ++i) {
+        carry += a->ob_digit[i];
+        z->ob_digit[i] = carry & PyLong_MASK;
+        carry >>= PyLong_SHIFT;
+    }
+    z->ob_digit[i] = carry;
+    return long_normalize(z);
+}
+
+/* Subtract the absolute values of two integers. */
+
+static PyLongObject *
+x_sub(PyLongObject *a, PyLongObject *b)
+{
+    Py_ssize_t size_a = ABS(Py_SIZE(a)), size_b = ABS(Py_SIZE(b));
+    PyLongObject *z;
+    Py_ssize_t i;
+    int sign = 1;
+    digit borrow = 0;
+
+    /* Ensure a is the larger of the two: */
+    if (size_a < size_b) {
+        sign = -1;
+        { PyLongObject *temp = a; a = b; b = temp; }
+        { Py_ssize_t size_temp = size_a;
+            size_a = size_b;
+            size_b = size_temp; }
+    }
+    else if (size_a == size_b) {
+        /* Find highest digit where a and b differ: */
+        i = size_a;
+        while (--i >= 0 && a->ob_digit[i] == b->ob_digit[i])
+            ;
+        if (i < 0)
+            return (PyLongObject *)PyLong_FromLong(0);
+        if (a->ob_digit[i] < b->ob_digit[i]) {
+            sign = -1;
+            { PyLongObject *temp = a; a = b; b = temp; }
+        }
+        size_a = size_b = i+1;
+    }
+    z = _PyLong_New(size_a);
+    if (z == NULL)
+        return NULL;
+    for (i = 0; i < size_b; ++i) {
+        /* The following assumes unsigned arithmetic
+           works module 2**N for some N>PyLong_SHIFT. */
+        borrow = a->ob_digit[i] - b->ob_digit[i] - borrow;
+        z->ob_digit[i] = borrow & PyLong_MASK;
+        borrow >>= PyLong_SHIFT;
+        borrow &= 1; /* Keep only one sign bit */
+    }
+    for (; i < size_a; ++i) {
+        borrow = a->ob_digit[i] - borrow;
+        z->ob_digit[i] = borrow & PyLong_MASK;
+        borrow >>= PyLong_SHIFT;
+        borrow &= 1; /* Keep only one sign bit */
+    }
+    assert(borrow == 0);
+    if (sign < 0)
+        NEGATE(z);
+    return long_normalize(z);
+}
+
+static PyObject *
+long_add(PyLongObject *a, PyLongObject *b)
+{
+    PyLongObject *z;
+
+    CHECK_BINOP(a, b);
+
+    if (ABS(Py_SIZE(a)) <= 1 && ABS(Py_SIZE(b)) <= 1) {
+        PyObject *result = PyLong_FromLong(MEDIUM_VALUE(a) +
+                                          MEDIUM_VALUE(b));
+        return result;
+    }
+    if (Py_SIZE(a) < 0) {
+        if (Py_SIZE(b) < 0) {
+            z = x_add(a, b);
+            if (z != NULL && Py_SIZE(z) != 0)
+                Py_SIZE(z) = -(Py_SIZE(z));
+        }
+        else
+            z = x_sub(b, a);
+    }
+    else {
+        if (Py_SIZE(b) < 0)
+            z = x_sub(a, b);
+        else
+            z = x_add(a, b);
+    }
+    return (PyObject *)z;
+}
+
+static PyObject *
+long_sub(PyLongObject *a, PyLongObject *b)
+{
+    PyLongObject *z;
+
+    CHECK_BINOP(a, b);
+
+    if (ABS(Py_SIZE(a)) <= 1 && ABS(Py_SIZE(b)) <= 1) {
+        PyObject* r;
+        r = PyLong_FromLong(MEDIUM_VALUE(a)-MEDIUM_VALUE(b));
+        return r;
+    }
+    if (Py_SIZE(a) < 0) {
+        if (Py_SIZE(b) < 0)
+            z = x_sub(a, b);
+        else
+            z = x_add(a, b);
+        if (z != NULL && Py_SIZE(z) != 0)
+            Py_SIZE(z) = -(Py_SIZE(z));
+    }
+    else {
+        if (Py_SIZE(b) < 0)
+            z = x_add(a, b);
+        else
+            z = x_sub(a, b);
+    }
+    return (PyObject *)z;
+}
+
+/* Grade school multiplication, ignoring the signs.
+ * Returns the absolute value of the product, or NULL if error.
+ */
+static PyLongObject *
+x_mul(PyLongObject *a, PyLongObject *b)
+{
+    PyLongObject *z;
+    Py_ssize_t size_a = ABS(Py_SIZE(a));
+    Py_ssize_t size_b = ABS(Py_SIZE(b));
+    Py_ssize_t i;
+
+    z = _PyLong_New(size_a + size_b);
+    if (z == NULL)
+        return NULL;
+
+    memset(z->ob_digit, 0, Py_SIZE(z) * sizeof(digit));
+    if (a == b) {
+        /* Efficient squaring per HAC, Algorithm 14.16:
+         * http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf
+         * Gives slightly less than a 2x speedup when a == b,
+         * via exploiting that each entry in the multiplication
+         * pyramid appears twice (except for the size_a squares).
+         */
+        for (i = 0; i < size_a; ++i) {
+            twodigits carry;
+            twodigits f = a->ob_digit[i];
+            digit *pz = z->ob_digit + (i << 1);
+            digit *pa = a->ob_digit + i + 1;
+            digit *paend = a->ob_digit + size_a;
+
+            SIGCHECK({
+                    Py_DECREF(z);
+                    return NULL;
+                });
+
+            carry = *pz + f * f;
+            *pz++ = (digit)(carry & PyLong_MASK);
+            carry >>= PyLong_SHIFT;
+            assert(carry <= PyLong_MASK);
+
+            /* Now f is added in twice in each column of the
+             * pyramid it appears.  Same as adding f<<1 once.
+             */
+            f <<= 1;
+            while (pa < paend) {
+                carry += *pz + *pa++ * f;
+                *pz++ = (digit)(carry & PyLong_MASK);
+                carry >>= PyLong_SHIFT;
+                assert(carry <= (PyLong_MASK << 1));
+            }
+            if (carry) {
+                carry += *pz;
+                *pz++ = (digit)(carry & PyLong_MASK);
+                carry >>= PyLong_SHIFT;
+            }
+            if (carry)
+                *pz += (digit)(carry & PyLong_MASK);
+            assert((carry >> PyLong_SHIFT) == 0);
+        }
+    }
+    else {      /* a is not the same as b -- gradeschool long mult */
+        for (i = 0; i < size_a; ++i) {
+            twodigits carry = 0;
+            twodigits f = a->ob_digit[i];
+            digit *pz = z->ob_digit + i;
+            digit *pb = b->ob_digit;
+            digit *pbend = b->ob_digit + size_b;
+
+            SIGCHECK({
+                    Py_DECREF(z);
+                    return NULL;
+                });
+
+            while (pb < pbend) {
+                carry += *pz + *pb++ * f;
+                *pz++ = (digit)(carry & PyLong_MASK);
+                carry >>= PyLong_SHIFT;
+                assert(carry <= PyLong_MASK);
+            }
+            if (carry)
+                *pz += (digit)(carry & PyLong_MASK);
+            assert((carry >> PyLong_SHIFT) == 0);
+        }
+    }
+    return long_normalize(z);
+}
+
+/* A helper for Karatsuba multiplication (k_mul).
+   Takes a long "n" and an integer "size" representing the place to
+   split, and sets low and high such that abs(n) == (high << size) + low,
+   viewing the shift as being by digits.  The sign bit is ignored, and
+   the return values are >= 0.
+   Returns 0 on success, -1 on failure.
+*/
+static int
+kmul_split(PyLongObject *n,
+           Py_ssize_t size,
+           PyLongObject **high,
+           PyLongObject **low)
+{
+    PyLongObject *hi, *lo;
+    Py_ssize_t size_lo, size_hi;
+    const Py_ssize_t size_n = ABS(Py_SIZE(n));
+
+    size_lo = MIN(size_n, size);
+    size_hi = size_n - size_lo;
+
+    if ((hi = _PyLong_New(size_hi)) == NULL)
+        return -1;
+    if ((lo = _PyLong_New(size_lo)) == NULL) {
+        Py_DECREF(hi);
+        return -1;
+    }
+
+    memcpy(lo->ob_digit, n->ob_digit, size_lo * sizeof(digit));
+    memcpy(hi->ob_digit, n->ob_digit + size_lo, size_hi * sizeof(digit));
+
+    *high = long_normalize(hi);
+    *low = long_normalize(lo);
+    return 0;
+}
+
+static PyLongObject *k_lopsided_mul(PyLongObject *a, PyLongObject *b);
+
+/* Karatsuba multiplication.  Ignores the input signs, and returns the
+ * absolute value of the product (or NULL if error).
+ * See Knuth Vol. 2 Chapter 4.3.3 (Pp. 294-295).
+ */
+static PyLongObject *
+k_mul(PyLongObject *a, PyLongObject *b)
+{
+    Py_ssize_t asize = ABS(Py_SIZE(a));
+    Py_ssize_t bsize = ABS(Py_SIZE(b));
+    PyLongObject *ah = NULL;
+    PyLongObject *al = NULL;
+    PyLongObject *bh = NULL;
+    PyLongObject *bl = NULL;
+    PyLongObject *ret = NULL;
+    PyLongObject *t1, *t2, *t3;
+    Py_ssize_t shift;           /* the number of digits we split off */
+    Py_ssize_t i;
+
+    /* (ah*X+al)(bh*X+bl) = ah*bh*X*X + (ah*bl + al*bh)*X + al*bl
+     * Let k = (ah+al)*(bh+bl) = ah*bl + al*bh  + ah*bh + al*bl
+     * Then the original product is
+     *     ah*bh*X*X + (k - ah*bh - al*bl)*X + al*bl
+     * By picking X to be a power of 2, "*X" is just shifting, and it's
+     * been reduced to 3 multiplies on numbers half the size.
+     */
+
+    /* We want to split based on the larger number; fiddle so that b
+     * is largest.
+     */
+    if (asize > bsize) {
+        t1 = a;
+        a = b;
+        b = t1;
+
+        i = asize;
+        asize = bsize;
+        bsize = i;
+    }
+
+    /* Use gradeschool math when either number is too small. */
+    i = a == b ? KARATSUBA_SQUARE_CUTOFF : KARATSUBA_CUTOFF;
+    if (asize <= i) {
+        if (asize == 0)
+            return (PyLongObject *)PyLong_FromLong(0);
+        else
+            return x_mul(a, b);
+    }
+
+    /* If a is small compared to b, splitting on b gives a degenerate
+     * case with ah==0, and Karatsuba may be (even much) less efficient
+     * than "grade school" then.  However, we can still win, by viewing
+     * b as a string of "big digits", each of width a->ob_size.  That
+     * leads to a sequence of balanced calls to k_mul.
+     */
+    if (2 * asize <= bsize)
+        return k_lopsided_mul(a, b);
+
+    /* Split a & b into hi & lo pieces. */
+    shift = bsize >> 1;
+    if (kmul_split(a, shift, &ah, &al) < 0) goto fail;
+    assert(Py_SIZE(ah) > 0);            /* the split isn't degenerate */
+
+    if (a == b) {
+        bh = ah;
+        bl = al;
+        Py_INCREF(bh);
+        Py_INCREF(bl);
+    }
+    else if (kmul_split(b, shift, &bh, &bl) < 0) goto fail;
+
+    /* The plan:
+     * 1. Allocate result space (asize + bsize digits:  that's always
+     *    enough).
+     * 2. Compute ah*bh, and copy into result at 2*shift.
+     * 3. Compute al*bl, and copy into result at 0.  Note that this
+     *    can't overlap with #2.
+     * 4. Subtract al*bl from the result, starting at shift.  This may
+     *    underflow (borrow out of the high digit), but we don't care:
+     *    we're effectively doing unsigned arithmetic mod
+     *    BASE**(sizea + sizeb), and so long as the *final* result fits,
+     *    borrows and carries out of the high digit can be ignored.
+     * 5. Subtract ah*bh from the result, starting at shift.
+     * 6. Compute (ah+al)*(bh+bl), and add it into the result starting
+     *    at shift.
+     */
+
+    /* 1. Allocate result space. */
+    ret = _PyLong_New(asize + bsize);
+    if (ret == NULL) goto fail;
+#ifdef Py_DEBUG
+    /* Fill with trash, to catch reference to uninitialized digits. */
+    memset(ret->ob_digit, 0xDF, Py_SIZE(ret) * sizeof(digit));
+#endif
+
+    /* 2. t1 <- ah*bh, and copy into high digits of result. */
+    if ((t1 = k_mul(ah, bh)) == NULL) goto fail;
+    assert(Py_SIZE(t1) >= 0);
+    assert(2*shift + Py_SIZE(t1) <= Py_SIZE(ret));
+    memcpy(ret->ob_digit + 2*shift, t1->ob_digit,
+           Py_SIZE(t1) * sizeof(digit));
+
+    /* Zero-out the digits higher than the ah*bh copy. */
+    i = Py_SIZE(ret) - 2*shift - Py_SIZE(t1);
+    if (i)
+        memset(ret->ob_digit + 2*shift + Py_SIZE(t1), 0,
+               i * sizeof(digit));
+
+    /* 3. t2 <- al*bl, and copy into the low digits. */
+    if ((t2 = k_mul(al, bl)) == NULL) {
+        Py_DECREF(t1);
+        goto fail;
+    }
+    assert(Py_SIZE(t2) >= 0);
+    assert(Py_SIZE(t2) <= 2*shift); /* no overlap with high digits */
+    memcpy(ret->ob_digit, t2->ob_digit, Py_SIZE(t2) * sizeof(digit));
+
+    /* Zero out remaining digits. */
+    i = 2*shift - Py_SIZE(t2);          /* number of uninitialized digits */
+    if (i)
+        memset(ret->ob_digit + Py_SIZE(t2), 0, i * sizeof(digit));
+
+    /* 4 & 5. Subtract ah*bh (t1) and al*bl (t2).  We do al*bl first
+     * because it's fresher in cache.
+     */
+    i = Py_SIZE(ret) - shift;  /* # digits after shift */
+    (void)v_isub(ret->ob_digit + shift, i, t2->ob_digit, Py_SIZE(t2));
+    Py_DECREF(t2);
+
+    (void)v_isub(ret->ob_digit + shift, i, t1->ob_digit, Py_SIZE(t1));
+    Py_DECREF(t1);
+
+    /* 6. t3 <- (ah+al)(bh+bl), and add into result. */
+    if ((t1 = x_add(ah, al)) == NULL) goto fail;
+    Py_DECREF(ah);
+    Py_DECREF(al);
+    ah = al = NULL;
+
+    if (a == b) {
+        t2 = t1;
+        Py_INCREF(t2);
+    }
+    else if ((t2 = x_add(bh, bl)) == NULL) {
+        Py_DECREF(t1);
+        goto fail;
+    }
+    Py_DECREF(bh);
+    Py_DECREF(bl);
+    bh = bl = NULL;
+
+    t3 = k_mul(t1, t2);
+    Py_DECREF(t1);
+    Py_DECREF(t2);
+    if (t3 == NULL) goto fail;
+    assert(Py_SIZE(t3) >= 0);
+
+    /* Add t3.  It's not obvious why we can't run out of room here.
+     * See the (*) comment after this function.
+     */
+    (void)v_iadd(ret->ob_digit + shift, i, t3->ob_digit, Py_SIZE(t3));
+    Py_DECREF(t3);
+
+    return long_normalize(ret);
+
+  fail:
+    Py_XDECREF(ret);
+    Py_XDECREF(ah);
+    Py_XDECREF(al);
+    Py_XDECREF(bh);
+    Py_XDECREF(bl);
+    return NULL;
+}
+
+/* (*) Why adding t3 can't "run out of room" above.
+
+Let f(x) mean the floor of x and c(x) mean the ceiling of x.  Some facts
+to start with:
+
+1. For any integer i, i = c(i/2) + f(i/2).  In particular,
+   bsize = c(bsize/2) + f(bsize/2).
+2. shift = f(bsize/2)
+3. asize <= bsize
+4. Since we call k_lopsided_mul if asize*2 <= bsize, asize*2 > bsize in this
+   routine, so asize > bsize/2 >= f(bsize/2) in this routine.
+
+We allocated asize + bsize result digits, and add t3 into them at an offset
+of shift.  This leaves asize+bsize-shift allocated digit positions for t3
+to fit into, = (by #1 and #2) asize + f(bsize/2) + c(bsize/2) - f(bsize/2) =
+asize + c(bsize/2) available digit positions.
+
+bh has c(bsize/2) digits, and bl at most f(size/2) digits.  So bh+hl has
+at most c(bsize/2) digits + 1 bit.
+
+If asize == bsize, ah has c(bsize/2) digits, else ah has at most f(bsize/2)
+digits, and al has at most f(bsize/2) digits in any case.  So ah+al has at
+most (asize == bsize ? c(bsize/2) : f(bsize/2)) digits + 1 bit.
+
+The product (ah+al)*(bh+bl) therefore has at most
+
+    c(bsize/2) + (asize == bsize ? c(bsize/2) : f(bsize/2)) digits + 2 bits
+
+and we have asize + c(bsize/2) available digit positions.  We need to show
+this is always enough.  An instance of c(bsize/2) cancels out in both, so
+the question reduces to whether asize digits is enough to hold
+(asize == bsize ? c(bsize/2) : f(bsize/2)) digits + 2 bits.  If asize < bsize,
+then we're asking whether asize digits >= f(bsize/2) digits + 2 bits.  By #4,
+asize is at least f(bsize/2)+1 digits, so this in turn reduces to whether 1
+digit is enough to hold 2 bits.  This is so since PyLong_SHIFT=15 >= 2.  If
+asize == bsize, then we're asking whether bsize digits is enough to hold
+c(bsize/2) digits + 2 bits, or equivalently (by #1) whether f(bsize/2) digits
+is enough to hold 2 bits.  This is so if bsize >= 2, which holds because
+bsize >= KARATSUBA_CUTOFF >= 2.
+
+Note that since there's always enough room for (ah+al)*(bh+bl), and that's
+clearly >= each of ah*bh and al*bl, there's always enough room to subtract
+ah*bh and al*bl too.
+*/
+
+/* b has at least twice the digits of a, and a is big enough that Karatsuba
+ * would pay off *if* the inputs had balanced sizes.  View b as a sequence
+ * of slices, each with a->ob_size digits, and multiply the slices by a,
+ * one at a time.  This gives k_mul balanced inputs to work with, and is
+ * also cache-friendly (we compute one double-width slice of the result
+ * at a time, then move on, never backtracking except for the helpful
+ * single-width slice overlap between successive partial sums).
+ */
+static PyLongObject *
+k_lopsided_mul(PyLongObject *a, PyLongObject *b)
+{
+    const Py_ssize_t asize = ABS(Py_SIZE(a));
+    Py_ssize_t bsize = ABS(Py_SIZE(b));
+    Py_ssize_t nbdone;          /* # of b digits already multiplied */
+    PyLongObject *ret;
+    PyLongObject *bslice = NULL;
+
+    assert(asize > KARATSUBA_CUTOFF);
+    assert(2 * asize <= bsize);
+
+    /* Allocate result space, and zero it out. */
+    ret = _PyLong_New(asize + bsize);
+    if (ret == NULL)
+        return NULL;
+    memset(ret->ob_digit, 0, Py_SIZE(ret) * sizeof(digit));
+
+    /* Successive slices of b are copied into bslice. */
+    bslice = _PyLong_New(asize);
+    if (bslice == NULL)
+        goto fail;
+
+    nbdone = 0;
+    while (bsize > 0) {
+        PyLongObject *product;
+        const Py_ssize_t nbtouse = MIN(bsize, asize);
+
+        /* Multiply the next slice of b by a. */
+        memcpy(bslice->ob_digit, b->ob_digit + nbdone,
+               nbtouse * sizeof(digit));
+        Py_SIZE(bslice) = nbtouse;
+        product = k_mul(a, bslice);
+        if (product == NULL)
+            goto fail;
+
+        /* Add into result. */
+        (void)v_iadd(ret->ob_digit + nbdone, Py_SIZE(ret) - nbdone,
+                     product->ob_digit, Py_SIZE(product));
+        Py_DECREF(product);
+
+        bsize -= nbtouse;
+        nbdone += nbtouse;
+    }
+
+    Py_DECREF(bslice);
+    return long_normalize(ret);
+
+  fail:
+    Py_DECREF(ret);
+    Py_XDECREF(bslice);
+    return NULL;
+}
+
+static PyObject *
+long_mul(PyLongObject *a, PyLongObject *b)
+{
+    PyLongObject *z;
+
+    CHECK_BINOP(a, b);
+
+    /* fast path for single-digit multiplication */
+    if (ABS(Py_SIZE(a)) <= 1 && ABS(Py_SIZE(b)) <= 1) {
+        stwodigits v = (stwodigits)(MEDIUM_VALUE(a)) * MEDIUM_VALUE(b);
+#ifdef HAVE_LONG_LONG
+        return PyLong_FromLongLong((PY_LONG_LONG)v);
+#else
+        /* if we don't have long long then we're almost certainly
+           using 15-bit digits, so v will fit in a long.  In the
+           unlikely event that we're using 30-bit digits on a platform
+           without long long, a large v will just cause us to fall
+           through to the general multiplication code below. */
+        if (v >= LONG_MIN && v <= LONG_MAX)
+            return PyLong_FromLong((long)v);
+#endif
+    }
+
+    z = k_mul(a, b);
+    /* Negate if exactly one of the inputs is negative. */
+    if (((Py_SIZE(a) ^ Py_SIZE(b)) < 0) && z)
+        NEGATE(z);
+    return (PyObject *)z;
+}
+
+/* The / and % operators are now defined in terms of divmod().
+   The expression a mod b has the value a - b*floor(a/b).
+   The long_divrem function gives the remainder after division of
+   |a| by |b|, with the sign of a.  This is also expressed
+   as a - b*trunc(a/b), if trunc truncates towards zero.
+   Some examples:
+     a           b      a rem b         a mod b
+     13          10      3               3
+    -13          10     -3               7
+     13         -10      3              -7
+    -13         -10     -3              -3
+   So, to get from rem to mod, we have to add b if a and b
+   have different signs.  We then subtract one from the 'div'
+   part of the outcome to keep the invariant intact. */
+
+/* Compute
+ *     *pdiv, *pmod = divmod(v, w)
+ * NULL can be passed for pdiv or pmod, in which case that part of
+ * the result is simply thrown away.  The caller owns a reference to
+ * each of these it requests (does not pass NULL for).
+ */
+static int
+l_divmod(PyLongObject *v, PyLongObject *w,
+         PyLongObject **pdiv, PyLongObject **pmod)
+{
+    PyLongObject *div, *mod;
+
+    if (long_divrem(v, w, &div, &mod) < 0)
+        return -1;
+    if ((Py_SIZE(mod) < 0 && Py_SIZE(w) > 0) ||
+        (Py_SIZE(mod) > 0 && Py_SIZE(w) < 0)) {
+        PyLongObject *temp;
+        PyLongObject *one;
+        temp = (PyLongObject *) long_add(mod, w);
+        Py_DECREF(mod);
+        mod = temp;
+        if (mod == NULL) {
+            Py_DECREF(div);
+            return -1;
+        }
+        one = (PyLongObject *) PyLong_FromLong(1L);
+        if (one == NULL ||
+            (temp = (PyLongObject *) long_sub(div, one)) == NULL) {
+            Py_DECREF(mod);
+            Py_DECREF(div);
+            Py_XDECREF(one);
+            return -1;
+        }
+        Py_DECREF(one);
+        Py_DECREF(div);
+        div = temp;
+    }
+    if (pdiv != NULL)
+        *pdiv = div;
+    else
+        Py_DECREF(div);
+
+    if (pmod != NULL)
+        *pmod = mod;
+    else
+        Py_DECREF(mod);
+
+    return 0;
+}
+
+static PyObject *
+long_div(PyObject *a, PyObject *b)
+{
+    PyLongObject *div;
+
+    CHECK_BINOP(a, b);
+    if (l_divmod((PyLongObject*)a, (PyLongObject*)b, &div, NULL) < 0)
+        div = NULL;
+    return (PyObject *)div;
+}
+
+/* PyLong/PyLong -> float, with correctly rounded result. */
+
+#define MANT_DIG_DIGITS (DBL_MANT_DIG / PyLong_SHIFT)
+#define MANT_DIG_BITS (DBL_MANT_DIG % PyLong_SHIFT)
+
+static PyObject *
+long_true_divide(PyObject *v, PyObject *w)
+{
+    PyLongObject *a, *b, *x;
+    Py_ssize_t a_size, b_size, shift, extra_bits, diff, x_size, x_bits;
+    digit mask, low;
+    int inexact, negate, a_is_small, b_is_small;
+    double dx, result;
+
+    CHECK_BINOP(v, w);
+    a = (PyLongObject *)v;
+    b = (PyLongObject *)w;
+
+    /*
+       Method in a nutshell:
+
+         0. reduce to case a, b > 0; filter out obvious underflow/overflow
+         1. choose a suitable integer 'shift'
+         2. use integer arithmetic to compute x = floor(2**-shift*a/b)
+         3. adjust x for correct rounding
+         4. convert x to a double dx with the same value
+         5. return ldexp(dx, shift).
+
+       In more detail:
+
+       0. For any a, a/0 raises ZeroDivisionError; for nonzero b, 0/b
+       returns either 0.0 or -0.0, depending on the sign of b.  For a and
+       b both nonzero, ignore signs of a and b, and add the sign back in
+       at the end.  Now write a_bits and b_bits for the bit lengths of a
+       and b respectively (that is, a_bits = 1 + floor(log_2(a)); likewise
+       for b).  Then
+
+          2**(a_bits - b_bits - 1) < a/b < 2**(a_bits - b_bits + 1).
+
+       So if a_bits - b_bits > DBL_MAX_EXP then a/b > 2**DBL_MAX_EXP and
+       so overflows.  Similarly, if a_bits - b_bits < DBL_MIN_EXP -
+       DBL_MANT_DIG - 1 then a/b underflows to 0.  With these cases out of
+       the way, we can assume that
+
+          DBL_MIN_EXP - DBL_MANT_DIG - 1 <= a_bits - b_bits <= DBL_MAX_EXP.
+
+       1. The integer 'shift' is chosen so that x has the right number of
+       bits for a double, plus two or three extra bits that will be used
+       in the rounding decisions.  Writing a_bits and b_bits for the
+       number of significant bits in a and b respectively, a
+       straightforward formula for shift is:
+
+          shift = a_bits - b_bits - DBL_MANT_DIG - 2
+
+       This is fine in the usual case, but if a/b is smaller than the
+       smallest normal float then it can lead to double rounding on an
+       IEEE 754 platform, giving incorrectly rounded results.  So we
+       adjust the formula slightly.  The actual formula used is:
+
+           shift = MAX(a_bits - b_bits, DBL_MIN_EXP) - DBL_MANT_DIG - 2
+
+       2. The quantity x is computed by first shifting a (left -shift bits
+       if shift <= 0, right shift bits if shift > 0) and then dividing by
+       b.  For both the shift and the division, we keep track of whether
+       the result is inexact, in a flag 'inexact'; this information is
+       needed at the rounding stage.
+
+       With the choice of shift above, together with our assumption that
+       a_bits - b_bits >= DBL_MIN_EXP - DBL_MANT_DIG - 1, it follows
+       that x >= 1.
+
+       3. Now x * 2**shift <= a/b < (x+1) * 2**shift.  We want to replace
+       this with an exactly representable float of the form
+
+          round(x/2**extra_bits) * 2**(extra_bits+shift).
+
+       For float representability, we need x/2**extra_bits <
+       2**DBL_MANT_DIG and extra_bits + shift >= DBL_MIN_EXP -
+       DBL_MANT_DIG.  This translates to the condition:
+
+          extra_bits >= MAX(x_bits, DBL_MIN_EXP - shift) - DBL_MANT_DIG
+
+       To round, we just modify the bottom digit of x in-place; this can
+       end up giving a digit with value > PyLONG_MASK, but that's not a
+       problem since digits can hold values up to 2*PyLONG_MASK+1.
+
+       With the original choices for shift above, extra_bits will always
+       be 2 or 3.  Then rounding under the round-half-to-even rule, we
+       round up iff the most significant of the extra bits is 1, and
+       either: (a) the computation of x in step 2 had an inexact result,
+       or (b) at least one other of the extra bits is 1, or (c) the least
+       significant bit of x (above those to be rounded) is 1.
+
+       4. Conversion to a double is straightforward; all floating-point
+       operations involved in the conversion are exact, so there's no
+       danger of rounding errors.
+
+       5. Use ldexp(x, shift) to compute x*2**shift, the final result.
+       The result will always be exactly representable as a double, except
+       in the case that it overflows.  To avoid dependence on the exact
+       behaviour of ldexp on overflow, we check for overflow before
+       applying ldexp.  The result of ldexp is adjusted for sign before
+       returning.
+    */
+
+    /* Reduce to case where a and b are both positive. */
+    a_size = ABS(Py_SIZE(a));
+    b_size = ABS(Py_SIZE(b));
+    negate = (Py_SIZE(a) < 0) ^ (Py_SIZE(b) < 0);
+    if (b_size == 0) {
+        PyErr_SetString(PyExc_ZeroDivisionError,
+                        "division by zero");
+        goto error;
+    }
+    if (a_size == 0)
+        goto underflow_or_zero;
+
+    /* Fast path for a and b small (exactly representable in a double).
+       Relies on floating-point division being correctly rounded; results
+       may be subject to double rounding on x86 machines that operate with
+       the x87 FPU set to 64-bit precision. */
+    a_is_small = a_size <= MANT_DIG_DIGITS ||
+        (a_size == MANT_DIG_DIGITS+1 &&
+         a->ob_digit[MANT_DIG_DIGITS] >> MANT_DIG_BITS == 0);
+    b_is_small = b_size <= MANT_DIG_DIGITS ||
+        (b_size == MANT_DIG_DIGITS+1 &&
+         b->ob_digit[MANT_DIG_DIGITS] >> MANT_DIG_BITS == 0);
+    if (a_is_small && b_is_small) {
+        double da, db;
+        da = a->ob_digit[--a_size];
+        while (a_size > 0)
+            da = da * PyLong_BASE + a->ob_digit[--a_size];
+        db = b->ob_digit[--b_size];
+        while (b_size > 0)
+            db = db * PyLong_BASE + b->ob_digit[--b_size];
+        result = da / db;
+        goto success;
+    }
+
+    /* Catch obvious cases of underflow and overflow */
+    diff = a_size - b_size;
+    if (diff > PY_SSIZE_T_MAX/PyLong_SHIFT - 1)
+        /* Extreme overflow */
+        goto overflow;
+    else if (diff < 1 - PY_SSIZE_T_MAX/PyLong_SHIFT)
+        /* Extreme underflow */
+        goto underflow_or_zero;
+    /* Next line is now safe from overflowing a Py_ssize_t */
+    diff = diff * PyLong_SHIFT + bits_in_digit(a->ob_digit[a_size - 1]) -
+        bits_in_digit(b->ob_digit[b_size - 1]);
+    /* Now diff = a_bits - b_bits. */
+    if (diff > DBL_MAX_EXP)
+        goto overflow;
+    else if (diff < DBL_MIN_EXP - DBL_MANT_DIG - 1)
+        goto underflow_or_zero;
+
+    /* Choose value for shift; see comments for step 1 above. */
+    shift = MAX(diff, DBL_MIN_EXP) - DBL_MANT_DIG - 2;
+
+    inexact = 0;
+
+    /* x = abs(a * 2**-shift) */
+    if (shift <= 0) {
+        Py_ssize_t i, shift_digits = -shift / PyLong_SHIFT;
+        digit rem;
+        /* x = a << -shift */
+        if (a_size >= PY_SSIZE_T_MAX - 1 - shift_digits) {
+            /* In practice, it's probably impossible to end up
+               here.  Both a and b would have to be enormous,
+               using close to SIZE_T_MAX bytes of memory each. */
+            PyErr_SetString(PyExc_OverflowError,
+                            "intermediate overflow during division");
+            goto error;
+        }
+        x = _PyLong_New(a_size + shift_digits + 1);
+        if (x == NULL)
+            goto error;
+        for (i = 0; i < shift_digits; i++)
+            x->ob_digit[i] = 0;
+        rem = v_lshift(x->ob_digit + shift_digits, a->ob_digit,
+                       a_size, -shift % PyLong_SHIFT);
+        x->ob_digit[a_size + shift_digits] = rem;
+    }
+    else {
+        Py_ssize_t shift_digits = shift / PyLong_SHIFT;
+        digit rem;
+        /* x = a >> shift */
+        assert(a_size >= shift_digits);
+        x = _PyLong_New(a_size - shift_digits);
+        if (x == NULL)
+            goto error;
+        rem = v_rshift(x->ob_digit, a->ob_digit + shift_digits,
+                       a_size - shift_digits, shift % PyLong_SHIFT);
+        /* set inexact if any of the bits shifted out is nonzero */
+        if (rem)
+            inexact = 1;
+        while (!inexact && shift_digits > 0)
+            if (a->ob_digit[--shift_digits])
+                inexact = 1;
+    }
+    long_normalize(x);
+    x_size = Py_SIZE(x);
+
+    /* x //= b. If the remainder is nonzero, set inexact.  We own the only
+       reference to x, so it's safe to modify it in-place. */
+    if (b_size == 1) {
+        digit rem = inplace_divrem1(x->ob_digit, x->ob_digit, x_size,
+                              b->ob_digit[0]);
+        long_normalize(x);
+        if (rem)
+            inexact = 1;
+    }
+    else {
+        PyLongObject *div, *rem;
+        div = x_divrem(x, b, &rem);
+        Py_DECREF(x);
+        x = div;
+        if (x == NULL)
+            goto error;
+        if (Py_SIZE(rem))
+            inexact = 1;
+        Py_DECREF(rem);
+    }
+    x_size = ABS(Py_SIZE(x));
+    assert(x_size > 0); /* result of division is never zero */
+    x_bits = (x_size-1)*PyLong_SHIFT+bits_in_digit(x->ob_digit[x_size-1]);
+
+    /* The number of extra bits that have to be rounded away. */
+    extra_bits = MAX(x_bits, DBL_MIN_EXP - shift) - DBL_MANT_DIG;
+    assert(extra_bits == 2 || extra_bits == 3);
+
+    /* Round by directly modifying the low digit of x. */
+    mask = (digit)1 << (extra_bits - 1);
+    low = x->ob_digit[0] | inexact;
+    if (low & mask && low & (3*mask-1))
+        low += mask;
+    x->ob_digit[0] = low & ~(mask-1U);
+
+    /* Convert x to a double dx; the conversion is exact. */
+    dx = x->ob_digit[--x_size];
+    while (x_size > 0)
+        dx = dx * PyLong_BASE + x->ob_digit[--x_size];
+    Py_DECREF(x);
+
+    /* Check whether ldexp result will overflow a double. */
+    if (shift + x_bits >= DBL_MAX_EXP &&
+        (shift + x_bits > DBL_MAX_EXP || dx == ldexp(1.0, (int)x_bits)))
+        goto overflow;
+    result = ldexp(dx, (int)shift);
+
+  success:
+    return PyFloat_FromDouble(negate ? -result : result);
+
+  underflow_or_zero:
+    return PyFloat_FromDouble(negate ? -0.0 : 0.0);
+
+  overflow:
+    PyErr_SetString(PyExc_OverflowError,
+                    "integer division result too large for a float");
+  error:
+    return NULL;
+}
+
+static PyObject *
+long_mod(PyObject *a, PyObject *b)
+{
+    PyLongObject *mod;
+
+    CHECK_BINOP(a, b);
+
+    if (l_divmod((PyLongObject*)a, (PyLongObject*)b, NULL, &mod) < 0)
+        mod = NULL;
+    return (PyObject *)mod;
+}
+
+static PyObject *
+long_divmod(PyObject *a, PyObject *b)
+{
+    PyLongObject *div, *mod;
+    PyObject *z;
+
+    CHECK_BINOP(a, b);
+
+    if (l_divmod((PyLongObject*)a, (PyLongObject*)b, &div, &mod) < 0) {
+        return NULL;
+    }
+    z = PyTuple_New(2);
+    if (z != NULL) {
+        PyTuple_SetItem(z, 0, (PyObject *) div);
+        PyTuple_SetItem(z, 1, (PyObject *) mod);
+    }
+    else {
+        Py_DECREF(div);
+        Py_DECREF(mod);
+    }
+    return z;
+}
+
+/* pow(v, w, x) */
+static PyObject *
+long_pow(PyObject *v, PyObject *w, PyObject *x)
+{
+    PyLongObject *a, *b, *c; /* a,b,c = v,w,x */
+    int negativeOutput = 0;  /* if x<0 return negative output */
+
+    PyLongObject *z = NULL;  /* accumulated result */
+    Py_ssize_t i, j, k;             /* counters */
+    PyLongObject *temp = NULL;
+
+    /* 5-ary values.  If the exponent is large enough, table is
+     * precomputed so that table[i] == a**i % c for i in range(32).
+     */
+    PyLongObject *table[32] = {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
+                               0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0};
+
+    /* a, b, c = v, w, x */
+    CHECK_BINOP(v, w);
+    a = (PyLongObject*)v; Py_INCREF(a);
+    b = (PyLongObject*)w; Py_INCREF(b);
+    if (PyLong_Check(x)) {
+        c = (PyLongObject *)x;
+        Py_INCREF(x);
+    }
+    else if (x == Py_None)
+        c = NULL;
+    else {
+        Py_DECREF(a);
+        Py_DECREF(b);
+        Py_RETURN_NOTIMPLEMENTED;
+    }
+
+    if (Py_SIZE(b) < 0) {  /* if exponent is negative */
+        if (c) {
+            PyErr_SetString(PyExc_TypeError, "pow() 2nd argument "
+                            "cannot be negative when 3rd argument specified");
+            goto Error;
+        }
+        else {
+            /* else return a float.  This works because we know
+               that this calls float_pow() which converts its
+               arguments to double. */
+            Py_DECREF(a);
+            Py_DECREF(b);
+            return PyFloat_Type.tp_as_number->nb_power(v, w, x);
+        }
+    }
+
+    if (c) {
+        /* if modulus == 0:
+               raise ValueError() */
+        if (Py_SIZE(c) == 0) {
+            PyErr_SetString(PyExc_ValueError,
+                            "pow() 3rd argument cannot be 0");
+            goto Error;
+        }
+
+        /* if modulus < 0:
+               negativeOutput = True
+               modulus = -modulus */
+        if (Py_SIZE(c) < 0) {
+            negativeOutput = 1;
+            temp = (PyLongObject *)_PyLong_Copy(c);
+            if (temp == NULL)
+                goto Error;
+            Py_DECREF(c);
+            c = temp;
+            temp = NULL;
+            NEGATE(c);
+        }
+
+        /* if modulus == 1:
+               return 0 */
+        if ((Py_SIZE(c) == 1) && (c->ob_digit[0] == 1)) {
+            z = (PyLongObject *)PyLong_FromLong(0L);
+            goto Done;
+        }
+
+        /* if base < 0:
+               base = base % modulus
+           Having the base positive just makes things easier. */
+        if (Py_SIZE(a) < 0) {
+            if (l_divmod(a, c, NULL, &temp) < 0)
+                goto Error;
+            Py_DECREF(a);
+            a = temp;
+            temp = NULL;
+        }
+    }
+
+    /* At this point a, b, and c are guaranteed non-negative UNLESS
+       c is NULL, in which case a may be negative. */
+
+    z = (PyLongObject *)PyLong_FromLong(1L);
+    if (z == NULL)
+        goto Error;
+
+    /* Perform a modular reduction, X = X % c, but leave X alone if c
+     * is NULL.
+     */
+#define REDUCE(X)                                       \
+    do {                                                \
+        if (c != NULL) {                                \
+            if (l_divmod(X, c, NULL, &temp) < 0)        \
+                goto Error;                             \
+            Py_XDECREF(X);                              \
+            X = temp;                                   \
+            temp = NULL;                                \
+        }                                               \
+    } while(0)
+
+    /* Multiply two values, then reduce the result:
+       result = X*Y % c.  If c is NULL, skip the mod. */
+#define MULT(X, Y, result)                      \
+    do {                                        \
+        temp = (PyLongObject *)long_mul(X, Y);  \
+        if (temp == NULL)                       \
+            goto Error;                         \
+        Py_XDECREF(result);                     \
+        result = temp;                          \
+        temp = NULL;                            \
+        REDUCE(result);                         \
+    } while(0)
+
+    if (Py_SIZE(b) <= FIVEARY_CUTOFF) {
+        /* Left-to-right binary exponentiation (HAC Algorithm 14.79) */
+        /* http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf    */
+        for (i = Py_SIZE(b) - 1; i >= 0; --i) {
+            digit bi = b->ob_digit[i];
+
+            for (j = (digit)1 << (PyLong_SHIFT-1); j != 0; j >>= 1) {
+                MULT(z, z, z);
+                if (bi & j)
+                    MULT(z, a, z);
+            }
+        }
+    }
+    else {
+        /* Left-to-right 5-ary exponentiation (HAC Algorithm 14.82) */
+        Py_INCREF(z);           /* still holds 1L */
+        table[0] = z;
+        for (i = 1; i < 32; ++i)
+            MULT(table[i-1], a, table[i]);
+
+        for (i = Py_SIZE(b) - 1; i >= 0; --i) {
+            const digit bi = b->ob_digit[i];
+
+            for (j = PyLong_SHIFT - 5; j >= 0; j -= 5) {
+                const int index = (bi >> j) & 0x1f;
+                for (k = 0; k < 5; ++k)
+                    MULT(z, z, z);
+                if (index)
+                    MULT(z, table[index], z);
+            }
+        }
+    }
+
+    if (negativeOutput && (Py_SIZE(z) != 0)) {
+        temp = (PyLongObject *)long_sub(z, c);
+        if (temp == NULL)
+            goto Error;
+        Py_DECREF(z);
+        z = temp;
+        temp = NULL;
+    }
+    goto Done;
+
+  Error:
+    if (z != NULL) {
+        Py_DECREF(z);
+        z = NULL;
+    }
+    /* fall through */
+  Done:
+    if (Py_SIZE(b) > FIVEARY_CUTOFF) {
+        for (i = 0; i < 32; ++i)
+            Py_XDECREF(table[i]);
+    }
+    Py_DECREF(a);
+    Py_DECREF(b);
+    Py_XDECREF(c);
+    Py_XDECREF(temp);
+    return (PyObject *)z;
+}
+
+static PyObject *
+long_invert(PyLongObject *v)
+{
+    /* Implement ~x as -(x+1) */
+    PyLongObject *x;
+    PyLongObject *w;
+    if (ABS(Py_SIZE(v)) <=1)
+        return PyLong_FromLong(-(MEDIUM_VALUE(v)+1));
+    w = (PyLongObject *)PyLong_FromLong(1L);
+    if (w == NULL)
+        return NULL;
+    x = (PyLongObject *) long_add(v, w);
+    Py_DECREF(w);
+    if (x == NULL)
+        return NULL;
+    Py_SIZE(x) = -(Py_SIZE(x));
+    return (PyObject *)maybe_small_long(x);
+}
+
+static PyObject *
+long_neg(PyLongObject *v)
+{
+    PyLongObject *z;
+    if (ABS(Py_SIZE(v)) <= 1)
+        return PyLong_FromLong(-MEDIUM_VALUE(v));
+    z = (PyLongObject *)_PyLong_Copy(v);
+    if (z != NULL)
+        Py_SIZE(z) = -(Py_SIZE(v));
+    return (PyObject *)z;
+}
+
+static PyObject *
+long_abs(PyLongObject *v)
+{
+    if (Py_SIZE(v) < 0)
+        return long_neg(v);
+    else
+        return long_long((PyObject *)v);
+}
+
+static int
+long_bool(PyLongObject *v)
+{
+    return Py_SIZE(v) != 0;
+}
+
+static PyObject *
+long_rshift(PyLongObject *a, PyLongObject *b)
+{
+    PyLongObject *z = NULL;
+    Py_ssize_t shiftby, newsize, wordshift, loshift, hishift, i, j;
+    digit lomask, himask;
+
+    CHECK_BINOP(a, b);
+
+    if (Py_SIZE(a) < 0) {
+        /* Right shifting negative numbers is harder */
+        PyLongObject *a1, *a2;
+        a1 = (PyLongObject *) long_invert(a);
+        if (a1 == NULL)
+            goto rshift_error;
+        a2 = (PyLongObject *) long_rshift(a1, b);
+        Py_DECREF(a1);
+        if (a2 == NULL)
+            goto rshift_error;
+        z = (PyLongObject *) long_invert(a2);
+        Py_DECREF(a2);
+    }
+    else {
+        shiftby = PyLong_AsSsize_t((PyObject *)b);
+        if (shiftby == -1L && PyErr_Occurred())
+            goto rshift_error;
+        if (shiftby < 0) {
+            PyErr_SetString(PyExc_ValueError,
+                            "negative shift count");
+            goto rshift_error;
+        }
+        wordshift = shiftby / PyLong_SHIFT;
+        newsize = ABS(Py_SIZE(a)) - wordshift;
+        if (newsize <= 0)
+            return PyLong_FromLong(0);
+        loshift = shiftby % PyLong_SHIFT;
+        hishift = PyLong_SHIFT - loshift;
+        lomask = ((digit)1 << hishift) - 1;
+        himask = PyLong_MASK ^ lomask;
+        z = _PyLong_New(newsize);
+        if (z == NULL)
+            goto rshift_error;
+        if (Py_SIZE(a) < 0)
+            Py_SIZE(z) = -(Py_SIZE(z));
+        for (i = 0, j = wordshift; i < newsize; i++, j++) {
+            z->ob_digit[i] = (a->ob_digit[j] >> loshift) & lomask;
+            if (i+1 < newsize)
+                z->ob_digit[i] |= (a->ob_digit[j+1] << hishift) & himask;
+        }
+        z = long_normalize(z);
+    }
+  rshift_error:
+    return (PyObject *) maybe_small_long(z);
+
+}
+
+static PyObject *
+long_lshift(PyObject *v, PyObject *w)
+{
+    /* This version due to Tim Peters */
+    PyLongObject *a = (PyLongObject*)v;
+    PyLongObject *b = (PyLongObject*)w;
+    PyLongObject *z = NULL;
+    Py_ssize_t shiftby, oldsize, newsize, wordshift, remshift, i, j;
+    twodigits accum;
+
+    CHECK_BINOP(a, b);
+
+    shiftby = PyLong_AsSsize_t((PyObject *)b);
+    if (shiftby == -1L && PyErr_Occurred())
+        goto lshift_error;
+    if (shiftby < 0) {
+        PyErr_SetString(PyExc_ValueError, "negative shift count");
+        goto lshift_error;
+    }
+    /* wordshift, remshift = divmod(shiftby, PyLong_SHIFT) */
+    wordshift = shiftby / PyLong_SHIFT;
+    remshift  = shiftby - wordshift * PyLong_SHIFT;
+
+    oldsize = ABS(Py_SIZE(a));
+    newsize = oldsize + wordshift;
+    if (remshift)
+        ++newsize;
+    z = _PyLong_New(newsize);
+    if (z == NULL)
+        goto lshift_error;
+    if (Py_SIZE(a) < 0)
+        NEGATE(z);
+    for (i = 0; i < wordshift; i++)
+        z->ob_digit[i] = 0;
+    accum = 0;
+    for (i = wordshift, j = 0; j < oldsize; i++, j++) {
+        accum |= (twodigits)a->ob_digit[j] << remshift;
+        z->ob_digit[i] = (digit)(accum & PyLong_MASK);
+        accum >>= PyLong_SHIFT;
+    }
+    if (remshift)
+        z->ob_digit[newsize-1] = (digit)accum;
+    else
+        assert(!accum);
+    z = long_normalize(z);
+  lshift_error:
+    return (PyObject *) maybe_small_long(z);
+}
+
+/* Compute two's complement of digit vector a[0:m], writing result to
+   z[0:m].  The digit vector a need not be normalized, but should not
+   be entirely zero.  a and z may point to the same digit vector. */
+
+static void
+v_complement(digit *z, digit *a, Py_ssize_t m)
+{
+    Py_ssize_t i;
+    digit carry = 1;
+    for (i = 0; i < m; ++i) {
+        carry += a[i] ^ PyLong_MASK;
+        z[i] = carry & PyLong_MASK;
+        carry >>= PyLong_SHIFT;
+    }
+    assert(carry == 0);
+}
+
+/* Bitwise and/xor/or operations */
+
+static PyObject *
+long_bitwise(PyLongObject *a,
+             int op,  /* '&', '|', '^' */
+             PyLongObject *b)
+{
+    int nega, negb, negz;
+    Py_ssize_t size_a, size_b, size_z, i;
+    PyLongObject *z;
+
+    /* Bitwise operations for negative numbers operate as though
+       on a two's complement representation.  So convert arguments
+       from sign-magnitude to two's complement, and convert the
+       result back to sign-magnitude at the end. */
+
+    /* If a is negative, replace it by its two's complement. */
+    size_a = ABS(Py_SIZE(a));
+    nega = Py_SIZE(a) < 0;
+    if (nega) {
+        z = _PyLong_New(size_a);
+        if (z == NULL)
+            return NULL;
+        v_complement(z->ob_digit, a->ob_digit, size_a);
+        a = z;
+    }
+    else
+        /* Keep reference count consistent. */
+        Py_INCREF(a);
+
+    /* Same for b. */
+    size_b = ABS(Py_SIZE(b));
+    negb = Py_SIZE(b) < 0;
+    if (negb) {
+        z = _PyLong_New(size_b);
+        if (z == NULL) {
+            Py_DECREF(a);
+            return NULL;
+        }
+        v_complement(z->ob_digit, b->ob_digit, size_b);
+        b = z;
+    }
+    else
+        Py_INCREF(b);
+
+    /* Swap a and b if necessary to ensure size_a >= size_b. */
+    if (size_a < size_b) {
+        z = a; a = b; b = z;
+        size_z = size_a; size_a = size_b; size_b = size_z;
+        negz = nega; nega = negb; negb = negz;
+    }
+
+    /* JRH: The original logic here was to allocate the result value (z)
+       as the longer of the two operands.  However, there are some cases
+       where the result is guaranteed to be shorter than that: AND of two
+       positives, OR of two negatives: use the shorter number.  AND with
+       mixed signs: use the positive number.  OR with mixed signs: use the
+       negative number.
+    */
+    switch (op) {
+    case '^':
+        negz = nega ^ negb;
+        size_z = size_a;
+        break;
+    case '&':
+        negz = nega & negb;
+        size_z = negb ? size_a : size_b;
+        break;
+    case '|':
+        negz = nega | negb;
+        size_z = negb ? size_b : size_a;
+        break;
+    default:
+        PyErr_BadArgument();
+        return NULL;
+    }
+
+    /* We allow an extra digit if z is negative, to make sure that
+       the final two's complement of z doesn't overflow. */
+    z = _PyLong_New(size_z + negz);
+    if (z == NULL) {
+        Py_DECREF(a);
+        Py_DECREF(b);
+        return NULL;
+    }
+
+    /* Compute digits for overlap of a and b. */
+    switch(op) {
+    case '&':
+        for (i = 0; i < size_b; ++i)
+            z->ob_digit[i] = a->ob_digit[i] & b->ob_digit[i];
+        break;
+    case '|':
+        for (i = 0; i < size_b; ++i)
+            z->ob_digit[i] = a->ob_digit[i] | b->ob_digit[i];
+        break;
+    case '^':
+        for (i = 0; i < size_b; ++i)
+            z->ob_digit[i] = a->ob_digit[i] ^ b->ob_digit[i];
+        break;
+    default:
+        PyErr_BadArgument();
+        return NULL;
+    }
+
+    /* Copy any remaining digits of a, inverting if necessary. */
+    if (op == '^' && negb)
+        for (; i < size_z; ++i)
+            z->ob_digit[i] = a->ob_digit[i] ^ PyLong_MASK;
+    else if (i < size_z)
+        memcpy(&z->ob_digit[i], &a->ob_digit[i],
+               (size_z-i)*sizeof(digit));
+
+    /* Complement result if negative. */
+    if (negz) {
+        Py_SIZE(z) = -(Py_SIZE(z));
+        z->ob_digit[size_z] = PyLong_MASK;
+        v_complement(z->ob_digit, z->ob_digit, size_z+1);
+    }
+
+    Py_DECREF(a);
+    Py_DECREF(b);
+    return (PyObject *)maybe_small_long(long_normalize(z));
+}
+
+static PyObject *
+long_and(PyObject *a, PyObject *b)
+{
+    PyObject *c;
+    CHECK_BINOP(a, b);
+    c = long_bitwise((PyLongObject*)a, '&', (PyLongObject*)b);
+    return c;
+}
+
+static PyObject *
+long_xor(PyObject *a, PyObject *b)
+{
+    PyObject *c;
+    CHECK_BINOP(a, b);
+    c = long_bitwise((PyLongObject*)a, '^', (PyLongObject*)b);
+    return c;
+}
+
+static PyObject *
+long_or(PyObject *a, PyObject *b)
+{
+    PyObject *c;
+    CHECK_BINOP(a, b);
+    c = long_bitwise((PyLongObject*)a, '|', (PyLongObject*)b);
+    return c;
+}
+
+static PyObject *
+long_long(PyObject *v)
+{
+    if (PyLong_CheckExact(v))
+        Py_INCREF(v);
+    else
+        v = _PyLong_Copy((PyLongObject *)v);
+    return v;
+}
+
+static PyObject *
+long_float(PyObject *v)
+{
+    double result;
+    result = PyLong_AsDouble(v);
+    if (result == -1.0 && PyErr_Occurred())
+        return NULL;
+    return PyFloat_FromDouble(result);
+}
+
+static PyObject *
+long_subtype_new(PyTypeObject *type, PyObject *args, PyObject *kwds);
+
+static PyObject *
+long_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
+{
+    PyObject *obase = NULL, *x = NULL;
+    long base;
+    int overflow;
+    static char *kwlist[] = {"x", "base", 0};
+
+    if (type != &PyLong_Type)
+        return long_subtype_new(type, args, kwds); /* Wimp out */
+    if (!PyArg_ParseTupleAndKeywords(args, kwds, "|OO:int", kwlist,
+                                     &x, &obase))
+        return NULL;
+    if (x == NULL)
+        return PyLong_FromLong(0L);
+    if (obase == NULL)
+        return PyNumber_Long(x);
+
+    base = PyLong_AsLongAndOverflow(obase, &overflow);
+    if (base == -1 && PyErr_Occurred())
+        return NULL;
+    if (overflow || (base != 0 && base < 2) || base > 36) {
+        PyErr_SetString(PyExc_ValueError,
+                        "int() arg 2 must be >= 2 and <= 36");
+        return NULL;
+    }
+
+    if (PyUnicode_Check(x))
+        return PyLong_FromUnicodeObject(x, (int)base);
+    else if (PyByteArray_Check(x) || PyBytes_Check(x)) {
+        /* Since PyLong_FromString doesn't have a length parameter,
+         * check here for possible NULs in the string. */
+        char *string;
+        Py_ssize_t size = Py_SIZE(x);
+        if (PyByteArray_Check(x))
+            string = PyByteArray_AS_STRING(x);
+        else
+            string = PyBytes_AS_STRING(x);
+        if (strlen(string) != (size_t)size) {
+            /* We only see this if there's a null byte in x,
+               x is a bytes or buffer, *and* a base is given. */
+            PyErr_Format(PyExc_ValueError,
+                         "invalid literal for int() with base %d: %R",
+                         (int)base, x);
+            return NULL;
+        }
+        return PyLong_FromString(string, NULL, (int)base);
+    }
+    else {
+        PyErr_SetString(PyExc_TypeError,
+                        "int() can't convert non-string with explicit base");
+        return NULL;
+    }
+}
+
+/* Wimpy, slow approach to tp_new calls for subtypes of long:
+   first create a regular long from whatever arguments we got,
+   then allocate a subtype instance and initialize it from
+   the regular long.  The regular long is then thrown away.
+*/
+static PyObject *
+long_subtype_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
+{
+    PyLongObject *tmp, *newobj;
+    Py_ssize_t i, n;
+
+    assert(PyType_IsSubtype(type, &PyLong_Type));
+    tmp = (PyLongObject *)long_new(&PyLong_Type, args, kwds);
+    if (tmp == NULL)
+        return NULL;
+    assert(PyLong_CheckExact(tmp));
+    n = Py_SIZE(tmp);
+    if (n < 0)
+        n = -n;
+    newobj = (PyLongObject *)type->tp_alloc(type, n);
+    if (newobj == NULL) {
+        Py_DECREF(tmp);
+        return NULL;
+    }
+    assert(PyLong_Check(newobj));
+    Py_SIZE(newobj) = Py_SIZE(tmp);
+    for (i = 0; i < n; i++)
+        newobj->ob_digit[i] = tmp->ob_digit[i];
+    Py_DECREF(tmp);
+    return (PyObject *)newobj;
+}
+
+static PyObject *
+long_getnewargs(PyLongObject *v)
+{
+    return Py_BuildValue("(N)", _PyLong_Copy(v));
+}
+
+static PyObject *
+long_get0(PyLongObject *v, void *context) {
+    return PyLong_FromLong(0L);
+}
+
+static PyObject *
+long_get1(PyLongObject *v, void *context) {
+    return PyLong_FromLong(1L);
+}
+
+static PyObject *
+long__format__(PyObject *self, PyObject *args)
+{
+    PyObject *format_spec;
+
+    if (!PyArg_ParseTuple(args, "U:__format__", &format_spec))
+        return NULL;
+    return _PyLong_FormatAdvanced(self, format_spec, 0,
+                                  PyUnicode_GET_LENGTH(format_spec));
+}
+
+/* Return a pair (q, r) such that a = b * q + r, and
+   abs(r) <= abs(b)/2, with equality possible only if q is even.
+   In other words, q == a / b, rounded to the nearest integer using
+   round-half-to-even. */
+
+PyObject *
+_PyLong_DivmodNear(PyObject *a, PyObject *b)
+{
+    PyLongObject *quo = NULL, *rem = NULL;
+    PyObject *one = NULL, *twice_rem, *result, *temp;
+    int cmp, quo_is_odd, quo_is_neg;
+
+    /* Equivalent Python code:
+
+       def divmod_near(a, b):
+           q, r = divmod(a, b)
+           # round up if either r / b > 0.5, or r / b == 0.5 and q is odd.
+           # The expression r / b > 0.5 is equivalent to 2 * r > b if b is
+           # positive, 2 * r < b if b negative.
+           greater_than_half = 2*r > b if b > 0 else 2*r < b
+           exactly_half = 2*r == b
+           if greater_than_half or exactly_half and q % 2 == 1:
+               q += 1
+               r -= b
+           return q, r
+
+    */
+    if (!PyLong_Check(a) || !PyLong_Check(b)) {
+        PyErr_SetString(PyExc_TypeError,
+                        "non-integer arguments in division");
+        return NULL;
+    }
+
+    /* Do a and b have different signs?  If so, quotient is negative. */
+    quo_is_neg = (Py_SIZE(a) < 0) != (Py_SIZE(b) < 0);
+
+    one = PyLong_FromLong(1L);
+    if (one == NULL)
+        return NULL;
+
+    if (long_divrem((PyLongObject*)a, (PyLongObject*)b, &quo, &rem) < 0)
+        goto error;
+
+    /* compare twice the remainder with the divisor, to see
+       if we need to adjust the quotient and remainder */
+    twice_rem = long_lshift((PyObject *)rem, one);
+    if (twice_rem == NULL)
+        goto error;
+    if (quo_is_neg) {
+        temp = long_neg((PyLongObject*)twice_rem);
+        Py_DECREF(twice_rem);
+        twice_rem = temp;
+        if (twice_rem == NULL)
+            goto error;
+    }
+    cmp = long_compare((PyLongObject *)twice_rem, (PyLongObject *)b);
+    Py_DECREF(twice_rem);
+
+    quo_is_odd = Py_SIZE(quo) != 0 && ((quo->ob_digit[0] & 1) != 0);
+    if ((Py_SIZE(b) < 0 ? cmp < 0 : cmp > 0) || (cmp == 0 && quo_is_odd)) {
+        /* fix up quotient */
+        if (quo_is_neg)
+            temp = long_sub(quo, (PyLongObject *)one);
+        else
+            temp = long_add(quo, (PyLongObject *)one);
+        Py_DECREF(quo);
+        quo = (PyLongObject *)temp;
+        if (quo == NULL)
+            goto error;
+        /* and remainder */
+        if (quo_is_neg)
+            temp = long_add(rem, (PyLongObject *)b);
+        else
+            temp = long_sub(rem, (PyLongObject *)b);
+        Py_DECREF(rem);
+        rem = (PyLongObject *)temp;
+        if (rem == NULL)
+            goto error;
+    }
+
+    result = PyTuple_New(2);
+    if (result == NULL)
+        goto error;
+
+    /* PyTuple_SET_ITEM steals references */
+    PyTuple_SET_ITEM(result, 0, (PyObject *)quo);
+    PyTuple_SET_ITEM(result, 1, (PyObject *)rem);
+    Py_DECREF(one);
+    return result;
+
+  error:
+    Py_XDECREF(quo);
+    Py_XDECREF(rem);
+    Py_XDECREF(one);
+    return NULL;
+}
+
+static PyObject *
+long_round(PyObject *self, PyObject *args)
+{
+    PyObject *o_ndigits=NULL, *temp, *result, *ndigits;
+
+    /* To round an integer m to the nearest 10**n (n positive), we make use of
+     * the divmod_near operation, defined by:
+     *
+     *   divmod_near(a, b) = (q, r)
+     *
+     * where q is the nearest integer to the quotient a / b (the
+     * nearest even integer in the case of a tie) and r == a - q * b.
+     * Hence q * b = a - r is the nearest multiple of b to a,
+     * preferring even multiples in the case of a tie.
+     *
+     * So the nearest multiple of 10**n to m is:
+     *
+     *   m - divmod_near(m, 10**n)[1].
+     */
+    if (!PyArg_ParseTuple(args, "|O", &o_ndigits))
+        return NULL;
+    if (o_ndigits == NULL)
+        return long_long(self);
+
+    ndigits = PyNumber_Index(o_ndigits);
+    if (ndigits == NULL)
+        return NULL;
+
+    /* if ndigits >= 0 then no rounding is necessary; return self unchanged */
+    if (Py_SIZE(ndigits) >= 0) {
+        Py_DECREF(ndigits);
+        return long_long(self);
+    }
+
+    /* result = self - divmod_near(self, 10 ** -ndigits)[1] */
+    temp = long_neg((PyLongObject*)ndigits);
+    Py_DECREF(ndigits);
+    ndigits = temp;
+    if (ndigits == NULL)
+        return NULL;
+
+    result = PyLong_FromLong(10L);
+    if (result == NULL) {
+        Py_DECREF(ndigits);
+        return NULL;
+    }
+
+    temp = long_pow(result, ndigits, Py_None);
+    Py_DECREF(ndigits);
+    Py_DECREF(result);
+    result = temp;
+    if (result == NULL)
+        return NULL;
+
+    temp = _PyLong_DivmodNear(self, result);
+    Py_DECREF(result);
+    result = temp;
+    if (result == NULL)
+        return NULL;
+
+    temp = long_sub((PyLongObject *)self,
+                    (PyLongObject *)PyTuple_GET_ITEM(result, 1));
+    Py_DECREF(result);
+    result = temp;
+
+    return result;
+}
+
+static PyObject *
+long_sizeof(PyLongObject *v)
+{
+    Py_ssize_t res;
+
+    res = offsetof(PyLongObject, ob_digit) + ABS(Py_SIZE(v))*sizeof(digit);
+    return PyLong_FromSsize_t(res);
+}
+
+static PyObject *
+long_bit_length(PyLongObject *v)
+{
+    PyLongObject *result, *x, *y;
+    Py_ssize_t ndigits, msd_bits = 0;
+    digit msd;
+
+    assert(v != NULL);
+    assert(PyLong_Check(v));
+
+    ndigits = ABS(Py_SIZE(v));
+    if (ndigits == 0)
+        return PyLong_FromLong(0);
+
+    msd = v->ob_digit[ndigits-1];
+    while (msd >= 32) {
+        msd_bits += 6;
+        msd >>= 6;
+    }
+    msd_bits += (long)(BitLengthTable[msd]);
+
+    if (ndigits <= PY_SSIZE_T_MAX/PyLong_SHIFT)
+        return PyLong_FromSsize_t((ndigits-1)*PyLong_SHIFT + msd_bits);
+
+    /* expression above may overflow; use Python integers instead */
+    result = (PyLongObject *)PyLong_FromSsize_t(ndigits - 1);
+    if (result == NULL)
+        return NULL;
+    x = (PyLongObject *)PyLong_FromLong(PyLong_SHIFT);
+    if (x == NULL)
+        goto error;
+    y = (PyLongObject *)long_mul(result, x);
+    Py_DECREF(x);
+    if (y == NULL)
+        goto error;
+    Py_DECREF(result);
+    result = y;
+
+    x = (PyLongObject *)PyLong_FromLong((long)msd_bits);
+    if (x == NULL)
+        goto error;
+    y = (PyLongObject *)long_add(result, x);
+    Py_DECREF(x);
+    if (y == NULL)
+        goto error;
+    Py_DECREF(result);
+    result = y;
+
+    return (PyObject *)result;
+
+  error:
+    Py_DECREF(result);
+    return NULL;
+}
+
+PyDoc_STRVAR(long_bit_length_doc,
+"int.bit_length() -> int\n\
+\n\
+Number of bits necessary to represent self in binary.\n\
+>>> bin(37)\n\
+'0b100101'\n\
+>>> (37).bit_length()\n\
+6");
+
+#if 0
+static PyObject *
+long_is_finite(PyObject *v)
+{
+    Py_RETURN_TRUE;
+}
+#endif
+
+
+static PyObject *
+long_to_bytes(PyLongObject *v, PyObject *args, PyObject *kwds)
+{
+    PyObject *byteorder_str;
+    PyObject *is_signed_obj = NULL;
+    Py_ssize_t length;
+    int little_endian;
+    int is_signed;
+    PyObject *bytes;
+    static char *kwlist[] = {"length", "byteorder", "signed", NULL};
+
+    if (!PyArg_ParseTupleAndKeywords(args, kwds, "nU|O:to_bytes", kwlist,
+                                     &length, &byteorder_str,
+                                     &is_signed_obj))
+        return NULL;
+
+    if (args != NULL && Py_SIZE(args) > 2) {
+        PyErr_SetString(PyExc_TypeError,
+            "'signed' is a keyword-only argument");
+        return NULL;
+    }
+
+    if (!PyUnicode_CompareWithASCIIString(byteorder_str, "little"))
+        little_endian = 1;
+    else if (!PyUnicode_CompareWithASCIIString(byteorder_str, "big"))
+        little_endian = 0;
+    else {
+        PyErr_SetString(PyExc_ValueError,
+            "byteorder must be either 'little' or 'big'");
+        return NULL;
+    }
+
+    if (is_signed_obj != NULL) {
+        int cmp = PyObject_IsTrue(is_signed_obj);
+        if (cmp < 0)
+            return NULL;
+        is_signed = cmp ? 1 : 0;
+    }
+    else {
+        /* If the signed argument was omitted, use False as the
+           default. */
+        is_signed = 0;
+    }
+
+    if (length < 0) {
+        PyErr_SetString(PyExc_ValueError,
+                        "length argument must be non-negative");
+        return NULL;
+    }
+
+    bytes = PyBytes_FromStringAndSize(NULL, length);
+    if (bytes == NULL)
+        return NULL;
+
+    if (_PyLong_AsByteArray(v, (unsigned char *)PyBytes_AS_STRING(bytes),
+                            length, little_endian, is_signed) < 0) {
+        Py_DECREF(bytes);
+        return NULL;
+    }
+
+    return bytes;
+}
+
+PyDoc_STRVAR(long_to_bytes_doc,
+"int.to_bytes(length, byteorder, *, signed=False) -> bytes\n\
+\n\
+Return an array of bytes representing an integer.\n\
+\n\
+The integer is represented using length bytes.  An OverflowError is\n\
+raised if the integer is not representable with the given number of\n\
+bytes.\n\
+\n\
+The byteorder argument determines the byte order used to represent the\n\
+integer.  If byteorder is 'big', the most significant byte is at the\n\
+beginning of the byte array.  If byteorder is 'little', the most\n\
+significant byte is at the end of the byte array.  To request the native\n\
+byte order of the host system, use `sys.byteorder' as the byte order value.\n\
+\n\
+The signed keyword-only argument determines whether two's complement is\n\
+used to represent the integer.  If signed is False and a negative integer\n\
+is given, an OverflowError is raised.");
+
+static PyObject *
+long_from_bytes(PyTypeObject *type, PyObject *args, PyObject *kwds)
+{
+    PyObject *byteorder_str;
+    PyObject *is_signed_obj = NULL;
+    int little_endian;
+    int is_signed;
+    PyObject *obj;
+    PyObject *bytes;
+    PyObject *long_obj;
+    static char *kwlist[] = {"bytes", "byteorder", "signed", NULL};
+
+    if (!PyArg_ParseTupleAndKeywords(args, kwds, "OU|O:from_bytes", kwlist,
+                                     &obj, &byteorder_str,
+                                     &is_signed_obj))
+        return NULL;
+
+    if (args != NULL && Py_SIZE(args) > 2) {
+        PyErr_SetString(PyExc_TypeError,
+            "'signed' is a keyword-only argument");
+        return NULL;
+    }
+
+    if (!PyUnicode_CompareWithASCIIString(byteorder_str, "little"))
+        little_endian = 1;
+    else if (!PyUnicode_CompareWithASCIIString(byteorder_str, "big"))
+        little_endian = 0;
+    else {
+        PyErr_SetString(PyExc_ValueError,
+            "byteorder must be either 'little' or 'big'");
+        return NULL;
+    }
+
+    if (is_signed_obj != NULL) {
+        int cmp = PyObject_IsTrue(is_signed_obj);
+        if (cmp < 0)
+            return NULL;
+        is_signed = cmp ? 1 : 0;
+    }
+    else {
+        /* If the signed argument was omitted, use False as the
+           default. */
+        is_signed = 0;
+    }
+
+    bytes = PyObject_Bytes(obj);
+    if (bytes == NULL)
+        return NULL;
+
+    long_obj = _PyLong_FromByteArray(
+        (unsigned char *)PyBytes_AS_STRING(bytes), Py_SIZE(bytes),
+        little_endian, is_signed);
+    Py_DECREF(bytes);
+
+    /* If from_bytes() was used on subclass, allocate new subclass
+     * instance, initialize it with decoded long value and return it.
+     */
+    if (type != &PyLong_Type && PyType_IsSubtype(type, &PyLong_Type)) {
+        PyLongObject *newobj;
+        int i;
+        Py_ssize_t n = ABS(Py_SIZE(long_obj));
+
+        newobj = (PyLongObject *)type->tp_alloc(type, n);
+        if (newobj == NULL) {
+            Py_DECREF(long_obj);
+            return NULL;
+        }
+        assert(PyLong_Check(newobj));
+        Py_SIZE(newobj) = Py_SIZE(long_obj);
+        for (i = 0; i < n; i++) {
+            newobj->ob_digit[i] =
+                ((PyLongObject *)long_obj)->ob_digit[i];
+        }
+        Py_DECREF(long_obj);
+        return (PyObject *)newobj;
+    }
+
+    return long_obj;
+}
+
+PyDoc_STRVAR(long_from_bytes_doc,
+"int.from_bytes(bytes, byteorder, *, signed=False) -> int\n\
+\n\
+Return the integer represented by the given array of bytes.\n\
+\n\
+The bytes argument must either support the buffer protocol or be an\n\
+iterable object producing bytes.  Bytes and bytearray are examples of\n\
+built-in objects that support the buffer protocol.\n\
+\n\
+The byteorder argument determines the byte order used to represent the\n\
+integer.  If byteorder is 'big', the most significant byte is at the\n\
+beginning of the byte array.  If byteorder is 'little', the most\n\
+significant byte is at the end of the byte array.  To request the native\n\
+byte order of the host system, use `sys.byteorder' as the byte order value.\n\
+\n\
+The signed keyword-only argument indicates whether two's complement is\n\
+used to represent the integer.");
+
+static PyMethodDef long_methods[] = {
+    {"conjugate",       (PyCFunction)long_long, METH_NOARGS,
+     "Returns self, the complex conjugate of any int."},
+    {"bit_length",      (PyCFunction)long_bit_length, METH_NOARGS,
+     long_bit_length_doc},
+#if 0
+    {"is_finite",       (PyCFunction)long_is_finite,    METH_NOARGS,
+     "Returns always True."},
+#endif
+    {"to_bytes",        (PyCFunction)long_to_bytes,
+     METH_VARARGS|METH_KEYWORDS, long_to_bytes_doc},
+    {"from_bytes",      (PyCFunction)long_from_bytes,
+     METH_VARARGS|METH_KEYWORDS|METH_CLASS, long_from_bytes_doc},
+    {"__trunc__",       (PyCFunction)long_long, METH_NOARGS,
+     "Truncating an Integral returns itself."},
+    {"__floor__",       (PyCFunction)long_long, METH_NOARGS,
+     "Flooring an Integral returns itself."},
+    {"__ceil__",        (PyCFunction)long_long, METH_NOARGS,
+     "Ceiling of an Integral returns itself."},
+    {"__round__",       (PyCFunction)long_round, METH_VARARGS,
+     "Rounding an Integral returns itself.\n"
+     "Rounding with an ndigits argument also returns an integer."},
+    {"__getnewargs__",          (PyCFunction)long_getnewargs,   METH_NOARGS},
+    {"__format__", (PyCFunction)long__format__, METH_VARARGS},
+    {"__sizeof__",      (PyCFunction)long_sizeof, METH_NOARGS,
+     "Returns size in memory, in bytes"},
+    {NULL,              NULL}           /* sentinel */
+};
+
+static PyGetSetDef long_getset[] = {
+    {"real",
+     (getter)long_long, (setter)NULL,
+     "the real part of a complex number",
+     NULL},
+    {"imag",
+     (getter)long_get0, (setter)NULL,
+     "the imaginary part of a complex number",
+     NULL},
+    {"numerator",
+     (getter)long_long, (setter)NULL,
+     "the numerator of a rational number in lowest terms",
+     NULL},
+    {"denominator",
+     (getter)long_get1, (setter)NULL,
+     "the denominator of a rational number in lowest terms",
+     NULL},
+    {NULL}  /* Sentinel */
+};
+
+PyDoc_STRVAR(long_doc,
+"int(x[, base]) -> integer\n\
+\n\
+Convert a string or number to an integer, if possible.  A floating\n\
+point argument will be truncated towards zero (this does not include a\n\
+string representation of a floating point number!)  When converting a\n\
+string, use the optional base.  It is an error to supply a base when\n\
+converting a non-string.");
+
+static PyNumberMethods long_as_number = {
+    (binaryfunc)long_add,       /*nb_add*/
+    (binaryfunc)long_sub,       /*nb_subtract*/
+    (binaryfunc)long_mul,       /*nb_multiply*/
+    long_mod,                   /*nb_remainder*/
+    long_divmod,                /*nb_divmod*/
+    long_pow,                   /*nb_power*/
+    (unaryfunc)long_neg,        /*nb_negative*/
+    (unaryfunc)long_long,       /*tp_positive*/
+    (unaryfunc)long_abs,        /*tp_absolute*/
+    (inquiry)long_bool,         /*tp_bool*/
+    (unaryfunc)long_invert,     /*nb_invert*/
+    long_lshift,                /*nb_lshift*/
+    (binaryfunc)long_rshift,    /*nb_rshift*/
+    long_and,                   /*nb_and*/
+    long_xor,                   /*nb_xor*/
+    long_or,                    /*nb_or*/
+    long_long,                  /*nb_int*/
+    0,                          /*nb_reserved*/
+    long_float,                 /*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 */
+    long_div,                   /* nb_floor_divide */
+    long_true_divide,           /* nb_true_divide */
+    0,                          /* nb_inplace_floor_divide */
+    0,                          /* nb_inplace_true_divide */
+    long_long,                  /* nb_index */
+};
+
+PyTypeObject PyLong_Type = {
+    PyVarObject_HEAD_INIT(&PyType_Type, 0)
+    "int",                                      /* tp_name */
+    offsetof(PyLongObject, ob_digit),           /* tp_basicsize */
+    sizeof(digit),                              /* tp_itemsize */
+    long_dealloc,                               /* tp_dealloc */
+    0,                                          /* tp_print */
+    0,                                          /* tp_getattr */
+    0,                                          /* tp_setattr */
+    0,                                          /* tp_reserved */
+    long_to_decimal_string,                     /* tp_repr */
+    &long_as_number,                            /* tp_as_number */
+    0,                                          /* tp_as_sequence */
+    0,                                          /* tp_as_mapping */
+    (hashfunc)long_hash,                        /* tp_hash */
+    0,                                          /* tp_call */
+    long_to_decimal_string,                     /* tp_str */
+    PyObject_GenericGetAttr,                    /* tp_getattro */
+    0,                                          /* tp_setattro */
+    0,                                          /* tp_as_buffer */
+    Py_TPFLAGS_DEFAULT | Py_TPFLAGS_BASETYPE |
+        Py_TPFLAGS_LONG_SUBCLASS,               /* tp_flags */
+    long_doc,                                   /* tp_doc */
+    0,                                          /* tp_traverse */
+    0,                                          /* tp_clear */
+    long_richcompare,                           /* tp_richcompare */
+    0,                                          /* tp_weaklistoffset */
+    0,                                          /* tp_iter */
+    0,                                          /* tp_iternext */
+    long_methods,                               /* tp_methods */
+    0,                                          /* tp_members */
+    long_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 */
+    long_new,                                   /* tp_new */
+    PyObject_Del,                               /* tp_free */
+};
+
+static PyTypeObject Int_InfoType;
+
+PyDoc_STRVAR(int_info__doc__,
+"sys.int_info\n\
+\n\
+A struct sequence that holds information about Python's\n\
+internal representation of integers.  The attributes are read only.");
+
+static PyStructSequence_Field int_info_fields[] = {
+    {"bits_per_digit", "size of a digit in bits"},
+    {"sizeof_digit", "size in bytes of the C type used to represent a digit"},
+    {NULL, NULL}
+};
+
+static PyStructSequence_Desc int_info_desc = {
+    "sys.int_info",   /* name */
+    int_info__doc__,  /* doc */
+    int_info_fields,  /* fields */
+    2                 /* number of fields */
+};
+
+PyObject *
+PyLong_GetInfo(void)
+{
+    PyObject* int_info;
+    int field = 0;
+    int_info = PyStructSequence_New(&Int_InfoType);
+    if (int_info == NULL)
+        return NULL;
+    PyStructSequence_SET_ITEM(int_info, field++,
+                              PyLong_FromLong(PyLong_SHIFT));
+    PyStructSequence_SET_ITEM(int_info, field++,
+                              PyLong_FromLong(sizeof(digit)));
+    if (PyErr_Occurred()) {
+        Py_CLEAR(int_info);
+        return NULL;
+    }
+    return int_info;
+}
+
+int
+_PyLong_Init(void)
+{
+#if NSMALLNEGINTS + NSMALLPOSINTS > 0
+    int ival, size;
+    PyLongObject *v = small_ints;
+
+    for (ival = -NSMALLNEGINTS; ival <  NSMALLPOSINTS; ival++, v++) {
+        size = (ival < 0) ? -1 : ((ival == 0) ? 0 : 1);
+        if (Py_TYPE(v) == &PyLong_Type) {
+            /* The element is already initialized, most likely
+             * the Python interpreter was initialized before.
+             */
+            Py_ssize_t refcnt;
+            PyObject* op = (PyObject*)v;
+
+            refcnt = Py_REFCNT(op) < 0 ? 0 : Py_REFCNT(op);
+            _Py_NewReference(op);
+            /* _Py_NewReference sets the ref count to 1 but
+             * the ref count might be larger. Set the refcnt
+             * to the original refcnt + 1 */
+            Py_REFCNT(op) = refcnt + 1;
+            assert(Py_SIZE(op) == size);
+            assert(v->ob_digit[0] == abs(ival));
+        }
+        else {
+            PyObject_INIT(v, &PyLong_Type);
+        }
+        Py_SIZE(v) = size;
+        v->ob_digit[0] = abs(ival);
+    }
+#endif
+    /* initialize int_info */
+    if (Int_InfoType.tp_name == 0)
+        PyStructSequence_InitType(&Int_InfoType, &int_info_desc);
+
+    return 1;
+}
+
+void
+PyLong_Fini(void)
+{
+    /* Integers are currently statically allocated. Py_DECREF is not
+       needed, but Python must forget about the reference or multiple
+       reinitializations will fail. */
+#if NSMALLNEGINTS + NSMALLPOSINTS > 0
+    int i;
+    PyLongObject *v = small_ints;
+    for (i = 0; i < NSMALLNEGINTS + NSMALLPOSINTS; i++, v++) {
+        _Py_DEC_REFTOTAL;
+        _Py_ForgetReference((PyObject*)v);
+    }
+#endif
+}