Changeset 388 for python/vendor/current/Objects/longobject.c

Timestamp:

Mar 19, 2014, 11:11:30 AM (11 years ago)

Author:

dmik

Message:

python: Update vendor to 2.7.6.

File:

• python/vendor/current/Objects/longobject.c (modified) (87 diffs)

python/vendor/current/Objects/longobject.c

@@ -1 @@
-
-
 /* Long (arbitrary precision) integer object implementation */
 
@@ -7 +5 @@
 #include "Python.h"
 #include "longintrepr.h"
-
+#include "structseq.h"
+
+#include <float.h>
 #include <ctype.h>
+#include <stddef.h>
 
 /* For long multiplication, use the O(N**2) school algorithm unless
@@ -31 +32 @@
 #define MIN(x, y) ((x) > (y) ? (y) : (x))
 
-/* Forward */
-static PyLongObject *long_normalize(PyLongObject *);
-static PyLongObject *mul1(PyLongObject *, wdigit);
-static PyLongObject *muladd1(PyLongObject *, wdigit, wdigit);
-static PyLongObject *divrem1(PyLongObject *, digit, digit *);
-
-#define SIGCHECK(PyTryBlock) \
-        if (--_Py_Ticker < 0) { \
-                _Py_Ticker = _Py_CheckInterval; \
-                if (PyErr_CheckSignals()) PyTryBlock \
-        }
+#define SIGCHECK(PyTryBlock)                            \
+    do {                                                \
+        if (--_Py_Ticker < 0) {                         \
+            _Py_Ticker = _Py_CheckInterval;             \
+            if (PyErr_CheckSignals()) PyTryBlock        \
+                                          }             \
+    } while(0)
 
 /* Normalize (remove leading zeros from) a long int object.
@@ -50 +47 @@
 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;
+    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;
 }
 
@@ -63 +60 @@
    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)
 {
-        if (size > PY_SSIZE_T_MAX) {
-                PyErr_NoMemory();
-                return NULL;
-        }
-        /* coverity[ampersand_in_size] */
-        /* XXX(nnorwitz): This can overflow --
-           PyObject_NEW_VAR / _PyObject_VAR_SIZE need to detect overflow */
-        return PyObject_NEW_VAR(PyLongObject, &PyLong_Type, size);
+    if (size > (Py_ssize_t)MAX_LONG_DIGITS) {
+        PyErr_SetString(PyExc_OverflowError,
+                        "too many digits in integer");
+        return NULL;
+    }
+    /* coverity[ampersand_in_size] */
+    /* XXX(nnorwitz): PyObject_NEW_VAR / _PyObject_VAR_SIZE need to detect
+       overflow */
+    return PyObject_NEW_VAR(PyLongObject, &PyLong_Type, size);
 }
 
@@ -79 +80 @@
 _PyLong_Copy(PyLongObject *src)
 {
-        PyLongObject *result;
-        Py_ssize_t i;
-
-        assert(src != NULL);
-        i = src->ob_size;
-        if (i < 0)
-                i = -(i);
-        result = _PyLong_New(i);
-        if (result != NULL) {
-                result->ob_size = src->ob_size;
-                while (--i >= 0)
-                        result->ob_digit[i] = src->ob_digit[i];
-        }
-        return (PyObject *)result;
+    PyLongObject *result;
+    Py_ssize_t i;
+
+    assert(src != NULL);
+    i = src->ob_size;
+    if (i < 0)
+        i = -(i);
+    result = _PyLong_New(i);
+    if (result != NULL) {
+        result->ob_size = src->ob_size;
+        while (--i >= 0)
+            result->ob_digit[i] = src->ob_digit[i];
+    }
+    return (PyObject *)result;
 }
 
@@ -100 +101 @@
 PyLong_FromLong(long ival)
 {
-        PyLongObject *v;
-        unsigned long abs_ival;
-        unsigned long t;  /* unsigned so >> doesn't propagate sign bit */
-        int ndigits = 0;
-        int negative = 0;
-
-        if (ival < 0) {
-                /* if LONG_MIN == -LONG_MAX-1 (true on most platforms) then
-                   ANSI C says that the result of -ival is undefined when ival
-                   == LONG_MIN.  Hence the following workaround. */
-                abs_ival = (unsigned long)(-1-ival) + 1;
-                negative = 1;
-        }
-        else {
-                abs_ival = (unsigned 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;
-                v->ob_size = negative ? -ndigits : ndigits;
-                t = abs_ival;
-                while (t) {
-                        *p++ = (digit)(t & PyLong_MASK);
-                        t >>= PyLong_SHIFT;
-                }
-        }
-        return (PyObject *)v;
+    PyLongObject *v;
+    unsigned long abs_ival;
+    unsigned long t;  /* unsigned so >> doesn't propagate sign bit */
+    int ndigits = 0;
+    int negative = 0;
+
+    if (ival < 0) {
+        /* if LONG_MIN == -LONG_MAX-1 (true on most platforms) then
+           ANSI C says that the result of -ival is undefined when ival
+           == LONG_MIN.  Hence the following workaround. */
+        abs_ival = (unsigned long)(-1-ival) + 1;
+        negative = 1;
+    }
+    else {
+        abs_ival = (unsigned 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;
+        v->ob_size = negative ? -ndigits : ndigits;
+        t = abs_ival;
+        while (t) {
+            *p++ = (digit)(t & PyLong_MASK);
+            t >>= PyLong_SHIFT;
+        }
+    }
+    return (PyObject *)v;
 }
 
@@ -144 +145 @@
 PyLong_FromUnsignedLong(unsigned long ival)
 {
-        PyLongObject *v;
-        unsigned long t;
-        int ndigits = 0;
-
-        /* 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;
+    PyLongObject *v;
+    unsigned long t;
+    int ndigits = 0;
+
+    /* 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;
 }
 
@@ -171 +172 @@
 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; ) {
-                long bits = (long)frac;
-                v->ob_digit[i] = (digit) bits;
-                frac = frac - (double)bits;
-                frac = ldexp(frac, PyLong_SHIFT);
-        }
-        if (neg)
-                Py_SIZE(v) = -(Py_SIZE(v));
-        return (PyObject *)v;
+    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;
 }
 
@@ -217 +218 @@
  * 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)
+#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 Python long or Python int object.
+   On overflow, returns -1 and sets *overflow to 1 or -1 depending
+   on the sign of the result.  Otherwise *overflow is 0.
+
+   For other errors (e.g., type error), returns -1 and sets an error
+   condition.
+*/
+
+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(PyInt_Check(vv))
+        return PyInt_AsLong(vv);
+
+    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(PyInt_Check(vv)) {
+            res = PyInt_AsLong(vv);
+            goto exit;
+        }
+        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.
@@ -224 +327 @@
 
 long
-PyLong_AsLong(PyObject *vv)
-{
-        /* This version by Tim Peters */
-        register PyLongObject *v;
-        unsigned long x, prev;
-        Py_ssize_t i;
-        int sign;
-
-        if (vv == NULL || !PyLong_Check(vv)) {
-                if (vv != NULL && PyInt_Check(vv))
-                        return PyInt_AsLong(vv);
-                PyErr_BadInternalCall();
-                return -1;
-        }
-        v = (PyLongObject *)vv;
-        i = v->ob_size;
-        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 long requires extra care
-         * (see comment above).
-         */
-        if (x <= (unsigned long)LONG_MAX) {
-                return (long)x * sign;
-        }
-        else if (sign < 0 && x == PY_ABS_LONG_MIN) {
-                return LONG_MIN;
-        }
-        /* else overflow */
-
- overflow:
-        PyErr_SetString(PyExc_OverflowError,
-                        "long int too large to convert to int");
-        return -1;
+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 C int from a long int object or any object that has an __int__
+   method.  Return -1 and set an error if overflow occurs. */
+
+int
+_PyLong_AsInt(PyObject *obj)
+{
+    int overflow;
+    long result = PyLong_AsLongAndOverflow(obj, &overflow);
+    if (overflow || result > INT_MAX || result < INT_MIN) {
+        /* XXX: could be cute and give a different
+           message for overflow == -1 */
+        PyErr_SetString(PyExc_OverflowError,
+                        "Python int too large to convert to C int");
+        return -1;
+    }
+    return (int)result;
 }
 
@@ -274 +363 @@
 Py_ssize_t
 PyLong_AsSsize_t(PyObject *vv) {
-        register PyLongObject *v;
-        size_t x, prev;
-        Py_ssize_t i;
-        int sign;
-
-        if (vv == NULL || !PyLong_Check(vv)) {
-                PyErr_BadInternalCall();
-                return -1;
-        }
-        v = (PyLongObject *)vv;
-        i = v->ob_size;
-        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,
-                        "long int too large to convert to int");
-        return -1;
+    register PyLongObject *v;
+    size_t x, prev;
+    Py_ssize_t i;
+    int sign;
+
+    if (vv == NULL || !PyLong_Check(vv)) {
+        PyErr_BadInternalCall();
+        return -1;
+    }
+    v = (PyLongObject *)vv;
+    i = v->ob_size;
+    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,
+                    "long int too large to convert to int");
+    return -1;
 }
 
@@ -320 +409 @@
 PyLong_AsUnsignedLong(PyObject *vv)
 {
-        register PyLongObject *v;
-        unsigned long x, prev;
-        Py_ssize_t i;
-
-        if (vv == NULL || !PyLong_Check(vv)) {
-                if (vv != NULL && PyInt_Check(vv)) {
-                        long val = PyInt_AsLong(vv);
-                        if (val < 0) {
-                                PyErr_SetString(PyExc_OverflowError,
-                                "can't convert negative value to unsigned long");
-                                return (unsigned long) -1;
-                        }
-                        return val;
-                }
-                PyErr_BadInternalCall();
-                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 long");
-                return (unsigned long) -1;
-        }
-        while (--i >= 0) {
-                prev = x;
-                x = (x << PyLong_SHIFT) + v->ob_digit[i];
-                if ((x >> PyLong_SHIFT) != prev) {
-                        PyErr_SetString(PyExc_OverflowError,
-                                "long int too large to convert");
-                        return (unsigned long) -1;
-                }
-        }
-        return x;
+    register PyLongObject *v;
+    unsigned long x, prev;
+    Py_ssize_t i;
+
+    if (vv == NULL || !PyLong_Check(vv)) {
+        if (vv != NULL && PyInt_Check(vv)) {
+            long val = PyInt_AsLong(vv);
+            if (val < 0) {
+                PyErr_SetString(PyExc_OverflowError,
+                                "can't convert negative value "
+                                "to unsigned long");
+                return (unsigned long) -1;
+            }
+            return val;
+        }
+        PyErr_BadInternalCall();
+        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 long");
+        return (unsigned long) -1;
+    }
+    while (--i >= 0) {
+        prev = x;
+        x = (x << PyLong_SHIFT) | v->ob_digit[i];
+        if ((x >> PyLong_SHIFT) != prev) {
+            PyErr_SetString(PyExc_OverflowError,
+                            "long int too large to convert");
+            return (unsigned long) -1;
+        }
+    }
+    return x;
 }
 
@@ -363 +453 @@
 PyLong_AsUnsignedLongMask(PyObject *vv)
 {
-        register PyLongObject *v;
-        unsigned long x;
-        Py_ssize_t i;
-        int sign;
-
-        if (vv == NULL || !PyLong_Check(vv)) {
-                if (vv != NULL && PyInt_Check(vv))
-                        return PyInt_AsUnsignedLongMask(vv);
-                PyErr_BadInternalCall();
-                return (unsigned long) -1;
-        }
-        v = (PyLongObject *)vv;
-        i = v->ob_size;
-        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;
+    register PyLongObject *v;
+    unsigned long x;
+    Py_ssize_t i;
+    int sign;
+
+    if (vv == NULL || !PyLong_Check(vv)) {
+        if (vv != NULL && PyInt_Check(vv))
+            return PyInt_AsUnsignedLongMask(vv);
+        PyErr_BadInternalCall();
+        return (unsigned long) -1;
+    }
+    v = (PyLongObject *)vv;
+    i = v->ob_size;
+    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;
 }
 
@@ -391 +481 @@
 _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);
+    PyLongObject *v = (PyLongObject *)vv;
+
+    assert(v != NULL);
+    assert(PyLong_Check(v));
+
+    return Py_SIZE(v) == 0 ? 0 : (Py_SIZE(v) < 0 ? -1 : 1);
 }
 
@@ -402 +492 @@
 _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, "long has too many bits "
-                        "to express in a platform size_t");
-        return (size_t)-1;
+    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, "long 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 */
-        size_t ndigits;                 /* number of Python long digits */
-        PyLongObject* v;                /* result */
-        int 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 insignficant 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. */
-        ndigits = (numsignificantbytes * 8 + PyLong_SHIFT - 1) / PyLong_SHIFT;
-        if (ndigits > (size_t)INT_MAX)
-                return PyErr_NoMemory();
-        v = _PyLong_New((int)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 < (int)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 < (int)ndigits);
-                        v->ob_digit[idigit] = (digit)accum;
-                        ++idigit;
-                }
-        }
-
-        Py_SIZE(v) = is_signed ? -idigit : idigit;
-        return (PyObject *)long_normalize(v);
+                      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_TypeError,
-                                "can't convert negative long 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, "long too big to convert");
-        return -1;
-
-}
-
-double
-_PyLong_AsScaledDouble(PyObject *vv, int *exponent)
-{
-/* NBITS_WANTED should be > the number of bits in a double's precision,
-   but small enough so that 2**NBITS_WANTED is within the normal double
-   range.  nbitsneeded is set to 1 less than that because the most-significant
-   Python digit contains at least 1 significant bit, but we don't want to
-   bother counting them (catering to the worst case cheaply).
-
-   57 is one more than VAX-D double precision; I (Tim) don't know of a double
-   format with more precision than that; it's 1 larger so that we add in at
-   least one round bit to stand in for the ignored least-significant bits.
-*/
-#define NBITS_WANTED 57
-        PyLongObject *v;
-        double x;
-        const double multiplier = (double)(1L << PyLong_SHIFT);
-        Py_ssize_t i;
-        int sign;
-        int nbitsneeded;
-
-        if (vv == NULL || !PyLong_Check(vv)) {
-                PyErr_BadInternalCall();
-                return -1;
-        }
-        v = (PyLongObject *)vv;
-        i = Py_SIZE(v);
-        sign = 1;
-        if (i < 0) {
-                sign = -1;
-                i = -(i);
-        }
-        else if (i == 0) {
-                *exponent = 0;
-                return 0.0;
-        }
-        --i;
-        x = (double)v->ob_digit[i];
-        nbitsneeded = NBITS_WANTED - 1;
-        /* Invariant:  i Python digits remain unaccounted for. */
-        while (i > 0 && nbitsneeded > 0) {
-                --i;
-                x = x * multiplier + (double)v->ob_digit[i];
-                nbitsneeded -= PyLong_SHIFT;
-        }
-        /* There are i digits we didn't shift in.  Pretending they're all
-           zeroes, the true value is x * 2**(i*PyLong_SHIFT). */
-        *exponent = i;
-        assert(x > 0.0);
-        return x * sign;
-#undef NBITS_WANTED
-}
-
-/* Get a C double from a long int object. */
-
-double
-PyLong_AsDouble(PyObject *vv)
-{
-        int e = -1;
-        double x;
-
-        if (vv == NULL || !PyLong_Check(vv)) {
-                PyErr_BadInternalCall();
-                return -1;
-        }
-        x = _PyLong_AsScaledDouble(vv, &e);
-        if (x == -1.0 && PyErr_Occurred())
-                return -1.0;
-        /* 'e' initialized to -1 to silence gcc-4.0.x, but it should be
-           set correctly after a successful _PyLong_AsScaledDouble() call */
-        assert(e >= 0);
-        if (e > INT_MAX / PyLong_SHIFT)
-                goto overflow;
-        errno = 0;
-        x = ldexp(x, e * PyLong_SHIFT);
-        if (Py_OVERFLOWED(x))
-                goto overflow;
-        return x;
-
-overflow:
-        PyErr_SetString(PyExc_OverflowError,
-                "long int too large to convert to float");
-        return -1.0;
+                    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 long 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, "long too big to convert");
+    return -1;
+
 }
 
@@ -763 +771 @@
 {
 #if SIZEOF_VOID_P <= SIZEOF_LONG
-        if ((long)p < 0)
-                return PyLong_FromUnsignedLong((unsigned long)p);
-        return PyInt_FromLong((long)p);
+    if ((long)p < 0)
+        return PyLong_FromUnsignedLong((unsigned long)p);
+    return PyInt_FromLong((long)p);
 #else
 
@@ -774 +782 @@
 #   error "PyLong_FromVoidPtr: sizeof(PY_LONG_LONG) < sizeof(void*)"
 #endif
-        /* optimize null pointers */
-        if (p == NULL)
-                return PyInt_FromLong(0);
-        return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG)p);
+    /* optimize null pointers */
+    if (p == NULL)
+        return PyInt_FromLong(0);
+    return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG)p);
 
 #endif /* SIZEOF_VOID_P <= SIZEOF_LONG */
@@ -787 +795 @@
 PyLong_AsVoidPtr(PyObject *vv)
 {
-        /* This function will allow int or long objects. If vv is neither,
-           then the PyLong_AsLong*() functions will raise the exception:
-           PyExc_SystemError, "bad argument to internal function"
-        */
+    /* This function will allow int or long objects. If vv is neither,
+       then the PyLong_AsLong*() functions will raise the exception:
+       PyExc_SystemError, "bad argument to internal function"
+    */
 #if SIZEOF_VOID_P <= SIZEOF_LONG
-        long x;
-
-        if (PyInt_Check(vv))
-                x = PyInt_AS_LONG(vv);
-        else if (PyLong_Check(vv) && _PyLong_Sign(vv) < 0)
-                x = PyLong_AsLong(vv);
-        else
-                x = PyLong_AsUnsignedLong(vv);
+    long x;
+
+    if (PyInt_Check(vv))
+        x = PyInt_AS_LONG(vv);
+    else if (PyLong_Check(vv) && _PyLong_Sign(vv) < 0)
+        x = PyLong_AsLong(vv);
+    else
+        x = PyLong_AsUnsignedLong(vv);
 #else
 
@@ -808 +816 @@
 #   error "PyLong_AsVoidPtr: sizeof(PY_LONG_LONG) < sizeof(void*)"
 #endif
-        PY_LONG_LONG x;
-
-        if (PyInt_Check(vv))
-                x = PyInt_AS_LONG(vv);
-        else if (PyLong_Check(vv) && _PyLong_Sign(vv) < 0)
-                x = PyLong_AsLongLong(vv);
-        else
-                x = PyLong_AsUnsignedLongLong(vv);
+    PY_LONG_LONG x;
+
+    if (PyInt_Check(vv))
+        x = PyInt_AS_LONG(vv);
+    else 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;
+    if (x == -1 && PyErr_Occurred())
+        return NULL;
+    return (void *)x;
 }
 
@@ -831 +839 @@
 
 #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. */
@@ -837 +846 @@
 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;
+    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;
 }
 
@@ -880 +889 @@
 PyLong_FromUnsignedLongLong(unsigned PY_LONG_LONG ival)
 {
-        PyLongObject *v;
-        unsigned PY_LONG_LONG t;
-        int ndigits = 0;
-
-        /* 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;
+    PyLongObject *v;
+    unsigned PY_LONG_LONG t;
+    int ndigits = 0;
+
+    /* 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;
 }
 
@@ -907 +916 @@
 PyLong_FromSsize_t(Py_ssize_t ival)
 {
-        Py_ssize_t bytes = ival;
-        int one = 1;
-        return _PyLong_FromByteArray(
-                        (unsigned char *)&bytes,
-                        SIZEOF_SIZE_T, IS_LITTLE_ENDIAN, 1);
+    Py_ssize_t bytes = ival;
+    int one = 1;
+    return _PyLong_FromByteArray((unsigned char *)&bytes,
+                                 SIZEOF_SIZE_T, IS_LITTLE_ENDIAN, 1);
 }
 
@@ -919 +927 @@
 PyLong_FromSize_t(size_t ival)
 {
-        size_t bytes = ival;
-        int one = 1;
-        return _PyLong_FromByteArray(
-                        (unsigned char *)&bytes,
-                        SIZEOF_SIZE_T, IS_LITTLE_ENDIAN, 0);
+    size_t bytes = ival;
+    int one = 1;
+    return _PyLong_FromByteArray((unsigned char *)&bytes,
+                                 SIZEOF_SIZE_T, IS_LITTLE_ENDIAN, 0);
 }
 
@@ -932 +939 @@
 PyLong_AsLongLong(PyObject *vv)
 {
-        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 (PyInt_Check(vv))
-                        return (PY_LONG_LONG)PyInt_AsLong(vv);
-                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 (PyInt_Check(io)) {
-                        bytes = PyInt_AsLong(io);
-                        Py_DECREF(io);
-                        return bytes;
-                }
-                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;
-        }
-
-        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;
+    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 (PyInt_Check(vv))
+            return (PY_LONG_LONG)PyInt_AsLong(vv);
+        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 (PyInt_Check(io)) {
+            bytes = PyInt_AsLong(io);
+            Py_DECREF(io);
+            return bytes;
+        }
+        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;
+    }
+
+    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;
 }
 
@@ -985 +991 @@
 PyLong_AsUnsignedLongLong(PyObject *vv)
 {
-        unsigned PY_LONG_LONG bytes;
-        int one = 1;
-        int res;
-
-        if (vv == NULL || !PyLong_Check(vv)) {
-                PyErr_BadInternalCall();
-                return (unsigned PY_LONG_LONG)-1;
-        }
-
-        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;
+    unsigned PY_LONG_LONG bytes;
+    int one = 1;
+    int res;
+
+    if (vv == NULL || !PyLong_Check(vv)) {
+        PyErr_BadInternalCall();
+        return (unsigned PY_LONG_LONG)-1;
+    }
+
+    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;
 }
 
@@ -1011 +1016 @@
 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;
-        i = v->ob_size;
-        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;
-}
+    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;
+    i = v->ob_size;
+    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;
+}
+
+/* Get a C long long int from a Python long or Python int object.
+   On overflow, returns -1 and sets *overflow to 1 or -1 depending
+   on the sign of the result.  Otherwise *overflow is 0.
+
+   For other errors (e.g., type error), returns -1 and sets an error
+   condition.
+*/
+
+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 (PyInt_Check(vv))
+        return PyInt_AsLong(vv);
+
+    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(PyInt_Check(vv)) {
+            res = PyInt_AsLong(vv);
+            goto exit;
+        }
+        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;
+}
+
 #undef IS_LITTLE_ENDIAN
 
@@ -1040 +1148 @@
 static int
 convert_binop(PyObject *v, PyObject *w, PyLongObject **a, PyLongObject **b) {
-        if (PyLong_Check(v)) {
-                *a = (PyLongObject *) v;
-                Py_INCREF(v);
-        }
-        else if (PyInt_Check(v)) {
-                *a = (PyLongObject *) PyLong_FromLong(PyInt_AS_LONG(v));
-        }
-        else {
-                return 0;
-        }
-        if (PyLong_Check(w)) {
-                *b = (PyLongObject *) w;
-                Py_INCREF(w);
-        }
-        else if (PyInt_Check(w)) {
-                *b = (PyLongObject *) PyLong_FromLong(PyInt_AS_LONG(w));
-        }
-        else {
-                Py_DECREF(*a);
-                return 0;
-        }
-        return 1;
-}
-
-#define CONVERT_BINOP(v, w, a, b) \
-        if (!convert_binop(v, w, a, b)) { \
-                Py_INCREF(Py_NotImplemented); \
-                return Py_NotImplemented; \
-        }
+    if (PyLong_Check(v)) {
+        *a = (PyLongObject *) v;
+        Py_INCREF(v);
+    }
+    else if (PyInt_Check(v)) {
+        *a = (PyLongObject *) PyLong_FromLong(PyInt_AS_LONG(v));
+    }
+    else {
+        return 0;
+    }
+    if (PyLong_Check(w)) {
+        *b = (PyLongObject *) w;
+        Py_INCREF(w);
+    }
+    else if (PyInt_Check(w)) {
+        *b = (PyLongObject *) PyLong_FromLong(PyInt_AS_LONG(w));
+    }
+    else {
+        Py_DECREF(*a);
+        return 0;
+    }
+    return 1;
+}
+
+#define CONVERT_BINOP(v, w, a, b)               \
+    do {                                        \
+        if (!convert_binop(v, w, a, b)) {       \
+            Py_INCREF(Py_NotImplemented);       \
+            return Py_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]
@@ -1077 +1207 @@
 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;
+    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;
 }
 
@@ -1103 +1233 @@
 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;
-}
-
-/* Multiply by a single digit, ignoring the sign. */
-
-static PyLongObject *
-mul1(PyLongObject *a, wdigit n)
-{
-        return muladd1(a, n, (digit)0);
-}
-
-/* Multiply by a single digit and add a single digit, ignoring the sign. */
-
-static PyLongObject *
-muladd1(PyLongObject *a, wdigit n, wdigit extra)
-{
-        Py_ssize_t size_a = ABS(Py_SIZE(a));
-        PyLongObject *z = _PyLong_New(size_a+1);
-        twodigits carry = extra;
-        Py_ssize_t i;
-
-        if (z == NULL)
-                return NULL;
-        for (i = 0; i < size_a; ++i) {
-                carry += (twodigits)a->ob_digit[i] * n;
-                z->ob_digit[i] = (digit) (carry & PyLong_MASK);
-                carry >>= PyLong_SHIFT;
-        }
-        z->ob_digit[i] = (digit) carry;
-        return long_normalize(z);
+    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;
 }
 
@@ -1160 +1298 @@
 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;
+    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;
 }
 
@@ -1181 +1319 @@
 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);
+    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, int addL)
+{
+    PyLongObject *scratch, *a;
+    PyObject *str;
+    Py_ssize_t size, strlen, size_a, i, j;
+    digit *pout, *pin, rem, tenpow;
+    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 = (addL != 0) + negative +
+        1 + (size - 1) * _PyLong_DECIMAL_SHIFT;
+    tenpow = 10;
+    rem = pout[size-1];
+    while (rem >= tenpow) {
+        tenpow *= 10;
+        strlen++;
+    }
+    str = PyString_FromStringAndSize(NULL, strlen);
+    if (str == NULL) {
+        Py_DECREF(scratch);
+        return NULL;
+    }
+
+    /* fill the string right-to-left */
+    p = PyString_AS_STRING(str) + strlen;
+    *p = '\0';
+    if (addL)
+        *--p = 'L';
+    /* 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 == PyString_AS_STRING(str));
+    Py_DECREF(scratch);
+    return (PyObject *)str;
 }
 
@@ -1200 +1455 @@
 _PyLong_Format(PyObject *aa, int base, int addL, int newstyle)
 {
-        register PyLongObject *a = (PyLongObject *)aa;
-        PyStringObject *str;
-        Py_ssize_t i, sz;
-        Py_ssize_t size_a;
-        char *p;
-        int bits;
-        char sign = '\0';
-
-        if (a == NULL || !PyLong_Check(a)) {
-                PyErr_BadInternalCall();
-                return NULL;
-        }
-        assert(base >= 2 && base <= 36);
-        size_a = ABS(Py_SIZE(a));
-
-        /* Compute a rough upper bound for the length of the string */
-        i = base;
-        bits = 0;
-        while (i > 1) {
-                ++bits;
-                i >>= 1;
-        }
-        i = 5 + (addL ? 1 : 0);
-        /* ensure we don't get signed overflow in sz calculation */
-        if (size_a > (PY_SSIZE_T_MAX - i) / PyLong_SHIFT) {
-                PyErr_SetString(PyExc_OverflowError,
-                                "long is too large to format");
-                return NULL;
-        }
-        sz = i + 1 + (size_a * PyLong_SHIFT - 1) / bits;
-        assert(sz >= 0);
-        str = (PyStringObject *) PyString_FromStringAndSize((char *)0, sz);
-        if (str == NULL)
-                return NULL;
-        p = PyString_AS_STRING(str) + sz;
-        *p = '\0';
-        if (addL)
-                *--p = 'L';
-        if (a->ob_size < 0)
-                sign = '-';
-
-        if (a->ob_size == 0) {
-                *--p = '0';
-        }
-        else if ((base & (base - 1)) == 0) {
-                /* JRH: special case for power-of-2 bases */
-                twodigits accum = 0;
-                int accumbits = 0;      /* # of bits in accum */
-                int basebits = 1;       /* # of bits in base-1 */
-                i = base;
-                while ((i >>= 1) > 1)
-                        ++basebits;
-
-                for (i = 0; i < size_a; ++i) {
-                        accum |= (twodigits)a->ob_digit[i] << accumbits;
-                        accumbits += PyLong_SHIFT;
-                        assert(accumbits >= basebits);
-                        do {
-                                char cdigit = (char)(accum & (base - 1));
-                                cdigit += (cdigit < 10) ? '0' : 'a'-10;
-                                assert(p > PyString_AS_STRING(str));
-                                *--p = cdigit;
-                                accumbits -= basebits;
-                                accum >>= basebits;
-                        } while (i < size_a-1 ? accumbits >= basebits :
-                                                accum > 0);
-                }
-        }
-        else {
-                /* Not 0, and base not a power of 2.  Divide repeatedly by
-                   base, but for speed use the highest power of base that
-                   fits in a digit. */
-                Py_ssize_t size = size_a;
-                digit *pin = a->ob_digit;
-                PyLongObject *scratch;
-                /* powbasw <- largest power of base that fits in a digit. */
-                digit powbase = base;  /* powbase == base ** power */
-                int power = 1;
-                for (;;) {
-                        unsigned long newpow = powbase * (unsigned long)base;
-                        if (newpow >> PyLong_SHIFT)
-                                /* doesn't fit in a digit */
-                                break;
-                        powbase = (digit)newpow;
-                        ++power;
-                }
-
-                /* Get a scratch area for repeated division. */
-                scratch = _PyLong_New(size);
-                if (scratch == NULL) {
-                        Py_DECREF(str);
-                        return NULL;
-                }
-
-                /* Repeatedly divide by powbase. */
-                do {
-                        int ntostore = power;
-                        digit rem = inplace_divrem1(scratch->ob_digit,
-                                                     pin, size, powbase);
-                        pin = scratch->ob_digit; /* no need to use a again */
-                        if (pin[size - 1] == 0)
-                                --size;
-                        SIGCHECK({
-                                Py_DECREF(scratch);
-                                Py_DECREF(str);
-                                return NULL;
-                        })
-
-                        /* Break rem into digits. */
-                        assert(ntostore > 0);
-                        do {
-                                digit nextrem = (digit)(rem / base);
-                                char c = (char)(rem - nextrem * base);
-                                assert(p > PyString_AS_STRING(str));
-                                c += (c < 10) ? '0' : 'a'-10;
-                                *--p = c;
-                                rem = nextrem;
-                                --ntostore;
-                                /* Termination is a bit delicate:  must not
-                                   store leading zeroes, so must get out if
-                                   remaining quotient and rem are both 0. */
-                        } while (ntostore && (size || rem));
-                } while (size != 0);
-                Py_DECREF(scratch);
-        }
-
-        if (base == 2) {
-                *--p = 'b';
-                *--p = '0';
-        }
-        else if (base == 8) {
-                if (newstyle) {
-                        *--p = 'o';
-                        *--p = '0';
-                }
-                else
-                        if (size_a != 0)
-                                *--p = '0';
-        }
-        else if (base == 16) {
-                *--p = 'x';
-                *--p = '0';
-        }
-        else if (base != 10) {
-                *--p = '#';
-                *--p = '0' + base%10;
-                if (base > 10)
-                        *--p = '0' + base/10;
-        }
-        if (sign)
-                *--p = sign;
-        if (p != PyString_AS_STRING(str)) {
-                char *q = PyString_AS_STRING(str);
-                assert(p > q);
-                do {
-                } while ((*q++ = *p++) != '\0');
-                q--;
-                _PyString_Resize((PyObject **)&str,
-                                 (Py_ssize_t) (q - PyString_AS_STRING(str)));
-        }
-        return (PyObject *)str;
+    register PyLongObject *a = (PyLongObject *)aa;
+    PyStringObject *str;
+    Py_ssize_t i, sz;
+    Py_ssize_t size_a;
+    char *p;
+    int bits;
+    char sign = '\0';
+
+    if (base == 10)
+        return long_to_decimal_string((PyObject *)a, addL);
+
+    if (a == NULL || !PyLong_Check(a)) {
+        PyErr_BadInternalCall();
+        return NULL;
+    }
+    assert(base >= 2 && base <= 36);
+    size_a = ABS(Py_SIZE(a));
+
+    /* Compute a rough upper bound for the length of the string */
+    i = base;
+    bits = 0;
+    while (i > 1) {
+        ++bits;
+        i >>= 1;
+    }
+    i = 5 + (addL ? 1 : 0);
+    /* ensure we don't get signed overflow in sz calculation */
+    if (size_a > (PY_SSIZE_T_MAX - i) / PyLong_SHIFT) {
+        PyErr_SetString(PyExc_OverflowError,
+                        "long is too large to format");
+        return NULL;
+    }
+    sz = i + 1 + (size_a * PyLong_SHIFT - 1) / bits;
+    assert(sz >= 0);
+    str = (PyStringObject *) PyString_FromStringAndSize((char *)0, sz);
+    if (str == NULL)
+        return NULL;
+    p = PyString_AS_STRING(str) + sz;
+    *p = '\0';
+    if (addL)
+        *--p = 'L';
+    if (a->ob_size < 0)
+        sign = '-';
+
+    if (a->ob_size == 0) {
+        *--p = '0';
+    }
+    else if ((base & (base - 1)) == 0) {
+        /* JRH: special case for power-of-2 bases */
+        twodigits accum = 0;
+        int accumbits = 0;              /* # of bits in accum */
+        int basebits = 1;               /* # of bits in base-1 */
+        i = base;
+        while ((i >>= 1) > 1)
+            ++basebits;
+
+        for (i = 0; i < size_a; ++i) {
+            accum |= (twodigits)a->ob_digit[i] << accumbits;
+            accumbits += PyLong_SHIFT;
+            assert(accumbits >= basebits);
+            do {
+                char cdigit = (char)(accum & (base - 1));
+                cdigit += (cdigit < 10) ? '0' : 'a'-10;
+                assert(p > PyString_AS_STRING(str));
+                *--p = cdigit;
+                accumbits -= basebits;
+                accum >>= basebits;
+            } while (i < size_a-1 ? accumbits >= basebits : accum > 0);
+        }
+    }
+    else {
+        /* Not 0, and base not a power of 2.  Divide repeatedly by
+           base, but for speed use the highest power of base that
+           fits in a digit. */
+        Py_ssize_t size = size_a;
+        digit *pin = a->ob_digit;
+        PyLongObject *scratch;
+        /* powbasw <- largest power of base that fits in a digit. */
+        digit powbase = base;  /* powbase == base ** power */
+        int power = 1;
+        for (;;) {
+            twodigits newpow = powbase * (twodigits)base;
+            if (newpow >> PyLong_SHIFT)
+                /* doesn't fit in a digit */
+                break;
+            powbase = (digit)newpow;
+            ++power;
+        }
+
+        /* Get a scratch area for repeated division. */
+        scratch = _PyLong_New(size);
+        if (scratch == NULL) {
+            Py_DECREF(str);
+            return NULL;
+        }
+
+        /* Repeatedly divide by powbase. */
+        do {
+            int ntostore = power;
+            digit rem = inplace_divrem1(scratch->ob_digit,
+                                        pin, size, powbase);
+            pin = scratch->ob_digit; /* no need to use a again */
+            if (pin[size - 1] == 0)
+                --size;
+            SIGCHECK({
+                    Py_DECREF(scratch);
+                    Py_DECREF(str);
+                    return NULL;
+                });
+
+            /* Break rem into digits. */
+            assert(ntostore > 0);
+            do {
+                digit nextrem = (digit)(rem / base);
+                char c = (char)(rem - nextrem * base);
+                assert(p > PyString_AS_STRING(str));
+                c += (c < 10) ? '0' : 'a'-10;
+                *--p = c;
+                rem = nextrem;
+                --ntostore;
+                /* Termination is a bit delicate:  must not
+                   store leading zeroes, so must get out if
+                   remaining quotient and rem are both 0. */
+            } while (ntostore && (size || rem));
+        } while (size != 0);
+        Py_DECREF(scratch);
+    }
+
+    if (base == 2) {
+        *--p = 'b';
+        *--p = '0';
+    }
+    else if (base == 8) {
+        if (newstyle) {
+            *--p = 'o';
+            *--p = '0';
+        }
+        else
+            if (size_a != 0)
+                *--p = '0';
+    }
+    else if (base == 16) {
+        *--p = 'x';
+        *--p = '0';
+    }
+    else if (base != 10) {
+        *--p = '#';
+        *--p = '0' + base%10;
+        if (base > 10)
+            *--p = '0' + base/10;
+    }
+    if (sign)
+        *--p = sign;
+    if (p != PyString_AS_STRING(str)) {
+        char *q = PyString_AS_STRING(str);
+        assert(p > q);
+        do {
+        } while ((*q++ = *p++) != '\0');
+        q--;
+        _PyString_Resize((PyObject **)&str,
+                         (Py_ssize_t) (q - PyString_AS_STRING(str)));
+    }
+    return (PyObject *)str;
 }
 
@@ -1371 +1628 @@
  */
 int _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,
+    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,
 };
 
@@ -1398 +1655 @@
 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,
-                                "long 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 = _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);
+    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,
+                        "long 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 = _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);
 }
 
@@ -1458 +1715 @@
 PyLong_FromString(char *str, char **pend, int base)
 {
-        int sign = 1;
-        char *start, *orig_str = str;
-        PyLongObject *z;
-        PyObject *strobj, *strrepr;
-        Py_ssize_t slen;
-
-        if ((base != 0 && base < 2) || base > 36) {
-                PyErr_SetString(PyExc_ValueError,
-                                "long() 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;
-        }
-        while (*str != '\0' && isspace(Py_CHARMASK(*str)))
-                str++;
-        if (base == 0) {
-                /* No base given.  Deduce the base from the contents
-                   of the string */
-                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, still valid in
-                           2.x, although illegal in 3.x */
-                        base = 8;
-        }
-        /* Whether or not we were deducing the base, skip leading chars
-           as needed */
-        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 {
+    int sign = 1;
+    char *start, *orig_str = str;
+    PyLongObject *z;
+    PyObject *strobj, *strrepr;
+    Py_ssize_t slen;
+
+    if ((base != 0 && base < 2) || base > 36) {
+        PyErr_SetString(PyExc_ValueError,
+                        "long() 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;
+    }
+    while (*str != '\0' && isspace(Py_CHARMASK(*str)))
+        str++;
+    if (base == 0) {
+        /* No base given.  Deduce the base from the contents
+           of the string */
+        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, still valid in
+               2.x, although illegal in 3.x */
+            base = 8;
+    }
+    /* Whether or not we were deducing the base, skip leading chars
+       as needed */
+    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
@@ -1520 +1777 @@
     n >= log(B**N)/log(PyLong_BASE) = N * log(B)/log(PyLong_BASE)
 
-The static array log_base_PyLong_BASE[base] == log(base)/log(PyLong_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 static array log_base_PyLong_BASE[base] == log(base)/log(PyLong_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 <= PyLong_BASE
+    convwidth_base[base] = the largest integer i such that
+                           base**i <= PyLong_BASE
     convmultmax_base[base] = base ** convwidth_base[base]
 
@@ -1551 +1809 @@
 
 below.  Two numeric concerns are how much space this can waste, and whether
-the computed result can be too small.  To be concrete, assume PyLong_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
+the computed result can be too small.  To be concrete, assume PyLong_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 PyLong_BASE so at most
-one allocated Python digit can remain unused on that count.  If
-N*log(B)/log(PyLong_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(PyLong_BASE) to be
+digits is about a factor of B, but B is small compared to PyLong_BASE so at
+most one allocated Python digit can remain unused on that count.  If
+N*log(B)/log(PyLong_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(PyLong_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(PyLong_BASE)
-is a little bit larger than an exact integer, but due to roundoff errors (in
-computing log(B), log(PyLong_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(PyLong_BASE) via continued
-fractions, giving a sequence i/j of "the best" rational approximations.  Then
-j*log(B)/log(PyLong_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:
+The computed result can be too small if the true value of
+N*log(B)/log(PyLong_BASE) is a little bit larger than an exact integer, but
+due to roundoff errors (in computing log(B), log(PyLong_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(PyLong_BASE) via continued fractions, giving a sequence i/j of "the
+best" rational approximations.  Then j*log(B)/log(PyLong_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
@@ -1592 +1851 @@
 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_PyLong_BASE[37] = {0.0e0,};
-                static int convwidth_base[37] = {0,};
-                static twodigits convmultmax_base[37] = {0,};
-
-                if (log_base_PyLong_BASE[base] == 0.0) {
-                        twodigits convmax = base;
-                        int i = 1;
-
-                        log_base_PyLong_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_PyLong_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 +
-                                        _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 (str == start)
-                goto onError;
-        if (sign < 0)
-                Py_SIZE(z) = -(Py_SIZE(z));
-        if (*str == 'L' || *str == 'l')
-                str++;
-        while (*str && isspace(Py_CHARMASK(*str)))
-                str++;
-        if (*str != '\0')
-                goto onError;
-        if (pend)
-                *pend = str;
-        return (PyObject *) z;
-
- onError:
-        Py_XDECREF(z);
-        slen = strlen(orig_str) < 200 ? strlen(orig_str) : 200;
-        strobj = PyString_FromStringAndSize(orig_str, slen);
-        if (strobj == NULL)
-                return NULL;
-        strrepr = PyObject_Repr(strobj);
-        Py_DECREF(strobj);
-        if (strrepr == NULL)
-                return NULL;
-        PyErr_Format(PyExc_ValueError,
-                     "invalid literal for long() with base %d: %s",
-                     base, PyString_AS_STRING(strrepr));
-        Py_DECREF(strrepr);
-        return NULL;
+        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_PyLong_BASE[37] = {0.0e0,};
+        static int convwidth_base[37] = {0,};
+        static twodigits convmultmax_base[37] = {0,};
+
+        if (log_base_PyLong_BASE[base] == 0.0) {
+            twodigits convmax = base;
+            int i = 1;
+
+            log_base_PyLong_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_PyLong_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 +
+                                _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 (str == start)
+        goto onError;
+    if (sign < 0)
+        Py_SIZE(z) = -(Py_SIZE(z));
+    if (*str == 'L' || *str == 'l')
+        str++;
+    while (*str && isspace(Py_CHARMASK(*str)))
+        str++;
+    if (*str != '\0')
+        goto onError;
+    if (pend)
+        *pend = str;
+    return (PyObject *) z;
+
+  onError:
+    Py_XDECREF(z);
+    slen = strlen(orig_str) < 200 ? strlen(orig_str) : 200;
+    strobj = PyString_FromStringAndSize(orig_str, slen);
+    if (strobj == NULL)
+        return NULL;
+    strrepr = PyObject_Repr(strobj);
+    Py_DECREF(strobj);
+    if (strrepr == NULL)
+        return NULL;
+    PyErr_Format(PyExc_ValueError,
+                 "invalid literal for long() with base %d: %s",
+                 base, PyString_AS_STRING(strrepr));
+    Py_DECREF(strrepr);
+    return NULL;
 }
 
@@ -1739 +1998 @@
 PyLong_FromUnicode(Py_UNICODE *u, Py_ssize_t length, int base)
 {
-        PyObject *result;
-        char *buffer = (char *)PyMem_MALLOC(length+1);
-
-        if (buffer == NULL)
-                return NULL;
-
-        if (PyUnicode_EncodeDecimal(u, length, buffer, NULL)) {
-                PyMem_FREE(buffer);
-                return NULL;
-        }
-        result = PyLong_FromString(buffer, NULL, base);
-        PyMem_FREE(buffer);
-        return result;
+    PyObject *result;
+    char *buffer = (char *)PyMem_MALLOC(length+1);
+
+    if (buffer == NULL)
+        return NULL;
+
+    if (PyUnicode_EncodeDecimal(u, length, buffer, NULL)) {
+        PyMem_FREE(buffer);
+        return NULL;
+    }
+    result = PyLong_FromString(buffer, NULL, base);
+    PyMem_FREE(buffer);
+    return result;
 }
 #endif
@@ -1757 +2016 @@
 /* forward */
 static PyLongObject *x_divrem
-        (PyLongObject *, PyLongObject *, PyLongObject **);
+    (PyLongObject *, PyLongObject *, PyLongObject **);
 static PyObject *long_long(PyObject *v);
-static int long_divrem(PyLongObject *, PyLongObject *,
-        PyLongObject **, PyLongObject **);
 
 /* Long division with remainder, top-level routine */
@@ -1766 +2023 @@
 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,
-                                "long 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 = _PyLong_New(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 ((a->ob_size < 0) != (b->ob_size < 0))
-                z->ob_size = -(z->ob_size);
-        if (a->ob_size < 0 && (*prem)->ob_size != 0)
-                (*prem)->ob_size = -((*prem)->ob_size);
-        *pdiv = z;
-        return 0;
-}
-
-/* Unsigned long division with remainder -- the algorithm */
+            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,
+                        "long 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 = _PyLong_New(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 ((a->ob_size < 0) != (b->ob_size < 0))
+        z->ob_size = -(z->ob_size);
+    if (a->ob_size < 0 && (*prem)->ob_size != 0)
+        (*prem)->ob_size = -((*prem)->ob_size);
+    *pdiv = 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)
 {
-        Py_ssize_t size_v = ABS(Py_SIZE(v1)), size_w = ABS(Py_SIZE(w1));
-        digit d = (digit) ((twodigits)PyLong_BASE / (w1->ob_digit[size_w-1] + 1));
-        PyLongObject *v = mul1(v1, d);
-        PyLongObject *w = mul1(w1, d);
-        PyLongObject *a;
-        Py_ssize_t j, k;
-
-        if (v == NULL || w == NULL) {
-                Py_XDECREF(v);
-                Py_XDECREF(w);
-                return NULL;
-        }
-
-        assert(size_v >= size_w && size_w > 1); /* Assert checks by div() */
-        assert(Py_REFCNT(v) == 1); /* Since v will be used as accumulator! */
-        assert(size_w == ABS(Py_SIZE(w))); /* That's how d was calculated */
-
-        size_v = ABS(Py_SIZE(v));
-        k = size_v - size_w;
-        a = _PyLong_New(k + 1);
-
-        for (j = size_v; a != NULL && k >= 0; --j, --k) {
-                digit vj = (j >= size_v) ? 0 : v->ob_digit[j];
-                twodigits q;
-                stwodigits carry = 0;
-                Py_ssize_t i;
-
-                SIGCHECK({
-                        Py_DECREF(a);
-                        a = NULL;
-                        break;
-                })
-                if (vj == w->ob_digit[size_w-1])
-                        q = PyLong_MASK;
-                else
-                        q = (((twodigits)vj << PyLong_SHIFT) + v->ob_digit[j-1]) /
-                                w->ob_digit[size_w-1];
-
-                while (w->ob_digit[size_w-2]*q >
-                                ((
-                                        ((twodigits)vj << PyLong_SHIFT)
-                                        + v->ob_digit[j-1]
-                                        - q*w->ob_digit[size_w-1]
-                                                                ) << PyLong_SHIFT)
-                                + v->ob_digit[j-2])
-                        --q;
-
-                for (i = 0; i < size_w && i+k < size_v; ++i) {
-                        twodigits z = w->ob_digit[i] * q;
-                        digit zz = (digit) (z >> PyLong_SHIFT);
-                        carry += v->ob_digit[i+k] - z
-                                + ((twodigits)zz << PyLong_SHIFT);
-                        v->ob_digit[i+k] = (digit)(carry & PyLong_MASK);
-                        carry = Py_ARITHMETIC_RIGHT_SHIFT(BASE_TWODIGITS_TYPE,
-                                                          carry, PyLong_SHIFT);
-                        carry -= zz;
-                }
-
-                if (i+k < size_v) {
-                        carry += v->ob_digit[i+k];
-                        v->ob_digit[i+k] = 0;
-                }
-
-                if (carry == 0)
-                        a->ob_digit[k] = (digit) q;
-                else {
-                        assert(carry == -1);
-                        a->ob_digit[k] = (digit) q-1;
-                        carry = 0;
-                        for (i = 0; i < size_w && i+k < size_v; ++i) {
-                                carry += v->ob_digit[i+k] + w->ob_digit[i];
-                                v->ob_digit[i+k] = (digit)(carry & PyLong_MASK);
-                                carry = Py_ARITHMETIC_RIGHT_SHIFT(
-                                                BASE_TWODIGITS_TYPE,
-                                                carry, PyLong_SHIFT);
-                        }
-                }
-        } /* for j, k */
-
-        if (a == NULL)
-                *prem = NULL;
-        else {
-                a = long_normalize(a);
-                *prem = divrem1(v, d, &d);
-                /* d receives the (unused) remainder */
-                if (*prem == NULL) {
-                        Py_DECREF(a);
-                        a = NULL;
-                }
-        }
-        Py_DECREF(v);
-        Py_DECREF(w);
-        return a;
+    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)(sizeof(x_digits)/sizeof(digit)));
+
+    /* 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 || !PyLong_Check(v)) {
+        PyErr_BadInternalCall();
+        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);
 }
 
@@ -1920 +2351 @@
 long_dealloc(PyObject *v)
 {
-        Py_TYPE(v)->tp_free(v);
+    Py_TYPE(v)->tp_free(v);
 }
 
@@ -1926 +2357 @@
 long_repr(PyObject *v)
 {
-        return _PyLong_Format(v, 10, 1, 0);
+    return _PyLong_Format(v, 10, 1, 0);
 }
 
@@ -1932 +2363 @@
 long_str(PyObject *v)
 {
-        return _PyLong_Format(v, 10, 0, 0);
+    return _PyLong_Format(v, 10, 0, 0);
 }
 
@@ -1938 +2369 @@
 long_compare(PyLongObject *a, PyLongObject *b)
 {
-        Py_ssize_t sign;
-
-        if (Py_SIZE(a) != Py_SIZE(b)) {
-                if (ABS(Py_SIZE(a)) == 0 && ABS(Py_SIZE(b)) == 0)
-                        sign = 0;
-                else
-                        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 = (int)a->ob_digit[i] - (int)b->ob_digit[i];
-                        if (Py_SIZE(a) < 0)
-                                sign = -sign;
-                }
-        }
-        return sign < 0 ? -1 : sign > 0 ? 1 : 0;
+    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;
 }
 
@@ -1964 +2392 @@
 long_hash(PyLongObject *v)
 {
-        unsigned long x;
-        Py_ssize_t i;
-        int sign;
-
-        /* This is designed so that Python ints and longs with the
-           same value hash to the same value, otherwise comparisons
-           of mapping keys will turn out weird */
-        i = v->ob_size;
-        sign = 1;
-        x = 0;
-        if (i < 0) {
-                sign = -1;
-                i = -(i);
-        }
-#define LONG_BIT_PyLong_SHIFT   (8*sizeof(long) - PyLong_SHIFT)
-        /* The following loop produces a C unsigned long x such that x is
-           congruent to the absolute value of v modulo ULONG_MAX.  The
-           resulting x is nonzero if and only if v is. */
-        while (--i >= 0) {
-                /* Force a native long #-bits (32 or 64) circular shift */
-                x = ((x << PyLong_SHIFT) & ~PyLong_MASK) |
-                        ((x >> LONG_BIT_PyLong_SHIFT) & PyLong_MASK);
-                x += v->ob_digit[i];
-                /* If the addition above overflowed we compensate by
-                   incrementing.  This preserves the value modulo
-                   ULONG_MAX. */
-                if (x < v->ob_digit[i])
-                        x++;
-        }
-#undef LONG_BIT_PyLong_SHIFT
-        x = x * sign;
-        if (x == -1)
-                x = -2;
-        return x;
+    unsigned long x;
+    Py_ssize_t i;
+    int sign;
+
+    /* This is designed so that Python ints and longs with the
+       same value hash to the same value, otherwise comparisons
+       of mapping keys will turn out weird */
+    i = v->ob_size;
+    sign = 1;
+    x = 0;
+    if (i < 0) {
+        sign = -1;
+        i = -(i);
+    }
+    /* The following loop produces a C unsigned long x such that x is
+       congruent to the absolute value of v modulo ULONG_MAX.  The
+       resulting x is nonzero if and only if v is. */
+    while (--i >= 0) {
+        /* Force a native long #-bits (32 or 64) circular shift */
+        x = (x >> (8*SIZEOF_LONG-PyLong_SHIFT)) | (x << PyLong_SHIFT);
+        x += v->ob_digit[i];
+        /* If the addition above overflowed we compensate by
+           incrementing.  This preserves the value modulo
+           ULONG_MAX. */
+        if (x < v->ob_digit[i])
+            x++;
+    }
+    x = x * sign;
+    if (x == (unsigned long)-1)
+        x = (unsigned long)-2;
+    return (long)x;
 }
 
@@ -2006 +2431 @@
 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);
+    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);
 }
 
@@ -2040 +2465 @@
 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 _PyLong_New(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)
-                z->ob_size = -(z->ob_size);
-        return long_normalize(z);
+    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 _PyLong_New(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)
+        z->ob_size = -(z->ob_size);
+    return long_normalize(z);
 }
 
@@ -2093 +2518 @@
 long_add(PyLongObject *v, PyLongObject *w)
 {
-        PyLongObject *a, *b, *z;
-
-        CONVERT_BINOP((PyObject *)v, (PyObject *)w, &a, &b);
-
-        if (a->ob_size < 0) {
-                if (b->ob_size < 0) {
-                        z = x_add(a, b);
-                        if (z != NULL && z->ob_size != 0)
-                                z->ob_size = -(z->ob_size);
-                }
-                else
-                        z = x_sub(b, a);
-        }
-        else {
-                if (b->ob_size < 0)
-                        z = x_sub(a, b);
-                else
-                        z = x_add(a, b);
-        }
-        Py_DECREF(a);
-        Py_DECREF(b);
-        return (PyObject *)z;
+    PyLongObject *a, *b, *z;
+
+    CONVERT_BINOP((PyObject *)v, (PyObject *)w, &a, &b);
+
+    if (a->ob_size < 0) {
+        if (b->ob_size < 0) {
+            z = x_add(a, b);
+            if (z != NULL && z->ob_size != 0)
+                z->ob_size = -(z->ob_size);
+        }
+        else
+            z = x_sub(b, a);
+    }
+    else {
+        if (b->ob_size < 0)
+            z = x_sub(a, b);
+        else
+            z = x_add(a, b);
+    }
+    Py_DECREF(a);
+    Py_DECREF(b);
+    return (PyObject *)z;
 }
 
@@ -2120 +2545 @@
 long_sub(PyLongObject *v, PyLongObject *w)
 {
-        PyLongObject *a, *b, *z;
-
-        CONVERT_BINOP((PyObject *)v, (PyObject *)w, &a, &b);
-
-        if (a->ob_size < 0) {
-                if (b->ob_size < 0)
-                        z = x_sub(a, b);
-                else
-                        z = x_add(a, b);
-                if (z != NULL && z->ob_size != 0)
-                        z->ob_size = -(z->ob_size);
-        }
-        else {
-                if (b->ob_size < 0)
-                        z = x_add(a, b);
-                else
-                        z = x_sub(a, b);
-        }
-        Py_DECREF(a);
-        Py_DECREF(b);
-        return (PyObject *)z;
+    PyLongObject *a, *b, *z;
+
+    CONVERT_BINOP((PyObject *)v, (PyObject *)w, &a, &b);
+
+    if (a->ob_size < 0) {
+        if (b->ob_size < 0)
+            z = x_sub(a, b);
+        else
+            z = x_add(a, b);
+        if (z != NULL && z->ob_size != 0)
+            z->ob_size = -(z->ob_size);
+    }
+    else {
+        if (b->ob_size < 0)
+            z = x_add(a, b);
+        else
+            z = x_sub(a, b);
+    }
+    Py_DECREF(a);
+    Py_DECREF(b);
+    return (PyObject *)z;
 }
 
@@ -2149 +2574 @@
 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);
+    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);
 }
 
@@ -2238 +2663 @@
 */
 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;
+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;
 }
 
@@ -2271 +2699 @@
 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 _PyLong_New(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
-         *    PyLong_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;
+    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 _PyLong_New(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
+     *    PyLong_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));
+    /* 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;
+    /* 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;
 }
 
@@ -2486 +2914 @@
  * 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 bactracking except for the helpful
+ * at a time, then move on, never backtracking except for the helpful
  * single-width slice overlap between successive partial sums).
  */
@@ -2492 +2920 @@
 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;
+    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;
 }
 
@@ -2546 +2974 @@
 long_mul(PyLongObject *v, PyLongObject *w)
 {
-        PyLongObject *a, *b, *z;
-
-        if (!convert_binop((PyObject *)v, (PyObject *)w, &a, &b)) {
-                Py_INCREF(Py_NotImplemented);
-                return Py_NotImplemented;
-        }
-
-        z = k_mul(a, b);
-        /* Negate if exactly one of the inputs is negative. */
-        if (((a->ob_size ^ b->ob_size) < 0) && z)
-                z->ob_size = -(z->ob_size);
-        Py_DECREF(a);
-        Py_DECREF(b);
-        return (PyObject *)z;
+    PyLongObject *a, *b, *z;
+
+    if (!convert_binop((PyObject *)v, (PyObject *)w, &a, &b)) {
+        Py_INCREF(Py_NotImplemented);
+        return Py_NotImplemented;
+    }
+
+    z = k_mul(a, b);
+    /* Negate if exactly one of the inputs is negative. */
+    if (((a->ob_size ^ b->ob_size) < 0) && z)
+        z->ob_size = -(z->ob_size);
+    Py_DECREF(a);
+    Py_DECREF(b);
+    return (PyObject *)z;
 }
 
@@ -2568 +2996 @@
    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
+     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'
@@ -2585 +3013 @@
 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;
+         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;
 }
 
@@ -2630 +3058 @@
 long_div(PyObject *v, PyObject *w)
 {
-        PyLongObject *a, *b, *div;
-
-        CONVERT_BINOP(v, w, &a, &b);
-        if (l_divmod(a, b, &div, NULL) < 0)
-                div = NULL;
-        Py_DECREF(a);
-        Py_DECREF(b);
-        return (PyObject *)div;
+    PyLongObject *a, *b, *div;
+
+    CONVERT_BINOP(v, w, &a, &b);
+    if (l_divmod(a, b, &div, NULL) < 0)
+        div = NULL;
+    Py_DECREF(a);
+    Py_DECREF(b);
+    return (PyObject *)div;
 }
 
@@ -2643 +3071 @@
 long_classic_div(PyObject *v, PyObject *w)
 {
-        PyLongObject *a, *b, *div;
-
-        CONVERT_BINOP(v, w, &a, &b);
-        if (Py_DivisionWarningFlag &&
-            PyErr_Warn(PyExc_DeprecationWarning, "classic long division") < 0)
-                div = NULL;
-        else if (l_divmod(a, b, &div, NULL) < 0)
-                div = NULL;
-        Py_DECREF(a);
-        Py_DECREF(b);
-        return (PyObject *)div;
-}
+    PyLongObject *a, *b, *div;
+
+    CONVERT_BINOP(v, w, &a, &b);
+    if (Py_DivisionWarningFlag &&
+        PyErr_Warn(PyExc_DeprecationWarning, "classic long division") < 0)
+        div = NULL;
+    else if (l_divmod(a, b, &div, NULL) < 0)
+        div = NULL;
+    Py_DECREF(a);
+    Py_DECREF(b);
+    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;
-        double ad, bd;
-        int failed, aexp = -1, bexp = -1;
-
-        CONVERT_BINOP(v, w, &a, &b);
-        ad = _PyLong_AsScaledDouble((PyObject *)a, &aexp);
-        bd = _PyLong_AsScaledDouble((PyObject *)b, &bexp);
-        failed = (ad == -1.0 || bd == -1.0) && PyErr_Occurred();
-        Py_DECREF(a);
-        Py_DECREF(b);
-        if (failed)
-                return NULL;
-        /* 'aexp' and 'bexp' were initialized to -1 to silence gcc-4.0.x,
-           but should really be set correctly after sucessful calls to
-           _PyLong_AsScaledDouble() */
-        assert(aexp >= 0 && bexp >= 0);
-
-        if (bd == 0.0) {
-                PyErr_SetString(PyExc_ZeroDivisionError,
-                        "long division or modulo by zero");
-                return NULL;
-        }
-
-        /* True value is very close to ad/bd * 2**(PyLong_SHIFT*(aexp-bexp)) */
-        ad /= bd;       /* overflow/underflow impossible here */
-        aexp -= bexp;
-        if (aexp > INT_MAX / PyLong_SHIFT)
-                goto overflow;
-        else if (aexp < -(INT_MAX / PyLong_SHIFT))
-                return PyFloat_FromDouble(0.0); /* underflow to 0 */
-        errno = 0;
-        ad = ldexp(ad, aexp * PyLong_SHIFT);
-        if (Py_OVERFLOWED(ad)) /* ignore underflow to 0.0 */
-                goto overflow;
-        return PyFloat_FromDouble(ad);
-
-overflow:
-        PyErr_SetString(PyExc_OverflowError,
-                "long/long too large for a float");
-        return NULL;
-
+    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;
+
+    CONVERT_BINOP(v, w, &a, &b);
+
+    /*
+       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:
+    Py_DECREF(a);
+    Py_DECREF(b);
+    return PyFloat_FromDouble(negate ? -result : result);
+
+  underflow_or_zero:
+    Py_DECREF(a);
+    Py_DECREF(b);
+    return PyFloat_FromDouble(negate ? -0.0 : 0.0);
+
+  overflow:
+    PyErr_SetString(PyExc_OverflowError,
+                    "integer division result too large for a float");
+  error:
+    Py_DECREF(a);
+    Py_DECREF(b);
+    return NULL;
 }
 
@@ -2705 +3354 @@
 long_mod(PyObject *v, PyObject *w)
 {
-        PyLongObject *a, *b, *mod;
-
-        CONVERT_BINOP(v, w, &a, &b);
-
-        if (l_divmod(a, b, NULL, &mod) < 0)
-                mod = NULL;
-        Py_DECREF(a);
-        Py_DECREF(b);
-        return (PyObject *)mod;
+    PyLongObject *a, *b, *mod;
+
+    CONVERT_BINOP(v, w, &a, &b);
+
+    if (l_divmod(a, b, NULL, &mod) < 0)
+        mod = NULL;
+    Py_DECREF(a);
+    Py_DECREF(b);
+    return (PyObject *)mod;
 }
 
@@ -2719 +3368 @@
 long_divmod(PyObject *v, PyObject *w)
 {
-        PyLongObject *a, *b, *div, *mod;
-        PyObject *z;
-
-        CONVERT_BINOP(v, w, &a, &b);
-
-        if (l_divmod(a, b, &div, &mod) < 0) {
-                Py_DECREF(a);
-                Py_DECREF(b);
-                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);
-        }
-        Py_DECREF(a);
-        Py_DECREF(b);
-        return z;
+    PyLongObject *a, *b, *div, *mod;
+    PyObject *z;
+
+    CONVERT_BINOP(v, w, &a, &b);
+
+    if (l_divmod(a, b, &div, &mod) < 0) {
+        Py_DECREF(a);
+        Py_DECREF(b);
+        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);
+    }
+    Py_DECREF(a);
+    Py_DECREF(b);
+    return z;
 }
 
@@ -2747 +3396 @@
 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 */
-        CONVERT_BINOP(v, w, &a, &b);
-        if (PyLong_Check(x)) {
-                c = (PyLongObject *)x;
-                Py_INCREF(x);
-        }
-        else if (PyInt_Check(x)) {
-                c = (PyLongObject *)PyLong_FromLong(PyInt_AS_LONG(x));
-                if (c == NULL)
-                        goto Error;
-        }
-        else if (x == Py_None)
-                c = NULL;
-        else {
-                Py_DECREF(a);
-                Py_DECREF(b);
-                Py_INCREF(Py_NotImplemented);
-                return Py_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;
-                        c->ob_size = - c->ob_size;
-                }
-
-                /* 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)                                       \
-        if (c != NULL) {                                \
-                if (l_divmod(X, c, NULL, &temp) < 0)    \
-                        goto Error;                     \
-                Py_XDECREF(X);                          \
-                X = temp;                               \
-                temp = NULL;                            \
-        }
-
-        /* Multiply two values, then reduce the result:
-           result = X*Y % c.  If c is NULL, skip the mod. */
-#define MULT(X, Y, result)                              \
-{                                                       \
-        temp = (PyLongObject *)long_mul(X, Y);          \
-        if (temp == NULL)                               \
-                goto Error;                             \
-        Py_XDECREF(result);                             \
-        result = temp;                                  \
-        temp = NULL;                                    \
-        REDUCE(result)                                  \
-}
-
-        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 = 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;
+    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 */
+    CONVERT_BINOP(v, w, &a, &b);
+    if (PyLong_Check(x)) {
+        c = (PyLongObject *)x;
+        Py_INCREF(x);
+    }
+    else if (PyInt_Check(x)) {
+        c = (PyLongObject *)PyLong_FromLong(PyInt_AS_LONG(x));
+        if (c == NULL)
+            goto Error;
+    }
+    else if (x == Py_None)
+        c = NULL;
+    else {
+        Py_DECREF(a);
+        Py_DECREF(b);
+        Py_INCREF(Py_NotImplemented);
+        return Py_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;
+            c->ob_size = - c->ob_size;
+        }
+
+        /* if modulus == 1:
+               return 0 */
+        if ((Py_SIZE(c) == 1) && (c->ob_digit[0] == 1)) {
+            z = (PyLongObject *)PyLong_FromLong(0L);
+            goto Done;
+        }
+
+        /* Reduce base by modulus in some cases:
+           1. If base < 0.  Forcing the base non-negative makes things easier.
+           2. If base is obviously larger than the modulus.  The "small
+              exponent" case later can multiply directly by base repeatedly,
+              while the "large exponent" case multiplies directly by base 31
+              times.  It can be unboundedly faster to multiply by
+              base % modulus instead.
+           We could _always_ do this reduction, but l_divmod() isn't cheap,
+           so we only do it when it buys something. */
+        if (Py_SIZE(a) < 0 || Py_SIZE(a) > Py_SIZE(c)) {
+            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;
 }
 
@@ -2934 +3591 @@
 long_invert(PyLongObject *v)
 {
-        /* Implement ~x as -(x+1) */
-        PyLongObject *x;
-        PyLongObject *w;
-        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 *)x;
+    /* Implement ~x as -(x+1) */
+    PyLongObject *x;
+    PyLongObject *w;
+    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 *)x;
 }
 
@@ -2951 +3608 @@
 long_neg(PyLongObject *v)
 {
-        PyLongObject *z;
-        if (v->ob_size == 0 && PyLong_CheckExact(v)) {
-                /* -0 == 0 */
-                Py_INCREF(v);
-                return (PyObject *) v;
-        }
-        z = (PyLongObject *)_PyLong_Copy(v);
-        if (z != NULL)
-                z->ob_size = -(v->ob_size);
-        return (PyObject *)z;
+    PyLongObject *z;
+    if (v->ob_size == 0 && PyLong_CheckExact(v)) {
+        /* -0 == 0 */
+        Py_INCREF(v);
+        return (PyObject *) v;
+    }
+    z = (PyLongObject *)_PyLong_Copy(v);
+    if (z != NULL)
+        z->ob_size = -(v->ob_size);
+    return (PyObject *)z;
 }
 
@@ -2966 +3623 @@
 long_abs(PyLongObject *v)
 {
-        if (v->ob_size < 0)
-                return long_neg(v);
-        else
-                return long_long((PyObject *)v);
+    if (v->ob_size < 0)
+        return long_neg(v);
+    else
+        return long_long((PyObject *)v);
 }
 
@@ -2975 +3632 @@
 long_nonzero(PyLongObject *v)
 {
-        return ABS(Py_SIZE(v)) != 0;
+    return Py_SIZE(v) != 0;
 }
 
@@ -2981 +3638 @@
 long_rshift(PyLongObject *v, PyLongObject *w)
 {
-        PyLongObject *a, *b;
-        PyLongObject *z = NULL;
-        long shiftby;
-        Py_ssize_t newsize, wordshift, loshift, hishift, i, j;
-        digit lomask, himask;
-
-        CONVERT_BINOP((PyObject *)v, (PyObject *)w, &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_AsLong((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) {
-                        z = _PyLong_New(0);
-                        Py_DECREF(a);
-                        Py_DECREF(b);
-                        return (PyObject *)z;
-                }
-                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:
-        Py_DECREF(a);
-        Py_DECREF(b);
-        return (PyObject *) z;
+    PyLongObject *a, *b;
+    PyLongObject *z = NULL;
+    Py_ssize_t shiftby, newsize, wordshift, loshift, hishift, i, j;
+    digit lomask, himask;
+
+    CONVERT_BINOP((PyObject *)v, (PyObject *)w, &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) {
+            z = _PyLong_New(0);
+            Py_DECREF(a);
+            Py_DECREF(b);
+            return (PyObject *)z;
+        }
+        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:
+    Py_DECREF(a);
+    Py_DECREF(b);
+    return (PyObject *) z;
 
 }
@@ -3047 +3701 @@
 long_lshift(PyObject *v, PyObject *w)
 {
-        /* This version due to Tim Peters */
-        PyLongObject *a, *b;
-        PyLongObject *z = NULL;
-        long shiftby;
-        Py_ssize_t oldsize, newsize, wordshift, remshift, i, j;
-        twodigits accum;
-
-        CONVERT_BINOP(v, w, &a, &b);
-
-        shiftby = PyLong_AsLong((PyObject *)b);
-        if (shiftby == -1L && PyErr_Occurred())
-                goto lshift_error;
-        if (shiftby < 0) {
-                PyErr_SetString(PyExc_ValueError, "negative shift count");
-                goto lshift_error;
-        }
-        if ((long)(int)shiftby != shiftby) {
-                PyErr_SetString(PyExc_ValueError,
-                                "outrageous left shift count");
-                goto lshift_error;
-        }
-        /* wordshift, remshift = divmod(shiftby, PyLong_SHIFT) */
-        wordshift = (int)shiftby / PyLong_SHIFT;
-        remshift  = (int)shiftby - wordshift * PyLong_SHIFT;
-
-        oldsize = ABS(a->ob_size);
-        newsize = oldsize + wordshift;
-        if (remshift)
-                ++newsize;
-        z = _PyLong_New(newsize);
-        if (z == NULL)
-                goto lshift_error;
-        if (a->ob_size < 0)
-                z->ob_size = -(z->ob_size);
-        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:
-        Py_DECREF(a);
-        Py_DECREF(b);
-        return (PyObject *) z;
-}
-
+    /* This version due to Tim Peters */
+    PyLongObject *a, *b;
+    PyLongObject *z = NULL;
+    Py_ssize_t shiftby, oldsize, newsize, wordshift, remshift, i, j;
+    twodigits accum;
+
+    CONVERT_BINOP(v, w, &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(a->ob_size);
+    newsize = oldsize + wordshift;
+    if (remshift)
+        ++newsize;
+    z = _PyLong_New(newsize);
+    if (z == NULL)
+        goto lshift_error;
+    if (a->ob_size < 0)
+        z->ob_size = -(z->ob_size);
+    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:
+    Py_DECREF(a);
+    Py_DECREF(b);
+    return (PyObject *) 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 */
@@ -3105 +3769 @@
 static PyObject *
 long_bitwise(PyLongObject *a,
-             int op,  /* '&', '|', '^' */
-             PyLongObject *b)
-{
-        digit maska, maskb; /* 0 or PyLong_MASK */
-        int negz;
-        Py_ssize_t size_a, size_b, size_z;
-        PyLongObject *z;
-        int i;
-        digit diga, digb;
-        PyObject *v;
-
-        if (Py_SIZE(a) < 0) {
-                a = (PyLongObject *) long_invert(a);
-                if (a == NULL)
-                        return NULL;
-                maska = PyLong_MASK;
-        }
-        else {
-                Py_INCREF(a);
-                maska = 0;
-        }
-        if (Py_SIZE(b) < 0) {
-                b = (PyLongObject *) long_invert(b);
-                if (b == NULL) {
-                        Py_DECREF(a);
-                        return NULL;
-                }
-                maskb = PyLong_MASK;
-        }
-        else {
-                Py_INCREF(b);
-                maskb = 0;
-        }
-
-        negz = 0;
-        switch (op) {
-        case '^':
-                if (maska != maskb) {
-                        maska ^= PyLong_MASK;
-                        negz = -1;
-                }
-                break;
-        case '&':
-                if (maska && maskb) {
-                        op = '|';
-                        maska ^= PyLong_MASK;
-                        maskb ^= PyLong_MASK;
-                        negz = -1;
-                }
-                break;
-        case '|':
-                if (maska || maskb) {
-                        op = '&';
-                        maska ^= PyLong_MASK;
-                        maskb ^= PyLong_MASK;
-                        negz = -1;
-                }
-                break;
-        }
-
-        /* 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.  After the transformations above, op will be '&'
-           iff one of these cases applies, and mask will be non-0 for operands
-           whose length should be ignored.
-        */
-
-        size_a = Py_SIZE(a);
-        size_b = Py_SIZE(b);
-        size_z = op == '&'
-                ? (maska
-                   ? size_b
-                   : (maskb ? size_a : MIN(size_a, size_b)))
-                : MAX(size_a, size_b);
-        z = _PyLong_New(size_z);
-        if (z == NULL) {
-                Py_DECREF(a);
-                Py_DECREF(b);
-                return NULL;
-        }
-
-        for (i = 0; i < size_z; ++i) {
-                diga = (i < size_a ? a->ob_digit[i] : 0) ^ maska;
-                digb = (i < size_b ? b->ob_digit[i] : 0) ^ maskb;
-                switch (op) {
-                case '&': z->ob_digit[i] = diga & digb; break;
-                case '|': z->ob_digit[i] = diga | digb; break;
-                case '^': z->ob_digit[i] = diga ^ digb; break;
-                }
-        }
-
-        Py_DECREF(a);
-        Py_DECREF(b);
-        z = long_normalize(z);
-        if (negz == 0)
-                return (PyObject *) z;
-        v = long_invert(z);
-        Py_DECREF(z);
-        return v;
+             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 *)long_normalize(z);
 }
 
@@ -3212 +3893 @@
 long_and(PyObject *v, PyObject *w)
 {
-        PyLongObject *a, *b;
-        PyObject *c;
-        CONVERT_BINOP(v, w, &a, &b);
-        c = long_bitwise(a, '&', b);
-        Py_DECREF(a);
-        Py_DECREF(b);
-        return c;
+    PyLongObject *a, *b;
+    PyObject *c;
+    CONVERT_BINOP(v, w, &a, &b);
+    c = long_bitwise(a, '&', b);
+    Py_DECREF(a);
+    Py_DECREF(b);
+    return c;
 }
 
@@ -3224 +3905 @@
 long_xor(PyObject *v, PyObject *w)
 {
-        PyLongObject *a, *b;
-        PyObject *c;
-        CONVERT_BINOP(v, w, &a, &b);
-        c = long_bitwise(a, '^', b);
-        Py_DECREF(a);
-        Py_DECREF(b);
-        return c;
+    PyLongObject *a, *b;
+    PyObject *c;
+    CONVERT_BINOP(v, w, &a, &b);
+    c = long_bitwise(a, '^', b);
+    Py_DECREF(a);
+    Py_DECREF(b);
+    return c;
 }
 
@@ -3236 +3917 @@
 long_or(PyObject *v, PyObject *w)
 {
-        PyLongObject *a, *b;
-        PyObject *c;
-        CONVERT_BINOP(v, w, &a, &b);
-        c = long_bitwise(a, '|', b);
-        Py_DECREF(a);
-        Py_DECREF(b);
-        return c;
+    PyLongObject *a, *b;
+    PyObject *c;
+    CONVERT_BINOP(v, w, &a, &b);
+    c = long_bitwise(a, '|', b);
+    Py_DECREF(a);
+    Py_DECREF(b);
+    return c;
 }
 
@@ -3248 +3929 @@
 long_coerce(PyObject **pv, PyObject **pw)
 {
-        if (PyInt_Check(*pw)) {
-                *pw = PyLong_FromLong(PyInt_AS_LONG(*pw));
-                if (*pw == NULL)
-                        return -1;
-                Py_INCREF(*pv);
-                return 0;
-        }
-        else if (PyLong_Check(*pw)) {
-                Py_INCREF(*pv);
-                Py_INCREF(*pw);
-                return 0;
-        }
-        return 1; /* Can't do it */
+    if (PyInt_Check(*pw)) {
+        *pw = PyLong_FromLong(PyInt_AS_LONG(*pw));
+        if (*pw == NULL)
+            return -1;
+        Py_INCREF(*pv);
+        return 0;
+    }
+    else if (PyLong_Check(*pw)) {
+        Py_INCREF(*pv);
+        Py_INCREF(*pw);
+        return 0;
+    }
+    return 1; /* Can't do it */
 }
 
@@ -3266 +3947 @@
 long_long(PyObject *v)
 {
-        if (PyLong_CheckExact(v))
-                Py_INCREF(v);
-        else
-                v = _PyLong_Copy((PyLongObject *)v);
-        return v;
+    if (PyLong_CheckExact(v))
+        Py_INCREF(v);
+    else
+        v = _PyLong_Copy((PyLongObject *)v);
+    return v;
 }
 
@@ -3276 +3957 @@
 long_int(PyObject *v)
 {
-        long x;
-        x = PyLong_AsLong(v);
-        if (PyErr_Occurred()) {
-                if (PyErr_ExceptionMatches(PyExc_OverflowError)) {
-                                PyErr_Clear();
-                                if (PyLong_CheckExact(v)) {
-                                        Py_INCREF(v);
-                                        return v;
-                                }
-                                else
-                                        return _PyLong_Copy((PyLongObject *)v);
-                }
-                else
-                        return NULL;
-        }
-        return PyInt_FromLong(x);
+    long x;
+    x = PyLong_AsLong(v);
+    if (PyErr_Occurred()) {
+        if (PyErr_ExceptionMatches(PyExc_OverflowError)) {
+            PyErr_Clear();
+            if (PyLong_CheckExact(v)) {
+                Py_INCREF(v);
+                return v;
+            }
+            else
+                return _PyLong_Copy((PyLongObject *)v);
+        }
+        else
+            return NULL;
+    }
+    return PyInt_FromLong(x);
 }
 
@@ -3297 +3978 @@
 long_float(PyObject *v)
 {
-        double result;
-        result = PyLong_AsDouble(v);
-        if (result == -1.0 && PyErr_Occurred())
-                return NULL;
-        return PyFloat_FromDouble(result);
+    double result;
+    result = PyLong_AsDouble(v);
+    if (result == -1.0 && PyErr_Occurred())
+        return NULL;
+    return PyFloat_FromDouble(result);
 }
 
@@ -3307 +3988 @@
 long_oct(PyObject *v)
 {
-        return _PyLong_Format(v, 8, 1, 0);
+    return _PyLong_Format(v, 8, 1, 0);
 }
 
@@ -3313 +3994 @@
 long_hex(PyObject *v)
 {
-        return _PyLong_Format(v, 16, 1, 0);
+    return _PyLong_Format(v, 16, 1, 0);
 }
 
@@ -3322 +4003 @@
 long_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
 {
-        PyObject *x = NULL;
-        int base = -909;                     /* unlikely! */
-        static char *kwlist[] = {"x", "base", 0};
-
-        if (type != &PyLong_Type)
-                return long_subtype_new(type, args, kwds); /* Wimp out */
-        if (!PyArg_ParseTupleAndKeywords(args, kwds, "|Oi:long", kwlist,
-                                         &x, &base))
-                return NULL;
-        if (x == NULL)
-                return PyLong_FromLong(0L);
-        if (base == -909)
-                return PyNumber_Long(x);
-        else if (PyString_Check(x)) {
-                /* Since PyLong_FromString doesn't have a length parameter,
-                 * check here for possible NULs in the string. */
-                char *string = PyString_AS_STRING(x);
-                if (strlen(string) != PyString_Size(x)) {
-                        /* create a repr() of the input string,
-                         * just like PyLong_FromString does. */
-                        PyObject *srepr;
-                        srepr = PyObject_Repr(x);
-                        if (srepr == NULL)
-                                return NULL;
-                        PyErr_Format(PyExc_ValueError,
-                             "invalid literal for long() with base %d: %s",
-                             base, PyString_AS_STRING(srepr));
-                        Py_DECREF(srepr);
-                        return NULL;
-                }
-                return PyLong_FromString(PyString_AS_STRING(x), NULL, base);
-        }
+    PyObject *x = NULL;
+    int base = -909;                         /* unlikely! */
+    static char *kwlist[] = {"x", "base", 0};
+
+    if (type != &PyLong_Type)
+        return long_subtype_new(type, args, kwds); /* Wimp out */
+    if (!PyArg_ParseTupleAndKeywords(args, kwds, "|Oi:long", kwlist,
+                                     &x, &base))
+        return NULL;
+    if (x == NULL) {
+        if (base != -909) {
+            PyErr_SetString(PyExc_TypeError,
+                            "long() missing string argument");
+            return NULL;
+        }
+        return PyLong_FromLong(0L);
+    }
+    if (base == -909)
+        return PyNumber_Long(x);
+    else if (PyString_Check(x)) {
+        /* Since PyLong_FromString doesn't have a length parameter,
+         * check here for possible NULs in the string. */
+        char *string = PyString_AS_STRING(x);
+        if (strlen(string) != (size_t)PyString_Size(x)) {
+            /* create a repr() of the input string,
+             * just like PyLong_FromString does. */
+            PyObject *srepr;
+            srepr = PyObject_Repr(x);
+            if (srepr == NULL)
+                return NULL;
+            PyErr_Format(PyExc_ValueError,
+                         "invalid literal for long() with base %d: %s",
+                         base, PyString_AS_STRING(srepr));
+            Py_DECREF(srepr);
+            return NULL;
+        }
+        return PyLong_FromString(PyString_AS_STRING(x), NULL, base);
+    }
 #ifdef Py_USING_UNICODE
-        else if (PyUnicode_Check(x))
-                return PyLong_FromUnicode(PyUnicode_AS_UNICODE(x),
-                                          PyUnicode_GET_SIZE(x),
-                                          base);
+    else if (PyUnicode_Check(x))
+        return PyLong_FromUnicode(PyUnicode_AS_UNICODE(x),
+                                  PyUnicode_GET_SIZE(x),
+                                  base);
 #endif
-        else {
-                PyErr_SetString(PyExc_TypeError,
-                        "long() can't convert non-string with explicit base");
-                return NULL;
-        }
+    else {
+        PyErr_SetString(PyExc_TypeError,
+                        "long() can't convert non-string with explicit base");
+        return NULL;
+    }
 }
 
@@ -3375 +4062 @@
 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;
+    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;
 }
 
@@ -3402 +4089 @@
 long_getnewargs(PyLongObject *v)
 {
-        return Py_BuildValue("(N)", _PyLong_Copy(v));
+    return Py_BuildValue("(N)", _PyLong_Copy(v));
 }
 
 static PyObject *
-long_getN(PyLongObject *v, void *context) {
-        return PyLong_FromLong((Py_intptr_t)context);
+long_get0(PyLongObject *v, void *context) {
+    return PyLong_FromLong(0L);
+}
+
+static PyObject *
+long_get1(PyLongObject *v, void *context) {
+    return PyLong_FromLong(1L);
 }
 
@@ -3413 +4105 @@
 long__format__(PyObject *self, PyObject *args)
 {
-        PyObject *format_spec;
-
-        if (!PyArg_ParseTuple(args, "O:__format__", &format_spec))
-                return NULL;
-        if (PyBytes_Check(format_spec))
-                return _PyLong_FormatAdvanced(self,
-                                              PyBytes_AS_STRING(format_spec),
-                                              PyBytes_GET_SIZE(format_spec));
-        if (PyUnicode_Check(format_spec)) {
-                /* Convert format_spec to a str */
-                PyObject *result;
-                PyObject *str_spec = PyObject_Str(format_spec);
-
-                if (str_spec == NULL)
-                        return NULL;
-
-                result = _PyLong_FormatAdvanced(self,
-                                                PyBytes_AS_STRING(str_spec),
-                                                PyBytes_GET_SIZE(str_spec));
-
-                Py_DECREF(str_spec);
-                return result;
-        }
-        PyErr_SetString(PyExc_TypeError, "__format__ requires str or unicode");
-        return NULL;
+    PyObject *format_spec;
+
+    if (!PyArg_ParseTuple(args, "O:__format__", &format_spec))
+        return NULL;
+    if (PyBytes_Check(format_spec))
+        return _PyLong_FormatAdvanced(self,
+                                      PyBytes_AS_STRING(format_spec),
+                                      PyBytes_GET_SIZE(format_spec));
+    if (PyUnicode_Check(format_spec)) {
+        /* Convert format_spec to a str */
+        PyObject *result;
+        PyObject *str_spec = PyObject_Str(format_spec);
+
+        if (str_spec == NULL)
+            return NULL;
+
+        result = _PyLong_FormatAdvanced(self,
+                                        PyBytes_AS_STRING(str_spec),
+                                        PyBytes_GET_SIZE(str_spec));
+
+        Py_DECREF(str_spec);
+        return result;
+    }
+    PyErr_SetString(PyExc_TypeError, "__format__ requires str or unicode");
+    return NULL;
 }
 
@@ -3443 +4135 @@
 long_sizeof(PyLongObject *v)
 {
-        Py_ssize_t res;
-
-        res = v->ob_type->tp_basicsize;
-        if (v->ob_size != 0)
-                res += abs(v->ob_size) * sizeof(digit);
-        return PyInt_FromSsize_t(res);
-}
+    Py_ssize_t res;
+
+    res = v->ob_type->tp_basicsize + ABS(Py_SIZE(v))*sizeof(digit);
+    return PyInt_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 PyInt_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 PyInt_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,
+"long.bit_length() -> int or long\n\
+\n\
+Number of bits necessary to represent self in binary.\n\
+>>> bin(37L)\n\
+'0b100101'\n\
+>>> (37L).bit_length()\n\
+6");
 
 #if 0
@@ -3455 +4209 @@
 long_is_finite(PyObject *v)
 {
-        Py_RETURN_TRUE;
+    Py_RETURN_TRUE;
 }
 #endif
 
 static PyMethodDef long_methods[] = {
-        {"conjugate",   (PyCFunction)long_long, METH_NOARGS,
-         "Returns self, the complex conjugate of any long."},
+    {"conjugate",       (PyCFunction)long_long, METH_NOARGS,
+     "Returns self, the complex conjugate of any long."},
+    {"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."},
+    {"is_finite",       (PyCFunction)long_is_finite,    METH_NOARGS,
+     "Returns always True."},
 #endif
-        {"__trunc__",   (PyCFunction)long_long, METH_NOARGS,
-         "Truncating an Integral returns itself."},
-        {"__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 */
+    {"__trunc__",       (PyCFunction)long_long, METH_NOARGS,
+     "Truncating an Integral returns itself."},
+    {"__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", 
+    {"real",
      (getter)long_long, (setter)NULL,
      "the real part of a complex number",
      NULL},
-    {"imag", 
-     (getter)long_getN, (setter)NULL,
+    {"imag",
+     (getter)long_get0, (setter)NULL,
      "the imaginary part of a complex number",
-     (void*)0},
-    {"numerator", 
+     NULL},
+    {"numerator",
      (getter)long_long, (setter)NULL,
      "the numerator of a rational number in lowest terms",
      NULL},
-    {"denominator", 
-     (getter)long_getN, (setter)NULL,
+    {"denominator",
+     (getter)long_get1, (setter)NULL,
      "the denominator of a rational number in lowest terms",
-     (void*)1},
+     NULL},
     {NULL}  /* Sentinel */
 };
 
 PyDoc_STRVAR(long_doc,
-"long(x[, base]) -> integer\n\
+"long(x=0) -> long\n\
+long(x, base=10) -> long\n\
 \n\
-Convert a string or number to a long 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.");
+Convert a number or string to a long integer, or return 0L if no arguments\n\
+are given.  If x is floating point, the conversion truncates towards zero.\n\
+\n\
+If x is not a number or if base is given, then x must be a string or\n\
+Unicode object representing an integer literal in the given base.  The\n\
+literal can be preceded by '+' or '-' and be surrounded by whitespace.\n\
+The base defaults to 10.  Valid bases are 0 and 2-36.  Base 0 means to\n\
+interpret the base from the string as an integer literal.\n\
+>>> int('0b100', base=0)\n\
+4L");
 
 static PyNumberMethods long_as_number = {
-        (binaryfunc)    long_add,       /*nb_add*/
-        (binaryfunc)    long_sub,       /*nb_subtract*/
-        (binaryfunc)    long_mul,       /*nb_multiply*/
-                        long_classic_div, /*nb_divide*/
-                        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_nonzero,   /*tp_nonzero*/
-        (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_coerce,    /*nb_coerce*/
-                        long_int,       /*nb_int*/
-                        long_long,      /*nb_long*/
-                        long_float,     /*nb_float*/
-                        long_oct,       /*nb_oct*/
-                        long_hex,       /*nb_hex*/
-        0,                              /* nb_inplace_add */
-        0,                              /* nb_inplace_subtract */
-        0,                              /* nb_inplace_multiply */
-        0,                              /* nb_inplace_divide */
-        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 */
+    (binaryfunc)long_add,       /*nb_add*/
+    (binaryfunc)long_sub,       /*nb_subtract*/
+    (binaryfunc)long_mul,       /*nb_multiply*/
+    long_classic_div,           /*nb_divide*/
+    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_nonzero,      /*tp_nonzero*/
+    (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_coerce,                /*nb_coerce*/
+    long_int,                   /*nb_int*/
+    long_long,                  /*nb_long*/
+    long_float,                 /*nb_float*/
+    long_oct,                   /*nb_oct*/
+    long_hex,                   /*nb_hex*/
+    0,                          /* nb_inplace_add */
+    0,                          /* nb_inplace_subtract */
+    0,                          /* nb_inplace_multiply */
+    0,                          /* nb_inplace_divide */
+    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 = {
-        PyObject_HEAD_INIT(&PyType_Type)
-        0,                                      /* ob_size */
-        "long",                                 /* tp_name */
-        sizeof(PyLongObject) - sizeof(digit),   /* tp_basicsize */
-        sizeof(digit),                          /* tp_itemsize */
-        long_dealloc,                           /* tp_dealloc */
-        0,                                      /* tp_print */
-        0,                                      /* tp_getattr */
-        0,                                      /* tp_setattr */
-        (cmpfunc)long_compare,                  /* tp_compare */
-        long_repr,                              /* 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_str,                               /* tp_str */
-        PyObject_GenericGetAttr,                /* tp_getattro */
-        0,                                      /* tp_setattro */
-        0,                                      /* tp_as_buffer */
-        Py_TPFLAGS_DEFAULT | Py_TPFLAGS_CHECKTYPES |
-                Py_TPFLAGS_BASETYPE | Py_TPFLAGS_LONG_SUBCLASS, /* tp_flags */
-        long_doc,                               /* tp_doc */
-        0,                                      /* tp_traverse */
-        0,                                      /* tp_clear */
-        0,                                      /* 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 */
+    PyObject_HEAD_INIT(&PyType_Type)
+    0,                                          /* ob_size */
+    "long",                                     /* 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 */
+    (cmpfunc)long_compare,                      /* tp_compare */
+    long_repr,                                  /* 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_str,                                   /* tp_str */
+    PyObject_GenericGetAttr,                    /* tp_getattro */
+    0,                                          /* tp_setattro */
+    0,                                          /* tp_as_buffer */
+    Py_TPFLAGS_DEFAULT | Py_TPFLAGS_CHECKTYPES |
+        Py_TPFLAGS_BASETYPE | Py_TPFLAGS_LONG_SUBCLASS, /* tp_flags */
+    long_doc,                                   /* tp_doc */
+    0,                                          /* tp_traverse */
+    0,                                          /* tp_clear */
+    0,                                          /* 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 Long_InfoType;
+
+PyDoc_STRVAR(long_info__doc__,
+"sys.long_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 long_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 long_info_desc = {
+    "sys.long_info",   /* name */
+    long_info__doc__,  /* doc */
+    long_info_fields,  /* fields */
+    2                  /* number of fields */
+};
+
+PyObject *
+PyLong_GetInfo(void)
+{
+    PyObject* long_info;
+    int field = 0;
+    long_info = PyStructSequence_New(&Long_InfoType);
+    if (long_info == NULL)
+        return NULL;
+    PyStructSequence_SET_ITEM(long_info, field++,
+                              PyInt_FromLong(PyLong_SHIFT));
+    PyStructSequence_SET_ITEM(long_info, field++,
+                              PyInt_FromLong(sizeof(digit)));
+    if (PyErr_Occurred()) {
+        Py_CLEAR(long_info);
+        return NULL;
+    }
+    return long_info;
+}
+
+int
+_PyLong_Init(void)
+{
+    /* initialize long_info */
+    if (Long_InfoType.tp_name == 0)
+        PyStructSequence_InitType(&Long_InfoType, &long_info_desc);
+    return 1;
+}