gh-123497: New limit for Python integers on 64-bit platforms (GH-123724)

Instead of be limited just by the size of addressable memory (2**63
bytes), Python integers are now also limited by the number of bits, so
the number of bit now always fit in a 64-bit integer.

Both limits are much larger than what might be available in practice,
so it doesn't affect users.

_PyLong_NumBits() and _PyLong_Frexp() are now always successful.

2 files changed, 71 insertions, 136 deletions

diff --git a/Objects/floatobject.c b/Objects/floatobject.c
index dc3d8a3..a48a210 100644
--- a/Objects/floatobject.c
+++ b/Objects/floatobject.c
@@ -406,19 +406,16 @@ float_richcompare(PyObject *v, PyObject *w, int op)
         }
         /* The signs are the same. */
         /* Convert w to a double if it fits.  In particular, 0 fits. */
-        uint64_t nbits64 = _PyLong_NumBits(w);
-        if (nbits64 > (unsigned int)DBL_MAX_EXP) {
+        int64_t nbits64 = _PyLong_NumBits(w);
+        assert(nbits64 >= 0);
+        assert(!PyErr_Occurred());
+        if (nbits64 > DBL_MAX_EXP) {
             /* This Python integer is larger than any finite C double.
              * Replace with little doubles
              * that give the same outcome -- w is so large that
              * its magnitude must exceed the magnitude of any
              * finite float.
              */
-            if (nbits64 == (uint64_t)-1 && PyErr_Occurred()) {
-                /* This Python integer is so large that uint64_t isn't
-                 * big enough to hold the # of bits. */
-                PyErr_Clear();
-            }
             i = (double)vsign;
             assert(wsign != 0);
             j = wsign * 2.0;
diff --git a/Objects/longobject.c b/Objects/longobject.c
index d34c8b6..9beb588 100644
--- a/Objects/longobject.c
+++ b/Objects/longobject.c
@@ -133,8 +133,16 @@ long_normalize(PyLongObject *v)
 /* Allocate a new int object with size digits.
    Return NULL and set exception if we run out of memory. */
 
-#define MAX_LONG_DIGITS \
+#if SIZEOF_SIZE_T < 8
+# define MAX_LONG_DIGITS \
     ((PY_SSIZE_T_MAX - offsetof(PyLongObject, long_value.ob_digit))/sizeof(digit))
+#else
+/* Guarantee that the number of bits fits in int64_t.
+   This is more than an exbibyte, that is more than many of modern
+   architectures support in principle.
+   -1 is added to avoid overflow in _PyLong_Frexp(). */
+# define MAX_LONG_DIGITS ((INT64_MAX-1) / PyLong_SHIFT)
+#endif
 
 PyLongObject *
 _PyLong_New(Py_ssize_t size)
@@ -804,11 +812,11 @@ bit_length_digit(digit x)
     return _Py_bit_length((unsigned long)x);
 }
 
-uint64_t
+int64_t
 _PyLong_NumBits(PyObject *vv)
 {
     PyLongObject *v = (PyLongObject *)vv;
-    uint64_t result = 0;
+    int64_t result = 0;
     Py_ssize_t ndigits;
     int msd_bits;
 
@@ -818,21 +826,12 @@ _PyLong_NumBits(PyObject *vv)
     assert(ndigits == 0 || v->long_value.ob_digit[ndigits - 1] != 0);
     if (ndigits > 0) {
         digit msd = v->long_value.ob_digit[ndigits - 1];
-        if ((uint64_t)(ndigits - 1) > UINT64_MAX / (uint64_t)PyLong_SHIFT)
-            goto Overflow;
-        result = (uint64_t)(ndigits - 1) * (uint64_t)PyLong_SHIFT;
+        assert(ndigits <= INT64_MAX / PyLong_SHIFT);
+        result = (int64_t)(ndigits - 1) * PyLong_SHIFT;
         msd_bits = bit_length_digit(msd);
-        if (UINT64_MAX - msd_bits < result)
-            goto Overflow;
         result += msd_bits;
     }
     return result;
-
-  Overflow:
-    /* Very unlikely. Such integer would require more than 2 exbibytes of RAM. */
-    PyErr_SetString(PyExc_OverflowError, "int has too many bits "
-                    "to express in a 64-bit integer");
-    return (uint64_t)-1;
 }
 
 PyObject *
@@ -1247,15 +1246,12 @@ PyLong_AsNativeBytes(PyObject* vv, void* buffer, Py_ssize_t n, int flags)
 
         /* Calculates the number of bits required for the *absolute* value
          * of v. This does not take sign into account, only magnitude. */
-        uint64_t nb = _PyLong_NumBits((PyObject *)v);
-        if (nb == (uint64_t)-1) {
-            res = -1;
-        } else {
-            /* Normally this would be((nb - 1) / 8) + 1 to avoid rounding up
-             * multiples of 8 to the next byte, but we add an implied bit for
-             * the sign and it cancels out. */
-            res = (Py_ssize_t)(nb / 8) + 1;
-        }
+        int64_t nb = _PyLong_NumBits((PyObject *)v);
+        assert(nb >= 0);
+        /* Normally this would be ((nb - 1) / 8) + 1 to avoid rounding up
+         * multiples of 8 to the next byte, but we add an implied bit for
+         * the sign and it cancels out. */
+        res = (Py_ssize_t)(nb / 8) + 1;
 
         /* Two edge cases exist that are best handled after extracting the
          * bits. These may result in us reporting overflow when the value
@@ -3415,7 +3411,8 @@ x_divrem(PyLongObject *v1, PyLongObject *w1, PyLongObject **prem)
 double
 _PyLong_Frexp(PyLongObject *a, int64_t *e)
 {
-    Py_ssize_t a_size, shift_digits, shift_bits, x_size;
+    Py_ssize_t a_size, shift_digits, x_size;
+    int shift_bits;
     int64_t a_bits;
     /* See below for why x_digits is always large enough. */
     digit rem;
@@ -3432,14 +3429,7 @@ _PyLong_Frexp(PyLongObject *a, int64_t *e)
         *e = 0;
         return 0.0;
     }
-    int msd_bits = bit_length_digit(a->long_value.ob_digit[a_size-1]);
-    /* The following is an overflow-free version of the check
-       "if ((a_size - 1) * PyLong_SHIFT + msd_bits > PY_SSIZE_T_MAX) ..." */
-    if (a_size >= (INT64_MAX - 1) / PyLong_SHIFT + 1 &&
-        (a_size > (INT64_MAX - 1) / PyLong_SHIFT + 1 ||
-         msd_bits > (INT64_MAX - 1) % PyLong_SHIFT + 1))
-        goto overflow;
-    a_bits = (int64_t)(a_size - 1) * PyLong_SHIFT + msd_bits;
+    a_bits = _PyLong_NumBits((PyObject *)a);
 
     /* 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).
@@ -3468,18 +3458,18 @@ _PyLong_Frexp(PyLongObject *a, int64_t *e)
     */
     if (a_bits <= DBL_MANT_DIG + 2) {
         shift_digits = (DBL_MANT_DIG + 2 - (Py_ssize_t)a_bits) / PyLong_SHIFT;
-        shift_bits = (DBL_MANT_DIG + 2 - (Py_ssize_t)a_bits) % PyLong_SHIFT;
+        shift_bits = (DBL_MANT_DIG + 2 - (int)a_bits) % PyLong_SHIFT;
         x_size = shift_digits;
         rem = v_lshift(x_digits + x_size, a->long_value.ob_digit, a_size,
-                       (int)shift_bits);
+                       shift_bits);
         x_size += a_size;
         x_digits[x_size++] = rem;
     }
     else {
         shift_digits = (Py_ssize_t)((a_bits - DBL_MANT_DIG - 2) / PyLong_SHIFT);
-        shift_bits = (Py_ssize_t)((a_bits - DBL_MANT_DIG - 2) % PyLong_SHIFT);
+        shift_bits = (int)((a_bits - DBL_MANT_DIG - 2) % PyLong_SHIFT);
         rem = v_rshift(x_digits, a->long_value.ob_digit + shift_digits,
-                       a_size - shift_digits, (int)shift_bits);
+                       a_size - shift_digits, 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
@@ -3505,21 +3495,13 @@ _PyLong_Frexp(PyLongObject *a, int64_t *e)
     /* Rescale;  make correction if result is 1.0. */
     dx /= 4.0 * EXP2_DBL_MANT_DIG;
     if (dx == 1.0) {
-        if (a_bits == INT64_MAX)
-            goto overflow;
+        assert(a_bits < INT64_MAX);
         dx = 0.5;
         a_bits += 1;
     }
 
     *e = a_bits;
     return _PyLong_IsNegative(a) ? -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 an int object.  Rounds to the nearest double,
@@ -3547,7 +3529,9 @@ PyLong_AsDouble(PyObject *v)
         return (double)medium_value((PyLongObject *)v);
     }
     x = _PyLong_Frexp((PyLongObject *)v, &exponent);
-    if ((x == -1.0 && PyErr_Occurred()) || exponent > DBL_MAX_EXP) {
+    assert(exponent >= 0);
+    assert(!PyErr_Occurred());
+    if (exponent > DBL_MAX_EXP) {
         PyErr_SetString(PyExc_OverflowError,
                         "int too large to convert to float");
         return -1.0;
@@ -5217,39 +5201,6 @@ long_bool(PyLongObject *v)
     return !_PyLong_IsZero(v);
 }
 
-/* wordshift, remshift = divmod(shiftby, PyLong_SHIFT) */
-static int
-divmod_shift(PyObject *shiftby, Py_ssize_t *wordshift, digit *remshift)
-{
-    assert(PyLong_Check(shiftby));
-    assert(!_PyLong_IsNegative((PyLongObject *)shiftby));
-    Py_ssize_t lshiftby = PyLong_AsSsize_t((PyObject *)shiftby);
-    if (lshiftby >= 0) {
-        *wordshift = lshiftby / PyLong_SHIFT;
-        *remshift = lshiftby % PyLong_SHIFT;
-        return 0;
-    }
-    /* PyLong_Check(shiftby) is true and shiftby is not negative, so it must
-       be that PyLong_AsSsize_t raised an OverflowError. */
-    assert(PyErr_ExceptionMatches(PyExc_OverflowError));
-    PyErr_Clear();
-    PyLongObject *wordshift_obj = divrem1((PyLongObject *)shiftby, PyLong_SHIFT, remshift);
-    if (wordshift_obj == NULL) {
-        return -1;
-    }
-    *wordshift = PyLong_AsSsize_t((PyObject *)wordshift_obj);
-    Py_DECREF(wordshift_obj);
-    if (*wordshift >= 0 && *wordshift < PY_SSIZE_T_MAX / (Py_ssize_t)sizeof(digit)) {
-        return 0;
-    }
-    PyErr_Clear();
-    /* Clip the value.  With such large wordshift the right shift
-       returns 0 and the left shift raises an error in _PyLong_New(). */
-    *wordshift = PY_SSIZE_T_MAX / sizeof(digit);
-    *remshift = 0;
-    return 0;
-}
-
 /* Inner function for both long_rshift and _PyLong_Rshift, shifting an
    integer right by PyLong_SHIFT*wordshift + remshift bits.
    wordshift should be nonnegative. */
@@ -5343,8 +5294,7 @@ long_rshift1(PyLongObject *a, Py_ssize_t wordshift, digit remshift)
 static PyObject *
 long_rshift(PyObject *a, PyObject *b)
 {
-    Py_ssize_t wordshift;
-    digit remshift;
+    int64_t shiftby;
 
     CHECK_BINOP(a, b);
 
@@ -5355,24 +5305,35 @@ long_rshift(PyObject *a, PyObject *b)
     if (_PyLong_IsZero((PyLongObject *)a)) {
         return PyLong_FromLong(0);
     }
-    if (divmod_shift(b, &wordshift, &remshift) < 0)
-        return NULL;
-    return long_rshift1((PyLongObject *)a, wordshift, remshift);
+    if (PyLong_AsInt64(b, &shiftby) < 0) {
+        if (!PyErr_ExceptionMatches(PyExc_OverflowError)) {
+            return NULL;
+        }
+        PyErr_Clear();
+        if (_PyLong_IsNegative((PyLongObject *)a)) {
+            return PyLong_FromLong(-1);
+        }
+        else {
+            return PyLong_FromLong(0);
+        }
+    }
+    return _PyLong_Rshift(a, shiftby);
 }
 
 /* Return a >> shiftby. */
 PyObject *
-_PyLong_Rshift(PyObject *a, uint64_t shiftby)
+_PyLong_Rshift(PyObject *a, int64_t shiftby)
 {
     Py_ssize_t wordshift;
     digit remshift;
 
     assert(PyLong_Check(a));
+    assert(shiftby >= 0);
     if (_PyLong_IsZero((PyLongObject *)a)) {
         return PyLong_FromLong(0);
     }
-#if PY_SSIZE_T_MAX <= UINT64_MAX / PyLong_SHIFT
-    if (shiftby > (uint64_t)PY_SSIZE_T_MAX * PyLong_SHIFT) {
+#if PY_SSIZE_T_MAX <= INT64_MAX / PyLong_SHIFT
+    if (shiftby > (int64_t)PY_SSIZE_T_MAX * PyLong_SHIFT) {
         if (_PyLong_IsNegative((PyLongObject *)a)) {
             return PyLong_FromLong(-1);
         }
@@ -5430,8 +5391,7 @@ long_lshift1(PyLongObject *a, Py_ssize_t wordshift, digit remshift)
 static PyObject *
 long_lshift(PyObject *a, PyObject *b)
 {
-    Py_ssize_t wordshift;
-    digit remshift;
+    int64_t shiftby;
 
     CHECK_BINOP(a, b);
 
@@ -5442,24 +5402,30 @@ long_lshift(PyObject *a, PyObject *b)
     if (_PyLong_IsZero((PyLongObject *)a)) {
         return PyLong_FromLong(0);
     }
-    if (divmod_shift(b, &wordshift, &remshift) < 0)
+    if (PyLong_AsInt64(b, &shiftby) < 0) {
+        if (PyErr_ExceptionMatches(PyExc_OverflowError)) {
+            PyErr_SetString(PyExc_OverflowError,
+                            "too many digits in integer");
+        }
         return NULL;
-    return long_lshift1((PyLongObject *)a, wordshift, remshift);
+    }
+    return _PyLong_Lshift(a, shiftby);
 }
 
 /* Return a << shiftby. */
 PyObject *
-_PyLong_Lshift(PyObject *a, uint64_t shiftby)
+_PyLong_Lshift(PyObject *a, int64_t shiftby)
 {
     Py_ssize_t wordshift;
     digit remshift;
 
     assert(PyLong_Check(a));
+    assert(shiftby >= 0);
     if (_PyLong_IsZero((PyLongObject *)a)) {
         return PyLong_FromLong(0);
     }
-#if PY_SSIZE_T_MAX <= UINT64_MAX / PyLong_SHIFT
-    if (shiftby > (uint64_t)PY_SSIZE_T_MAX * PyLong_SHIFT) {
+#if PY_SSIZE_T_MAX <= INT64_MAX / PyLong_SHIFT
+    if (shiftby > (int64_t)PY_SSIZE_T_MAX * PyLong_SHIFT) {
         PyErr_SetString(PyExc_OverflowError,
                         "too many digits in integer");
         return NULL;
@@ -6213,11 +6179,10 @@ static PyObject *
 int_bit_length_impl(PyObject *self)
 /*[clinic end generated code: output=fc1977c9353d6a59 input=e4eb7a587e849a32]*/
 {
-    uint64_t nbits = _PyLong_NumBits(self);
-    if (nbits == (uint64_t)-1) {
-        return NULL;
-    }
-    return PyLong_FromUnsignedLongLong(nbits);
+    int64_t nbits = _PyLong_NumBits(self);
+    assert(nbits >= 0);
+    assert(!PyErr_Occurred());
+    return PyLong_FromInt64(nbits);
 }
 
 static int
@@ -6251,40 +6216,13 @@ int_bit_count_impl(PyObject *self)
 
     PyLongObject *z = (PyLongObject *)self;
     Py_ssize_t ndigits = _PyLong_DigitCount(z);
-    Py_ssize_t bit_count = 0;
+    int64_t bit_count = 0;
 
-    /* Each digit has up to PyLong_SHIFT ones, so the accumulated bit count
-       from the first PY_SSIZE_T_MAX/PyLong_SHIFT digits can't overflow a
-       Py_ssize_t. */
-    Py_ssize_t ndigits_fast = Py_MIN(ndigits, PY_SSIZE_T_MAX/PyLong_SHIFT);
-    for (Py_ssize_t i = 0; i < ndigits_fast; i++) {
+    for (Py_ssize_t i = 0; i < ndigits; i++) {
         bit_count += popcount_digit(z->long_value.ob_digit[i]);
     }
 
-    PyObject *result = PyLong_FromSsize_t(bit_count);
-    if (result == NULL) {
-        return NULL;
-    }
-
-    /* Use Python integers if bit_count would overflow. */
-    for (Py_ssize_t i = ndigits_fast; i < ndigits; i++) {
-        PyObject *x = PyLong_FromLong(popcount_digit(z->long_value.ob_digit[i]));
-        if (x == NULL) {
-            goto error;
-        }
-        PyObject *y = long_add((PyLongObject *)result, (PyLongObject *)x);
-        Py_DECREF(x);
-        if (y == NULL) {
-            goto error;
-        }
-        Py_SETREF(result, y);
-    }
-
-    return result;
-
-  error:
-    Py_DECREF(result);
-    return NULL;
+    return PyLong_FromInt64(bit_count);
 }
 
 /*[clinic input]