Why random.randint() is much slower than random.getrandbits()

randint uses randrange which uses _randbelow which is _randbelow_with_get_randbits (if it is present) which uses getrandbits. However, randrange includes overhead on top of the underlying call to getrandbits because it must check for the start and step arguments. Even though there are fast paths for these checks, they are still there. There are definitely other things contributing to the 6.5 slowdown when using randint, but this answer atleast shows you that randint will always be slower than getrandbits.

getrandbits() is a very short function going to native code almost immediately:

def getrandbits(self, k):
    """getrandbits(k) -> x.  Generates an int with k random bits."""
    if k < 0:
        raise ValueError('number of bits must be non-negative')
    numbytes = (k + 7) // 8                       # bits / 8 and rounded up
    x = int.from_bytes(_urandom(numbytes), 'big')
    return x >> (numbytes * 8 - k)                # trim excess bits

_urandom is os.urandom, which you can't even find in os.py in the same folder, as it's native code. See details here: Where can I find the source code of os.urandom()?

randint() is a return self.randrange(a, b+1) call, where randrange() is a long and versatile function, almost 100 lines of Python code, its "fast track" ends in a return istart + self._randbelow(width) after circa 50 lines of checking and initializing.

_randbelow() is actually a choice, depending on the existence of getrandbits() which exists in your case, so probably this one is running:

def _randbelow_with_getrandbits(self, n):
    "Return a random int in the range [0,n).  Returns 0 if n==0."

    if not n:
        return 0
    getrandbits = self.getrandbits
    k = n.bit_length()  # don't use (n-1) here because n can be 1
    r = getrandbits(k)  # 0 <= r < 2**k
    while r >= n:
        r = getrandbits(k)
    return r

so randint() ends in the same getrandbits() after doing a lot of other things, and that's pretty much how it's slower than it.

The underlying reason is the function that getrandbits calls is written in C, look at the source code at GitHub Python repository

You will find that getrandbits under the hood calls urandom from os module, and if you look at the implementation of this function, you'll find that it is indeed written in C.

os_urandom_impl(PyObject *module, Py_ssize_t size)
/*[clinic end generated code: output=42c5cca9d18068e9 input=4067cdb1b6776c29]*/
{
    PyObject *bytes;
    int result;

    if (size < 0)
        return PyErr_Format(PyExc_ValueError,
                            "negative argument not allowed");
    bytes = PyBytes_FromStringAndSize(NULL, size);
    if (bytes == NULL)
        return NULL;

    result = _PyOS_URandom(PyBytes_AS_STRING(bytes), PyBytes_GET_SIZE(bytes));
    if (result == -1) {
        Py_DECREF(bytes);
        return NULL;
    }
    return bytes;
}

Talking about randint, if you look at the source code for this function, it calls randrange, which further calls _randbelow_with_get_randbits.

    def randrange(self, start, stop=None, step=_ONE):
        """Choose a random item from range(start, stop[, step]).
        This fixes the problem with randint() which includes the
        endpoint; in Python this is usually not what you want.
        """

        # This code is a bit messy to make it fast for the
        # common case while still doing adequate error checking.
        try:
            istart = _index(start)
        except TypeError:
            istart = int(start)
            if istart != start:
                _warn('randrange() will raise TypeError in the future',
                      DeprecationWarning, 2)
                raise ValueError("non-integer arg 1 for randrange()")
            _warn('non-integer arguments to randrange() have been deprecated '
                  'since Python 3.10 and will be removed in a subsequent '
                  'version',
                  DeprecationWarning, 2)
        if stop is None:
            # We don't check for "step != 1" because it hasn't been
            # type checked and converted to an integer yet.
            if step is not _ONE:
                raise TypeError('Missing a non-None stop argument')
            if istart > 0:
                return self._randbelow(istart)
            raise ValueError("empty range for randrange()")

        # stop argument supplied.
        try:
            istop = _index(stop)
        except TypeError:
            istop = int(stop)
            if istop != stop:
                _warn('randrange() will raise TypeError in the future',
                      DeprecationWarning, 2)
                raise ValueError("non-integer stop for randrange()")
            _warn('non-integer arguments to randrange() have been deprecated '
                  'since Python 3.10 and will be removed in a subsequent '
                  'version',
                  DeprecationWarning, 2)
        width = istop - istart
        try:
            istep = _index(step)
        except TypeError:
            istep = int(step)
            if istep != step:
                _warn('randrange() will raise TypeError in the future',
                      DeprecationWarning, 2)
                raise ValueError("non-integer step for randrange()")
            _warn('non-integer arguments to randrange() have been deprecated '
                  'since Python 3.10 and will be removed in a subsequent '
                  'version',
                  DeprecationWarning, 2)
        # Fast path.
        if istep == 1:
            if width > 0:
                return istart + self._randbelow(width)
            raise ValueError("empty range for randrange() (%d, %d, %d)" % (istart, istop, width))

        # Non-unit step argument supplied.
        if istep > 0:
            n = (width + istep - 1) // istep
        elif istep < 0:
            n = (width + istep + 1) // istep
        else:
            raise ValueError("zero step for randrange()")
        if n <= 0:
            raise ValueError("empty range for randrange()")
        return istart + istep * self._randbelow(n)

    def randint(self, a, b):
        """Return random integer in range [a, b], including both end points.
        """

        return self.randrange(a, b+1)

As you can see, there are so many things going on with Try/Except block in randrange function and as they are written in Python, due to all these overheads and control flow, it's slow.