Is there a way to handle negative indices without if statements?

Question

Python handles negative indices so that they subtract from the length. For example, if we have this list xs = [1,2,3,4], doing xs[-1] would give us 4, the last element, which would be the same as xs[len(xs)-1]. Now, an easy way to handle this would be the following:

def handle_index(index: int, length: int) -> int:
  if index < 0:
    return length + index
  return index

I tried looking into the source code of CPython and NumPy, but I had a bit of trouble finding where they handled negative indices.

Edit: Python lists and Numpy arrays already handle this. I’m implementing a data structure that uses neither of those, and I would like to know how to efficiently support negative indices.

Asked By: Lefol

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Source

Answer 1

In CPython, sliceobject.c handles converting a slice like start:stop:stride into bare indices. Negative start and stop are handled with code like this:

start = evaluate_slice_index(self->start);
if (start == NULL)
    goto error;

if (_PyLong_Sign(start) < 0) {
    /* start += length */
    PyObject *tmp = PyNumber_Add(start, length);

(Note that the correct calculation in your code would be return length + index not length - index, since index is negative.)

The full code has no shortage of if statements:

/* Compute slice indices given a slice and length.  Return -1 on failure.  Used
   by slice.indices and rangeobject slicing.  Assumes that `len` is a
   nonnegative instance of PyLong. */

int
_PySlice_GetLongIndices(PySliceObject *self, PyObject *length,
                        PyObject **start_ptr, PyObject **stop_ptr,
                        PyObject **step_ptr)
{
    PyObject *start=NULL, *stop=NULL, *step=NULL;
    PyObject *upper=NULL, *lower=NULL;
    int step_is_negative, cmp_result;

    /* Convert step to an integer; raise for zero step. */
    if (self->step == Py_None) {
        step = _PyLong_GetOne();
        Py_INCREF(step);
        step_is_negative = 0;
    }
    else {
        int step_sign;
        step = evaluate_slice_index(self->step);
        if (step == NULL)
            goto error;
        step_sign = _PyLong_Sign(step);
        if (step_sign == 0) {
            PyErr_SetString(PyExc_ValueError,
                            "slice step cannot be zero");
            goto error;
        }
        step_is_negative = step_sign < 0;
    }

    /* Find lower and upper bounds for start and stop. */
    if (step_is_negative) {
        lower = PyLong_FromLong(-1L);
        if (lower == NULL)
            goto error;

        upper = PyNumber_Add(length, lower);
        if (upper == NULL)
            goto error;
    }
    else {
        lower = _PyLong_GetZero();
        Py_INCREF(lower);
        upper = length;
        Py_INCREF(upper);
    }

    /* Compute start. */
    if (self->start == Py_None) {
        start = step_is_negative ? upper : lower;
        Py_INCREF(start);
    }
    else {
        start = evaluate_slice_index(self->start);
        if (start == NULL)
            goto error;

        if (_PyLong_Sign(start) < 0) {
            /* start += length */
            PyObject *tmp = PyNumber_Add(start, length);
            Py_DECREF(start);
            start = tmp;
            if (start == NULL)
                goto error;

            cmp_result = PyObject_RichCompareBool(start, lower, Py_LT);
            if (cmp_result < 0)
                goto error;
            if (cmp_result) {
                Py_INCREF(lower);
                Py_DECREF(start);
                start = lower;
            }
        }
        else {
            cmp_result = PyObject_RichCompareBool(start, upper, Py_GT);
            if (cmp_result < 0)
                goto error;
            if (cmp_result) {
                Py_INCREF(upper);
                Py_DECREF(start);
                start = upper;
            }
        }
    }

    /* Compute stop. */
    if (self->stop == Py_None) {
        stop = step_is_negative ? lower : upper;
        Py_INCREF(stop);
    }
    else {
        stop = evaluate_slice_index(self->stop);
        if (stop == NULL)
            goto error;

        if (_PyLong_Sign(stop) < 0) {
            /* stop += length */
            PyObject *tmp = PyNumber_Add(stop, length);
            Py_DECREF(stop);
            stop = tmp;
            if (stop == NULL)
                goto error;

            cmp_result = PyObject_RichCompareBool(stop, lower, Py_LT);
            if (cmp_result < 0)
                goto error;
            if (cmp_result) {
                Py_INCREF(lower);
                Py_DECREF(stop);
                stop = lower;
            }
        }
        else {
            cmp_result = PyObject_RichCompareBool(stop, upper, Py_GT);
            if (cmp_result < 0)
                goto error;
            if (cmp_result) {
                Py_INCREF(upper);
                Py_DECREF(stop);
                stop = upper;
            }
        }
    }

    *start_ptr = start;
    *stop_ptr = stop;
    *step_ptr = step;
    Py_DECREF(upper);
    Py_DECREF(lower);
    return 0;

  error:
    *start_ptr = *stop_ptr = *step_ptr = NULL;
    Py_XDECREF(start);
    Py_XDECREF(stop);
    Py_XDECREF(step);
    Py_XDECREF(upper);
    Py_XDECREF(lower);
    return -1;
}

Answered By: John Kugelman

Is there a way to handle negative indices without if statements?

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