BUG: implement new engine for codes-based MultiIndex indexing

closes pandas-dev#18519
closes pandas-dev#18818
closes pandas-dev#18520
closes pandas-dev#18485
closes pandas-dev#15994
closes pandas-dev#19086

Author: toobaz

doc/source/whatsnew/v0.23.0.txt

@@ -380,6 +380,7 @@ Performance Improvements
 - Improved performance of ``DatetimeIndex`` and ``Series`` arithmetic operations with Business-Month and Business-Quarter frequencies (:issue:`18489`)
 - :func:`Series` / :func:`DataFrame` tab completion limits to 100 values, for better performance. (:issue:`18587`)
 - Improved performance of :func:`DataFrame.median` with ``axis=1`` when bottleneck is not installed (:issue:`16468`)
+- Improved performance of :func:`MultiIndex.get_loc` for large indexes, at the cost of a reduction in performance for small ones (:issue:`18519`)
 
 
 .. _whatsnew_0230.docs:
@@ -476,7 +477,11 @@ MultiIndex
 - Bug in :func:`MultiIndex.get_level_values` which would return an invalid index on level of ints with missing values (:issue:`17924`)
 - Bug in :func:`MultiIndex.remove_unused_levels` which would fill nan values (:issue:`18417`)
 - Bug in :func:`MultiIndex.from_tuples`` which would fail to take zipped tuples in python3 (:issue:`18434`)
--
+- Bug in :func:`MultiIndex.get_loc`` which would fail to automatically cast values between float and int (:issue:`18818`, :issue:`15994`)
+- Bug in :func:`MultiIndex.get_loc`` which would cast boolean to integer labels (:issue:`19086`)
+- Bug in :func:`MultiIndex.get_loc`` which would fail to locate keys containing ``NaN`` (:issue:`18485`)
+- Bug in :func:`MultiIndex.get_loc`` in large :class:`MultiIndex`, would fail when levels had different dtypes (:issue:`18520`)
+
 
 I/O
 ^^^

pandas/_libs/index.pyx

@@ -26,6 +26,7 @@ from hashtable cimport HashTable
 from pandas._libs import algos, hashtable as _hash
 from pandas._libs.tslibs import period as periodlib
 from pandas._libs.tslib import Timestamp, Timedelta
+from pandas._libs.missing import checknull
 
 cdef int64_t iNaT = util.get_nat()
 
@@ -585,6 +586,141 @@ cpdef convert_scalar(ndarray arr, object value):
     return value
 
 
+cdef class BaseMultiIndexCodesEngine:
+    """
+    Base class for MultiIndexUIntEngine and MultiIndexPyIntEngine, which
+    represent each label in a MultiIndex as an integer, by juxtaposing the bits
+    encoding each level, with appropriate offsets.
+
+    For instance: if 3 levels have respectively 3, 6 and 1 possible values,
+    then their labels can be represented using respectively 2, 3 and 1 bits,
+    as follows:
+     _ _ _ _____ _ __ __ __
+    |0|0|0| ... |0| 0|a1|a0| -> offset 0 (first level)
+     — — — ————— — —— —— ——
+    |0|0|0| ... |0|b2|b1|b0| -> offset 2 (bits required for first level)
+     — — — ————— — —— —— ——
+    |0|0|0| ... |0| 0| 0|c0| -> offset 5 (bits required for first two levels)
+     ‾ ‾ ‾ ‾‾‾‾‾ ‾ ‾‾ ‾‾ ‾‾
+    and the resulting unsigned integer representation will be:
+     _ _ _ _____ _ __ __ __ __ __ __
+    |0|0|0| ... |0|c0|b2|b1|b0|a1|a0|
+     ‾ ‾ ‾ ‾‾‾‾‾ ‾ ‾‾ ‾‾ ‾‾ ‾‾ ‾‾ ‾‾
+
+    Offsets are calculated at initialization, labels are transformed by method
+    _codes_to_ints.
+
+    Keys are located by first locating each component against the respective
+    level, then locating (the integer representation of) codes.
+    """
+    def __init__(self, object levels, object labels,
+                 ndarray[uint64_t, ndim=1] offsets):
+        """
+        Parameters
+        ----------
+        levels : list-like of numpy arrays
+            Levels of the MultiIndex
+        labels : list-like of numpy arrays of integer dtype
+            Labels of the MultiIndex
+        offsets : numpy array of uint64 dtype
+            Pre-calculated offsets, one for each level of the index
+        """
+
+        self.levels = levels
+        self.offsets = offsets
+
+        # Transform labels in a single array, and add 1 so that we are working
+        # with positive integers (-1 for NaN becomes 0):
+        codes = (np.array(labels, dtype='int64').T + 1).astype('uint64',
+                                                               copy=False)
+
+        # Map each codes combination in the index to an integer unambiguously
+        # (no collisions possible), based on the "offsets", which describe the
+        # number of bits to switch labels for each level:
+        lab_ints = self._codes_to_ints(codes)
+
+        # Initialize underlying index (e.g. libindex.UInt64Engine) with
+        # integers representing labels: we will use its get_loc and get_indexer
+        self._base.__init__(self, lambda: lab_ints, len(lab_ints))
+
+    def _extract_level_codes(self, object target, object method=None):
+        """
+        Map the requested list of (tuple) keys to their integer representations
+        for searching in the underlying integer index.
+
+        Parameters
+        ----------
+        target : list-like of keys
+            Each key is a tuple, with a label for each level of the index.
+
+        Returns
+        ------
+        int_keys : 1-dimensional array of dtype uint64 or object
+            Integers representing one combination each
+        """
+
+        level_codes = [lev.get_indexer(codes) + 1 for lev, codes
+                       in zip(self.levels, zip(*target))]
+        return self._codes_to_ints(np.array(level_codes, dtype='uint64').T)
+
+    def get_indexer(self, object target, object method=None,
+                    object limit=None):
+        lab_ints = self._extract_level_codes(target)
+
+        # All methods (exact, backfill, pad) directly map to the respective
+        # methods of the underlying (integers) index...
+        if method is not None:
+            # but underlying backfill and pad methods require index and keys
+            # to be sorted. The index already is (checked in
+            # Index._get_fill_indexer), sort (integer representations of) keys:
+            order = np.argsort(lab_ints)
+            lab_ints = lab_ints[order]
+            indexer = (getattr(self._base, 'get_{}_indexer'.format(method))
+                       (self, lab_ints, limit=limit))
+            indexer = indexer[order]
+        else:
+            indexer = self._base.get_indexer(self, lab_ints)
+
+        return indexer
+
+    def get_loc(self, object key):
+        if is_definitely_invalid_key(key):
+            raise TypeError("'{key}' is an invalid key".format(key=key))
+        if not PyTuple_Check(key):
+            raise KeyError(key)
+        try:
+            indices = [0 if checknull(v) else lev.get_loc(v) + 1
+                       for lev, v in zip(self.levels, key)]
+        except KeyError:
+            raise KeyError(key)
+
+        # ndmin=2 because codes_to_ints expects multiple labels:
+        indices = np.array(indices, ndmin=2, dtype='uint64')
+        # ... and returns a (length 1, in this case) array of integers:
+        lab_int = self._codes_to_ints(indices)[0]
+
+        return self._base.get_loc(self, lab_int)
+
+    def get_indexer_non_unique(self, object target):
+        # This needs to be overridden just because the default one works on
+        # target._values, and target can be itself a MultiIndex.
+
+        lab_ints = self._extract_level_codes(target)
+        indexer = self._base.get_indexer_non_unique(self, lab_ints)
+
+        return indexer
+
+    def __contains__(self, object val):
+        # Default __contains__ looks in the underlying mapping, which in this
+        # case only contains integer representations.
+        try:
+            self.get_loc(val)
+            return True
+        except (KeyError, TypeError, ValueError):
+            return False
+
+
+
 cdef class MultiIndexObjectEngine(ObjectEngine):
     """
     provide the same interface as the MultiIndexEngine

pandas/core/indexes/multi.py

@@ -45,6 +45,77 @@
          target_klass='MultiIndex or list of tuples'))
 
 
+class MultiIndexUIntEngine(libindex.BaseMultiIndexCodesEngine,
+                           libindex.UInt64Engine):
+    """
+    This class manages a MultiIndex by mapping label combinations to positive
+    integers.
+    """
+    _base = libindex.UInt64Engine
+
+    def _codes_to_ints(self, codes):
+        """
+        Transform each row of a 2d array of uint64 in a uint64, in a strictly
+        monotonic way (i.e. respecting the lexicographic order of integer
+        combinations): see BaseMultiIndexCodesEngine documentation.
+
+        Parameters
+        ----------
+        codes : 2-dimensional array of dtype uint64
+            Combinations of integers (one per row)
+
+        Returns
+        ------
+        int_keys : 1-dimensional array of dtype uint64
+            Integers representing one combination each
+        """
+        # Shift the representation of each level by the pre-calculated number
+        # of bits:
+        codes <<= self.offsets
+
+        # Now sum and OR are in fact interchangeable. This is a simple
+        # composition of the (disjunct) significant bits of each level (i.e.
+        # each column in "codes") in a single positive integer (per row):
+        return np.bitwise_or.reduce(codes, axis=1)
+
+
+class MultiIndexPyIntEngine(libindex.BaseMultiIndexCodesEngine,
+                            libindex.ObjectEngine):
+    """
+    This class manages those (extreme) cases in which the number of possible
+    label combinations overflows the 64 bits integers, and uses an ObjectEngine
+    containing Python integers.
+    """
+    _base = libindex.ObjectEngine
+
+    def _codes_to_ints(self, codes):
+        """
+        Transform each row of a 2d array of uint64 in a Python integer, in a
+        strictly monotonic way (i.e. respecting the lexicographic order of
+        integer combinations): see BaseMultiIndexCodesEngine documentation.
+
+        Parameters
+        ----------
+        codes : 2-dimensional array of dtype uint64
+            Combinations of integers (one per row)
+
+        Returns
+        ------
+        int_keys : 1-dimensional array of dtype object
+            Integers representing one combination each
+        """
+
+        # Shift the representation of each level by the pre-calculated number
+        # of bits. Since this can overflow uint64, first make sure we are
+        # working with Python integers:
+        codes = codes.astype('object') << self.offsets
+
+        # Now sum and OR are in fact interchangeable. This is a simple
+        # composition of the (disjunct) significant bits of each level (i.e.
+        # each column in "codes") in a single positive integer (per row):
+        return np.bitwise_or.reduce(codes, axis=1)
+
+
 class MultiIndex(Index):
     """
     A multi-level, or hierarchical, index object for pandas objects
@@ -687,16 +758,25 @@ def _get_level_number(self, level):
 
     @cache_readonly
     def _engine(self):
-
-        # choose our engine based on our size
-        # the hashing based MultiIndex for larger
-        # sizes, and the MultiIndexOjbect for smaller
-        # xref: https://github.com/pandas-dev/pandas/pull/16324
-        l = len(self)
-        if l > 10000:
-            return libindex.MultiIndexHashEngine(lambda: self, l)
-
-        return libindex.MultiIndexObjectEngine(lambda: self.values, l)
+        # Calculate the number of bits needed to represent labels in each
+        # level, as log2 of their sizes (including -1 for NaN):
+        sizes = np.ceil(np.log2([len(l) + 1 for l in self.levels]))
+
+        # Sum bit counts, starting from the _right_....
+        lev_bits = np.cumsum(sizes[::-1])[::-1]
+
+        # ... in order to obtain offsets such that sorting the combination of
+        # shifted codes (one for each level, resulting in a unique integer) is
+        # equivalent to sorting lexicographically the codes themselves. Notice
+        # that each level needs to be shifted by the number of bits needed to
+        # represent the _previous_ ones:
+        offsets = np.concatenate([lev_bits[1:], [0]]).astype('uint64')
+
+        # Check the total number of bits needed for our representation:
+        if lev_bits[0] > 64:
+            # The levels would overflow a 64 bit uint - use Python integers:
+            return MultiIndexPyIntEngine(self.levels, self.labels, offsets)
+        return MultiIndexUIntEngine(self.levels, self.labels, offsets)
 
     @property
     def values(self):
@@ -1885,7 +1965,7 @@ def get_indexer(self, target, method=None, limit=None, tolerance=None):
             if tolerance is not None:
                 raise NotImplementedError("tolerance not implemented yet "
                                           'for MultiIndex')
-            indexer = self._get_fill_indexer(target, method, limit)
+            indexer = self._engine.get_indexer(target, method, limit)
         elif method == 'nearest':
             raise NotImplementedError("method='nearest' not implemented yet "
                                       'for MultiIndex; see GitHub issue 9365')