PERF: MultiIndex.size

[lukemanley]

• Tests added and passed if fixing a bug or adding a new feature
• All code checks passed.
• Added type annotations to new arguments/methods/functions.
• Added an entry in the latest doc/source/whatsnew/v1.6.0.rst file if fixing a bug or adding a new feature.

Improvement comes from avoiding MultiIndex._values

import pandas as pd
import numpy as np

mi = pd.MultiIndex.from_product(
    [
        pd.date_range('1970-01-01', periods=1000),
        np.arange(1000),
    ]
)

%timeit mi.copy().size

111 ms ± 9.11 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)       <- main
17.7 µs ± 1.1 µs per loop (mean ± std. dev. of 7 runs, 100,000 loops each)  <- PR

At least one existing asv shows improvement (there may be others):

 before           after         ratio
     [cda0f6be]       [8395c77a]
     <main>           <multiindex-size>
-      25.1±0.4ms         18.3±1ms     0.73  multiindex_object.SetOperations.time_operation('non_monotonic', 'string', 'symmetric_difference')
-      24.8±0.4ms         16.7±2ms     0.68  multiindex_object.SetOperations.time_operation('monotonic', 'ea_int', 'symmetric_difference')
-      24.4±0.8ms       15.8±0.3ms     0.65  multiindex_object.SetOperations.time_operation('monotonic', 'string', 'symmetric_difference')
-      25.3±0.4ms         16.4±1ms     0.65  multiindex_object.SetOperations.time_operation('non_monotonic', 'ea_int', 'symmetric_difference')
-      23.9±0.4ms       13.5±0.2ms     0.57  multiindex_object.SetOperations.time_operation('non_monotonic', 'datetime', 'symmetric_difference')
-      23.0±0.6ms         12.1±2ms     0.53  multiindex_object.SetOperations.time_operation('non_monotonic', 'int', 'symmetric_difference')
-        25.1±1ms       13.0±0.6ms     0.52  multiindex_object.SetOperations.time_operation('monotonic', 'datetime', 'symmetric_difference')
-      23.0±0.4ms       11.2±0.6ms     0.49  multiindex_object.SetOperations.time_operation('monotonic', 'int', 'symmetric_difference')

[mroeschke]

Thanks @lukemanley