random.draw: size dispatch diverges between the Python and jitted paths for numpy integers

quantecon.random.draw decides whether size requests an array of draws or a single scalar draw in two different places, using two different tests that do not agree:

A NumPy integer is not a Python int, but it is a types.Integer to Numba. A Python bool is the reverse: it passes isinstance(x, int) but Numba types it as Boolean, not Integer. So the same call returns different things depending on whether the call site is jit-compiled — with no error either way.

Reproducing

Verified on numba 0.62.1 / numpy 2.3.5 / python 3.13.9, against current main:

import numpy as np
from numba import njit
from quantecon.random import draw

@njit
def draw_jit(cdf, size):
    return draw(cdf, size)

cdf = np.cumsum([0.4, 0.6])

draw(cdf, np.int64(10))       # np.int64(1)                    <- ONE scalar
draw_jit(cdf, np.int64(10))   # array([1, 0, 0, 1, 1, 1, 1, 1, 0, 0])   <- 10 draws

draw(cdf, True)               # TypeError
draw_jit(cdf, True)           # 1        <- a scalar draw

Full dispatch table:

The numpy-integer rows are the ones that matter in practice. Nothing warns, nothing raises — the caller gets a scalar where they asked for an array, and downstream code sees a shape it did not expect.

Why this is easy to hit

A NumPy integer is what you get from most numpy-valued expressions, so size arrives as np.int64 without the caller doing anything unusual: an element of an integer array (counts[i]), a reduction (arr.sum(), arr.argmax()), a // result involving an array, or a value read out of a structured/record array. Plain len(x) and arr.shape[0] return Python ints and are fine, which is part of why this survives casual testing.

Suggested fix

Align the Python body with the overload:

if isinstance(size, (int, np.integer)) and not isinstance(size, bool):

The not isinstance(size, bool) clause is needed because bool subclasses int in Python but Numba types it as Boolean; without it the two paths would still disagree for size=True. I verified this predicate agrees with the overload's isinstance(t, types.Integer) on every case in the table above, including None.

There is a compatibility judgement for the team here rather than a purely mechanical fix. draw(cdf, np.int64(10)) currently returns a scalar from Python, and the fix changes that to a 10-element array. That is the behaviour the caller asked for and the behaviour the jitted path already gives, but it is a silent behaviour change for anyone who relied on the current result. It may deserve a release note, and possibly a decision on whether size=True should raise rather than quietly mean "one draw".

Provenance

Found while implementing #916 (PR #917), which adds a random_state argument to draw. This divergence predates that work and is untouched by it — deliberately left out so the behaviour change would not ride along in a feature PR and muddy the release note and the bisect story. probvec and sample_without_replacement are not affected; they build size internally and never dispatch on its type.

Start in quantecon/random/utilities.py at draw's pure Python body and its @overload implementation. Reproduce the listed NumPy integer and bool cases in both paths, then add regression coverage showing that their dispatch agrees; confirm the intended compatibility decision for size behavior and any release-note requirement.