Repository: jax-ml/jax
Issue category: Feature Request

shape hint arguments in lax numpy functions to enable compilation
Several functions in `jax.numpy` are not `jit`-compilable for shape-level arguments. Specifically, we can't decide their output shape from input shapes alone.

We've given [`jax.numpy.bincount`](https://github.com/google/jax/blob/db8f66d508d536e1312291ba966905ddf910582d/jax/numpy/lax_numpy.py#L1309) an optional `length` argument that's not in standard numpy because it determines the output shape (when it is static/concrete). It's not uncommon for callers to have this information on hand.

We could consider extending other functions similarly to accept optional shape hints:
- [x] argwhere (#6915)
- [x] compress (#21090)
- [x] extract (#21090)
- [x] nonzero (#6501 #7592)
- [x] flatnonzero (#6913)
- [x] 1-argument where (#6910)
- [x] repeat (#3670)
- [x] unique (#6912, #8121, #8186)
- [x] setdiff1d (#8144)
- [x] union1d (#6930, #8143)
- [x] intersect1d (#22979)
- [x] setxor1d (#23020)


Functions to edit:
jax/_src/numpy/setops.py:setxor1d
jax/_src/numpy/setops.py:_intersect1d_size
Functions added: jax/_src/numpy/setops.py:_concat_unique
jax/_src/numpy/setops.py:_setxor1d_size

Patch:
diff --git a/jax/_src/numpy/setops.py b/jax/_src/numpy/setops.py
index db4237dbd069..8e0162660951 100644
--- a/jax/_src/numpy/setops.py
+++ b/jax/_src/numpy/setops.py
@@ -61,6 +61,17 @@ def _in1d(ar1: ArrayLike, ar2: ArrayLike, invert: bool) -> Array:
     return (ar1_flat[:, None] == ar2_flat[None, :]).any(-1)
 
 
+def _concat_unique(arr1: Array, arr2: Array) -> tuple[Array, Array]:
+  """Utility to concatenate the unique values from two arrays."""
+  arr1, arr2 = ravel(arr1), ravel(arr2)
+  arr1, num_unique1 = _unique(arr1, axis=0, size=arr1.size, return_true_size=True)
+  arr2, num_unique2 = _unique(arr2, axis=0, size=arr2.size, return_true_size=True)
+  arr = zeros(arr1.size + arr2.size, dtype=dtypes.result_type(arr1, arr2))
+  arr = lax.dynamic_update_slice(arr, arr1, (0,))
+  arr = lax.dynamic_update_slice(arr, arr2, (num_unique1,))
+  return arr, num_unique1 + num_unique2
+
+
 def setdiff1d(ar1: ArrayLike, ar2: ArrayLike, assume_unique: bool = False,
               *, size: int | None = None, fill_value: ArrayLike | None = None) -> Array:
   """Compute the set difference of two 1D arrays.
@@ -220,7 +231,39 @@ def union1d(ar1: ArrayLike, ar2: ArrayLike,
   return cast(Array, out)
 
 
-def setxor1d(ar1: ArrayLike, ar2: ArrayLike, assume_unique: bool = False) -> Array:
+@partial(jit, static_argnames=['assume_unique', 'size'])
+def _setxor1d_size(arr1: Array, arr2: Array, fill_value: ArrayLike | None, *,
+                   assume_unique: bool, size: int, ) -> Array:
+  # Ensured by caller
+  assert arr1.ndim == arr2.ndim == 1
+  assert arr1.dtype == arr2.dtype
+
+  if assume_unique:
+    arr = concatenate([arr1, arr2])
+    aux = sort(concatenate([arr1, arr2]))
+    flag = concatenate((bool(aux.size), aux[1:] != aux[:-1], True), axis=None)
+  else:
+    arr, num_unique = _concat_unique(arr1, arr2)
+    mask = arange(arr.size + 1) < num_unique + 1
+    _, aux = lax.sort([~mask[1:], arr], is_stable=True, num_keys=2)
+    flag = mask & concatenate((bool(aux.size), aux[1:] != aux[:-1], False),
+                              axis=None).at[num_unique].set(True)
+  aux_mask = flag[1:] & flag[:-1]
+  num_results = aux_mask.sum()
+  if aux.size:
+    indices = nonzero(aux_mask, size=size, fill_value=len(aux))[0]
+    vals = aux.at[indices].get(mode='fill', fill_value=0)
+  else:
+    vals = zeros(size, aux.dtype)
+  if fill_value is None:
+    vals = where(arange(len(vals)) < num_results, vals, vals.max())
+    return where(arange(len(vals)) < num_results, vals, vals.min())
+  else:
+    return where(arange(len(vals)) < num_results, vals, fill_value)
+
+
+def setxor1d(ar1: ArrayLike, ar2: ArrayLike, assume_unique: bool = False, *,
+             size: int | None = None, fill_value: ArrayLike | None = None) -> Array:
   """Compute the set-wise xor of elements in two arrays.
 
   JAX implementation of :func:`numpy.setxor1d`.
@@ -234,6 +277,12 @@ def setxor1d(ar1: ArrayLike, ar2: ArrayLike, assume_unique: bool = False) -> Arr
     assume_unique: if True, assume the input arrays contain unique values. This allows
       a more efficient implementation, but if ``assume_unique`` is True and the input
       arrays contain duplicates, the behavior is undefined. default: False.
+    size: if specified, return only the first ``size`` sorted elements. If there are fewer
+      elements than ``size`` indicates, the return value will be padded with ``fill_value``,
+      and returned indices will be padded with an out-of-bound index.
+    fill_value: when ``size`` is specified and there are fewer than the indicated number of
+      elements, fill the remaining entries ``fill_value``. Defaults to the smallest value
+      in the xor result.
 
   Returns:
     An array of values that are found in exactly one of the input arrays.
@@ -250,22 +299,21 @@ def setxor1d(ar1: ArrayLike, ar2: ArrayLike, assume_unique: bool = False) -> Arr
     Array([1, 2, 5, 6], dtype=int32)
   """
   check_arraylike("setxor1d", ar1, ar2)
-  ar1 = core.concrete_or_error(None, ar1, "The error arose in setxor1d()")
-  ar2 = core.concrete_or_error(None, ar2, "The error arose in setxor1d()")
+  arr1, arr2 = promote_dtypes(ravel(ar1), ravel(ar2))
+  del ar1, ar2
 
-  ar1 = ravel(ar1)
-  ar2 = ravel(ar2)
+  if size is not None:
+    return _setxor1d_size(arr1, arr2, fill_value=fill_value,
+                          assume_unique=assume_unique, size=size)
 
   if not assume_unique:
-    ar1 = unique(ar1)
-    ar2 = unique(ar2)
-
-  aux = concatenate((ar1, ar2))
+    arr1 = unique(arr1)
+    arr2 = unique(arr2)
+  aux = concatenate((arr1, arr2))
   if aux.size == 0:
     return aux
-
   aux = sort(aux)
-  flag = concatenate((array([True]), aux[1:] != aux[:-1], array([True])))
+  flag = concatenate((True, aux[1:] != aux[:-1], True), axis=None)
   return aux[flag[1:] & flag[:-1]]
 
 
@@ -312,7 +360,7 @@ def _intersect1d_size(arr1: Array, arr2: Array, fill_value: ArrayLike | None, as
     arr1, ind1, num_unique1 = _unique(arr1, 0, size=arr1.size, return_index=True, return_true_size=True, fill_value=0)
     arr2, ind2, num_unique2 = _unique(arr2, 0, size=arr2.size, return_index=True, return_true_size=True, fill_value=0)
     arr = zeros(arr1.size + arr2.size, dtype=dtypes.result_type(arr1, arr2))
-    arr = arr.at[:arr1.size].set(arr1)
+    arr = lax.dynamic_update_slice(arr, arr1, (0,))
     arr = lax.dynamic_update_slice(arr, arr2, (num_unique1,))
     mask = arange(arr.size) < num_unique1 + num_unique2
     _, aux, aux_sort_indices = lax.sort([~mask, arr, arange(arr.size)], is_stable=True, num_keys=2)
@@ -326,8 +374,11 @@ def _intersect1d_size(arr1: Array, arr2: Array, fill_value: ArrayLike | None, as
   #         and vals[num_results:] contains the appropriate fill_value.
   aux_mask = (aux[1:] == aux[:-1]) & mask[1:]
   num_results = aux_mask.sum()
-  val_indices = nonzero(aux_mask, size=size, fill_value=aux.size)[0]
-  vals = aux.at[val_indices].get(mode='fill', fill_value=0)
+  if aux.size:
+    val_indices = nonzero(aux_mask, size=size, fill_value=aux.size)[0]
+    vals = aux.at[val_indices].get(mode='fill', fill_value=0)
+  else:
+    vals = zeros(size, aux.dtype)
   if fill_value is None:
     vals = where(arange(len(vals)) < num_results, vals, vals.max())
     vals = where(arange(len(vals)) < num_results, vals, vals.min())

Test patch: diff --git a/tests/lax_numpy_test.py b/tests/lax_numpy_test.py
index d5efe1e03f31..860b3358d2ef 100644
--- a/tests/lax_numpy_test.py
+++ b/tests/lax_numpy_test.py
@@ -18,7 +18,7 @@
 import collections
 from collections.abc import Iterator
 import copy
-from functools import partial
+from functools import partial, wraps
 import inspect
 import io
 import itertools
@@ -174,10 +174,25 @@ def arrays_with_overlapping_values(rng, shapes, dtypes, unique=False, overlap=0.
   else:
     vals = jtu.rand_default(rng)((total_size,), 'int32')
   offsets = [int(sum(sizes[:i]) * (1 - overlap)) for i in range(len(sizes))]
-  return [np.random.permutation(vals[offset: offset + size]).reshape(shape).astype(dtype)
+  return [rng.permutation(vals[offset: offset + size]).reshape(shape).astype(dtype)
           for (offset, size, shape, dtype) in zip(offsets, sizes, shapes, dtypes)]
 
 
+def with_size_argument(fun):
+  @wraps(fun)
+  def wrapped(*args, size=None, fill_value=None, **kwargs):
+    result = fun(*args, **kwargs)
+    if size is None or size == len(result):
+      return result
+    elif size < len(result):
+      return result[:size]
+    else:
+      if fill_value is None:
+        fill_value = result.min() if result.size else 0
+      return np.pad(result, (0, size - len(result)), constant_values=fill_value)
+  return wrapped
+
+
 class LaxBackedNumpyTests(jtu.JaxTestCase):
   """Tests for LAX-backed Numpy implementation."""
 
@@ -786,19 +801,22 @@ def jnp_fun(arg1, arg2):
     shape1=all_shapes,
     shape2=all_shapes,
     assume_unique=[False, True],
+    size=[None, 2, 5],
+    fill_value=[None, 99],
     overlap=[0.1, 0.5, 0.9],
   )
-  def testSetxor1d(self, shape1, dtype1, shape2, dtype2, assume_unique, overlap):
+  def testSetxor1d(self, shape1, dtype1, shape2, dtype2, assume_unique, size, fill_value, overlap):
     args_maker = partial(arrays_with_overlapping_values, self.rng(),
                          shapes=[shape1, shape2], dtypes=[dtype1, dtype2],
                          overlap=overlap)
-    jnp_fun = lambda ar1, ar2: jnp.setxor1d(ar1, ar2, assume_unique=assume_unique)
+    jnp_fun = lambda ar1, ar2: jnp.setxor1d(ar1, ar2, assume_unique=assume_unique,
+                                            size=size, fill_value=fill_value)
     def np_fun(ar1, ar2):
       if assume_unique:
         # numpy requires 1D inputs when assume_unique is True.
         ar1 = np.ravel(ar1)
         ar2 = np.ravel(ar2)
-      return np.setxor1d(ar1, ar2, assume_unique)
+      return with_size_argument(np.setxor1d)(ar1, ar2, assume_unique, size=size, fill_value=fill_value)
     with jtu.strict_promotion_if_dtypes_match([dtype1, dtype2]):
       self._CheckAgainstNumpy(np_fun, jnp_fun, args_maker, check_dtypes=False)