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# SPDX-FileCopyrightText: Copyright (c) 2026 NVIDIA CORPORATION & AFFILIATES. All rights reserved.
# SPDX-License-Identifier: Apache-2.0
"""
Unit tests for pycute.composition
"""
import logging
import pytest
import sympy
from pycute import *
logger = logging.getLogger()
class TestComposition:
def postcondition_composition(self, A, B):
R = composition(A, B)
logger.info(f" {A} o {B} => {R}")
# Post-condition: R is compatible with B
assert compatible(B, R)
# Post-condition: R(c) = A(B(c)) for all coordinates c in B
for i in range(size(R)):
assert R(i) == A(B(i))
def test_composition_1(self):
# Test all combinations with shapes/strides < 4
for AD in range(0,4):
for BD in range(0,4):
for AS in range(1,4):
for BS in range(1,4):
self.postcondition_composition(Layout(AS,AD), Layout(BS,BD))
def test_composition_2(self):
self.postcondition_composition(Layout(12), Layout((4,3)))
self.postcondition_composition(Layout(12, 2), Layout((4,3)))
self.postcondition_composition(Layout(12), Layout((4,3), (3,1)))
self.postcondition_composition(Layout(12, 2), Layout((4,3), (3,1)))
self.postcondition_composition(Layout(12), Layout((2,3), (2,4)))
self.postcondition_composition(Layout((4,3)), Layout((4,3)))
self.postcondition_composition(Layout((4,3)), Layout(12))
self.postcondition_composition(Layout((4,3)), Layout(6, 2))
self.postcondition_composition(Layout((4,3)), Layout((6,2), (2,1)))
self.postcondition_composition(Layout((4,3), (3,1)), Layout((4,3)))
self.postcondition_composition(Layout((4,3), (3,1)), Layout(12))
self.postcondition_composition(Layout((4,3), (3,1)), Layout(6, 2))
self.postcondition_composition(Layout((4,3), (3,1)), Layout((6,2), (2,1)))
self.postcondition_composition(Layout((8,8)), Layout(((2,2,2), (2,2,2)),((1,16,4), (8,2,32))))
self.postcondition_composition(Layout((8,8), (8,1)), Layout(((2,2,2), (2,2,2)),((1,16,4), (8,2,32))))
self.postcondition_composition(Layout(((2,2,2), (2,2,2)),((1,16,4), (8,2,32))), Layout(8, 4))
self.postcondition_composition(Layout(((4,2)), ((1,16))), Layout((4,2), (2,1)))
self.postcondition_composition(Layout((2,2), (2,1)), Layout((2,2), (2,1)))
self.postcondition_composition(Layout((4,8,2)), Layout((2,2,2), (2,8,1)))
self.postcondition_composition(Layout((4,8,2), (2,8,1)), Layout((2,2,2), (1,8,2)))
self.postcondition_composition(Layout((4,8,2), (2,8,1)), Layout((4,2,2), (2,8,1)))
# Pre-coalesced LHS
self.postcondition_composition(Layout((4,6,8), (1,4,7)), Layout(6, 1))
# Mid-layout truncation
self.postcondition_composition(Layout((4,6,8,10), (2,3,5,7)), Layout(6,12))
self.postcondition_composition(Layout((5,126,7), (1,13,0)), Layout(21, 30))
self.postcondition_composition(Layout((23,5), (2,120)), Layout(7, 3))
# Over the end
self.postcondition_composition(Layout((4,6,1), (2,3,0)), Layout(30, 4))
self.postcondition_composition(Layout((4,6,1), (1,4,0)), Layout((6,8)))
# Other
self.postcondition_composition(Layout((5,5), (5,5)), Layout(5, 5))
self.postcondition_composition(Layout(7, 11), Layout(3, 4))
self.postcondition_composition(Layout(7, 11), Layout((3,5), (6,3)))
def test_composition_fails(self):
# Violates stride divisibility condition
with pytest.raises(ValueError):
self.postcondition_composition(Layout((5,3), (7,1)), Layout(2,3))
# Violates shape divisibility condition
with pytest.raises(ValueError):
self.postcondition_composition(Layout((5,3), (7,1)), Layout(7,1))
def test_composition_coords(self):
# LHS Coords
self.postcondition_composition(Layout(12, E(0)), Layout((4,3)))
self.postcondition_composition(Layout(12, 2*E(1)), Layout((4,3)))
self.postcondition_composition(Layout(12, E(0)), Layout((4,3), (3,1)))
self.postcondition_composition(Layout(12, 2*E(1)), Layout((4,3), (3,1)))
self.postcondition_composition(Layout(12, E(1,1)), Layout((2,3), (2,4)))
self.postcondition_composition(Layout((4,3), (E(0),E(1))), Layout((4,3)))
self.postcondition_composition(Layout((4,3), (E(0),E(1))), Layout(12))
self.postcondition_composition(Layout((4,3), (E(0),E(1))), Layout(6, 2))
self.postcondition_composition(Layout((4,3), (E(0),E(1))), Layout((6,2), (2,1)))
self.postcondition_composition(Layout((4,3), (E(1),E(0))), Layout((4,3)))
self.postcondition_composition(Layout((4,3), (E(1),E(0))), Layout(12))
self.postcondition_composition(Layout((4,3), (E(1),E(0))), Layout(6, 2))
self.postcondition_composition(Layout((4,3), (E(1),E(0))), Layout((6,2), (2,1)))
self.postcondition_composition(Layout((4,3), (6*E(1),2*E(1))), Layout((4,3)))
self.postcondition_composition(Layout((4,3), (6*E(1),2*E(1))), Layout(12))
self.postcondition_composition(Layout((4,3), (6*E(1),2*E(1))), Layout(6, 2))
self.postcondition_composition(Layout((4,3), (6*E(1),2*E(1))), Layout((6,2), (2,1)))
self.postcondition_composition(Layout((4,4), (ArithTuple(1,1),ArithTuple(3,1))), Layout((4,2), (2,1)))
self.postcondition_composition(Layout((4,6,8), (E(0),E(1),E(2))), Layout((2,2,2)))
# RHS Coords
self.postcondition_composition(Layout((4,4), (4,1)), Layout((4,4), (E(0),E(1))))
self.postcondition_composition(Layout((4,4), (4,1)), Layout((4,4), (E(1),E(0))))
self.postcondition_composition(Layout((4,5),(5,1)), Layout(30, E(0)))
self.postcondition_composition(Layout((4,5),(5,1)), Layout(12, E(1)))
self.postcondition_composition(Layout((4,(4,3),1),(3,(12,1),0)), Layout(12, E(1)))
self.postcondition_composition(Layout((4,(4,3),1),(3,(12,1),0)), Layout(12, E(1,0)))
self.postcondition_composition(Layout((4,(2,3)),(6,(3,1))), Layout((2,4), (E(1,1),E(0))))
self.postcondition_composition(Layout((4,6,8)), Layout((2,2,2), (E(0),E(1),E(2))))
self.postcondition_composition(Layout((4,6,8)), Layout((2,2,2), (E(2),E(0),E(1))))
self.postcondition_composition(Layout((4,6,8), (E(0),E(1),E(2))), Layout((2,2,2), (E(0),E(1),E(2))))
self.postcondition_composition(Layout((3,5,7,11), (E(0),E(1),E(2),E(3))), Layout(3, 4*E(2)))
self.postcondition_composition(Layout((3,5,7,11), (E(0),E(1),E(2),E(3))), Layout(3, 4*E(2) + 2*E(3)))
self.postcondition_composition(Layout((3,5,7,11), (E(0),E(1),E(2),E(3))), Layout(3, ArithTuple(1,0,0,1)))
# Other
# Diag
self.postcondition_composition(Layout((4,4), (3,42)), Layout(4, ArithTuple(1,1)))
# Skew Diag
self.postcondition_composition(Layout((4,8), (3,42)), Layout(4, ArithTuple(1,2)))
def postcondition_associativity(self, A, B, C):
"""In general, composition is associative:
composition(composition(A, B), C) == composition(A, composition(B, C)).
The one caveat is the *extended domain*: `composition(A, B)` only guarantees
`R(i) == A(B(i))` for `i in Z(B)`. So the equality holds whenever each
intermediate result is evaluated inside its guaranteed domain -- every `C(i)`
is a coordinate of `B` (`< size(B)`) and every `B(C(i))` a coordinate of `A`
(`< size(A)`). When that nesting holds, both groupings agree on all of `Z(C)`.
"""
AB_C = composition(composition(A, B), C)
A_BC = composition(A, composition(B, C))
logger.info(f" (({A} o {B}) o {C}) = {AB_C}")
logger.info(f" ({A} o ({B} o {C})) = {A_BC}")
for i in range(size(C)):
ABC = A(B(C(i)))
assert AB_C(i) == ABC
assert A_BC(i) == ABC
assert AB_C(i) == A_BC(i)
def test_associativity(self):
cases = [
(Layout((4, 3), (3, 1)), Layout((4, 3), (1, 4)), Layout((4, 3), (1, 4))),
(Layout((4, 3), (3, 1)), Layout((4, 3), (1, 4)), Layout(6, 2)),
(Layout((4, 3), (1, 4)), Layout((4, 3), (3, 1)), Layout((4, 3), (1, 4))),
(Layout((4, 3), (1, 4)), Layout((4, 3), (3, 1)), Layout(6, 2)),
(Layout((6, 4), (4, 1)), Layout((4, 3), (3, 1)), Layout((4, 3), (1, 4))),
(Layout((6, 4), (4, 1)), Layout((4, 3), (3, 1)), Layout(6, 2)),
(Layout(6, 2), Layout((2, 3), (3, 1)), Layout((2, 3), (1, 2))),
(Layout(6, 2), Layout((2, 3), (1, 2)), Layout((2, 3), (3, 1))),
(Layout((2, 3), (3, 1)), Layout((2, 3), (1, 2)), Layout((2, 3), (1, 2))),
(Layout((8, 8), (8, 1)), Layout((6, 4), (4, 1)), Layout(6, 2)),
(Layout((8, 8), (8, 1)), Layout((6, 4), (4, 1)), Layout((2, 3), (1, 2))),
(Layout((4, 6), (1, 4)), Layout((4, 3), (3, 1)), Layout((4, 3), (1, 4))),
]
for layoutA, layoutB, layoutC in cases:
self.postcondition_associativity(layoutA, layoutB, layoutC)
def test_composition_sympy(self):
N, X, Y = sympy.symbols("N X Y", positive=True, integer=True)
self.postcondition_composition(Layout(N, X), Layout(3, 4))
self.postcondition_composition(Layout(N, X), Layout(2, 1))
self.postcondition_composition(Layout(N, 1), Layout(3, 4))
self.postcondition_composition(Layout(N, X), Layout((2, 3), (1, 2)))
self.postcondition_composition(Layout((12, N), (X, Y)), Layout(6, 4))
self.postcondition_composition(Layout((8, N), (X, Y)), Layout(4, 1))
self.postcondition_composition(Layout((4, N), (X, Y)), Layout((2, 2), (2, 1)))
def test_composition_sympy_fails(self):
# Dividing the concrete tile by a *symbolic* leading shape factor is an
# unverifiable divisibility condition, so composition must raise rather
# than emit a silently-unchecked symbolic result.
N, X, Y = sympy.symbols("N X Y", positive=True, integer=True)
with pytest.raises(ValueError):
composition(Layout((N, 8), (X, Y)), Layout(4, 1))