tinygrad/test/unit/test_symbolic.py

#!/usr/bin/env python
import unittest, pickle
from tinygrad.shape.symbolic import MulNode, SumNode, Variable, NumNode, LtNode, ModNode, Node, sym_render, sym_infer, create_lt_node, create_ge_node

class TestSymbolicPickle(unittest.TestCase):
  def _test_pickle_unpickle(self, x): self.assertEqual(x, pickle.loads(pickle.dumps(x)))
  def test_pickle_variable(self): self._test_pickle_unpickle(Variable("a", 3, 8))
  def test_pickle_variable_times_2(self): self._test_pickle_unpickle(Variable("a", 3, 8)*2)

class TestSymbolic(unittest.TestCase):
  def helper_test_variable(self, v, n, m, s):
    self.assertEqual(v.render(), s)
    self.assertEqual(v.min, n)
    self.assertEqual(v.max, m)

  def test_ge(self):
    self.helper_test_variable(create_ge_node(Variable("a", 3, 8), 77), 0, 0, "0")
    self.helper_test_variable(create_ge_node(Variable("a", 3, 8), 9), 0, 0, "0")
    self.helper_test_variable(create_ge_node(Variable("a", 3, 8), 8), 0, 1, "((a*-1)<-7)")
    self.helper_test_variable(create_ge_node(Variable("a", 3, 8), 4), 0, 1, "((a*-1)<-3)")
    self.helper_test_variable(create_ge_node(Variable("a", 3, 8), 3), 1, 1, "1")
    self.helper_test_variable(create_ge_node(Variable("a", 3, 8), 2), 1, 1, "1")

  def test_lt(self):
    self.helper_test_variable(create_lt_node(Variable("a", 3, 8), 77), 1, 1, "1")
    self.helper_test_variable(create_lt_node(Variable("a", 3, 8), 9), 1, 1, "1")
    self.helper_test_variable(create_lt_node(Variable("a", 3, 8), 8), 0, 1, "(a<8)")
    self.helper_test_variable(create_lt_node(Variable("a", 3, 8), 4), 0, 1, "(a<4)")
    self.helper_test_variable(create_lt_node(Variable("a", 3, 8), 3), 0, 0, "0")
    self.helper_test_variable(create_lt_node(Variable("a", 3, 8), 2), 0, 0, "0")

  def test_ge_divides(self):
    expr = create_lt_node(Variable("idx", 0, 511)*4 + Variable("FLOAT4_INDEX", 0, 3), 512)
    self.helper_test_variable(expr, 0, 1, "(idx<128)")

  def test_ge_divides_and(self):
    expr = Node.ands([create_lt_node(Variable("idx1", 0, 511)*4 + Variable("FLOAT4_INDEX", 0, 3), 512),
                      create_lt_node(Variable("idx2", 0, 511)*4 + Variable("FLOAT4_INDEX", 0, 3), 512)])
    self.helper_test_variable(expr, 0, 1, "((idx1<128) and (idx2<128))")
    expr = Node.ands([create_lt_node(Variable("idx1", 0, 511)*4 + Variable("FLOAT4_INDEX", 0, 3), 512),
                      create_lt_node(Variable("idx2", 0, 511)*4 + Variable("FLOAT8_INDEX", 0, 7), 512)])
    self.helper_test_variable(expr//4, 0, 0, "0")

  def test_lt_factors(self):
    expr = create_lt_node(Variable("idx1", 0, 511)*4 + Variable("FLOAT4_INDEX", 0, 256), 512)
    self.helper_test_variable(expr, 0, 1, "(((idx1*4)+FLOAT4_INDEX)<512)")

  def test_div_reduction(self):
    self.helper_test_variable(Variable("a", 2, 3)//2, 1, 1, "1")

  def test_var_becomes_num(self):
    assert isinstance(Variable("a", 2, 2), NumNode)

  def test_equality(self):
    idx1 = Variable("idx1", 0, 3)
    idx2 = Variable("idx2", 0, 3)
    assert idx1 == idx1
    assert idx1 != idx2
    assert idx1*4 == idx1*4
    assert idx1*4 != idx1*3
    assert idx1*4 != idx1+4
    assert idx1*4 != idx2*4
    assert idx1+idx2 == idx1+idx2
    assert idx1+idx2 == idx2+idx1
    assert idx1+idx2 != idx2
    assert idx1*idx2 == idx2*idx1

  def test_numnode_eq_int(self):
    n1 = NumNode(1)
    n2 = NumNode(2)
    assert n1 == 1
    assert n2 == 2
    assert n1 != n2
    assert hash(n1) == hash(1)
    assert hash(n2) == hash(2)

  def test_factorize(self):
    a = Variable("a", 0, 8)
    self.helper_test_variable(a*2+a*3, 0, 8*5, "(a*5)")

  def test_factorize_no_mul(self):
    a = Variable("a", 0, 8)
    self.helper_test_variable(a+a*3, 0, 8*4, "(a*4)")

  def test_neg(self):
    self.helper_test_variable(-Variable("a", 0, 8), -8, 0, "(a*-1)")

  def test_add_1(self):
    self.helper_test_variable(Variable("a", 0, 8)+1, 1, 9, "(1+a)")

  def test_add_num_1(self):
    self.helper_test_variable(Variable("a", 0, 8)+NumNode(1), 1, 9, "(1+a)")

  def test_sub_1(self):
    self.helper_test_variable(Variable("a", 0, 8)-1, -1, 7, "(-1+a)")

  def test_sub_num_1(self):
    self.helper_test_variable(Variable("a", 0, 8)-NumNode(1), -1, 7, "(-1+a)")

  def test_sub_self(self):
    a = Variable("a", 0, 8)
    self.helper_test_variable(a*3-a, 0, 16, "(a*2)")

  def test_mul_0(self):
    self.helper_test_variable(Variable("a", 0, 8)*0, 0, 0, "0")

  def test_mul_1(self):
    self.helper_test_variable(Variable("a", 0, 8)*1, 0, 8, "a")

  def test_mul_neg_1(self):
    self.helper_test_variable((Variable("a", 0, 2)*-1)//3, -1, 0, "((((a*-1)+3)//3)+-1)")

  def test_mul_2(self):
    self.helper_test_variable(Variable("a", 0, 8)*2, 0, 16, "(a*2)")

  def test_div_1(self):
    self.helper_test_variable(Variable("a", 0, 8)//1, 0, 8, "a")

  def test_mod_1(self):
    self.helper_test_variable(Variable("a", 0, 8)%1, 0, 0, "0")

  def test_add_min_max(self):
    self.helper_test_variable(Variable("a", 0, 8) * 2 + 12, 12, 16+12, "((a*2)+12)")

  def test_div_remove(self):
    self.helper_test_variable(Variable("a", 0, 7) // 20, 0, 0, "0")

  def test_div_min_max(self):
    self.helper_test_variable(Variable("a", 0, 7) // 2, 0, 3, "(a//2)")

  def test_div_neg_min_max(self):
    self.helper_test_variable(Variable("a", 0, 7) // -2, -4, 0, "((((a*-1)+8)//2)+-4)")
    self.helper_test_variable(Variable("a", 0, 6) // -2, -3, 0, "((((a*-1)+6)//2)+-3)")

  def test_sum_div_remove(self):
    self.helper_test_variable(Node.sum([Variable("a", 0, 7), Variable("b", 0, 3)]) // 20, 0, 0, "0")

  def test_sum_div_min_max(self):
    self.helper_test_variable(Node.sum([Variable("a", 0, 7), Variable("b", 0, 3)]) // 2, 0, 5, "((a+b)//2)")

  def test_sum_div_mod_factor(self):
    self.helper_test_variable(Node.sum([Variable("a", 0, 7)*4, Variable("b", 0, 3)*4]) // 2, 0, 20, "((a*2)+(b*2))")
    self.helper_test_variable(Node.sum([Variable("a", 0, 7)*4, Variable("b", 0, 3)*4]) % 2, 0, 0, "0")

  def test_sum_div_some_factor(self):
    self.helper_test_variable(Node.sum([Variable("a", 0, 7)*5, Variable("b", 0, 3)*4]) // 2, 0, 23, "(((a*5)//2)+(b*2))")

  def test_sum_div_trim_const(self):
    self.helper_test_variable((Variable("a", 0, 7)*4 + Variable("b", 0, 3)*4 + 7) // 16, 0, 2, "((1+a+b)//4)")

  def test_sum_div_some_partial_factor(self):
    self.helper_test_variable(Node.sum([Variable("a", 0, 7)*6, Variable("b", 0, 7)*6]) // 16, 0, 5, "(((a*3)+(b*3))//8)")
    self.helper_test_variable(Node.sum([NumNode(16), Variable("a", 0, 7)*6, Variable("b", 0, 7)*6]) // 16, 1, 6, "((((a*3)+(b*3))//8)+1)")
    self.helper_test_variable((Variable("a", 0, 7)*30+20)//20, 1, 11, "(((a*3)//2)+1)")

  def test_sum_div_no_factor(self):
    self.helper_test_variable(Node.sum([Variable("a", 0, 7)*5, Variable("b", 0, 3)*5]) // 2, 0, 25, "(((a*5)+(b*5))//2)")

  def test_mod_factor(self):
    # NOTE: even though the mod max is 50, it can't know this without knowing about the mul
    self.helper_test_variable(Node.sum([Variable("a", 0, 7)*100, Variable("b", 0, 3)*50]) % 100, 0, 99, "((b*50)%100)")

  def test_mod_to_sub(self):
    # This is mod reduction
    self.helper_test_variable((1+Variable("a",1,2))%2, 0, 1, "(-1+a)")

  def test_sum_div_const(self):
    self.helper_test_variable(Node.sum([Variable("a", 0, 7)*4, NumNode(3)]) // 4, 0, 7, "a")

  def test_sum_div_const_big(self):
    self.helper_test_variable(Node.sum([Variable("a", 0, 7)*4, NumNode(3)]) // 16, 0, 1, "(a//4)")

  def test_sum_lt_fold(self):
    self.helper_test_variable(create_lt_node(Node.sum([Variable("a", 0, 7) * 4, Variable("b", 0, 3)]), 16), 0, 1, "(a<4)")
    self.helper_test_variable(create_lt_node(Node.sum([Variable("a", 0, 7) * 4, Variable("b", 0, 4)]), 16), 0, 1, "(((a*4)+b)<16)")
    self.helper_test_variable(create_lt_node(Node.sum([Variable("uidx", 0, 3), Variable("a", 0, 1529) * 12]), (4 * 67)), 0, 1, "(a<23)")

  def test_mul_mod_large(self):
    self.helper_test_variable((Variable("a", 0, 20)*10)%9, 0, 8, "(a%9)")

  def test_mul_mod_small(self):
    self.helper_test_variable((Variable("a", 0, 5)*10)%9, 0, 5, "a")

  def test_mod_mod(self):
    self.helper_test_variable((Variable("a", 0, 31)%12)%4, 0, 3, "(a%4)")
    self.helper_test_variable(((4*Variable("a", 0, 31)) % 12) % 4, 0, 0, "0")
    self.helper_test_variable(((5*Variable("a", 0, 31)) % 12) % 5, 0, 4, "(((a*5)%12)%5)")
    self.helper_test_variable((Variable("a", 0, 31) % 4) % 12, 0, 3, "(a%4)")

  def test_mul_mul(self):
    self.helper_test_variable((Variable("a", 0, 5)*10)*9, 0, 5*10*9, "(a*90)")

  def test_mul_lt(self):
    self.helper_test_variable(create_lt_node(Variable("a", 0, 5)*4,13), 0, 1, "(a<4)")
    self.helper_test_variable(create_lt_node(Variable("a", 0, 5)*4,16), 0, 1, "(a<4)")
    self.helper_test_variable(create_ge_node(Variable("a", 0, 5)*4,12), 0, 1, "((a*-1)<-2)")
    self.helper_test_variable(create_ge_node(Variable("a", 0, 5)*4,13), 0, 1, "((a*-1)<-3)")

  def test_div_div(self):
    self.helper_test_variable((Variable("a", 0, 1800)//10)//9, 0, 20, "(a//90)")

  def test_distribute_mul(self):
    self.helper_test_variable(Node.sum([Variable("a", 0, 3), Variable("b", 0, 5)])*3, 0, 24, "((a*3)+(b*3))")
    self.helper_test_variable((1+Variable("a", 0, 3))*(-2)+12, 4, 10, "((a*-2)+10)")

  def test_mod_mul_sum(self):
    self.helper_test_variable(Node.sum([Variable("b", 0, 2), Variable("a", 0, 5)*10])%9, 0, 7, "(a+b)")

  def test_sum_0(self):
    self.helper_test_variable(Node.sum([Variable("a", 0, 7)]), 0, 7, "a")

  def test_mod_remove(self):
    self.helper_test_variable(Variable("a", 0, 6)%100, 0, 6, "a")

  def test_big_mod(self):
    # NOTE: we no longer support negative variables
    #self.helper_test_variable(Variable("a", -20, 20)%10, -9, 9, "(a%10)")
    #self.helper_test_variable(Variable("a", -20, 0)%10, -9, 0, "(a%10)")
    #self.helper_test_variable(Variable("a", -20, 1)%10, -9, 1, "(a%10)")
    self.helper_test_variable(Variable("a", 0, 20)%10, 0, 9, "(a%10)")
    #self.helper_test_variable(Variable("a", -1, 20)%10, -1, 9, "(a%10)")

  def test_ge_remove(self):
    self.helper_test_variable(create_ge_node(Variable("a", 0, 6), 25), 0, 0, "0")

  def test_lt_remove(self):
    self.helper_test_variable(create_lt_node(Variable("a", 0, 6), -3), 0, 0, "0")
    self.helper_test_variable(create_lt_node(Variable("a", 0, 6), 3), 0, 1, "(a<3)")
    self.helper_test_variable(create_lt_node(Variable("a", 0, 6), 8), 1, 1, "1")

  def test_lt_sum_remove(self):
    self.helper_test_variable(create_lt_node(Variable("a", 0, 6) + 2, 3), 0, 1, "(a<1)")

  def test_and_fold(self):
    self.helper_test_variable(Node.ands([NumNode(0), Variable("a", 0, 1)]), 0, 0, "0")

  def test_and_remove(self):
    self.helper_test_variable(Node.ands([NumNode(1), Variable("a", 0, 1)]), 0, 1, "a")

  def test_mod_factor_negative(self):
    self.helper_test_variable(Node.sum([NumNode(-29), Variable("a", 0, 10), Variable("b", 0, 10)*28]) % 28, 0, 27, "((27+a)%28)")
    self.helper_test_variable(Node.sum([NumNode(-29), Variable("a", 0, 100), Variable("b", 0, 10)*28]) % 28, 0, 27, "((27+a)%28)")

  def test_sum_combine_num(self):
    self.helper_test_variable(Node.sum([NumNode(29), Variable("a", 0, 10), NumNode(-23)]), 6, 16, "(6+a)")

  def test_sum_num_hoisted_and_factors_cancel_out(self):
    self.helper_test_variable(Node.sum([Variable("a", 0, 1) * -4 + 1, Variable("a", 0, 1) * 4]), 1, 1, "1")

  def test_div_cancel(self):
    self.helper_test_variable(Node.sum([NumNode(-40), Variable("a", 0, 10)*2, Variable("b", 0, 10)*40]) // 40, -1, 9, "(-1+b)")

  def test_mod_cancel(self):
    self.helper_test_variable(Node.sum([NumNode(-40), Variable("a", 0, 10)*2, Variable("b", 0, 10)*40]) % 40, 0, 20, "(a*2)")

  def test_mul_div(self):
    self.helper_test_variable((Variable("a", 0, 10)*4)//4, 0, 10, "a")

  def test_mul_div_factor_mul(self):
    self.helper_test_variable((Variable("a", 0, 10)*8)//4, 0, 20, "(a*2)")

  def test_mul_div_factor_div(self):
    self.helper_test_variable((Variable("a", 0, 10)*4)//8, 0, 5, "(a//2)")

  def test_sum_div_partial_remove(self):
    self.helper_test_variable(Node.sum([Variable("idx0", 0, 127)*4, Variable("idx2", 0, 3)])//4, 0, 127, "idx0")

  def test_div_numerator_negative(self):
    self.helper_test_variable((Variable("idx", 0, 9)*-10)//11, -9, 0, "((((idx*-10)+99)//11)+-9)")

  def test_div_into_mod(self):
    self.helper_test_variable((Variable("idx", 0, 16)*4)%8//4, 0, 1, "(idx%2)")

  def test_div_neg_cancel(self):
    self.helper_test_variable((-Variable("idx", 0, 100)+199)//-4 + 50, 0, 25, "((1+idx)//4)")
    self.helper_test_variable((-Variable("idx", 0, 100)+200)//-4 + 50, 0, 25, "(idx//4)")
    self.helper_test_variable((-Variable("idx", 0, 100)+201)//-4 + 50, -1, 24, "(((3+idx)//4)+-1)")

  def test_sum_div_big_const(self):
    gidx0 = Variable("gidx0", 0, 24)
    self.helper_test_variable((gidx0+19)//20, 0, 2, "((19+gidx0)//20)")
    self.helper_test_variable((gidx0+20)//20, 1, 2, "((gidx0//20)+1)")
    self.helper_test_variable((gidx0+21)//20, 1, 2, "(((1+gidx0)//20)+1)")

  def test_sum_div_complex1(self):
    gidx0 = Variable("gidx0", 0, 24)
    gidx1 = Variable("gidx1", 0, 1)
    gidx2 = Variable("gidx2", 0, 255)
    lidx0 = Variable("lidx0", 0, 1)
    lidx1 = Variable("lidx1", 0, 15)
    lidx2 = Variable("lidx2", 0, 3)
    alu0 = gidx2*640+gidx1*160+(gidx0//5)*2+lidx0*320+lidx1*10
    self.helper_test_variable((alu0+lidx2*2+1)//20, 0, 8192, "((((((gidx0//5)+lidx2)//5)+lidx1)//2)+(gidx1*8)+(gidx2*32)+(lidx0*16))")

  def test_sum_div_complex2(self):
    gidx0 = Variable("gidx0", 0, 7)
    lidx2 = Variable("lidx2", 0, 1)
    lidx3 = Variable("lidx3", 0, 1)
    self.helper_test_variable((gidx0*4+lidx2*2+1)//10, 0, 3, "(((gidx0*2)+lidx2)//5)")
    self.helper_test_variable((gidx0*4+lidx2*2+lidx3)//10, 0, 3, "(((gidx0*2)+lidx2)//5)")
    self.helper_test_variable((gidx0*2+lidx2)//10, 0, 1, "(gidx0//5)")

  def test_sum_div_complex3(self):
    gidx0 = Variable("gidx0", 0, 7)
    lidx2 = Variable("lidx2", 0, 12)
    lidx3 = Variable("lidx3", 0, 1)
    self.helper_test_variable((gidx0*4+lidx2*2+lidx3)//12, 0, 4, "(((lidx2//2)+gidx0)//3)")
    self.helper_test_variable((lidx2*2+gidx0*4+lidx3)//12, 0, 4, "(((lidx2//2)+gidx0)//3)")

class TestSymbolicNumeric(unittest.TestCase):
  def helper_test_numeric(self, f):
    # TODO: why are the negative tests broken? (even if we did support negative variables)
    #MIN, MAX = -10, 10
    MIN, MAX = 0, 10
    # one number
    for i in range(MIN, MAX):
      v = f(NumNode(i))
      #print(i, f(i), v.min, v.max)
      self.assertEqual(v.min, v.max)
      self.assertEqual(v.min, f(i))
    for kmin in range(MIN, MAX):
      for kmax in range(MIN, MAX):
        if kmin > kmax: continue
        v = f(Variable("tmp", kmin, kmax))
        values = [f(rv) for rv in range(kmin, kmax+1)]
        # the min and max may not be exact
        self.assertLessEqual(v.min, min(values))
        self.assertGreaterEqual(v.max, max(values))

  def test_mod_4(self): self.helper_test_numeric(lambda x: (x%4))
  def test_div_4(self): self.helper_test_numeric(lambda x: (x//4))
  def test_plus_1_div_2(self): self.helper_test_numeric(lambda x: (x+1)//2)
  def test_plus_1_mod_2(self): self.helper_test_numeric(lambda x: (x+1)%2)
  def test_times_2(self): self.helper_test_numeric(lambda x: x*2)
  def test_times_2_plus_3(self): self.helper_test_numeric(lambda x: x*2 + 3)
  def test_times_2_plus_3_mod_4(self): self.helper_test_numeric(lambda x: (x*2 + 3)%4)
  def test_times_2_plus_3_div_4(self): self.helper_test_numeric(lambda x: (x*2 + 3)//4)
  def test_times_2_plus_3_div_4_mod_4(self): self.helper_test_numeric(lambda x: ((x*2 + 3)//4)%4)

class TestSymbolicVars(unittest.TestCase):
  def test_simple(self):
    z = NumNode(0)
    a = Variable("a", 0, 10)
    b = Variable("b", 0, 10)
    c = Variable("c", 0, 10)
    assert z.vars() == z.vars() == set()
    assert a.vars() == a.vars() == {a}
    m = MulNode(a, 3)
    assert m.vars() == {a}
    s = SumNode([a, b, c])
    assert s.vars() == {a, b, c}

  def test_compound(self):
    a = Variable("a", 0, 10)
    b = Variable("b", 0, 10)
    c = Variable("c", 0, 10)
    assert (a + b * c).vars() == {a, b, c}
    assert (a % 3 + b // 5).vars() == {a, b}
    assert (a + b + c - a).vars() == {b, c}

  def test_dedup(self):
    a = Variable("a", 0, 10)
    assert (a * a).vars() == {a}
    assert (a//4 + a//6).vars() == {a}

class TestSymbolicMinMax(unittest.TestCase):
  def test_min_max_known(self):
    a = Variable("a", 1, 8)
    assert max(1, a) == max(a, 1) == a
    assert min(1, a) == min(a, 1) == 1

class TestSymRender(unittest.TestCase):
  def test_sym_render(self):
    a = Variable("a", 1, 8)
    b = Variable("b", 1, 10)
    assert sym_render(a) == "a"
    assert sym_render(1) == "1"
    assert sym_render(a+1) == "(1+a)"
    assert sym_render(a*b) == "(a*b)"

class TestSymInfer(unittest.TestCase):
  def test_sym_infer(self):
    a = Variable("a", 0, 10)
    b = Variable("b", 0, 10)
    c = Variable("c", 0, 10)
    var_vals = {a: 2, b: 3, c: 4}
    assert sym_infer(5, var_vals) == 5
    assert sym_infer(a, var_vals) == 2
    assert sym_infer(b, var_vals) == 3
    assert sym_infer(a+b, var_vals) == 5
    assert sym_infer(a-b, var_vals) == -1
    assert sym_infer(a+b+c, var_vals) == 9
    assert sym_infer(a*b, var_vals) == 6
    assert sym_infer(a*b+c, var_vals) == 10

class TestSymbolicSymbolicOps(unittest.TestCase):
  def test_node_divmod_node(self):
    i = Variable("i", 1, 10)
    idx0 = Variable("idx0", 0, i*3-1)
    assert NumNode(0) // (Variable("i", 1, 10)*128) == 0
    assert NumNode(0) % (Variable("i", 1, 10)*128) == 0
    assert NumNode(127) // (Variable("i", 1, 10)*128) == 0
    assert NumNode(127) % (Variable("i", 1, 10)*128) == 127
    assert 127 // (Variable("i", 1, 10)*128) == 0
    assert 127 % (Variable("i", 1, 10)*128) == 127
    assert NumNode(128) // (Variable("i", 1, 10)*128 + 128) == 0
    assert NumNode(128) % (Variable("i", 1, 10)*128 + 128) == 128
    assert 128 // (Variable("i", 1, 10)*128 + 128) == 0
    assert 128 % (Variable("i", 1, 10)*128 + 128) == 128
    assert 0 // (Variable("i", 1, 10)*128) == 0
    assert 0 % (Variable("i", 1, 10)*128) == 0
    assert idx0 // (i*3) == 0
    assert idx0 % (i*3) == idx0
    assert i // i == 1
    assert i % i == 0
    assert 128 // NumNode(4) == 32
    assert 128 % NumNode(4) == 0
    assert NumNode(128) // NumNode(4) == 32
    assert NumNode(128) % NumNode(4) == 0

  def test_mulnode_divmod_node(self):
    i = Variable("i", 1, 10)
    idx0 = Variable("idx0", 0, 31)
    # assert (idx0*(i*4+4)) // (i+1) == (idx0*4)
    # assert (idx0*(i*4+4)) % (i+1) == 0
    assert (idx0*i) % i == 0

  def test_sumnode_divmod_sumnode(self):
    i = Variable("i", 1, 10)
    # idx0 = Variable("idx0", 0, 7)
    # idx1 = Variable("idx1", 0, 3)
    # idx2 = Variable("idx2", 0, i)
    # assert (idx0*(i*4+4)+idx1*(i+1)+idx2) // (i+1) == idx0*4+idx1
    # assert (idx0*(i*4+4)+idx1*(i+1)+idx2) % (i+1) == idx2
    assert (i+1) // (i*128+128) == 0
    assert (i+1) % (i*128+128) == (i+1)
    # assert (i+1+idx2) // (i+1) == 1
    # assert (i+1+idx2) % (i+1) == idx2
    # assert (idx0*(i*4+4)+i+1+idx2) // (i+1) == idx0*4+1
    # assert (idx0*(i*4+4)+i+1+idx2) % (i+1) == idx2
    # assert (i*128+128)*2 // (i*128+128) == 2
    # assert (i*128+128)*2 % (i*128+128) == 0

  def test_sumnode_div_numnode_no_factoring(self):
    gid = Variable("gid", 0, 1023)
    lid = Variable("lid", 0, 3)
    expr_before_div = NumNode(-1019)-4*lid-gid
    unfactored_expr = Node.__floordiv__(expr_before_div, NumNode(-16), False)
    factored_expr = Node.__floordiv__(expr_before_div, NumNode(-16), True)
    self.assertEqual(unfactored_expr.render(), "(((lid*4)+1019+gid)//16)")
    self.assertEqual(factored_expr.render(), "(((((3+gid)//4)+2+lid)//4)+63)")

  def test_mod_node_max(self):
    i = Variable("i", 1, 128)
    gidx0 = Variable("gidx0", 0, i)
    mod = gidx0 % 8
    assert isinstance(mod, ModNode) and mod.a == gidx0 and mod.b == 8
    mod = gidx0 % 2
    assert isinstance(mod, ModNode) and mod.a == gidx0 and mod.b == 2

    gidx0 = Variable("gidx0", 0, i*8+7)
    mod = gidx0 % 8
    assert isinstance(mod, ModNode) and mod.a == gidx0 and mod.b == 8
    mod = gidx0 % 2
    assert isinstance(mod, ModNode) and mod.a == gidx0 and mod.b == 2

  def test_node_lt_node(self):
    a = Variable("a", 1, 5)
    b = Variable("b", 6, 9)
    c = Variable("c", 1, 10)
    d = Variable("d", 5, 10)
    # if the comparison output is always the same, it folds to num
    assert create_lt_node(a, b) == NumNode(1)
    assert create_lt_node(b, a) == NumNode(0)
    assert create_lt_node(d, a) == NumNode(0)
    assert create_lt_node(a, a) == NumNode(0)
    assert create_lt_node(a, a) == NumNode(0)
    # if it remains as a LtNode, bool is always true and (min, max) == (0, 1)
    a_lt_c = create_lt_node(a, c)
    assert isinstance(a_lt_c, LtNode) and a_lt_c.min == 0 and a_lt_c.max == 1
    assert a_lt_c
    # same when comparing with a constant
    a_lt_3 = create_lt_node(a, 3)
    assert a_lt_3 and a_lt_3.min == 0 and a_lt_3.max == 1

  def test_sumnode_mulnode_lt(self):
    a = Variable("a", 1, 2)
    b = Variable("b", 1, 2)
    c = Variable("c", 1, 2)
    x = SumNode([MulNode(a, b), c])
    with self.assertRaises(AssertionError):
      create_lt_node(x, 3)

  def test_nested_variable_mod(self):
    i = Variable("i", 1, 5)
    idx0 = Variable("idx0", 0, i)
    with self.assertRaises(AssertionError):
      assert idx0 % 2 == idx0

  def test_num_node_mul_node(self):
    a = Variable("a", 1, 5)
    b = NumNode(2) * a
    assert b == a * 2
    assert isinstance(b, MulNode)
    b = NumNode(1) * a
    assert b == a
    assert isinstance(b, Variable)
    b = NumNode(0) * a
    assert b == 0
    assert isinstance(b, NumNode)

  def test_substitute(self):
    a = Variable("idx0", 1, 3)
    b = a + 1
    c = b.substitute({a: NumNode(1)})
    assert c == NumNode(2)

class TestSymbolicRealWorld(unittest.TestCase):
  def test_resnet_half(self):
    gidx0 = Variable("gidx0", 0, 3)
    gidx1 = Variable("gidx1", 0, 127)
    gidx2 = Variable("gidx2", 0, 7)
    lidx3 = Variable("lidx3", 0, 7)
    lidx4 = Variable("lidx4", 0, 1)
    lidx5 = Variable("lidx5", 0, 15)

    idx = ((((1+lidx5)%16)*49)+(((262145+lidx5)//16)*802816)+(gidx0*3211264)+(gidx1*784)+(gidx2*8)+(lidx4*100352)+-13151129600+lidx3)
    print(idx.render())
    # NOTE: this used to have 13,151,129,600 in the output which is out of int32 range.
    assert idx.render() == "((((1+lidx5)%16)*49)+(((1+lidx5)//16)*802816)+(gidx0*3211264)+(gidx1*784)+(gidx2*8)+(lidx4*100352)+2207744+lidx3)"

if __name__ == '__main__':
  unittest.main()