symbolic shapetracker (#1506)

* symbolic shapetracker

* no need

* keep only symbolic and clean up

* explicit // and % Node support

* NumNode * Node

test/test_symbolic_shapetracker.py

@@ -1,5 +1,5 @@
 import unittest
-from tinygrad.shape.shapetracker import ShapeTracker
+from tinygrad.shape.shapetracker import ShapeTracker, View
 from tinygrad.shape.symbolic import Variable
 from tinygrad.tensor import Tensor
 
@@ -99,3 +99,20 @@ class TestSymbolicExpand(unittest.TestCase):
     a = Tensor.rand(3, 4).reshape(3, vi)
     a = a + 1
     assert a.shape == (3, vi)
+
+class TestSymbolicShapeExpr(unittest.TestCase):
+  def test_symbolic_expr_idxs(self):
+    # taken from symbolic shape llama
+    i = Variable("i", 1, 120)
+    gidx0 = Variable("gidx0", 0, i)
+    lidx1 = Variable("lidx1", 0, 7)
+    idx = (gidx0, lidx1, Variable.num(1))
+    shape = (i+1, 8, 4)
+    strides = (1, (i*4)+4, i+1)
+    view = View(shape, strides)
+    st = ShapeTracker(shape, [view])
+    idx, valid = st.expr_idxs(idx)
+    assert idx.render() == "(((1+i)*1)+(lidx1*((i*4)+4))+gidx0)"
+
+if __name__ == '__main__':
+  unittest.main()

test/unit/test_symbolic.py

@@ -1,6 +1,6 @@
 #!/usr/bin/env python
 import unittest
-from tinygrad.shape.symbolic import MulNode, SumNode, Variable, NumNode, sym_vars
+from tinygrad.shape.symbolic import MulNode, SumNode, Variable, NumNode, LtNode, sym_vars, sym_render
 
 class TestSymbolic(unittest.TestCase):
   def helper_test_variable(self, v, n, m, s):
@@ -257,8 +257,7 @@ class TestSymbolicVars(unittest.TestCase):
     a = Variable("a", 0, 10)
     b = Variable("b", 0, 10)
     c = Variable("c", 0, 10)
-    # TODO: update this after we support symbolic * symbolic
-    assert (a + b * c).vars() == [a, b]
+    assert (a + b * c).vars() == [a, b, c]
     assert (a % 3 + b // 5).vars() == [a, b]
     assert (a + b + c - a).vars() == [b, c]
 
@@ -276,6 +275,73 @@ class TestSymbolicMinMax(unittest.TestCase):
     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 TestSymbolicSymbolicOps(unittest.TestCase):
+  def test_node_div_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(127) // (Variable("i", 1, 10)*128) == 0
+    assert idx0 // (i*3) == 0
+
+  def test_node_mod_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(127) % (Variable("i", 1, 10)*128) == 127
+    assert NumNode(128) % (Variable("i", 1, 10)*128 + 128) == 128
+    assert 0 % (Variable("i", 1, 10)*128) == 0
+    assert 127 % (Variable("i", 1, 10)*128) == 127
+    assert 128 % (Variable("i", 1, 10)*128 + 128) == 128
+    assert idx0 % (i*3) == idx0
+    assert i % i == 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) == (i+1)
+
+  def test_node_lt_node(self):
+    a = Variable("a", 1, 5)
+    b = Variable("b", 6, 9)
+    c = Variable("c", 1, 10)
+    # if the value is always the same, it folds to num
+    assert (a < b) == 1
+    # if it remains as a LtNode, bool is always true and we need to test against min to test if it always evals to True
+    assert (a < c).__class__ is LtNode and (a < c).min == 0 and (a < c).max == 1
+    assert a < c
+    assert not (a < c).min
+    assert (a > c).__class__ is LtNode and (a > c).min == 0 and (a > c).max == 1
+    assert not (a > c).min
+    # same when comparing with a constant
+    assert a < 3
+    assert a > 3
+
+  def test_num_node_mul_node(self):
+    a = NumNode(2)
+    b = Variable("b", 1, 5)
+    c = a * b
+    assert c == b * 2
+    assert isinstance(c, MulNode)
+
 if __name__ == '__main__':
   unittest.main()
-

tinygrad/shape/symbolic.py

@@ -8,7 +8,7 @@ from typing import List, Dict, Callable, Tuple, Type, Union, Optional, Any
 # NOTE: Python has different behavior for negative mod and floor div than c
 # symbolic matches the Python behavior, but the code output is agnostic, and will never have negative numbers in div or mod
 
-def is_sym_int(x: Any) -> bool: return isinstance(x, int) or isinstance(x, Node)
+def is_sym_int(x: Any) -> bool: return isinstance(x, (int, Node))
 def sym_vars(x: Union[Node, int]) -> List[Variable]: return [] if isinstance(x, int) else x.vars()
 
 class Node:
@@ -40,9 +40,8 @@ class Node:
   def __gt__(self, b:Union[Node,int]): return (-self) < (-b)
   def __ge__(self, b:Union[Node,int]): return (-self) < (-b+1)
   def __lt__(self, b:Union[Node,int]):
-    if self == b: return NumNode(0)
     lhs = self
-    if isinstance(lhs, SumNode):
+    if isinstance(lhs, SumNode) and isinstance(b, int):
       muls, others = partition(lhs.nodes, lambda x: isinstance(x, MulNode) and x.b > 0 and x.max >= b)
       if len(muls):
         # NOTE: gcd in python 3.8 takes exactly 2 args
@@ -58,12 +57,17 @@ class Node:
   def __mul__(self, b:Union[Node, int]):
     if b == 0: return NumNode(0)
     if b == 1: return self
+    if self.__class__ is NumNode: return NumNode(self.b*b) if isinstance(b, int) else create_node(MulNode(b, self.b))
     return create_node(MulNode(self, b))
   def __rmul__(self, b:int): return self*b
 
   # *** complex ops ***
 
-  def __floordiv__(self, b:int, factoring_allowed=True):
+  def __rfloordiv__(self, b:int): raise RuntimeError(f"not supported: {b} // {self}")
+  def __floordiv__(self, b:Union[Node,int], factoring_allowed=True):
+    if isinstance(b, Node):
+      if (b > self).min > 0 and self.min >= 0: return NumNode(0)
+      raise RuntimeError(f"not supported: {self} // {b}")
     assert b != 0
     if b < 0: return (self//-b)*-1
     if b == 1: return self
@@ -75,7 +79,14 @@ class Node:
       return (self + -offset*b).__floordiv__(b, factoring_allowed=False) + offset
     return create_node(DivNode(self, b))
 
-  def __mod__(self, b:int):
+  def __rmod__(self, b:int):
+    if self.min > b >= 0: return NumNode(b)
+    raise RuntimeError(f"not supported: {b} % {self}")
+  def __mod__(self, b:Union[Node,int]):
+    if isinstance(b, Node):
+      if self == b: return NumNode(0)
+      if (b - self).min > 0 and self.min >= 0: return self # b - self simplifies the node
+      raise RuntimeError(f"not supported: {self} % {b}")
     assert b > 0
     if b == 1: return NumNode(0)
     if self.min >= 0 and self.max < b: return self
@@ -137,6 +148,8 @@ class NumNode(Node):
   def __init__(self, num:int):
     self.b, self.min, self.max = num, num, num
   def __int__(self): return self.b
+  def __eq__(self, other): return self.b == other
+  def __hash__(self): return self.hash  # needed with __eq__ override
 
 def create_node(ret:Node):
   assert ret.min <= ret.max, f"min greater than max! {ret.min} {ret.max} when creating {type(ret)} {ret}"
@@ -147,38 +160,37 @@ class OpNode(Node):
   def __init__(self, a:Node, b:Union[Node, int]):
     self.a, self.b = a, b
     self.min, self.max = self.get_bounds()
-  def vars(self): return self.a.vars()
+  def vars(self): return self.a.vars() + (self.b.vars() if isinstance(self.b, Node) else [])
   @abstractmethod
   def get_bounds(self) -> Tuple[int, int]: pass
 
 class LtNode(OpNode):
   def __mul__(self, b: Union[Node, int]): return (self.a*b) < (self.b*b)
-  def __floordiv__(self, b: int, _=False): return (self.a//b) < (self.b//b)
+  def __floordiv__(self, b: Union[Node, int], _=False): return (self.a//b) < (self.b//b)
   def get_bounds(self) -> Tuple[int, int]:
     if isinstance(self.b, int): return int(self.a.max < self.b), int(self.a.min < self.b)
     return (1, 1) if self.a.max < self.b.min else (0, 0) if self.a.min > self.b.max else (0, 1)
 
 class MulNode(OpNode):
   def __mul__(self, b: Union[Node, int]): return self.a*(self.b*b) # two muls in one mul
-  def __floordiv__(self, b: int, factoring_allowed=False): # NOTE: mod negative isn't handled right
-    assert isinstance(self.b, int)
+  def __floordiv__(self, b: Union[Node, int], factoring_allowed=False): # NOTE: mod negative isn't handled right
     if self.b % b == 0: return self.a*(self.b//b)
     if b % self.b == 0 and self.b > 0: return self.a//(b//self.b)
     return Node.__floordiv__(self, b, factoring_allowed)
-  def __mod__(self, b: int):
+  def __mod__(self, b: Union[Node, int]):
     a = (self.a * (self.b%b))
     return Node.__mod__(a, b)
   def get_bounds(self) -> Tuple[int, int]:
     return (self.a.min*self.b, self.a.max*self.b) if self.b >= 0 else (self.a.max*self.b, self.a.min*self.b)
 
 class DivNode(OpNode):
-  def __floordiv__(self, b: int, _=False): return self.a//(self.b*b) # two divs is one div
+  def __floordiv__(self, b: Union[Node, int], _=False): return self.a//(self.b*b) # two divs is one div
   def get_bounds(self) -> Tuple[int, int]:
     assert self.a.min >= 0 and isinstance(self.b, int)
     return self.a.min//self.b, self.a.max//self.b
 
 class ModNode(OpNode):
-  def __floordiv__(self, b: int, factoring_allowed=True):
+  def __floordiv__(self, b: Union[Node, int], factoring_allowed=True):
     if (self.b % b == 0): return (self.a//b) % (self.b//b) # put the div inside mod
     return Node.__floordiv__(self, b, factoring_allowed)
   def get_bounds(self) -> Tuple[int, int]:
@@ -191,11 +203,22 @@ class RedNode(Node):
 
 class SumNode(RedNode):
   def __mul__(self, b: Union[Node, int]): return Node.sum([x*b for x in self.nodes]) # distribute mul into sum
-  def __floordiv__(self, b: int, factoring_allowed=True):
-    if b == 1: return self
-    if not factoring_allowed: return Node.__floordiv__(self, b, factoring_allowed)
+  def __floordiv__(self, b: Union[Node, int], factoring_allowed=True):
     fully_divided: List[Node] = []
     rest: List[Node] = []
+    if isinstance(b, SumNode):
+      nu_num = sum(node.b for node in self.flat_components if node.__class__ is NumNode)
+      de_num = sum(node.b for node in b.flat_components if node.__class__ is NumNode)
+      if de_num and nu_num % de_num == 0 and b * (d := nu_num // de_num) == self: return NumNode(d)
+    if isinstance(b, Node):
+      for x in self.flat_components:
+        if x % b == 0: fully_divided.append(x // b)
+        else: rest.append(x)
+      if (b > (sum_rest:=create_rednode(SumNode, rest))).min and (sum_rest >= 0).min: return create_rednode(SumNode, fully_divided)
+      return Node.__floordiv__(self, b, False)
+    if b == 1: return self
+    if not factoring_allowed: return Node.__floordiv__(self, b, factoring_allowed)
+    fully_divided, rest = [], []
     _gcd = b
     divisor = 1
     for x in self.flat_components:
@@ -212,7 +235,12 @@ class SumNode(RedNode):
     if divisor > 1: return Node.sum(fully_divided) + Node.sum(rest).__floordiv__(divisor) // (b//divisor)
     return Node.sum(fully_divided) + Node.__floordiv__(Node.sum(rest), b)
 
-  def __mod__(self, b: int):
+  def __mod__(self, b: Union[Node, int]):
+    if isinstance(b, SumNode):
+      nu_num = sum(node.b for node in self.flat_components if node.__class__ is NumNode)
+      de_num = sum(node.b for node in b.flat_components if node.__class__ is NumNode)
+      if de_num and nu_num % de_num == 0 and b * (nu_num // de_num) == self: return NumNode(0)
+    if isinstance(b, Node) and (b - self).min > 0: return self # b - self simplifies the node
     new_nodes: List[Node] = []
     for x in self.nodes:
       if x.__class__ is NumNode: new_nodes.append(Variable.num(x.b%b))
@@ -228,7 +256,7 @@ class SumNode(RedNode):
 
 class AndNode(RedNode):
   def __mul__(self, b: Union[Node, int]): Variable.ands([x*b for x in self.nodes])
-  def __floordiv__(self, b: int, _=True): return Variable.ands([x//b for x in self.nodes])
+  def __floordiv__(self, b: Union[Node, int], _=True): return Variable.ands([x//b for x in self.nodes])
 
 def create_rednode(typ:Type[RedNode], nodes:List[Node]):
   ret = typ(nodes)
@@ -236,13 +264,15 @@ def create_rednode(typ:Type[RedNode], nodes:List[Node]):
   elif typ == AndNode: ret.min, ret.max = (min([x.min for x in nodes]), max([x.max for x in nodes]))
   return create_node(ret)
 
+def sym_render(a: Union[Node, int], ops=None, ctx=None) -> str: return str(a) if isinstance(a, int) else a.render(ops, ctx)
+
 render_python: Dict[Type, Callable] = {
   Variable: lambda self,ops,ctx: f"{self.expr}[{self.min}-{self.max}]" if ctx == "DEBUG" else f"{self.expr}",
   NumNode: lambda self,ops,ctx: f"{self.b}",
-  MulNode: lambda self,ops,ctx: f"({self.a.render(ops,ctx)}*{self.b})",
+  MulNode: lambda self,ops,ctx: f"({self.a.render(ops,ctx)}*{sym_render(self.b,ops,ctx)})",
   DivNode: lambda self,ops,ctx: f"({self.a.render(ops,ctx)}//{self.b})",
   ModNode: lambda self,ops,ctx: f"({self.a.render(ops,ctx)}%{self.b})",
-  LtNode: lambda self,ops,ctx: f"({self.a.render(ops,ctx)}<{self.b})",
+  LtNode: lambda self,ops,ctx: f"({self.a.render(ops,ctx)}<{sym_render(self.b,ops,ctx)})",
   SumNode: lambda self,ops,ctx: f"({'+'.join(sorted([x.render(ops,ctx) for x in self.nodes]))})",
   AndNode: lambda self,ops,ctx: f"({' and '.join(sorted([x.render(ops,ctx) for x in self.nodes]))})"
 }