add expr simplify and canonical

python/tvm/expr.py

 """Base class of symbolic expression"""
 from __future__ import absolute_import as _abs
 from numbers import Number as _Number
-from . import op as _op
 from . import var_name as _name
 
+__addop__ = None
+__subop__ = None
+__mulop__ = None
+__divop__ = None
+
 class Expr(object):
     """Base class of expression.
 
@@ -20,28 +24,28 @@ class Expr(object):
         return ()
 
     def __add__(self, other):
-        return BinaryOpExpr(_op.add, self, other)
+        return BinaryOpExpr(__addop__, self, other)
 
     def __radd__(self, other):
         return self.__add__(other)
 
     def __sub__(self, other):
-        return BinaryOpExpr(_op.sub, self, other)
+        return BinaryOpExpr(__subop__, self, other)
 
     def __rsub__(self, other):
-        return BinaryOpExpr(_op.sub, other, self)
+        return BinaryOpExpr(__subop__, other, self)
 
     def __mul__(self, other):
-        return BinaryOpExpr(_op.mul, self, other)
+        return BinaryOpExpr(__mulop__, self, other)
 
     def __rmul__(self, other):
-        return BinaryOpExpr(_op.mul, other, self)
+        return BinaryOpExpr(__mulop__, other, self)
 
     def __div__(self, other):
-        return BinaryOpExpr(_op.div, self, other)
+        return BinaryOpExpr(__divop__, self, other)
 
     def __rdiv__(self, other):
-        return BinaryOpExpr(_op.div, other, self)
+        return BinaryOpExpr(__divop__, other, self)
 
     def __truediv__(self, other):
         return self.__div__(other)
@@ -75,7 +79,8 @@ class Var(Expr):
         optional name to the var.
     """
     def __init__(self, name=None):
-        self.name = name if name else _name.NameManager.current.get(name)
+        if name is None: name = 'i'
+        self.name = _name.NameManager.current.get(name)
 
 
 class ConstExpr(Expr):
@@ -95,7 +100,6 @@ class BinaryOpExpr(Expr):
     def children(self):
         return (self.lhs, self.rhs)
 
-_op.binary_op_cls = BinaryOpExpr
     
 class UnaryOpExpr(Expr):
     """Unary operator expression."""

python/tvm/expr_util.py

 """Utilities to manipulate expression"""
 from __future__ import absolute_import as _abs
 from . import expr as _expr
+from . import op as _op
 
 def expr_with_new_children(e, children):
     """Returns same expr as e but with new children
@@ -48,6 +49,7 @@ def transform(e, f):
     result : return value of f
         The final result of transformation.
     """
+    assert isinstance(e, _expr.Expr)
     return f(e , [transform(c, f) for c in e.children()])
 
 
@@ -77,6 +79,32 @@ def format_str(expr):
             raise TypeError("Do not know how to handle type " + str(type(e)))
     return transform(expr, make_str)
 
+def simplify(expr):
+    """simplify expression
+
+    Parameters
+    ----------
+    expr : Expr
+        Input expression
+
+    Returns
+    -------
+    e : Expr
+       Simplified expression
+    """
+    def canonical(e, result_children):
+        if isinstance(e, _expr.BinaryOpExpr):
+            return e.op.canonical(result_children[0], result_children[1])
+        elif isinstance(e, _expr.UnaryOpExpr):
+            return e.op.canonical(result_children[0])
+        elif isinstance(e, _expr.ConstExpr):
+            return {_op.constant_canonical_key: e.value}
+        elif isinstance(e, _expr.Var):
+            return {e: 1}
+        else:
+            raise TypeError("Do not know how to handle type " + str(type(e)))
+    return _op.canonical_to_expr(transform(expr, canonical))
+
 
 def bind(expr, update_dict):
     """Replace the variable in e by specification from kwarg

python/tvm/op.py

 from __future__ import absolute_import as _abs
+from . import expr as _expr
 
-_binary_op_cls = None
+constant_canonical_key = '__constant__'
+
+def canonical_to_expr(c):
+    elements = []
+    for k, v in sorted(c.items()):
+        if k == constant_canonical_key:
+            elements.append(_expr.const(v))
+        elif v == 0:
+            continue
+        elif v == 1:
+            elements.append(k)
+        else:
+            elements.append(k * v)
+    if elements:
+        expr = elements[0]
+        for i in range(1, len(elements)):
+            expr = expr + elements[i]
+        return expr
+    else:
+        return _expr.const(0)
 
 class BinaryOp(object):
     """Base class of binary operator"""
     def __call__(self, lhs, rhs):
-        return _binary_op_cls(self, lhs, rhs)
+        return _expr.BinaryOpExpr(self, lhs, rhs)
 
 class AddOp(BinaryOp):
     def format_str(self, lhs, rhs):
         return '(%s + %s)' % (lhs, rhs)
 
+    def canonical(self, lhs, rhs):
+        lhs = lhs.copy()
+        for k, v in rhs.items():
+            if k in lhs:
+                lhs[k] += v
+            else:
+                lhs[k] = v
+        return lhs
+
 class SubOp(BinaryOp):
     def format_str(self, lhs, rhs):
         return '(%s - %s)' % (lhs, rhs)
 
+    def canonical(self, lhs, rhs):
+        lhs = lhs.copy()
+        for k, v in rhs.items():
+            if k in lhs:
+                lhs[k] -= v
+            else:
+                lhs[k] = -v
+        return lhs
+
 class MulOp(BinaryOp):
     def format_str(self, lhs, rhs):
         return '(%s * %s)' % (lhs, rhs)
 
+    def canonical(self, lhs, rhs):
+        elhs = canonical_to_expr(lhs)
+        erhs = canonical_to_expr(rhs)
+        if isinstance(erhs, _expr.ConstExpr):
+            lhs = lhs.copy()
+            for k, v in lhs.items():
+                lhs[k] *= erhs.value
+            return lhs
+        if isinstance(elhs, _expr.ConstExpr):
+            rhs = rhs.copy()
+            for k, v in rhs.items():
+                rhs[k] *= elhs.value
+            return rhs
+        return {elhs * erhs: 1}
+
 class DivOp(BinaryOp):
     def format_str(self, lhs, rhs):
         return '(%s / %s)' % (lhs, rhs)
 
+    def canonical(self, lhs, rhs):
+        erhs = canonical_to_expr(rhs)
+        if isinstance(erhs, _expr.ConstExpr):
+            lhs = lhs.copy()
+            for k, v in lhs.items():
+                lhs[k] /= erhs.value
+            return lhs
+        elhs = canonical_to_expr(lhs)
+        return {elhs / erhs: 1}
+
+class MaxOp(BinaryOp):
+    def format_str(self, lhs, rhs):
+        return 'max(%s, %s)' % (lhs, rhs)
+
+    def canonical(self, lhs, rhs):
+        diff = SubOp().canonical(lhs, rhs)
+        ediff = canonical_to_expr(diff)
+        if isinstance(ediff, _expr.ConstExpr):
+            return lhs if ediff.value >= 0 else rhs
+        return {MaxOp()(lhs, rhs): 1}
+
+class MinOp(BinaryOp):
+    def format_str(self, lhs, rhs):
+        return 'min(%s, %s)' % (lhs, rhs)
+
+    def canonical(self, lhs, rhs):
+        diff = SubOp().canonical(lhs, rhs)
+        ediff = canonical_to_expr(diff)
+        if isinstance(ediff, _expr.ConstExpr):
+            return rhs if ediff.value >= 0 else lhs
+        return {MinOp()(lhs, rhs): 1}
+
 
 add = AddOp()
 sub = SubOp()
 mul = MulOp()
 div = DivOp()
+max = MaxOp()
+min = MinOp()
+
+_expr.__addop__ = add
+_expr.__subop__ = sub
+_expr.__mulop__ = mul
+_expr.__divop__ = div

tests/python/test_basic.py

@@ -9,12 +9,24 @@ def test_bind():
 
 
 def test_basic():
-    a= tvm.Var('a')
+    a = tvm.Var('a')
     b = tvm.Var('b')
     c =  a + b
     assert tvm.format_str(c) == '(%s + %s)' % (a.name, b.name)
 
+def test_simplify():
+    a = tvm.Var('a')
+    b = tvm.Var('b')
+    e1 = a * (2 + 1) + b * 1
+    e2 = a * (2 + 1) - b * 1
+    e3 = tvm.max(a * 3.3 + 5, 3 + 3.3 * a)
+    e4 = a - a
+    assert tvm.format_str(tvm.simplify(e1)) == '((%s * 3) + %s)' % (a.name, b.name)
+    assert tvm.format_str(tvm.simplify(e2)) == '((%s * 3) + (%s * -1))' % (a.name, b.name)
+    assert tvm.format_str(tvm.simplify(e3)) == '((%s * 3.3) + 5)' % (a.name)
+    assert tvm.format_str(tvm.simplify(e4)) == '0'
 
 if __name__ == "__main__":
+    test_simplify()
     test_basic()
     test_bind()