diff --git a/lib/ir/dispatch.cc b/lib/ir/dispatch.cc
index 477f4dce0..c616b2fd4 100644
--- a/lib/ir/dispatch.cc
+++ b/lib/ir/dispatch.cc
@@ -33,21 +33,28 @@ ir::type *integer_promote(ir::type* a_ty, ir::type* b_ty){
   return a_rank > b_rank ? a_ty : b_ty;
 }
 
-ir::type *computation_type(ir::type* a_ty, ir::type* b_ty){
+enum class DivOrMod { NO, YES };
+
+ir::type *computation_type(ir::type* a_ty, ir::type* b_ty, DivOrMod div_or_mod) {
   context &ctx = a_ty->get_context();
   // 1) if one operand is double, the other is implicitly
   //    converted to double
-  if(a_ty->is_fp64_ty() || b_ty->is_fp64_ty())
+  if (a_ty->is_fp64_ty() || b_ty->is_fp64_ty())
     return type::get_fp64_ty(ctx);
   // 2) if one operand is float, the other is implicitly
   //    converted to float
-  if(a_ty->is_fp32_ty() || b_ty->is_fp32_ty())
+  if (a_ty->is_fp32_ty() || b_ty->is_fp32_ty())
     return type::get_fp32_ty(ctx);
-  // 3 ) if one operand is half, the other is implicitly
-  //     converted to half
-  if(a_ty->is_fp16_ty() || b_ty->is_fp16_ty())
-    return type::get_fp16_ty(ctx);
-  if(!a_ty->is_integer_ty() || !b_ty->is_integer_ty())
+  // 3 ) if one operand is half, the other is implicitly converted to half
+  //     unless we're doing / or %, which do not exist natively in PTX for fp16.
+  if (a_ty->is_fp16_ty() || b_ty->is_fp16_ty()) {
+    if (div_or_mod == DivOrMod::YES) {
+      return type::get_fp32_ty(ctx);
+    } else {
+      return type::get_fp16_ty(ctx);
+    }
+  }
+  if (!a_ty->is_integer_ty() || !b_ty->is_integer_ty())
     throw_unreachable("augment_types");
   // 4 ) both operands are integer and undergo
   //    integer promotion
@@ -78,7 +85,7 @@ void check_ptr_type(ir::type* type_a, ir::type* type_b, bool allow_ptr_a){
 
 void binary_op_type_checking(ir::value*& lhs, ir::value*& rhs, ir::builder* builder,
                              bool allow_lhs_ptr = false, bool allow_rhs_ptr = false,
-                             bool arithmetic_check = true){
+                             bool arithmetic_check = true, DivOrMod div_or_mod = DivOrMod::NO) {
   // implicit broadcasting
   std::tie(lhs, rhs) = dispatch::broadcast(lhs, rhs, builder);
   // implicit typecasting
@@ -86,8 +93,8 @@ void binary_op_type_checking(ir::value*& lhs, ir::value*& rhs, ir::builder* buil
   ir::type *rhs_sca_ty = rhs->get_type()->get_scalar_ty();
   check_ptr_type(lhs_sca_ty, rhs_sca_ty, allow_lhs_ptr);
   check_ptr_type(rhs_sca_ty, lhs_sca_ty, allow_rhs_ptr);
-  if(arithmetic_check && !lhs_sca_ty->is_pointer_ty() && !rhs_sca_ty->is_pointer_ty()){
-    ir::type *ret_sca_ty = computation_type(lhs_sca_ty, rhs_sca_ty);
+  if (arithmetic_check && !lhs_sca_ty->is_pointer_ty() && !rhs_sca_ty->is_pointer_ty()) {
+    ir::type *ret_sca_ty = computation_type(lhs_sca_ty, rhs_sca_ty, div_or_mod);
     lhs = dispatch::cast(lhs, ret_sca_ty, builder);
     rhs = dispatch::cast(rhs, ret_sca_ty, builder);
   }
@@ -140,7 +147,7 @@ ir::value *dispatch::mul(ir::value *input, ir::value *other, ir::builder *builde
 }
 
 ir::value *dispatch::truediv(ir::value *input, ir::value *other, ir::builder *builder) {
-  binary_op_type_checking(input, other, builder, false, false, false);
+  binary_op_type_checking(input, other, builder, false, false, true, DivOrMod::YES);
   ir::type *input_scalar_ty = input->get_type()->get_scalar_ty();
   ir::type *other_scalar_ty = other->get_type()->get_scalar_ty();
   // float / int
@@ -168,7 +175,7 @@ ir::value *dispatch::truediv(ir::value *input, ir::value *other, ir::builder *bu
 }
 
 ir::value *dispatch::floordiv(ir::value *input, ir::value *other, ir::builder *builder){
-  binary_op_type_checking(input, other, builder, false, false, false);
+  binary_op_type_checking(input, other, builder, false, false, true, DivOrMod::YES);
   ir::type *input_scalar_ty = input->get_type()->get_scalar_ty();
   ir::type *other_scalar_ty = other->get_type()->get_scalar_ty();
   if(input_scalar_ty->is_integer_ty() && other_scalar_ty->is_integer_ty()){
@@ -181,7 +188,7 @@ ir::value *dispatch::floordiv(ir::value *input, ir::value *other, ir::builder *b
 }
 
 ir::value *dispatch::mod(ir::value *input, ir::value *other, ir::builder *builder) {
-  binary_op_type_checking(input, other, builder);
+  binary_op_type_checking(input, other, builder, false, false, true, DivOrMod::YES);
   ir::type *scalar_ty = input->get_type()->get_scalar_ty();
   // float % int
   if (scalar_ty->is_floating_point_ty())
@@ -193,51 +200,43 @@ ir::value *dispatch::mod(ir::value *input, ir::value *other, ir::builder *builde
 }
 
 
-void bitwise_op_type_checking(ir::value *&input, ir::value *&other, ir::builder *builder, bool force_lhs_type = false){
+void bitwise_op_type_checking(ir::value *&input, ir::value *&other, ir::builder *builder) {
   binary_op_type_checking(input, other, builder, false, false, false);
   ir::type *input_sca_ty = input->get_type()->get_scalar_ty();
   ir::type *other_sca_ty = other->get_type()->get_scalar_ty();
   if(!input_sca_ty->is_integer_ty() || !other_sca_ty->is_integer_ty())
     throw_incompatible_types(input_sca_ty, other_sca_ty);
-  // for some reason pytorch assigns the result of binary op to have the type of the lhs...
-  if(force_lhs_type){
-    if(input_sca_ty->get_integer_bitwidth() != other_sca_ty->get_integer_bitwidth())
-      other = dispatch::cast(other, input_sca_ty, builder);
-  }
-  else{
-    if(input_sca_ty->get_integer_bitwidth() < other_sca_ty->get_integer_bitwidth())
-      input = dispatch::cast(input, other_sca_ty, builder);
-    else if(other_sca_ty->get_integer_bitwidth() < input_sca_ty->get_integer_bitwidth())
-      other = dispatch::cast(other, input_sca_ty, builder);
-  }
-
+  if(input_sca_ty->get_integer_bitwidth() < other_sca_ty->get_integer_bitwidth())
+    input = dispatch::cast(input, other_sca_ty, builder);
+  else if(other_sca_ty->get_integer_bitwidth() < input_sca_ty->get_integer_bitwidth())
+    other = dispatch::cast(other, input_sca_ty, builder);
 }
 
 ir::value *dispatch::and_(ir::value *input, ir::value *other, ir::builder *builder) {
-  bitwise_op_type_checking(input, other, builder, true);
+  bitwise_op_type_checking(input, other, builder);
   return builder->create_and(input, other);
 }
 
 ir::value *dispatch::or_(ir::value *input, ir::value *other, ir::builder *builder) {
-  bitwise_op_type_checking(input, other, builder, true);
+  bitwise_op_type_checking(input, other, builder);
   return builder->create_or(input, other);
 }
 
 
 ir::value *dispatch::xor_(ir::value *input, ir::value *other, ir::builder *builder) {
-  bitwise_op_type_checking(input, other, builder, true);
+  bitwise_op_type_checking(input, other, builder);
   return builder->create_xor(input, other);
 }
 
 
 ir::value *dispatch::lshr(ir::value *input, ir::value *other, ir::builder *builder) {
-  bitwise_op_type_checking(input, other, builder, false);
+  bitwise_op_type_checking(input, other, builder);
   return builder->create_lshr(input, other);
 }
 
 
 ir::value *dispatch::shl(ir::value *input, ir::value *other, ir::builder *builder) {
-  bitwise_op_type_checking(input, other, builder, false);
+  bitwise_op_type_checking(input, other, builder);
   return builder->create_shl(input, other);
 }
 
diff --git a/python/test/unit/language/test_core.py b/python/test/unit/language/test_core.py
index e85c399b3..785ca49ac 100644
--- a/python/test/unit/language/test_core.py
+++ b/python/test/unit/language/test_core.py
@@ -69,7 +69,7 @@ def _test_unary(dtype_x, expr, torch_expr=None, device='cuda'):
     triton.testing.assert_almost_equal(z_ref, z_tri)
 
 
-def _test_binary(dtype_x, dtype_y, expr, mode_x='real', mode_y='real', device='cuda'):
+def _test_binary(dtype_x, dtype_y, expr, torch_expr=None, mode_x='real', mode_y='real', device='cuda'):
     SIZE = 128
     # define the kernel / launch-grid
     @triton.jit
@@ -82,12 +82,12 @@ def _test_binary(dtype_x, dtype_y, expr, mode_x='real', mode_y='real', device='c
 
     kernel = patch_kernel(kernel, {'GENERATE_TEST_HERE': expr})
     # inputs
-    x = triton.testing.random(SIZE, dtype=cvt[dtype_x], device=device)
-    y = triton.testing.random(SIZE, dtype=cvt[dtype_y], device=device)
+    x = triton.testing.random(SIZE, dtype=cvt[dtype_x], device=device, seed=17)
+    y = triton.testing.random(SIZE, dtype=cvt[dtype_y], device=device, seed=144)
     if mode_x == 'nan': x[:] = float('nan')
     if mode_y == 'nan': y[:] = float('nan')
     # reference result
-    z_ref = eval(expr)
+    z_ref = eval(expr if torch_expr is None else torch_expr)
     # triton result
     z_tri = torch.empty(SIZE, dtype=z_ref.dtype, device=device)
     kernel[(1, )](z_tri, x, y, SIZE=SIZE, num_warps=4)
@@ -95,17 +95,56 @@ def _test_binary(dtype_x, dtype_y, expr, mode_x='real', mode_y='real', device='c
     triton.testing.assert_almost_equal(z_ref, z_tri, err_msg=expr)
 
 
+def _fake_fmod(x, y):
+    """
+    Triton % (for both integers and floats) has the same semantics as torch
+    fmod, but torch fmod doesn't work on integers until torch 1.8.
+    `_fake_fmod` gives the same semantics but works on all versions of torch.
+    """
+    z = torch.remainder(x, y)
+    return torch.where((torch.sign(x) != torch.sign(y)) & (z != 0), z - y, z)
+
+
+def _mod_operation_ill_conditioned(dtype_x, dtype_y) -> bool:
+    # The result of x % y is ill-conditioned if x % y is much smaller than x.
+    # pytorch/CUDA has slightly different (probably better) rounding on
+    # remainders than stock LLVM. We currently don't expect to match it
+    # bit-for-bit.
+    return (dtype_x, dtype_y) in [
+        ('int32', 'float16'),
+        ('int32', 'float32'),
+        ('int64', 'float16'),
+        ('int64', 'float32'),
+        ('int64', 'float64'),
+    ]
+
 # ---------------
 # test binary ops
 # ---------------
-@pytest.mark.parametrize("dtype_x, dtype_y, expr", [
-    (dtype_x, dtype_y, f' x {op} y') \
-  for op in ['+', '-', '*', '/', '%'] \
-  for dtype_x in dtypes \
+@pytest.mark.parametrize("dtype_x, dtype_y, op", [
+    (dtype_x, dtype_y, op)
+  for op in ['+', '-', '*', '/', '%']
+  for dtype_x in dtypes
   for dtype_y in dtypes
 ])
-def test_bin_op(dtype_x, dtype_y, expr, device='cuda'):
-    _test_binary(dtype_x, dtype_y, expr, device=device)
+def test_bin_op(dtype_x, dtype_y, op, device='cuda'):
+    expr = f' x {op} y'
+    if op == '%' and dtype_x in int_dtypes and dtype_y in int_dtypes:
+        # LLVM has 'torch.fmod', not 'torch.remainder' semantics on integer remainders.
+        torch_expr = '_fake_fmod(x, y)'
+    elif op in ('/', '%') and dtype_x in ('int16', 'float16') and dtype_y in ('int16', 'float16'):
+        # Triton promotes 16-bit floating-point / and % to 32-bit because there
+        # are no native div or FRem operations on float16. Since we have to
+        # convert anyway, we may as well take the accuracy bump.
+        torch_expr = f'x.to(torch.float32) {op} y.to(torch.float32)'
+    else:
+        torch_expr = None
+    if op == '%' and _mod_operation_ill_conditioned(dtype_x, dtype_y):
+        with pytest.raises(AssertionError, match='Arrays are not almost equal'):
+            _test_binary(dtype_x, dtype_y, expr, torch_expr=torch_expr, device=device)
+    else:
+        _test_binary(dtype_x, dtype_y, expr, torch_expr=torch_expr, device=device)
+
 
 
 # ---------------
diff --git a/python/triton/code_gen.py b/python/triton/code_gen.py
index 688508265..e1091eff7 100644
--- a/python/triton/code_gen.py
+++ b/python/triton/code_gen.py
@@ -482,7 +482,8 @@ class CodeGenerator(ast.NodeVisitor):
         with warnings.catch_warnings():
             # The ast library added visit_Constant and deprecated some other
             # methods but we can't move to that without breaking Python 3.6 and 3.7.
-            warnings.simplefilter("ignore", DeprecationWarning)
+            warnings.simplefilter("ignore", DeprecationWarning)  # python 3.9
+            warnings.simplefilter("ignore", PendingDeprecationWarning)  # python 3.8
             return super().visit(node)
 
     def generic_visit(self, node):
@@ -905,7 +906,7 @@ class JITFunction:
             node = generator.last_node
             if node is None or isinstance(e, (NotImplementedError, CompilationError)):
                 raise e
-            raise CompilationError(self.src, node, e)
+            raise CompilationError(self.src, node) from e
 
     # - when `.src` attribute is set, cache path needs
     #   to be reinitialized
diff --git a/python/triton/testing.py b/python/triton/testing.py
index 08ad62580..051a8f378 100644
--- a/python/triton/testing.py
+++ b/python/triton/testing.py
@@ -89,14 +89,21 @@ def assert_allclose(x, y, tol=1e-2):
     assert allclose(x, y, tol)
 
 
-def random(shape, dtype, device):
-    torch.manual_seed(0)
+def random(shape, dtype, device, seed=0):
+    """
+    Override the seed in tests if you're calling this function twice and don't
+    want the same result for both calls.
+    """
+    torch.manual_seed(seed)
     if isinstance(shape, int):
         shape = (shape, )
     if dtype == torch.bool:
         return torch.randint(0, 2, shape, dtype=dtype, device=device)
     if dtype in [torch.int8, torch.int16, torch.int32, torch.int64]:
-        return torch.randint(1, 32, shape, dtype=dtype, device=device)
+        iinfo = torch.iinfo(dtype)
+        x = torch.randint(iinfo.min, iinfo.max, shape, dtype=dtype, device=device)
+        x[x == 0] = 1  # Hack. Never return zero so tests of division don't error out.
+        return x
     if dtype in [torch.float16, torch.float32, torch.float64]:
         return torch.normal(0, 1, shape, dtype=dtype, device=device)
     raise RuntimeError(f'Unknown dtype {dtype}')