Decouple dtype from shape for Random multinomial (#15980)

* change int to index t and remove the check

* fix lint

* Trigger notification

* Trigger notification coz of laop crash

src/operator/random/sample_multinomial_op.h

@@ -70,11 +70,6 @@ inline bool SampleMultinomialOpShape(const nnvm::NodeAttrs& attrs,
   const mxnet::TShape& ishape = (*in_attrs)[0];
   if (!ndim_is_known(ishape)) return false;
 
-  MSHADOW_TYPE_SWITCH(param.dtype, DType, {
-    CHECK_LE(ishape[ishape.ndim() - 1], mxnet::common::MaxIntegerValue<DType>())
-    << "'dtype' does not have a sufficient precision to represent the indices of the input array.";
-  });
-
   if (ishape.ndim() == 1) {
     if (param.shape.ndim() > 0) {
       SHAPE_ASSIGN_CHECK(*out_attrs, 0, param.shape);
@@ -121,7 +116,7 @@ inline bool SampleMultinomialOpType(const nnvm::NodeAttrs& attrs,
 
 struct SampleMultinomialKernel {
   template<typename DType, typename IType>
-  MSHADOW_XINLINE static void Map(int i, index_t K, index_t M,
+  MSHADOW_XINLINE static void Map(index_t i, index_t K, index_t M,
                                   DType* dist, float* uniform, float* cum_table,
                                   IType* out, DType* prob) {
     double acc = 0.0;