diff --git a/cpp/src/arrow/compute/kernels/aggregate_basic.cc b/cpp/src/arrow/compute/kernels/aggregate_basic.cc
index 0bc839be8e3cc..53fa2d2d7f702 100644
--- a/cpp/src/arrow/compute/kernels/aggregate_basic.cc
+++ b/cpp/src/arrow/compute/kernels/aggregate_basic.cc
@@ -422,9 +422,8 @@ void AddMinOrMaxAggKernel(ScalarAggregateFunction* func,
   auto init = [min_max_func](
                   KernelContext* ctx,
                   const KernelInitArgs& args) -> Result<std::unique_ptr<KernelState>> {
-    std::vector<ValueDescr> inputs = args.inputs;
-    ARROW_ASSIGN_OR_RAISE(auto kernel, min_max_func->DispatchBest(&inputs));
-    KernelInitArgs new_args{kernel, inputs, args.options};
+    ARROW_ASSIGN_OR_RAISE(auto kernel, min_max_func->DispatchExact(args.inputs));
+    KernelInitArgs new_args{kernel, args.inputs, args.options};
     return kernel->init(ctx, new_args);
   };
 
diff --git a/cpp/src/arrow/compute/kernels/aggregate_internal.h b/cpp/src/arrow/compute/kernels/aggregate_internal.h
index 22a54558f4e8a..946ec01900c5b 100644
--- a/cpp/src/arrow/compute/kernels/aggregate_internal.h
+++ b/cpp/src/arrow/compute/kernels/aggregate_internal.h
@@ -21,6 +21,7 @@
 #include "arrow/type.h"
 #include "arrow/type_traits.h"
 #include "arrow/util/bit_run_reader.h"
+#include "arrow/util/int128_internal.h"
 #include "arrow/util/logging.h"
 
 namespace arrow {
@@ -111,6 +112,26 @@ void AddAggKernel(std::shared_ptr<KernelSignature> sig, KernelInit init,
                   ScalarAggregateFinalize finalize, ScalarAggregateFunction* func,
                   SimdLevel::type simd_level = SimdLevel::NONE);
 
+using arrow::internal::VisitSetBitRunsVoid;
+
+template <typename T, typename Enable = void>
+struct GetSumType;
+
+template <typename T>
+struct GetSumType<T, enable_if_floating_point<T>> {
+  using SumType = double;
+};
+
+template <typename T>
+struct GetSumType<T, enable_if_integer<T>> {
+  using SumType = arrow::internal::int128_t;
+};
+
+template <typename T>
+struct GetSumType<T, enable_if_decimal<T>> {
+  using SumType = typename TypeTraits<T>::CType;
+};
+
 // SumArray must be parameterized with the SIMD level since it's called both from
 // translation units with and without vectorization. Normally it gets inlined but
 // if not, without the parameter, we'll have multiple definitions of the same
diff --git a/cpp/src/arrow/compute/kernels/aggregate_mode.cc b/cpp/src/arrow/compute/kernels/aggregate_mode.cc
index f225f6bf569c3..6a50556a13efd 100644
--- a/cpp/src/arrow/compute/kernels/aggregate_mode.cc
+++ b/cpp/src/arrow/compute/kernels/aggregate_mode.cc
@@ -40,10 +40,13 @@ constexpr char kCountFieldName[] = "count";
 
 constexpr uint64_t kCountEOF = ~0ULL;
 
-template <typename InType, typename CType = typename InType::c_type>
+template <typename InType, typename CType = typename TypeTraits<InType>::CType>
 Result<std::pair<CType*, int64_t*>> PrepareOutput(int64_t n, KernelContext* ctx,
                                                   Datum* out) {
-  const auto& mode_type = TypeTraits<InType>::type_singleton();
+  DCHECK_EQ(Type::STRUCT, out->type()->id());
+  const auto& out_type = checked_cast<const StructType&>(*out->type());
+  DCHECK_EQ(2, out_type.num_fields());
+  const auto& mode_type = out_type.field(0)->type();
   const auto& count_type = int64();
 
   auto mode_data = ArrayData::Make(mode_type, /*length=*/n, /*null_count=*/0);
@@ -61,10 +64,7 @@ Result<std::pair<CType*, int64_t*>> PrepareOutput(int64_t n, KernelContext* ctx,
     count_buffer = count_data->template GetMutableValues<int64_t>(1);
   }
 
-  const auto& out_type =
-      struct_({field(kModeFieldName, mode_type), field(kCountFieldName, count_type)});
-  *out = Datum(ArrayData::Make(out_type, n, {nullptr}, {mode_data, count_data}, 0));
-
+  *out = Datum(ArrayData::Make(out->type(), n, {nullptr}, {mode_data, count_data}, 0));
   return std::make_pair(mode_buffer, count_buffer);
 }
 
@@ -72,7 +72,7 @@ Result<std::pair<CType*, int64_t*>> PrepareOutput(int64_t n, KernelContext* ctx,
 // suboptimal for tiny or large n, possibly okay as we're not in hot path
 template <typename InType, typename Generator>
 Status Finalize(KernelContext* ctx, Datum* out, Generator&& gen) {
-  using CType = typename InType::c_type;
+  using CType = typename TypeTraits<InType>::CType;
 
   using ValueCountPair = std::pair<CType, uint64_t>;
   auto gt = [](const ValueCountPair& lhs, const ValueCountPair& rhs) {
@@ -203,13 +203,25 @@ struct CountModer<BooleanType> {
   }
 };
 
-// copy and sort approach for floating points or integers with wide value range
+// copy and sort approach for floating points, decimals, or integers with wide
+// value range
 // O(n) space, O(nlogn) time
 template <typename T>
 struct SortModer {
-  using CType = typename T::c_type;
+  using CType = typename TypeTraits<T>::CType;
   using Allocator = arrow::stl::allocator<CType>;
 
+  template <typename Type = T>
+  static enable_if_floating_point<Type, CType> GetNan() {
+    return static_cast<CType>(NAN);
+  }
+
+  template <typename Type = T>
+  static enable_if_t<!is_floating_type<Type>::value, CType> GetNan() {
+    DCHECK(false);
+    return static_cast<CType>(0);
+  }
+
   Status Exec(KernelContext* ctx, const ExecBatch& batch, Datum* out) {
     const Datum& datum = batch[0];
     const int64_t in_length = datum.length() - datum.null_count();
@@ -246,7 +258,7 @@ struct SortModer {
       if (ARROW_PREDICT_FALSE(it == in_buffer.cend())) {
         // handle NAN at last
         if (nan_count > 0) {
-          auto value_count = std::make_pair(static_cast<CType>(NAN), nan_count);
+          auto value_count = std::make_pair(GetNan(), nan_count);
           nan_count = 0;
           return value_count;
         }
@@ -318,13 +330,18 @@ struct Moder<InType, enable_if_t<(is_integer_type<InType>::value &&
 };
 
 template <typename InType>
-struct Moder<InType, enable_if_t<is_floating_type<InType>::value>> {
+struct Moder<InType, enable_if_floating_point<InType>> {
+  SortModer<InType> impl;
+};
+
+template <typename InType>
+struct Moder<InType, enable_if_decimal<InType>> {
   SortModer<InType> impl;
 };
 
 template <typename T>
 Status ScalarMode(KernelContext* ctx, const Scalar& scalar, Datum* out) {
-  using CType = typename T::c_type;
+  using CType = typename TypeTraits<T>::CType;
 
   const ModeOptions& options = ModeState::Get(ctx);
   if ((!options.skip_nulls && !scalar.is_valid) ||
@@ -366,30 +383,33 @@ struct ModeExecutor {
   }
 };
 
-VectorKernel NewModeKernel(const std::shared_ptr<DataType>& in_type) {
+Result<ValueDescr> ModeType(KernelContext*, const std::vector<ValueDescr>& descrs) {
+  return ValueDescr::Array(
+      struct_({field(kModeFieldName, descrs[0].type), field(kCountFieldName, int64())}));
+}
+
+VectorKernel NewModeKernel(const std::shared_ptr<DataType>& in_type,
+                           ArrayKernelExec exec) {
   VectorKernel kernel;
   kernel.init = ModeState::Init;
   kernel.can_execute_chunkwise = false;
   kernel.output_chunked = false;
-  auto out_type =
-      struct_({field(kModeFieldName, in_type), field(kCountFieldName, int64())});
-  kernel.signature =
-      KernelSignature::Make({InputType(in_type)}, ValueDescr::Array(out_type));
-  return kernel;
-}
-
-void AddBooleanModeKernel(VectorFunction* func) {
-  VectorKernel kernel = NewModeKernel(boolean());
-  kernel.exec = ModeExecutor<StructType, BooleanType>::Exec;
-  DCHECK_OK(func->AddKernel(kernel));
-}
-
-void AddNumericModeKernels(VectorFunction* func) {
-  for (const auto& type : NumericTypes()) {
-    VectorKernel kernel = NewModeKernel(type);
-    kernel.exec = GenerateNumeric<ModeExecutor, StructType>(*type);
-    DCHECK_OK(func->AddKernel(kernel));
+  switch (in_type->id()) {
+    case Type::DECIMAL128:
+    case Type::DECIMAL256:
+      kernel.signature =
+          KernelSignature::Make({InputType(in_type->id())}, OutputType(ModeType));
+      break;
+    default: {
+      auto out_type =
+          struct_({field(kModeFieldName, in_type), field(kCountFieldName, int64())});
+      kernel.signature = KernelSignature::Make({InputType(in_type->id())},
+                                               ValueDescr::Array(std::move(out_type)));
+      break;
+    }
   }
+  kernel.exec = std::move(exec);
+  return kernel;
 }
 
 const FunctionDoc mode_doc{
@@ -409,8 +429,17 @@ void RegisterScalarAggregateMode(FunctionRegistry* registry) {
   static auto default_options = ModeOptions::Defaults();
   auto func = std::make_shared<VectorFunction>("mode", Arity::Unary(), &mode_doc,
                                                &default_options);
-  AddBooleanModeKernel(func.get());
-  AddNumericModeKernels(func.get());
+  DCHECK_OK(func->AddKernel(
+      NewModeKernel(boolean(), ModeExecutor<StructType, BooleanType>::Exec)));
+  for (const auto& type : NumericTypes()) {
+    DCHECK_OK(func->AddKernel(
+        NewModeKernel(type, GenerateNumeric<ModeExecutor, StructType>(*type))));
+  }
+  // Type parameters are ignored
+  DCHECK_OK(func->AddKernel(
+      NewModeKernel(decimal128(1, 0), ModeExecutor<StructType, Decimal128Type>::Exec)));
+  DCHECK_OK(func->AddKernel(
+      NewModeKernel(decimal256(1, 0), ModeExecutor<StructType, Decimal256Type>::Exec)));
   DCHECK_OK(registry->AddFunction(std::move(func)));
 }
 
diff --git a/cpp/src/arrow/compute/kernels/aggregate_quantile.cc b/cpp/src/arrow/compute/kernels/aggregate_quantile.cc
index 62e375e695087..cd2410cc9eb75 100644
--- a/cpp/src/arrow/compute/kernels/aggregate_quantile.cc
+++ b/cpp/src/arrow/compute/kernels/aggregate_quantile.cc
@@ -71,10 +71,21 @@ uint64_t QuantileToDataPoint(size_t length, double q,
   return datapoint_index;
 }
 
+template <typename T>
+double DataPointToDouble(T value, const DataType&) {
+  return static_cast<double>(value);
+}
+double DataPointToDouble(const Decimal128& value, const DataType& ty) {
+  return value.ToDouble(checked_cast<const DecimalType&>(ty).scale());
+}
+double DataPointToDouble(const Decimal256& value, const DataType& ty) {
+  return value.ToDouble(checked_cast<const DecimalType&>(ty).scale());
+}
+
 // copy and nth_element approach, large memory footprint
 template <typename InType>
 struct SortQuantiler {
-  using CType = typename InType::c_type;
+  using CType = typename TypeTraits<InType>::CType;
   using Allocator = arrow::stl::allocator<CType>;
 
   Status Exec(KernelContext* ctx, const ExecBatch& batch, Datum* out) {
@@ -106,8 +117,7 @@ struct SortQuantiler {
     // prepare out array
     // out type depends on options
     const bool is_datapoint = IsDataPoint(options);
-    const std::shared_ptr<DataType> out_type =
-        is_datapoint ? TypeTraits<InType>::type_singleton() : float64();
+    const std::shared_ptr<DataType> out_type = is_datapoint ? datum.type() : float64();
     int64_t out_length = options.q.size();
     if (in_buffer.empty()) {
       return MakeArrayOfNull(out_type, out_length, ctx->memory_pool()).Value(out);
@@ -142,8 +152,9 @@ struct SortQuantiler {
         double* out_buffer = out_data->template GetMutableValues<double>(1);
         for (int64_t i = 0; i < out_length; ++i) {
           const int64_t q_index = q_indices[i];
-          out_buffer[q_index] = GetQuantileByInterp(
-              in_buffer, &last_index, options.q[q_index], options.interpolation);
+          out_buffer[q_index] =
+              GetQuantileByInterp(in_buffer, &last_index, options.q[q_index],
+                                  options.interpolation, *datum.type());
         }
       }
     }
@@ -170,8 +181,8 @@ struct SortQuantiler {
 
   // return quantile interpolated from adjacent input data points
   double GetQuantileByInterp(std::vector<CType, Allocator>& in, uint64_t* last_index,
-                             double q,
-                             enum QuantileOptions::Interpolation interpolation) {
+                             double q, enum QuantileOptions::Interpolation interpolation,
+                             const DataType& in_type) {
     const double index = (in.size() - 1) * q;
     const uint64_t lower_index = static_cast<uint64_t>(index);
     const double fraction = index - lower_index;
@@ -181,7 +192,7 @@ struct SortQuantiler {
       std::nth_element(in.begin(), in.begin() + lower_index, in.begin() + *last_index);
     }
 
-    const double lower_value = static_cast<double>(in[lower_index]);
+    const double lower_value = DataPointToDouble(in[lower_index], in_type);
     if (fraction == 0) {
       *last_index = lower_index;
       return lower_value;
@@ -197,7 +208,7 @@ struct SortQuantiler {
     }
     *last_index = lower_index;
 
-    const double higher_value = static_cast<double>(in[higher_index]);
+    const double higher_value = DataPointToDouble(in[higher_index], in_type);
 
     if (interpolation == QuantileOptions::LINEAR) {
       // more stable than naive linear interpolation
@@ -399,10 +410,15 @@ struct ExactQuantiler<InType, enable_if_t<is_floating_type<InType>::value>> {
   SortQuantiler<InType> impl;
 };
 
+template <typename InType>
+struct ExactQuantiler<InType, enable_if_t<is_decimal_type<InType>::value>> {
+  SortQuantiler<InType> impl;
+};
+
 template <typename T>
 Status ScalarQuantile(KernelContext* ctx, const QuantileOptions& options,
                       const Scalar& scalar, Datum* out) {
-  using CType = typename T::c_type;
+  using CType = typename TypeTraits<T>::CType;
   ArrayData* output = out->mutable_array();
   output->length = options.q.size();
   auto out_type = IsDataPoint(options) ? scalar.type : float64();
@@ -433,7 +449,7 @@ Status ScalarQuantile(KernelContext* ctx, const QuantileOptions& options,
   } else {
     double* out_buffer = output->template GetMutableValues<double>(1);
     for (int64_t i = 0; i < output->length; i++) {
-      out_buffer[i] = static_cast<double>(UnboxScalar<T>::Unbox(scalar));
+      out_buffer[i] = DataPointToDouble(UnboxScalar<T>::Unbox(scalar), *scalar.type);
     }
   }
   return Status::OK();
@@ -486,6 +502,18 @@ void AddQuantileKernels(VectorFunction* func) {
     base.exec = GenerateNumeric<QuantileExecutor, NullType>(*ty);
     DCHECK_OK(func->AddKernel(base));
   }
+  {
+    base.signature =
+        KernelSignature::Make({InputType(Type::DECIMAL128)}, OutputType(ResolveOutput));
+    base.exec = QuantileExecutor<NullType, Decimal128Type>::Exec;
+    DCHECK_OK(func->AddKernel(base));
+  }
+  {
+    base.signature =
+        KernelSignature::Make({InputType(Type::DECIMAL256)}, OutputType(ResolveOutput));
+    base.exec = QuantileExecutor<NullType, Decimal256Type>::Exec;
+    DCHECK_OK(func->AddKernel(base));
+  }
 }
 
 const FunctionDoc quantile_doc{
diff --git a/cpp/src/arrow/compute/kernels/aggregate_tdigest.cc b/cpp/src/arrow/compute/kernels/aggregate_tdigest.cc
index 0fddf38f575c9..7c86267d94006 100644
--- a/cpp/src/arrow/compute/kernels/aggregate_tdigest.cc
+++ b/cpp/src/arrow/compute/kernels/aggregate_tdigest.cc
@@ -34,13 +34,25 @@ template <typename ArrowType>
 struct TDigestImpl : public ScalarAggregator {
   using ThisType = TDigestImpl<ArrowType>;
   using ArrayType = typename TypeTraits<ArrowType>::ArrayType;
-  using CType = typename ArrowType::c_type;
+  using CType = typename TypeTraits<ArrowType>::CType;
 
-  explicit TDigestImpl(const TDigestOptions& options)
+  TDigestImpl(const TDigestOptions& options, const DataType& in_type)
       : options{options},
         tdigest{options.delta, options.buffer_size},
         count{0},
-        all_valid{true} {}
+        decimal_scale{0},
+        all_valid{true} {
+    if (is_decimal_type<ArrowType>::value) {
+      decimal_scale = checked_cast<const DecimalType&>(in_type).scale();
+    }
+  }
+
+  template <typename T>
+  double ToDouble(T value) const {
+    return static_cast<double>(value);
+  }
+  double ToDouble(const Decimal128& value) const { return value.ToDouble(decimal_scale); }
+  double ToDouble(const Decimal256& value) const { return value.ToDouble(decimal_scale); }
 
   Status Consume(KernelContext*, const ExecBatch& batch) override {
     if (!this->all_valid) return Status::OK();
@@ -57,7 +69,7 @@ struct TDigestImpl : public ScalarAggregator {
         VisitSetBitRunsVoid(data.buffers[0], data.offset, data.length,
                             [&](int64_t pos, int64_t len) {
                               for (int64_t i = 0; i < len; ++i) {
-                                this->tdigest.NanAdd(values[pos + i]);
+                                this->tdigest.NanAdd(ToDouble(values[pos + i]));
                               }
                             });
       }
@@ -66,7 +78,7 @@ struct TDigestImpl : public ScalarAggregator {
       if (batch[0].scalar()->is_valid) {
         this->count += 1;
         for (int64_t i = 0; i < batch.length; i++) {
-          this->tdigest.NanAdd(value);
+          this->tdigest.NanAdd(ToDouble(value));
         }
       }
     }
@@ -110,6 +122,7 @@ struct TDigestImpl : public ScalarAggregator {
   const TDigestOptions options;
   TDigest tdigest;
   int64_t count;
+  int32_t decimal_scale;
   bool all_valid;
 };
 
@@ -132,8 +145,14 @@ struct TDigestInitState {
   }
 
   template <typename Type>
-  enable_if_t<is_number_type<Type>::value, Status> Visit(const Type&) {
-    state.reset(new TDigestImpl<Type>(options));
+  enable_if_number<Type, Status> Visit(const Type&) {
+    state.reset(new TDigestImpl<Type>(options, in_type));
+    return Status::OK();
+  }
+
+  template <typename Type>
+  enable_if_decimal<Type, Status> Visit(const Type&) {
+    state.reset(new TDigestImpl<Type>(options, in_type));
     return Status::OK();
   }
 
@@ -154,7 +173,7 @@ void AddTDigestKernels(KernelInit init,
                        const std::vector<std::shared_ptr<DataType>>& types,
                        ScalarAggregateFunction* func) {
   for (const auto& ty : types) {
-    auto sig = KernelSignature::Make({InputType(ty)}, float64());
+    auto sig = KernelSignature::Make({InputType(ty->id())}, float64());
     AddAggKernel(std::move(sig), init, func);
   }
 }
@@ -179,6 +198,7 @@ std::shared_ptr<ScalarAggregateFunction> AddTDigestAggKernels() {
   auto func = std::make_shared<ScalarAggregateFunction>(
       "tdigest", Arity::Unary(), &tdigest_doc, &default_tdigest_options);
   AddTDigestKernels(TDigestInit, NumericTypes(), func.get());
+  AddTDigestKernels(TDigestInit, {decimal128(1, 1), decimal256(1, 1)}, func.get());
   return func;
 }
 
diff --git a/cpp/src/arrow/compute/kernels/aggregate_test.cc b/cpp/src/arrow/compute/kernels/aggregate_test.cc
index c5355a8f4521f..c8b13862ae361 100644
--- a/cpp/src/arrow/compute/kernels/aggregate_test.cc
+++ b/cpp/src/arrow/compute/kernels/aggregate_test.cc
@@ -2334,6 +2334,26 @@ TEST(TestIndexKernel, Errors) {
 // Mode
 //
 
+template <typename CType>
+void CheckModes(const Datum& array, const ModeOptions options,
+                const std::vector<CType>& expected_modes,
+                const std::vector<int64_t>& expected_counts) {
+  ASSERT_OK_AND_ASSIGN(Datum out, Mode(array, options));
+  ValidateOutput(out);
+  const StructArray out_array(out.array());
+  ASSERT_EQ(out_array.length(), expected_modes.size());
+  ASSERT_EQ(out_array.num_fields(), 2);
+
+  const CType* out_modes = out_array.field(0)->data()->GetValues<CType>(1);
+  const int64_t* out_counts = out_array.field(1)->data()->GetValues<int64_t>(1);
+  for (int i = 0; i < out_array.length(); ++i) {
+    // equal or nan equal
+    ASSERT_TRUE((expected_modes[i] == out_modes[i]) ||
+                (expected_modes[i] != expected_modes[i] && out_modes[i] != out_modes[i]));
+    ASSERT_EQ(expected_counts[i], out_counts[i]);
+  }
+}
+
 template <typename T>
 class TestPrimitiveModeKernel : public ::testing::Test {
  public:
@@ -2344,21 +2364,7 @@ class TestPrimitiveModeKernel : public ::testing::Test {
   void AssertModesAre(const Datum& array, const ModeOptions options,
                       const std::vector<CType>& expected_modes,
                       const std::vector<int64_t>& expected_counts) {
-    ASSERT_OK_AND_ASSIGN(Datum out, Mode(array, options));
-    ValidateOutput(out);
-    const StructArray out_array(out.array());
-    ASSERT_EQ(out_array.length(), expected_modes.size());
-    ASSERT_EQ(out_array.num_fields(), 2);
-
-    const CType* out_modes = out_array.field(0)->data()->GetValues<CType>(1);
-    const int64_t* out_counts = out_array.field(1)->data()->GetValues<int64_t>(1);
-    for (int i = 0; i < out_array.length(); ++i) {
-      // equal or nan equal
-      ASSERT_TRUE(
-          (expected_modes[i] == out_modes[i]) ||
-          (expected_modes[i] != expected_modes[i] && out_modes[i] != out_modes[i]));
-      ASSERT_EQ(expected_counts[i], out_counts[i]);
-    }
+    CheckModes(array, options, expected_modes, expected_counts);
   }
 
   void AssertModesAre(const std::string& json, const int n,
@@ -2587,6 +2593,89 @@ TYPED_TEST(TestFloatingModeKernel, Floats) {
   this->AssertModesEmpty(ScalarFromJSON(in_ty, "null"), ModeOptions(/*n=*/1));
 }
 
+template <typename ArrowType>
+class TestDecimalModeKernel : public ::testing::Test {
+ public:
+  using CType = typename TypeTraits<ArrowType>::CType;
+
+  void AssertModesAre(const Datum& array, const ModeOptions options,
+                      const std::vector<std::string>& expected_modes,
+                      const std::vector<int64_t>& expected_counts) {
+    CheckModes<CType>(array, options, values(expected_modes), expected_counts);
+  }
+
+  CType value(const std::string& s) const {
+    EXPECT_OK_AND_ASSIGN(auto out, CType::FromString(s));
+    return out;
+  }
+
+  std::vector<CType> values(const std::vector<std::string>& strings) const {
+    std::vector<CType> values;
+    for (const auto& s : strings) {
+      values.push_back(value(s));
+    }
+    return values;
+  }
+
+  std::shared_ptr<DataType> type_instance() { return std::make_shared<ArrowType>(4, 2); }
+};
+
+TYPED_TEST_SUITE(TestDecimalModeKernel, DecimalArrowTypes);
+
+TYPED_TEST(TestDecimalModeKernel, Decimals) {
+  auto ty = this->type_instance();
+  this->AssertModesAre(ArrayFromJSON(ty, R"(["5.01", "-1.42", "-1.42", "5.01", "5.01"])"),
+                       ModeOptions(1), {"5.01"}, {3});
+  this->AssertModesAre(
+      ArrayFromJSON(ty, R"(["5.01", "-1.42", "-1.42", "5.01", "5.01", "-1.42"])"),
+      ModeOptions(1), {"-1.42"}, {3});
+  this->AssertModesAre(
+      ArrayFromJSON(ty, R"(["5.01", "-1.42", "-1.42", "5.01", "5.01", "-1.42"])"),
+      ModeOptions(2), {"-1.42", "5.01"}, {3, 3});
+
+  this->AssertModesAre(ArrayFromJSON(ty, "[]"), ModeOptions(1), {}, {});
+
+  this->AssertModesAre(ArrayFromJSON(ty, R"(["1.86", "-2.00", "-2.00", null])"),
+                       ModeOptions(/*n=*/1), {"-2.00"}, {2});
+  this->AssertModesAre(ArrayFromJSON(ty, R"(["1.86", "-2.00", "-2.00", null])"),
+                       ModeOptions(/*n=*/1, /*skip_nulls=*/false), {}, {});
+  this->AssertModesAre(ArrayFromJSON(ty, R"(["1.86", "-2.00", "-2.00", null])"),
+                       ModeOptions(/*n=*/1, /*skip_nulls=*/true, /*min_count=*/3),
+                       {"-2.00"}, {2});
+  this->AssertModesAre(ArrayFromJSON(ty, R"(["-2.00", "-2.00", null])"),
+                       ModeOptions(/*n=*/1, /*skip_nulls=*/true, /*min_count=*/3), {},
+                       {});
+  this->AssertModesAre(ArrayFromJSON(ty, R"(["1.86", "-2.00", "-2.00"])"),
+                       ModeOptions(/*n=*/1, /*skip_nulls=*/false, /*min_count=*/3),
+                       {"-2.00"}, {2});
+  this->AssertModesAre(ArrayFromJSON(ty, R"(["1.86", "-2.00", "-2.00", null])"),
+                       ModeOptions(/*n=*/1, /*skip_nulls=*/false, /*min_count=*/3), {},
+                       {});
+  this->AssertModesAre(ArrayFromJSON(ty, R"(["1.86", "-2.00"])"),
+                       ModeOptions(/*n=*/1, /*skip_nulls=*/false, /*min_count=*/3), {},
+                       {});
+
+  this->AssertModesAre(ScalarFromJSON(ty, R"("0.00")"),
+                       ModeOptions(/*n=*/1, /*skip_nulls=*/false), {"0.00"}, {1});
+  this->AssertModesAre(ScalarFromJSON(ty, "null"),
+                       ModeOptions(/*n=*/1, /*skip_nulls=*/false), {}, {});
+  this->AssertModesAre(ScalarFromJSON(ty, R"("0.00")"),
+                       ModeOptions(/*n=*/1, /*skip_nulls=*/true, /*min_count=*/2), {},
+                       {});
+  this->AssertModesAre(ScalarFromJSON(ty, "null"),
+                       ModeOptions(/*n=*/1, /*skip_nulls=*/true, /*min_count=*/2), {},
+                       {});
+  this->AssertModesAre(ScalarFromJSON(ty, R"("0.00")"),
+                       ModeOptions(/*n=*/1, /*skip_nulls=*/false, /*min_count=*/2), {},
+                       {});
+  this->AssertModesAre(ScalarFromJSON(ty, "null"),
+                       ModeOptions(/*n=*/1, /*skip_nulls=*/false, /*min_count=*/2), {},
+                       {});
+  this->AssertModesAre(ScalarFromJSON(ty, R"("5.00")"), ModeOptions(/*n=*/1), {"5.00"},
+                       {1});
+  this->AssertModesAre(ScalarFromJSON(ty, "null"), ModeOptions(/*n=*/1), {}, {});
+}
+
 TEST_F(TestInt8ModeKernelValueRange, Basics) {
   this->AssertModeIs("[0, 127, -128, -128]", -128, 2);
   this->AssertModeIs("[127, 127, 127]", 127, 3);
@@ -2689,6 +2778,24 @@ TEST_F(TestInt32ModeKernel, Sliced) {
 // Variance/Stddev
 //
 
+void CheckVarStd(const Datum& array, const VarianceOptions& options,
+                 double expected_var) {
+  ASSERT_OK_AND_ASSIGN(Datum out_var, Variance(array, options));
+  ASSERT_OK_AND_ASSIGN(Datum out_std, Stddev(array, options));
+  auto var = checked_cast<const DoubleScalar*>(out_var.scalar().get());
+  auto std = checked_cast<const DoubleScalar*>(out_std.scalar().get());
+  ASSERT_TRUE(var->is_valid && std->is_valid);
+  // Near zero these macros don't work as well
+  // (and MinGW can give results slightly off from zero)
+  if (std::abs(expected_var) < 1e-20) {
+    ASSERT_NEAR(std->value * std->value, var->value, 1e-20);
+    ASSERT_NEAR(var->value, expected_var, 1e-20);
+  } else {
+    ASSERT_DOUBLE_EQ(std->value * std->value, var->value);
+    ASSERT_DOUBLE_EQ(var->value, expected_var);  // < 4ULP
+  }
+}
+
 template <typename ArrowType>
 class TestPrimitiveVarStdKernel : public ::testing::Test {
  public:
@@ -2697,12 +2804,12 @@ class TestPrimitiveVarStdKernel : public ::testing::Test {
 
   void AssertVarStdIs(const Array& array, const VarianceOptions& options,
                       double expected_var) {
-    AssertVarStdIsInternal(array, options, expected_var);
+    CheckVarStd(array, options, expected_var);
   }
 
   void AssertVarStdIs(const std::shared_ptr<ChunkedArray>& array,
                       const VarianceOptions& options, double expected_var) {
-    AssertVarStdIsInternal(array, options, expected_var);
+    CheckVarStd(array, options, expected_var);
   }
 
   void AssertVarStdIs(const std::string& json, const VarianceOptions& options,
@@ -2740,17 +2847,6 @@ class TestPrimitiveVarStdKernel : public ::testing::Test {
   std::shared_ptr<DataType> type_singleton() { return Traits::type_singleton(); }
 
  private:
-  void AssertVarStdIsInternal(const Datum& array, const VarianceOptions& options,
-                              double expected_var) {
-    ASSERT_OK_AND_ASSIGN(Datum out_var, Variance(array, options));
-    ASSERT_OK_AND_ASSIGN(Datum out_std, Stddev(array, options));
-    auto var = checked_cast<const ScalarType*>(out_var.scalar().get());
-    auto std = checked_cast<const ScalarType*>(out_std.scalar().get());
-    ASSERT_TRUE(var->is_valid && std->is_valid);
-    ASSERT_DOUBLE_EQ(std->value * std->value, var->value);
-    ASSERT_DOUBLE_EQ(var->value, expected_var);  // < 4ULP
-  }
-
   void AssertVarStdIsInvalidInternal(const Datum& array, const VarianceOptions& options) {
     ASSERT_OK_AND_ASSIGN(Datum out_var, Variance(array, options));
     ASSERT_OK_AND_ASSIGN(Datum out_std, Stddev(array, options));
@@ -3000,6 +3096,18 @@ TEST_F(TestVarStdKernelIntegerLength, Basics) {
 }
 #endif
 
+TEST(TestVarStdKernel, Decimal) {
+  // Effectively treated as double, sanity check results here
+  for (const auto& ty : {decimal128(3, 2), decimal256(3, 2)}) {
+    CheckVarStd(ArrayFromJSON(ty, R"(["1.00"])"), VarianceOptions(), 0);
+    CheckVarStd(ArrayFromJSON(ty, R"([null, "1.00", "2.00", "3.00"])"), VarianceOptions(),
+                0.6666666666666666);
+    CheckVarStd(ScalarFromJSON(ty, R"("1.00")"), VarianceOptions(), 0);
+    CheckVarStd(ArrayFromJSON(ty, R"([null, "1.00", "2.00"])"),
+                VarianceOptions(/*ddof=*/1), 0.5);
+  }
+}
+
 //
 // Quantile
 //
@@ -3541,6 +3649,24 @@ TEST(TestQuantileKernel, AllNullsOrNaNs) {
   }
 }
 
+TEST(TestQuantileKernel, Decimal) {
+  auto check = [](const std::shared_ptr<Array>& input, QuantileOptions options,
+                  const std::shared_ptr<Array>& expected) {
+    ASSERT_OK_AND_ASSIGN(Datum out, Quantile(input, options));
+    auto out_array = out.make_array();
+    ValidateOutput(*out_array);
+    AssertArraysEqual(*expected, *out_array, /*verbose=*/true);
+  };
+  for (const auto& ty : {decimal128(3, 2), decimal256(3, 2)}) {
+    check(ArrayFromJSON(ty, R"(["1.00", "5.00", null])"),
+          QuantileOptions(0.5, QuantileOptions::LINEAR),
+          ArrayFromJSON(float64(), R"([3.00])"));
+    check(ArrayFromJSON(ty, R"(["1.00", "2.00", "5.00"])"),
+          QuantileOptions(0.5, QuantileOptions::NEAREST),
+          ArrayFromJSON(ty, R"(["2.00"])"));
+  }
+}
+
 TEST(TestQuantileKernel, Scalar) {
   for (const auto& ty : {float64(), int64(), uint64()}) {
     QuantileOptions options(std::vector<double>{0.0, 0.5, 1.0});
@@ -3608,6 +3734,17 @@ TEST(TestTDigestKernel, AllNullsOrNaNs) {
   }
 }
 
+TEST(TestTDigestKernel, Decimal) {
+  for (const auto& ty : {decimal128(3, 2), decimal256(3, 2)}) {
+    ASSERT_OK_AND_ASSIGN(auto decimal_array,
+                         TDigest(ArrayFromJSON(ty, R"(["1.00", "2.00", "3.25"])")));
+    ASSERT_OK_AND_ASSIGN(auto float_array,
+                         TDigest(ArrayFromJSON(float64(), "[1, 2, 3.25]")));
+    AssertArraysApproxEqual(*float_array.make_array(), *decimal_array.make_array(),
+                            /*verbose=*/true);
+  }
+}
+
 TEST(TestTDigestKernel, Scalar) {
   for (const auto& ty : {float64(), int64(), uint64()}) {
     TDigestOptions options(std::vector<double>{0.0, 0.5, 1.0});
diff --git a/cpp/src/arrow/compute/kernels/aggregate_var_std.cc b/cpp/src/arrow/compute/kernels/aggregate_var_std.cc
index d0d3c514fae2e..feb98718aee3c 100644
--- a/cpp/src/arrow/compute/kernels/aggregate_var_std.cc
+++ b/cpp/src/arrow/compute/kernels/aggregate_var_std.cc
@@ -36,12 +36,21 @@ using arrow::internal::VisitSetBitRunsVoid;
 template <typename ArrowType>
 struct VarStdState {
   using ArrayType = typename TypeTraits<ArrowType>::ArrayType;
-  using CType = typename ArrowType::c_type;
+  using CType = typename TypeTraits<ArrowType>::CType;
   using ThisType = VarStdState<ArrowType>;
 
-  explicit VarStdState(VarianceOptions options) : options(options) {}
+  explicit VarStdState(int32_t decimal_scale, VarianceOptions options)
+      : decimal_scale(decimal_scale), options(options) {}
 
-  // float/double/int64: calculate `m2` (sum((X-mean)^2)) with `two pass algorithm`
+  template <typename T>
+  double ToDouble(T value) const {
+    return static_cast<double>(value);
+  }
+  double ToDouble(const Decimal128& value) const { return value.ToDouble(decimal_scale); }
+  double ToDouble(const Decimal256& value) const { return value.ToDouble(decimal_scale); }
+
+  // float/double/int64/decimal: calculate `m2` (sum((X-mean)^2)) with `two pass
+  // algorithm`
   // https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Two-pass_algorithm
   template <typename T = ArrowType>
   enable_if_t<is_floating_type<T>::value || (sizeof(CType) > 4)> Consume(
@@ -52,14 +61,13 @@ struct VarStdState {
       return;
     }
 
-    using SumType =
-        typename std::conditional<is_floating_type<T>::value, double, int128_t>::type;
-    SumType sum = SumArray<CType, SumType, SimdLevel::NONE>(*array.data());
+    using SumType = typename internal::GetSumType<T>::SumType;
+    SumType sum = internal::SumArray<CType, SumType, SimdLevel::NONE>(*array.data());
 
-    const double mean = static_cast<double>(sum) / count;
-    const double m2 =
-        SumArray<CType, double, SimdLevel::NONE>(*array.data(), [mean](CType value) {
-          const double v = static_cast<double>(value);
+    const double mean = ToDouble(sum) / count;
+    const double m2 = internal::SumArray<CType, double, SimdLevel::NONE>(
+        *array.data(), [this, mean](CType value) {
+          const double v = ToDouble(value);
           return (v - mean) * (v - mean);
         });
 
@@ -102,7 +110,7 @@ struct VarStdState {
                             });
 
         // merge variance
-        ThisType state(options);
+        ThisType state(decimal_scale, options);
         state.count = var_std.count;
         state.mean = var_std.mean();
         state.m2 = var_std.m2();
@@ -116,7 +124,7 @@ struct VarStdState {
     this->m2 = 0;
     if (scalar.is_valid) {
       this->count = count;
-      this->mean = static_cast<double>(UnboxScalar<ArrowType>::Unbox(scalar));
+      this->mean = ToDouble(UnboxScalar<ArrowType>::Unbox(scalar));
     } else {
       this->count = 0;
       this->mean = 0;
@@ -141,6 +149,7 @@ struct VarStdState {
                 &this->mean, &this->m2);
   }
 
+  const int32_t decimal_scale;
   const VarianceOptions options;
   int64_t count = 0;
   double mean = 0;
@@ -153,9 +162,9 @@ struct VarStdImpl : public ScalarAggregator {
   using ThisType = VarStdImpl<ArrowType>;
   using ArrayType = typename TypeTraits<ArrowType>::ArrayType;
 
-  explicit VarStdImpl(const std::shared_ptr<DataType>& out_type,
+  explicit VarStdImpl(int32_t decimal_scale, const std::shared_ptr<DataType>& out_type,
                       const VarianceOptions& options, VarOrStd return_type)
-      : out_type(out_type), state(options), return_type(return_type) {}
+      : out_type(out_type), state(decimal_scale, options), return_type(return_type) {}
 
   Status Consume(KernelContext*, const ExecBatch& batch) override {
     if (batch[0].is_array()) {
@@ -216,8 +225,16 @@ struct VarStdInitState {
   }
 
   template <typename Type>
-  enable_if_t<is_number_type<Type>::value, Status> Visit(const Type&) {
-    state.reset(new VarStdImpl<Type>(out_type, options, return_type));
+  enable_if_number<Type, Status> Visit(const Type&) {
+    state.reset(
+        new VarStdImpl<Type>(/*decimal_scale=*/0, out_type, options, return_type));
+    return Status::OK();
+  }
+
+  template <typename Type>
+  enable_if_decimal<Type, Status> Visit(const Type&) {
+    state.reset(new VarStdImpl<Type>(checked_cast<const DecimalType&>(in_type).scale(),
+                                     out_type, options, return_type));
     return Status::OK();
   }
 
@@ -247,7 +264,7 @@ void AddVarStdKernels(KernelInit init,
                       const std::vector<std::shared_ptr<DataType>>& types,
                       ScalarAggregateFunction* func) {
   for (const auto& ty : types) {
-    auto sig = KernelSignature::Make({InputType(ty)}, float64());
+    auto sig = KernelSignature::Make({InputType(ty->id())}, float64());
     AddAggKernel(std::move(sig), init, func);
   }
 }
@@ -275,6 +292,7 @@ std::shared_ptr<ScalarAggregateFunction> AddStddevAggKernels() {
   auto func = std::make_shared<ScalarAggregateFunction>(
       "stddev", Arity::Unary(), &stddev_doc, &default_std_options);
   AddVarStdKernels(StddevInit, NumericTypes(), func.get());
+  AddVarStdKernels(StddevInit, {decimal128(1, 1), decimal256(1, 1)}, func.get());
   return func;
 }
 
@@ -283,6 +301,7 @@ std::shared_ptr<ScalarAggregateFunction> AddVarianceAggKernels() {
   auto func = std::make_shared<ScalarAggregateFunction>(
       "variance", Arity::Unary(), &variance_doc, &default_var_options);
   AddVarStdKernels(VarianceInit, NumericTypes(), func.get());
+  AddVarStdKernels(VarianceInit, {decimal128(1, 1), decimal256(1, 1)}, func.get());
   return func;
 }
 
diff --git a/cpp/src/arrow/compute/kernels/hash_aggregate.cc b/cpp/src/arrow/compute/kernels/hash_aggregate.cc
index 73c8f9d26c0e0..9f53267535511 100644
--- a/cpp/src/arrow/compute/kernels/hash_aggregate.cc
+++ b/cpp/src/arrow/compute/kernels/hash_aggregate.cc
@@ -519,7 +519,8 @@ struct GrouperFastImpl : Grouper {
 /// Implementations should be default constructible and perform initialization in
 /// Init().
 struct GroupedAggregator : KernelState {
-  virtual Status Init(ExecContext*, const FunctionOptions*) = 0;
+  virtual Status Init(ExecContext*, const std::vector<ValueDescr>& inputs,
+                      const FunctionOptions*) = 0;
 
   virtual Status Resize(int64_t new_num_groups) = 0;
 
@@ -536,7 +537,7 @@ template <typename Impl>
 Result<std::unique_ptr<KernelState>> HashAggregateInit(KernelContext* ctx,
                                                        const KernelInitArgs& args) {
   auto impl = ::arrow::internal::make_unique<Impl>();
-  RETURN_NOT_OK(impl->Init(ctx->exec_context(), args.options));
+  RETURN_NOT_OK(impl->Init(ctx->exec_context(), args.inputs, args.options));
   return std::move(impl);
 }
 
@@ -636,7 +637,8 @@ void VisitGroupedValuesNonNull(const ExecBatch& batch, ConsumeValue&& valid_func
 // Count implementation
 
 struct GroupedCountImpl : public GroupedAggregator {
-  Status Init(ExecContext* ctx, const FunctionOptions* options) override {
+  Status Init(ExecContext* ctx, const std::vector<ValueDescr>&,
+              const FunctionOptions* options) override {
     options_ = checked_cast<const CountOptions&>(*options);
     counts_ = BufferBuilder(ctx->memory_pool());
     return Status::OK();
@@ -725,13 +727,14 @@ struct GroupedReducingAggregator : public GroupedAggregator {
   using CType = typename TypeTraits<AccType>::CType;
   using InputCType = typename TypeTraits<Type>::CType;
 
-  Status Init(ExecContext* ctx, const FunctionOptions* options) override {
+  Status Init(ExecContext* ctx, const std::vector<ValueDescr>& inputs,
+              const FunctionOptions* options) override {
     pool_ = ctx->memory_pool();
     options_ = checked_cast<const ScalarAggregateOptions&>(*options);
     reduced_ = TypedBufferBuilder<CType>(pool_);
     counts_ = TypedBufferBuilder<int64_t>(pool_);
     no_nulls_ = TypedBufferBuilder<bool>(pool_);
-    // out_type_ initialized by SumInit
+    out_type_ = GetOutType(inputs[0].type);
     return Status::OK();
   }
 
@@ -829,6 +832,18 @@ struct GroupedReducingAggregator : public GroupedAggregator {
 
   std::shared_ptr<DataType> out_type() const override { return out_type_; }
 
+  template <typename T = Type>
+  static enable_if_t<!is_decimal_type<T>::value, std::shared_ptr<DataType>> GetOutType(
+      const std::shared_ptr<DataType>& in_type) {
+    return TypeTraits<AccType>::type_singleton();
+  }
+
+  template <typename T = Type>
+  static enable_if_decimal<T, std::shared_ptr<DataType>> GetOutType(
+      const std::shared_ptr<DataType>& in_type) {
+    return in_type;
+  }
+
   int64_t num_groups_ = 0;
   ScalarAggregateOptions options_;
   TypedBufferBuilder<CType> reduced_;
@@ -838,76 +853,35 @@ struct GroupedReducingAggregator : public GroupedAggregator {
   MemoryPool* pool_;
 };
 
-// ----------------------------------------------------------------------
-// Sum implementation
-
-template <typename Type>
-struct GroupedSumImpl : public GroupedReducingAggregator<Type, GroupedSumImpl<Type>> {
-  using Base = GroupedReducingAggregator<Type, GroupedSumImpl<Type>>;
-  using CType = typename Base::CType;
-  using InputCType = typename Base::InputCType;
-
-  // Default value for a group
-  static CType NullValue(const DataType&) { return CType(0); }
-
-  template <typename T = Type>
-  static enable_if_number<T, CType> Reduce(const DataType&, const CType u,
-                                           const InputCType v) {
-    return static_cast<CType>(to_unsigned(u) + to_unsigned(static_cast<CType>(v)));
-  }
-
-  static CType Reduce(const DataType&, const CType u, const CType v) {
-    return static_cast<CType>(to_unsigned(u) + to_unsigned(v));
-  }
-
-  using Base::Finish;
-};
-
-template <template <typename T> class Impl, typename T>
-Result<std::unique_ptr<KernelState>> SumInit(KernelContext* ctx,
-                                             const KernelInitArgs& args) {
-  ARROW_ASSIGN_OR_RAISE(auto impl, HashAggregateInit<Impl<T>>(ctx, args));
-  static_cast<Impl<T>*>(impl.get())->out_type_ =
-      TypeTraits<typename Impl<T>::AccType>::type_singleton();
-  return std::move(impl);
-}
-
-template <typename Impl>
-Result<std::unique_ptr<KernelState>> DecimalSumInit(KernelContext* ctx,
-                                                    const KernelInitArgs& args) {
-  ARROW_ASSIGN_OR_RAISE(auto impl, HashAggregateInit<Impl>(ctx, args));
-  static_cast<Impl*>(impl.get())->out_type_ = args.inputs[0].type;
-  return std::move(impl);
-}
-
-struct GroupedSumFactory {
+template <template <typename> class Impl, const char* kFriendlyName>
+struct GroupedReducingFactory {
   template <typename T, typename AccType = typename FindAccumulatorType<T>::Type>
   Status Visit(const T&) {
-    kernel = MakeKernel(std::move(argument_type), SumInit<GroupedSumImpl, T>);
+    kernel = MakeKernel(std::move(argument_type), HashAggregateInit<Impl<T>>);
     return Status::OK();
   }
 
   Status Visit(const Decimal128Type&) {
-    kernel = MakeKernel(std::move(argument_type),
-                        DecimalSumInit<GroupedSumImpl<Decimal128Type>>);
+    kernel =
+        MakeKernel(std::move(argument_type), HashAggregateInit<Impl<Decimal128Type>>);
     return Status::OK();
   }
   Status Visit(const Decimal256Type&) {
-    kernel = MakeKernel(std::move(argument_type),
-                        DecimalSumInit<GroupedSumImpl<Decimal256Type>>);
+    kernel =
+        MakeKernel(std::move(argument_type), HashAggregateInit<Impl<Decimal256Type>>);
     return Status::OK();
   }
 
   Status Visit(const HalfFloatType& type) {
-    return Status::NotImplemented("Summing data of type ", type);
+    return Status::NotImplemented("Computing ", kFriendlyName, " of type ", type);
   }
 
   Status Visit(const DataType& type) {
-    return Status::NotImplemented("Summing data of type ", type);
+    return Status::NotImplemented("Computing ", kFriendlyName, " of type ", type);
   }
 
   static Result<HashAggregateKernel> Make(const std::shared_ptr<DataType>& type) {
-    GroupedSumFactory factory;
+    GroupedReducingFactory<Impl, kFriendlyName> factory;
     factory.argument_type = InputType::Array(type->id());
     RETURN_NOT_OK(VisitTypeInline(*type, &factory));
     return std::move(factory.kernel);
@@ -917,6 +891,34 @@ struct GroupedSumFactory {
   InputType argument_type;
 };
 
+// ----------------------------------------------------------------------
+// Sum implementation
+
+template <typename Type>
+struct GroupedSumImpl : public GroupedReducingAggregator<Type, GroupedSumImpl<Type>> {
+  using Base = GroupedReducingAggregator<Type, GroupedSumImpl<Type>>;
+  using CType = typename Base::CType;
+  using InputCType = typename Base::InputCType;
+
+  // Default value for a group
+  static CType NullValue(const DataType&) { return CType(0); }
+
+  template <typename T = Type>
+  static enable_if_number<T, CType> Reduce(const DataType&, const CType u,
+                                           const InputCType v) {
+    return static_cast<CType>(to_unsigned(u) + to_unsigned(static_cast<CType>(v)));
+  }
+
+  static CType Reduce(const DataType&, const CType u, const CType v) {
+    return static_cast<CType>(to_unsigned(u) + to_unsigned(v));
+  }
+
+  using Base::Finish;
+};
+
+static constexpr const char kSumName[] = "sum";
+using GroupedSumFactory = GroupedReducingFactory<GroupedSumImpl, kSumName>;
+
 // ----------------------------------------------------------------------
 // Product implementation
 
@@ -945,43 +947,8 @@ struct GroupedProductImpl final
   using Base::Finish;
 };
 
-struct GroupedProductFactory {
-  template <typename T, typename AccType = typename FindAccumulatorType<T>::Type>
-  Status Visit(const T&) {
-    kernel = MakeKernel(std::move(argument_type), SumInit<GroupedProductImpl, T>);
-    return Status::OK();
-  }
-
-  Status Visit(const Decimal128Type&) {
-    kernel = MakeKernel(std::move(argument_type),
-                        DecimalSumInit<GroupedProductImpl<Decimal128Type>>);
-    return Status::OK();
-  }
-
-  Status Visit(const Decimal256Type&) {
-    kernel = MakeKernel(std::move(argument_type),
-                        DecimalSumInit<GroupedProductImpl<Decimal256Type>>);
-    return Status::OK();
-  }
-
-  Status Visit(const HalfFloatType& type) {
-    return Status::NotImplemented("Taking product of data of type ", type);
-  }
-
-  Status Visit(const DataType& type) {
-    return Status::NotImplemented("Taking product of data of type ", type);
-  }
-
-  static Result<HashAggregateKernel> Make(const std::shared_ptr<DataType>& type) {
-    GroupedProductFactory factory;
-    factory.argument_type = InputType::Array(type->id());
-    RETURN_NOT_OK(VisitTypeInline(*type, &factory));
-    return std::move(factory.kernel);
-  }
-
-  HashAggregateKernel kernel;
-  InputType argument_type;
-};
+static constexpr const char kProductName[] = "product";
+using GroupedProductFactory = GroupedReducingFactory<GroupedProductImpl, kProductName>;
 
 // ----------------------------------------------------------------------
 // Mean implementation
@@ -1040,43 +1007,8 @@ struct GroupedMeanImpl : public GroupedReducingAggregator<Type, GroupedMeanImpl<
   }
 };
 
-struct GroupedMeanFactory {
-  template <typename T, typename AccType = typename FindAccumulatorType<T>::Type>
-  Status Visit(const T&) {
-    kernel = MakeKernel(std::move(argument_type), SumInit<GroupedMeanImpl, T>);
-    return Status::OK();
-  }
-
-  Status Visit(const Decimal128Type&) {
-    kernel = MakeKernel(std::move(argument_type),
-                        DecimalSumInit<GroupedMeanImpl<Decimal128Type>>);
-    return Status::OK();
-  }
-
-  Status Visit(const Decimal256Type&) {
-    kernel = MakeKernel(std::move(argument_type),
-                        DecimalSumInit<GroupedMeanImpl<Decimal256Type>>);
-    return Status::OK();
-  }
-
-  Status Visit(const HalfFloatType& type) {
-    return Status::NotImplemented("Computing mean of type ", type);
-  }
-
-  Status Visit(const DataType& type) {
-    return Status::NotImplemented("Computing mean of type ", type);
-  }
-
-  static Result<HashAggregateKernel> Make(const std::shared_ptr<DataType>& type) {
-    GroupedMeanFactory factory;
-    factory.argument_type = InputType::Array(type->id());
-    RETURN_NOT_OK(VisitTypeInline(*type, &factory));
-    return std::move(factory.kernel);
-  }
-
-  HashAggregateKernel kernel;
-  InputType argument_type;
-};
+static constexpr const char kMeanName[] = "mean";
+using GroupedMeanFactory = GroupedReducingFactory<GroupedMeanImpl, kMeanName>;
 
 // Variance/Stdev implementation
 
@@ -1084,10 +1016,22 @@ using arrow::internal::int128_t;
 
 template <typename Type>
 struct GroupedVarStdImpl : public GroupedAggregator {
-  using CType = typename Type::c_type;
+  using CType = typename TypeTraits<Type>::CType;
+
+  Status Init(ExecContext* ctx, const std::vector<ValueDescr>& inputs,
+              const FunctionOptions* options) override {
+    options_ = *checked_cast<const VarianceOptions*>(options);
+    if (is_decimal_type<Type>::value) {
+      const int32_t scale = checked_cast<const DecimalType&>(*inputs[0].type).scale();
+      return InitInternal(ctx, scale, options);
+    }
+    return InitInternal(ctx, 0, options);
+  }
 
-  Status Init(ExecContext* ctx, const FunctionOptions* options) override {
+  Status InitInternal(ExecContext* ctx, int32_t decimal_scale,
+                      const FunctionOptions* options) {
     options_ = *checked_cast<const VarianceOptions*>(options);
+    decimal_scale_ = decimal_scale;
     ctx_ = ctx;
     pool_ = ctx->memory_pool();
     counts_ = TypedBufferBuilder<int64_t>(pool_);
@@ -1107,18 +1051,28 @@ struct GroupedVarStdImpl : public GroupedAggregator {
     return Status::OK();
   }
 
+  template <typename T>
+  double ToDouble(T value) const {
+    return static_cast<double>(value);
+  }
+  double ToDouble(const Decimal128& value) const {
+    return value.ToDouble(decimal_scale_);
+  }
+  double ToDouble(const Decimal256& value) const {
+    return value.ToDouble(decimal_scale_);
+  }
+
   Status Consume(const ExecBatch& batch) override { return ConsumeImpl(batch); }
 
-  // float/double/int64: calculate `m2` (sum((X-mean)^2)) with `two pass algorithm`
-  // (see aggregate_var_std.cc)
+  // float/double/int64/decimal: calculate `m2` (sum((X-mean)^2)) with
+  // `two pass algorithm` (see aggregate_var_std.cc)
   template <typename T = Type>
   enable_if_t<is_floating_type<T>::value || (sizeof(CType) > 4), Status> ConsumeImpl(
       const ExecBatch& batch) {
-    using SumType =
-        typename std::conditional<is_floating_type<T>::value, double, int128_t>::type;
+    using SumType = typename internal::GetSumType<T>::SumType;
 
     GroupedVarStdImpl<Type> state;
-    RETURN_NOT_OK(state.Init(ctx_, &options_));
+    RETURN_NOT_OK(state.InitInternal(ctx_, decimal_scale_, &options_));
     RETURN_NOT_OK(state.Resize(num_groups_));
     int64_t* counts = state.counts_.mutable_data();
     double* means = state.means_.mutable_data();
@@ -1137,12 +1091,12 @@ struct GroupedVarStdImpl : public GroupedAggregator {
         [&](uint32_t g) { BitUtil::ClearBit(no_nulls, g); });
 
     for (int64_t i = 0; i < num_groups_; i++) {
-      means[i] = static_cast<double>(sums[i]) / counts[i];
+      means[i] = ToDouble(sums[i]) / counts[i];
     }
 
     VisitGroupedValuesNonNull<Type>(
         batch, [&](uint32_t g, typename TypeTraits<Type>::CType value) {
-          const double v = static_cast<double>(value);
+          const double v = ToDouble(value);
           m2s[g] += (v - means[g]) * (v - means[g]);
         });
 
@@ -1192,7 +1146,7 @@ struct GroupedVarStdImpl : public GroupedAggregator {
       var_std.clear();
       var_std.resize(num_groups_);
       GroupedVarStdImpl<Type> state;
-      RETURN_NOT_OK(state.Init(ctx_, &options_));
+      RETURN_NOT_OK(state.InitInternal(ctx_, decimal_scale_, &options_));
       RETURN_NOT_OK(state.Resize(num_groups_));
       int64_t* other_counts = state.counts_.mutable_data();
       double* other_means = state.means_.mutable_data();
@@ -1319,6 +1273,7 @@ struct GroupedVarStdImpl : public GroupedAggregator {
   std::shared_ptr<DataType> out_type() const override { return float64(); }
 
   VarOrStd result_type_;
+  int32_t decimal_scale_;
   VarianceOptions options_;
   int64_t num_groups_ = 0;
   // m2 = count * s2 = sum((X-mean)^2)
@@ -1334,14 +1289,15 @@ Result<std::unique_ptr<KernelState>> VarStdInit(KernelContext* ctx,
                                                 const KernelInitArgs& args) {
   auto impl = ::arrow::internal::make_unique<GroupedVarStdImpl<T>>();
   impl->result_type_ = result_type;
-  RETURN_NOT_OK(impl->Init(ctx->exec_context(), args.options));
+  RETURN_NOT_OK(impl->Init(ctx->exec_context(), args.inputs, args.options));
   return std::move(impl);
 }
 
 template <VarOrStd result_type>
 struct GroupedVarStdFactory {
   template <typename T, typename Enable = enable_if_t<is_integer_type<T>::value ||
-                                                      is_floating_type<T>::value>>
+                                                      is_floating_type<T>::value ||
+                                                      is_decimal_type<T>::value>>
   Status Visit(const T&) {
     kernel = MakeKernel(std::move(argument_type), VarStdInit<T, result_type>);
     return Status::OK();
@@ -1357,7 +1313,7 @@ struct GroupedVarStdFactory {
 
   static Result<HashAggregateKernel> Make(const std::shared_ptr<DataType>& type) {
     GroupedVarStdFactory factory;
-    factory.argument_type = InputType::Array(type);
+    factory.argument_type = InputType::Array(type->id());
     RETURN_NOT_OK(VisitTypeInline(*type, &factory));
     return std::move(factory.kernel);
   }
@@ -1373,10 +1329,16 @@ using arrow::internal::TDigest;
 
 template <typename Type>
 struct GroupedTDigestImpl : public GroupedAggregator {
-  using CType = typename Type::c_type;
+  using CType = typename TypeTraits<Type>::CType;
 
-  Status Init(ExecContext* ctx, const FunctionOptions* options) override {
+  Status Init(ExecContext* ctx, const std::vector<ValueDescr>& inputs,
+              const FunctionOptions* options) override {
     options_ = *checked_cast<const TDigestOptions*>(options);
+    if (is_decimal_type<Type>::value) {
+      decimal_scale_ = checked_cast<const DecimalType&>(*inputs[0].type).scale();
+    } else {
+      decimal_scale_ = 0;
+    }
     ctx_ = ctx;
     pool_ = ctx->memory_pool();
     counts_ = TypedBufferBuilder<int64_t>(pool_);
@@ -1395,13 +1357,24 @@ struct GroupedTDigestImpl : public GroupedAggregator {
     return Status::OK();
   }
 
+  template <typename T>
+  double ToDouble(T value) const {
+    return static_cast<double>(value);
+  }
+  double ToDouble(const Decimal128& value) const {
+    return value.ToDouble(decimal_scale_);
+  }
+  double ToDouble(const Decimal256& value) const {
+    return value.ToDouble(decimal_scale_);
+  }
+
   Status Consume(const ExecBatch& batch) override {
     int64_t* counts = counts_.mutable_data();
     uint8_t* no_nulls = no_nulls_.mutable_data();
     VisitGroupedValues<Type>(
         batch,
         [&](uint32_t g, CType value) {
-          tdigests_[g].NanAdd(value);
+          tdigests_[g].NanAdd(ToDouble(value));
           counts[g]++;
         },
         [&](uint32_t g) { BitUtil::SetBitTo(no_nulls, g, false); });
@@ -1470,6 +1443,7 @@ struct GroupedTDigestImpl : public GroupedAggregator {
   }
 
   TDigestOptions options_;
+  int32_t decimal_scale_;
   std::vector<TDigest> tdigests_;
   TypedBufferBuilder<int64_t> counts_;
   TypedBufferBuilder<bool> no_nulls_;
@@ -1485,6 +1459,13 @@ struct GroupedTDigestFactory {
     return Status::OK();
   }
 
+  template <typename T>
+  enable_if_decimal<T, Status> Visit(const T&) {
+    kernel =
+        MakeKernel(std::move(argument_type), HashAggregateInit<GroupedTDigestImpl<T>>);
+    return Status::OK();
+  }
+
   Status Visit(const HalfFloatType& type) {
     return Status::NotImplemented("Computing t-digest of data of type ", type);
   }
@@ -1495,7 +1476,7 @@ struct GroupedTDigestFactory {
 
   static Result<HashAggregateKernel> Make(const std::shared_ptr<DataType>& type) {
     GroupedTDigestFactory factory;
-    factory.argument_type = InputType::Array(type);
+    factory.argument_type = InputType::Array(type->id());
     RETURN_NOT_OK(VisitTypeInline(*type, &factory));
     return std::move(factory.kernel);
   }
@@ -1509,15 +1490,14 @@ HashAggregateKernel MakeApproximateMedianKernel(HashAggregateFunction* tdigest_f
   kernel.init = [tdigest_func](
                     KernelContext* ctx,
                     const KernelInitArgs& args) -> Result<std::unique_ptr<KernelState>> {
-    std::vector<ValueDescr> inputs = args.inputs;
-    ARROW_ASSIGN_OR_RAISE(auto kernel, tdigest_func->DispatchBest(&inputs));
+    ARROW_ASSIGN_OR_RAISE(auto kernel, tdigest_func->DispatchExact(args.inputs));
     const auto& scalar_options =
         checked_cast<const ScalarAggregateOptions&>(*args.options);
     TDigestOptions options;
     // Default q = 0.5
     options.min_count = scalar_options.min_count;
     options.skip_nulls = scalar_options.skip_nulls;
-    KernelInitArgs new_args{kernel, inputs, &options};
+    KernelInitArgs new_args{kernel, args.inputs, &options};
     return kernel->init(ctx, new_args);
   };
   kernel.signature =
@@ -1581,7 +1561,8 @@ struct GroupedMinMaxImpl final : public GroupedAggregator {
   using ArrType =
       typename std::conditional<is_boolean_type<Type>::value, uint8_t, CType>::type;
 
-  Status Init(ExecContext* ctx, const FunctionOptions* options) override {
+  Status Init(ExecContext* ctx, const std::vector<ValueDescr>&,
+              const FunctionOptions* options) override {
     options_ = *checked_cast<const ScalarAggregateOptions*>(options);
     // type_ initialized by MinMaxInit
     mins_ = TypedBufferBuilder<CType>(ctx->memory_pool());
@@ -1678,7 +1659,10 @@ struct GroupedMinMaxImpl final : public GroupedAggregator {
 };
 
 struct GroupedNullMinMaxImpl final : public GroupedAggregator {
-  Status Init(ExecContext* ctx, const FunctionOptions*) override { return Status::OK(); }
+  Status Init(ExecContext* ctx, const std::vector<ValueDescr>&,
+              const FunctionOptions*) override {
+    return Status::OK();
+  }
 
   Status Resize(int64_t new_num_groups) override {
     num_groups_ = new_num_groups;
@@ -1723,7 +1707,7 @@ HashAggregateKernel MakeMinOrMaxKernel(HashAggregateFunction* min_max_func) {
                     KernelContext* ctx,
                     const KernelInitArgs& args) -> Result<std::unique_ptr<KernelState>> {
     std::vector<ValueDescr> inputs = args.inputs;
-    ARROW_ASSIGN_OR_RAISE(auto kernel, min_max_func->DispatchBest(&inputs));
+    ARROW_ASSIGN_OR_RAISE(auto kernel, min_max_func->DispatchExact(args.inputs));
     KernelInitArgs new_args{kernel, inputs, args.options};
     return kernel->init(ctx, new_args);
   };
@@ -1806,7 +1790,8 @@ struct GroupedMinMaxFactory {
 
 template <typename Impl>
 struct GroupedBooleanAggregator : public GroupedAggregator {
-  Status Init(ExecContext* ctx, const FunctionOptions* options) override {
+  Status Init(ExecContext* ctx, const std::vector<ValueDescr>&,
+              const FunctionOptions* options) override {
     options_ = checked_cast<const ScalarAggregateOptions&>(*options);
     pool_ = ctx->memory_pool();
     reduced_ = TypedBufferBuilder<bool>(pool_);
@@ -1976,7 +1961,8 @@ struct GroupedAllImpl : public GroupedBooleanAggregator<GroupedAllImpl> {
 // CountDistinct/Distinct implementation
 
 struct GroupedCountDistinctImpl : public GroupedAggregator {
-  Status Init(ExecContext* ctx, const FunctionOptions* options) override {
+  Status Init(ExecContext* ctx, const std::vector<ValueDescr>&,
+              const FunctionOptions* options) override {
     ctx_ = ctx;
     pool_ = ctx->memory_pool();
     options_ = checked_cast<const CountOptions&>(*options);
@@ -2554,6 +2540,8 @@ void RegisterHashAggregateBasic(FunctionRegistry* registry) {
                                 GroupedVarStdFactory<VarOrStd::Std>::Make, func.get()));
     DCHECK_OK(AddHashAggKernels(FloatingPointTypes(),
                                 GroupedVarStdFactory<VarOrStd::Std>::Make, func.get()));
+    DCHECK_OK(AddHashAggKernels({decimal128(1, 1), decimal256(1, 1)},
+                                GroupedVarStdFactory<VarOrStd::Std>::Make, func.get()));
     DCHECK_OK(registry->AddFunction(std::move(func)));
   }
 
@@ -2566,6 +2554,8 @@ void RegisterHashAggregateBasic(FunctionRegistry* registry) {
                                 GroupedVarStdFactory<VarOrStd::Var>::Make, func.get()));
     DCHECK_OK(AddHashAggKernels(FloatingPointTypes(),
                                 GroupedVarStdFactory<VarOrStd::Var>::Make, func.get()));
+    DCHECK_OK(AddHashAggKernels({decimal128(1, 1), decimal256(1, 1)},
+                                GroupedVarStdFactory<VarOrStd::Var>::Make, func.get()));
     DCHECK_OK(registry->AddFunction(std::move(func)));
   }
 
@@ -2579,6 +2569,9 @@ void RegisterHashAggregateBasic(FunctionRegistry* registry) {
         AddHashAggKernels(UnsignedIntTypes(), GroupedTDigestFactory::Make, func.get()));
     DCHECK_OK(
         AddHashAggKernels(FloatingPointTypes(), GroupedTDigestFactory::Make, func.get()));
+    // Type parameters are ignored
+    DCHECK_OK(AddHashAggKernels({decimal128(1, 1), decimal256(1, 1)},
+                                GroupedTDigestFactory::Make, func.get()));
     tdigest_func = func.get();
     DCHECK_OK(registry->AddFunction(std::move(func)));
   }
diff --git a/cpp/src/arrow/compute/kernels/hash_aggregate_test.cc b/cpp/src/arrow/compute/kernels/hash_aggregate_test.cc
index 412290aa777fc..e53c5d43ca88d 100644
--- a/cpp/src/arrow/compute/kernels/hash_aggregate_test.cc
+++ b/cpp/src/arrow/compute/kernels/hash_aggregate_test.cc
@@ -1130,6 +1130,55 @@ TEST(GroupBy, VarianceAndStddev) {
                           /*verbose=*/true);
 }
 
+TEST(GroupBy, VarianceAndStddevDecimal) {
+  auto batch = RecordBatchFromJSON(
+      schema({field("argument0", decimal128(3, 2)), field("argument1", decimal128(3, 2)),
+              field("key", int64())}),
+      R"([
+    ["1.00",  "1.00",  1],
+    [null,    null,    1],
+    ["0.00",  "0.00",  2],
+    ["4.00",  "4.00",  null],
+    ["3.00",  "3.00",  1],
+    ["0.00",  "0.00",  2],
+    ["-1.00", "-1.00", 2],
+    ["1.00",  "1.00",  null]
+  ])");
+
+  ASSERT_OK_AND_ASSIGN(Datum aggregated_and_grouped,
+                       internal::GroupBy(
+                           {
+                               batch->GetColumnByName("argument0"),
+                               batch->GetColumnByName("argument0"),
+                               batch->GetColumnByName("argument1"),
+                               batch->GetColumnByName("argument1"),
+                           },
+                           {
+                               batch->GetColumnByName("key"),
+                           },
+                           {
+                               {"hash_variance", nullptr},
+                               {"hash_stddev", nullptr},
+                               {"hash_variance", nullptr},
+                               {"hash_stddev", nullptr},
+                           }));
+
+  AssertDatumsApproxEqual(ArrayFromJSON(struct_({
+                                            field("hash_variance", float64()),
+                                            field("hash_stddev", float64()),
+                                            field("hash_variance", float64()),
+                                            field("hash_stddev", float64()),
+                                            field("key_0", int64()),
+                                        }),
+                                        R"([
+    [1.0,                 1.0,                1.0,                 1.0,                1],
+    [0.22222222222222224, 0.4714045207910317, 0.22222222222222224, 0.4714045207910317, 2],
+    [2.25,                1.5,                2.25,                1.5,                null]
+  ])"),
+                          aggregated_and_grouped,
+                          /*verbose=*/true);
+}
+
 TEST(GroupBy, TDigest) {
   auto batch = RecordBatchFromJSON(
       schema({field("argument", float64()), field("key", int64())}), R"([
@@ -1201,6 +1250,48 @@ TEST(GroupBy, TDigest) {
       /*verbose=*/true);
 }
 
+TEST(GroupBy, TDigestDecimal) {
+  auto batch = RecordBatchFromJSON(
+      schema({field("argument0", decimal128(3, 2)), field("argument1", decimal256(3, 2)),
+              field("key", int64())}),
+      R"([
+    ["1.01",  "1.01",  1],
+    [null,    null,    1],
+    ["0.00",  "0.00",  2],
+    ["4.42",  "4.42",  null],
+    ["3.86",  "3.86",  1],
+    ["0.00",  "0.00",  2],
+    ["-1.93", "-1.93", 2],
+    ["1.85",  "1.85",  null]
+  ])");
+
+  ASSERT_OK_AND_ASSIGN(Datum aggregated_and_grouped,
+                       internal::GroupBy(
+                           {
+                               batch->GetColumnByName("argument0"),
+                               batch->GetColumnByName("argument1"),
+                           },
+                           {batch->GetColumnByName("key")},
+                           {
+                               {"hash_tdigest", nullptr},
+                               {"hash_tdigest", nullptr},
+                           }));
+
+  AssertDatumsApproxEqual(
+      ArrayFromJSON(struct_({
+                        field("hash_tdigest", fixed_size_list(float64(), 1)),
+                        field("hash_tdigest", fixed_size_list(float64(), 1)),
+                        field("key_0", int64()),
+                    }),
+                    R"([
+    [[1.01], [1.01], 1],
+    [[0.0],  [0.0],  2],
+    [[1.85], [1.85], null]
+  ])"),
+      aggregated_and_grouped,
+      /*verbose=*/true);
+}
+
 TEST(GroupBy, ApproximateMedian) {
   for (const auto& type : {float64(), int8()}) {
     auto batch =
diff --git a/cpp/src/arrow/compute/kernels/scalar_arithmetic.cc b/cpp/src/arrow/compute/kernels/scalar_arithmetic.cc
index 1a60ed31e0a47..db122ca81f3eb 100644
--- a/cpp/src/arrow/compute/kernels/scalar_arithmetic.cc
+++ b/cpp/src/arrow/compute/kernels/scalar_arithmetic.cc
@@ -71,6 +71,12 @@ struct AbsoluteValue {
                                                                Status* st) {
     return (arg < 0) ? arrow::internal::SafeSignedNegate(arg) : arg;
   }
+
+  template <typename T, typename Arg>
+  static constexpr enable_if_decimal_value<Arg, T> Call(KernelContext*, Arg arg,
+                                                        Status*) {
+    return arg.Abs();
+  }
 };
 
 struct AbsoluteValueChecked {
@@ -98,6 +104,12 @@ struct AbsoluteValueChecked {
     static_assert(std::is_same<T, Arg>::value, "");
     return std::fabs(arg);
   }
+
+  template <typename T, typename Arg>
+  static constexpr enable_if_decimal_value<Arg, T> Call(KernelContext*, Arg arg,
+                                                        Status*) {
+    return arg.Abs();
+  }
 };
 
 struct Add {
@@ -363,6 +375,12 @@ struct Negate {
                                                           Status*) {
     return arrow::internal::SafeSignedNegate(arg);
   }
+
+  template <typename T, typename Arg>
+  static constexpr enable_if_decimal_value<Arg, T> Call(KernelContext*, Arg arg,
+                                                        Status*) {
+    return arg.Negate();
+  }
 };
 
 struct NegateChecked {
@@ -392,6 +410,12 @@ struct NegateChecked {
     static_assert(std::is_same<T, Arg>::value, "");
     return -arg;
   }
+
+  template <typename T, typename Arg>
+  static constexpr enable_if_decimal_value<Arg, T> Call(KernelContext*, Arg arg,
+                                                        Status*) {
+    return arg.Negate();
+  }
 };
 
 struct Power {
@@ -475,6 +499,12 @@ struct Sign {
                                                                Status*) {
     return (arg > 0) ? 1 : ((arg == 0) ? 0 : -1);
   }
+
+  template <typename T, typename Arg>
+  static constexpr enable_if_decimal_value<Arg, T> Call(KernelContext*, Arg arg,
+                                                        Status*) {
+    return (arg == 0) ? 0 : arg.Sign();
+  }
 };
 
 // Bitwise operations
@@ -1583,8 +1613,18 @@ Result<ValueDescr> ResolveDecimalDivisionOutput(KernelContext*,
 }
 
 template <typename Op>
-void AddDecimalBinaryKernels(const std::string& name,
-                             std::shared_ptr<ScalarFunction>* func) {
+void AddDecimalUnaryKernels(ScalarFunction* func) {
+  OutputType out_type(FirstType);
+  auto in_type128 = InputType(Type::DECIMAL128);
+  auto in_type256 = InputType(Type::DECIMAL256);
+  auto exec128 = ScalarUnaryNotNull<Decimal128Type, Decimal128Type, Op>::Exec;
+  auto exec256 = ScalarUnaryNotNull<Decimal256Type, Decimal256Type, Op>::Exec;
+  DCHECK_OK(func->AddKernel({in_type128}, out_type, exec128));
+  DCHECK_OK(func->AddKernel({in_type256}, out_type, exec256));
+}
+
+template <typename Op>
+void AddDecimalBinaryKernels(const std::string& name, ScalarFunction* func) {
   OutputType out_type(null());
   const std::string op = name.substr(0, name.find("_"));
   if (op == "add" || op == "subtract") {
@@ -1601,8 +1641,8 @@ void AddDecimalBinaryKernels(const std::string& name,
   auto in_type256 = InputType(Type::DECIMAL256);
   auto exec128 = ScalarBinaryNotNullEqualTypes<Decimal128Type, Decimal128Type, Op>::Exec;
   auto exec256 = ScalarBinaryNotNullEqualTypes<Decimal256Type, Decimal256Type, Op>::Exec;
-  DCHECK_OK((*func)->AddKernel({in_type128, in_type128}, out_type, exec128));
-  DCHECK_OK((*func)->AddKernel({in_type256, in_type256}, out_type, exec256));
+  DCHECK_OK(func->AddKernel({in_type128, in_type128}, out_type, exec128));
+  DCHECK_OK(func->AddKernel({in_type256, in_type256}, out_type, exec256));
 }
 
 // Generate a kernel given an arithmetic functor
@@ -1683,6 +1723,36 @@ struct ArithmeticFunction : ScalarFunction {
   }
 };
 
+/// An ArithmeticFunction that promotes only decimal arguments to double.
+struct ArithmeticDecimalToFloatingPointFunction : public ArithmeticFunction {
+  using ArithmeticFunction::ArithmeticFunction;
+
+  Result<const Kernel*> DispatchBest(std::vector<ValueDescr>* values) const override {
+    RETURN_NOT_OK(CheckArity(*values));
+
+    using arrow::compute::detail::DispatchExactImpl;
+    if (auto kernel = DispatchExactImpl(this, *values)) return kernel;
+
+    EnsureDictionaryDecoded(values);
+
+    if (values->size() == 2) {
+      ReplaceNullWithOtherType(values);
+    }
+
+    for (auto& descr : *values) {
+      if (is_decimal(descr.type->id())) {
+        descr.type = float64();
+      }
+    }
+    if (auto type = CommonNumeric(*values)) {
+      ReplaceTypes(type, values);
+    }
+
+    if (auto kernel = DispatchExactImpl(this, *values)) return kernel;
+    return arrow::compute::detail::NoMatchingKernel(this, *values);
+  }
+};
+
 /// An ArithmeticFunction that promotes only integer arguments to double.
 struct ArithmeticIntegerToFloatingPointFunction : public ArithmeticFunction {
   using ArithmeticFunction::ArithmeticFunction;
@@ -1714,13 +1784,12 @@ struct ArithmeticIntegerToFloatingPointFunction : public ArithmeticFunction {
   }
 };
 
-/// An ArithmeticFunction that promotes integer arguments to double.
+/// An ArithmeticFunction that promotes integer and decimal arguments to double.
 struct ArithmeticFloatingPointFunction : public ArithmeticFunction {
   using ArithmeticFunction::ArithmeticFunction;
 
   Result<const Kernel*> DispatchBest(std::vector<ValueDescr>* values) const override {
     RETURN_NOT_OK(CheckArity(*values));
-    RETURN_NOT_OK(CheckDecimals(values));
 
     using arrow::compute::detail::DispatchExactImpl;
     if (auto kernel = DispatchExactImpl(this, *values)) return kernel;
@@ -1732,7 +1801,7 @@ struct ArithmeticFloatingPointFunction : public ArithmeticFunction {
     }
 
     for (auto& descr : *values) {
-      if (is_integer(descr.type->id())) {
+      if (is_integer(descr.type->id()) || is_decimal(descr.type->id())) {
         descr.type = float64();
       }
     }
@@ -1755,10 +1824,10 @@ void AddNullExec(ScalarFunction* func) {
   DCHECK_OK(func->AddKernel(std::move(input_types), OutputType(null()), NullToNullExec));
 }
 
-template <typename Op>
+template <typename Op, typename FunctionImpl = ArithmeticFunction>
 std::shared_ptr<ScalarFunction> MakeArithmeticFunction(std::string name,
                                                        const FunctionDoc* doc) {
-  auto func = std::make_shared<ArithmeticFunction>(name, Arity::Binary(), doc);
+  auto func = std::make_shared<FunctionImpl>(name, Arity::Binary(), doc);
   for (const auto& ty : NumericTypes()) {
     auto exec = ArithmeticExecFromOp<ScalarBinaryEqualTypes, Op>(ty);
     DCHECK_OK(func->AddKernel({ty, ty}, ty, exec));
@@ -1769,10 +1838,10 @@ std::shared_ptr<ScalarFunction> MakeArithmeticFunction(std::string name,
 
 // Like MakeArithmeticFunction, but for arithmetic ops that need to run
 // only on non-null output.
-template <typename Op>
+template <typename Op, typename FunctionImpl = ArithmeticFunction>
 std::shared_ptr<ScalarFunction> MakeArithmeticFunctionNotNull(std::string name,
                                                               const FunctionDoc* doc) {
-  auto func = std::make_shared<ArithmeticFunction>(name, Arity::Binary(), doc);
+  auto func = std::make_shared<FunctionImpl>(name, Arity::Binary(), doc);
   for (const auto& ty : NumericTypes()) {
     auto exec = ArithmeticExecFromOp<ScalarBinaryNotNullEqualTypes, Op>(ty);
     DCHECK_OK(func->AddKernel({ty, ty}, ty, exec));
@@ -1805,6 +1874,12 @@ std::shared_ptr<ScalarFunction> MakeUnaryArithmeticFunctionWithFixedIntOutType(
     auto exec = GenerateArithmeticWithFixedIntOutType<ScalarUnary, IntOutType, Op>(ty);
     DCHECK_OK(func->AddKernel({ty}, out_ty, exec));
   }
+  {
+    auto exec = ScalarUnary<Int64Type, Decimal128Type, Op>::Exec;
+    DCHECK_OK(func->AddKernel({InputType(Type::DECIMAL128)}, int64(), exec));
+    exec = ScalarUnary<Int64Type, Decimal256Type, Op>::Exec;
+    DCHECK_OK(func->AddKernel({InputType(Type::DECIMAL256)}, int64(), exec));
+  }
   AddNullExec(func.get());
   return func;
 }
@@ -2338,27 +2413,29 @@ void RegisterScalarArithmetic(FunctionRegistry* registry) {
   // ----------------------------------------------------------------------
   auto absolute_value =
       MakeUnaryArithmeticFunction<AbsoluteValue>("abs", &absolute_value_doc);
+  AddDecimalUnaryKernels<AbsoluteValue>(absolute_value.get());
   DCHECK_OK(registry->AddFunction(std::move(absolute_value)));
 
   // ----------------------------------------------------------------------
   auto absolute_value_checked = MakeUnaryArithmeticFunctionNotNull<AbsoluteValueChecked>(
       "abs_checked", &absolute_value_checked_doc);
+  AddDecimalUnaryKernels<AbsoluteValueChecked>(absolute_value_checked.get());
   DCHECK_OK(registry->AddFunction(std::move(absolute_value_checked)));
 
   // ----------------------------------------------------------------------
   auto add = MakeArithmeticFunction<Add>("add", &add_doc);
-  AddDecimalBinaryKernels<Add>("add", &add);
+  AddDecimalBinaryKernels<Add>("add", add.get());
   DCHECK_OK(registry->AddFunction(std::move(add)));
 
   // ----------------------------------------------------------------------
   auto add_checked =
       MakeArithmeticFunctionNotNull<AddChecked>("add_checked", &add_checked_doc);
-  AddDecimalBinaryKernels<AddChecked>("add_checked", &add_checked);
+  AddDecimalBinaryKernels<AddChecked>("add_checked", add_checked.get());
   DCHECK_OK(registry->AddFunction(std::move(add_checked)));
 
   // ----------------------------------------------------------------------
   auto subtract = MakeArithmeticFunction<Subtract>("subtract", &sub_doc);
-  AddDecimalBinaryKernels<Subtract>("subtract", &subtract);
+  AddDecimalBinaryKernels<Subtract>("subtract", subtract.get());
 
   // Add subtract(timestamp, timestamp) -> duration
   for (auto unit : TimeUnit::values()) {
@@ -2372,47 +2449,52 @@ void RegisterScalarArithmetic(FunctionRegistry* registry) {
   // ----------------------------------------------------------------------
   auto subtract_checked = MakeArithmeticFunctionNotNull<SubtractChecked>(
       "subtract_checked", &sub_checked_doc);
-  AddDecimalBinaryKernels<SubtractChecked>("subtract_checked", &subtract_checked);
+  AddDecimalBinaryKernels<SubtractChecked>("subtract_checked", subtract_checked.get());
   DCHECK_OK(registry->AddFunction(std::move(subtract_checked)));
 
   // ----------------------------------------------------------------------
   auto multiply = MakeArithmeticFunction<Multiply>("multiply", &mul_doc);
-  AddDecimalBinaryKernels<Multiply>("multiply", &multiply);
+  AddDecimalBinaryKernels<Multiply>("multiply", multiply.get());
   DCHECK_OK(registry->AddFunction(std::move(multiply)));
 
   // ----------------------------------------------------------------------
   auto multiply_checked = MakeArithmeticFunctionNotNull<MultiplyChecked>(
       "multiply_checked", &mul_checked_doc);
-  AddDecimalBinaryKernels<MultiplyChecked>("multiply_checked", &multiply_checked);
+  AddDecimalBinaryKernels<MultiplyChecked>("multiply_checked", multiply_checked.get());
   DCHECK_OK(registry->AddFunction(std::move(multiply_checked)));
 
   // ----------------------------------------------------------------------
   auto divide = MakeArithmeticFunctionNotNull<Divide>("divide", &div_doc);
-  AddDecimalBinaryKernels<Divide>("divide", &divide);
+  AddDecimalBinaryKernels<Divide>("divide", divide.get());
   DCHECK_OK(registry->AddFunction(std::move(divide)));
 
   // ----------------------------------------------------------------------
   auto divide_checked =
       MakeArithmeticFunctionNotNull<DivideChecked>("divide_checked", &div_checked_doc);
-  AddDecimalBinaryKernels<DivideChecked>("divide_checked", &divide_checked);
+  AddDecimalBinaryKernels<DivideChecked>("divide_checked", divide_checked.get());
   DCHECK_OK(registry->AddFunction(std::move(divide_checked)));
 
   // ----------------------------------------------------------------------
   auto negate = MakeUnaryArithmeticFunction<Negate>("negate", &negate_doc);
+  AddDecimalUnaryKernels<Negate>(negate.get());
   DCHECK_OK(registry->AddFunction(std::move(negate)));
 
   // ----------------------------------------------------------------------
   auto negate_checked = MakeUnarySignedArithmeticFunctionNotNull<NegateChecked>(
       "negate_checked", &negate_checked_doc);
+  AddDecimalUnaryKernels<NegateChecked>(negate_checked.get());
   DCHECK_OK(registry->AddFunction(std::move(negate_checked)));
 
   // ----------------------------------------------------------------------
-  auto power = MakeArithmeticFunction<Power>("power", &pow_doc);
+  auto power = MakeArithmeticFunction<Power, ArithmeticDecimalToFloatingPointFunction>(
+      "power", &pow_doc);
   DCHECK_OK(registry->AddFunction(std::move(power)));
 
   // ----------------------------------------------------------------------
   auto power_checked =
-      MakeArithmeticFunctionNotNull<PowerChecked>("power_checked", &pow_checked_doc);
+      MakeArithmeticFunctionNotNull<PowerChecked,
+                                    ArithmeticDecimalToFloatingPointFunction>(
+          "power_checked", &pow_checked_doc);
   DCHECK_OK(registry->AddFunction(std::move(power_checked)));
 
   // ----------------------------------------------------------------------
diff --git a/cpp/src/arrow/compute/kernels/scalar_arithmetic_test.cc b/cpp/src/arrow/compute/kernels/scalar_arithmetic_test.cc
index 09681b2763bee..52414042e926f 100644
--- a/cpp/src/arrow/compute/kernels/scalar_arithmetic_test.cc
+++ b/cpp/src/arrow/compute/kernels/scalar_arithmetic_test.cc
@@ -294,7 +294,7 @@ class TestArithmeticDecimal : public ::testing::Test {
   }
 
   void CheckRaises(const std::string& func, const DatumVector& args,
-                   const std::string& substr, FunctionOptions* options = nullptr) {
+                   const std::string& substr, const FunctionOptions* options = nullptr) {
     EXPECT_RAISES_WITH_MESSAGE_THAT(Invalid, ::testing::HasSubstr(substr),
                                     CallFunction(func, args, options));
   }
@@ -1487,6 +1487,83 @@ TYPED_TEST(TestUnaryArithmeticFloating, AbsoluteValue) {
 
 class TestUnaryArithmeticDecimal : public TestArithmeticDecimal {};
 
+TEST_F(TestUnaryArithmeticDecimal, AbsoluteValue) {
+  auto max128 = Decimal128::GetMaxValue(38);
+  auto max256 = Decimal256::GetMaxValue(76);
+  for (const auto& func : {"abs", "abs_checked"}) {
+    for (const auto& ty : PositiveScaleTypes()) {
+      CheckScalar(func, {ArrayFromJSON(ty, R"([])")}, ArrayFromJSON(ty, R"([])"));
+      CheckScalar(func, {ArrayFromJSON(ty, R"(["1.00", "-42.15", null])")},
+                  ArrayFromJSON(ty, R"(["1.00", "42.15", null])"));
+    }
+    CheckScalar(func, {std::make_shared<Decimal128Scalar>(-max128, decimal128(38, 0))},
+                std::make_shared<Decimal128Scalar>(max128, decimal128(38, 0)));
+    CheckScalar(func, {std::make_shared<Decimal256Scalar>(-max256, decimal256(76, 0))},
+                std::make_shared<Decimal256Scalar>(max256, decimal256(76, 0)));
+    for (const auto& ty : NegativeScaleTypes()) {
+      CheckScalar(func, {ArrayFromJSON(ty, R"([])")}, ArrayFromJSON(ty, R"([])"));
+      CheckScalar(func, {DecimalArrayFromJSON(ty, R"(["12E2", "-42E2", null])")},
+                  DecimalArrayFromJSON(ty, R"(["12E2", "42E2", null])"));
+    }
+  }
+}
+
+TEST_F(TestUnaryArithmeticDecimal, Log) {
+  std::vector<std::string> unchecked = {"ln", "log2", "log10", "log1p"};
+  std::vector<std::string> checked = {"ln_checked", "log2_checked", "log10_checked",
+                                      "log1p_checked"};
+  std::vector<std::string> all = unchecked;
+  all.insert(all.end(), checked.begin(), checked.end());
+
+  for (const auto& func : all) {
+    for (const auto& ty : PositiveScaleTypes()) {
+      CheckDecimalToFloat(func, {ArrayFromJSON(ty, R"([])")});
+      CheckDecimalToFloat(func, {ArrayFromJSON(ty, R"(["0.01", "1.00", "4.42", null])")});
+    }
+    for (const auto& ty : NegativeScaleTypes()) {
+      CheckDecimalToFloat(func, {ArrayFromJSON(ty, R"([])")});
+      CheckDecimalToFloat(func, {DecimalArrayFromJSON(ty, R"(["12E2", "42E2", null])")});
+    }
+  }
+
+  for (const auto& func : unchecked) {
+    for (const auto& ty : PositiveScaleTypes()) {
+      CheckDecimalToFloat(func, {ArrayFromJSON(ty, R"(["-2.00"])")});
+    }
+  }
+  for (const auto& func : checked) {
+    for (const auto& ty : PositiveScaleTypes()) {
+      CheckRaises(func, {DecimalArrayFromJSON(ty, R"(["-2.00"])")},
+                  "logarithm of negative number");
+    }
+  }
+}
+
+TEST_F(TestUnaryArithmeticDecimal, Negate) {
+  auto max128 = Decimal128::GetMaxValue(38);
+  auto max256 = Decimal256::GetMaxValue(76);
+  for (const auto& func : {"negate", "negate_checked"}) {
+    for (const auto& ty : PositiveScaleTypes()) {
+      CheckScalar(func, {ArrayFromJSON(ty, R"([])")}, ArrayFromJSON(ty, R"([])"));
+      CheckScalar(func, {ArrayFromJSON(ty, R"(["0.00", "1.00", "-42.15", null])")},
+                  ArrayFromJSON(ty, R"(["0.00", "-1.00", "42.15", null])"));
+    }
+    CheckScalar(func, {std::make_shared<Decimal128Scalar>(-max128, decimal128(38, 0))},
+                std::make_shared<Decimal128Scalar>(max128, decimal128(38, 0)));
+    CheckScalar(func, {std::make_shared<Decimal128Scalar>(max128, decimal128(38, 0))},
+                std::make_shared<Decimal128Scalar>(-max128, decimal128(38, 0)));
+    CheckScalar(func, {std::make_shared<Decimal256Scalar>(-max256, decimal256(76, 0))},
+                std::make_shared<Decimal256Scalar>(max256, decimal256(76, 0)));
+    CheckScalar(func, {std::make_shared<Decimal256Scalar>(max256, decimal256(76, 0))},
+                std::make_shared<Decimal256Scalar>(-max256, decimal256(76, 0)));
+    for (const auto& ty : NegativeScaleTypes()) {
+      CheckScalar(func, {ArrayFromJSON(ty, R"([])")}, ArrayFromJSON(ty, R"([])"));
+      CheckScalar(func, {DecimalArrayFromJSON(ty, R"(["0", "12E2", "-42E2", null])")},
+                  DecimalArrayFromJSON(ty, R"(["0", "-12E2", "42E2", null])"));
+    }
+  }
+}
+
 // Check two modes exhaustively, give all modes a simple test
 TEST_F(TestUnaryArithmeticDecimal, Round) {
   const auto func = "round";
@@ -1973,6 +2050,116 @@ TEST_F(TestUnaryArithmeticDecimal, RoundToMultipleHalfToOdd) {
   }
 }
 
+TEST_F(TestUnaryArithmeticDecimal, Sign) {
+  auto max128 = Decimal128::GetMaxValue(38);
+  auto max256 = Decimal256::GetMaxValue(76);
+  const auto func = "sign";
+  for (const auto& ty : PositiveScaleTypes()) {
+    CheckScalar(func, {ArrayFromJSON(ty, R"([])")}, ArrayFromJSON(int64(), "[]"));
+    CheckScalar(func, {ArrayFromJSON(ty, R"(["1.00", "0.00", "-42.15", null])")},
+                ArrayFromJSON(int64(), "[1, 0, -1, null]"));
+  }
+  CheckScalar(func, {std::make_shared<Decimal128Scalar>(max128, decimal128(38, 0))},
+              ScalarFromJSON(int64(), "1"));
+  CheckScalar(func, {std::make_shared<Decimal128Scalar>(-max128, decimal128(38, 0))},
+              ScalarFromJSON(int64(), "-1"));
+  CheckScalar(func, {std::make_shared<Decimal256Scalar>(max256, decimal256(76, 0))},
+              ScalarFromJSON(int64(), "1"));
+  CheckScalar(func, {std::make_shared<Decimal256Scalar>(-max256, decimal256(76, 0))},
+              ScalarFromJSON(int64(), "-1"));
+  for (const auto& ty : NegativeScaleTypes()) {
+    CheckScalar(func, {ArrayFromJSON(ty, R"([])")}, ArrayFromJSON(int64(), "[]"));
+    CheckScalar(func, {DecimalArrayFromJSON(ty, R"(["12E2", "0", "-42E2", null])")},
+                ArrayFromJSON(int64(), "[1, 0, -1, null]"));
+  }
+}
+
+TEST_F(TestUnaryArithmeticDecimal, TrigAcos) {
+  for (const auto& func : {"acos", "acos_checked"}) {
+    for (const auto& ty : PositiveScaleTypes()) {
+      CheckDecimalToFloat(func, {ArrayFromJSON(ty, R"([])")});
+      CheckDecimalToFloat(func,
+                          {ArrayFromJSON(ty, R"(["0.00", "-1.00", "1.00", null])")});
+    }
+  }
+  for (const auto& ty : NegativeScaleTypes()) {
+    CheckDecimalToFloat("acos", {DecimalArrayFromJSON(ty, R"(["12E2", "-42E2", null])")});
+    CheckRaises("acos_checked", {DecimalArrayFromJSON(ty, R"(["12E2", "-42E2", null])")},
+                "domain error");
+  }
+}
+
+TEST_F(TestUnaryArithmeticDecimal, TrigAsin) {
+  for (const auto& func : {"asin", "asin_checked"}) {
+    for (const auto& ty : PositiveScaleTypes()) {
+      CheckDecimalToFloat(func, {ArrayFromJSON(ty, R"([])")});
+      CheckDecimalToFloat(func,
+                          {ArrayFromJSON(ty, R"(["0.00", "-1.00", "1.00", null])")});
+    }
+  }
+  for (const auto& ty : NegativeScaleTypes()) {
+    CheckDecimalToFloat("asin", {DecimalArrayFromJSON(ty, R"(["12E2", "-42E2", null])")});
+    EXPECT_RAISES_WITH_MESSAGE_THAT(
+        Invalid, ::testing::HasSubstr("domain error"),
+        CallFunction("asin_checked",
+                     {DecimalArrayFromJSON(ty, R"(["12E2", "-42E2", null])")}));
+  }
+}
+
+TEST_F(TestUnaryArithmeticDecimal, TrigAtan) {
+  const auto func = "atan";
+  for (const auto& ty : PositiveScaleTypes()) {
+    CheckDecimalToFloat(func, {ArrayFromJSON(ty, R"([])")});
+    CheckDecimalToFloat(func, {ArrayFromJSON(ty, R"(["0.00", "-1.00", "1.00", null])")});
+  }
+  for (const auto& ty : NegativeScaleTypes()) {
+    CheckDecimalToFloat(func, {ArrayFromJSON(ty, R"([])")});
+    CheckDecimalToFloat(func, {DecimalArrayFromJSON(ty, R"(["12E2", "-42E2", null])")});
+  }
+}
+
+TEST_F(TestUnaryArithmeticDecimal, TrigCos) {
+  for (const auto& func : {"cos", "cos_checked"}) {
+    for (const auto& ty : PositiveScaleTypes()) {
+      CheckDecimalToFloat(func, {ArrayFromJSON(ty, R"([])")});
+      CheckDecimalToFloat(func,
+                          {ArrayFromJSON(ty, R"(["0.00", "-1.00", "1.00", null])")});
+    }
+    for (const auto& ty : NegativeScaleTypes()) {
+      CheckDecimalToFloat(func, {ArrayFromJSON(ty, R"([])")});
+      CheckDecimalToFloat(func, {DecimalArrayFromJSON(ty, R"(["12E2", "-42E2", null])")});
+    }
+  }
+}
+
+TEST_F(TestUnaryArithmeticDecimal, TrigSin) {
+  for (const auto& func : {"sin", "sin_checked"}) {
+    for (const auto& ty : PositiveScaleTypes()) {
+      CheckDecimalToFloat(func, {ArrayFromJSON(ty, R"([])")});
+      CheckDecimalToFloat(func,
+                          {ArrayFromJSON(ty, R"(["0.00", "-1.00", "1.00", null])")});
+    }
+    for (const auto& ty : NegativeScaleTypes()) {
+      CheckDecimalToFloat(func, {ArrayFromJSON(ty, R"([])")});
+      CheckDecimalToFloat(func, {DecimalArrayFromJSON(ty, R"(["12E2", "-42E2", null])")});
+    }
+  }
+}
+
+TEST_F(TestUnaryArithmeticDecimal, TrigTan) {
+  for (const auto& func : {"tan", "tan_checked"}) {
+    for (const auto& ty : PositiveScaleTypes()) {
+      CheckDecimalToFloat(func, {ArrayFromJSON(ty, R"([])")});
+      CheckDecimalToFloat(func,
+                          {ArrayFromJSON(ty, R"(["0.00", "-1.00", "1.00", null])")});
+    }
+    for (const auto& ty : NegativeScaleTypes()) {
+      CheckDecimalToFloat(func, {ArrayFromJSON(ty, R"([])")});
+      CheckDecimalToFloat(func, {DecimalArrayFromJSON(ty, R"(["12E2", "-42E2", null])")});
+    }
+  }
+}
+
 TYPED_TEST_SUITE(TestUnaryRoundIntegral, IntegralTypes);
 TYPED_TEST_SUITE(TestUnaryRoundSigned, SignedIntegerTypes);
 TYPED_TEST_SUITE(TestUnaryRoundUnsigned, UnsignedIntegerTypes);
@@ -2179,7 +2366,9 @@ TYPED_TEST(TestUnaryRoundToMultipleFloating, RoundToMultiple) {
   this->AssertUnaryOpRaises(RoundToMultiple, values, "multiple must be positive");
 }
 
-TEST(TestBinaryDecimalArithmetic, DispatchBest) {
+class TestBinaryArithmeticDecimal : public TestArithmeticDecimal {};
+
+TEST_F(TestBinaryArithmeticDecimal, DispatchBest) {
   // decimal, floating point
   for (std::string name : {"add", "subtract", "multiply", "divide"}) {
     for (std::string suffix : {"", "_checked"}) {
@@ -2269,10 +2458,18 @@ TEST(TestBinaryDecimalArithmetic, DispatchBest) {
                         {decimal128(5, 4), decimal128(2, 0)});
     }
   }
+  for (std::string name : {"atan2", "logb", "logb_checked", "power", "power_checked"}) {
+    CheckDispatchBest(name, {decimal128(2, 1), decimal128(2, 1)}, {float64(), float64()});
+    CheckDispatchBest(name, {decimal256(2, 1), decimal256(2, 1)}, {float64(), float64()});
+    CheckDispatchBest(name, {decimal128(2, 1), int64()}, {float64(), float64()});
+    CheckDispatchBest(name, {int32(), decimal128(2, 1)}, {float64(), float64()});
+    CheckDispatchBest(name, {decimal128(2, 1), float64()}, {float64(), float64()});
+    CheckDispatchBest(name, {float32(), decimal128(2, 1)}, {float64(), float64()});
+  }
 }
 
 // reference result from bc (precsion=100, scale=40)
-TEST(TestBinaryArithmeticDecimal, AddSubtract) {
+TEST_F(TestBinaryArithmeticDecimal, AddSubtract) {
   // array array, decimal128
   {
     auto left = ArrayFromJSON(decimal128(30, 3),
@@ -2386,7 +2583,14 @@ TEST(TestBinaryArithmeticDecimal, AddSubtract) {
     CheckScalarBinary("add", right, left, added);
   }
 
-  // TODO: decimal integer
+  // decimal integer
+  {
+    auto left = ScalarFromJSON(decimal128(3, 0), R"("666")");
+    auto right = ScalarFromJSON(int64(), "888");
+    CheckScalarBinary("add", left, right, ScalarFromJSON(decimal128(20, 0), R"("1554")"));
+    CheckScalarBinary("subtract", left, right,
+                      ScalarFromJSON(decimal128(20, 0), R"("-222")"));
+  }
 
   // failed case: result maybe overflow
   {
@@ -2404,7 +2608,7 @@ TEST(TestBinaryArithmeticDecimal, AddSubtract) {
   }
 }
 
-TEST(TestBinaryArithmeticDecimal, Multiply) {
+TEST_F(TestBinaryArithmeticDecimal, Multiply) {
   // array array, decimal128
   {
     auto left = ArrayFromJSON(decimal128(20, 10),
@@ -2428,7 +2632,7 @@ TEST(TestBinaryArithmeticDecimal, Multiply) {
     CheckScalarBinary("multiply", left, right, expected);
   }
 
-  // array array, decimal26
+  // array array, decimal256
   {
     auto left = ArrayFromJSON(decimal256(30, 3),
                               R"([
@@ -2484,7 +2688,13 @@ TEST(TestBinaryArithmeticDecimal, Multiply) {
     CheckScalarBinary("multiply", right, left, expected);
   }
 
-  // TODO: decimal integer
+  // decimal integer
+  {
+    auto left = ScalarFromJSON(decimal128(3, 0), R"("666")");
+    auto right = ScalarFromJSON(int64(), "888");
+    auto expected = ScalarFromJSON(decimal128(23, 0), R"("591408")");
+    CheckScalarBinary("multiply", left, right, expected);
+  }
 
   // failed case: result maybe overflow
   {
@@ -2494,7 +2704,7 @@ TEST(TestBinaryArithmeticDecimal, Multiply) {
   }
 }
 
-TEST(TestBinaryArithmeticDecimal, Divide) {
+TEST_F(TestBinaryArithmeticDecimal, Divide) {
   // array array, decimal128
   {
     auto left = ArrayFromJSON(decimal128(13, 3), R"(["1234567890.123", "0.001"])");
@@ -2555,7 +2765,16 @@ TEST(TestBinaryArithmeticDecimal, Divide) {
     CheckScalarBinary("divide", right, left, right_div_left);
   }
 
-  // TODO: decimal integer
+  // decimal integer
+  {
+    auto left = ScalarFromJSON(decimal128(3, 0), R"("100")");
+    auto right = ScalarFromJSON(int64(), "50");
+    auto left_div_right =
+        ScalarFromJSON(decimal128(23, 20), R"("2.00000000000000000000")");
+    auto right_div_left = ScalarFromJSON(decimal128(23, 4), R"("0.5000")");
+    CheckScalarBinary("divide", left, right, left_div_right);
+    CheckScalarBinary("divide", right, left, right_div_left);
+  }
 
   // failed case: result maybe overflow
   {
@@ -2572,6 +2791,96 @@ TEST(TestBinaryArithmeticDecimal, Divide) {
   }
 }
 
+TEST_F(TestBinaryArithmeticDecimal, Atan2) {
+  // Decimal arguments promoted to double, sanity check here
+  const auto func = "atan2";
+  for (const auto& ty : PositiveScaleTypes()) {
+    CheckDecimalToFloat(func, {ArrayFromJSON(ty, R"([])"), ArrayFromJSON(ty, R"([])")});
+    CheckDecimalToFloat(
+        func, {ArrayFromJSON(ty, R"(["1.00", "10.00", "1.00", "2.00", null])"),
+               ArrayFromJSON(ty, R"(["10.00", "10.00", "2.00", "2.00", null])")});
+    CheckDecimalToFloat(
+        func,
+        {ArrayFromJSON(ty, R"(["1.00", "10.00", "1.00", "2.00", null])"),
+         ArrayFromJSON(decimal128(4, 2), R"(["10.00", "10.00", "2.00", "2.00", null])")});
+    CheckDecimalToFloat(func,
+                        {ArrayFromJSON(ty, R"(["1.00", "10.00", "1.00", "2.00", null])"),
+                         ScalarFromJSON(int64(), "10")});
+    CheckDecimalToFloat(func,
+                        {ArrayFromJSON(ty, R"(["1.00", "10.00", "1.00", "2.00", null])"),
+                         ScalarFromJSON(float64(), "10")});
+    CheckDecimalToFloat(func, {ArrayFromJSON(float64(), "[1, 10, 1, 2, null]"),
+                               ScalarFromJSON(ty, R"("10.00")")});
+    CheckDecimalToFloat(func, {ArrayFromJSON(int64(), "[1, 10, 1, 2, null]"),
+                               ScalarFromJSON(ty, R"("10.00")")});
+  }
+  for (const auto& ty : NegativeScaleTypes()) {
+    CheckDecimalToFloat(func, {ArrayFromJSON(ty, R"([])"), ArrayFromJSON(ty, R"([])")});
+    CheckDecimalToFloat(func, {DecimalArrayFromJSON(ty, R"(["12E2", "42E2", null])"),
+                               DecimalArrayFromJSON(ty, R"(["12E2", "42E2", null])")});
+    CheckDecimalToFloat(
+        func, {DecimalArrayFromJSON(ty, R"(["12E2", "42E2", null])"),
+               DecimalArrayFromJSON(decimal128(2, -2), R"(["12E2", "42E2", null])")});
+    CheckDecimalToFloat(func, {DecimalArrayFromJSON(ty, R"(["12E2", "42E2", null])"),
+                               ScalarFromJSON(int64(), "10")});
+  }
+}
+
+TEST_F(TestBinaryArithmeticDecimal, Logb) {
+  // Decimal arguments promoted to double, sanity check here
+  for (const auto& func : {"logb", "logb_checked"}) {
+    for (const auto& ty : PositiveScaleTypes()) {
+      CheckDecimalToFloat(func, {ArrayFromJSON(ty, R"([])"), ArrayFromJSON(ty, R"([])")});
+      CheckDecimalToFloat(
+          func, {ArrayFromJSON(ty, R"(["1.00", "10.00", "1.00", "2.00", null])"),
+                 ArrayFromJSON(ty, R"(["10.00", "10.00", "2.00", "2.00", null])")});
+      CheckDecimalToFloat(
+          func, {ArrayFromJSON(ty, R"(["1.00", "10.00", "1.00", "2.00", null])"),
+                 ArrayFromJSON(decimal128(4, 2),
+                               R"(["10.00", "10.00", "2.00", "2.00", null])")});
+      CheckDecimalToFloat(
+          func, {ArrayFromJSON(ty, R"(["1.00", "10.00", "1.00", "2.00", null])"),
+                 ScalarFromJSON(int64(), "10")});
+      CheckDecimalToFloat(
+          func, {ArrayFromJSON(ty, R"(["1.00", "10.00", "1.00", "2.00", null])"),
+                 ScalarFromJSON(float64(), "10")});
+      CheckDecimalToFloat(func, {ArrayFromJSON(float64(), "[1, 10, 1, 2, null]"),
+                                 ScalarFromJSON(ty, R"("10.00")")});
+      CheckDecimalToFloat(func, {ArrayFromJSON(int64(), "[1, 10, 1, 2, null]"),
+                                 ScalarFromJSON(ty, R"("10.00")")});
+    }
+    for (const auto& ty : NegativeScaleTypes()) {
+      CheckDecimalToFloat(func, {ArrayFromJSON(ty, R"([])"), ArrayFromJSON(ty, R"([])")});
+      CheckDecimalToFloat(func, {DecimalArrayFromJSON(ty, R"(["12E2", "42E2", null])"),
+                                 DecimalArrayFromJSON(ty, R"(["12E2", "42E2", null])")});
+      CheckDecimalToFloat(
+          func, {DecimalArrayFromJSON(ty, R"(["12E2", "42E2", null])"),
+                 DecimalArrayFromJSON(decimal128(2, -2), R"(["12E2", "42E2", null])")});
+      CheckDecimalToFloat(func, {DecimalArrayFromJSON(ty, R"(["12E2", "42E2", null])"),
+                                 ScalarFromJSON(int64(), "10")});
+    }
+  }
+}
+
+TEST_F(TestBinaryArithmeticDecimal, Power) {
+  // Decimal arguments promoted to double, sanity check here
+  for (const auto& func : {"logb", "logb_checked"}) {
+    for (const auto& ty : PositiveScaleTypes()) {
+      CheckDecimalToFloat(func, {ArrayFromJSON(ty, R"([])"), ArrayFromJSON(ty, R"([])")});
+      CheckDecimalToFloat(func, {ArrayFromJSON(ty, R"(["1.00", "2.00", null])"),
+                                 ArrayFromJSON(ty, R"(["1.23", null, "3.45"])")});
+      CheckDecimalToFloat(func, {ArrayFromJSON(ty, R"(["1.00", "2.00", null])"),
+                                 ArrayFromJSON(float64(), R"([1.23, null, 3.45])")});
+      CheckDecimalToFloat(func, {ArrayFromJSON(float64(), R"([1.00, 2.00, null])"),
+                                 ArrayFromJSON(ty, R"(["1.23", null, "3.45"])")});
+      CheckDecimalToFloat(func, {ArrayFromJSON(ty, R"(["1.00", "2.00", null])"),
+                                 ArrayFromJSON(int64(), R"([1, null, 3])")});
+      CheckDecimalToFloat(func, {ArrayFromJSON(int64(), R"([1, 2, null])"),
+                                 ArrayFromJSON(ty, R"(["1.23", null, "3.45"])")});
+    }
+  }
+}
+
 TYPED_TEST(TestBinaryArithmeticIntegral, ShiftLeft) {
   for (auto check_overflow : {false, true}) {
     this->SetOverflowCheck(check_overflow);
diff --git a/cpp/src/arrow/compute/kernels/scalar_validity.cc b/cpp/src/arrow/compute/kernels/scalar_validity.cc
index d23a909c6fd88..3f0a6a4178383 100644
--- a/cpp/src/arrow/compute/kernels/scalar_validity.cc
+++ b/cpp/src/arrow/compute/kernels/scalar_validity.cc
@@ -176,6 +176,18 @@ void AddFloatValidityKernel(const std::shared_ptr<DataType>& ty, ScalarFunction*
                             applicator::ScalarUnary<BooleanType, InType, Op>::Exec));
 }
 
+template <bool kConstant>
+Status ConstBoolExec(KernelContext* ctx, const ExecBatch& batch, Datum* out) {
+  if (batch.values[0].is_scalar()) {
+    checked_cast<BooleanScalar*>(out->scalar().get())->value = kConstant;
+    return Status::OK();
+  }
+  ArrayData* array = out->mutable_array();
+  BitUtil::SetBitsTo(array->buffers[1]->mutable_data(), array->offset, array->length,
+                     kConstant);
+  return Status::OK();
+}
+
 std::shared_ptr<ScalarFunction> MakeIsFiniteFunction(std::string name,
                                                      const FunctionDoc* doc) {
   auto func = std::make_shared<ScalarFunction>(name, Arity::Unary(), doc);
@@ -183,6 +195,15 @@ std::shared_ptr<ScalarFunction> MakeIsFiniteFunction(std::string name,
   AddFloatValidityKernel<FloatType, IsFiniteOperator>(float32(), func.get());
   AddFloatValidityKernel<DoubleType, IsFiniteOperator>(float64(), func.get());
 
+  for (const auto& ty : IntTypes()) {
+    DCHECK_OK(func->AddKernel({InputType(ty->id())}, boolean(), ConstBoolExec<true>));
+  }
+  DCHECK_OK(func->AddKernel({InputType(Type::NA)}, boolean(), ConstBoolExec<true>));
+  DCHECK_OK(
+      func->AddKernel({InputType(Type::DECIMAL128)}, boolean(), ConstBoolExec<true>));
+  DCHECK_OK(
+      func->AddKernel({InputType(Type::DECIMAL256)}, boolean(), ConstBoolExec<true>));
+
   return func;
 }
 
@@ -193,6 +214,15 @@ std::shared_ptr<ScalarFunction> MakeIsInfFunction(std::string name,
   AddFloatValidityKernel<FloatType, IsInfOperator>(float32(), func.get());
   AddFloatValidityKernel<DoubleType, IsInfOperator>(float64(), func.get());
 
+  for (const auto& ty : IntTypes()) {
+    DCHECK_OK(func->AddKernel({InputType(ty->id())}, boolean(), ConstBoolExec<false>));
+  }
+  DCHECK_OK(func->AddKernel({InputType(Type::NA)}, boolean(), ConstBoolExec<false>));
+  DCHECK_OK(
+      func->AddKernel({InputType(Type::DECIMAL128)}, boolean(), ConstBoolExec<false>));
+  DCHECK_OK(
+      func->AddKernel({InputType(Type::DECIMAL256)}, boolean(), ConstBoolExec<false>));
+
   return func;
 }
 
@@ -203,6 +233,15 @@ std::shared_ptr<ScalarFunction> MakeIsNanFunction(std::string name,
   AddFloatValidityKernel<FloatType, IsNanOperator>(float32(), func.get());
   AddFloatValidityKernel<DoubleType, IsNanOperator>(float64(), func.get());
 
+  for (const auto& ty : IntTypes()) {
+    DCHECK_OK(func->AddKernel({InputType(ty->id())}, boolean(), ConstBoolExec<false>));
+  }
+  DCHECK_OK(func->AddKernel({InputType(Type::NA)}, boolean(), ConstBoolExec<false>));
+  DCHECK_OK(
+      func->AddKernel({InputType(Type::DECIMAL128)}, boolean(), ConstBoolExec<false>));
+  DCHECK_OK(
+      func->AddKernel({InputType(Type::DECIMAL256)}, boolean(), ConstBoolExec<false>));
+
   return func;
 }
 
diff --git a/cpp/src/arrow/compute/kernels/scalar_validity_test.cc b/cpp/src/arrow/compute/kernels/scalar_validity_test.cc
index 35a6b831ef45a..5b0934828a23b 100644
--- a/cpp/src/arrow/compute/kernels/scalar_validity_test.cc
+++ b/cpp/src/arrow/compute/kernels/scalar_validity_test.cc
@@ -80,6 +80,45 @@ TEST_F(TestBooleanValidityKernels, IsNull) {
                    "[true, false, false, true]", &nan_is_null_options);
 }
 
+TEST(TestValidityKernels, IsFinite) {
+  for (const auto& ty : IntTypes()) {
+    CheckScalar("is_finite", {ArrayFromJSON(ty, "[0, 1, 42, null]")},
+                ArrayFromJSON(boolean(), "[true, true, true, null]"));
+  }
+  for (const auto& ty : {decimal128(4, 2), decimal256(4, 2)}) {
+    CheckScalar("is_finite", {ArrayFromJSON(ty, R"(["0.00", "1.01", "-42.00", null])")},
+                ArrayFromJSON(boolean(), "[true, true, true, null]"));
+  }
+  CheckScalar("is_finite", {std::make_shared<NullArray>(4)},
+              ArrayFromJSON(boolean(), "[null, null, null, null]"));
+}
+
+TEST(TestValidityKernels, IsInf) {
+  for (const auto& ty : IntTypes()) {
+    CheckScalar("is_inf", {ArrayFromJSON(ty, "[0, 1, 42, null]")},
+                ArrayFromJSON(boolean(), "[false, false, false, null]"));
+  }
+  for (const auto& ty : {decimal128(4, 2), decimal256(4, 2)}) {
+    CheckScalar("is_inf", {ArrayFromJSON(ty, R"(["0.00", "1.01", "-42.00", null])")},
+                ArrayFromJSON(boolean(), "[false, false, false, null]"));
+  }
+  CheckScalar("is_inf", {std::make_shared<NullArray>(4)},
+              ArrayFromJSON(boolean(), "[null, null, null, null]"));
+}
+
+TEST(TestValidityKernels, IsNan) {
+  for (const auto& ty : IntTypes()) {
+    CheckScalar("is_nan", {ArrayFromJSON(ty, "[0, 1, 42, null]")},
+                ArrayFromJSON(boolean(), "[false, false, false, null]"));
+  }
+  for (const auto& ty : {decimal128(4, 2), decimal256(4, 2)}) {
+    CheckScalar("is_nan", {ArrayFromJSON(ty, R"(["0.00", "1.01", "-42.00", null])")},
+                ArrayFromJSON(boolean(), "[false, false, false, null]"));
+  }
+  CheckScalar("is_nan", {std::make_shared<NullArray>(4)},
+              ArrayFromJSON(boolean(), "[null, null, null, null]"));
+}
+
 TEST(TestValidityKernels, IsValidIsNullNullType) {
   CheckScalarUnary("is_null", std::make_shared<NullArray>(5),
                    ArrayFromJSON(boolean(), "[true, true, true, true, true]"));
diff --git a/cpp/src/arrow/util/basic_decimal.cc b/cpp/src/arrow/util/basic_decimal.cc
index 1832bf5c4f9e7..c3b9d0272e86f 100644
--- a/cpp/src/arrow/util/basic_decimal.cc
+++ b/cpp/src/arrow/util/basic_decimal.cc
@@ -1115,6 +1115,12 @@ const BasicDecimal128& BasicDecimal128::GetHalfScaleMultiplier(int32_t scale) {
 
 const BasicDecimal128& BasicDecimal128::GetMaxValue() { return kMaxValue; }
 
+BasicDecimal128 BasicDecimal128::GetMaxValue(int32_t precision) {
+  DCHECK_GE(precision, 0);
+  DCHECK_LE(precision, 38);
+  return ScaleMultipliers[precision] - 1;
+}
+
 BasicDecimal128 BasicDecimal128::IncreaseScaleBy(int32_t increase_by) const {
   DCHECK_GE(increase_by, 0);
   DCHECK_LE(increase_by, 38);
@@ -1330,6 +1336,12 @@ const BasicDecimal256& BasicDecimal256::GetHalfScaleMultiplier(int32_t scale) {
   return ScaleMultipliersHalfDecimal256[scale];
 }
 
+BasicDecimal256 BasicDecimal256::GetMaxValue(int32_t precision) {
+  DCHECK_GE(precision, 0);
+  DCHECK_LE(precision, 76);
+  return ScaleMultipliersDecimal256[precision] + (-1);
+}
+
 BasicDecimal256 operator*(const BasicDecimal256& left, const BasicDecimal256& right) {
   BasicDecimal256 result = left;
   result *= right;
diff --git a/cpp/src/arrow/util/basic_decimal.h b/cpp/src/arrow/util/basic_decimal.h
index a4df3285596b5..93dced967e32d 100644
--- a/cpp/src/arrow/util/basic_decimal.h
+++ b/cpp/src/arrow/util/basic_decimal.h
@@ -227,6 +227,9 @@ class ARROW_EXPORT BasicDecimal128 {
   /// \brief Get the maximum valid unscaled decimal value.
   static const BasicDecimal128& GetMaxValue();
 
+  /// \brief Get the maximum valid unscaled decimal value for the given precision.
+  static BasicDecimal128 GetMaxValue(int32_t precision);
+
   /// \brief Get the maximum decimal value (is not a valid value).
   static inline constexpr BasicDecimal128 GetMaxSentinel() {
     return BasicDecimal128(/*high=*/std::numeric_limits<int64_t>::max(),
@@ -427,6 +430,9 @@ class ARROW_EXPORT BasicDecimal256 {
   /// \brief In-place division.
   BasicDecimal256& operator/=(const BasicDecimal256& right);
 
+  /// \brief Get the maximum valid unscaled decimal value for the given precision.
+  static BasicDecimal256 GetMaxValue(int32_t precision);
+
   /// \brief Get the maximum decimal value (is not a valid value).
   static inline constexpr BasicDecimal256 GetMaxSentinel() {
 #if ARROW_LITTLE_ENDIAN
diff --git a/docs/source/cpp/compute.rst b/docs/source/cpp/compute.rst
index 34b1f3448da7c..26c44a67e5bb7 100644
--- a/docs/source/cpp/compute.rst
+++ b/docs/source/cpp/compute.rst
@@ -219,13 +219,13 @@ the input to a single output value.
 +--------------------+-------+------------------+------------------------+----------------------------------+-------+
 | quantile           | Unary | Numeric          | Scalar Numeric         | :struct:`QuantileOptions`        | \(7)  |
 +--------------------+-------+------------------+------------------------+----------------------------------+-------+
-| stddev             | Unary | Numeric          | Scalar Float64         | :struct:`VarianceOptions`        |       |
+| stddev             | Unary | Numeric          | Scalar Float64         | :struct:`VarianceOptions`        | \(8)  |
 +--------------------+-------+------------------+------------------------+----------------------------------+-------+
 | sum                | Unary | Numeric          | Scalar Numeric         | :struct:`ScalarAggregateOptions` | \(6)  |
 +--------------------+-------+------------------+------------------------+----------------------------------+-------+
-| tdigest            | Unary | Numeric          | Float64                | :struct:`TDigestOptions`         | \(8)  |
+| tdigest            | Unary | Numeric          | Float64                | :struct:`TDigestOptions`         | \(9)  |
 +--------------------+-------+------------------+------------------------+----------------------------------+-------+
-| variance           | Unary | Numeric          | Scalar Float64         | :struct:`VarianceOptions`        |       |
+| variance           | Unary | Numeric          | Scalar Float64         | :struct:`VarianceOptions`        | \(8)  |
 +--------------------+-------+------------------+------------------------+----------------------------------+-------+
 
 * \(1) If null values are taken into account, by setting the
@@ -255,10 +255,14 @@ the input to a single output value.
 
 * \(7) Output is Float64 or input type, depending on QuantileOptions.
 
-* \(8) tdigest/t-digest computes approximate quantiles, and so only needs a
+* \(8) Decimal arguments are cast to Float64 first.
+
+* \(9) tdigest/t-digest computes approximate quantiles, and so only needs a
   fixed amount of memory. See the `reference implementation
   <https://github.com/tdunning/t-digest>`_ for details.
 
+  Decimal arguments are cast to Float64 first.
+
 Grouped Aggregations ("group by")
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
@@ -330,13 +334,13 @@ equivalents above and reflects how they are implemented internally.
 +-------------------------+-------+------------------------------------+------------------------+----------------------------------+-------+
 | hash_product            | Unary | Numeric                            | Numeric                | :struct:`ScalarAggregateOptions` | \(4)  |
 +-------------------------+-------+------------------------------------+------------------------+----------------------------------+-------+
-| hash_stddev             | Unary | Numeric                            | Float64                | :struct:`VarianceOptions`        |       |
+| hash_stddev             | Unary | Numeric                            | Float64                | :struct:`VarianceOptions`        | \(5)  |
 +-------------------------+-------+------------------------------------+------------------------+----------------------------------+-------+
 | hash_sum                | Unary | Numeric                            | Numeric                | :struct:`ScalarAggregateOptions` | \(4)  |
 +-------------------------+-------+------------------------------------+------------------------+----------------------------------+-------+
-| hash_tdigest            | Unary | Numeric                            | FixedSizeList[Float64] | :struct:`TDigestOptions`         | \(5)  |
+| hash_tdigest            | Unary | Numeric                            | FixedSizeList[Float64] | :struct:`TDigestOptions`         | \(6)  |
 +-------------------------+-------+------------------------------------+------------------------+----------------------------------+-------+
-| hash_variance           | Unary | Numeric                            | Float64                | :struct:`VarianceOptions`        |       |
+| hash_variance           | Unary | Numeric                            | Float64                | :struct:`VarianceOptions`        | \(5)  |
 +-------------------------+-------+------------------------------------+------------------------+----------------------------------+-------+
 
 * \(1) If null values are taken into account, by setting the
@@ -357,10 +361,14 @@ equivalents above and reflects how they are implemented internally.
 * \(4) Output is Int64, UInt64, Float64, or Decimal128/256, depending on the
   input type.
 
-* \(5) T-digest computes approximate quantiles, and so only needs a
+* \(5) Decimal arguments are cast to Float64 first.
+
+* \(6) T-digest computes approximate quantiles, and so only needs a
   fixed amount of memory. See the `reference implementation
   <https://github.com/tdunning/t-digest>`_ for details.
 
+  Decimal arguments are cast to Float64 first.
+
 Element-wise ("scalar") functions
 ---------------------------------
 
@@ -456,8 +464,8 @@ decimal and integer arguments will cast all arguments to decimals.
   enough scale kept. Error is returned if the result precision is beyond the
   decimal value range.
 
-* \(2) Output is any of (-1,1) for nonzero inputs and 0 for zero input.
-  NaN values return NaN.  Integral values return signedness as Int8 and
+* \(2) Output is any of (-1,1) for nonzero inputs and 0 for zero input.  NaN
+  values return NaN.  Integral and decimal values return signedness as Int8 and
   floating-point values return it with the same type as the input values.
 
 Bit-wise functions
@@ -585,29 +593,31 @@ Logarithmic functions
 Logarithmic functions are also supported, and also offer ``_checked``
 variants that check for domain errors if needed.
 
-+--------------------------+------------+--------------------+---------------------+
-| Function name            | Arity      | Input types        | Output type         |
-+==========================+============+====================+=====================+
-| ln                       | Unary      | Float32/Float64    | Float32/Float64     |
-+--------------------------+------------+--------------------+---------------------+
-| ln_checked               | Unary      | Float32/Float64    | Float32/Float64     |
-+--------------------------+------------+--------------------+---------------------+
-| log10                    | Unary      | Float32/Float64    | Float32/Float64     |
-+--------------------------+------------+--------------------+---------------------+
-| log10_checked            | Unary      | Float32/Float64    | Float32/Float64     |
-+--------------------------+------------+--------------------+---------------------+
-| log1p                    | Unary      | Float32/Float64    | Float32/Float64     |
-+--------------------------+------------+--------------------+---------------------+
-| log1p_checked            | Unary      | Float32/Float64    | Float32/Float64     |
-+--------------------------+------------+--------------------+---------------------+
-| log2                     | Unary      | Float32/Float64    | Float32/Float64     |
-+--------------------------+------------+--------------------+---------------------+
-| log2_checked             | Unary      | Float32/Float64    | Float32/Float64     |
-+--------------------------+------------+--------------------+---------------------+
-| logb                     | Binary     | Float32/Float64    | Float32/Float64     |
-+--------------------------+------------+--------------------+---------------------+
-| logb_checked             | Binary     | Float32/Float64    | Float32/Float64     |
-+--------------------------+------------+--------------------+---------------------+
+Decimal values are accepted, but are cast to Float64 first.
+
++--------------------------+------------+-------------------------+---------------------+
+| Function name            | Arity      | Input types             | Output type         |
++==========================+============+=========================+=====================+
+| ln                       | Unary      | Float32/Float64/Decimal | Float32/Float64     |
++--------------------------+------------+-------------------------+---------------------+
+| ln_checked               | Unary      | Float32/Float64/Decimal | Float32/Float64     |
++--------------------------+------------+-------------------------+---------------------+
+| log10                    | Unary      | Float32/Float64/Decimal | Float32/Float64     |
++--------------------------+------------+-------------------------+---------------------+
+| log10_checked            | Unary      | Float32/Float64/Decimal | Float32/Float64     |
++--------------------------+------------+-------------------------+---------------------+
+| log1p                    | Unary      | Float32/Float64/Decimal | Float32/Float64     |
++--------------------------+------------+-------------------------+---------------------+
+| log1p_checked            | Unary      | Float32/Float64/Decimal | Float32/Float64     |
++--------------------------+------------+-------------------------+---------------------+
+| log2                     | Unary      | Float32/Float64/Decimal | Float32/Float64     |
++--------------------------+------------+-------------------------+---------------------+
+| log2_checked             | Unary      | Float32/Float64/Decimal | Float32/Float64     |
++--------------------------+------------+-------------------------+---------------------+
+| logb                     | Binary     | Float32/Float64/Decimal | Float32/Float64     |
++--------------------------+------------+-------------------------+---------------------+
+| logb_checked             | Binary     | Float32/Float64/Decimal | Float32/Float64     |
++--------------------------+------------+-------------------------+---------------------+
 
 Trigonometric functions
 ~~~~~~~~~~~~~~~~~~~~~~~
@@ -615,33 +625,35 @@ Trigonometric functions
 Trigonometric functions are also supported, and also offer ``_checked``
 variants that check for domain errors if needed.
 
-+--------------------------+------------+--------------------+---------------------+
-| Function name            | Arity      | Input types        | Output type         |
-+==========================+============+====================+=====================+
-| acos                     | Unary      | Float32/Float64    | Float32/Float64     |
-+--------------------------+------------+--------------------+---------------------+
-| acos_checked             | Unary      | Float32/Float64    | Float32/Float64     |
-+--------------------------+------------+--------------------+---------------------+
-| asin                     | Unary      | Float32/Float64    | Float32/Float64     |
-+--------------------------+------------+--------------------+---------------------+
-| asin_checked             | Unary      | Float32/Float64    | Float32/Float64     |
-+--------------------------+------------+--------------------+---------------------+
-| atan                     | Unary      | Float32/Float64    | Float32/Float64     |
-+--------------------------+------------+--------------------+---------------------+
-| atan2                    | Binary     | Float32/Float64    | Float32/Float64     |
-+--------------------------+------------+--------------------+---------------------+
-| cos                      | Unary      | Float32/Float64    | Float32/Float64     |
-+--------------------------+------------+--------------------+---------------------+
-| cos_checked              | Unary      | Float32/Float64    | Float32/Float64     |
-+--------------------------+------------+--------------------+---------------------+
-| sin                      | Unary      | Float32/Float64    | Float32/Float64     |
-+--------------------------+------------+--------------------+---------------------+
-| sin_checked              | Unary      | Float32/Float64    | Float32/Float64     |
-+--------------------------+------------+--------------------+---------------------+
-| tan                      | Unary      | Float32/Float64    | Float32/Float64     |
-+--------------------------+------------+--------------------+---------------------+
-| tan_checked              | Unary      | Float32/Float64    | Float32/Float64     |
-+--------------------------+------------+--------------------+---------------------+
+Decimal values are accepted, but are cast to Float64 first.
+
++--------------------------+------------+-------------------------+---------------------+
+| Function name            | Arity      | Input types             | Output type         |
++==========================+============+=========================+=====================+
+| acos                     | Unary      | Float32/Float64/Decimal | Float32/Float64     |
++--------------------------+------------+-------------------------+---------------------+
+| acos_checked             | Unary      | Float32/Float64/Decimal | Float32/Float64     |
++--------------------------+------------+-------------------------+---------------------+
+| asin                     | Unary      | Float32/Float64/Decimal | Float32/Float64     |
++--------------------------+------------+-------------------------+---------------------+
+| asin_checked             | Unary      | Float32/Float64/Decimal | Float32/Float64     |
++--------------------------+------------+-------------------------+---------------------+
+| atan                     | Unary      | Float32/Float64/Decimal | Float32/Float64     |
++--------------------------+------------+-------------------------+---------------------+
+| atan2                    | Binary     | Float32/Float64/Decimal | Float32/Float64     |
++--------------------------+------------+-------------------------+---------------------+
+| cos                      | Unary      | Float32/Float64/Decimal | Float32/Float64     |
++--------------------------+------------+-------------------------+---------------------+
+| cos_checked              | Unary      | Float32/Float64/Decimal | Float32/Float64     |
++--------------------------+------------+-------------------------+---------------------+
+| sin                      | Unary      | Float32/Float64/Decimal | Float32/Float64     |
++--------------------------+------------+-------------------------+---------------------+
+| sin_checked              | Unary      | Float32/Float64/Decimal | Float32/Float64     |
++--------------------------+------------+-------------------------+---------------------+
+| tan                      | Unary      | Float32/Float64/Decimal | Float32/Float64     |
++--------------------------+------------+-------------------------+---------------------+
+| tan_checked              | Unary      | Float32/Float64/Decimal | Float32/Float64     |
++--------------------------+------------+-------------------------+---------------------+
 
 Comparisons
 ~~~~~~~~~~~
@@ -1117,26 +1129,28 @@ Containment tests
 Categorizations
 ~~~~~~~~~~~~~~~
 
-+-------------------+------------+---------------------+---------------------+------------------------+---------+
-| Function name     | Arity      | Input types         | Output type         | Options class          | Notes   |
-+===================+============+=====================+=====================+========================+=========+
-| is_finite         | Unary      | Float, Double       | Boolean             |                        | \(1)    |
-+-------------------+------------+---------------------+---------------------+------------------------+---------+
-| is_inf            | Unary      | Float, Double       | Boolean             |                        | \(2)    |
-+-------------------+------------+---------------------+---------------------+------------------------+---------+
-| is_nan            | Unary      | Float, Double       | Boolean             |                        | \(3)    |
-+-------------------+------------+---------------------+---------------------+------------------------+---------+
-| is_null           | Unary      | Any                 | Boolean             | :struct:`NullOptions`  | \(4)    |
-+-------------------+------------+---------------------+---------------------+------------------------+---------+
-| is_valid          | Unary      | Any                 | Boolean             |                        | \(5)    |
-+-------------------+------------+---------------------+---------------------+------------------------+---------+
++-------------------+------------+-------------------------+---------------------+------------------------+---------+
+| Function name     | Arity      | Input types             | Output type         | Options class          | Notes   |
++===================+============+=========================+=====================+========================+=========+
+| is_finite         | Unary      | Null, Numeric           | Boolean             |                        | \(1)    |
++-------------------+------------+-------------------------+---------------------+------------------------+---------+
+| is_inf            | Unary      | Null, Numeric           | Boolean             |                        | \(2)    |
++-------------------+------------+-------------------------+---------------------+------------------------+---------+
+| is_nan            | Unary      | Null, Numeric           | Boolean             |                        | \(3)    |
++-------------------+------------+-------------------------+---------------------+------------------------+---------+
+| is_null           | Unary      | Any                     | Boolean             | :struct:`NullOptions`  | \(4)    |
++-------------------+------------+-------------------------+---------------------+------------------------+---------+
+| is_valid          | Unary      | Any                     | Boolean             |                        | \(5)    |
++-------------------+------------+-------------------------+---------------------+------------------------+---------+
 
 * \(1) Output is true iff the corresponding input element is finite (neither Infinity,
-  -Infinity, nor NaN).
+  -Infinity, nor NaN). Hence, for Decimal and integer inputs this always returns true.
 
 * \(2) Output is true iff the corresponding input element is Infinity/-Infinity.
+  Hence, for Decimal and integer inputs this always returns false.
 
 * \(3) Output is true iff the corresponding input element is NaN.
+  Hence, for Decimal and integer inputs this always returns false.
 
 * \(4) Output is true iff the corresponding input element is null. NaN values
   can also be considered null by setting :member:`NullOptions::nan_is_null`.