GH-45190: [C++][Compute] Add rank_quantile function (#45259)

### Rationale for this change

Add a "rank_quantile" function following the Wikipedia definition:
https://en.wikipedia.org/wiki/Percentile_rank

### Are these changes tested?

Yes.

### Are there any user-facing changes?

Yes, an additional compute function.

* GitHub Issue: #45190

Lead-authored-by: Antoine Pitrou <antoine@python.org>
Co-authored-by: Rossi Sun <zanmato1984@gmail.com>
Co-authored-by: Antoine Pitrou <pitrou@free.fr>
Signed-off-by: Antoine Pitrou <antoine@python.org>

Author: pitrou

cpp/src/arrow/compute/api_vector.cc

@@ -48,6 +48,7 @@ using compute::DictionaryEncodeOptions;
 using compute::FilterOptions;
 using compute::NullPlacement;
 using compute::RankOptions;
+using compute::RankQuantileOptions;
 
 template <>
 struct EnumTraits<FilterOptions::NullSelectionBehavior>
@@ -151,6 +152,9 @@ static auto kRankOptionsType = GetFunctionOptionsType<RankOptions>(
     DataMember("sort_keys", &RankOptions::sort_keys),
     DataMember("null_placement", &RankOptions::null_placement),
     DataMember("tiebreaker", &RankOptions::tiebreaker));
+static auto kRankQuantileOptionsType = GetFunctionOptionsType<RankQuantileOptions>(
+    DataMember("sort_keys", &RankQuantileOptions::sort_keys),
+    DataMember("null_placement", &RankQuantileOptions::null_placement));
 static auto kPairwiseOptionsType = GetFunctionOptionsType<PairwiseOptions>(
     DataMember("periods", &PairwiseOptions::periods));
 static auto kListFlattenOptionsType = GetFunctionOptionsType<ListFlattenOptions>(
@@ -228,6 +232,13 @@ RankOptions::RankOptions(std::vector<SortKey> sort_keys, NullPlacement null_plac
       tiebreaker(tiebreaker) {}
 constexpr char RankOptions::kTypeName[];
 
+RankQuantileOptions::RankQuantileOptions(std::vector<SortKey> sort_keys,
+                                         NullPlacement null_placement)
+    : FunctionOptions(internal::kRankQuantileOptionsType),
+      sort_keys(std::move(sort_keys)),
+      null_placement(null_placement) {}
+constexpr char RankQuantileOptions::kTypeName[];
+
 PairwiseOptions::PairwiseOptions(int64_t periods)
     : FunctionOptions(internal::kPairwiseOptionsType), periods(periods) {}
 constexpr char PairwiseOptions::kTypeName[];

cpp/src/arrow/compute/api_vector.h

@@ -195,6 +195,25 @@ class ARROW_EXPORT RankOptions : public FunctionOptions {
   Tiebreaker tiebreaker;
 };
 
+/// \brief Quantile rank options
+class ARROW_EXPORT RankQuantileOptions : public FunctionOptions {
+ public:
+  explicit RankQuantileOptions(std::vector<SortKey> sort_keys = {},
+                               NullPlacement null_placement = NullPlacement::AtEnd);
+  /// Convenience constructor for array inputs
+  explicit RankQuantileOptions(SortOrder order,
+                               NullPlacement null_placement = NullPlacement::AtEnd)
+      : RankQuantileOptions({SortKey("", order)}, null_placement) {}
+
+  static constexpr char const kTypeName[] = "RankQuantileOptions";
+  static RankQuantileOptions Defaults() { return RankQuantileOptions(); }
+
+  /// Column key(s) to order by and how to order by these sort keys.
+  std::vector<SortKey> sort_keys;
+  /// Whether nulls and NaNs are placed at the start or at the end
+  NullPlacement null_placement;
+};
+
 /// \brief Partitioning options for NthToIndices
 class ARROW_EXPORT PartitionNthOptions : public FunctionOptions {
  public: