sort-scalars

Author: izvolov

libcxx/include/__algorithm/radix_sort.h

@@ -29,9 +29,11 @@
 
 #include <__algorithm/for_each.h>
 #include <__algorithm/move.h>
+#include <__bit/bit_cast.h>
 #include <__bit/bit_log2.h>
 #include <__bit/countl.h>
 #include <__config>
+#include <__cstddef/size_t.h>
 #include <__functional/identity.h>
 #include <__iterator/access.h>
 #include <__iterator/distance.h>
@@ -44,9 +46,12 @@
 #include <__type_traits/enable_if.h>
 #include <__type_traits/invoke.h>
 #include <__type_traits/is_assignable.h>
+#include <__type_traits/is_enum.h>
+#include <__type_traits/is_floating_point.h>
 #include <__type_traits/is_integral.h>
 #include <__type_traits/is_unsigned.h>
 #include <__type_traits/make_unsigned.h>
+#include <__type_traits/underlying_type.h>
 #include <__utility/forward.h>
 #include <__utility/integer_sequence.h>
 #include <__utility/move.h>
@@ -298,6 +303,94 @@ _LIBCPP_HIDE_FROM_ABI constexpr auto __shift_to_unsigned(_Ip __n) {
   return static_cast<make_unsigned_t<_Ip> >(__n ^ __min_value);
 }
 
+template <size_t _Size>
+struct __unsigned_integer_of_size {};
+
+template <>
+struct __unsigned_integer_of_size<1> {
+  using type = uint8_t;
+};
+
+template <>
+struct __unsigned_integer_of_size<2> {
+  using type = uint16_t;
+};
+
+template <>
+struct __unsigned_integer_of_size<4> {
+  using type = uint32_t;
+};
+
+template <>
+struct __unsigned_integer_of_size<8> {
+  using type = uint64_t;
+};
+
+template <>
+struct __unsigned_integer_of_size<16> {
+#  if _LIBCPP_HAS_INT128
+  using type = __int128;
+#  endif
+};
+
+template <size_t _Size>
+using __unsigned_integer_of_size_t _LIBCPP_NODEBUG = typename __unsigned_integer_of_size<_Size>::type;
+
+template <class _Sc>
+using __unsigned_representation_for_t _LIBCPP_NODEBUG = __unsigned_integer_of_size_t<sizeof(_Sc)>;
+
+// Represent a scalar type as an ordered integer
+
+// The function is defined for ordered scalar types: integers, floating-point numbers, pointers, and enums.
+// Returns an integer representation such that for any `x` and `y` such that `x < y`, the expression
+// `__to_ordered_integral(x) < __to_ordered_integral(y)` is true, where `x`, `y` are values of the `Scalar` type.
+// __unsigned_representation_for_t<_Scalar> __to_ordered_integral(_Scalar);
+
+template <class _Integral, enable_if_t< is_integral_v<_Integral>, int> = 0>
+_LIBCPP_HIDE_FROM_ABI constexpr auto __to_ordered_integral(_Integral __n) {
+  return __n;
+}
+
+// An overload for floating-point numbers
+
+// From the IEEE 754 standard, we know that:
+// 1. The bit representation of positive floats directly reflects their order:
+//    When comparing floats by magnitude, the number with the larger exponent is greater, and if the exponents are
+//    equal, the one with the larger mantissa is greater.
+// 2. The bit representation of negative floats reflects their reverse order (for the same reasons).
+// 3. The most significant bit (sign bit) is zero for positive floats and one for negative floats. Therefore, in the raw
+//    bit representation, any negative number will be greater than any positive number.
+
+// The only exception from this rule is `NaN`, which is unordered by definition.
+
+// Based on the above, to obtain correctly ordered integral representation of floating-point numbers, we need to:
+// 1. Invert the bit representation (including the sign bit) of negative floats to switch from reverse order to direct
+//    order;
+// 2. Invert the sign bit for positive floats.
+
+// Thus, in final integral representation, we have reversed the order for negative floats and made all negative floats
+// smaller than all positive numbers (by inverting the sign bit).
+template <class _Floating, enable_if_t< is_floating_point_v<_Floating>, int> = 0>
+_LIBCPP_HIDE_FROM_ABI constexpr auto __to_ordered_integral(_Floating __f) {
+  using __integral_type          = __unsigned_representation_for_t<_Floating>;
+  constexpr auto __bit_count     = std::numeric_limits<__integral_type>::digits;
+  constexpr auto __sign_bit_mask = static_cast<__integral_type>(__integral_type{1} << (__bit_count - 1));
+
+  const auto __u = std::__bit_cast<__integral_type>(__f);
+
+  return static_cast<__integral_type>(__u & __sign_bit_mask ? ~__u : __u ^ __sign_bit_mask);
+}
+
+template <class _Enum, enable_if_t< is_enum_v<_Enum>, int> = 0>
+_LIBCPP_HIDE_FROM_ABI constexpr auto __to_ordered_integral(_Enum __e) {
+  return static_cast<std::underlying_type_t<_Enum>>(__e);
+}
+
+template <class _Pointer>
+_LIBCPP_HIDE_FROM_ABI constexpr auto __to_ordered_integral(_Pointer* __ptr) {
+  return std::__bit_cast<__unsigned_representation_for_t<_Pointer*>>(__ptr);
+}
+
 struct __low_byte_fn {
   template <class _Ip>
   _LIBCPP_HIDE_FROM_ABI constexpr uint8_t operator()(_Ip __integer) const {
@@ -314,7 +407,9 @@ __radix_sort(_RandomAccessIterator1 __first,
              _RandomAccessIterator2 __buffer,
              _Map __map,
              _Radix __radix) {
-  auto __map_to_unsigned = [__map = std::move(__map)](const auto& __x) { return std::__shift_to_unsigned(__map(__x)); };
+  auto __map_to_unsigned = [__map = std::move(__map)](const auto& __x) {
+    return std::__shift_to_unsigned(__map(std::__to_ordered_integral(__x)));
+  };
   std::__radix_sort_impl(__first, __last, __buffer, __map_to_unsigned, __radix);
 }
 

libcxx/include/__algorithm/stable_sort.h

@@ -25,9 +25,10 @@
 #include <__memory/unique_temporary_buffer.h>
 #include <__type_traits/desugars_to.h>
 #include <__type_traits/enable_if.h>
+#include <__type_traits/invoke.h>
 #include <__type_traits/is_constant_evaluated.h>
-#include <__type_traits/is_integral.h>
 #include <__type_traits/is_same.h>
+#include <__type_traits/is_scalar.h>
 #include <__type_traits/is_trivially_assignable.h>
 #include <__type_traits/remove_cvref.h>
 #include <__utility/move.h>
@@ -202,7 +203,7 @@ struct __stable_sort_switch {
 #if _LIBCPP_STD_VER >= 17
 template <class _Tp>
 _LIBCPP_HIDE_FROM_ABI constexpr unsigned __radix_sort_min_bound() {
-  static_assert(is_integral<_Tp>::value);
+  static_assert(is_scalar<_Tp>::value);
   if constexpr (sizeof(_Tp) == 1) {
     return 1 << 8;
   }
@@ -212,13 +213,14 @@ _LIBCPP_HIDE_FROM_ABI constexpr unsigned __radix_sort_min_bound() {
 
 template <class _Tp>
 _LIBCPP_HIDE_FROM_ABI constexpr unsigned __radix_sort_max_bound() {
-  static_assert(is_integral<_Tp>::value);
+  static_assert(is_scalar<_Tp>::value);
   if constexpr (sizeof(_Tp) >= 8) {
     return 1 << 15;
   }
 
   return 1 << 16;
 }
+
 #endif // _LIBCPP_STD_VER >= 17
 
 template <class _AlgPolicy, class _Compare, class _RandomAccessIterator>
@@ -246,12 +248,12 @@ _LIBCPP_CONSTEXPR_SINCE_CXX26 void __stable_sort(
   }
 
 #if _LIBCPP_STD_VER >= 17
-  constexpr auto __default_comp =
-      __desugars_to_v<__totally_ordered_less_tag, __remove_cvref_t<_Compare>, value_type, value_type >;
-  constexpr auto __integral_value =
-      is_integral_v<value_type > && is_same_v< value_type&, __iter_reference<_RandomAccessIterator>>;
-  constexpr auto __allowed_radix_sort = __default_comp && __integral_value;
-  if constexpr (__allowed_radix_sort) {
+  constexpr auto __default_comp = __desugars_to_v<__less_tag, __remove_cvref_t<_Compare>, value_type, value_type >;
+  constexpr auto __scalar_value =
+      is_scalar_v<value_type > && is_same_v< value_type&, __iter_reference<_RandomAccessIterator>>;
+  // There are non-comparable scalars (std::nullptr_t, pointers to members), so we need to exclude them.
+  constexpr auto __comparable_value = is_invocable_r_v<bool, _Compare, value_type, value_type>;
+  if constexpr (__default_comp && __scalar_value && __comparable_value) {
     if (__len <= __buff_size && __len >= static_cast<difference_type>(std::__radix_sort_min_bound<value_type>()) &&
         __len <= static_cast<difference_type>(std::__radix_sort_max_bound<value_type>())) {
       if (__libcpp_is_constant_evaluated()) {