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A.18.26 Array Sorting

1/3
{AI95-00302-03} {AI05-0001-1} The language-defined generic procedures Containers.Generic_Array_Sort, Containers.Generic_Constrained_Array_Sort, and Containers.Generic_Sort provide sorting on arbitrary array types. 

Static Semantics

2/2
{AI95-00302-03} The generic library procedure Containers.Generic_Array_Sort has the following declaration: 
3/2
generic
   type Index_Type is (<>);
   type Element_Type is private;
   type Array_Type is array (Index_Type range <>) of Element_Type;
   with function "<" (Left, Right : Element_Type)
      return Boolean is <>;
procedure Ada.Containers.Generic_Array_Sort (Container : in out Array_Type);
pragma Pure(Ada.Containers.Generic_Array_Sort);
4/2
Reorders the elements of Container such that the elements are sorted smallest first as determined by the generic formal "<" operator provided. Any exception raised during evaluation of "<" is propagated.
5/3
{AI05-0044-1} {AI05-0262-1} The actual function for the generic formal function "<" of Generic_Array_Sort is expected to return the same value each time it is called with a particular pair of element values. It should define a strict weak ordering relationship (see A.18); it should not modify Container. If the actual for "<" behaves in some other manner, the behavior of the instance of Generic_Array_Sort is unspecified. The number of times Generic_Array_Sort calls "<" is unspecified.
5.a/2
Ramification: This implies swapping the elements, usually including an intermediate copy. This of course means that the elements will be copied. Since the elements are nonlimited, this usually will not be a problem. Note that there is Implementation Advice below that the implementation should use a sort that minimizes copying of elements.
5.b/2
The sort is not required to be stable (and the fast algorithm required will not be stable). If a stable sort is needed, the user can include the original location of the element as an extra "sort key". We considered requiring the implementation to do that, but it is mostly extra overhead -- usually there is something already in the element that provides the needed stability. 
6/2
{AI95-00302-03} The generic library procedure Containers.Generic_Constrained_Array_Sort has the following declaration: 
7/2
generic
   type Index_Type is (<>);
   type Element_Type is private;
   type Array_Type is array (Index_Type) of Element_Type;
   with function "<" (Left, Right : Element_Type)
      return Boolean is <>;
procedure Ada.Containers.Generic_Constrained_Array_Sort
      (Container : in out Array_Type);
pragma Pure(Ada.Containers.Generic_Constrained_Array_Sort);
8/2
Reorders the elements of Container such that the elements are sorted smallest first as determined by the generic formal "<" operator provided. Any exception raised during evaluation of "<" is propagated.
9/3
{AI05-0044-1} {AI05-0262-1} The actual function for the generic formal function "<" of Generic_Constrained_Array_Sort is expected to return the same value each time it is called with a particular pair of element values. It should define a strict weak ordering relationship (see A.18); it should not modify Container. If the actual for "<" behaves in some other manner, the behavior of the instance of Generic_Constrained_Array_Sort is unspecified. The number of times Generic_Constrained_Array_Sort calls "<" is unspecified.
9.1/3
  {AI05-0001-1} The generic library procedure Containers.Generic_Sort has the following declaration: 
9.2/4
{AI12-0056-1} generic
   type Index_Type is (<>);
   with function Before (Left, Right : Index_Type) return Boolean;
   with procedure Swap (Left, Right : in Index_Type);
procedure Ada.Containers.Generic_Sort
      (First, Last : Index_Type'Base);
pragma Pure(Ada.Containers.Generic_Sort);
9.3/3
{AI05-0001-1} {AI05-0248-1} Reorders the elements of an indexable structure, over the range First .. Last, such that the elements are sorted in the ordering determined by the generic formal function Before; Before should return True if Left is to be sorted before Right. The generic formal Before compares the elements having the given indices, and the generic formal Swap exchanges the values of the indicated elements. Any exception raised during evaluation of Before or Swap is propagated.
9.4/3
The actual function for the generic formal function Before of Generic_Sort is expected to return the same value each time it is called with index values that identify a particular pair of element values. It should define a strict weak ordering relationship (see A.18); it should not modify the elements. The actual function for the generic formal Swap should exchange the values of the indicated elements. If the actual for either Before or Swap behaves in some other manner, the behavior of Generic_Sort is unspecified. The number of times the Generic_Sort calls Before or Swap is unspecified.

Implementation Advice

10/2
 {AI95-00302-03} The worst-case time complexity of a call on an instance of Containers.Generic_Array_Sort or Containers.Generic_Constrained_Array_Sort should be O(N**2) or better, and the average time complexity should be better than O(N**2), where N is the length of the Container parameter. 
10.a/2
Implementation Advice: Containers.Generic_Array_Sort and Containers.Generic_Constrained_Array_Sort should have an average time complexity better than O(N**2) and worst case no worse than O(N**2).
10.b/2
Discussion: In other words, we're requiring the use of a sorting algorithm better than O(N**2), such as Quicksort. No bubble sorts allowed! 
11/2
 {AI95-00302-03} Containers.Generic_Array_Sort and Containers.Generic_Constrained_Array_Sort should minimize copying of elements. 
11.a/2
Implementation Advice: Containers.Generic_Array_Sort and Containers.Generic_Constrained_Array_Sort should minimize copying of elements.
11.b/2
To be honest: We do not mean “absolutely minimize” here; we're not intending to require a single copy for each element. Rather, we want to suggest that the sorting algorithm chosen is one that does not copy items unnecessarily. Bubble sort would not meet this advice, for instance. 
12/3
 {AI05-0248-1} The worst-case time complexity of a call on an instance of Containers.Generic_Sort should be O(N**2) or better, and the average time complexity should be better than O(N**2), where N is the difference between the Last and First parameters plus 1. 
12.a.1/3
Implementation Advice: Containers.Generic_Sort should have an average time complexity better than O(N**2) and worst case no worse than O(N**2).
13/3
 {AI05-0248-1} Containers.Generic_Sort should minimize calls to the generic formal Swap.
13.a.1/3
Implementation Advice: Containers.Generic_Sort should minimize calls to the generic formal Swap.

Extensions to Ada 95

13.a/2
{AI95-00302-03} The generic procedures Containers.Generic_Array_Sort and Containers.Generic_Constrained_Array_Sort are new. 

Extensions to Ada 2005

13.b/3
{AI05-0001-1} {AI05-0248-1} The generic procedure Containers.Generic_Sort is new. 

Wording Changes from Ada 2005

13.c/3
{AI05-0044-1} Correction: Redefined "<" actuals to require a strict weak ordering; the old definition allowed indeterminant comparisons that would not have worked in a sort. 

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