# NAG CL Interfacem01csc (quicksort)

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## 1Purpose

m01csc rearranges a vector of arbitrary type objects into ascending or descending order.

## 2Specification

 #include
void  m01csc (Pointer vec, size_t n, size_t size, ptrdiff_t stride,
 Integer (*compare)(const Nag_Pointer a, const Nag_Pointer b),
Nag_SortOrder order, NagError *fail)
The function may be called by the names: m01csc, nag_sort_quicksort or nag_quicksort.

## 3Description

m01csc sorts a set of $n$ data objects of arbitrary type, which are stored in the elements of an array at intervals of length stride. The function may be used to sort a column of a two-dimensional array. Either ascending or descending sort order may be specified.
m01csc is based on Singleton's implementation of the ‘median-of-three’ Quicksort algorithm, Singleton (1969), but with two additional modifications. First, small subfiles are sorted by an insertion sort on a separate final pass, Sedgewick (1978). Second, if a subfile is partitioned into two very unbalanced subfiles, the larger of them is flagged for special treatment: before it is partitioned, its end-points are swapped with two random points within it; this makes the worst case behaviour extremely unlikely.

## 4References

Maclaren N M (1985) Comput. J. 28 448
Sedgewick R (1978) Implementing Quicksort programs Comm. ACM 21 847–857
Singleton R C (1969) An efficient algorithm for sorting with minimal storage: Algorithm 347 Comm. ACM 12 185–187

## 5Arguments

1: $\mathbf{vec}\left[{\mathbf{n}}\right]$Pointer  Input/Output
On entry: the array of objects to be sorted.
On exit: the objects rearranged into sorted order.
2: $\mathbf{n}$size_t Input
On entry: the number, $n$, of objects to be sorted.
Constraint: $0\le {\mathbf{n}}\le \mathrm{MAX_LENGTH}$, where $\mathrm{MAX_LENGTH}$ is an implementation-dependent value for the maximum size of an array.
3: $\mathbf{size}$size_t Input
On entry: the size of each object to be sorted.
Constraint: $1\le {\mathbf{size}}\le p$, where $p$ is an implementation-dependent value for the maximum size_t size on the system, divided by n if n is positive.
4: $\mathbf{stride}$ptrdiff_t Input
On entry: the increment between data items in vec to be sorted.
Note: if stride is positive, vec should point at the first data object; otherwise vec should point at the last data object.
Constraint: ${\mathbf{size}}\le |{\mathbf{stride}}|\le p$, where $p$ is an implementation-dependent value for the maximum size_t size on the system, divided by n if n is positive.
5: $\mathbf{compare}$function, supplied by the user External Function
m01csc compares two data objects. If its arguments are pointers to a structure, this function must allow for the offset of the data field in the structure (if it is not the first).
The function must return:
 $-1$ if the first data field is less than the second, $\phantom{-}0$ if the first data field is equal to the second, $\phantom{-}1$ if the first data field is greater than the second.
The specification of compare is:
 Integer compare (const Nag_Pointer a, const Nag_Pointer b)
1: $\mathbf{a}$const Nag_Pointer  Input
On entry: the first data field.
2: $\mathbf{b}$const Nag_Pointer  Input
On entry: the second data field.
6: $\mathbf{order}$Nag_SortOrder Input
On entry: specifies whether the array is to be sorted into ascending or descending order.
Constraint: ${\mathbf{order}}=\mathrm{Nag_Ascending}$ or $\mathrm{Nag_Descending}$.
7: $\mathbf{fail}$NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

## 6Error Indicators and Warnings

NE_2_INT_ARG_LT
On entry, $|{\mathbf{stride}}|=⟨\mathit{\text{value}}⟩$ while ${\mathbf{size}}=⟨\mathit{\text{value}}⟩$. These arguments must satisfy $|{\mathbf{stride}}|\ge {\mathbf{size}}$.
NE_ALLOC_FAIL
Dynamic memory allocation failed.
On entry, argument order had an illegal value.
NE_INT_ARG_GT
On entry, $|{\mathbf{stride}}|=⟨\mathit{\text{value}}⟩$.
Constraint: $|{\mathbf{stride}}|\le ⟨\mathit{\text{value}}⟩$, an implementation-dependent size that is printed in the error message.
On entry, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{n}}\le ⟨\mathit{\text{value}}⟩$, an implementation-dependent size that is printed in the error message.
On entry, ${\mathbf{size}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{size}}\le ⟨\mathit{\text{value}}⟩$, an implementation-dependent size that is printed in the error message.
NE_INT_ARG_LT
On entry, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{n}}\ge 0$.
On entry, ${\mathbf{size}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{size}}\ge 1$.

Not applicable.

## 8Parallelism and Performance

m01csc is not threaded in any implementation.

The average time taken by the function is approximately proportional to $n\mathrm{log}\left(n\right)$. The worst case time is proportional to ${n}^{2}$ but this is extremely unlikely to occur.

## 10Example

The example program reads a two-dimensional array of numbers and sorts the second column into ascending order.

### 10.1Program Text

Program Text (m01csce.c)

### 10.2Program Data

Program Data (m01csce.d)

### 10.3Program Results

Program Results (m01csce.r)