# NAG CL Interfacem01ctc (stable_​sort)

## 1Purpose

m01ctc rearranges a vector of arbitrary type objects into ascending or descending order.

## 2Specification

 #include
void  m01ctc (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: m01ctc, nag_sort_stable_sort or nag_stable_sort.

## 3Description

m01ctc 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.
A stable sort is one which preserves the order of distinct data items that compare equal. This function uses m01dsc, m01zac and m01esc in order to carry out a stable sort with the same specification as m01csc. m01ctc will be faster than m01csc if the comparison function compare is slow or the data items are large. Internally a large amount of workspace may be required compared with m01csc.

## 4References

Knuth D E (1973) The Art of Computer Programming (Volume 3) (2nd Edition) Addison–Wesley

## 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: ${\mathbf{size}}\le \left|{\mathbf{stride}}\right|\le p$, 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
m01ctc 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, $\left|{\mathbf{stride}}\right|=〈\mathit{\text{value}}〉$ while ${\mathbf{size}}=〈\mathit{\text{value}}〉$. These arguments must satisfy $\left|{\mathbf{stride}}\right|\ge {\mathbf{size}}$.
NE_ALLOC_FAIL
Dynamic memory allocation failed.
On entry, argument order had an illegal value.
NE_INT_ARG_GT
On entry, ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
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.
On entry, ${\mathbf{stride}}=〈\mathit{\text{value}}〉$.
Constraint: $\left|{\mathbf{stride}}\right|\le 〈\mathit{\text{value}}〉$, 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

m01ctc is not threaded in any implementation.

The time taken by m01ctc is approximately proportional to $n\mathrm{log}\left(n\right)$.

## 10Example

The example program reads a three column matrix of real numbers and sorts the first column into ascending order.

### 10.1Program Text

Program Text (m01ctce.c)

### 10.2Program Data

Program Data (m01ctce.d)

### 10.3Program Results

Program Results (m01ctce.r)