NAG CL Interfacem01cac (realvec_​sort)

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1Purpose

m01cac rearranges a vector of real numbers into ascending or descending order.

2Specification

 #include
 void m01cac (double vec[], size_t n, Nag_SortOrder order, NagError *fail)
The function may be called by the names: m01cac, nag_sort_realvec_sort or nag_double_sort.

3Description

m01cac is based on Singleton's implementation of the ‘median-of-three’ Quicksort algorithm, see Singleton (1969), but with two additional modifications. First, small subfiles are sorted by an insertion sort on a separate final pass, see 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: $\mathbf{vec}\left[{\mathbf{n}}\right]$double Input/Output
On entry: elements of vec must contain real values to be sorted.
On exit: these values are rearranged into sorted order.
2: $\mathbf{n}$size_t Input
On entry: the length of vec.
Constraint: $1\le {\mathbf{n}}\le \mathrm{MAX_LENGTH}$, where $\mathrm{MAX_LENGTH}$ is an implementation-dependent value for the maximum size of an array.
3: $\mathbf{order}$Nag_SortOrder Input
On entry: specifies whether the array will be sorted into ascending or descending order.
Constraint: ${\mathbf{order}}=\mathrm{Nag_Ascending}$ or $\mathrm{Nag_Descending}$.
4: $\mathbf{fail}$NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6Error Indicators and Warnings

NE_BAD_PARAM
On entry, 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.
NE_INT_ARG_LT
On entry, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{n}}\ge 1$.

Not applicable.

8Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
m01cac is not threaded in any implementation.

9Further Comments

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 list of real numbers and sorts them into ascending order.

10.1Program Text

Program Text (m01cace.c)

10.2Program Data

Program Data (m01cace.d)

10.3Program Results

Program Results (m01cace.r)