Mathematical algorithms and functions that execute on a range of elements. More...

Functions
template<class FwdIter , class Val , class Comp >
FwdIter	LowerBound (FwdIter begin, FwdIter end, const Val &val, Comp comp)
	Finds the furthermost iterator `lb` in the range `[begin, end]` such that for any iterator `it` in the range `[begin, lb)` it holds that `comp(*it, val) == true`.
template<class FwdIter , class Val >
FwdIter	LowerBound (FwdIter begin, FwdIter end, const Val &val)
	Finds the furthermost iterator `lb` in the range `[begin, end]` such that for any iterator `it` in the range `[begin, lb)` it holds that `*it < val`.
template<class FwdIter >
Type::IteratorTraits< FwdIter > ::ValType	Product (FwdIter begin, FwdIter end)
	Compute the product of elements in the range `[begin, end)`.
template<class FwdIter >
Type::IteratorTraits< FwdIter > ::ValType	Sum (FwdIter begin, FwdIter end)
	Compute the sum of elements in the range `[begin, end)`.
template<class FwdIter , class Val , class Comp >
FwdIter	UpperBound (FwdIter begin, FwdIter end, const Val &val, Comp comp)
	Finds the furthermost iterator `ub` in the range `[begin, end]` such that for any iterator `it` in the range `[begin, ub)` it holds that `comp(val, *it) == false`.
template<class FwdIter , class Val >
FwdIter	UpperBound (FwdIter begin, FwdIter end, const Val &val)
	Finds the furthermost iterator `ub` in the range `[begin, end]` such that for any iterator `it` in the range `[begin, ub)` it holds that `!(val < *it)`.

Detailed Description

Mathematical algorithms and functions that execute on a range of elements.

See also:: Saf::Algo::Range.

Function Documentation

template<class FwdIter , class Val , class Comp >

FwdIter Saf::Math::Range::LowerBound	(	FwdIter	begin,
		FwdIter	end,
		const Val &	val,
		Comp	comp
	)		`[inline]`

Finds the furthermost iterator lb in the range [begin, end] such that for any iterator it in the range [begin, lb) it holds that comp(*it, val) == true.

The input range is assumed to be sorted according to the comp predicate.

Properties:

Minimum iterator category: Forward.
Worst-case time complexity: $\mathcal{O}(\mathrm{Range::Distance(begin, end)})$ .
Number of comparisons: $\mathcal{O}(\log \mathrm{Range::Distance(begin, end)})$ .

Parameters:

[in]	begin	Iterator to the beginning of the sequence.
[in]	end	Iterator to the end of the sequence.
[in]	val	The value.
[in]	comp	Comparison predicate (accepting `Val` as the first parameter).

template<class FwdIter , class Val >

FwdIter Saf::Math::Range::LowerBound	(	FwdIter	begin,
		FwdIter	end,
		const Val &	val
	)		`[inline]`

Finds the furthermost iterator lb in the range [begin, end] such that for any iterator it in the range [begin, lb) it holds that *it < val.

The input range is assumed to be sorted according to the Algo::Predicate::Less predicate.

Properties:

Minimum iterator category: Forward.
Worst-case time complexity: $\mathcal{O}(\mathrm{Range::Distance(begin, end)})$ .
Number of comparisons: $\mathcal{O}(\log \mathrm{Range::Distance(begin, end)})$ .

Parameters:

[in]	begin	Iterator to the beginning of the sequence.
[in]	end	Iterator to the end of the sequence.
[in]	val	The value.

See also:: Algo::Predicate::Less.

Remarks:: Same as LowerBound(begin, end, Algo::Predicate::Less<Val>()).

template<class FwdIter >

Type::IteratorTraits<FwdIter>::ValType Saf::Math::Range::Product	(	FwdIter	begin,
		FwdIter	end
	)		`[inline]`

Compute the product of elements in the range [begin, end).

Properties:

Minimum iterator category: Forward.
Time complexity: $\mathcal{O}(\mathrm{Range::Distance(begin, end)})$ .

template<class FwdIter >

Type::IteratorTraits<FwdIter>::ValType Saf::Math::Range::Sum	(	FwdIter	begin,
		FwdIter	end
	)		`[inline]`

Compute the sum of elements in the range [begin, end).

Properties:

Minimum iterator category: Forward.
Time complexity: $\mathcal{O}(\mathrm{Range::Distance(begin, end)})$ .

template<class FwdIter , class Val , class Comp >

FwdIter Saf::Math::Range::UpperBound	(	FwdIter	begin,
		FwdIter	end,
		const Val &	val,
		Comp	comp
	)		`[inline]`

Finds the furthermost iterator ub in the range [begin, end] such that for any iterator it in the range [begin, ub) it holds that comp(val, *it) == false.

The input range is assumed to be sorted according to the comp predicate.

Properties:

Minimum iterator category: Forward.
Worst-case time complexity: $\mathcal{O}(\mathrm{Range::Distance(begin, end)})$ .
Number of comparisons: $\mathcal{O}(\log \mathrm{Range::Distance(begin, end)})$ .

Parameters:

[in]	begin	Iterator to the beginning of the sequence.
[in]	end	Iterator to the end of the sequence.
[in]	val	The value.
[in]	comp	Comparison predicate (accepting `Val` as the first parameter).

template<class FwdIter , class Val >

FwdIter Saf::Math::Range::UpperBound	(	FwdIter	begin,
		FwdIter	end,
		const Val &	val
	)		`[inline]`

Finds the furthermost iterator ub in the range [begin, end] such that for any iterator it in the range [begin, ub) it holds that !(val < *it).

The input range is assumed to be sorted according to the Algo::Predicate::Less predicate.

Properties:

Minimum iterator category: Forward.
Worst-case time complexity: $\mathcal{O}(\mathrm{Range::Distance(begin, end)})$ .
Number of comparisons: $\mathcal{O}(\log \mathrm{Range::Distance(begin, end)})$ .

Parameters:

[in]	begin	Iterator to the beginning of the sequence.
[in]	end	Iterator to the end of the sequence.
[in]	val	The value.

See also:: Algo::Predicate::Less.

Remarks:: Same as UpperBound(begin, end, Algo::Predicate::Less<Val>()).

Functions

Detailed Description

Function Documentation