Generalized Numeric operations

Collaboration diagram for Generalized Numeric operations:

Functions
template<typename _InputIterator , typename _Tp >
constexpr _Tp	std::accumulate (_InputIterator __first, _InputIterator __last, _Tp __init)
template<typename _InputIterator , typename _Tp , typename _BinaryOperation >
constexpr _Tp	std::accumulate (_InputIterator __first, _InputIterator __last, _Tp __init, _BinaryOperation __binary_op)
template<typename _InputIterator , typename _OutputIterator >
constexpr _OutputIterator	std::adjacent_difference (_InputIterator __first, _InputIterator __last, _OutputIterator __result)
template<typename _InputIterator , typename _OutputIterator , typename _BinaryOperation >
constexpr _OutputIterator	std::adjacent_difference (_InputIterator __first, _InputIterator __last, _OutputIterator __result, _BinaryOperation __binary_op)
template<typename _InputIterator , typename _OutputIterator , typename _Tp >
constexpr _OutputIterator	std::exclusive_scan (_InputIterator __first, _InputIterator __last, _OutputIterator __result, _Tp __init)
template<typename _InputIterator , typename _OutputIterator , typename _Tp , typename _BinaryOperation >
constexpr _OutputIterator	std::exclusive_scan (_InputIterator __first, _InputIterator __last, _OutputIterator __result, _Tp __init, _BinaryOperation __binary_op)
template<typename _InputIterator , typename _OutputIterator >
constexpr _OutputIterator	std::inclusive_scan (_InputIterator __first, _InputIterator __last, _OutputIterator __result)
template<typename _InputIterator , typename _OutputIterator , typename _BinaryOperation >
constexpr _OutputIterator	std::inclusive_scan (_InputIterator __first, _InputIterator __last, _OutputIterator __result, _BinaryOperation __binary_op)
template<typename _InputIterator , typename _OutputIterator , typename _BinaryOperation , typename _Tp >
constexpr _OutputIterator	std::inclusive_scan (_InputIterator __first, _InputIterator __last, _OutputIterator __result, _BinaryOperation __binary_op, _Tp __init)
template<typename _InputIterator1 , typename _InputIterator2 , typename _Tp >
constexpr _Tp	std::inner_product (_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2, _Tp __init)
template<typename _InputIterator1 , typename _InputIterator2 , typename _Tp , typename _BinaryOperation1 , typename _BinaryOperation2 >
constexpr _Tp	std::inner_product (_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2, _Tp __init, _BinaryOperation1 __binary_op1, _BinaryOperation2 __binary_op2)
template<typename _ForwardIterator , typename _Tp >
constexpr void	std::iota (_ForwardIterator __first, _ForwardIterator __last, _Tp __value)
template<typename _InputIterator , typename _OutputIterator >
constexpr _OutputIterator	std::partial_sum (_InputIterator __first, _InputIterator __last, _OutputIterator __result)
template<typename _InputIterator , typename _OutputIterator , typename _BinaryOperation >
constexpr _OutputIterator	std::partial_sum (_InputIterator __first, _InputIterator __last, _OutputIterator __result, _BinaryOperation __binary_op)
template<typename _InputIterator >
constexpr iterator_traits< _InputIterator >::value_type	std::reduce (_InputIterator __first, _InputIterator __last)
template<typename _InputIterator , typename _Tp >
constexpr _Tp	std::reduce (_InputIterator __first, _InputIterator __last, _Tp __init)
template<typename _InputIterator , typename _Tp , typename _BinaryOperation >
constexpr _Tp	std::reduce (_InputIterator __first, _InputIterator __last, _Tp __init, _BinaryOperation __binary_op)
template<typename _InputIterator , typename _OutputIterator , typename _Tp , typename _BinaryOperation , typename _UnaryOperation >
constexpr _OutputIterator	std::transform_exclusive_scan (_InputIterator __first, _InputIterator __last, _OutputIterator __result, _Tp __init, _BinaryOperation __binary_op, _UnaryOperation __unary_op)
template<typename _InputIterator , typename _OutputIterator , typename _BinaryOperation , typename _UnaryOperation >
constexpr _OutputIterator	std::transform_inclusive_scan (_InputIterator __first, _InputIterator __last, _OutputIterator __result, _BinaryOperation __binary_op, _UnaryOperation __unary_op)
template<typename _InputIterator , typename _OutputIterator , typename _BinaryOperation , typename _UnaryOperation , typename _Tp >
constexpr _OutputIterator	std::transform_inclusive_scan (_InputIterator __first, _InputIterator __last, _OutputIterator __result, _BinaryOperation __binary_op, _UnaryOperation __unary_op, _Tp __init)
template<typename _InputIterator , typename _Tp , typename _BinaryOperation , typename _UnaryOperation >
constexpr _Tp	std::transform_reduce (_InputIterator __first, _InputIterator __last, _Tp __init, _BinaryOperation __binary_op, _UnaryOperation __unary_op)
template<typename _InputIterator1 , typename _InputIterator2 , typename _Tp >
constexpr _Tp	std::transform_reduce (_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2, _Tp __init)
template<typename _InputIterator1 , typename _InputIterator2 , typename _Tp , typename _BinaryOperation1 , typename _BinaryOperation2 >
constexpr _Tp	std::transform_reduce (_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2, _Tp __init, _BinaryOperation1 __binary_op1, _BinaryOperation2 __binary_op2)

Detailed Description

Function Documentation

accumulate() [1/2]

template<typename _InputIterator , typename _Tp >

constexpr _Tp std::accumulate ( _InputIterator  __first, _InputIterator  __last, _Tp  __init  )

inlineconstexpr

Accumulate values in a range.

Accumulates the values in the range [first,last) using operator+(). The initial value is init. The values are processed in order.

Parameters

__first	Start of range.
__last	End of range.
__init	Starting value to add other values to.

Returns

The final sum.

Definition at line 134 of file stl_numeric.h.

accumulate() [2/2]

template<typename _InputIterator , typename _Tp , typename _BinaryOperation >

constexpr _Tp std::accumulate ( _InputIterator  __first, _InputIterator  __last, _Tp  __init, _BinaryOperation  __binary_op  )

inlineconstexpr

Accumulate values in a range with operation.

Accumulates the values in the range [first,last) using the function object __binary_op. The initial value is __init. The values are processed in order.

Parameters

__first	Start of range.
__last	End of range.
__init	Starting value to add other values to.
__binary_op	Function object to accumulate with.

Returns

The final sum.

Definition at line 161 of file stl_numeric.h.

adjacent_difference() [1/2]

template<typename _InputIterator , typename _OutputIterator >

constexpr _OutputIterator std::adjacent_difference ( _InputIterator  __first, _InputIterator  __last, _OutputIterator  __result  )

constexpr

Return differences between adjacent values.

Computes the difference between adjacent values in the range [first,last) using operator-() and writes the result to __result.

Parameters

__first	Start of input range.
__last	End of input range.
__result	Output sums.

Returns

Iterator pointing just beyond the values written to result.

_GLIBCXX_RESOLVE_LIB_DEFECTS DR 539. partial_sum and adjacent_difference should mention requirements

Definition at line 338 of file stl_numeric.h.

adjacent_difference() [2/2]

template<typename _InputIterator , typename _OutputIterator , typename _BinaryOperation >

constexpr _OutputIterator std::adjacent_difference ( _InputIterator  __first, _InputIterator  __last, _OutputIterator  __result, _BinaryOperation  __binary_op  )

constexpr

Return differences between adjacent values.

Computes the difference between adjacent values in the range [__first,__last) using the function object __binary_op and writes the result to __result.

Parameters

__first	Start of input range.
__last	End of input range.
__result	Output sum.
__binary_op	Function object.

Returns

Iterator pointing just beyond the values written to result.

_GLIBCXX_RESOLVE_LIB_DEFECTS DR 539. partial_sum and adjacent_difference should mention requirements

Definition at line 382 of file stl_numeric.h.

exclusive_scan() [1/2]

template<typename _InputIterator , typename _OutputIterator , typename _Tp >

constexpr _OutputIterator std::exclusive_scan ( _InputIterator  __first, _InputIterator  __last, _OutputIterator  __result, _Tp  __init  )

inlineconstexpr

Output the cumulative sum of one range to a second range.

Parameters

__first	Start of input range.
__last	End of input range.
__result	Start of output range.
__init	Initial value.

Returns

The end of the output range.

Write the cumulative sum (aka prefix sum, aka scan) of the input range to the output range. Each element of the output range contains the running total of all earlier elements (and the initial value), using std::plus<> for summation.

This function generates an "exclusive" scan, meaning the Nth element of the output range is the sum of the first N-1 input elements, so the Nth input element is not included.

Definition at line 516 of file numeric.

exclusive_scan() [2/2]

template<typename _InputIterator , typename _OutputIterator , typename _Tp , typename _BinaryOperation >

constexpr _OutputIterator std::exclusive_scan ( _InputIterator  __first, _InputIterator  __last, _OutputIterator  __result, _Tp  __init, _BinaryOperation  __binary_op  )

constexpr

Output the cumulative sum of one range to a second range.

Parameters

__first	Start of input range.
__last	End of input range.
__result	Start of output range.
__init	Initial value.
__binary_op	Function to perform summation.

Returns

The end of the output range.

Write the cumulative sum (aka prefix sum, aka scan) of the input range to the output range. Each element of the output range contains the running total of all earlier elements (and the initial value), using binary_op for summation.

This function generates an "exclusive" scan, meaning the Nth element of the output range is the sum of the first N-1 input elements, so the Nth input element is not included.

Definition at line 482 of file numeric.

inclusive_scan() [1/3]

template<typename _InputIterator , typename _OutputIterator >

constexpr _OutputIterator std::inclusive_scan ( _InputIterator  __first, _InputIterator  __last, _OutputIterator  __result  )

inlineconstexpr

Output the cumulative sum of one range to a second range.

Parameters

__first	Start of input range.
__last	End of input range.
__result	Start of output range.

Returns

The end of the output range.

Write the cumulative sum (aka prefix sum, aka scan) of the input range to the output range. Each element of the output range contains the running total of all earlier elements, using std::plus<> for summation.

This function generates an "inclusive" scan, meaning the Nth element of the output range is the sum of the first N input elements, so the Nth input element is included.

Definition at line 607 of file numeric.

inclusive_scan() [2/3]

template<typename _InputIterator , typename _OutputIterator , typename _BinaryOperation >

constexpr _OutputIterator std::inclusive_scan ( _InputIterator  __first, _InputIterator  __last, _OutputIterator  __result, _BinaryOperation  __binary_op  )

constexpr

Output the cumulative sum of one range to a second range.

Parameters

__first	Start of input range.
__last	End of input range.
__result	Start of output range.
__binary_op	Function to perform summation.

Returns

The end of the output range.

Write the cumulative sum (aka prefix sum, aka scan) of the input range to the output range. Each element of the output range contains the running total of all earlier elements, using binary_op for summation.

This function generates an "inclusive" scan, meaning the Nth element of the output range is the sum of the first N input elements, so the Nth input element is included.

Definition at line 574 of file numeric.

inclusive_scan() [3/3]

template<typename _InputIterator , typename _OutputIterator , typename _BinaryOperation , typename _Tp >

constexpr _OutputIterator std::inclusive_scan ( _InputIterator  __first, _InputIterator  __last, _OutputIterator  __result, _BinaryOperation  __binary_op, _Tp  __init  )

constexpr

Output the cumulative sum of one range to a second range.

Parameters

__first	Start of input range.
__last	End of input range.
__result	Start of output range.
__binary_op	Function to perform summation.
__init	Initial value.

Returns

The end of the output range.

Write the cumulative sum (aka prefix sum, aka scan) of the input range to the output range. Each element of the output range contains the running total of all earlier elements (and the initial value), using binary_op for summation.

This function generates an "inclusive" scan, meaning the Nth element of the output range is the sum of the first N input elements, so the Nth input element is included.

Definition at line 545 of file numeric.

inner_product() [1/2]

template<typename _InputIterator1 , typename _InputIterator2 , typename _Tp >

constexpr _Tp std::inner_product ( _InputIterator1  __first1, _InputIterator1  __last1, _InputIterator2  __first2, _Tp  __init  )

inlineconstexpr

Compute inner product of two ranges.

Starting with an initial value of __init, multiplies successive elements from the two ranges and adds each product into the accumulated value using operator+(). The values in the ranges are processed in order.

Parameters

__first1	Start of range 1.
__last1	End of range 1.
__first2	Start of range 2.
__init	Starting value to add other values to.

Returns

The final inner product.

Definition at line 190 of file stl_numeric.h.

inner_product() [2/2]

template<typename _InputIterator1 , typename _InputIterator2 , typename _Tp , typename _BinaryOperation1 , typename _BinaryOperation2 >

constexpr _Tp std::inner_product ( _InputIterator1  __first1, _InputIterator1  __last1, _InputIterator2  __first2, _Tp  __init, _BinaryOperation1  __binary_op1, _BinaryOperation2  __binary_op2  )

inlineconstexpr

Compute inner product of two ranges.

Starting with an initial value of __init, applies __binary_op2 to successive elements from the two ranges and accumulates each result into the accumulated value using __binary_op1. The values in the ranges are processed in order.

Parameters

__first1	Start of range 1.
__last1	End of range 1.
__first2	Start of range 2.
__init	Starting value to add other values to.
__binary_op1	Function object to accumulate with.
__binary_op2	Function object to apply to pairs of input values.

Returns

The final inner product.

Definition at line 223 of file stl_numeric.h.

iota()

template<typename _ForwardIterator , typename _Tp >

constexpr void std::iota ( _ForwardIterator  __first, _ForwardIterator  __last, _Tp  __value  )

constexpr

Create a range of sequentially increasing values.

For each element in the range [first,last) assigns value and increments value as if by ++value.

Parameters

__first	Start of range.
__last	End of range.
__value	Starting value.

Returns

Nothing.

Definition at line 88 of file stl_numeric.h.

partial_sum() [1/2]

template<typename _InputIterator , typename _OutputIterator >

constexpr _OutputIterator std::partial_sum ( _InputIterator  __first, _InputIterator  __last, _OutputIterator  __result  )

constexpr

Return list of partial sums.

Accumulates the values in the range [first,last) using the + operator. As each successive input value is added into the total, that partial sum is written to __result. Therefore, the first value in __result is the first value of the input, the second value in __result is the sum of the first and second input values, and so on.

Parameters

__first	Start of input range.
__last	End of input range.
__result	Output sum.

Returns

Iterator pointing just beyond the values written to __result.

Definition at line 256 of file stl_numeric.h.

Referenced by __gnu_parallel::__parallel_random_shuffle_drs_pu(), and __gnu_parallel::__sequential_random_shuffle().

partial_sum() [2/2]

template<typename _InputIterator , typename _OutputIterator , typename _BinaryOperation >

constexpr _OutputIterator std::partial_sum ( _InputIterator  __first, _InputIterator  __last, _OutputIterator  __result, _BinaryOperation  __binary_op  )

constexpr

Return list of partial sums.

Accumulates the values in the range [first,last) using __binary_op. As each successive input value is added into the total, that partial sum is written to __result. Therefore, the first value in __result is the first value of the input, the second value in __result is the sum of the first and second input values, and so on.

Parameters

__first	Start of input range.
__last	End of input range.
__result	Output sum.
__binary_op	Function object.

Returns

Iterator pointing just beyond the values written to __result.

Definition at line 298 of file stl_numeric.h.

reduce() [1/3]

template<typename _InputIterator >

constexpr iterator_traits< _InputIterator >::value_type std::reduce ( _InputIterator  __first, _InputIterator  __last  )

inlineconstexpr

Calculate reduction of values in a range.

Parameters

__first	Start of range.
__last	End of range.

Returns

The final sum.

Reduce the values in the range [first,last) using addition, with an initial value of T{}, where T is the iterator's value type. Equivalent to calling std::reduce(first, last, T{}, std::plus<>()).

Definition at line 342 of file numeric.

reduce() [2/3]

template<typename _InputIterator , typename _Tp >

constexpr _Tp std::reduce ( _InputIterator  __first, _InputIterator  __last, _Tp  __init  )

inlineconstexpr

Calculate reduction of values in a range.

Parameters

__first	Start of range.
__last	End of range.
__init	Starting value to add other values to.

Returns

The final sum.

Reduce the values in the range [first,last) using addition. Equivalent to calling std::reduce(first, last, init, std::plus<>()).

Definition at line 325 of file numeric.

reduce() [3/3]

template<typename _InputIterator , typename _Tp , typename _BinaryOperation >

constexpr _Tp std::reduce ( _InputIterator  __first, _InputIterator  __last, _Tp  __init, _BinaryOperation  __binary_op  )

constexpr

Calculate reduction of values in a range.

Parameters

__first	Start of range.
__last	End of range.
__init	Starting value to add other values to.
__binary_op	A binary function object.

Returns

The final sum.

Reduce the values in the range [first,last) using a binary operation. The initial value is init. The values are not necessarily processed in order.

This algorithm is similar to std::accumulate but is not required to perform the operations in order from first to last. For operations that are commutative and associative the result will be the same as for std::accumulate, but for other operations (such as floating point arithmetic) the result can be different.

Definition at line 287 of file numeric.

transform_exclusive_scan()

template<typename _InputIterator , typename _OutputIterator , typename _Tp , typename _BinaryOperation , typename _UnaryOperation >

constexpr _OutputIterator std::transform_exclusive_scan ( _InputIterator  __first, _InputIterator  __last, _OutputIterator  __result, _Tp  __init, _BinaryOperation  __binary_op, _UnaryOperation  __unary_op  )

constexpr

Output the cumulative sum of one range to a second range.

Parameters

__first	Start of input range.
__last	End of input range.
__result	Start of output range.
__init	Initial value.
__binary_op	Function to perform summation.
__unary_op	Function to transform elements of the input range.

Returns

The end of the output range.

Write the cumulative sum (aka prefix sum, aka scan) of the input range to the output range. Each element of the output range contains the running total of all earlier elements (and the initial value), using __unary_op to transform the input elements and using __binary_op for summation.

This function generates an "exclusive" scan, meaning the Nth element of the output range is the sum of the first N-1 input elements, so the Nth input element is not included.

Definition at line 635 of file numeric.

transform_inclusive_scan() [1/2]

template<typename _InputIterator , typename _OutputIterator , typename _BinaryOperation , typename _UnaryOperation >

constexpr _OutputIterator std::transform_inclusive_scan ( _InputIterator  __first, _InputIterator  __last, _OutputIterator  __result, _BinaryOperation  __binary_op, _UnaryOperation  __unary_op  )

constexpr

Output the cumulative sum of one range to a second range.

Parameters

__first	Start of input range.
__last	End of input range.
__result	Start of output range.
__binary_op	Function to perform summation.
__unary_op	Function to transform elements of the input range.

Returns

The end of the output range.

Write the cumulative sum (aka prefix sum, aka scan) of the input range to the output range. Each element of the output range contains the running total of all earlier elements, using __unary_op to transform the input elements and using __binary_op for summation.

This function generates an "inclusive" scan, meaning the Nth element of the output range is the sum of the first N input elements, so the Nth input element is included.

Definition at line 708 of file numeric.

transform_inclusive_scan() [2/2]

template<typename _InputIterator , typename _OutputIterator , typename _BinaryOperation , typename _UnaryOperation , typename _Tp >

constexpr _OutputIterator std::transform_inclusive_scan ( _InputIterator  __first, _InputIterator  __last, _OutputIterator  __result, _BinaryOperation  __binary_op, _UnaryOperation  __unary_op, _Tp  __init  )

constexpr

Output the cumulative sum of one range to a second range.

Parameters

__first	Start of input range.
__last	End of input range.
__result	Start of output range.
__binary_op	Function to perform summation.
__unary_op	Function to transform elements of the input range.
__init	Initial value.

Returns

The end of the output range.

Write the cumulative sum (aka prefix sum, aka scan) of the input range to the output range. Each element of the output range contains the running total of all earlier elements (and the initial value), using __unary_op to transform the input elements and using __binary_op for summation.

This function generates an "inclusive" scan, meaning the Nth element of the output range is the sum of the first N input elements, so the Nth input element is included.

Definition at line 674 of file numeric.

transform_reduce() [1/3]

template<typename _InputIterator , typename _Tp , typename _BinaryOperation , typename _UnaryOperation >

constexpr _Tp std::transform_reduce ( _InputIterator  __first, _InputIterator  __last, _Tp  __init, _BinaryOperation  __binary_op, _UnaryOperation  __unary_op  )

constexpr

Transform the elements of a range and reduce.

Parameters

__first	Start of range.
__last	End of range.
__init	Starting value to add other values to.
__binary_op	The function used to perform reduction.
__unary_op	The function used to transform values from the range.

Returns

The final sum.

Call unary_op(first[n]) for each n in [0,last-first) and then use binary_op to reduce the values returned by unary_op to a single value of type T.

Definition at line 439 of file numeric.

transform_reduce() [2/3]

template<typename _InputIterator1 , typename _InputIterator2 , typename _Tp >

constexpr _Tp std::transform_reduce ( _InputIterator1  __first1, _InputIterator1  __last1, _InputIterator2  __first2, _Tp  __init  )

inlineconstexpr

Combine elements from two ranges and reduce.

Parameters

__first1	Start of first range.
__last1	End of first range.
__first2	Start of second range.
__init	Starting value to add other values to.

Returns

The final sum.

Call first1[n]*first2[n] for each n in [0,last1-first1) and then use addition to sum those products to a single value of type T.

The range beginning at first2 must contain at least last1-first1 elements.

Definition at line 413 of file numeric.

transform_reduce() [3/3]

template<typename _InputIterator1 , typename _InputIterator2 , typename _Tp , typename _BinaryOperation1 , typename _BinaryOperation2 >

constexpr _Tp std::transform_reduce ( _InputIterator1  __first1, _InputIterator1  __last1, _InputIterator2  __first2, _Tp  __init, _BinaryOperation1  __binary_op1, _BinaryOperation2  __binary_op2  )

constexpr

Combine elements from two ranges and reduce.

Parameters

__first1	Start of first range.
__last1	End of first range.
__first2	Start of second range.
__init	Starting value to add other values to.
__binary_op1	The function used to perform reduction.
__binary_op2	The function used to combine values from the ranges.

Returns

The final sum.

Call binary_op2(first1[n],first2[n]) for each n in [0,last1-first1) and then use binary_op1 to reduce the values returned by binary_op2 to a single value of type T.

The range beginning at first2 must contain at least last1-first1 elements.

Definition at line 370 of file numeric.