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cppdraft/simd/reductions.md
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cppdraft/simd/reductions.md
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[simd.reductions]
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# 29 Numerics library [[numerics]](./#numerics)
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## 29.10 Data-parallel types [[simd]](simd#reductions)
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### 29.10.8 basic_vec non-member operations [[simd.nonmembers]](simd.nonmembers#simd.reductions)
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#### 29.10.8.5 basic_vec reductions [simd.reductions]
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[ð](#lib:reduce,simd)
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`template<class T, class Abi, class BinaryOperation = plus<>>
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constexpr T reduce(const basic_vec<T, Abi>& x, BinaryOperation binary_op = {});
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`
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[1](#1)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L18313)
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*Constraints*: BinaryOperation models[*reduction-binary-operation*](simd.expos.defn#concept:reduction-binary-operation "29.10.2.1 Exposition-only helpers [simd.expos.defn]")<T>[.](#1.sentence-1)
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[2](#2)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L18318)
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*Preconditions*: binary_op does not modify x[.](#2.sentence-1)
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[3](#3)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L18322)
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*Returns*: *GENERALIZED_SUM*(binary_op, vec<T, 1>(x[0]), …,
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vec<T, 1>(x[x.size() - 1]))[0] ([[numerics.defns]](numerics.defns "26.10.2 Definitions"))[.](#3.sentence-1)
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[4](#4)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L18327)
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*Throws*: Any exception thrown from binary_op[.](#4.sentence-1)
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[ð](#lib:reduce,simd_)
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`template<class T, class Abi, class BinaryOperation = plus<>>
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constexpr T reduce(
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const basic_vec<T, Abi>& x, const typename basic_vec<T, Abi>::mask_type& mask,
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BinaryOperation binary_op = {}, type_identity_t<T> identity_element = see below);
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`
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[5](#5)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L18341)
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*Constraints*:
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- [(5.1)](#5.1)
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BinaryOperation models [*reduction-binary-operation*](simd.expos.defn#concept:reduction-binary-operation "29.10.2.1 Exposition-only helpers [simd.expos.defn]")<T>[.](#5.1.sentence-1)
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- [(5.2)](#5.2)
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An argument for identity_element is provided for the invocation,
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unless BinaryOperation is one of plus<>, multiplies<>, bit_and<>, bit_or<>, or bit_xor<>[.](#5.2.sentence-1)
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[6](#6)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L18354)
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*Preconditions*:
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- [(6.1)](#6.1)
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binary_op does not modify x[.](#6.1.sentence-1)
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- [(6.2)](#6.2)
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For all finite values y representable by T, the results of y == binary_op(vec<T, 1>(identity_element), vec<T, 1>(y))[0] and y == binary_op(vec<T, 1>(y), vec<T, 1>(identity_element))[0] are true[.](#6.2.sentence-1)
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[7](#7)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L18366)
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*Returns*: If none_of(mask) is true, returns identity_element[.](#7.sentence-1)
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Otherwise, returns *GENERALIZED_SUM*(binary_op, vec<T,1>(x[k0]), …, vec<T, 1>(x[kn]))[0] where k0,â¦,kn are
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the selected indices of mask[.](#7.sentence-2)
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[8](#8)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L18373)
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*Throws*: Any exception thrown from binary_op[.](#8.sentence-1)
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[9](#9)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L18377)
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*Remarks*: The default argument for identity_element is equal to
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- [(9.1)](#9.1)
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T() if BinaryOperation is plus<>,
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- [(9.2)](#9.2)
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T(1) if BinaryOperation is multiplies<>,
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- [(9.3)](#9.3)
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T(~T()) if BinaryOperation is bit_and<>,
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- [(9.4)](#9.4)
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T() if BinaryOperation is bit_or<>, or
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- [(9.5)](#9.5)
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T() if BinaryOperation is bit_xor<>[.](#9.sentence-1)
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[ð](#lib:reduce_min,simd)
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`template<class T, class Abi> constexpr T reduce_min(const basic_vec<T, Abi>& x) noexcept;
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`
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[10](#10)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L18395)
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*Constraints*: T models [totally_ordered](concept.totallyordered#concept:totally_ordered "18.5.5 Concept totally_ordered [concept.totallyordered]")[.](#10.sentence-1)
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[11](#11)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L18399)
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*Returns*: The value of an element x[j] for which x[i] < x[j] isfalse for all i in the range of [0, basic_vec<T, Abi>::size())[.](#11.sentence-1)
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[ð](#lib:reduce_min,simd_)
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`template<class T, class Abi>
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constexpr T reduce_min(
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const basic_vec<T, Abi>&, const typename basic_vec<T, Abi>::mask_type&) noexcept;
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`
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[12](#12)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L18413)
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*Constraints*: T models [totally_ordered](concept.totallyordered#concept:totally_ordered "18.5.5 Concept totally_ordered [concept.totallyordered]")[.](#12.sentence-1)
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[13](#13)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L18417)
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*Returns*: If none_of(mask) is true, returnsnumeric_limits<T>::max()[.](#13.sentence-1)
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Otherwise, returns the value of a selected element x[j] for whichx[i] < x[j] is false for all selected indices i ofmask[.](#13.sentence-2)
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[ð](#lib:reduce_max,simd)
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`template<class T, class Abi> constexpr T reduce_max(const basic_vec<T, Abi>& x) noexcept;
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`
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[14](#14)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L18432)
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*Constraints*: T models [totally_ordered](concept.totallyordered#concept:totally_ordered "18.5.5 Concept totally_ordered [concept.totallyordered]")[.](#14.sentence-1)
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[15](#15)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L18436)
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*Returns*: The value of an element x[j] for which x[j] < x[i] isfalse for all i in the range of [0, basic_vec<T, Abi>::size())[.](#15.sentence-1)
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[ð](#lib:reduce_max,simd_)
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`template<class T, class Abi>
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constexpr T reduce_max(
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const basic_vec<T, Abi>&, const typename basic_vec<T, Abi>::mask_type&) noexcept;
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`
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[16](#16)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L18450)
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*Constraints*: T models [totally_ordered](concept.totallyordered#concept:totally_ordered "18.5.5 Concept totally_ordered [concept.totallyordered]")[.](#16.sentence-1)
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[17](#17)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L18454)
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*Returns*: If none_of(mask) is true, returnsnumeric_limits<V::value_type>::lowest()[.](#17.sentence-1)
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Otherwise, returns the value of a selected element x[j] for whichx[j] < x[i] is false for all selected indices i ofmask[.](#17.sentence-2)
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