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--- a/cppdraft/simd/expos/abi.md
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+[simd.expos.abi]
+
+# 29 Numerics library [[numerics]](./#numerics)
+
+## 29.10 Data-parallel types [[simd]](simd#expos.abi)
+
+### 29.10.2 Exposition-only types, variables, and concepts [[simd.expos]](simd.expos#abi)
+
+#### 29.10.2.2 simd ABI tags [simd.expos.abi]
+
+[ð](#itemdecl:1)
+
+`template<class T> using native-abi = see below;
+template<class T, simd-size-type N> using deduce-abi-t = see below;
+`
+
+[1](#1)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L16425)
+
+An [*ABI tag*](#def:ABI_tag "29.10.2.2 simd ABI tags [simd.expos.abi]") is a type that indicates a choice of size and binary
+representation for objects of data-parallel type[.](#1.sentence-1)
+
+[*Note [1](#note-1)*:
+
+The intent is for the size and binary representation to depend on the target
+architecture and compiler flags[.](#1.sentence-2)
+
+The ABI tag, together with a given element type, implies the width[.](#1.sentence-3)
+
+â *end note*]
+
+[2](#2)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L16434)
+
+[*Note [2](#note-2)*:
+
+The ABI tag is orthogonal to selecting the machine instruction set[.](#2.sentence-1)
+
+The selected machine instruction set limits the usable ABI tag types, though
+(see [[simd.overview]](simd.overview "29.10.7.1 Class template basic_vec overview"))[.](#2.sentence-2)
+
+The ABI tags enable users to safely pass objects of data-parallel type between
+translation unit boundaries (e.g., function calls or I/O)[.](#2.sentence-3)
+
+â *end note*]
+
+[3](#3)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L16443)
+
+An implementation defines ABI tag types as necessary for the following aliases[.](#3.sentence-1)
+
+[4](#4)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L16446)
+
+*deduce-abi-t*<T, N> is defined if
+
+- [(4.1)](#4.1)
+
+T is a vectorizable type,
+
+- [(4.2)](#4.2)
+
+N is greater than zero, and
+
+- [(4.3)](#4.3)
+
+N is not larger than an implementation-defined maximum[.](#4.sentence-1)
+
+The implementation-defined maximum forN is not smaller than 64 and can differ depending on T[.](#4.sentence-2)
+
+[5](#5)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L16456)
+
+Where present, *deduce-abi-t*<T, N> names an ABI tag type such
+that
+
+- [(5.1)](#5.1)
+
+*simd-size-v*<T, *deduce-abi-t*<T, N>> equals N,
+
+- [(5.2)](#5.2)
+
+basic_vec<T, *deduce-abi-t*<T, N>> is
+ enabled ([[simd.overview]](simd.overview "29.10.7.1 Class template basic_vec overview")), and
+
+- [(5.3)](#5.3)
+
+basic_mask<sizeof(T), *deduce-abi-t*<*integer-from*<sizeof(T)>, N>> is enabled[.](#5.sentence-1)
+
+[6](#6)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L16469)
+
+*native-abi*<T> is an implementation-defined alias for an ABI tag[.](#6.sentence-1)
+
+basic_vec<T, *native-abi*<T>> is an enabled specialization[.](#6.sentence-2)
+
+[*Note [3](#note-3)*:
+
+The intent is to use the ABI tag producing the most efficient data-parallel
+execution for the element type T on the currently targeted system[.](#6.sentence-3)
+
+For target architectures with ISA extensions, compiler flags can change the type
+of the *native-abi*<T> alias[.](#6.sentence-4)
+
+â *end note*]
+
+[*Example [1](#example-1)*:
+
+Consider a target architecture supporting the ABI tags __simd128 and__simd256, where hardware support for __simd256 exists only for
+floating-point types[.](#6.sentence-5)
+
+The implementation therefore defines *native-abi*<T> as an alias
+for
+
+- [(6.1)](#6.1)
+
+__simd256 if T is a floating-point type, and
+
+- [(6.2)](#6.2)
+
+__simd128 otherwise[.](#6.sentence-6)
+
+â *end example*]
--- a/cppdraft/simd/expos/defn.md
+++ b/cppdraft/simd/expos/defn.md
@@ -0,0 +1,182 @@
+[simd.expos.defn]
+
+# 29 Numerics library [[numerics]](./#numerics)
+
+## 29.10 Data-parallel types [[simd]](simd#expos.defn)
+
+### 29.10.2 Exposition-only types, variables, and concepts [[simd.expos]](simd.expos#defn)
+
+#### 29.10.2.1 Exposition-only helpers [simd.expos.defn]
+
+[ð](#itemdecl:1)
+
+`using simd-size-type = see below;
+`
+
+[1](#1)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L16280)
+
+*simd-size-type* is an alias for a signed integer type[.](#1.sentence-1)
+
+[ð](#itemdecl:2)
+
+`template<size_t Bytes> using integer-from = see below;
+`
+
+[2](#2)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L16289)
+
+*integer-from*<Bytes> is an alias for a signed integer typeT such that sizeof(T) equals Bytes[.](#2.sentence-1)
+
+[ð](#itemdecl:3)
+
+`template<class T, class Abi>
+  constexpr simd-size-type simd-size-v = see below;
+`
+
+[3](#3)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L16300)
+
+*simd-size-v*<T, Abi> denotes the width of basic_vec<T,
+Abi> if the specialization basic_vec<T, Abi> is enabled, or 0 otherwise[.](#3.sentence-1)
+
+[ð](#itemdecl:4)
+
+`template<class T> constexpr size_t mask-element-size = see below;
+`
+
+[4](#4)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L16311)
+
+*mask-element-size*<basic_mask<Bytes, Abi>> has the valueBytes[.](#4.sentence-1)
+
+[ð](#itemdecl:5)
+
+`template<class T> using deduced-vec-t = see below;
+`
+
+[5](#5)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L16321)
+
+Let x denote an lvalue of type const T[.](#5.sentence-1)
+
+[6](#6)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L16324)
+
+*deduced-vec-t*<T> is an alias for
+
+- [(6.1)](#6.1)
+
+decltype(x + x), if the type of x + x is an enabled
+ specialization of basic_vec; otherwise
+
+- [(6.2)](#6.2)
+
+void[.](#6.sentence-1)
+
+[ð](#itemdecl:6)
+
+`template<class V, class T> using make-compatible-simd-t = see below;
+`
+
+[7](#7)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L16340)
+
+Let x denote an lvalue of type const T[.](#7.sentence-1)
+
+[8](#8)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L16343)
+
+*make-compatible-simd-t*<V, T> is an alias for
+
+- [(8.1)](#8.1)
+
+*deduced-vec-t*<T>, if that type is not void,
+ otherwise
+
+- [(8.2)](#8.2)
+
+vec<decltype(x + x), V::size()>[.](#8.sentence-1)
+
+[ð](#itemdecl:7)
+
+`template<class... Ts>
+  requires [math-floating-point](simd.expos#concept:math-floating-point "29.10.2 Exposition-only types, variables, and concepts [simd.expos]")<Ts...>
+    using math-common-simd-t = see below;
+`
+
+[9](#9)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L16361)
+
+Let T0 denote Ts...[0][.](#9.sentence-1)
+
+Let T1 denote Ts...[1][.](#9.sentence-2)
+
+Let TRest denote a pack such that T0, T1, TRest... is equivalent
+to Ts...[.](#9.sentence-3)
+
+[10](#10)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L16367)
+
+Let *math-common-simd-t*<Ts...> be an alias for
+
+- [(10.1)](#10.1)
+
+*deduced-vec-t*<T0>, if sizeof...(Ts) equals 1;
+ otherwise
+
+- [(10.2)](#10.2)
+
+common_type_t<*deduced-vec-t*<T0>, *deduced-vec-t*<T1>>, if sizeof...(Ts) equals 2 and [*math-floating-point*](simd.expos#concept:math-floating-point "29.10.2 Exposition-only types, variables, and concepts [simd.expos]")<T0> &&[*math-floating-point*](simd.expos#concept:math-floating-point "29.10.2 Exposition-only types, variables, and concepts [simd.expos]")<T1> is true; otherwise
+
+- [(10.3)](#10.3)
+
+common_type_t<*deduced-vec-t*<T0>, T1>, if sizeof...(Ts) equals 2 and *math-floating-point*<T0> is true; otherwise
+
+- [(10.4)](#10.4)
+
+common_type_t<T0, *deduced-vec-t*<T1>>, if sizeof...(Ts) equals 2; otherwise
+
+- [(10.5)](#10.5)
+
+common_type_t<*math-common-simd-t*<T0, T1>, TRest...>, if *math-common-simd-t*<T0, T1> is valid and denotes a type;
+ otherwise
+
+- [(10.6)](#10.6)
+
+common_type_t<*math-common-simd-t*<TRest...>, T0, T1>[.](#10.sentence-1)
+
+[ð](#concept:reduction-binary-operation)
+
+`template<class BinaryOperation, class T>
+  concept [reduction-binary-operation](#concept:reduction-binary-operation "29.10.2.1 Exposition-only helpers [simd.expos.defn]") =
+    requires (const BinaryOperation binary_op, const vec<T, 1> v) {
+      { binary_op(v, v) } -> [same_as](concept.same#concept:same_as "18.4.2 Concept same_as [concept.same]")<vec<T, 1>>;
+    };
+`
+
+[11](#11)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L16404)
+
+Types BinaryOperation and T model[*reduction-binary-operation*](#concept:reduction-binary-operation "29.10.2.1 Exposition-only helpers [simd.expos.defn]")<BinaryOperation, T> only if:
+
+- [(11.1)](#11.1)
+
+  BinaryOperation is a binary element-wise operation and the
+operation is commutative[.](#11.1.sentence-1)
+
+- [(11.2)](#11.2)
+
+  An object of type BinaryOperation can be invoked with two
+arguments of type basic_vec<T, Abi>, with unspecified ABI tagAbi, returning a basic_vec<T, Abi>[.](#11.2.sentence-1)