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cppdraft/class/gslice.md

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+[class.gslice]
+
+# 29 Numerics library [[numerics]](./#numerics)
+
+## 29.6 Numeric arrays [[numarray]](numarray#class.gslice)
+
+### 29.6.6 The gslice class [class.gslice]
+
+#### [29.6.6.1](#overview) Overview [[class.gslice.overview]](class.gslice.overview)
+
+[🔗](#lib:gslice)
+
+namespace std {class gslice {public: gslice();
+ gslice(size_t s, const valarray<size_t>& l, const valarray<size_t>& d);
+
+ size_t start() const;
+ valarray<size_t> size() const;
+ valarray<size_t> stride() const; };}
+
+[1](#overview-1)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L8619)
+
+This class represents a generalized slice out of an array[.](#overview-1.sentence-1)
+
+Agslice is defined by a starting offset (s),
+a set of lengths (lj),
+and a set of strides (dj)[.](#overview-1.sentence-2)
+
+The number of lengths shall equal the number of strides[.](#overview-1.sentence-3)
+
+[2](#overview-2)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L8628)
+
+Agslice represents a mapping from a set of indices (ij),
+equal in number to the number of strides, to a single index k[.](#overview-2.sentence-1)
+
+It is useful for building multidimensional array classes using
+thevalarray template, which is one-dimensional[.](#overview-2.sentence-2)
+
+The set of one-dimensional index values specified by a gslice are  
+k=s+∑jijdj where the multidimensional indices ij range in value from
+0 to lij−1[.](#overview-2.sentence-3)
+
+[3](#overview-3)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L8642)
+
+[*Example [1](#overview-example-1)*:
+
+Thegslice specificationstart = 3 length = {2, 4, 3} stride = {19, 4, 1} yields the sequence of one-dimensional indices  
+k=3+(0,1)×19+(0,1,2,3)×4+(0,1,2)×1 which are ordered as shown in the following table:
+
+```
+	(i0,i1,i2,k)=
+		(0,  0,  0,   3),    
+		(0,  0,  1,   4),    
+		(0,  0,  2,   5),    
+		(0,  1,  0,   7),    
+		(0,  1,  1,   8),    
+		(0,  1,  2,   9),    
+		(0,  2,  0,  11), 
+		(0,  2,  1,  12), 
+		(0,  2,  2,  13), 
+		(0,  3,  0,  15), 
+		(0,  3,  1,  16), 
+		(0,  3,  2,  17), 
+		(1,  0,  0,  22), 
+		(1,  0,  1,  23), 
+		…      
+		(1,  3,  2,  36)
+
+```
+
+That is, the highest-ordered index turns fastest[.](#overview-3.sentence-2)
+
+— *end example*]
+
+[4](#overview-4)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L8680)
+
+It is possible to have degenerate generalized slices in which an address
+is repeated[.](#overview-4.sentence-1)
+
+[5](#overview-5)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L8684)
+
+[*Example [2](#overview-example-2)*:
+
+If the stride parameters in the previous
+example are changed to {1, 1, 1}, the first few elements of the
+resulting sequence of indices will be
+
+```
+	(0,  0,  0,   3),  
+	(0,  0,  1,   4),  
+	(0,  0,  2,   5),  
+	(0,  1,  0,   4),  
+	(0,  1,  1,   5),  
+	(0,  1,  2,   6),  
+	…
+
+```
+ — *end example*]
+
+[6](#overview-6)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L8702)
+
+If a degenerate slice is used as the argument to the
+non-const version ofoperator[](const gslice&),
+the behavior is undefined[.](#overview-6.sentence-1)
+
+#### [29.6.6.2](#gslice.cons) Constructors [[gslice.cons]](gslice.cons)
+
+[🔗](#lib:gslice,constructor)
+
+`gslice();
+gslice(size_t start, const valarray<size_t>& lengths,
+       const valarray<size_t>& strides);
+`
+
+[1](#gslice.cons-1)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L8720)
+
+The default constructor is equivalent togslice(0, valarray<size_t>(), valarray<size_t>())[.](#gslice.cons-1.sentence-1)
+
+The constructor with arguments builds agslice based on a specification of start, lengths, and strides, as explained
+in the previous subclause[.](#gslice.cons-1.sentence-2)
+
+#### [29.6.6.3](#gslice.access) Access functions [[gslice.access]](gslice.access)
+
+[🔗](#lib:start,gslice)
+
+`size_t           start()  const;
+valarray<size_t> size() const;
+valarray<size_t> stride() const;
+`
+
+[1](#gslice.access-1)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L8741)
+
+*Returns*: The representation of the
+start, lengths, or strides specified for the gslice[.](#gslice.access-1.sentence-1)
+
+[2](#gslice.access-2)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L8746)
+
+*Complexity*: start() is constant time[.](#gslice.access-2.sentence-1)
+
+size() and stride() are linear in the number of strides[.](#gslice.access-2.sentence-2)