203 lines
7.1 KiB
Plaintext
203 lines
7.1 KiB
Plaintext
[/
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Copyright (c) 2008-2010 Joachim Faulhaber
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or copy at
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http://www.boost.org/LICENSE_1_0.txt)
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]
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[/ //= Subtraction ============================================================]
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[section Subtraction]
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[section Synopsis]
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[table
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[[Subtraction] [__ch_itvs__][__ch_itv_sets__][__ch_itv_maps__][__ch_ele_sets__][__ch_ele_maps__]]
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[[`T& T::subtract(const P&)`] [ ] [__ei] [__bp] [ ] [__b] ]
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[[`T& subtract(T&, const P&)`] [ ] [__ei] [__bp] [__e] [__b] ]
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[[`T& operator -=(T&, const P&)`] [ ] [__eiS][__eiS __bpM][__es] [__bm] ]
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[[`T operator - (T, const P&)`] [ ] [__eiS][__eiS __bpM][__es] [__bm] ]
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[[`T left_subtract(T, const T&)`] [1] [ ] [ ] [ ] [ ] ]
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[[`T right_subtract(T, const T&)`] [1] [ ] [ ] [ ] [ ] ]
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]
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Functions and operators that implement ['*Subtraction*] on *icl* objects
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are given in the table above.
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[table
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[[] [Description of Subtraction]]
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[[`Sets`][Subtraction on Sets implements ['*set difference*]]]
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[[`Maps`][Subtraction on Maps implements a ['*map difference*] function similar to /set difference/.
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If, on subtraction of an element value pair `(k,v)` it's key `k` is in the map
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already, the subtraction function is propagated to the associated value.
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On the associated value an aggregation is performed, that reverses
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the effect of the corresponding addition function.
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Find more on
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[link boost_icl.concepts.aggrovering ['subtractability of maps]]
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and related
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[link boost_icl.semantics.maps ['semantic issues]]
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following the links.
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]]
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]
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[endsect][/ Synopsis]
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[section Functions][/ Subtraction]
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The admissible combinations of types for subtraction functions
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can be summarized in the
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['*overload table*] below:
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``
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// overload table for T\P| e i b p
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T& T::subtract(const P&) ---+--------
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T& subtract(T&, const P&) s | s
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m | m
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S | S S
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M | M M
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``
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The next table contains complexity characteristics for `subtract`.
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[table Time Complexity for function subtract on icl containers
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[[`T& T::subtract(const P&)`\n
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`T& subtract(T&, const P&)`] [__ch_dom_t__][__ch_itv_t__][__ch_dom_mp_t__][__ch_itv_mp_t__]]
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[[__icl_set__] [__Olgn__] [] [] [] ]
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[[__icl_map__] [__Olgn__] [] [__Olgn__] [] ]
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[[__itv_sets__] [__Olgn__] [__a_Olgn__] [] [] ]
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[[__itv_maps__] [__Olgn__] [__On__] [__Olgn__] [__On__] ]
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]
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[endsect][/ Member function Subtraction]
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[section Inplace operators][/ Subtraction]
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As presented in the overload tables for `operator -=`
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more type combinations are provided for subtraction than for
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addition.
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``
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// overload tables for element containers: interval containers:
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T& operator -= (T&, const P&) -= | e b s m -= | e i b p S M
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---+-------- ---+------------
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s | s s S | S S S
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m | m m m m M | M M M M M M
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``
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Subtraction provides the /reverse/ operation
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of an addition for these overloads,
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``
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// Reverse addition -= | e b s m -= | e i b p S M
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---+-------- ---+------------
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s | s s S | S S S
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m | m m M | M M M
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``
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[*and] you can erase parts of __icl_maps__ or __itv_maps__
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using
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/key values/, /intervals/ or /element or interval sets/
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using these overloads:
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``
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// Erasure by key objects -= | e b s m -= | e i b p S M
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---+-------- ---+------------
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s | s s S | S S S
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m | m m M | M M M
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``
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On Sets both function groups fall together
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as ['*set difference*].
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Complexity characteristics for inplace subtraction operations are
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given by the next tables where
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``
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n = iterative_size(y);
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m = iterative_size(x); //if P is a container type
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``
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[table Time Complexity for inplace Subtraction on element containers
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[[`T& operator -= (T&, const P&)`][__ch_dom_t__][__ch_dom_mp_t__][__ch_icl_set__][__ch_icl_map__]]
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[[__icl_set__] [__Olgn__] [] [__Omlgn__] [] ]
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[[__icl_map__] [__Olgn__] [__Olgn__] [__Omlgn__] [__Omlgn__] ]
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]
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[table Time Complexity for inplace Subtraction on interval containers
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[[`T& operator -= (T&, const P&)`][__ch_dom_t__][__ch_itv_t__][__ch_dom_mp_t__][__ch_itv_mp_t__][__ch_itv_sets__][__ch_itv_maps__]]
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[[interval_sets] [__Olgn__] [__a_Olgn__] [] [] [__Omlgnpm__] [] ]
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[[interval_maps] [__Olgn__] [__a_Olgn__] [__Olgn__] [__On__] [__Omlgnpm__] [__Omlgnpm__] ]
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]
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[endsect][/ Inplace operators Subtraction]
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[section Infix operators][/-Subtraction]
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The admissible overloads for the infix
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/subtraction/ `operator -`
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which is a non commutative
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operation
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is given by the next overload table.
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``
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// overload tables for - | e b s m - | e i b p S M
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T operator - (T, const P&) ---+-------- ---+------------
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s | s s S | S S S
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m | m m m m M | M M M M M M
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``
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[endsect][/- Infix operator Subtraction]
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[section Subtraction on Intervals]
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[table
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[[['*Subtraction*]] [Types] [Description] ]
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[[`T left_subtract(T right, const T& left_minuend)`] [__i]
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[subtract `left_minuend` from the interval `right` on it's left side.
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``
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right_over = left_subtract(right, left_minuend);
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... d) : right
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... c) : left_minuend
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[c d) : right_over
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``
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] ]
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[[`T right_subtract(T left, const T& right_minuend)`] [__i]
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[subtract `right_minuend` from the interval `left` on it's right side.
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``
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left_over = right_subtract(left, right_minuend);
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[a ... : left
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[b ... : right_minuend
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[a b) : left_over
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``
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] ]
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]
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[endsect][/ Subtraction on Intervals]
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['*See also . . .*]
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[table
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[]
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[[[link boost_icl.function_reference.addition ['*Addition*]] ]]
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[[[link boost_icl.function_reference.erasure ['*Erasure*]] ]]
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]
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['*Back to section . . .*]
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[table
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[]
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[[[link function_synopsis_table ['*Function Synopsis*]] ]]
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[[[link boost_icl.interface ['*Interface*]] ]]
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]
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[endsect][/ Subtraction]
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