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68 lines
2.9 KiB
TeX
68 lines
2.9 KiB
TeX
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\section{Induction}
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\label{sec:induction}
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This section covers ways to perform inductions in \kcode{distribute}, worksharing-loop, \kcode{taskloop}, and SIMD regions.
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\subsection{\kcode{induction} Clause}
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\label{subsec:induction}
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\index{clauses!induction@\kcode{induction}}
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\index{induction clause@\kcode{induction} clause}
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\index{inductions!induction clause@\kcode{induction} clause}
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\index{inductions!closed form}
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The following example demonstrates the basic use of the \kcode{induction} clause
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in Case 1 for variable \ucode{xi} in a loop in routine \ucode{comp_poly} to
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evaluate the polynomial of variable \ucode{x}.
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For this case, the induction operation is
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with the inductor `\scode{*}' and induction step \ucode{x}.
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The intermediate value of \ucode{xi} is used in producing
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the reduction sum \ucode{result}.
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The last value of \ucode{xi} is well defined after the loop and
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is printed out together with the final value of \ucode{result}.
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An alternative approach is to use an \plc{inscan} reduction
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as illustrated in Case 2, but this may not be as optimal as Case 1.
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An equivalent code without the \kcode{induction} clause is given in Case 3
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where a non-recursive closed form of the induction operation is used to
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compute the intermediate value of \ucode{xi}.
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The last value of \ucode{xi} is returned with the \kcode{lastprivate} clause
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for this case.
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\cexample[6.0]{induction}{1}
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\ffreeexample[6.0]{induction}{1}
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\subsection{User-defined Induction}
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\label{subsec:user-defined-induction}
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\index{directives!declare induction@\kcode{declare induction}}
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\index{declare induction directive@\kcode{declare induction} directive}
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\index{inductions!declare induction directive@\kcode{declare induction} directive}
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\index{inductions!inductor clause@\kcode{inductor} clause}
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\index{inductions!collector clause@\kcode{collector} clause}
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\index{inductions!user-defined}
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\index{OpenMP variable identifiers!omp_var@\kcode{omp_var}}
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\index{OpenMP variable identifiers!omp_step@\kcode{omp_step}}
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\index{OpenMP variable identifiers!omp_idx@\kcode{omp_idx}}
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The following is a user-defined induction example that uses the
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\kcode{declare induction} directive and the \kcode{induction} clause.
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The example processes in parallel $N$ points along a line of a given slope
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starting from a given point, and where adjacent points are separated by
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a fixed distance.
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The induction variable \ucode{P} represents a point, and
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the step expression is the distance. The induction identifier \ucode{next}
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is defined in the \kcode{declare induction} directive with an
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appropriate \plc{inductor} via the \kcode{inductor} clause and
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\plc{collector} via the \kcode{collector} clause.
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This identifier together with the \kcode{step(\ucode{Separation})}
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modifier is specified in the \kcode{induction} clause
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for the \kcode{parallel for}/\kcode{do} construct
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in routine \ucode{processPointsInLine}.
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\cppexample[6.0]{induction}{2}
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\ffreeexample[6.0]{induction}{2}
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