Parallel efficiency calculation method and apparatus
This parallel efficiency calculation method can be applied, even in a case where a load balance is not kept, to many parallel processing including a heterogeneous computer system environment, and quantitatively correlates a parallel efficiency with a load balance contribution ratio and a virtual parallelization ratio, as parallel performance evaluation indexes, and parallel performance impediment factor contribution ratios. A parallel efficiency E p (p) is calculated by using a load balance contribution ratio Rb(p) representing a load balance degree between respective processors included in a parallel computer system, a virtual parallelization ratio Rp(p) representing a ratio, with respect to time, of a portion calculated in parallel by the respective processors to processing executed in the parallel computer system, and a parallel performance impediment factor contribution ratio Rj(p) representing a ratio of a processing time of a portion of each parallel performance impediment factor to a total processing time of all the processors.
1. A parallel efficiency calculation apparatus for calculating a parallel efficiency of a parallel computer system executing a specific processing as a whole, comprising:
a storage device;
a first calculator calculating and storing into said storage device, a load balance contribution ratio Rb(p) according to
R
b
(
p
)
≡
∑
i
=
1
p
τ
i
(
p
)
τ
(
p
)
·
p
by using a processing time γ i (p) of a parallel processing portion within a processing executed in each said processor i, a processing time χ i,j (p) of each parallel performance impediment factor j within said processing executed in each said processor i and a number p of processors of said parallel computer system, wherein
τ
i
(
p
)
≡
γ
i
(
p
)
+
∑
j
=
1
j
Others
χ
i
,
j
(
p
)
,
and
τ
(
p
)
≡
Max
i
=
1
p
(
τ
i
(
p
)
)
;
a second calculator calculating and storing into said storage device, a virtual parallelization ratio R p (p) according to
R
p
(
p
)
≡
∑
i
=
1
p
γ
i
(
p
)
τ
(
1
)
by using said processing time γ i (p), said number p of processors of said parallel computer system and τ(1), which is substantially equivalent to a processing time in case where only one processor executes said specific processing;
a third calculator calculating and storing into said storage device, a parallel performance impediment factor contribution ratio Rj(p) according to
R
j
(
p
)
≡
∑
i
=
1
p
χ
i
,
j
(
p
)
∑
i
=
1
p
τ
i
(
p
)
by using said processing time χ i,j (p) and said number p of processors of said parallel computer system; and
a fourth calculator calculating and storing into said storage device, a parallel efficiency Ep(p)
E
p
(
p
)
=
R
b
(
p
)
·
1
R
p
(
p
)
·
(
1
-
∑
j
=
1
j
Others
R
j
(
p
)
)
by using said load balance contribution ratio, said virtual parallelization ratio, and said parallel performance impediment factor contribution ratio; and
a display device displaying the calculated parallel efficiency that is stored in said storage device.
2. A parallel efficiency calculation method for calculating a parallel efficiency of a parallel computer system executing a specific processing as a whole, said parallel efficiency calculation method comprising:
providing a system separate from said parallel computer system comprising a first calculator, a second calculator, a third calculator, a fourth calculator, and a storage device;
providing a measuring unit in said parallel computer system;
measuring, in each processor i of said parallel computer system, a processing time γ i (p) of a parallel processing portion within a processing executed in each said processor, and a processing time χ i,j (p) of each parallel performance impediment factor j within said processing executed in each said processor, wherein said measuring is executed by said measuring unit in said parallel computer system;
calculating and storing into said storage device, by said first calculator, a load balance contribution ratio Rb(p) according to
R
b
(
p
)
≡
∑
i
=
1
p
τ
i
(
p
)
τ
(
p
)
·
p
by using the measured processing time γ i (p), said processing time χ i,j (p) and a number p of processors of said parallel computer system, wherein
τ
i
(
p
)
≡
γ
i
(
p
)
+
∑
j
=
1
j
Others
χ
i
,
j
(
p
)
,
and
τ
(
p
)
≡
Max
i
=
1
p
(
τ
i
(
p
)
)
;
calculating and storing into said storage device, by said second calculator, a virtual parallelization ratio R p (p) according to
R
p
(
p
)
≡
∑
i
=
1
p
γ
i
(
p
)
τ
(
1
)
by using the measured processing time γ i (p), said number p of processors of said parallel computer system and τ(1), which is substantially equivalent to a processing time in case where only one processor executes said specific processing;
calculating and storing into said storage device, by said third calculator, a parallel performance impediment factor contribution ratio Rj(p) according to
R
j
(
p
)
≡
∑
i
=
1
p
χ
i
,
j
(
p
)
∑
i
=
1
p
τ
i
(
p
)
by using said processing time χ i,j (p) and said number p of processors of said parallel computer system; and
calculating and storing into said storage device, by said fourth calculator, a parallel efficiency Ep(p)
E
p
(
p
)
=
R
b
(
p
)
·
1
R
p
(
p
)
·
(
1
-
∑
j
=
1
j
Others
R
j
(
p
)
)
by using said load balance contribution ratio, said virtual parallelization ratio, and said parallel performance impediment factor contribution ratio; and
outputting the calculated parallel efficiency that is stored in said storage device to a display device.
3. A computer readable storage medium embodying a program for causing a computer to execute operations calculating a parallel efficiency of a parallel computer system executing a specific processing as a whole, said operations comprising:
a storage device;
calculating and storing into said storage device, a load balance contribution ratio Rb(p) according to
R
b
(
p
)
≡
∑
i
=
1
p
τ
i
(
p
)
τ
(
p
)
·
p
by using a processing time γ i (p) of a parallel processing portion within a processing executed in each said processor i, a processing time χ i,j (p) of each parallel performance impediment factor j within said processing executed in each said processor i and a number p of processors of said parallel computer system, wherein
τ
i
(
p
)
≡
γ
i
(
p
)
+
∑
j
=
1
j
Others
χ
i
,
j
(
p
)
,
and
τ
(
p
)
≡
Max
i
=
1
p
(
τ
i
(
p
)
)
;
calculating and storing into said storage device, a virtual parallelization ratio R p (p) according to
R
p
(
p
)
≡
∑
i
=
1
p
γ
i
(
p
)
τ
(
1
)
by using said processing time γ i (p), said number p of processors of said parallel computer system and τ(1), which is substantially equivalent to a processing time in case where only one processor executes said specific processing;
calculating and storing into said storage device, a parallel performance impediment factor contribution ratio Rj(p) according to
R
j
(
p
)
≡
∑
i
=
1
p
χ
i
,
j
(
p
)
∑
i
=
1
p
τ
i
(
p
)
by using said processing time χ i,j (p) and said number p of processors of said parallel computer system; and
calculating and storing into said storage device, a parallel efficiency Ep(p)
E
p
(
p
)
=
R
b
(
p
)
·
1
R
p
(
p
)
·
(
1
-
∑
j
=
1
j
Others
R
j
(
p
)
)
by using said load balance contribution ratio, said virtual parallelization ratio, and said parallel performance impediment factor contribution ratio; and
outputting the calculated parallel efficiency that is stored in said storage device to a display device.