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code
pugs
Commits
c24daac7
Commit
c24daac7
authored
1 year ago
by
Stéphane Del Pino
Browse files
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Plain Diff
Add more tests for floating point reproducible summations
parent
99d69ad1
No related branches found
No related tags found
1 merge request
!172
Reproducible summation of floating point arrays
Changes
1
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1 changed file
tests/test_Array.cpp
+704
-0
704 additions, 0 deletions
tests/test_Array.cpp
with
704 additions
and
0 deletions
tests/test_Array.cpp
+
704
−
0
View file @
c24daac7
...
...
@@ -325,6 +325,14 @@ TEST_CASE("Array", "[utils]")
SECTION
(
"reproducible floating point sum"
)
{
auto
direct_sum
=
[](
auto
array
)
{
auto
sum
=
array
[
0
];
for
(
size_t
i
=
1
;
i
<
array
.
size
();
++
i
)
{
sum
+=
array
[
i
];
}
return
sum
;
};
SECTION
(
"reproducible double sum"
)
{
Array
<
double
>
array
(
10'000
);
...
...
@@ -340,6 +348,8 @@ TEST_CASE("Array", "[utils]")
const
auto
sum_after_shuffle
=
sum
(
array
);
REQUIRE
(
sum_before_shuffle
==
sum_after_shuffle
);
REQUIRE
(
sum_before_shuffle
==
Catch
::
Approx
(
direct_sum
(
array
)));
}
SECTION
(
"reproducible float sum"
)
...
...
@@ -357,6 +367,8 @@ TEST_CASE("Array", "[utils]")
const
auto
sum_after_shuffle
=
sum
(
array
);
REQUIRE
(
sum_before_shuffle
==
sum_after_shuffle
);
REQUIRE
(
sum_before_shuffle
==
Catch
::
Approx
(
direct_sum
(
array
)));
}
SECTION
(
"reproducible TinyVector<3,double> sum"
)
...
...
@@ -379,6 +391,11 @@ TEST_CASE("Array", "[utils]")
const
auto
sum_after_shuffle
=
sum
(
array
);
REQUIRE
(
sum_before_shuffle
==
sum_after_shuffle
);
auto
naive_sum
=
direct_sum
(
array
);
REQUIRE
(
sum_before_shuffle
[
0
]
==
Catch
::
Approx
(
naive_sum
[
0
]));
REQUIRE
(
sum_before_shuffle
[
1
]
==
Catch
::
Approx
(
naive_sum
[
1
]));
REQUIRE
(
sum_before_shuffle
[
2
]
==
Catch
::
Approx
(
naive_sum
[
2
]));
}
SECTION
(
"reproducible TinyVector<3,float> sum"
)
...
...
@@ -401,6 +418,11 @@ TEST_CASE("Array", "[utils]")
const
auto
sum_after_shuffle
=
sum
(
array
);
REQUIRE
(
sum_before_shuffle
==
sum_after_shuffle
);
auto
naive_sum
=
direct_sum
(
array
);
REQUIRE
(
sum_before_shuffle
[
0
]
==
Catch
::
Approx
(
naive_sum
[
0
]));
REQUIRE
(
sum_before_shuffle
[
1
]
==
Catch
::
Approx
(
naive_sum
[
1
]));
REQUIRE
(
sum_before_shuffle
[
2
]
==
Catch
::
Approx
(
naive_sum
[
2
]));
}
SECTION
(
"reproducible TinyMatrix<2, 3> sum"
)
...
...
@@ -424,6 +446,14 @@ TEST_CASE("Array", "[utils]")
const
auto
sum_after_shuffle
=
sum
(
array
);
REQUIRE
(
sum_before_shuffle
==
sum_after_shuffle
);
auto
naive_sum
=
direct_sum
(
array
);
REQUIRE
(
sum_before_shuffle
(
0
,
0
)
==
Catch
::
Approx
(
naive_sum
(
0
,
0
)));
REQUIRE
(
sum_before_shuffle
(
0
,
1
)
==
Catch
::
Approx
(
naive_sum
(
0
,
1
)));
REQUIRE
(
sum_before_shuffle
(
0
,
2
)
==
Catch
::
Approx
(
naive_sum
(
0
,
2
)));
REQUIRE
(
sum_before_shuffle
(
1
,
0
)
==
Catch
::
Approx
(
naive_sum
(
1
,
0
)));
REQUIRE
(
sum_before_shuffle
(
1
,
1
)
==
Catch
::
Approx
(
naive_sum
(
1
,
1
)));
REQUIRE
(
sum_before_shuffle
(
1
,
2
)
==
Catch
::
Approx
(
naive_sum
(
1
,
2
)));
}
SECTION
(
"reproducible TinyMatrix<2, 3, float> sum"
)
...
...
@@ -447,6 +477,680 @@ TEST_CASE("Array", "[utils]")
const
auto
sum_after_shuffle
=
sum
(
array
);
REQUIRE
(
sum_before_shuffle
==
sum_after_shuffle
);
auto
naive_sum
=
direct_sum
(
array
);
REQUIRE
(
sum_before_shuffle
(
0
,
0
)
==
Catch
::
Approx
(
naive_sum
(
0
,
0
)));
REQUIRE
(
sum_before_shuffle
(
0
,
1
)
==
Catch
::
Approx
(
naive_sum
(
0
,
1
)));
REQUIRE
(
sum_before_shuffle
(
0
,
2
)
==
Catch
::
Approx
(
naive_sum
(
0
,
2
)));
REQUIRE
(
sum_before_shuffle
(
1
,
0
)
==
Catch
::
Approx
(
naive_sum
(
1
,
0
)).
epsilon
(
1E-4
));
REQUIRE
(
sum_before_shuffle
(
1
,
1
)
==
Catch
::
Approx
(
naive_sum
(
1
,
1
)).
margin
(
1E-6
));
REQUIRE
(
sum_before_shuffle
(
1
,
2
)
==
Catch
::
Approx
(
naive_sum
(
1
,
2
)));
}
SECTION
(
"scalar bin summation"
)
{
SECTION
(
"small arrays"
)
{
Array
<
double
>
array1
(
122
);
for
(
size_t
i
=
0
;
i
<
array1
.
size
();
++
i
)
{
array1
[
i
]
=
((
i
<
(
array1
.
size
()
/
10
))
*
1E25
+
1E10
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
);
}
Array
<
double
>
array2
(
357
);
for
(
size_t
i
=
0
;
i
<
array2
.
size
();
++
i
)
{
array2
[
i
]
=
((
i
<
(
array2
.
size
()
/
10
))
*
1E25
+
1E10
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
);
}
Array
<
double
>
array3
(
283
);
for
(
size_t
i
=
0
;
i
<
array3
.
size
();
++
i
)
{
array3
[
i
]
=
((
i
<
(
array3
.
size
()
/
10
))
*
1E25
+
1E10
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
);
}
Array
<
double
>
array
(
array1
.
size
()
+
array2
.
size
()
+
array3
.
size
());
{
size_t
I
=
0
;
for
(
size_t
i
=
0
;
i
<
array1
.
size
();
++
i
)
{
array
[
I
++
]
=
array1
[
i
];
}
for
(
size_t
i
=
0
;
i
<
array2
.
size
();
++
i
)
{
array
[
I
++
]
=
array2
[
i
];
}
for
(
size_t
i
=
0
;
i
<
array3
.
size
();
++
i
)
{
array
[
I
++
]
=
array3
[
i
];
}
}
ReproducibleScalarSum
s1
(
array1
);
ReproducibleScalarSum
s2
(
array2
);
ReproducibleScalarSum
s3
(
array3
);
using
RSumT
=
decltype
(
s1
);
RSumT
::
Bin
bin1
=
s1
.
getSummationBin
();
RSumT
::
Bin
bin2
=
s2
.
getSummationBin
();
RSumT
::
Bin
bin3
=
s3
.
getSummationBin
();
{
RSumT
::
Bin
bin_sum
=
zero
;
RSumT
::
addBinTo
(
bin1
,
bin_sum
);
RSumT
::
addBinTo
(
bin2
,
bin_sum
);
RSumT
::
addBinTo
(
bin3
,
bin_sum
);
REQUIRE
(
sum
(
array
)
==
RSumT
::
getValue
(
bin_sum
));
}
{
RSumT
::
Bin
bin_sum
=
zero
;
RSumT
::
addBinTo
(
bin3
,
bin_sum
);
RSumT
::
addBinTo
(
bin2
,
bin_sum
);
RSumT
::
addBinTo
(
bin1
,
bin_sum
);
REQUIRE
(
sum
(
array
)
==
RSumT
::
getValue
(
bin_sum
));
}
}
SECTION
(
"small and large arrays"
)
{
Array
<
double
>
array1
(
122
);
for
(
size_t
i
=
0
;
i
<
array1
.
size
();
++
i
)
{
array1
[
i
]
=
((
i
<
(
array1
.
size
()
/
100
))
*
1E25
+
1E10
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
);
}
Array
<
double
>
array2
(
7357
);
for
(
size_t
i
=
0
;
i
<
array2
.
size
();
++
i
)
{
array2
[
i
]
=
((
i
<
(
array2
.
size
()
/
1000
))
*
1E25
+
1E10
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
);
}
Array
<
double
>
array3
(
283
);
for
(
size_t
i
=
0
;
i
<
array3
.
size
();
++
i
)
{
array3
[
i
]
=
((
i
<
(
array3
.
size
()
/
30
))
*
1E25
+
1E10
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
);
}
Array
<
double
>
array
(
array1
.
size
()
+
array2
.
size
()
+
array3
.
size
());
{
size_t
I
=
0
;
for
(
size_t
i
=
0
;
i
<
array1
.
size
();
++
i
)
{
array
[
I
++
]
=
array1
[
i
];
}
for
(
size_t
i
=
0
;
i
<
array2
.
size
();
++
i
)
{
array
[
I
++
]
=
array2
[
i
];
}
for
(
size_t
i
=
0
;
i
<
array3
.
size
();
++
i
)
{
array
[
I
++
]
=
array3
[
i
];
}
}
ReproducibleScalarSum
s1
(
array1
);
ReproducibleScalarSum
s2
(
array2
);
ReproducibleScalarSum
s3
(
array3
);
using
RSumT
=
decltype
(
s1
);
RSumT
::
Bin
bin1
=
s1
.
getSummationBin
();
RSumT
::
Bin
bin2
=
s2
.
getSummationBin
();
RSumT
::
Bin
bin3
=
s3
.
getSummationBin
();
{
RSumT
::
Bin
bin_sum
=
zero
;
RSumT
::
addBinTo
(
bin1
,
bin_sum
);
RSumT
::
addBinTo
(
bin2
,
bin_sum
);
RSumT
::
addBinTo
(
bin3
,
bin_sum
);
REQUIRE
(
sum
(
array
)
==
RSumT
::
getValue
(
bin_sum
));
}
{
RSumT
::
Bin
bin_sum
=
zero
;
RSumT
::
addBinTo
(
bin3
,
bin_sum
);
RSumT
::
addBinTo
(
bin2
,
bin_sum
);
RSumT
::
addBinTo
(
bin1
,
bin_sum
);
REQUIRE
(
sum
(
array
)
==
RSumT
::
getValue
(
bin_sum
));
}
}
SECTION
(
"large arrays"
)
{
Array
<
double
>
array1
(
5122
);
for
(
size_t
i
=
0
;
i
<
array1
.
size
();
++
i
)
{
array1
[
i
]
=
((
i
<
(
array1
.
size
()
/
100
))
*
1E25
+
1E10
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
);
}
Array
<
double
>
array2
(
7357
);
for
(
size_t
i
=
0
;
i
<
array2
.
size
();
++
i
)
{
array2
[
i
]
=
((
i
<
(
array2
.
size
()
/
1000
))
*
1E25
+
1E10
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
);
}
Array
<
double
>
array3
(
6283
);
for
(
size_t
i
=
0
;
i
<
array3
.
size
();
++
i
)
{
array3
[
i
]
=
((
i
<
(
array3
.
size
()
/
300
))
*
1E25
+
1E10
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
);
}
Array
<
double
>
array
(
array1
.
size
()
+
array2
.
size
()
+
array3
.
size
());
{
size_t
I
=
0
;
for
(
size_t
i
=
0
;
i
<
array1
.
size
();
++
i
)
{
array
[
I
++
]
=
array1
[
i
];
}
for
(
size_t
i
=
0
;
i
<
array2
.
size
();
++
i
)
{
array
[
I
++
]
=
array2
[
i
];
}
for
(
size_t
i
=
0
;
i
<
array3
.
size
();
++
i
)
{
array
[
I
++
]
=
array3
[
i
];
}
}
ReproducibleScalarSum
s1
(
array1
);
ReproducibleScalarSum
s2
(
array2
);
ReproducibleScalarSum
s3
(
array3
);
using
RSumT
=
decltype
(
s1
);
RSumT
::
Bin
bin1
=
s1
.
getSummationBin
();
RSumT
::
Bin
bin2
=
s2
.
getSummationBin
();
RSumT
::
Bin
bin3
=
s3
.
getSummationBin
();
{
RSumT
::
Bin
bin_sum
=
zero
;
RSumT
::
addBinTo
(
bin1
,
bin_sum
);
RSumT
::
addBinTo
(
bin2
,
bin_sum
);
RSumT
::
addBinTo
(
bin3
,
bin_sum
);
REQUIRE
(
sum
(
array
)
==
RSumT
::
getValue
(
bin_sum
));
}
{
RSumT
::
Bin
bin_sum
=
zero
;
RSumT
::
addBinTo
(
bin3
,
bin_sum
);
RSumT
::
addBinTo
(
bin2
,
bin_sum
);
RSumT
::
addBinTo
(
bin1
,
bin_sum
);
REQUIRE
(
sum
(
array
)
==
RSumT
::
getValue
(
bin_sum
));
}
}
}
SECTION
(
"TinyVector bin summation"
)
{
SECTION
(
"small arrays"
)
{
Array
<
TinyVector
<
3
,
double
>>
array1
(
122
);
for
(
size_t
i
=
0
;
i
<
array1
.
size
();
++
i
)
{
array1
[
i
]
=
TinyVector
<
3
,
double
>
(((
i
<
(
array1
.
size
()
/
10
))
*
1E25
+
1E20
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
),
((
i
<
(
array1
.
size
()
/
50
))
*
1E15
+
1E10
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
3
*
i
+
1
),
((
i
<
(
array1
.
size
()
/
20
))
*
1E7
+
1E10
)
*
((
i
+
1
)
%
10
)
*
std
::
tan
(
3
*
i
+
1
));
}
Array
<
TinyVector
<
3
,
double
>>
array2
(
357
);
for
(
size_t
i
=
0
;
i
<
array2
.
size
();
++
i
)
{
array2
[
i
]
=
TinyVector
<
3
,
double
>
(((
i
<
(
array2
.
size
()
/
10
))
*
1E25
+
1E20
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
),
((
i
<
(
array2
.
size
()
/
50
))
*
1E15
+
1E10
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
3
*
i
+
1
),
((
i
<
(
array2
.
size
()
/
20
))
*
1E7
+
1E10
)
*
((
i
+
1
)
%
10
)
*
std
::
tan
(
3
*
i
+
1
));
}
Array
<
TinyVector
<
3
,
double
>>
array3
(
283
);
for
(
size_t
i
=
0
;
i
<
array3
.
size
();
++
i
)
{
array3
[
i
]
=
TinyVector
<
3
,
double
>
(((
i
<
(
array3
.
size
()
/
10
))
*
1E25
+
1E20
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
),
((
i
<
(
array3
.
size
()
/
50
))
*
1E15
+
1E10
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
3
*
i
+
1
),
((
i
<
(
array3
.
size
()
/
20
))
*
1E7
+
1E10
)
*
((
i
+
1
)
%
10
)
*
std
::
tan
(
3
*
i
+
1
));
}
Array
<
TinyVector
<
3
,
double
>>
array
(
array1
.
size
()
+
array2
.
size
()
+
array3
.
size
());
{
size_t
I
=
0
;
for
(
size_t
i
=
0
;
i
<
array1
.
size
();
++
i
)
{
array
[
I
++
]
=
array1
[
i
];
}
for
(
size_t
i
=
0
;
i
<
array2
.
size
();
++
i
)
{
array
[
I
++
]
=
array2
[
i
];
}
for
(
size_t
i
=
0
;
i
<
array3
.
size
();
++
i
)
{
array
[
I
++
]
=
array3
[
i
];
}
}
ReproducibleTinyVectorSum
s1
(
array1
);
ReproducibleTinyVectorSum
s2
(
array2
);
ReproducibleTinyVectorSum
s3
(
array3
);
using
RSumT
=
decltype
(
s1
);
RSumT
::
Bin
bin1
=
s1
.
getSummationBin
();
RSumT
::
Bin
bin2
=
s2
.
getSummationBin
();
RSumT
::
Bin
bin3
=
s3
.
getSummationBin
();
{
RSumT
::
Bin
bin_sum
=
zero
;
RSumT
::
addBinTo
(
bin1
,
bin_sum
);
RSumT
::
addBinTo
(
bin2
,
bin_sum
);
RSumT
::
addBinTo
(
bin3
,
bin_sum
);
REQUIRE
(
sum
(
array
)
==
RSumT
::
getValue
(
bin_sum
));
}
{
RSumT
::
Bin
bin_sum
=
zero
;
RSumT
::
addBinTo
(
bin3
,
bin_sum
);
RSumT
::
addBinTo
(
bin2
,
bin_sum
);
RSumT
::
addBinTo
(
bin1
,
bin_sum
);
REQUIRE
(
sum
(
array
)
==
RSumT
::
getValue
(
bin_sum
));
}
}
SECTION
(
"small and large arrays"
)
{
Array
<
TinyVector
<
3
,
double
>>
array1
(
122
);
for
(
size_t
i
=
0
;
i
<
array1
.
size
();
++
i
)
{
array1
[
i
]
=
TinyVector
<
3
,
double
>
(((
i
<
(
array1
.
size
()
/
10
))
*
1E25
+
1E20
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
),
((
i
<
(
array1
.
size
()
/
50
))
*
1E15
+
1E10
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
3
*
i
+
1
),
((
i
<
(
array1
.
size
()
/
20
))
*
1E7
+
1E10
)
*
((
i
+
1
)
%
10
)
*
std
::
tan
(
3
*
i
+
1
));
}
Array
<
TinyVector
<
3
,
double
>>
array2
(
7357
);
for
(
size_t
i
=
0
;
i
<
array2
.
size
();
++
i
)
{
array2
[
i
]
=
TinyVector
<
3
,
double
>
(((
i
<
(
array2
.
size
()
/
10
))
*
1E25
+
1E20
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
),
((
i
<
(
array2
.
size
()
/
50
))
*
1E15
+
1E10
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
3
*
i
+
1
),
((
i
<
(
array2
.
size
()
/
20
))
*
1E7
+
1E10
)
*
((
i
+
1
)
%
10
)
*
std
::
tan
(
3
*
i
+
1
));
}
Array
<
TinyVector
<
3
,
double
>>
array3
(
283
);
for
(
size_t
i
=
0
;
i
<
array3
.
size
();
++
i
)
{
array3
[
i
]
=
TinyVector
<
3
,
double
>
(((
i
<
(
array3
.
size
()
/
10
))
*
1E25
+
1E20
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
),
((
i
<
(
array3
.
size
()
/
50
))
*
1E15
+
1E10
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
3
*
i
+
1
),
((
i
<
(
array3
.
size
()
/
20
))
*
1E7
+
1E10
)
*
((
i
+
1
)
%
10
)
*
std
::
tan
(
3
*
i
+
1
));
}
Array
<
TinyVector
<
3
,
double
>>
array
(
array1
.
size
()
+
array2
.
size
()
+
array3
.
size
());
{
size_t
I
=
0
;
for
(
size_t
i
=
0
;
i
<
array1
.
size
();
++
i
)
{
array
[
I
++
]
=
array1
[
i
];
}
for
(
size_t
i
=
0
;
i
<
array2
.
size
();
++
i
)
{
array
[
I
++
]
=
array2
[
i
];
}
for
(
size_t
i
=
0
;
i
<
array3
.
size
();
++
i
)
{
array
[
I
++
]
=
array3
[
i
];
}
}
ReproducibleTinyVectorSum
s1
(
array1
);
ReproducibleTinyVectorSum
s2
(
array2
);
ReproducibleTinyVectorSum
s3
(
array3
);
using
RSumT
=
decltype
(
s1
);
RSumT
::
Bin
bin1
=
s1
.
getSummationBin
();
RSumT
::
Bin
bin2
=
s2
.
getSummationBin
();
RSumT
::
Bin
bin3
=
s3
.
getSummationBin
();
{
RSumT
::
Bin
bin_sum
=
zero
;
RSumT
::
addBinTo
(
bin1
,
bin_sum
);
RSumT
::
addBinTo
(
bin2
,
bin_sum
);
RSumT
::
addBinTo
(
bin3
,
bin_sum
);
REQUIRE
(
sum
(
array
)
==
RSumT
::
getValue
(
bin_sum
));
}
{
RSumT
::
Bin
bin_sum
=
zero
;
RSumT
::
addBinTo
(
bin3
,
bin_sum
);
RSumT
::
addBinTo
(
bin2
,
bin_sum
);
RSumT
::
addBinTo
(
bin1
,
bin_sum
);
REQUIRE
(
sum
(
array
)
==
RSumT
::
getValue
(
bin_sum
));
}
}
SECTION
(
"large arrays"
)
{
Array
<
TinyVector
<
3
,
double
>>
array1
(
5122
);
for
(
size_t
i
=
0
;
i
<
array1
.
size
();
++
i
)
{
array1
[
i
]
=
TinyVector
<
3
,
double
>
(((
i
<
(
array1
.
size
()
/
10
))
*
1E25
+
1E20
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
),
((
i
<
(
array1
.
size
()
/
50
))
*
1E15
+
1E10
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
3
*
i
+
1
),
((
i
<
(
array1
.
size
()
/
20
))
*
1E7
+
1E10
)
*
((
i
+
1
)
%
10
)
*
std
::
tan
(
3
*
i
+
1
));
}
Array
<
TinyVector
<
3
,
double
>>
array2
(
7357
);
for
(
size_t
i
=
0
;
i
<
array2
.
size
();
++
i
)
{
array2
[
i
]
=
TinyVector
<
3
,
double
>
(((
i
<
(
array2
.
size
()
/
10
))
*
1E25
+
1E20
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
),
((
i
<
(
array2
.
size
()
/
50
))
*
1E15
+
1E10
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
3
*
i
+
1
),
((
i
<
(
array2
.
size
()
/
20
))
*
1E7
+
1E10
)
*
((
i
+
1
)
%
10
)
*
std
::
tan
(
3
*
i
+
1
));
}
Array
<
TinyVector
<
3
,
double
>>
array3
(
4283
);
for
(
size_t
i
=
0
;
i
<
array3
.
size
();
++
i
)
{
array3
[
i
]
=
TinyVector
<
3
,
double
>
(((
i
<
(
array3
.
size
()
/
10
))
*
1E25
+
1E20
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
),
((
i
<
(
array3
.
size
()
/
50
))
*
1E15
+
1E10
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
3
*
i
+
1
),
((
i
<
(
array3
.
size
()
/
20
))
*
1E7
+
1E10
)
*
((
i
+
1
)
%
10
)
*
std
::
tan
(
3
*
i
+
1
));
}
Array
<
TinyVector
<
3
,
double
>>
array
(
array1
.
size
()
+
array2
.
size
()
+
array3
.
size
());
{
size_t
I
=
0
;
for
(
size_t
i
=
0
;
i
<
array1
.
size
();
++
i
)
{
array
[
I
++
]
=
array1
[
i
];
}
for
(
size_t
i
=
0
;
i
<
array2
.
size
();
++
i
)
{
array
[
I
++
]
=
array2
[
i
];
}
for
(
size_t
i
=
0
;
i
<
array3
.
size
();
++
i
)
{
array
[
I
++
]
=
array3
[
i
];
}
}
ReproducibleTinyVectorSum
s1
(
array1
);
ReproducibleTinyVectorSum
s2
(
array2
);
ReproducibleTinyVectorSum
s3
(
array3
);
using
RSumT
=
decltype
(
s1
);
RSumT
::
Bin
bin1
=
s1
.
getSummationBin
();
RSumT
::
Bin
bin2
=
s2
.
getSummationBin
();
RSumT
::
Bin
bin3
=
s3
.
getSummationBin
();
{
RSumT
::
Bin
bin_sum
=
zero
;
RSumT
::
addBinTo
(
bin1
,
bin_sum
);
RSumT
::
addBinTo
(
bin2
,
bin_sum
);
RSumT
::
addBinTo
(
bin3
,
bin_sum
);
REQUIRE
(
sum
(
array
)
==
RSumT
::
getValue
(
bin_sum
));
}
{
RSumT
::
Bin
bin_sum
=
zero
;
RSumT
::
addBinTo
(
bin3
,
bin_sum
);
RSumT
::
addBinTo
(
bin2
,
bin_sum
);
RSumT
::
addBinTo
(
bin1
,
bin_sum
);
REQUIRE
(
sum
(
array
)
==
RSumT
::
getValue
(
bin_sum
));
}
}
}
SECTION
(
"TinyMatrix bin summation"
)
{
SECTION
(
"small arrays"
)
{
Array
<
TinyMatrix
<
2
,
3
,
double
>>
array1
(
122
);
for
(
size_t
i
=
0
;
i
<
array1
.
size
();
++
i
)
{
array1
[
i
]
=
TinyMatrix
<
2
,
3
,
double
>
(((
i
<
(
array1
.
size
()
/
10
))
*
1E25
+
1E20
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
),
((
i
<
(
array1
.
size
()
/
50
))
*
1E15
+
1E10
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
3
*
i
+
1
),
((
i
<
(
array1
.
size
()
/
20
))
*
1E7
+
1E10
)
*
((
i
+
1
)
%
10
)
*
std
::
tan
(
3
*
i
+
1
),
((
i
<
(
array1
.
size
()
/
30
))
*
1E6
+
1E11
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
4
*
i
+
1
),
((
i
<
(
array1
.
size
()
/
70
))
*
1E8
+
1E13
)
*
((
i
+
1
)
%
100
)
*
std
::
sin
(
4
*
i
+
1
),
((
i
<
(
array1
.
size
()
/
11
))
*
1E8
+
1E9
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
4
*
i
+
1
));
}
Array
<
TinyMatrix
<
2
,
3
,
double
>>
array2
(
357
);
for
(
size_t
i
=
0
;
i
<
array2
.
size
();
++
i
)
{
array2
[
i
]
=
TinyMatrix
<
2
,
3
,
double
>
(((
i
<
(
array2
.
size
()
/
20
))
*
1E25
+
1E20
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
),
((
i
<
(
array2
.
size
()
/
70
))
*
1E15
+
1E10
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
3
*
i
+
1
),
((
i
<
(
array2
.
size
()
/
32
))
*
1E7
+
1E10
)
*
((
i
+
1
)
%
10
)
*
std
::
tan
(
3
*
i
+
1
),
((
i
<
(
array2
.
size
()
/
45
))
*
1E6
+
1E11
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
4
*
i
+
1
),
((
i
<
(
array2
.
size
()
/
66
))
*
1E8
+
1E13
)
*
((
i
+
1
)
%
100
)
*
std
::
sin
(
4
*
i
+
1
),
((
i
<
(
array2
.
size
()
/
13
))
*
1E8
+
1E9
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
4
*
i
+
1
));
}
Array
<
TinyMatrix
<
2
,
3
,
double
>>
array3
(
283
);
for
(
size_t
i
=
0
;
i
<
array3
.
size
();
++
i
)
{
array3
[
i
]
=
TinyMatrix
<
2
,
3
,
double
>
(((
i
<
(
array3
.
size
()
/
23
))
*
1E15
+
1E17
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
),
((
i
<
(
array3
.
size
()
/
67
))
*
1E15
+
1E10
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
3
*
i
+
1
),
((
i
<
(
array3
.
size
()
/
62
))
*
1E7
+
1E10
)
*
((
i
+
1
)
%
10
)
*
std
::
tan
(
3
*
i
+
1
),
((
i
<
(
array3
.
size
()
/
35
))
*
1E8
+
1E11
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
4
*
i
+
1
),
((
i
<
(
array3
.
size
()
/
63
))
*
1E7
+
1E12
)
*
((
i
+
1
)
%
100
)
*
std
::
sin
(
4
*
i
+
1
),
((
i
<
(
array3
.
size
()
/
17
))
*
1E9
+
1E8
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
4
*
i
+
1
));
}
Array
<
TinyMatrix
<
2
,
3
,
double
>>
array
(
array1
.
size
()
+
array2
.
size
()
+
array3
.
size
());
{
size_t
I
=
0
;
for
(
size_t
i
=
0
;
i
<
array1
.
size
();
++
i
)
{
array
[
I
++
]
=
array1
[
i
];
}
for
(
size_t
i
=
0
;
i
<
array2
.
size
();
++
i
)
{
array
[
I
++
]
=
array2
[
i
];
}
for
(
size_t
i
=
0
;
i
<
array3
.
size
();
++
i
)
{
array
[
I
++
]
=
array3
[
i
];
}
}
ReproducibleTinyMatrixSum
s1
(
array1
);
ReproducibleTinyMatrixSum
s2
(
array2
);
ReproducibleTinyMatrixSum
s3
(
array3
);
using
RSumT
=
decltype
(
s1
);
RSumT
::
Bin
bin1
=
s1
.
getSummationBin
();
RSumT
::
Bin
bin2
=
s2
.
getSummationBin
();
RSumT
::
Bin
bin3
=
s3
.
getSummationBin
();
{
RSumT
::
Bin
bin_sum
=
zero
;
RSumT
::
addBinTo
(
bin1
,
bin_sum
);
RSumT
::
addBinTo
(
bin2
,
bin_sum
);
RSumT
::
addBinTo
(
bin3
,
bin_sum
);
REQUIRE
(
sum
(
array
)
==
RSumT
::
getValue
(
bin_sum
));
}
{
RSumT
::
Bin
bin_sum
=
zero
;
RSumT
::
addBinTo
(
bin3
,
bin_sum
);
RSumT
::
addBinTo
(
bin2
,
bin_sum
);
RSumT
::
addBinTo
(
bin1
,
bin_sum
);
REQUIRE
(
sum
(
array
)
==
RSumT
::
getValue
(
bin_sum
));
}
}
SECTION
(
"small and large arrays"
)
{
Array
<
TinyMatrix
<
2
,
3
,
double
>>
array1
(
122
);
for
(
size_t
i
=
0
;
i
<
array1
.
size
();
++
i
)
{
array1
[
i
]
=
TinyMatrix
<
2
,
3
,
double
>
(((
i
<
(
array1
.
size
()
/
10
))
*
1E25
+
1E20
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
),
((
i
<
(
array1
.
size
()
/
50
))
*
1E15
+
1E10
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
3
*
i
+
1
),
((
i
<
(
array1
.
size
()
/
20
))
*
1E7
+
1E10
)
*
((
i
+
1
)
%
10
)
*
std
::
tan
(
3
*
i
+
1
),
((
i
<
(
array1
.
size
()
/
30
))
*
1E6
+
1E11
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
4
*
i
+
1
),
((
i
<
(
array1
.
size
()
/
70
))
*
1E8
+
1E13
)
*
((
i
+
1
)
%
100
)
*
std
::
sin
(
4
*
i
+
1
),
((
i
<
(
array1
.
size
()
/
11
))
*
1E8
+
1E9
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
4
*
i
+
1
));
}
Array
<
TinyMatrix
<
2
,
3
,
double
>>
array2
(
7357
);
for
(
size_t
i
=
0
;
i
<
array2
.
size
();
++
i
)
{
array2
[
i
]
=
TinyMatrix
<
2
,
3
,
double
>
(((
i
<
(
array2
.
size
()
/
20
))
*
1E25
+
1E20
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
),
((
i
<
(
array2
.
size
()
/
70
))
*
1E15
+
1E10
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
3
*
i
+
1
),
((
i
<
(
array2
.
size
()
/
32
))
*
1E7
+
1E10
)
*
((
i
+
1
)
%
10
)
*
std
::
tan
(
3
*
i
+
1
),
((
i
<
(
array2
.
size
()
/
45
))
*
1E6
+
1E11
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
4
*
i
+
1
),
((
i
<
(
array2
.
size
()
/
66
))
*
1E8
+
1E13
)
*
((
i
+
1
)
%
100
)
*
std
::
sin
(
4
*
i
+
1
),
((
i
<
(
array2
.
size
()
/
13
))
*
1E8
+
1E9
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
4
*
i
+
1
));
}
Array
<
TinyMatrix
<
2
,
3
,
double
>>
array3
(
283
);
for
(
size_t
i
=
0
;
i
<
array3
.
size
();
++
i
)
{
array3
[
i
]
=
TinyMatrix
<
2
,
3
,
double
>
(((
i
<
(
array3
.
size
()
/
23
))
*
1E15
+
1E17
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
),
((
i
<
(
array3
.
size
()
/
67
))
*
1E15
+
1E10
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
3
*
i
+
1
),
((
i
<
(
array3
.
size
()
/
62
))
*
1E7
+
1E10
)
*
((
i
+
1
)
%
10
)
*
std
::
tan
(
3
*
i
+
1
),
((
i
<
(
array3
.
size
()
/
35
))
*
1E8
+
1E11
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
4
*
i
+
1
),
((
i
<
(
array3
.
size
()
/
63
))
*
1E7
+
1E12
)
*
((
i
+
1
)
%
100
)
*
std
::
sin
(
4
*
i
+
1
),
((
i
<
(
array3
.
size
()
/
17
))
*
1E9
+
1E8
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
4
*
i
+
1
));
}
Array
<
TinyMatrix
<
2
,
3
,
double
>>
array
(
array1
.
size
()
+
array2
.
size
()
+
array3
.
size
());
{
size_t
I
=
0
;
for
(
size_t
i
=
0
;
i
<
array1
.
size
();
++
i
)
{
array
[
I
++
]
=
array1
[
i
];
}
for
(
size_t
i
=
0
;
i
<
array2
.
size
();
++
i
)
{
array
[
I
++
]
=
array2
[
i
];
}
for
(
size_t
i
=
0
;
i
<
array3
.
size
();
++
i
)
{
array
[
I
++
]
=
array3
[
i
];
}
}
ReproducibleTinyMatrixSum
s1
(
array1
);
ReproducibleTinyMatrixSum
s2
(
array2
);
ReproducibleTinyMatrixSum
s3
(
array3
);
using
RSumT
=
decltype
(
s1
);
RSumT
::
Bin
bin1
=
s1
.
getSummationBin
();
RSumT
::
Bin
bin2
=
s2
.
getSummationBin
();
RSumT
::
Bin
bin3
=
s3
.
getSummationBin
();
{
RSumT
::
Bin
bin_sum
=
zero
;
RSumT
::
addBinTo
(
bin1
,
bin_sum
);
RSumT
::
addBinTo
(
bin2
,
bin_sum
);
RSumT
::
addBinTo
(
bin3
,
bin_sum
);
REQUIRE
(
sum
(
array
)
==
RSumT
::
getValue
(
bin_sum
));
}
{
RSumT
::
Bin
bin_sum
=
zero
;
RSumT
::
addBinTo
(
bin3
,
bin_sum
);
RSumT
::
addBinTo
(
bin2
,
bin_sum
);
RSumT
::
addBinTo
(
bin1
,
bin_sum
);
REQUIRE
(
sum
(
array
)
==
RSumT
::
getValue
(
bin_sum
));
}
}
SECTION
(
"large arrays"
)
{
Array
<
TinyMatrix
<
2
,
3
,
double
>>
array1
(
3762
);
for
(
size_t
i
=
0
;
i
<
array1
.
size
();
++
i
)
{
array1
[
i
]
=
TinyMatrix
<
2
,
3
,
double
>
(((
i
<
(
array1
.
size
()
/
10
))
*
1E25
+
1E20
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
),
((
i
<
(
array1
.
size
()
/
50
))
*
1E15
+
1E10
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
3
*
i
+
1
),
((
i
<
(
array1
.
size
()
/
20
))
*
1E7
+
1E10
)
*
((
i
+
1
)
%
10
)
*
std
::
tan
(
3
*
i
+
1
),
((
i
<
(
array1
.
size
()
/
30
))
*
1E6
+
1E11
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
4
*
i
+
1
),
((
i
<
(
array1
.
size
()
/
70
))
*
1E8
+
1E13
)
*
((
i
+
1
)
%
100
)
*
std
::
sin
(
4
*
i
+
1
),
((
i
<
(
array1
.
size
()
/
11
))
*
1E8
+
1E9
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
4
*
i
+
1
));
}
Array
<
TinyMatrix
<
2
,
3
,
double
>>
array2
(
7357
);
for
(
size_t
i
=
0
;
i
<
array2
.
size
();
++
i
)
{
array2
[
i
]
=
TinyMatrix
<
2
,
3
,
double
>
(((
i
<
(
array2
.
size
()
/
20
))
*
1E25
+
1E20
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
),
((
i
<
(
array2
.
size
()
/
70
))
*
1E15
+
1E10
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
3
*
i
+
1
),
((
i
<
(
array2
.
size
()
/
32
))
*
1E7
+
1E10
)
*
((
i
+
1
)
%
10
)
*
std
::
tan
(
3
*
i
+
1
),
((
i
<
(
array2
.
size
()
/
45
))
*
1E6
+
1E11
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
4
*
i
+
1
),
((
i
<
(
array2
.
size
()
/
66
))
*
1E8
+
1E13
)
*
((
i
+
1
)
%
100
)
*
std
::
sin
(
4
*
i
+
1
),
((
i
<
(
array2
.
size
()
/
13
))
*
1E8
+
1E9
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
4
*
i
+
1
));
}
Array
<
TinyMatrix
<
2
,
3
,
double
>>
array3
(
6283
);
for
(
size_t
i
=
0
;
i
<
array3
.
size
();
++
i
)
{
array3
[
i
]
=
TinyMatrix
<
2
,
3
,
double
>
(((
i
<
(
array3
.
size
()
/
23
))
*
1E15
+
1E17
)
*
((
i
+
1
)
%
1'000
)
*
std
::
sin
(
3
*
i
+
1
),
((
i
<
(
array3
.
size
()
/
67
))
*
1E15
+
1E10
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
3
*
i
+
1
),
((
i
<
(
array3
.
size
()
/
62
))
*
1E7
+
1E10
)
*
((
i
+
1
)
%
10
)
*
std
::
tan
(
3
*
i
+
1
),
((
i
<
(
array3
.
size
()
/
35
))
*
1E8
+
1E11
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
4
*
i
+
1
),
((
i
<
(
array3
.
size
()
/
63
))
*
1E7
+
1E12
)
*
((
i
+
1
)
%
100
)
*
std
::
sin
(
4
*
i
+
1
),
((
i
<
(
array3
.
size
()
/
17
))
*
1E9
+
1E8
)
*
((
i
+
1
)
%
100
)
*
std
::
cos
(
4
*
i
+
1
));
}
Array
<
TinyMatrix
<
2
,
3
,
double
>>
array
(
array1
.
size
()
+
array2
.
size
()
+
array3
.
size
());
{
size_t
I
=
0
;
for
(
size_t
i
=
0
;
i
<
array1
.
size
();
++
i
)
{
array
[
I
++
]
=
array1
[
i
];
}
for
(
size_t
i
=
0
;
i
<
array2
.
size
();
++
i
)
{
array
[
I
++
]
=
array2
[
i
];
}
for
(
size_t
i
=
0
;
i
<
array3
.
size
();
++
i
)
{
array
[
I
++
]
=
array3
[
i
];
}
}
ReproducibleTinyMatrixSum
s1
(
array1
);
ReproducibleTinyMatrixSum
s2
(
array2
);
ReproducibleTinyMatrixSum
s3
(
array3
);
using
RSumT
=
decltype
(
s1
);
RSumT
::
Bin
bin1
=
s1
.
getSummationBin
();
RSumT
::
Bin
bin2
=
s2
.
getSummationBin
();
RSumT
::
Bin
bin3
=
s3
.
getSummationBin
();
{
RSumT
::
Bin
bin_sum
=
zero
;
RSumT
::
addBinTo
(
bin1
,
bin_sum
);
RSumT
::
addBinTo
(
bin2
,
bin_sum
);
RSumT
::
addBinTo
(
bin3
,
bin_sum
);
REQUIRE
(
sum
(
array
)
==
RSumT
::
getValue
(
bin_sum
));
}
{
RSumT
::
Bin
bin_sum
=
zero
;
RSumT
::
addBinTo
(
bin3
,
bin_sum
);
RSumT
::
addBinTo
(
bin2
,
bin_sum
);
RSumT
::
addBinTo
(
bin1
,
bin_sum
);
REQUIRE
(
sum
(
array
)
==
RSumT
::
getValue
(
bin_sum
));
}
}
}
}
...
...
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