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Martin Reinecke
ducc
Commits
c37e6c89
Commit
c37e6c89
authored
Jul 02, 2020
by
Martin Reinecke
Browse files
smaller
parent
656634b4
Pipeline
#77751
passed with stages
in 13 minutes and 3 seconds
Changes
1
Pipelines
1
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Inline
Side-by-side
src/ducc0/math/horner_kernel.h
View file @
c37e6c89
...
...
@@ -34,6 +34,48 @@ namespace detail_horner_kernel {
using
namespace
std
;
constexpr
double
pi
=
3.141592653589793238462643383279502884197
;
template
<
typename
Func
>
vector
<
double
>
getCoeffs
(
size_t
W
,
size_t
D
,
Func
func
)
{
vector
<
double
>
coeff
(
W
*
(
D
+
1
));
vector
<
double
>
chebroot
(
D
+
1
);
for
(
size_t
i
=
0
;
i
<=
D
;
++
i
)
chebroot
[
i
]
=
cos
((
2
*
i
+
1.
)
*
pi
/
(
2
*
D
+
2
));
vector
<
double
>
y
(
D
+
1
),
lcf
(
D
+
1
),
C
((
D
+
1
)
*
(
D
+
1
)),
lcf2
(
D
+
1
);
for
(
size_t
i
=
0
;
i
<
W
;
++
i
)
{
double
l
=
-
1
+
2.
*
i
/
double
(
W
);
double
r
=
-
1
+
2.
*
(
i
+
1
)
/
double
(
W
);
// function values at Chebyshev nodes
for
(
size_t
j
=
0
;
j
<=
D
;
++
j
)
y
[
j
]
=
func
(
chebroot
[
j
]
*
(
r
-
l
)
*
0.5
+
(
r
+
l
)
*
0.5
);
// Chebyshev coefficients
for
(
size_t
j
=
0
;
j
<=
D
;
++
j
)
{
lcf
[
j
]
=
0
;
for
(
size_t
k
=
0
;
k
<=
D
;
++
k
)
lcf
[
j
]
+=
2.
/
(
D
+
1
)
*
y
[
k
]
*
cos
(
j
*
(
2
*
k
+
1
)
*
pi
/
(
2
*
D
+
2
));
}
lcf
[
0
]
*=
0.5
;
// Polynomial coefficients
fill
(
C
.
begin
(),
C
.
end
(),
0.
);
C
[
0
]
=
1.
;
C
[
1
*
(
D
+
1
)
+
1
]
=
1.
;
for
(
size_t
j
=
2
;
j
<=
D
;
++
j
)
{
C
[
j
*
(
D
+
1
)
+
0
]
=
-
C
[(
j
-
2
)
*
(
D
+
1
)
+
0
];
for
(
size_t
k
=
1
;
k
<=
j
;
++
k
)
C
[
j
*
(
D
+
1
)
+
k
]
=
2
*
C
[(
j
-
1
)
*
(
D
+
1
)
+
k
-
1
]
-
C
[(
j
-
2
)
*
(
D
+
1
)
+
k
];
}
for
(
size_t
j
=
0
;
j
<=
D
;
++
j
)
lcf2
[
j
]
=
0
;
for
(
size_t
j
=
0
;
j
<=
D
;
++
j
)
for
(
size_t
k
=
0
;
k
<=
D
;
++
k
)
lcf2
[
k
]
+=
C
[
j
*
(
D
+
1
)
+
k
]
*
lcf
[
j
];
for
(
size_t
j
=
0
;
j
<=
D
;
++
j
)
coeff
[
j
*
W
+
i
]
=
lcf2
[
D
-
j
];
}
return
coeff
;
}
/*! Class providing fast piecewise polynomial approximation of a function which
is defined on the interval [-1;1]
...
...
@@ -58,49 +100,13 @@ template<size_t W, size_t D, typename T> class HornerKernel
public:
template
<
typename
Func
>
HornerKernel
(
Func
func
)
{
for
(
size_t
i
=
0
;
i
<=
D
;
++
i
)
for
(
size_t
j
=
0
;
j
<
nvec
;
++
j
)
coeff
[
i
][
j
]
=
0
;
array
<
double
,
D
+
1
>
chebroot
;
for
(
size_t
i
=
0
;
i
<=
D
;
++
i
)
chebroot
[
i
]
=
cos
((
2
*
i
+
1.
)
*
pi
/
(
2
*
D
+
2
));
for
(
size_t
i
=
0
;
i
<
W
;
++
i
)
auto
coeff_raw
=
getCoeffs
(
W
,
D
,
func
);
for
(
size_t
j
=
0
;
j
<=
D
;
++
j
)
{
double
l
=
-
1
+
2.
*
i
/
double
(
W
);
double
r
=
-
1
+
2.
*
(
i
+
1
)
/
double
(
W
);
// function values at Chebyshev nodes
array
<
double
,
D
+
1
>
y
;
for
(
size_t
j
=
0
;
j
<=
D
;
++
j
)
y
[
j
]
=
func
(
chebroot
[
j
]
*
(
r
-
l
)
*
0.5
+
(
r
+
l
)
*
0.5
);
// Chebyshev coefficients
array
<
double
,
D
+
1
>
lcf
;
for
(
size_t
j
=
0
;
j
<=
D
;
++
j
)
{
lcf
[
j
]
=
0
;
for
(
size_t
k
=
0
;
k
<=
D
;
++
k
)
lcf
[
j
]
+=
2.
/
(
D
+
1
)
*
y
[
k
]
*
cos
(
j
*
(
2
*
k
+
1
)
*
pi
/
(
2
*
D
+
2
));
}
lcf
[
0
]
*=
0.5
;
// Polynomial coefficients
array
<
array
<
double
,
D
+
1
>
,
D
+
1
>
C
;
for
(
size_t
j
=
0
;
j
<=
D
;
++
j
)
for
(
size_t
k
=
0
;
k
<=
D
;
++
k
)
C
[
j
][
k
]
=
0
;
C
[
0
][
0
]
=
1.
;
C
[
1
][
1
]
=
1.
;
for
(
size_t
j
=
2
;
j
<=
D
;
++
j
)
{
C
[
j
][
0
]
=
-
C
[
j
-
2
][
0
];
for
(
size_t
k
=
1
;
k
<=
j
;
++
k
)
C
[
j
][
k
]
=
2
*
C
[
j
-
1
][
k
-
1
]
-
C
[
j
-
2
][
k
];
}
array
<
double
,
D
+
1
>
lcf2
;
for
(
size_t
j
=
0
;
j
<=
D
;
++
j
)
lcf2
[
j
]
=
0
;
for
(
size_t
j
=
0
;
j
<=
D
;
++
j
)
for
(
size_t
k
=
0
;
k
<=
D
;
++
k
)
lcf2
[
k
]
+=
C
[
j
][
k
]
*
lcf
[
j
];
for
(
size_t
j
=
0
;
j
<=
D
;
++
j
)
coeff
[
j
][
i
/
vlen
][
i
%
vlen
]
=
T
(
lcf2
[
D
-
j
]);
for
(
size_t
i
=
0
;
i
<
W
;
++
i
)
coeff
[
j
][
i
/
vlen
][
i
%
vlen
]
=
T
(
coeff_raw
[
j
*
W
+
i
]);
for
(
size_t
i
=
W
;
i
<
vlen
*
nvec
;
++
i
)
coeff
[
j
][
i
/
vlen
][
i
%
vlen
]
=
T
(
0
);
}
}
...
...
@@ -187,41 +193,13 @@ template<typename T> class HornerKernelFlexible
:
W
(
W_
),
D
(
D_
),
nvec
((
W
+
vlen
-
1
)
/
vlen
),
res
(
nvec
),
coeff
(
nvec
*
(
D
+
1
),
0
),
evalfunc
(
evfhelper1
<
1
>
())
{
vector
<
double
>
chebroot
(
D
+
1
);
for
(
size_t
i
=
0
;
i
<=
D
;
++
i
)
chebroot
[
i
]
=
cos
((
2
*
i
+
1.
)
*
pi
/
(
2
*
D
+
2
));
vector
<
double
>
y
(
D
+
1
),
lcf
(
D
+
1
),
C
((
D
+
1
)
*
(
D
+
1
)),
lcf2
(
D
+
1
);
for
(
size_t
i
=
0
;
i
<
W
;
++
i
)
auto
coeff_raw
=
getCoeffs
(
W
,
D
,
func
);
for
(
size_t
j
=
0
;
j
<=
D
;
++
j
)
{
double
l
=
-
1
+
2.
*
i
/
double
(
W
);
double
r
=
-
1
+
2.
*
(
i
+
1
)
/
double
(
W
);
// function values at Chebyshev nodes
for
(
size_t
j
=
0
;
j
<=
D
;
++
j
)
y
[
j
]
=
func
(
chebroot
[
j
]
*
(
r
-
l
)
*
0.5
+
(
r
+
l
)
*
0.5
);
// Chebyshev coefficients
for
(
size_t
j
=
0
;
j
<=
D
;
++
j
)
{
lcf
[
j
]
=
0
;
for
(
size_t
k
=
0
;
k
<=
D
;
++
k
)
lcf
[
j
]
+=
2.
/
(
D
+
1
)
*
y
[
k
]
*
cos
(
j
*
(
2
*
k
+
1
)
*
pi
/
(
2
*
D
+
2
));
}
lcf
[
0
]
*=
0.5
;
// Polynomial coefficients
fill
(
C
.
begin
(),
C
.
end
(),
0.
);
C
[
0
]
=
1.
;
C
[
1
*
(
D
+
1
)
+
1
]
=
1.
;
for
(
size_t
j
=
2
;
j
<=
D
;
++
j
)
{
C
[
j
*
(
D
+
1
)
+
0
]
=
-
C
[(
j
-
2
)
*
(
D
+
1
)
+
0
];
for
(
size_t
k
=
1
;
k
<=
j
;
++
k
)
C
[
j
*
(
D
+
1
)
+
k
]
=
2
*
C
[(
j
-
1
)
*
(
D
+
1
)
+
k
-
1
]
-
C
[(
j
-
2
)
*
(
D
+
1
)
+
k
];
}
for
(
size_t
j
=
0
;
j
<=
D
;
++
j
)
lcf2
[
j
]
=
0
;
for
(
size_t
j
=
0
;
j
<=
D
;
++
j
)
for
(
size_t
k
=
0
;
k
<=
D
;
++
k
)
lcf2
[
k
]
+=
C
[
j
*
(
D
+
1
)
+
k
]
*
lcf
[
j
];
for
(
size_t
j
=
0
;
j
<=
D
;
++
j
)
coeff
[
j
*
nvec
+
i
/
vlen
][
i
%
vlen
]
=
T
(
lcf2
[
D
-
j
]);
for
(
size_t
i
=
0
;
i
<
W
;
++
i
)
coeff
[
j
*
nvec
+
i
/
vlen
][
i
%
vlen
]
=
T
(
coeff_raw
[
j
*
W
+
i
]);
for
(
size_t
i
=
W
;
i
<
vlen
*
nvec
;
++
i
)
coeff
[
j
*
nvec
+
i
/
vlen
][
i
%
vlen
]
=
T
(
0
);
}
}
...
...
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