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pypocketfft
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Martin Reinecke
pypocketfft
Commits
50476533
Commit
50476533
authored
Jul 22, 2019
by
Martin Reinecke
Browse files
Options
Browse Files
Download
Plain Diff
Merge branch 'cleanup' into 'master'
Cleanup See merge request
!15
parents
656b2373
88f64fcf
Changes
1
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1 changed file
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133 additions
and
237 deletions
+133
-237
pocketfft_hdronly.h
pocketfft_hdronly.h
+133
-237
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pocketfft_hdronly.h
View file @
50476533
...
@@ -209,13 +209,19 @@ template<typename T> struct cmplx {
...
@@ -209,13 +209,19 @@ template<typename T> struct cmplx {
r
=
tmp
;
r
=
tmp
;
return
*
this
;
return
*
this
;
}
}
cmplx
operator
+
(
const
cmplx
&
other
)
const
template
<
typename
T2
>
cmplx
&
operator
+=
(
const
cmplx
<
T2
>
&
other
)
{
r
eturn
cmplx
(
r
+
other
.
r
,
i
+
other
.
i
)
;
}
{
r
+=
other
.
r
;
i
+=
other
.
i
;
return
*
this
;
}
cmplx
operator
-
(
const
cmplx
&
other
)
const
template
<
typename
T2
>
cmplx
&
operator
-=
(
const
cmplx
<
T2
>
&
other
)
{
r
eturn
cmplx
(
r
-
other
.
r
,
i
-
other
.
i
)
;
}
{
r
-=
other
.
r
;
i
-=
other
.
i
;
return
*
this
;
}
template
<
typename
T2
>
auto
operator
*
(
const
T2
&
other
)
const
template
<
typename
T2
>
auto
operator
*
(
const
T2
&
other
)
const
->
cmplx
<
decltype
(
r
*
other
)
>
->
cmplx
<
decltype
(
r
*
other
)
>
{
return
{
r
*
other
,
i
*
other
};
}
{
return
{
r
*
other
,
i
*
other
};
}
template
<
typename
T2
>
auto
operator
+
(
const
cmplx
<
T2
>
&
other
)
const
->
cmplx
<
decltype
(
r
+
other
.
r
)
>
{
return
{
r
+
other
.
r
,
i
+
other
.
i
};
}
template
<
typename
T2
>
auto
operator
-
(
const
cmplx
<
T2
>
&
other
)
const
->
cmplx
<
decltype
(
r
+
other
.
r
)
>
{
return
{
r
-
other
.
r
,
i
-
other
.
i
};
}
template
<
typename
T2
>
auto
operator
*
(
const
cmplx
<
T2
>
&
other
)
const
template
<
typename
T2
>
auto
operator
*
(
const
cmplx
<
T2
>
&
other
)
const
->
cmplx
<
decltype
(
r
+
other
.
r
)
>
->
cmplx
<
decltype
(
r
+
other
.
r
)
>
{
return
{
r
*
other
.
r
-
i
*
other
.
i
,
r
*
other
.
i
+
i
*
other
.
r
};
}
{
return
{
r
*
other
.
r
-
i
*
other
.
i
,
r
*
other
.
i
+
i
*
other
.
r
};
}
...
@@ -227,8 +233,9 @@ template<typename T> struct cmplx {
...
@@ -227,8 +233,9 @@ template<typename T> struct cmplx {
:
Tres
(
r
*
other
.
r
-
i
*
other
.
i
,
r
*
other
.
i
+
i
*
other
.
r
);
:
Tres
(
r
*
other
.
r
-
i
*
other
.
i
,
r
*
other
.
i
+
i
*
other
.
r
);
}
}
};
};
template
<
typename
T
>
void
PMC
(
cmplx
<
T
>
&
a
,
cmplx
<
T
>
&
b
,
template
<
typename
T
>
inline
void
PMINPLACE
(
T
&
a
,
T
&
b
)
const
cmplx
<
T
>
&
c
,
const
cmplx
<
T
>
&
d
)
{
T
t
=
a
;
a
+=
b
;
b
=
t
-
b
;
}
template
<
typename
T
>
void
PMC
(
T
&
a
,
T
&
b
,
const
T
&
c
,
const
T
&
d
)
{
a
=
c
+
d
;
b
=
c
-
d
;
}
{
a
=
c
+
d
;
b
=
c
-
d
;
}
template
<
typename
T
>
cmplx
<
T
>
conj
(
const
cmplx
<
T
>
&
a
)
template
<
typename
T
>
cmplx
<
T
>
conj
(
const
cmplx
<
T
>
&
a
)
{
return
{
a
.
r
,
-
a
.
i
};
}
{
return
{
a
.
r
,
-
a
.
i
};
}
...
@@ -845,8 +852,6 @@ template <bool fwd, typename T> void ROTX135(T &a)
...
@@ -845,8 +852,6 @@ template <bool fwd, typename T> void ROTX135(T &a)
else
else
{
auto
tmp_
=
a
.
r
;
a
.
r
=
hsqt2
*
(
-
a
.
r
-
a
.
i
);
a
.
i
=
hsqt2
*
(
tmp_
-
a
.
i
);
}
{
auto
tmp_
=
a
.
r
;
a
.
r
=
hsqt2
*
(
-
a
.
r
-
a
.
i
);
a
.
i
=
hsqt2
*
(
tmp_
-
a
.
i
);
}
}
}
template
<
typename
T
>
inline
void
PMINPLACE
(
T
&
a
,
T
&
b
)
{
T
t
=
a
;
a
.
r
+=
b
.
r
;
a
.
i
+=
b
.
i
;
b
.
r
=
t
.
r
-
b
.
r
;
b
.
i
=
t
.
i
-
b
.
i
;
}
template
<
bool
fwd
,
typename
T
>
void
pass8
(
size_t
ido
,
size_t
l1
,
template
<
bool
fwd
,
typename
T
>
void
pass8
(
size_t
ido
,
size_t
l1
,
const
T
*
POCKETFFT_RESTRICT
cc
,
T
*
POCKETFFT_RESTRICT
ch
,
const
T
*
POCKETFFT_RESTRICT
cc
,
T
*
POCKETFFT_RESTRICT
ch
,
...
@@ -2293,6 +2298,7 @@ template<typename T0> class pocketfft_r
...
@@ -2293,6 +2298,7 @@ template<typename T0> class pocketfft_r
//
//
// sine/cosine transforms
// sine/cosine transforms
//
//
template
<
typename
T0
>
class
T_dct1
template
<
typename
T0
>
class
T_dct1
{
{
private:
private:
...
@@ -2302,7 +2308,8 @@ template<typename T0> class T_dct1
...
@@ -2302,7 +2308,8 @@ template<typename T0> class T_dct1
POCKETFFT_NOINLINE
T_dct1
(
size_t
length
)
POCKETFFT_NOINLINE
T_dct1
(
size_t
length
)
:
fftplan
(
2
*
(
length
-
1
))
{}
:
fftplan
(
2
*
(
length
-
1
))
{}
template
<
typename
T
>
POCKETFFT_NOINLINE
void
exec
(
T
c
[],
T0
fct
,
bool
ortho
)
const
template
<
typename
T
>
POCKETFFT_NOINLINE
void
exec
(
T
c
[],
T0
fct
,
bool
ortho
,
int
/*type*/
,
bool
/*cosine*/
)
const
{
{
constexpr
T0
sqrt2
=
T0
(
1.414213562373095048801688724209698
L
);
constexpr
T0
sqrt2
=
T0
(
1.414213562373095048801688724209698
L
);
size_t
N
=
fftplan
.
length
(),
n
=
N
/
2
+
1
;
size_t
N
=
fftplan
.
length
(),
n
=
N
/
2
+
1
;
...
@@ -2323,126 +2330,124 @@ template<typename T0> class T_dct1
...
@@ -2323,126 +2330,124 @@ template<typename T0> class T_dct1
size_t
length
()
const
{
return
fftplan
.
length
()
/
2
+
1
;
}
size_t
length
()
const
{
return
fftplan
.
length
()
/
2
+
1
;
}
};
};
template
<
typename
T0
>
class
T_d
ct2
template
<
typename
T0
>
class
T_d
st1
{
{
private:
private:
pocketfft_r
<
T0
>
fftplan
;
pocketfft_r
<
T0
>
fftplan
;
vector
<
T0
>
twiddle
;
public:
public:
POCKETFFT_NOINLINE
T_dct2
(
size_t
length
)
POCKETFFT_NOINLINE
T_dst1
(
size_t
length
)
:
fftplan
(
length
),
twiddle
(
length
)
:
fftplan
(
2
*
(
length
+
1
))
{}
{
constexpr
T0
pi
=
T0
(
3.141592653589793238462643383279502884197
L
);
for
(
size_t
i
=
0
;
i
<
length
;
++
i
)
twiddle
[
i
]
=
T0
(
cos
(
0.5
*
pi
*
T0
(
i
+
1
)
/
T0
(
length
)));
}
template
<
typename
T
>
POCKETFFT_NOINLINE
void
exec
(
T
c
[],
T0
fct
,
bool
ortho
)
const
template
<
typename
T
>
POCKETFFT_NOINLINE
void
exec
(
T
c
[],
T0
fct
,
bool
/*ortho*/
,
int
/*type*/
,
bool
/*cosine*/
)
const
{
{
constexpr
T0
sqrt2
=
T0
(
1.414213562373095048801688724209698
L
);
size_t
N
=
fftplan
.
length
(),
n
=
N
/
2
-
1
;
size_t
N
=
length
();
arr
<
T
>
tmp
(
N
);
if
(
N
==
1
)
tmp
[
0
]
=
tmp
[
n
+
1
]
=
c
[
0
]
*
0
;
c
[
0
]
*=
2
*
fct
;
for
(
size_t
i
=
0
;
i
<
n
;
++
i
)
else
if
(
N
==
2
)
{
T
x1
=
2
*
fct
*
(
c
[
0
]
+
c
[
1
]);
c
[
1
]
=
sqrt2
*
fct
*
(
c
[
0
]
-
c
[
1
]);
c
[
0
]
=
x1
;
}
else
{
{
size_t
NS2
=
(
N
+
1
)
/
2
;
tmp
[
i
+
1
]
=
c
[
i
];
for
(
size_t
i
=
2
;
i
<
N
;
i
+=
2
)
tmp
[
N
-
1
-
i
]
=
-
c
[
i
];
{
T
xim1
=
T0
(
0.5
)
*
(
c
[
i
-
1
]
+
c
[
i
]);
c
[
i
]
=
T0
(
0.5
)
*
(
c
[
i
]
-
c
[
i
-
1
]);
c
[
i
-
1
]
=
xim1
;
}
fftplan
.
backward
(
c
,
fct
);
for
(
size_t
k
=
1
,
kc
=
N
-
1
;
k
<
NS2
;
++
k
,
--
kc
)
{
T
tmp
=
twiddle
[
k
-
1
]
*
c
[
kc
]
+
twiddle
[
kc
-
1
]
*
c
[
k
];
c
[
kc
]
=
twiddle
[
k
-
1
]
*
c
[
k
]
-
twiddle
[
kc
-
1
]
*
c
[
kc
];
c
[
k
]
=
tmp
;
}
if
((
N
&
1
)
==
0
)
c
[
NS2
]
=
twiddle
[
NS2
-
1
]
*
(
c
[
NS2
]
+
c
[
NS2
]);
for
(
size_t
k
=
1
,
kc
=
N
-
1
;
k
<
NS2
;
++
k
,
--
kc
)
{
T
tmp
=
c
[
k
]
+
c
[
kc
];
c
[
kc
]
=
c
[
k
]
-
c
[
kc
];
c
[
k
]
=
tmp
;
}
c
[
0
]
*=
2
;
}
}
if
(
ortho
)
c
[
0
]
/=
sqrt2
;
fftplan
.
forward
(
tmp
.
data
(),
fct
);
for
(
size_t
i
=
0
;
i
<
n
;
++
i
)
c
[
i
]
=
-
tmp
[
2
*
i
+
2
];
}
}
size_t
length
()
const
{
return
fftplan
.
length
();
}
size_t
length
()
const
{
return
fftplan
.
length
()
/
2
-
1
;
}
};
};
template
<
typename
T0
>
class
T_dc
t
3
template
<
typename
T0
>
class
T_dc
st2
3
{
{
private:
private:
pocketfft_r
<
T0
>
fftplan
;
pocketfft_r
<
T0
>
fftplan
;
vector
<
T0
>
twiddle
;
vector
<
T0
>
twiddle
;
public:
template
<
typename
T
>
POCKETFFT_NOINLINE
void
exec2
(
T
c
[],
T0
fct
,
POCKETFFT_NOINLINE
T_dct3
(
size_t
length
)
bool
ortho
,
bool
cosine
)
const
:
fftplan
(
length
),
twiddle
(
length
)
{
{
constexpr
T0
pi
=
T0
(
3.141592653589793238462643383279502884197
L
);
constexpr
T0
sqrt2
=
T0
(
1.414213562373095048801688724209698
L
);
for
(
size_t
i
=
0
;
i
<
length
;
++
i
)
size_t
N
=
length
();
twiddle
[
i
]
=
T0
(
cos
(
0.5
*
pi
*
T0
(
i
+
1
)
/
T0
(
length
)));
size_t
NS2
=
(
N
+
1
)
/
2
;
if
(
!
cosine
)
for
(
size_t
k
=
1
;
k
<
N
;
k
+=
2
)
c
[
k
]
=
-
c
[
k
];
for
(
size_t
i
=
2
;
i
<
N
;
i
+=
2
)
{
T
xim1
=
T0
(
0.5
)
*
(
c
[
i
-
1
]
+
c
[
i
]);
c
[
i
]
=
T0
(
0.5
)
*
(
c
[
i
]
-
c
[
i
-
1
]);
c
[
i
-
1
]
=
xim1
;
}
fftplan
.
backward
(
c
,
fct
);
for
(
size_t
k
=
1
,
kc
=
N
-
1
;
k
<
NS2
;
++
k
,
--
kc
)
{
T
tmp
=
twiddle
[
k
-
1
]
*
c
[
kc
]
+
twiddle
[
kc
-
1
]
*
c
[
k
];
c
[
kc
]
=
twiddle
[
k
-
1
]
*
c
[
k
]
-
twiddle
[
kc
-
1
]
*
c
[
kc
];
c
[
k
]
=
tmp
;
}
if
((
N
&
1
)
==
0
)
c
[
NS2
]
=
twiddle
[
NS2
-
1
]
*
(
c
[
NS2
]
+
c
[
NS2
]);
for
(
size_t
k
=
1
,
kc
=
N
-
1
;
k
<
NS2
;
++
k
,
--
kc
)
PMINPLACE
(
c
[
k
],
c
[
kc
]);
c
[
0
]
*=
2
;
if
(
!
cosine
)
for
(
size_t
k
=
0
,
kc
=
N
-
1
;
k
<
kc
;
++
k
,
--
kc
)
swap
(
c
[
k
],
c
[
kc
]);
if
(
ortho
)
c
[
0
]
/=
sqrt2
;
}
}
template
<
typename
T
>
POCKETFFT_NOINLINE
void
exec
(
T
c
[],
T0
fct
,
bool
ortho
)
const
template
<
typename
T
>
POCKETFFT_NOINLINE
void
exec3
(
T
c
[],
T0
fct
,
bool
ortho
,
bool
cosine
)
const
{
{
constexpr
T0
sqrt2
=
T0
(
1.414213562373095048801688724209698
L
);
constexpr
T0
sqrt2
=
T0
(
1.414213562373095048801688724209698
L
);
size_t
N
=
length
();
size_t
N
=
length
();
if
(
ortho
)
c
[
0
]
*=
sqrt2
;
if
(
ortho
)
c
[
0
]
*=
sqrt2
;
if
(
N
==
1
)
size_t
NS2
=
(
N
+
1
)
/
2
;
c
[
0
]
*=
fct
;
if
(
!
cosine
)
else
if
(
N
==
2
)
for
(
size_t
k
=
0
,
kc
=
N
-
1
;
k
<
NS2
;
++
k
,
--
kc
)
swap
(
c
[
k
],
c
[
kc
]);
for
(
size_t
k
=
1
,
kc
=
N
-
1
;
k
<
NS2
;
++
k
,
--
kc
)
PMINPLACE
(
c
[
k
],
c
[
kc
]);
if
((
N
&
1
)
==
0
)
c
[
NS2
]
=
c
[
NS2
]
+
c
[
NS2
];
for
(
size_t
k
=
1
,
kc
=
N
-
1
;
k
<
NS2
;
++
k
,
--
kc
)
{
{
T
TSQX
=
sqrt2
*
c
[
1
];
T
tmp
=
twiddle
[
k
-
1
]
*
c
[
k
]
-
twiddle
[
kc
-
1
]
*
c
[
kc
];
c
[
1
]
=
fct
*
(
c
[
0
]
-
TSQX
)
;
c
[
k
]
=
twiddle
[
k
-
1
]
*
c
[
kc
]
+
twiddle
[
kc
-
1
]
*
c
[
k
]
;
c
[
0
]
=
fct
*
(
c
[
0
]
+
TSQX
)
;
c
[
kc
]
=
tmp
;
}
}
else
if
((
N
&
1
)
==
0
)
c
[
NS2
]
=
twiddle
[
NS2
-
1
]
*
c
[
NS2
];
fftplan
.
forward
(
c
,
fct
);
for
(
size_t
i
=
2
;
i
<
N
;
i
+=
2
)
{
{
size_t
NS2
=
(
N
+
1
)
/
2
;
T
xim1
=
c
[
i
-
1
]
-
c
[
i
];
for
(
size_t
k
=
1
,
kc
=
N
-
1
;
k
<
NS2
;
++
k
,
--
kc
)
c
[
i
]
+=
c
[
i
-
1
];
{
c
[
i
-
1
]
=
xim1
;
T
tmp
=
c
[
k
]
-
c
[
kc
];
c
[
k
]
=
c
[
k
]
+
c
[
kc
];
c
[
kc
]
=
tmp
;
}
if
((
N
&
1
)
==
0
)
c
[
NS2
]
=
c
[
NS2
]
+
c
[
NS2
];
for
(
size_t
k
=
1
,
kc
=
N
-
1
;
k
<
NS2
;
++
k
,
--
kc
)
{
T
tmp
=
twiddle
[
k
-
1
]
*
c
[
k
]
-
twiddle
[
kc
-
1
]
*
c
[
kc
];
c
[
k
]
=
twiddle
[
k
-
1
]
*
c
[
kc
]
+
twiddle
[
kc
-
1
]
*
c
[
k
];
c
[
kc
]
=
tmp
;
}
if
((
N
&
1
)
==
0
)
c
[
NS2
]
=
twiddle
[
NS2
-
1
]
*
c
[
NS2
];
fftplan
.
forward
(
c
,
fct
);
for
(
size_t
i
=
2
;
i
<
N
;
i
+=
2
)
{
T
xim1
=
c
[
i
-
1
]
-
c
[
i
];
c
[
i
]
+=
c
[
i
-
1
];
c
[
i
-
1
]
=
xim1
;
}
}
}
if
(
!
cosine
)
for
(
size_t
k
=
1
;
k
<
N
;
k
+=
2
)
c
[
k
]
=
-
c
[
k
];
}
public:
POCKETFFT_NOINLINE
T_dcst23
(
size_t
length
)
:
fftplan
(
length
),
twiddle
(
length
)
{
constexpr
T0
pi
=
T0
(
3.141592653589793238462643383279502884197
L
);
for
(
size_t
i
=
0
;
i
<
length
;
++
i
)
twiddle
[
i
]
=
T0
(
cos
(
0.5
*
pi
*
T0
(
i
+
1
)
/
T0
(
length
)));
}
}
template
<
typename
T
>
POCKETFFT_NOINLINE
void
exec
(
T
c
[],
T0
fct
,
bool
ortho
,
int
type
,
bool
cosine
)
const
{
type
==
2
?
exec2
(
c
,
fct
,
ortho
,
cosine
)
:
exec3
(
c
,
fct
,
ortho
,
cosine
);
}
size_t
length
()
const
{
return
fftplan
.
length
();
}
size_t
length
()
const
{
return
fftplan
.
length
();
}
};
};
template
<
typename
T0
>
class
T_dct4
template
<
typename
T0
>
class
T_dc
s
t4
{
{
// even length algorithm from
// even length algorithm from
// https://www.appletonaudio.com/blog/2013/derivation-of-fast-dct-4-algorithm-based-on-dft/
// https://www.appletonaudio.com/blog/2013/derivation-of-fast-dct-4-algorithm-based-on-dft/
...
@@ -2453,7 +2458,7 @@ template<typename T0> class T_dct4
...
@@ -2453,7 +2458,7 @@ template<typename T0> class T_dct4
arr
<
cmplx
<
T0
>>
C2
;
arr
<
cmplx
<
T0
>>
C2
;
public:
public:
POCKETFFT_NOINLINE
T_dct4
(
size_t
length
)
POCKETFFT_NOINLINE
T_dc
s
t4
(
size_t
length
)
:
N
(
length
),
:
N
(
length
),
fft
((
N
&
1
)
?
nullptr
:
new
pocketfft_c
<
T0
>
(
N
/
2
)),
fft
((
N
&
1
)
?
nullptr
:
new
pocketfft_c
<
T0
>
(
N
/
2
)),
rfft
((
N
&
1
)
?
new
pocketfft_r
<
T0
>
(
N
)
:
nullptr
),
rfft
((
N
&
1
)
?
new
pocketfft_r
<
T0
>
(
N
)
:
nullptr
),
...
@@ -2468,9 +2473,14 @@ template<typename T0> class T_dct4
...
@@ -2468,9 +2473,14 @@ template<typename T0> class T_dct4
}
}
}
}
template
<
typename
T
>
POCKETFFT_NOINLINE
void
exec
(
T
c
[],
T0
fct
,
bool
/*ortho*/
)
const
template
<
typename
T
>
POCKETFFT_NOINLINE
void
exec
(
T
c
[],
T0
fct
,
bool
/*ortho*/
,
int
/*type*/
,
bool
cosine
)
const
{
{
constexpr
T0
sqrt2
=
T0
(
1.414213562373095048801688724209698
L
);
constexpr
T0
sqrt2
=
T0
(
1.414213562373095048801688724209698
L
);
size_t
n2
=
N
/
2
;
if
(
!
cosine
)
for
(
size_t
k
=
0
,
kc
=
N
-
1
;
k
<
n2
;
++
k
,
--
kc
)
swap
(
c
[
k
],
c
[
kc
]);
if
(
N
&
1
)
if
(
N
&
1
)
{
{
// The following code is derived from the FFTW3 function apply_re11()
// The following code is derived from the FFTW3 function apply_re11()
...
@@ -2479,11 +2489,9 @@ template<typename T0> class T_dct4
...
@@ -2479,11 +2489,9 @@ template<typename T0> class T_dct4
auto
SGN_SET
=
[](
T
x
,
size_t
i
)
{
return
(
i
%
2
)
?
-
x
:
x
;};
auto
SGN_SET
=
[](
T
x
,
size_t
i
)
{
return
(
i
%
2
)
?
-
x
:
x
;};
arr
<
T
>
y
(
N
);
arr
<
T
>
y
(
N
);
size_t
n2
=
N
/
2
;
size_t
i
;
{
{
size_t
m
;
size_t
i
=
0
,
m
=
n2
;
for
(
i
=
0
,
m
=
n2
;
m
<
N
;
++
i
,
m
+=
4
)
for
(;
m
<
N
;
++
i
,
m
+=
4
)
y
[
i
]
=
c
[
m
];
y
[
i
]
=
c
[
m
];
for
(;
m
<
2
*
N
;
++
i
,
m
+=
4
)
for
(;
m
<
2
*
N
;
++
i
,
m
+=
4
)
y
[
i
]
=
-
c
[
2
*
N
-
m
-
1
];
y
[
i
]
=
-
c
[
2
*
N
-
m
-
1
];
...
@@ -2496,7 +2504,9 @@ template<typename T0> class T_dct4
...
@@ -2496,7 +2504,9 @@ template<typename T0> class T_dct4
y
[
i
]
=
c
[
m
];
y
[
i
]
=
c
[
m
];
}
}
rfft
->
forward
(
y
.
data
(),
fct
);
rfft
->
forward
(
y
.
data
(),
fct
);
for
(
i
=
0
;
i
+
i
+
1
<
n2
;
++
i
)
{
size_t
i
=
0
;
for
(;
i
+
i
+
1
<
n2
;
++
i
)
{
{
size_t
k
=
i
+
i
+
1
;
size_t
k
=
i
+
i
+
1
;
T
c1
=
y
[
2
*
k
-
1
],
s1
=
y
[
2
*
k
],
c2
=
y
[
2
*
k
+
1
],
s2
=
y
[
2
*
k
+
2
];
T
c1
=
y
[
2
*
k
-
1
],
s1
=
y
[
2
*
k
],
c2
=
y
[
2
*
k
+
1
],
s2
=
y
[
2
*
k
+
2
];
...
@@ -2511,140 +2521,34 @@ template<typename T0> class T_dct4
...
@@ -2511,140 +2521,34 @@ template<typename T0> class T_dct4
c
[
i
]
=
sqrt2
*
(
SGN_SET
(
cx
,
(
i
+
1
)
/
2
)
+
SGN_SET
(
sx
,
i
/
2
));
c
[
i
]
=
sqrt2
*
(
SGN_SET
(
cx
,
(
i
+
1
)
/
2
)
+
SGN_SET
(
sx
,
i
/
2
));
c
[
N
-
(
i
+
1
)]
=
sqrt2
*
(
SGN_SET
(
cx
,
(
i
+
2
)
/
2
)
+
SGN_SET
(
sx
,
(
i
+
1
)
/
2
));
c
[
N
-
(
i
+
1
)]
=
sqrt2
*
(
SGN_SET
(
cx
,
(
i
+
2
)
/
2
)
+
SGN_SET
(
sx
,
(
i
+
1
)
/
2
));
}
}
}
c
[
n2
]
=
sqrt2
*
SGN_SET
(
y
[
0
],
(
n2
+
1
)
/
2
);
c
[
n2
]
=
sqrt2
*
SGN_SET
(
y
[
0
],
(
n2
+
1
)
/
2
);
// FFTW-derived code ends here
// FFTW-derived code ends here
}
}
else
else
{
{
arr
<
cmplx
<
T
>>
y
(
N
/
2
);
// even length algorithm from
for
(
size_t
i
=
0
;
i
<
N
/
2
;
++
i
)
// https://www.appletonaudio.com/blog/2013/derivation-of-fast-dct-4-algorithm-based-on-dft/
arr
<
cmplx
<
T
>>
y
(
n2
);
for
(
size_t
i
=
0
;
i
<
n2
;
++
i
)
{
{
y
[
i
].
Set
(
c
[
2
*
i
],
c
[
N
-
1
-
2
*
i
]);
y
[
i
].
Set
(
c
[
2
*
i
],
c
[
N
-
1
-
2
*
i
]);
y
[
i
]
*=
C2
[
i
];
y
[
i
]
*=
C2
[
i
];
}
}
fft
->
forward
(
y
.
data
(),
fct
);
fft
->
forward
(
y
.
data
(),
fct
);
for
(
size_t
i
=
0
;
i
<
N
/
2
;
++
i
)
for
(
size_t
i
=
0
,
ic
=
n2
-
1
;
i
<
n2
;
++
i
,
--
ic
)
y
[
i
]
*=
C2
[
i
];
for
(
size_t
i
=
0
;
i
<
N
/
2
;
++
i
)
{
{
c
[
2
*
i
]
=
2
*
y
[
i
].
r
;
c
[
2
*
i
]
=
2
*
(
y
[
i
].
r
*
C2
[
i
].
r
-
y
[
i
].
i
*
C2
[
i
].
i
)
;
c
[
2
*
i
+
1
]
=
-
2
*
y
[
N
/
2
-
1
-
i
].
i
;
c
[
2
*
i
+
1
]
=
-
2
*
(
y
[
ic
].
i
*
C2
[
ic
].
r
+
y
[
ic
].
r
*
C2
[
ic
].
i
)
;
}
}
}
}
}
if
(
!
cosine
)
size_t
length
()
const
{
return
N
;
}
};
template
<
typename
T0
>
class
T_dst1
{
private:
pocketfft_r
<
T0
>
fftplan
;
public:
POCKETFFT_NOINLINE
T_dst1
(
size_t
length
)
:
fftplan
(
2
*
(
length
+
1
))
{}
template
<
typename
T
>
POCKETFFT_NOINLINE
void
exec
(
T
c
[],
T0
fct
,
bool
/*ortho*/
)
const
{
size_t
N
=
fftplan
.
length
(),
n
=
N
/
2
-
1
;
arr
<
T
>
tmp
(
N
);
tmp
[
0
]
=
tmp
[
n
+
1
]
=
c
[
0
]
*
0
;
for
(
size_t
i
=
0
;
i
<
n
;
++
i
)
{
tmp
[
i
+
1
]
=
c
[
i
];
tmp
[
N
-
1
-
i
]
=
-
c
[
i
];
}
fftplan
.
forward
(
tmp
.
data
(),
fct
);
for
(
size_t
i
=
0
;
i
<
n
;
++
i
)
c
[
i
]
=
-
tmp
[
2
*
i
+
2
];
}
size_t
length
()
const
{
return
fftplan
.
length
()
/
2
-
1
;
}
};
template
<
typename
T0
>
class
T_dst2
{
private:
T_dct2
<
T0
>
dct
;
public:
POCKETFFT_NOINLINE
T_dst2
(
size_t
length
)
:
dct
(
length
)
{}
template
<
typename
T
>
POCKETFFT_NOINLINE
void
exec
(
T
c
[],
T0
fct
,
bool
ortho
)
const
{
constexpr
T0
sqrt2
=
T0
(
1.414213562373095048801688724209698
L
);
size_t
N
=
length
();
if
(
N
==
1
)
c
[
0
]
*=
2
*
fct
;
else
{
for
(
size_t
k
=
1
;
k
<
N
;
k
+=
2
)
for
(
size_t
k
=
1
;
k
<
N
;
k
+=
2
)
c
[
k
]
=
-
c
[
k
];
c
[
k
]
=
-
c
[
k
];
dct
.
exec
(
c
,
fct
,
false
);
for
(
size_t
k
=
0
,
kc
=
N
-
1
;
k
<
kc
;
++
k
,
--
kc
)
swap
(
c
[
k
],
c
[
kc
]);
}
if
(
ortho
)
c
[
0
]
/=
sqrt2
;
}
}
size_t
length
()
const
{
return
dct
.
length
();
}
size_t
length
()
const
{
return
N
;
}
};
template
<
typename
T0
>
class
T_dst3
{
private:
T_dct3
<
T0
>
dct
;
public:
POCKETFFT_NOINLINE
T_dst3
(
size_t
length
)
:
dct
(
length
)
{}
template
<
typename
T
>
POCKETFFT_NOINLINE
void
exec
(
T
c
[],
T0
fct
,
bool
ortho
)
{
constexpr
T0
sqrt2
=
T0
(
1.414213562373095048801688724209698
L
);
size_t
N
=
length
();
if
(
ortho
)
c
[
0
]
*=
sqrt2
;
if
(
N
==
1
)
c
[
0
]
*=
fct
;
else
{
size_t
NS2
=
N
/
2
;
for
(
size_t
k
=
0
,
kc
=
N
-
1
;
k
<
NS2
;
++
k
,
--
kc
)
swap
(
c
[
k
],
c
[
kc
]);
dct
.
exec
(
c
,
fct
,
false
);
for
(
size_t
k
=
1
;
k
<
N
;
k
+=
2
)
c
[
k
]
=
-
c
[
k
];
}
}
size_t
length
()
const
{
return
dct
.
length
();
}
};
template
<
typename
T0
>
class
T_dst4
{
private:
T_dct4
<
T0
>
dct
;
public:
POCKETFFT_NOINLINE
T_dst4
(
size_t
length
)
:
dct
(
length
)
{}
template
<
typename
T
>
POCKETFFT_NOINLINE
void
exec
(
T
c
[],
T0
fct
,
bool
/*ortho*/
)
{
size_t
N
=
length
();
//if (N==1) { c[0]*=fct; return; }
size_t
NS2
=
N
/
2
;
for
(
size_t
k
=
0
,
kc
=
N
-
1
;
k
<
NS2
;
++
k
,
--
kc
)
swap
(
c
[
k
],
c
[
kc
]);
dct
.
exec
(
c
,
fct
,
false
);
for
(
size_t
k
=
1
;
k
<
N
;
k
+=
2
)
c
[
k
]
=
-
c
[
k
];
}
size_t
length
()
const
{
return
dct
.
length
();
}
};
};
...
@@ -3093,7 +2997,7 @@ template<typename T> POCKETFFT_NOINLINE void general_hartley(
...
@@ -3093,7 +2997,7 @@ template<typename T> POCKETFFT_NOINLINE void general_hartley(
template
<
typename
Trafo
,
typename
T
>
POCKETFFT_NOINLINE
void
general_dcst
(
template
<
typename
Trafo
,
typename
T
>
POCKETFFT_NOINLINE
void
general_dcst
(
const
cndarr
<
T
>
&
in
,
ndarr
<
T
>
&
out
,
const
shape_t
&
axes
,
const
cndarr
<
T
>
&
in
,
ndarr
<
T
>
&
out
,
const
shape_t
&
axes
,
T
fct
,
bool
ortho
,
size_t
POCKETFFT_NTHREADS
)
T
fct
,
bool
ortho
,
int
type
,
bool
cosine
,
size_t
POCKETFFT_NTHREADS
)
{
{
shared_ptr
<
Trafo
>
plan
;
shared_ptr
<
Trafo
>
plan
;
...
@@ -3121,7 +3025,7 @@ template<typename Trafo, typename T> POCKETFFT_NOINLINE void general_dcst(
...
@@ -3121,7 +3025,7 @@ template<typename Trafo, typename T> POCKETFFT_NOINLINE void general_dcst(
for
(
size_t
i
=
0
;
i
<
len
;
++
i
)
for
(
size_t
i
=
0
;
i
<
len
;
++
i
)
for
(
size_t
j
=
0
;
j
<
vlen
;
++
j
)
for
(
size_t
j
=
0
;
j
<
vlen
;
++
j
)
tdatav
[
i
][
j
]
=
tin
[
it
.
iofs
(
j
,
i
)];
tdatav
[
i
][
j
]
=
tin
[
it
.
iofs
(
j
,
i
)];
plan
->
exec
(
tdatav
,
fct
,
ortho
);
plan
->
exec
(
tdatav
,
fct
,
ortho
,
type
,
cosine
);
for
(
size_t
i
=
0
;
i
<
len
;
++
i
)
for
(
size_t
i
=
0
;
i
<
len
;
++
i
)
for
(
size_t
j
=
0
;
j
<
vlen
;
++
j
)
for
(
size_t
j
=
0
;
j
<
vlen
;
++
j
)
out
[
it
.
oofs
(
j
,
i
)]
=
tdatav
[
i
][
j
];
out
[
it
.
oofs
(
j
,
i
)]
=
tdatav
[
i
][
j
];
...
@@ -3132,18 +3036,18 @@ template<typename Trafo, typename T> POCKETFFT_NOINLINE void general_dcst(
...
@@ -3132,18 +3036,18 @@ template<typename Trafo, typename T> POCKETFFT_NOINLINE void general_dcst(
it
.
advance
(
1
);
it
.
advance
(
1
);
auto
tdata
=
reinterpret_cast
<
T
*>
(
storage
.
data
());
auto
tdata
=
reinterpret_cast
<
T
*>
(
storage
.
data
());
if
((
&
tin
[
0
]
==&
out
[
0
])
&&
(
it
.
stride_out
()
==
sizeof
(
T
)))
// fully in-place
if
((
&
tin
[
0
]
==&
out
[
0
])
&&
(
it
.
stride_out
()
==
sizeof
(
T
)))
// fully in-place
plan
->
exec
(
&
out
[
it
.
oofs
(
0
)],
fct
,
ortho
);
plan
->
exec
(
&
out
[
it
.
oofs
(
0
)],
fct
,
ortho
,
type
,
cosine
);
else
if
(
it
.
stride_out
()
==
sizeof
(
T
))
// compute FFT in output location
else
if
(
it
.
stride_out
()
==
sizeof
(
T
))
// compute FFT in output location
{
{
for
(
size_t
i
=
0
;
i
<
len
;
++
i
)
for
(
size_t
i
=
0
;
i
<
len
;
++
i
)
out
[
it
.
oofs
(
i
)]
=
tin
[
it
.
iofs
(
i
)];