Improve performance of sinf/cosf/sincosf
Here is the correct patch with both filenames and int cast fixed:
This patch is a complete rewrite of sinf, cosf and sincosf. The new version
is significantly faster, as well as simple and accurate.
The worst-case ULP is 0.56072, maximum relative error is 0.5303p-23 over all
4 billion inputs. In non-nearest rounding modes the error is 1ULP.
The algorithm uses 3 main cases: small inputs which don't need argument
reduction, small inputs which need a simple range reduction and large inputs
requiring complex range reduction. The code uses approximate integer
comparisons to quickly decide between these cases - on some targets this may
be slow, so this can be configured to use floating point comparisons.
The small range reducer uses a single reduction step to handle values up to
120.0. It is fastest on targets which support inlined round instructions.
The large range reducer uses integer arithmetic for simplicity. It does a
32x96 bit multiply to compute a 64-bit modulo result. This is more than
accurate enough to handle the worst-case cancellation for values close to
an integer multiple of PI/4. It could be further optimized, however it is
already much faster than necessary.
Simple benchmark showing speedup factor on AArch64 for various ranges:
range 0.7853982 sinf 1.7 cosf 2.2 sincosf 2.8
range 1.570796 sinf 1.9 cosf 1.9 sincosf 2.7
range 3.141593 sinf 2.0 cosf 2.0 sincosf 3.5
range 6.283185 sinf 2.3 cosf 2.3 sincosf 4.2
range 125.6637 sinf 2.9 cosf 3.0 sincosf 5.1
range 1.1259e15 sinf 26.8 cosf 26.8 sincosf 45.2
ChangeLog:
2018-05-18 Wilco Dijkstra <wdijkstr@arm.com>
* newlib/libm/common/Makefile.in: Regenerated.
* newlib/libm/common/Makefile.am: Add sinf.c, cosf.c, sincosf.c
sincosf.h, sincosf_data.c. Add -fbuiltin -fno-math-errno to CFLAGS.
* newlib/libm/common/math_config.h: Add HAVE_FAST_ROUND, HAVE_FAST_LROUND,
roundtoint, converttoint, force_eval_float, force_eval_double, eval_as_float,
eval_as_double, likely, unlikely.
* newlib/libm/common/cosf.c: New file.
* newlib/libm/common/sinf.c: Likewise.
* newlib/libm/common/sincosf.h: Likewise.
* newlib/libm/common/sincosf.c: Likewise.
* newlib/libm/common/sincosf_data.c: Likewise.
* newlib/libm/math/sf_cos.c: Add #if to build conditionally.
* newlib/libm/math/sf_sin.c: Likewise.
* newlib/libm/math/wf_sincos.c: Likewise.
--
2018-06-20 20:07:22 +08:00
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/* Data definitions for sinf, cosf and sincosf.
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Copyright (c) 2018 Arm Ltd. All rights reserved.
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2018-09-28 01:03:32 +08:00
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SPDX-License-Identifier: BSD-3-Clause
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Improve performance of sinf/cosf/sincosf
Here is the correct patch with both filenames and int cast fixed:
This patch is a complete rewrite of sinf, cosf and sincosf. The new version
is significantly faster, as well as simple and accurate.
The worst-case ULP is 0.56072, maximum relative error is 0.5303p-23 over all
4 billion inputs. In non-nearest rounding modes the error is 1ULP.
The algorithm uses 3 main cases: small inputs which don't need argument
reduction, small inputs which need a simple range reduction and large inputs
requiring complex range reduction. The code uses approximate integer
comparisons to quickly decide between these cases - on some targets this may
be slow, so this can be configured to use floating point comparisons.
The small range reducer uses a single reduction step to handle values up to
120.0. It is fastest on targets which support inlined round instructions.
The large range reducer uses integer arithmetic for simplicity. It does a
32x96 bit multiply to compute a 64-bit modulo result. This is more than
accurate enough to handle the worst-case cancellation for values close to
an integer multiple of PI/4. It could be further optimized, however it is
already much faster than necessary.
Simple benchmark showing speedup factor on AArch64 for various ranges:
range 0.7853982 sinf 1.7 cosf 2.2 sincosf 2.8
range 1.570796 sinf 1.9 cosf 1.9 sincosf 2.7
range 3.141593 sinf 2.0 cosf 2.0 sincosf 3.5
range 6.283185 sinf 2.3 cosf 2.3 sincosf 4.2
range 125.6637 sinf 2.9 cosf 3.0 sincosf 5.1
range 1.1259e15 sinf 26.8 cosf 26.8 sincosf 45.2
ChangeLog:
2018-05-18 Wilco Dijkstra <wdijkstr@arm.com>
* newlib/libm/common/Makefile.in: Regenerated.
* newlib/libm/common/Makefile.am: Add sinf.c, cosf.c, sincosf.c
sincosf.h, sincosf_data.c. Add -fbuiltin -fno-math-errno to CFLAGS.
* newlib/libm/common/math_config.h: Add HAVE_FAST_ROUND, HAVE_FAST_LROUND,
roundtoint, converttoint, force_eval_float, force_eval_double, eval_as_float,
eval_as_double, likely, unlikely.
* newlib/libm/common/cosf.c: New file.
* newlib/libm/common/sinf.c: Likewise.
* newlib/libm/common/sincosf.h: Likewise.
* newlib/libm/common/sincosf.c: Likewise.
* newlib/libm/common/sincosf_data.c: Likewise.
* newlib/libm/math/sf_cos.c: Add #if to build conditionally.
* newlib/libm/math/sf_sin.c: Likewise.
* newlib/libm/math/wf_sincos.c: Likewise.
--
2018-06-20 20:07:22 +08:00
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions
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are met:
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1. Redistributions of source code must retain the above copyright
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notice, this list of conditions and the following disclaimer.
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2. Redistributions in binary form must reproduce the above copyright
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notice, this list of conditions and the following disclaimer in the
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documentation and/or other materials provided with the distribution.
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3. The name of the company may not be used to endorse or promote
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products derived from this software without specific prior written
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permission.
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2018-09-28 01:03:32 +08:00
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THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS'' AND ANY EXPRESS OR IMPLIED
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Improve performance of sinf/cosf/sincosf
Here is the correct patch with both filenames and int cast fixed:
This patch is a complete rewrite of sinf, cosf and sincosf. The new version
is significantly faster, as well as simple and accurate.
The worst-case ULP is 0.56072, maximum relative error is 0.5303p-23 over all
4 billion inputs. In non-nearest rounding modes the error is 1ULP.
The algorithm uses 3 main cases: small inputs which don't need argument
reduction, small inputs which need a simple range reduction and large inputs
requiring complex range reduction. The code uses approximate integer
comparisons to quickly decide between these cases - on some targets this may
be slow, so this can be configured to use floating point comparisons.
The small range reducer uses a single reduction step to handle values up to
120.0. It is fastest on targets which support inlined round instructions.
The large range reducer uses integer arithmetic for simplicity. It does a
32x96 bit multiply to compute a 64-bit modulo result. This is more than
accurate enough to handle the worst-case cancellation for values close to
an integer multiple of PI/4. It could be further optimized, however it is
already much faster than necessary.
Simple benchmark showing speedup factor on AArch64 for various ranges:
range 0.7853982 sinf 1.7 cosf 2.2 sincosf 2.8
range 1.570796 sinf 1.9 cosf 1.9 sincosf 2.7
range 3.141593 sinf 2.0 cosf 2.0 sincosf 3.5
range 6.283185 sinf 2.3 cosf 2.3 sincosf 4.2
range 125.6637 sinf 2.9 cosf 3.0 sincosf 5.1
range 1.1259e15 sinf 26.8 cosf 26.8 sincosf 45.2
ChangeLog:
2018-05-18 Wilco Dijkstra <wdijkstr@arm.com>
* newlib/libm/common/Makefile.in: Regenerated.
* newlib/libm/common/Makefile.am: Add sinf.c, cosf.c, sincosf.c
sincosf.h, sincosf_data.c. Add -fbuiltin -fno-math-errno to CFLAGS.
* newlib/libm/common/math_config.h: Add HAVE_FAST_ROUND, HAVE_FAST_LROUND,
roundtoint, converttoint, force_eval_float, force_eval_double, eval_as_float,
eval_as_double, likely, unlikely.
* newlib/libm/common/cosf.c: New file.
* newlib/libm/common/sinf.c: Likewise.
* newlib/libm/common/sincosf.h: Likewise.
* newlib/libm/common/sincosf.c: Likewise.
* newlib/libm/common/sincosf_data.c: Likewise.
* newlib/libm/math/sf_cos.c: Add #if to build conditionally.
* newlib/libm/math/sf_sin.c: Likewise.
* newlib/libm/math/wf_sincos.c: Likewise.
--
2018-06-20 20:07:22 +08:00
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WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
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MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
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IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
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TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
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LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
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#include "fdlibm.h"
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#if !__OBSOLETE_MATH
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#include <stdint.h>
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#include <math.h>
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#include "math_config.h"
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#include "sincosf.h"
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/* The constants and polynomials for sine and cosine. The 2nd entry
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computes -cos (x) rather than cos (x) to get negation for free. */
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2018-07-05 00:52:36 +08:00
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const sincos_t __sincosf_table[2] =
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Improve performance of sinf/cosf/sincosf
Here is the correct patch with both filenames and int cast fixed:
This patch is a complete rewrite of sinf, cosf and sincosf. The new version
is significantly faster, as well as simple and accurate.
The worst-case ULP is 0.56072, maximum relative error is 0.5303p-23 over all
4 billion inputs. In non-nearest rounding modes the error is 1ULP.
The algorithm uses 3 main cases: small inputs which don't need argument
reduction, small inputs which need a simple range reduction and large inputs
requiring complex range reduction. The code uses approximate integer
comparisons to quickly decide between these cases - on some targets this may
be slow, so this can be configured to use floating point comparisons.
The small range reducer uses a single reduction step to handle values up to
120.0. It is fastest on targets which support inlined round instructions.
The large range reducer uses integer arithmetic for simplicity. It does a
32x96 bit multiply to compute a 64-bit modulo result. This is more than
accurate enough to handle the worst-case cancellation for values close to
an integer multiple of PI/4. It could be further optimized, however it is
already much faster than necessary.
Simple benchmark showing speedup factor on AArch64 for various ranges:
range 0.7853982 sinf 1.7 cosf 2.2 sincosf 2.8
range 1.570796 sinf 1.9 cosf 1.9 sincosf 2.7
range 3.141593 sinf 2.0 cosf 2.0 sincosf 3.5
range 6.283185 sinf 2.3 cosf 2.3 sincosf 4.2
range 125.6637 sinf 2.9 cosf 3.0 sincosf 5.1
range 1.1259e15 sinf 26.8 cosf 26.8 sincosf 45.2
ChangeLog:
2018-05-18 Wilco Dijkstra <wdijkstr@arm.com>
* newlib/libm/common/Makefile.in: Regenerated.
* newlib/libm/common/Makefile.am: Add sinf.c, cosf.c, sincosf.c
sincosf.h, sincosf_data.c. Add -fbuiltin -fno-math-errno to CFLAGS.
* newlib/libm/common/math_config.h: Add HAVE_FAST_ROUND, HAVE_FAST_LROUND,
roundtoint, converttoint, force_eval_float, force_eval_double, eval_as_float,
eval_as_double, likely, unlikely.
* newlib/libm/common/cosf.c: New file.
* newlib/libm/common/sinf.c: Likewise.
* newlib/libm/common/sincosf.h: Likewise.
* newlib/libm/common/sincosf.c: Likewise.
* newlib/libm/common/sincosf_data.c: Likewise.
* newlib/libm/math/sf_cos.c: Add #if to build conditionally.
* newlib/libm/math/sf_sin.c: Likewise.
* newlib/libm/math/wf_sincos.c: Likewise.
--
2018-06-20 20:07:22 +08:00
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{
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{
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{ 1.0, -1.0, -1.0, 1.0 },
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#if TOINT_INTRINSICS
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0x1.45F306DC9C883p-1,
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#else
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0x1.45F306DC9C883p+23,
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#endif
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0x1.921FB54442D18p0,
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0x1p0,
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-0x1.ffffffd0c621cp-2,
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0x1.55553e1068f19p-5,
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-0x1.6c087e89a359dp-10,
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0x1.99343027bf8c3p-16,
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-0x1.555545995a603p-3,
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0x1.1107605230bc4p-7,
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-0x1.994eb3774cf24p-13
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},
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{
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{ 1.0, -1.0, -1.0, 1.0 },
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#if TOINT_INTRINSICS
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0x1.45F306DC9C883p-1,
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#else
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0x1.45F306DC9C883p+23,
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#endif
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0x1.921FB54442D18p0,
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-0x1p0,
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0x1.ffffffd0c621cp-2,
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-0x1.55553e1068f19p-5,
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0x1.6c087e89a359dp-10,
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-0x1.99343027bf8c3p-16,
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-0x1.555545995a603p-3,
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0x1.1107605230bc4p-7,
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-0x1.994eb3774cf24p-13
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}
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};
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/* Table with 4/PI to 192 bit precision. To avoid unaligned accesses
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only 8 new bits are added per entry, making the table 4 times larger. */
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2018-07-05 00:52:36 +08:00
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const uint32_t __inv_pio4[24] =
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Improve performance of sinf/cosf/sincosf
Here is the correct patch with both filenames and int cast fixed:
This patch is a complete rewrite of sinf, cosf and sincosf. The new version
is significantly faster, as well as simple and accurate.
The worst-case ULP is 0.56072, maximum relative error is 0.5303p-23 over all
4 billion inputs. In non-nearest rounding modes the error is 1ULP.
The algorithm uses 3 main cases: small inputs which don't need argument
reduction, small inputs which need a simple range reduction and large inputs
requiring complex range reduction. The code uses approximate integer
comparisons to quickly decide between these cases - on some targets this may
be slow, so this can be configured to use floating point comparisons.
The small range reducer uses a single reduction step to handle values up to
120.0. It is fastest on targets which support inlined round instructions.
The large range reducer uses integer arithmetic for simplicity. It does a
32x96 bit multiply to compute a 64-bit modulo result. This is more than
accurate enough to handle the worst-case cancellation for values close to
an integer multiple of PI/4. It could be further optimized, however it is
already much faster than necessary.
Simple benchmark showing speedup factor on AArch64 for various ranges:
range 0.7853982 sinf 1.7 cosf 2.2 sincosf 2.8
range 1.570796 sinf 1.9 cosf 1.9 sincosf 2.7
range 3.141593 sinf 2.0 cosf 2.0 sincosf 3.5
range 6.283185 sinf 2.3 cosf 2.3 sincosf 4.2
range 125.6637 sinf 2.9 cosf 3.0 sincosf 5.1
range 1.1259e15 sinf 26.8 cosf 26.8 sincosf 45.2
ChangeLog:
2018-05-18 Wilco Dijkstra <wdijkstr@arm.com>
* newlib/libm/common/Makefile.in: Regenerated.
* newlib/libm/common/Makefile.am: Add sinf.c, cosf.c, sincosf.c
sincosf.h, sincosf_data.c. Add -fbuiltin -fno-math-errno to CFLAGS.
* newlib/libm/common/math_config.h: Add HAVE_FAST_ROUND, HAVE_FAST_LROUND,
roundtoint, converttoint, force_eval_float, force_eval_double, eval_as_float,
eval_as_double, likely, unlikely.
* newlib/libm/common/cosf.c: New file.
* newlib/libm/common/sinf.c: Likewise.
* newlib/libm/common/sincosf.h: Likewise.
* newlib/libm/common/sincosf.c: Likewise.
* newlib/libm/common/sincosf_data.c: Likewise.
* newlib/libm/math/sf_cos.c: Add #if to build conditionally.
* newlib/libm/math/sf_sin.c: Likewise.
* newlib/libm/math/wf_sincos.c: Likewise.
--
2018-06-20 20:07:22 +08:00
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{
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0xa2, 0xa2f9, 0xa2f983, 0xa2f9836e,
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0xf9836e4e, 0x836e4e44, 0x6e4e4415, 0x4e441529,
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0x441529fc, 0x1529fc27, 0x29fc2757, 0xfc2757d1,
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0x2757d1f5, 0x57d1f534, 0xd1f534dd, 0xf534ddc0,
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0x34ddc0db, 0xddc0db62, 0xc0db6295, 0xdb629599,
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0x6295993c, 0x95993c43, 0x993c4390, 0x3c439041
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};
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#endif
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