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Add a library of general (non-cryptographic) hash functions, currently

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consisting of the Pearson string hash function and the Murmur3-32 hash
function.
This commit is contained in:
Dag-Erling Smørgrav 2014-07-19 06:03:57 +00:00 committed by des
parent 541d65a3cc
commit 0023f57ab5
10 changed files with 597 additions and 0 deletions
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1
configure.ac
View file

@ -121,6 +121,7 @@ AC_CONFIG_FILES([
lib/core/Makefile
lib/digest/Makefile
lib/enc/Makefile
lib/hash/Makefile
lib/mac/Makefile
lib/oath/Makefile
lib/rand/Makefile

1
include/cryb/Makefile.am
View file

@ -7,6 +7,7 @@ cryb_HEADERS = \
attributes.h \
bitwise.h \
digest.h \
hash.h \
hmac.h \
hmac_sha1.h \
hmac_sha224.h \

41
include/cryb/hash.h Normal file
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@ -0,0 +1,41 @@
/*-
* Copyright (c) 2014 Dag-Erling Smørgrav
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. The name of the author may not be used to endorse or promote
* products derived from this software without specific prior written
* permission.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
#ifndef CRYB_HASH_H_INCLUDED
#define CRYB_HASH_H_INCLUDED
#define pearson_hash cryb_pearson_hash
#define pearson_hash_str cryb_pearson_hash_str
#define murmur3_32_hash cryb_murmur3_32_hash
uint8_t pearson_hash(const void *, size_t len);
uint8_t pearson_hash_str(const char *);
uint32_t murmur3_32_hash(const void *, size_t, uint32_t);
#endif

1
lib/Makefile.am
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@ -4,6 +4,7 @@ SUBDIRS = \
core \
digest \
enc \
hash \
mac \
rand \
oath

9
lib/hash/Makefile.am Normal file
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@ -0,0 +1,9 @@
# $Cryb$
AM_CPPFLAGS = -I$(top_srcdir)/include
lib_LTLIBRARIES = libcryb-hash.la
libcryb_hash_la_SOURCES = \
murmur3_32.c \
pearson.c

110
lib/hash/murmur3_32.c Normal file
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@ -0,0 +1,110 @@
/*-
* Copyright (c) 2014 Dag-Erling Smørgrav
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. The name of the author may not be used to endorse or promote
* products derived from this software without specific prior written
* permission.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
#include "cryb/impl.h"
#ifdef HAVE_SYS_ENDIAN_H
#include <sys/endian.h>
#endif
#ifdef HAVE_ENDIAN_H
#define _BSD_SOURCE
#include <endian.h>
#endif
#include <stdint.h>
#include <string.h>
#include <cryb/bitwise.h>
#include <cryb/hash.h>
/*
* Simple implementation of the Murmur3-32 hash function.
*
* This implementation is slow but safe. It can be made significantly
* faster if the caller guarantees that the input is correctly aligned for
* 32-bit reads, and slightly faster yet if the caller guarantees that the
* length of the input is always a multiple of 4 bytes.
*/
uint32_t
murmur3_32_hash(const void *data, size_t len, uint32_t seed)
{
const uint8_t *bytes;
uint32_t hash, k;
size_t res;
/* initialization */
bytes = data;
res = len;
hash = seed;
/* main loop */
while (res >= 4) {
/* replace with le32toh() if input is aligned */
k = le32dec(bytes);
bytes += 4;
res -= 4;
k *= 0xcc9e2d51;
k = rol(k, 15);
k *= 0x1b873593;
hash ^= k;
hash = rol(hash, 13);
hash *= 5;
hash += 0xe6546b64;
}
/* remainder */
/* remove if input length is a multiple of 4 */
if (res > 0) {
k = 0;
switch (res) {
case 3:
k |= bytes[2] << 16;
case 2:
k |= bytes[1] << 8;
case 1:
k |= bytes[0];
k *= 0xcc9e2d51;
k = rol(k, 15);
k *= 0x1b873593;
hash ^= k;
break;
CRYB_NO_DEFAULT_CASE;
}
}
/* finalize */
hash ^= (uint32_t)len;
hash ^= hash >> 16;
hash *= 0x85ebca6b;
hash ^= hash >> 13;
hash *= 0xc2b2ae35;
hash ^= hash >> 16;
return (hash);
}

97
lib/hash/pearson.c Normal file
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@ -0,0 +1,97 @@
/*-
* Copyright (c) 2014 The University of Oslo
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. The name of the author may not be used to endorse or promote
* products derived from this software without specific prior written
* permission.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
#include "cryb/impl.h"
#include <stdint.h>
#include <string.h>
#include <cryb/hash.h>
/*
* Implementation of the hash function described in Pearson, Peter
* K. (June 1990), "Fast Hashing of Variable-Length Text Strings",
* Communications of the ACM 33 (6): 677, doi:10.1145/78973.78978
*/
static const uint8_t T[256] = {
0x01, 0x57, 0x31, 0x0c, 0xb0, 0xb2, 0x66, 0xa6,
0x79, 0xc1, 0x06, 0x54, 0xf9, 0xe6, 0x2c, 0xa3,
0x0e, 0xc5, 0xd5, 0xb5, 0xa1, 0x55, 0xda, 0x50,
0x40, 0xef, 0x18, 0xe2, 0xec, 0x8e, 0x26, 0xc8,
0x6e, 0xb1, 0x68, 0x67, 0x8d, 0xfd, 0xff, 0x32,
0x4d, 0x65, 0x51, 0x12, 0x2d, 0x60, 0x1f, 0xde,
0x19, 0x6b, 0xbe, 0x46, 0x56, 0xed, 0xf0, 0x22,
0x48, 0xf2, 0x14, 0xd6, 0xf4, 0xe3, 0x95, 0xeb,
0x61, 0xea, 0x39, 0x16, 0x3c, 0xfa, 0x52, 0xaf,
0xd0, 0x05, 0x7f, 0xc7, 0x6f, 0x3e, 0x87, 0xf8,
0xae, 0xa9, 0xd3, 0x3a, 0x42, 0x9a, 0x6a, 0xc3,
0xf5, 0xab, 0x11, 0xbb, 0xb6, 0xb3, 0x00, 0xf3,
0x84, 0x38, 0x94, 0x4b, 0x80, 0x85, 0x9e, 0x64,
0x82, 0x7e, 0x5b, 0x0d, 0x99, 0xf6, 0xd8, 0xdb,
0x77, 0x44, 0xdf, 0x4e, 0x53, 0x58, 0xc9, 0x63,
0x7a, 0x0b, 0x5c, 0x20, 0x88, 0x72, 0x34, 0x0a,
0x8a, 0x1e, 0x30, 0xb7, 0x9c, 0x23, 0x3d, 0x1a,
0x8f, 0x4a, 0xfb, 0x5e, 0x81, 0xa2, 0x3f, 0x98,
0xaa, 0x07, 0x73, 0xa7, 0xf1, 0xce, 0x03, 0x96,
0x37, 0x3b, 0x97, 0xdc, 0x5a, 0x35, 0x17, 0x83,
0x7d, 0xad, 0x0f, 0xee, 0x4f, 0x5f, 0x59, 0x10,
0x69, 0x89, 0xe1, 0xe0, 0xd9, 0xa0, 0x25, 0x7b,
0x76, 0x49, 0x02, 0x9d, 0x2e, 0x74, 0x09, 0x91,
0x86, 0xe4, 0xcf, 0xd4, 0xca, 0xd7, 0x45, 0xe5,
0x1b, 0xbc, 0x43, 0x7c, 0xa8, 0xfc, 0x2a, 0x04,
0x1d, 0x6c, 0x15, 0xf7, 0x13, 0xcd, 0x27, 0xcb,
0xe9, 0x28, 0xba, 0x93, 0xc6, 0xc0, 0x9b, 0x21,
0xa4, 0xbf, 0x62, 0xcc, 0xa5, 0xb4, 0x75, 0x4c,
0x8c, 0x24, 0xd2, 0xac, 0x29, 0x36, 0x9f, 0x08,
0xb9, 0xe8, 0x71, 0xc4, 0xe7, 0x2f, 0x92, 0x78,
0x33, 0x41, 0x1c, 0x90, 0xfe, 0xdd, 0x5d, 0xbd,
0xc2, 0x8b, 0x70, 0x2b, 0x47, 0x6d, 0xb8, 0xd1,
};
uint8_t
pearson_hash(const void *data, size_t len)
{
const uint8_t *p;
uint8_t h;
for (p = data, h = 0; len > 0; ++p, --len)
h = T[h ^ *p];
return (h);
}
uint8_t
pearson_hash_str(const char *str)
{
uint8_t h;
for (h = 0; *str != '\0'; ++str)
h = T[h ^ (uint8_t)*str];
return (h);
}

4
t/Makefile.am
View file

@ -13,6 +13,7 @@ LDADD = $(builddir)/libt.la \
$(top_builddir)/lib/core/libcryb-core.la \
$(top_builddir)/lib/enc/libcryb-enc.la \
$(top_builddir)/lib/digest/libcryb-digest.la \
$(top_builddir)/lib/hash/libcryb-hash.la \
$(top_builddir)/lib/mac/libcryb-mac.la \
$(top_builddir)/lib/rand/libcryb-rand.la \
$(top_builddir)/lib/oath/libcryb-oath.la
@ -81,6 +82,9 @@ t_sha512_openssl_CFLAGS = $(OPENSSL_INCLUDES) $(OPENSSL_CFLAGS)
t_sha512_openssl_LDADD = $(OPENSSL_LDADD)
endif
# libcryb-hash
TESTS += t_murmur3_32 t_pearson
# libcryb-mac
TESTS += t_hmac_sha1 t_hmac_sha224 t_hmac_sha256 t_hmac_sha384 t_hmac_sha512
if WITH_OPENSSL

218
t/t_murmur3_32.c Normal file
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@ -0,0 +1,218 @@
/*-
* Copyright (c) 2014 Dag-Erling Smørgrav
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. The name of the author may not be used to endorse or promote
* products derived from this software without specific prior written
* permission.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*
* Author: Dag-Erling Smørgrav <des@des.no>
*
* $Cryb$
*/
#include "cryb/impl.h"
#include <stdint.h>
#include <stdio.h>
#include <string.h>
#include <cryb/hash.h>
#include "t.h"
struct t_case {
const char *desc;
const char *data;
size_t len;
uint32_t seed;
uint32_t hash;
};
/***************************************************************************
* Test cases
*/
static struct t_case t_cases[] = {
{
.desc = "00000000 { }",
.data = "murmur3",
.len = 0,
.seed = 0x00000000,
.hash = 0x00000000,
},
{
.desc = "ffffffff { }",
.data = "murmur3",
.len = 0,
.seed = 0xffffffff,
.hash = 0x81f16f39,
},
{
.desc = "00000000 { 'm' }",
.data = "murmur3",
.len = 1,
.seed = 0x00000000,
.hash = 0x5ae4385c,
},
{
.desc = "ffffffff { 'm' }",
.data = "murmur3",
.len = 1,
.seed = 0xffffffff,
.hash = 0x7aca074a,
},
{
.desc = "00000000 { 'm' 'u' }",
.data = "murmur3",
.len = 2,
.seed = 0x00000000,
.hash = 0xb93a5ae8,
},
{
.desc = "ffffffff { 'm' 'u' }",
.data = "murmur3",
.len = 2,
.seed = 0xffffffff,
.hash = 0xb3906f0a,
},
{
.desc = "00000000 { 'm' 'u' 'r' }",
.data = "murmur3",
.len = 3,
.seed = 0x00000000,
.hash = 0x44b7f9ca,
},
{
.desc = "ffffffff { 'm' 'u' 'r' }",
.data = "murmur3",
.len = 3,
.seed = 0xffffffff,
.hash = 0xe75eba0,
},
{
.desc = "00000000 { 'm' 'u' 'r' 'm' }",
.data = "murmur3",
.len = 4,
.seed = 0x00000000,
.hash = 0x48bcf87d,
},
{
.desc = "ffffffff { 'm' 'u' 'r' 'm' }",
.data = "murmur3",
.len = 4,
.seed = 0xffffffff,
.hash = 0x5771291b,
},
{
.desc = "00000000 { 'm' 'u' 'r' 'm' 'u' }",
.data = "murmur3",
.len = 5,
.seed = 0x00000000,
.hash = 0x6865a0a3,
},
{
.desc = "ffffffff { 'm' 'u' 'r' 'm' 'u' }",
.data = "murmur3",
.len = 5,
.seed = 0xffffffff,
.hash = 0xbed94c57,
},
{
.desc = "00000000 { 'm' 'u' 'r' 'm' 'u' 'r' }",
.data = "murmur3",
.len = 6,
.seed = 0x00000000,
.hash = 0x73f313cd,
},
{
.desc = "ffffffff { 'm' 'u' 'r' 'm' 'u' 'r' }",
.data = "murmur3",
.len = 6,
.seed = 0xffffffff,
.hash = 0x1a77802a,
},
{
.desc = "00000000 { 'm' 'u' 'r' 'm' 'u' 'r' '3' }",
.data = "murmur3",
.len = 7,
.seed = 0x00000000,
.hash = 0x845098a5,
},
{
.desc = "ffffffff { 'm' 'u' 'r' 'm' 'u' 'r' '3' }",
.data = "murmur3",
.len = 7,
.seed = 0xffffffff,
.hash = 0x6e66a973,
},
{
.desc = "00000000 { 'm' 'u' 'r' 'm' 'u' 'r' '3' '\\0' }",
.data = "murmur3",
.len = 8,
.seed = 0x00000000,
.hash = 0x7d525b5e,
},
{
.desc = "ffffffff { 'm' 'u' 'r' 'm' 'u' 'r' '3' '\\0' }",
.data = "murmur3",
.len = 8,
.seed = 0xffffffff,
.hash = 0x18b2eab2,
},
};
/***************************************************************************
* Test function
*/
static int
t_murmur3_32(char **desc CRYB_UNUSED, void *arg)
{
struct t_case *t = arg;
uint32_t hash;
hash = murmur3_32_hash(t->data, t->len, t->seed);
return (t_compare_x32(t->hash, hash));
}
/***************************************************************************
* Boilerplate
*/
int
t_prepare(int argc, char *argv[])
{
int i, n;
(void)argc;
(void)argv;
n = sizeof t_cases / sizeof t_cases[0];
for (i = 0; i < n; ++i)
t_add_test(t_murmur3_32, &t_cases[i], t_cases[i].desc);
return (0);
}
void
t_cleanup(void)
{
}

115
t/t_pearson.c Normal file
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@ -0,0 +1,115 @@
/*-
* Copyright (c) 2014 Dag-Erling Smørgrav
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. The name of the author may not be used to endorse or promote
* products derived from this software without specific prior written
* permission.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*
* Author: Dag-Erling Smørgrav <des@des.no>
*
* $Cryb$
*/
#include "cryb/impl.h"
#include <stdint.h>
#include <stdio.h>
#include <string.h>
#include <cryb/hash.h>
#include "t.h"
#define T_MAGIC_WORD_1 "squeamish"
#define T_MAGIC_WORD_2 "ossifrage"
#define T_MAGIC_STR T_MAGIC_WORD_1 " " T_MAGIC_WORD_2
struct t_case {
const char *desc;
const char *str;
uint8_t hash;
};
/***************************************************************************
* Test cases
*/
static struct t_case t_cases[] = {
{
.desc = "\"\"",
.str = "",
.hash = 0x00,
},
{
.desc = "\"" T_MAGIC_WORD_1 "\"",
.str = T_MAGIC_WORD_1,
.hash = 0xe9,
},
{
.desc = "\"" T_MAGIC_WORD_2 "\"",
.str = T_MAGIC_WORD_2,
.hash = 0x47,
},
{
.desc = "\"" T_MAGIC_STR "\"",
.str = T_MAGIC_STR,
.hash = 0xba,
},
};
/***************************************************************************
* Test function
*/
static int
t_pearson(char **desc CRYB_UNUSED, void *arg)
{
struct t_case *t = arg;
int ret;
ret = t_compare_x8(t->hash, pearson_hash(t->str, strlen(t->str)));
ret &= t_compare_x8(t->hash, pearson_hash_str(t->str));
return (ret);
}
/***************************************************************************
* Boilerplate
*/
int
t_prepare(int argc, char *argv[])
{
int i, n;
(void)argc;
(void)argv;
n = sizeof t_cases / sizeof t_cases[0];
for (i = 0; i < n; ++i)
t_add_test(t_pearson, &t_cases[i], t_cases[i].desc);
return (0);
}
void
t_cleanup(void)
{
}