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phobos/std/random.d
Walter Bright d57e203dc9 fold in some OSX changes
2009-02-10 02:21:15 +00:00

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// Written in the D programming language
/**
Facilities for random number generation. The old-style functions
$(D_PARAM rand_seed) and $(D_PARAM rand) will soon be deprecated as
they rely on global state and as such are subjected to various
thread-related issues.
The new-style generator objects hold their own state so they are
immune of threading issues. The generators feature a number of
well-known and well-documented methods of generating random
numbers. An overall fast and reliable means to generate random numbers
is the $(D_PARAM Mt19937) generator, which derives its name from
"$(WEB math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html, Mersenne
Twister) with a period of 2 to the power of 19937". In
memory-constrained situations, $(WEB
en.wikipedia.org/wiki/Linear_congruential_generator, linear
congruential) generators such as $(D MinstdRand0) and $(D MinstdRand)
might be useful. The standard library provides an alias $(D_PARAM
Random) for whichever generator it finds the most fit for the target
environment.
Example:
----
Random gen;
// Generate a uniformly-distributed integer in the range [0, 15]
auto i = uniform!(int)(gen, 0, 15);
// Generate a uniformly-distributed real in the range [0, 100$(RPAREN)
auto r = uniform!(real)(gen, 0.0L, 100.0L);
----
In addition to random number generators, this module features
distributions, which skew a generator's output statistical
distribution in various ways. So far the uniform distribution for
integers and real numbers have been implemented.
Author:
$(WEB erdani.org, Andrei Alexandrescu)
Credits:
The entire random number library architecture is derived from the
excellent $(WEB
open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2461.pdf, C++0X) random
number facility proposed by Jens Maurer and contributed to by
researchers at the Fermi laboratory.
Macros:
WIKI = Phobos/StdRandom
*/
// random.d
// www.digitalmars.com
module std.random;
import std.stdio, std.math, std.c.time, std.traits, std.contracts, std.conv,
std.algorithm, std.process, std.date;
// Segments of the code in this file Copyright (c) 1997 by Rick Booth
// From "Inner Loops" by Rick Booth, Addison-Wesley
// Work derived from:
/*
A C-program for MT19937, with initialization improved 2002/1/26.
Coded by Takuji Nishimura and Makoto Matsumoto.
Before using, initialize the state by using init_genrand(seed)
or init_by_array(init_key, key_length).
Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
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 names of its contributors may not be used to endorse or promote
products derived from this software without specific prior written
permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS 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 COPYRIGHT OWNER 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.
Any feedback is very welcome.
http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space)
*/
version (Win32)
{
extern(Windows) int QueryPerformanceCounter(ulong *count);
}
version (Posix)
{
private import std.c.linux.linux;
}
/**
Linear Congruential generator.
*/
struct LinearCongruentialEngine(UIntType, UIntType a, UIntType c, UIntType m)
{
/// Alias for the generated type $(D_PARAM UIntType).
alias UIntType ResultType;
static invariant
{
/// Does this generator have a fixed range? ($(D_PARAM true)).
bool hasFixedRange = true;
/// Lowest generated value.
ResultType min = ( c == 0 ? 1 : 0 );
/// Highest generated value.
ResultType max = m - 1;
/**
The parameters of this distribution. The random number is $(D_PARAM x =
(x * a + c) % m).
*/
UIntType
multiplier = a,
///ditto
increment = c,
///ditto
modulus = m;
}
static assert(isIntegral!(UIntType));
static assert(m == 0 || a < m);
static assert(m == 0 || c < m);
static assert(m == 0 ||
(cast(ulong)a * (m-1) + c) % m == (c < a ? c - a + m : c - a));
/**
Constructs a $(D_PARAM LinearCongruentialEngine) generator.
*/
static LinearCongruentialEngine opCall(UIntType x0 = 1)
{
LinearCongruentialEngine result;
result.seed(x0);
return result;
}
/**
(Re)seeds the generator.
*/
void seed(UIntType x0 = 1)
{
static if (c == 0)
{
enforce(x0, "Invalid (zero) seed for "
~LinearCongruentialEngine.stringof);
}
_x = modulus ? (x0 % modulus) : x0;
}
/**
Returns the next number in the random sequence.
*/
UIntType next()
{
static if (m)
_x = cast(UIntType) ((cast(ulong) a * _x + c) % m);
else
_x = a * _x + c;
return _x;
}
/**
Discards next $(D_PARAM n) samples.
*/
void discard(ulong n)
{
while (n--) next;
}
/**
Compares against $(D_PARAM rhs) for equality.
*/
bool opEquals(LinearCongruentialEngine rhs)
{
return _x == rhs._x;
}
private UIntType _x = 1;
};
/**
Define $(D_PARAM LinearCongruentialEngine) generators with "good"
parameters.
Example:
----
// seed with a constant
auto rnd0 = MinstdRand0(1);
auto n = rnd0.next; // same for each run
// Seed with an unpredictable value
rnd0.seed(unpredictableSeed);
n = rnd0.next; // different across runs
----
*/
alias LinearCongruentialEngine!(uint, 16807, 0, 2147483647) MinstdRand0;
/// ditto
alias LinearCongruentialEngine!(uint, 48271, 0, 2147483647) MinstdRand;
unittest
{
// The correct numbers are taken from The Database of Integer Sequences
// http://www.research.att.com/~njas/sequences/eisBTfry00128.txt
auto checking0 = [
16807UL,282475249,1622650073,984943658,1144108930,470211272,
101027544,1457850878,1458777923,2007237709,823564440,1115438165,
1784484492,74243042,114807987,1137522503,1441282327,16531729,
823378840,143542612 ];
auto rnd0 = MinstdRand0(1);
foreach (e; checking0)
{
assert(rnd0.next == e);
}
// Test the 10000th invocation
// Correct value taken from:
// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2461.pdf
rnd0.seed;
rnd0.discard(9999);
assert(rnd0.next == 1043618065);
// Test MinstdRand
auto checking = [48271UL,182605794,1291394886,1914720637,2078669041,
407355683];
auto rnd = MinstdRand(1);
foreach (e; checking)
{
assert(rnd.next == e);
}
// Test the 10000th invocation
// Correct value taken from:
// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2461.pdf
rnd.seed;
rnd.discard(9999);
assert(rnd.next == 399268537);
}
/**
The $(LINK2 http://math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html,
Mersenne Twister generator).
*/
struct MersenneTwisterEngine(
UIntType, size_t w, size_t n, size_t m, size_t r,
UIntType a, size_t u, size_t s,
UIntType b, size_t t,
UIntType c, size_t l)
{
/// Result type (an alias for $(D_PARAM UIntType)).
alias UIntType ResultType;
/**
Parameter for the generator.
*/
static invariant
{
size_t wordSize = w;
size_t stateSize = n;
size_t shiftSize = m;
size_t maskBits = r;
UIntType xorMask = a;
UIntType temperingU = u;
size_t temperingS = s;
UIntType temperingB = b;
size_t temperingT = t;
UIntType temperingC = c;
size_t temperingL = l;
}
/// Smallest generated value (0).
static invariant UIntType min = 0;
/// Largest generated value.
static invariant UIntType max =
w == UIntType.sizeof * 8 ? UIntType.max : (1u << w) - 1;
/// The default seed value.
static invariant UIntType defaultSeed = 5489u;
static assert(1 <= m && m <= n);
static assert(0 <= r && 0 <= u && 0 <= s && 0 <= t && 0 <= l);
static assert(r <= w && u <= w && s <= w && t <= w && l <= w);
static assert(0 <= a && 0 <= b && 0 <= c);
static assert(a <= max && b <= max && c <= max);
/**
Constructs a MersenneTwisterEngine object
*/
static MersenneTwisterEngine opCall(ResultType value)
{
MersenneTwisterEngine result;
result.seed(value);
return result;
}
/**
Constructs a MersenneTwisterEngine object
*/
void seed(ResultType value = defaultSeed)
{
static if (w == ResultType.sizeof * 8)
{
mt[0] = value;
}
else
{
static assert(max + 1 > 0);
mt[0] = value % (max + 1);
}
for (mti = 1; mti < n; ++mti) {
mt[mti] =
cast(UIntType)
(1812433253UL * (mt[mti-1] ^ (mt[mti-1] >> (w - 2))) + mti);
/* See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier. */
/* In the previous versions, MSBs of the seed affect */
/* only MSBs of the array mt[]. */
/* 2002/01/09 modified by Makoto Matsumoto */
mt[mti] &= ResultType.max;
/* for >32 bit machines */
}
}
/**
Returns the next random value.
*/
uint next()
{
static invariant ResultType
upperMask = ~((cast(ResultType) 1u <<
(ResultType.sizeof * 8 - (w - r))) - 1),
lowerMask = (cast(ResultType) 1u << r) - 1;
ulong y = void;
static invariant ResultType mag01[2] = [0x0UL, a];
if (mti >= n)
{
/* generate N words at one time */
if (mti == n + 1) /* if init_genrand() has not been called, */
seed(5489UL); /* a default initial seed is used */
int kk = 0;
for (; kk < n - m; ++kk)
{
y = (mt[kk] & upperMask)|(mt[kk + 1] & lowerMask);
mt[kk] = cast(UIntType) (mt[kk + m] ^ (y >> 1)
^ mag01[cast(UIntType) y & 0x1U]);
}
for (; kk < n - 1; ++kk)
{
y = (mt[kk] & upperMask)|(mt[kk + 1] & lowerMask);
mt[kk] = cast(UIntType) (mt[kk + (m -n)] ^ (y >> 1)
^ mag01[cast(UIntType) y & 0x1U]);
}
y = (mt[n -1] & upperMask)|(mt[0] & lowerMask);
mt[n - 1] = cast(UIntType) (mt[m - 1] ^ (y >> 1)
^ mag01[cast(UIntType) y & 0x1U]);
mti = 0;
}
y = mt[mti++];
/* Tempering */
y ^= (y >> temperingU);
y ^= (y << temperingS) & temperingB;
y ^= (y << temperingT) & temperingC;
y ^= (y >> temperingL);
return cast(UIntType) y;
}
/**
Discards next $(D_PARAM n) samples.
*/
void discard(ulong n)
{
while (n--) next;
}
private ResultType mt[n];
private size_t mti = n + 1; /* means mt is not initialized */
}
/**
A $(D MersenneTwisterEngine) instantiated with the parameters of the
original engine $(WEB math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html,
MT19937), generating uniformly-distributed 32-bit numbers with a
period of 2 to the power of 19937. Recommended for random number
generation unless memory is severely restricted, in which case a $(D
LinearCongruentialEngine) would be the generator of choice.
Example:
----
// seed with a constant
Mt19937 gen;
auto n = gen.next; // same for each run
// Seed with an unpredictable value
gen.seed(unpredictableSeed);
n = gen.next; // different across runs
----
*/
alias MersenneTwisterEngine!(uint, 32, 624, 397, 31, 0x9908b0df, 11, 7,
0x9d2c5680, 15, 0xefc60000, 18)
Mt19937;
unittest
{
Mt19937 gen;
gen.discard(9999);
assert(gen.next == 4123659995);
}
/**
The "default", "favorite", "suggested" random number generator on the
current platform. It is a typedef for one of the previously-defined
generators. You may want to use it if (1) you need to generate some
nice random numbers, and (2) you don't care for the minutiae of the
method being used.
*/
alias Mt19937 Random;
/**
A "good" seed for initializing random number engines. Initializing
with $(D_PARAM unpredictableSeed) makes engines generate different
random number sequences every run.
Example:
----
auto rnd = Random(unpredictableSeed);
auto n = rnd.next;
...
----
*/
uint unpredictableSeed()
{
static bool seeded;
static MinstdRand0 rand;
if (!seeded) {
rand.seed(getpid ^ cast(uint)getUTCtime);
seeded = true;
}
return cast(uint) (getUTCtime ^ rand.next);
}
unittest
{
// not much to test here
auto a = unpredictableSeed;
static assert(is(typeof(a) == uint));
}
/**
Generates uniformly-distributed numbers within a range using an
external generator. The $(D boundaries) parameter controls the shape
of the interval (open vs. closed on either side). Valid values for $(D
boundaries) are "[]", "$(LPAREN)]", "[$(RPAREN)", and "()". The
default interval is [a, b$(RPAREN).
Example:
----
auto a = new double[20];
Random gen;
auto rndIndex = UniformDistribution!(uint)(0, a.length);
auto rndValue = UniformDistribution!(double)(0, 1);
// Get a random index into the array
auto i = rndIndex.next(gen);
// Get a random probability, i.e., a real number in [0, 1$(RPAREN)
auto p = rndValue.next(gen);
// Assign that value to that array element
a[i] = p;
auto digits = UniformDistribution!(char, "[]")('0', '9');
auto percentages = UniformDistribution!(double, "$(LPAREN)]")(0.0, 100.0);
// Get a digit in ['0', '9']
auto digit = digits.next(gen);
// Get a number in $(LPAREN)0.0, 100.0]
auto p = percentages.next(gen);
----
*/
struct UniformDistribution(NumberType, string boundaries = "[)")
{
enum char leftLim = boundaries[0], rightLim = boundaries[1];
static assert((leftLim == '[' || leftLim == '(')
&& (rightLim == ']' || rightLim == ')'));
alias NumberType InputType;
alias NumberType ResultType;
/**
Constructs a $(D UniformDistribution) able to generate numbers between
$(D a) and $(D b). The bounds of the interval are controlled by the
template argument, e.g. $(D UniformDistribution!(double, "[]")(0, 1))
generates numbers in the interval [0.0, 1.0].
*/
static UniformDistribution opCall(NumberType a, NumberType b)
{
UniformDistribution result;
static if (leftLim == '(')
result._a = nextLarger(a);
else
result._a = a;
static if (rightLim == ')')
result._b = nextSmaller(b);
else
result._b = b;
enforce(result._a <= result._b,
"Invalid distribution range: " ~ leftLim ~ to!(string)(a)
~ ", " ~ to!(string)(b) ~ rightLim);
return result;
}
/**
Returns the left bound of the random value generated.
*/
ResultType a() { return leftLim == '[' ? _a : nextSmaller(_a); }
/**
Returns the the right bound of the random value generated.
*/
ResultType b() { return rightLim == ']' ? _b : nextLarger(_b); }
/**
Does nothing (provided for conformity with other distributions).
*/
void reset()
{
}
/**
Returns a random number using $(D UniformRandomNumberGenerator) as
back-end.
*/
ResultType next(UniformRandomNumberGenerator)
(ref UniformRandomNumberGenerator urng)
{
static if (isIntegral!(NumberType))
{
auto myRange = _b - _a;
if (!myRange) return _a;
assert(urng.max - urng.min >= myRange,
"UniformIntGenerator.next not implemented for large ranges");
unsigned!(typeof((urng.max - urng.min + 1) / (myRange + 1)))
bucketSize = 1 + (urng.max - urng.min - myRange) / (myRange + 1);
assert(bucketSize, to!(string)(myRange));
ResultType r = void;
do
{
r = (urng.next - urng.min) / bucketSize;
}
while (r > myRange);
return _a + r;
}
else
{
return _a + (_b - _a) * cast(NumberType) (urng.next - urng.min)
/ (urng.max - urng.min);
}
}
private:
NumberType _a = 0, _b = NumberType.max;
static NumberType nextLarger(NumberType x)
{
static if (isIntegral!(NumberType))
return x + 1;
else
return nextafter(x, x.infinity);
}
static NumberType nextSmaller(NumberType x)
{
static if (isIntegral!(NumberType))
return x - 1;
else
return nextafter(x, -x.infinity);
}
}
unittest
{
MinstdRand0 gen;
auto rnd1 = UniformDistribution!(int)(0, 15);
foreach (i; 0 .. 20)
{
auto x = rnd1.next(gen);
assert(0 <= x && x <= 15);
//writeln(x);
}
}
unittest
{
MinstdRand0 gen;
foreach (i; 0 .. 20)
{
auto x = uniform!(double)(gen, 0., 15.);
assert(0 <= x && x <= 15);
//writeln(x);
}
}
/**
Convenience function that generates a number in an interval by
forwarding to $(D UniformDistribution!(T, boundaries)(a, b).next).
Example:
----
Random gen(unpredictableSeed);
// Generate an integer in [0, 1024$(RPAREN)
auto a = uniform(gen, 0, 1024);
// Generate a float in [0, 1$(RPAREN)
auto a = uniform(gen, 0.0f, 1.0f);
----
*/
T1 uniform(T1, string boundaries = "[)", UniformRandomNumberGenerator, T2)
(ref UniformRandomNumberGenerator gen, T1 a, T2 b)
{
alias typeof(return) Result;
auto dist = UniformDistribution!(Result, boundaries)(a, b);
return dist.next(gen);
}
unittest
{
auto gen = Mt19937(unpredictableSeed);
auto a = uniform(gen, 0, 1024);
assert(0 <= a && a <= 1024);
auto b = uniform(gen, 0.0f, 1.0f);
assert(0 <= b && b < 1, to!(string)(b));
}
/**
Shuffles elements of $(D array) using $(D r) as a shuffler.
*/
void randomShuffle(T, SomeRandomGen)(T[] array, ref SomeRandomGen r)
{
foreach (i; 0 .. array.length)
{
// generate a random number i .. n
invariant which = i + uniform!(size_t)(r, 0u, array.length - i);
swap(array[i], array[which]);
}
}
unittest
{
auto a = ([ 1, 2, 3, 4, 5, 6, 7, 8, 9 ]).dup;
auto b = a.dup;
Mt19937 gen;
randomShuffle(a, gen);
//assert(a == expectedA);
assert(a.sort == b.sort);
}
/**
Throws a dice with relative probabilities stored in $(D
proportions). Returns the index in $(D proportions) that was chosen.
Example:
----
auto x = dice(0.5, 0.5); // x is 0 or 1 in equal proportions
auto y = dice(50, 50); // y is 0 or 1 in equal proportions
auto z = dice(70, 20, 10); // z is 0 70% of the time, 1 30% of the time,
// and 2 10% of the time
----
*/
size_t dice(R)(ref R rnd, double[] proportions...) {
invariant sum = reduce!("(assert(b >= 0), a + b)")(0.0, proportions);
enforce(sum > 0, "Proportions in a dice cannot sum to zero");
invariant point = uniform(rnd, 0.0, sum);
assert(point < sum);
auto mass = 0.0;
foreach (i, e; proportions) {
mass += e;
if (point < mass) return i;
}
// this point should not be reached
assert(false);
}
unittest {
auto rnd = Random(unpredictableSeed);
auto i = dice(rnd, 0.0, 100.0);
assert(i == 1);
i = dice(rnd, 100.0, 0.0);
assert(i == 0);
}
/* ===================== Random ========================= */
// BUG: not multithreaded
private uint seed; // starting seed
private uint index; // ith random number
/**
The random number generator is seeded at program startup with a random
value. This ensures that each program generates a different sequence
of random numbers. To generate a repeatable sequence, use $(D
rand_seed()) to start the sequence. seed and index start it, and each
successive value increments index. This means that the $(I n)th
random number of the sequence can be directly generated by passing
index + $(I n) to $(D rand_seed()).
Note: This is more random, but slower, than C's $(D rand()) function.
To use C's $(D rand()) instead, import $(D std.c.stdlib).
BUGS: Shares a global single state, not multithreaded. SCHEDULED FOR
DEPRECATION.
*/
void rand_seed(uint seed, uint index)
{
.seed = seed;
.index = index;
}
/**
Get the next random number in sequence.
BUGS: Shares a global single state, not multithreaded.
SCHEDULED FOR DEPRECATION.
*/
uint rand()
{
static uint xormix1[20] =
[
0xbaa96887, 0x1e17d32c, 0x03bcdc3c, 0x0f33d1b2,
0x76a6491d, 0xc570d85d, 0xe382b1e3, 0x78db4362,
0x7439a9d4, 0x9cea8ac5, 0x89537c5c, 0x2588f55d,
0x415b5e1d, 0x216e3d95, 0x85c662e7, 0x5e8ab368,
0x3ea5cc8c, 0xd26a0f74, 0xf3a9222b, 0x48aad7e4
];
static uint xormix2[20] =
[
0x4b0f3b58, 0xe874f0c3, 0x6955c5a6, 0x55a7ca46,
0x4d9a9d86, 0xfe28a195, 0xb1ca7865, 0x6b235751,
0x9a997a61, 0xaa6e95c8, 0xaaa98ee1, 0x5af9154c,
0xfc8e2263, 0x390f5e8c, 0x58ffd802, 0xac0a5eba,
0xac4874f6, 0xa9df0913, 0x86be4c74, 0xed2c123b
];
uint hiword, loword, hihold, temp, itmpl, itmph, i;
loword = seed;
hiword = index++;
for (i = 0; i < 4; i++) // loop limit can be 2..20, we choose 4
{
hihold = hiword; // save hiword for later
temp = hihold ^ xormix1[i]; // mix up bits of hiword
itmpl = temp & 0xffff; // decompose to hi & lo
itmph = temp >> 16; // 16-bit words
temp = itmpl * itmpl + ~(itmph * itmph); // do a multiplicative mix
temp = (temp >> 16) | (temp << 16); // swap hi and lo halves
hiword = loword ^ ((temp ^ xormix2[i]) + itmpl * itmph); //loword mix
loword = hihold; // old hiword is loword
}
return hiword;
}
static this()
{
ulong s;
version(Win32)
{
QueryPerformanceCounter(&s);
}
version(Posix)
{
// time.h
// sys/time.h
timeval tv;
if (gettimeofday(&tv, null))
{ // Some error happened - try time() instead
s = std.c.linux.linux.time(null);
}
else
{
s = cast(ulong)((cast(long)tv.tv_sec << 32) + tv.tv_usec);
}
}
rand_seed(cast(uint) s, cast(uint)(s >> 32));
}
unittest
{
static uint results[10] =
[
0x8c0188cb,
0xb161200c,
0xfc904ac5,
0x2702e049,
0x9705a923,
0x1c139d89,
0x346b6d1f,
0xf8c33e32,
0xdb9fef76,
0xa97fcb3f
];
int i;
uint seedsave = seed;
uint indexsave = index;
rand_seed(1234, 5678);
for (i = 0; i < 10; i++)
{ uint r = rand();
//printf("0x%x,\n", rand());
assert(r == results[i]);
}
seed = seedsave;
index = indexsave;
}
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