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Speeding up Random.Shuffle by batching #111015

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Speeding up Random.Shuffle by batching #111015

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f9a70c1
Speeding up `Random.Shuffle` by batching
andanteyk Jan 1, 2025
1d08e67
Safe swap, add comment
andanteyk Jan 2, 2025
4d41ce6
Add comments
andanteyk Jan 3, 2025
904aa9d
Add statistical tests to `RandomNumberGenerator.Shuffle()`
andanteyk Jan 4, 2025
8ff424e
Moved Shuffle code to Impl
andanteyk Jan 7, 2025
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36 changes: 36 additions & 0 deletions src/libraries/System.Private.CoreLib/src/System/Random.CompatImpl.cs
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Original file line number Diff line number Diff line change
Expand Up @@ -98,6 +98,23 @@ public override float NextSingle()
public override void NextBytes(byte[] buffer) => _prng.NextBytes(buffer);

public override void NextBytes(Span<byte> buffer) => _prng.NextBytes(buffer);

public override void Shuffle<T>(Span<T> values)
{
int n = values.Length;

for (int i = 0; i < n - 1; i++)
{
int j = Next(i, n);

if (j != i)
{
T temp = values[i];
values[i] = values[j];
values[j] = temp;
}
}
}
}

/// <summary>
Expand Down Expand Up @@ -231,6 +248,25 @@ public override void NextBytes(Span<byte> buffer)
buffer[i] = (byte)_parent.Next();
}
}

public override void Shuffle<T>(Span<T> values)
{
_prng.EnsureInitialized(_seed);

int n = values.Length;

for (int i = 0; i < n - 1; i++)
{
int j = Next(i, n);

if (j != i)
{
T temp = values[i];
values[i] = values[j];
values[j] = temp;
}
}
}
}

/// <summary>
Expand Down
2 changes: 2 additions & 0 deletions src/libraries/System.Private.CoreLib/src/System/Random.ImplBase.cs
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Original file line number Diff line number Diff line change
Expand Up @@ -33,6 +33,8 @@ internal abstract class ImplBase

public abstract void NextBytes(Span<byte> buffer);

public abstract void Shuffle<T>(Span<T> values);

// NextUInt32/64 algorithms based on https://arxiv.org/pdf/1805.10941.pdf and https://github.com/lemire/fastrange.

[MethodImpl(MethodImplOptions.AggressiveInlining)]
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77 changes: 77 additions & 0 deletions src/libraries/System.Private.CoreLib/src/System/Random.Xoshiro128StarStarImpl.cs
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Original file line number Diff line number Diff line change
Expand Up @@ -224,6 +224,83 @@ ref MemoryMarshal.GetReference(buffer),
_s3 = s3;
}

public override void Shuffle<T>(Span<T> values)
{
// The upper limit of the first random number generated.
// 2432902008176640000 == 20! (Largest factorial smaller than 2^64)
ulong bound = 2432902008176640000;
int nextIndex = Math.Min(20, values.Length);

for (int i = 1; i < values.Length;)
{
ulong r = NextUInt64();

// Correct r to be unbiased.
// Ensure that the result of `Math.BigMul(r, bound, out _)` is
// uniformly distributed between 0 <= result < bound without bias.
ulong rbound = r * bound;

// Look at the lower 64 bits of r * bound,
// and if there is a carryover possibility...
// (The maximum value added in subsequent processing is bound - 1,
// so if rbound <= (2^64) - bound, no carryover occurs.)
if (rbound > 0 - bound)
{
ulong sum, carry;
do
{
// Generate an additional random number t and check if it carries over
// [rhi] . [rlo] -> r * bound; upper rhi, lower rlo
// + 0 . [thi] [tlo] -> t * bound; upper thi, lower tlo
// ---------------------
// [carry. sum] [tlo] -> rhi + carry is the result
ulong t = NextUInt64();
ulong thi = Math.BigMul(t, bound, out ulong tlo);
sum = rbound + thi;
carry = sum < rbound ? 1ul : 0ul;
rbound = tlo;

// If sum == 0xff...ff, there is a possibility of a carry
// in the future, so calculate it again.
// If not, there will be no more carry,
// so add the carry and finish.
} while (sum == ~0ul);
r += carry;
}

// Do the Fisher-Yates shuffle based on r.
// For example, the result of `Math.BigMul(r, 20!, out _)` is expressed as
// (0..2) * 20!/2! + (0..3) * 20!/3! + ... + (0..20) * 20!/20!
// Imagine extracting the numbers inside the parentheses.
for (int m = i; m < nextIndex; m++)
{
int index = (int)Math.BigMul(r, (ulong)(m + 1), out r);

// Swap span[m] <-> span[index]
T temp = values[m];
values[m] = values[index];
values[index] = temp;
}

i = nextIndex;

// Calculates next bound.
// bound is (i + 1) * (i + 2) * ... * (nextIndex) < 2^64
bound = (ulong)(i + 1);
for (nextIndex = i + 1; nextIndex < values.Length; nextIndex++)
{
if (Math.BigMul(bound, (ulong)(nextIndex + 1), out var newbound) == 0)
{
bound = newbound;
}
else
{
break;
}
}
}
}

public override double NextDouble() =>
// See comment in Xoshiro256StarStarImpl.
(NextUInt64() >> 11) * (1.0 / (1ul << 53));
Expand Down
77 changes: 77 additions & 0 deletions src/libraries/System.Private.CoreLib/src/System/Random.Xoshiro256StarStarImpl.cs
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Original file line number Diff line number Diff line change
Expand Up @@ -181,6 +181,83 @@ ref MemoryMarshal.GetReference(buffer),
_s3 = s3;
}

public override void Shuffle<T>(Span<T> values)
{
// The upper limit of the first random number generated.
// 2432902008176640000 == 20! (Largest factorial smaller than 2^64)
ulong bound = 2432902008176640000;
int nextIndex = Math.Min(20, values.Length);

for (int i = 1; i < values.Length;)
{
ulong r = NextUInt64();

// Correct r to be unbiased.
// Ensure that the result of `Math.BigMul(r, bound, out _)` is
// uniformly distributed between 0 <= result < bound without bias.
ulong rbound = r * bound;

// Look at the lower 64 bits of r * bound,
// and if there is a carryover possibility...
// (The maximum value added in subsequent processing is bound - 1,
// so if rbound <= (2^64) - bound, no carryover occurs.)
if (rbound > 0 - bound)
{
ulong sum, carry;
do
{
// Generate an additional random number t and check if it carries over
// [rhi] . [rlo] -> r * bound; upper rhi, lower rlo
// + 0 . [thi] [tlo] -> t * bound; upper thi, lower tlo
// ---------------------
// [carry. sum] [tlo] -> rhi + carry is the result
ulong t = NextUInt64();
ulong thi = Math.BigMul(t, bound, out ulong tlo);
sum = rbound + thi;
carry = sum < rbound ? 1ul : 0ul;
rbound = tlo;

// If sum == 0xff...ff, there is a possibility of a carry
// in the future, so calculate it again.
// If not, there will be no more carry,
// so add the carry and finish.
} while (sum == ~0ul);
r += carry;
}

// Do the Fisher-Yates shuffle based on r.
// For example, the result of `Math.BigMul(r, 20!, out _)` is expressed as
// (0..2) * 20!/2! + (0..3) * 20!/3! + ... + (0..20) * 20!/20!
// Imagine extracting the numbers inside the parentheses.
for (int m = i; m < nextIndex; m++)
{
int index = (int)Math.BigMul(r, (ulong)(m + 1), out r);

// Swap span[m] <-> span[index]
T temp = values[m];
values[m] = values[index];
values[index] = temp;
}

i = nextIndex;

// Calculates next bound.
// bound is (i + 1) * (i + 2) * ... * (nextIndex) < 2^64
bound = (ulong)(i + 1);
for (nextIndex = i + 1; nextIndex < values.Length; nextIndex++)
{
if (Math.BigMul(bound, (ulong)(nextIndex + 1), out var newbound) == 0)
{
bound = newbound;
}
else
{
break;
}
}
}
}

public override double NextDouble() =>
// As described in http://prng.di.unimi.it/:
// "A standard double (64-bit) floating-point number in IEEE floating point format has 52 bits of significand,
Expand Down
14 changes: 1 addition & 13 deletions src/libraries/System.Private.CoreLib/src/System/Random.cs
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Original file line number Diff line number Diff line change
Expand Up @@ -363,19 +363,7 @@ public void Shuffle<T>(T[] values)
/// </remarks>
public void Shuffle<T>(Span<T> values)
{
int n = values.Length;

for (int i = 0; i < n - 1; i++)
{
int j = Next(i, n);

if (j != i)
{
T temp = values[i];
values[i] = values[j];
values[j] = temp;
}
}
_impl.Shuffle(values);
}

/// <summary>Returns a random floating-point number between 0.0 and 1.0.</summary>
Expand Down
78 changes: 71 additions & 7 deletions ...es/System.Security.Cryptography/src/System/Security/Cryptography/RandomNumberGenerator.cs
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Original file line number Diff line number Diff line change
Expand Up @@ -5,6 +5,7 @@
using System.Diagnostics;
using System.Diagnostics.CodeAnalysis;
using System.Numerics;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;

namespace System.Security.Cryptography
Expand Down Expand Up @@ -288,17 +289,80 @@ public static string GetHexString(int stringLength, bool lowercase = false)
/// <typeparam name="T">The type of span.</typeparam>
public static void Shuffle<T>(Span<T> values)
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Changes for cryptographic RNG may subject to more careful review for security requirements.

{
int n = values.Length;
// The upper limit of the first random number generated.
// 2432902008176640000 == 20! (Largest factorial smaller than 2^64)
ulong bound = 2432902008176640000;
int nextIndex = Math.Min(20, values.Length);

for (int i = 0; i < n - 1; i++)
for (int i = 1; i < values.Length;)
{
int j = GetInt32(i, n);
ulong r = 0;
RandomNumberGeneratorImplementation.FillSpan(MemoryMarshal.AsBytes(new Span<ulong>(ref r)));

// Correct r to be unbiased.
// Ensure that the result of `Math.BigMul(r, bound, out _)` is
// uniformly distributed between 0 <= result < bound without bias.
ulong rbound = r * bound;

// Look at the lower 64 bits of r * bound,
// and if there is a carryover possibility...
// (The maximum value added in subsequent processing is bound - 1,
// so if rbound <= (2^64) - bound, no carryover occurs.)
if (rbound > 0 - bound)
{
ulong sum, carry;
do
{
// Generate an additional random number t and check if it carries over
// [rhi] . [rlo] -> r * bound; upper rhi, lower rlo
// + 0 . [thi] [tlo] -> t * bound; upper thi, lower tlo
// ---------------------
// [carry. sum] [tlo] -> rhi + carry is the result
ulong t = 0;
RandomNumberGeneratorImplementation.FillSpan(MemoryMarshal.AsBytes(new Span<ulong>(ref t)));

ulong thi = Math.BigMul(t, bound, out ulong tlo);
sum = rbound + thi;
carry = sum < rbound ? 1ul : 0ul;
rbound = tlo;

// If sum == 0xff...ff, there is a possibility of a carry
// in the future, so calculate it again.
// If not, there will be no more carry,
// so add the carry and finish.
} while (sum == ~0ul);
r += carry;
}

// Do the Fisher-Yates shuffle based on r.
// For example, the result of `Math.BigMul(r, 20!, out _)` is expressed as
// (0..2) * 20!/2! + (0..3) * 20!/3! + ... + (0..20) * 20!/20!
// Imagine extracting the numbers inside the parentheses.
for (int m = i; m < nextIndex; m++)
{
int index = (int)Math.BigMul(r, (ulong)(m + 1), out r);

// Swap span[m] <-> span[index]
T temp = values[m];
values[m] = values[index];
values[index] = temp;
}

i = nextIndex;

if (i != j)
// Calculates next bound.
// bound is (i + 1) * (i + 2) * ... * (nextIndex) < 2^64
bound = (ulong)(i + 1);
for (nextIndex = i + 1; nextIndex < values.Length; nextIndex++)
{
T temp = values[i];
values[i] = values[j];
values[j] = temp;
if (Math.BigMul(bound, (ulong)(nextIndex + 1), out var newbound) == 0)
{
bound = newbound;
}
else
{
break;
}
}
}
}
Expand Down
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