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Spannified internals of BigInteger (dotnet#35565)
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* Unsafe pointers replaced with managed pointers

* Duplicate code replaced with static local

* Spannified internals

* Spannified compare

* Spannified div/rem operations

* Minus two array allocations for each bitwise operation

* Removed redundant locals

* Code review feedback (code style)

* Code review feedback

* LeadingZeroes replaced with BitOperations

* stackalloc in Divide without remainder

* Reduced memory allocation for bitwise operations

* Managed pointer replaced with Span

* Removed namespace imports

* Removed delegate type

* Reduced memory allocation in the end of each bitwise operation

* Code review feedback

* Removed redundant array allocation

* Trivial division moved to stack alloc

* Reduced memory allocation for divide operator

* Reduced memory allocation for shift operations

* Array pooling for Square operation

* Fixed bound check for bitwise operations

* Multiply now uses array pooling

* Removed namespace import

* Reduced memory allocation for Add

* Removed swap of arguments

* Reduced memory allocations for multiply operator

* Reduced memory allocations for modulo operator

* Temporarily spannify ActualLength method

* Spannify FastReducer

* Spannify initial parts of GCD alg

* Simple GCD test for debugging

* Simple test for debugging

* Removed debug code

* Spannified GCD algorithm

* Removed arg passing by ref

* Complete migration of gcd to span

* Removed memory allocation for trivial case of GCD

* Reorganize utility code

* Removed redundant parameter

* Reduced memory alloc for trivial case of Pow alg

* Use span for trivial modulus pow case

* Use span for trivial cases of pow modulus

* Fixed buffer cleanup

* Reduced memory allocation of ModPow operations

* BitsBuffer replaced with span

* Reorganize utility methods

* Reduced visibility scope

* Removed temporary code for bits cleanup

* Fill leading bits with zeroes

* Unify order of parameters

* Unify order of parameters

* Unify order of parameters

* Reuse the same local var

* Removed whtespace

* Code review feedback

* Avoid misleading with Span.CopyTo

* Clarify purpose of slicing

Co-authored-by: Günther Foidl <[email protected]>

* Replace mentioning of uint[] in comments

* Fixed code formatting issues

* Share StackAllocThreshold const

* Ignore const threshold values in Release config

* Literal field cannot be discovered with TypeInfo.GetDeclaredField

* Removed invalid assertion

* Removed invalid assertion

* Removed invalid assertion

* Code review feedback

* Fixed header

* Fixed overflow of result buffer

* Reduced ctor visibility

* Eliminated bounds check

* Returned optimization using Math.DivRem

* Added braces to be consistent with other branches

* Fixed location of the comment

* Combine slice and conversion as the single line

* Combine slice and conversion as the single line

* Merge with parsing optimizations

* Reduced checks

* Removed redundant global const

* Replaced magic consts with their named equivalents

* Removed useless asserts

* Manual merge with dotnet#53984 PR

* Review feedback (use const for stackalloc)

* Review feedback

* Unsafe code replaced with span indexer where possible

* Removed unused local

* Review feedback

Co-authored-by: Günther Foidl <[email protected]>
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@sakno @gfoidl
sakno and gfoidl authored Oct 8, 2021
1 parent 3649506 commit 22b516c
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Showing 15 changed files with 1,374 additions and 1,409 deletions.
3 changes: 2 additions & 1 deletion src/libraries/System.Runtime.Numerics/src/System.Runtime.Numerics.csproj
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Expand Up @@ -7,12 +7,12 @@
</PropertyGroup>
<ItemGroup>
<Compile Include="System\Numerics\BigIntegerCalculator.AddSub.cs" />
<Compile Include="System\Numerics\BigIntegerCalculator.BitsBuffer.cs" />
<Compile Include="System\Numerics\BigIntegerCalculator.DivRem.cs" />
<Compile Include="System\Numerics\BigIntegerCalculator.FastReducer.cs" />
<Compile Include="System\Numerics\BigIntegerCalculator.GcdInv.cs" />
<Compile Include="System\Numerics\BigIntegerCalculator.PowMod.cs" />
<Compile Include="System\Numerics\BigIntegerCalculator.SquMul.cs" />
<Compile Include="System\Numerics\BigIntegerCalculator.Utils.cs" />
<Compile Include="System\Numerics\BigInteger.cs" />
<Compile Include="System\Numerics\BigNumber.cs" />
<Compile Include="System\Numerics\NumericsHelpers.cs" />
Expand All @@ -30,5 +30,6 @@
<Reference Include="System.Memory" />
<Reference Include="System.Runtime" />
<Reference Include="System.Runtime.Extensions" />
<Reference Include="System.Runtime.CompilerServices.Unsafe" />
</ItemGroup>
</Project>
871 changes: 573 additions & 298 deletions src/libraries/System.Runtime.Numerics/src/System/Numerics/BigInteger.cs
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226 changes: 67 additions & 159 deletions src/libraries/System.Runtime.Numerics/src/System/Numerics/BigIntegerCalculator.AddSub.cs
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Expand Up @@ -2,112 +2,89 @@
// The .NET Foundation licenses this file to you under the MIT license.

using System.Diagnostics;
using System.Security;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;

namespace System.Numerics
{
internal static partial class BigIntegerCalculator
{
public static uint[] Add(uint[] left, uint right)
public static void Add(ReadOnlySpan<uint> left, uint right, Span<uint> bits)
{
Debug.Assert(left != null);
Debug.Assert(left.Length >= 1);
Debug.Assert(bits.Length == left.Length + 1);

// Executes the addition for one big and one 32-bit integer.
// Thus, we've similar code than below, but there is no loop for
// processing the 32-bit integer, since it's a single element.

uint[] bits = new uint[left.Length + 1];
long carry = right;

long digit = (long)left[0] + right;
bits[0] = unchecked((uint)digit);
long carry = digit >> 32;

for (int i = 1; i < left.Length; i++)
for (int i = 0; i < left.Length; i++)
{
digit = left[i] + carry;
long digit = left[i] + carry;
bits[i] = unchecked((uint)digit);
carry = digit >> 32;
}
bits[left.Length] = (uint)carry;

return bits;
bits[left.Length] = (uint)carry;
}

public static unsafe uint[] Add(uint[] left, uint[] right)
public static void Add(ReadOnlySpan<uint> left, ReadOnlySpan<uint> right, Span<uint> bits)
{
Debug.Assert(left != null);
Debug.Assert(right != null);
Debug.Assert(left.Length >= right.Length);
Debug.Assert(bits.Length == left.Length + 1);

// Switching to unsafe pointers helps sparing
// some nasty index calculations...

uint[] bits = new uint[left.Length + 1];

fixed (uint* l = left, r = right, b = &bits[0])
{
Add(l, left.Length,
r, right.Length,
b, bits.Length);
}

return bits;
}
int i = 0;
long carry = 0L;

private static unsafe void Add(uint* left, int leftLength,
uint* right, int rightLength,
uint* bits, int bitsLength)
{
Debug.Assert(leftLength >= 0);
Debug.Assert(rightLength >= 0);
Debug.Assert(leftLength >= rightLength);
Debug.Assert(bitsLength == leftLength + 1);
// Switching to managed references helps eliminating
// index bounds check...
ref uint leftPtr = ref MemoryMarshal.GetReference(left);
ref uint resultPtr = ref MemoryMarshal.GetReference(bits);

// Executes the "grammar-school" algorithm for computing z = a + b.
// While calculating z_i = a_i + b_i we take care of overflow:
// Since a_i + b_i + c <= 2(2^32 - 1) + 1 = 2^33 - 1, our carry c
// has always the value 1 or 0; hence, we're safe here.

int i = 0;
long carry = 0L;

for (; i < rightLength; i++)
for ( ; i < right.Length; i++)
{
long digit = (left[i] + carry) + right[i];
bits[i] = unchecked((uint)digit);
long digit = (Unsafe.Add(ref leftPtr, i) + carry) + right[i];
Unsafe.Add(ref resultPtr, i) = unchecked((uint)digit);
carry = digit >> 32;
}
for (; i < leftLength; i++)
for ( ; i < left.Length; i++)
{
long digit = left[i] + carry;
bits[i] = unchecked((uint)digit);
Unsafe.Add(ref resultPtr, i) = unchecked((uint)digit);
carry = digit >> 32;
}
bits[i] = (uint)carry;
Unsafe.Add(ref resultPtr, i) = (uint)carry;
}

private static unsafe void AddSelf(uint* left, int leftLength,
uint* right, int rightLength)
private static void AddSelf(Span<uint> left, ReadOnlySpan<uint> right)
{
Debug.Assert(leftLength >= 0);
Debug.Assert(rightLength >= 0);
Debug.Assert(leftLength >= rightLength);
Debug.Assert(left.Length >= right.Length);

int i = 0;
long carry = 0L;

// Switching to managed references helps eliminating
// index bounds check...
ref uint leftPtr = ref MemoryMarshal.GetReference(left);

// Executes the "grammar-school" algorithm for computing z = a + b.
// Same as above, but we're writing the result directly to a and
// stop execution, if we're out of b and c is already 0.

int i = 0;
long carry = 0L;

for (; i < rightLength; i++)
for ( ; i < right.Length; i++)
{
long digit = (left[i] + carry) + right[i];
left[i] = unchecked((uint)digit);
long digit = (Unsafe.Add(ref leftPtr, i) + carry) + right[i];
Unsafe.Add(ref leftPtr, i) = unchecked((uint)digit);
carry = digit >> 32;
}
for (; carry != 0 && i < leftLength; i++)
for ( ; carry != 0 && i < left.Length; i++)
{
long digit = left[i] + carry;
left[i] = (uint)digit;
Expand All @@ -117,110 +94,84 @@ private static unsafe void AddSelf(uint* left, int leftLength,
Debug.Assert(carry == 0);
}

public static uint[] Subtract(uint[] left, uint right)
public static void Subtract(ReadOnlySpan<uint> left, uint right, Span<uint> bits)
{
Debug.Assert(left != null);
Debug.Assert(left.Length >= 1);
Debug.Assert(left[0] >= right || left.Length >= 2);
Debug.Assert(bits.Length == left.Length);

// Executes the subtraction for one big and one 32-bit integer.
// Thus, we've similar code than below, but there is no loop for
// processing the 32-bit integer, since it's a single element.

uint[] bits = new uint[left.Length];
long carry = -right;

long digit = (long)left[0] - right;
bits[0] = unchecked((uint)digit);
long carry = digit >> 32;

for (int i = 1; i < left.Length; i++)
for (int i = 0; i < left.Length; i++)
{
digit = left[i] + carry;
long digit = left[i] + carry;
bits[i] = unchecked((uint)digit);
carry = digit >> 32;
}

return bits;
}

public static unsafe uint[] Subtract(uint[] left, uint[] right)
public static void Subtract(ReadOnlySpan<uint> left, ReadOnlySpan<uint> right, Span<uint> bits)
{
Debug.Assert(left != null);
Debug.Assert(right != null);
Debug.Assert(left.Length >= right.Length);
Debug.Assert(Compare(left, right) >= 0);
Debug.Assert(bits.Length == left.Length);

// Switching to unsafe pointers helps sparing
// some nasty index calculations...

uint[] bits = new uint[left.Length];

fixed (uint* l = left, r = right, b = bits)
{
Subtract(l, left.Length,
r, right.Length,
b, bits.Length);
}

return bits;
}
int i = 0;
long carry = 0L;

private static unsafe void Subtract(uint* left, int leftLength,
uint* right, int rightLength,
uint* bits, int bitsLength)
{
Debug.Assert(leftLength >= 0);
Debug.Assert(rightLength >= 0);
Debug.Assert(leftLength >= rightLength);
Debug.Assert(Compare(left, leftLength, right, rightLength) >= 0);
Debug.Assert(bitsLength == leftLength);
// Switching to managed references helps eliminating
// index bounds check...
ref uint leftPtr = ref MemoryMarshal.GetReference(left);
ref uint resultPtr = ref MemoryMarshal.GetReference(bits);

// Executes the "grammar-school" algorithm for computing z = a - b.
// While calculating z_i = a_i - b_i we take care of overflow:
// Since a_i - b_i doesn't need any additional bit, our carry c
// has always the value -1 or 0; hence, we're safe here.

int i = 0;
long carry = 0L;

for (; i < rightLength; i++)
for ( ; i < right.Length; i++)
{
long digit = (left[i] + carry) - right[i];
bits[i] = unchecked((uint)digit);
long digit = (Unsafe.Add(ref leftPtr, i) + carry) - right[i];
Unsafe.Add(ref resultPtr, i) = unchecked((uint)digit);
carry = digit >> 32;
}
for (; i < leftLength; i++)
for ( ; i < left.Length; i++)
{
long digit = left[i] + carry;
bits[i] = (uint)digit;
Unsafe.Add(ref resultPtr, i) = (uint)digit;
carry = digit >> 32;
}

Debug.Assert(carry == 0);
}

private static unsafe void SubtractSelf(uint* left, int leftLength,
uint* right, int rightLength)
private static void SubtractSelf(Span<uint> left, ReadOnlySpan<uint> right)
{
Debug.Assert(leftLength >= 0);
Debug.Assert(rightLength >= 0);
Debug.Assert(leftLength >= rightLength);
Debug.Assert(Compare(left, leftLength, right, rightLength) >= 0);
Debug.Assert(left.Length >= right.Length);
Debug.Assert(Compare(left, right) >= 0);

int i = 0;
long carry = 0L;

// Switching to managed references helps eliminating
// index bounds check...
ref uint leftPtr = ref MemoryMarshal.GetReference(left);

// Executes the "grammar-school" algorithm for computing z = a - b.
// Same as above, but we're writing the result directly to a and
// stop execution, if we're out of b and c is already 0.

int i = 0;
long carry = 0L;

for (; i < rightLength; i++)
for (; i < right.Length; i++)
{
long digit = (left[i] + carry) - right[i];
left[i] = unchecked((uint)digit);
long digit = (Unsafe.Add(ref leftPtr, i) + carry) - right[i];
Unsafe.Add(ref leftPtr, i) = unchecked((uint)digit);
carry = digit >> 32;
}
for (; carry != 0 && i < leftLength; i++)
for (; carry != 0 && i < left.Length; i++)
{
long digit = left[i] + carry;
left[i] = (uint)digit;
Expand All @@ -229,48 +180,5 @@ private static unsafe void SubtractSelf(uint* left, int leftLength,

Debug.Assert(carry == 0);
}

public static int Compare(uint[] left, uint[] right)
{
Debug.Assert(left != null);
Debug.Assert(right != null);

if (left.Length < right.Length)
return -1;
if (left.Length > right.Length)
return 1;

for (int i = left.Length - 1; i >= 0; i--)
{
if (left[i] < right[i])
return -1;
if (left[i] > right[i])
return 1;
}

return 0;
}

private static unsafe int Compare(uint* left, int leftLength,
uint* right, int rightLength)
{
Debug.Assert(leftLength >= 0);
Debug.Assert(rightLength >= 0);

if (leftLength < rightLength)
return -1;
if (leftLength > rightLength)
return 1;

for (int i = leftLength - 1; i >= 0; i--)
{
if (left[i] < right[i])
return -1;
if (left[i] > right[i])
return 1;
}

return 0;
}
}
}
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