#if !NET6_0_OR_GREATER
// Licensed to the .NET Foundation under one or more agreements.
// The .NET Foundation licenses this file to you under the MIT license.
// See the LICENSE file in the project root for more information.
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
// Some routines inspired by the Stanford Bit Twiddling Hacks by Sean Eron Anderson:
// http://graphics.stanford.edu/~seander/bithacks.html
namespace System.Numerics
{
///
/// Utility methods for intrinsic bit-twiddling operations.
/// The methods use hardware intrinsics when available on the underlying platform,
/// otherwise they use optimized software fallbacks.
///
internal static class BitOperations
{
// C# no-alloc optimization that directly wraps the data section of the dll (similar to string constants)
// https://github.com/dotnet/roslyn/pull/24621
private static ReadOnlySpan TrailingZeroCountDeBruijn => new byte[32]
{
00, 01, 28, 02, 29, 14, 24, 03,
30, 22, 20, 15, 25, 17, 04, 08,
31, 27, 13, 23, 21, 19, 16, 07,
26, 12, 18, 06, 11, 05, 10, 09
};
private static ReadOnlySpan Log2DeBruijn => new byte[32]
{
00, 09, 01, 10, 13, 21, 02, 29,
11, 14, 16, 18, 22, 25, 03, 30,
08, 12, 20, 28, 15, 17, 24, 07,
19, 27, 23, 06, 26, 05, 04, 31
};
///
/// Count the number of leading zero bits in a mask.
/// Similar in behavior to the x86 instruction LZCNT.
///
/// The value.
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static int LeadingZeroCount(uint value)
{
// Unguarded fallback contract is 0->31
if (value == 0)
{
return 32;
}
return 31 - Log2SoftwareFallback(value);
}
///
/// Count the number of leading zero bits in a mask.
/// Similar in behavior to the x86 instruction LZCNT.
///
/// The value.
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static int LeadingZeroCount(ulong value)
{
uint hi = (uint)(value >> 32);
if (hi == 0)
{
return 32 + LeadingZeroCount((uint)value);
}
return LeadingZeroCount(hi);
}
///
/// Returns the integer (floor) log of the specified value, base 2.
/// Note that by convention, input value 0 returns 0 since Log(0) is undefined.
///
/// The value.
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static int Log2(uint value)
{
// Fallback contract is 0->0
return Log2SoftwareFallback(value);
}
///
/// Returns the integer (floor) log of the specified value, base 2.
/// Note that by convention, input value 0 returns 0 since Log(0) is undefined.
///
/// The value.
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static int Log2(ulong value)
{
uint hi = (uint)(value >> 32);
if (hi == 0)
{
return Log2((uint)value);
}
return 32 + Log2(hi);
}
///
/// Returns the integer (floor) log of the specified value, base 2.
/// Note that by convention, input value 0 returns 0 since Log(0) is undefined.
/// Does not directly use any hardware intrinsics, nor does it incur branching.
///
/// The value.
private static int Log2SoftwareFallback(uint value)
{
// No AggressiveInlining due to large method size
// Has conventional contract 0->0 (Log(0) is undefined)
// Fill trailing zeros with ones, eg 00010010 becomes 00011111
value |= value >> 01;
value |= value >> 02;
value |= value >> 04;
value |= value >> 08;
value |= value >> 16;
// uint.MaxValue >> 27 is always in range [0 - 31] so we use Unsafe.AddByteOffset to avoid bounds check
return Unsafe.AddByteOffset(
// Using deBruijn sequence, k=2, n=5 (2^5=32) : 0b_0000_0111_1100_0100_1010_1100_1101_1101u
ref MemoryMarshal.GetReference(Log2DeBruijn),
// uint|long -> IntPtr cast on 32-bit platforms does expensive overflow checks not needed here
(IntPtr)(int)((value * 0x07C4ACDDu) >> 27));
}
///
/// Returns the population count (number of bits set) of a mask.
/// Similar in behavior to the x86 instruction POPCNT.
///
/// The value.
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static int PopCount(uint value)
{
const uint c1 = 0x_55555555u;
const uint c2 = 0x_33333333u;
const uint c3 = 0x_0F0F0F0Fu;
const uint c4 = 0x_01010101u;
value -= (value >> 1) & c1;
value = (value & c2) + ((value >> 2) & c2);
value = (((value + (value >> 4)) & c3) * c4) >> 24;
return (int)value;
}
///
/// Returns the population count (number of bits set) of a mask.
/// Similar in behavior to the x86 instruction POPCNT.
///
/// The value.
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static int PopCount(ulong value)
{
if (IntPtr.Size == 4)
{
return PopCount((uint)value) // lo
+ PopCount((uint)(value >> 32)); // hi
}
else
{
const ulong c1 = 0x_55555555_55555555ul;
const ulong c2 = 0x_33333333_33333333ul;
const ulong c3 = 0x_0F0F0F0F_0F0F0F0Ful;
const ulong c4 = 0x_01010101_01010101ul;
value -= (value >> 1) & c1;
value = (value & c2) + ((value >> 2) & c2);
value = (((value + (value >> 4)) & c3) * c4) >> 56;
return (int)value;
}
}
///
/// Count the number of trailing zero bits in an integer value.
/// Similar in behavior to the x86 instruction TZCNT.
///
/// The value.
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static int TrailingZeroCount(int value)
=> TrailingZeroCount((uint)value);
///
/// Count the number of trailing zero bits in an integer value.
/// Similar in behavior to the x86 instruction TZCNT.
///
/// The value.
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static int TrailingZeroCount(uint value)
{
// Unguarded fallback contract is 0->0
if (value == 0)
{
return 32;
}
// uint.MaxValue >> 27 is always in range [0 - 31] so we use Unsafe.AddByteOffset to avoid bounds check
return Unsafe.AddByteOffset(
// Using deBruijn sequence, k=2, n=5 (2^5=32) : 0b_0000_0111_0111_1100_1011_0101_0011_0001u
ref MemoryMarshal.GetReference(TrailingZeroCountDeBruijn),
// uint|long -> IntPtr cast on 32-bit platforms does expensive overflow checks not needed here
(IntPtr)(int)(((value & (uint)-(int)value) * 0x077CB531u) >> 27)); // Multi-cast mitigates redundant conv.u8
}
///
/// Count the number of trailing zero bits in a mask.
/// Similar in behavior to the x86 instruction TZCNT.
///
/// The value.
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static int TrailingZeroCount(long value)
=> TrailingZeroCount((ulong)value);
///
/// Count the number of trailing zero bits in a mask.
/// Similar in behavior to the x86 instruction TZCNT.
///
/// The value.
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static int TrailingZeroCount(ulong value)
{
uint lo = (uint)value;
if (lo == 0)
{
return 32 + TrailingZeroCount((uint)(value >> 32));
}
return TrailingZeroCount(lo);
}
///
/// Rotates the specified value left by the specified number of bits.
/// Similar in behavior to the x86 instruction ROL.
///
/// The value to rotate.
/// The number of bits to rotate by.
/// Any value outside the range [0..31] is treated as congruent mod 32.
/// The rotated value.
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static uint RotateLeft(uint value, int offset)
=> (value << offset) | (value >> (32 - offset));
///
/// Rotates the specified value left by the specified number of bits.
/// Similar in behavior to the x86 instruction ROL.
///
/// The value to rotate.
/// The number of bits to rotate by.
/// Any value outside the range [0..63] is treated as congruent mod 64.
/// The rotated value.
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static ulong RotateLeft(ulong value, int offset)
=> (value << offset) | (value >> (64 - offset));
///
/// Rotates the specified value right by the specified number of bits.
/// Similar in behavior to the x86 instruction ROR.
///
/// The value to rotate.
/// The number of bits to rotate by.
/// Any value outside the range [0..31] is treated as congruent mod 32.
/// The rotated value.
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static uint RotateRight(uint value, int offset)
=> (value >> offset) | (value << (32 - offset));
///
/// Rotates the specified value right by the specified number of bits.
/// Similar in behavior to the x86 instruction ROR.
///
/// The value to rotate.
/// The number of bits to rotate by.
/// Any value outside the range [0..63] is treated as congruent mod 64.
/// The rotated value.
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static ulong RotateRight(ulong value, int offset)
=> (value >> offset) | (value << (64 - offset));
}
}
#endif