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Various micro- and medium- optimizations

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Marek Lemańczyk committed 2025-10-07 22:14:34 +02:00
1 parent 2eb622030e
commit cd1debe9d6
25 files changed
+4403 -3210
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PerfectNumbers.Core/Gpu/GpuUInt128.cs
+65 -737
View File
@@ -8,7 +8,6 @@ namespace PerfectNumbers.Core.Gpu;
public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
{
public ulong High;
public ulong Low;
private const int NativeModuloChunkBits = 8;
@@ -21,690 +20,8 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
private const int Pow2WindowOddPowerCount = 1 << (Pow2WindowSizeBits - 1);
private const int Pow2WindowMaxExponent = (1 << Pow2WindowSizeBits) - 1;
private struct Pow2OddPowerTable
{
public GpuUInt128 Element0;
public GpuUInt128 Element1;
public GpuUInt128 Element2;
public GpuUInt128 Element3;
public GpuUInt128 Element4;
public GpuUInt128 Element5;
public GpuUInt128 Element6;
public GpuUInt128 Element7;
public GpuUInt128 Element8;
public GpuUInt128 Element9;
public GpuUInt128 Element10;
public GpuUInt128 Element11;
public GpuUInt128 Element12;
public GpuUInt128 Element13;
public GpuUInt128 Element14;
public GpuUInt128 Element15;
public GpuUInt128 Element16;
public GpuUInt128 Element17;
public GpuUInt128 Element18;
public GpuUInt128 Element19;
public GpuUInt128 Element20;
public GpuUInt128 Element21;
public GpuUInt128 Element22;
public GpuUInt128 Element23;
public GpuUInt128 Element24;
public GpuUInt128 Element25;
public GpuUInt128 Element26;
public GpuUInt128 Element27;
public GpuUInt128 Element28;
public GpuUInt128 Element29;
public GpuUInt128 Element30;
public GpuUInt128 Element31;
public GpuUInt128 Element32;
public GpuUInt128 Element33;
public GpuUInt128 Element34;
public GpuUInt128 Element35;
public GpuUInt128 Element36;
public GpuUInt128 Element37;
public GpuUInt128 Element38;
public GpuUInt128 Element39;
public GpuUInt128 Element40;
public GpuUInt128 Element41;
public GpuUInt128 Element42;
public GpuUInt128 Element43;
public GpuUInt128 Element44;
public GpuUInt128 Element45;
public GpuUInt128 Element46;
public GpuUInt128 Element47;
public GpuUInt128 Element48;
public GpuUInt128 Element49;
public GpuUInt128 Element50;
public GpuUInt128 Element51;
public GpuUInt128 Element52;
public GpuUInt128 Element53;
public GpuUInt128 Element54;
public GpuUInt128 Element55;
public GpuUInt128 Element56;
public GpuUInt128 Element57;
public GpuUInt128 Element58;
public GpuUInt128 Element59;
public GpuUInt128 Element60;
public GpuUInt128 Element61;
public GpuUInt128 Element62;
public GpuUInt128 Element63;
public GpuUInt128 Element64;
public GpuUInt128 Element65;
public GpuUInt128 Element66;
public GpuUInt128 Element67;
public GpuUInt128 Element68;
public GpuUInt128 Element69;
public GpuUInt128 Element70;
public GpuUInt128 Element71;
public GpuUInt128 Element72;
public GpuUInt128 Element73;
public GpuUInt128 Element74;
public GpuUInt128 Element75;
public GpuUInt128 Element76;
public GpuUInt128 Element77;
public GpuUInt128 Element78;
public GpuUInt128 Element79;
public GpuUInt128 Element80;
public GpuUInt128 Element81;
public GpuUInt128 Element82;
public GpuUInt128 Element83;
public GpuUInt128 Element84;
public GpuUInt128 Element85;
public GpuUInt128 Element86;
public GpuUInt128 Element87;
public GpuUInt128 Element88;
public GpuUInt128 Element89;
public GpuUInt128 Element90;
public GpuUInt128 Element91;
public GpuUInt128 Element92;
public GpuUInt128 Element93;
public GpuUInt128 Element94;
public GpuUInt128 Element95;
public GpuUInt128 Element96;
public GpuUInt128 Element97;
public GpuUInt128 Element98;
public GpuUInt128 Element99;
public GpuUInt128 Element100;
public GpuUInt128 Element101;
public GpuUInt128 Element102;
public GpuUInt128 Element103;
public GpuUInt128 Element104;
public GpuUInt128 Element105;
public GpuUInt128 Element106;
public GpuUInt128 Element107;
public GpuUInt128 Element108;
public GpuUInt128 Element109;
public GpuUInt128 Element110;
public GpuUInt128 Element111;
public GpuUInt128 Element112;
public GpuUInt128 Element113;
public GpuUInt128 Element114;
public GpuUInt128 Element115;
public GpuUInt128 Element116;
public GpuUInt128 Element117;
public GpuUInt128 Element118;
public GpuUInt128 Element119;
public GpuUInt128 Element120;
public GpuUInt128 Element121;
public GpuUInt128 Element122;
public GpuUInt128 Element123;
public GpuUInt128 Element124;
public GpuUInt128 Element125;
public GpuUInt128 Element126;
public GpuUInt128 Element127;
public GpuUInt128 this[int index]
{
readonly get
{
return GetElement(index);
}
set
{
SetElement(index, value);
}
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private readonly GpuUInt128 GetElement(int index) => index switch
{
0 => Element0,
1 => Element1,
2 => Element2,
3 => Element3,
4 => Element4,
5 => Element5,
6 => Element6,
7 => Element7,
8 => Element8,
9 => Element9,
10 => Element10,
11 => Element11,
12 => Element12,
13 => Element13,
14 => Element14,
15 => Element15,
16 => Element16,
17 => Element17,
18 => Element18,
19 => Element19,
20 => Element20,
21 => Element21,
22 => Element22,
23 => Element23,
24 => Element24,
25 => Element25,
26 => Element26,
27 => Element27,
28 => Element28,
29 => Element29,
30 => Element30,
31 => Element31,
32 => Element32,
33 => Element33,
34 => Element34,
35 => Element35,
36 => Element36,
37 => Element37,
38 => Element38,
39 => Element39,
40 => Element40,
41 => Element41,
42 => Element42,
43 => Element43,
44 => Element44,
45 => Element45,
46 => Element46,
47 => Element47,
48 => Element48,
49 => Element49,
50 => Element50,
51 => Element51,
52 => Element52,
53 => Element53,
54 => Element54,
55 => Element55,
56 => Element56,
57 => Element57,
58 => Element58,
59 => Element59,
60 => Element60,
61 => Element61,
62 => Element62,
63 => Element63,
64 => Element64,
65 => Element65,
66 => Element66,
67 => Element67,
68 => Element68,
69 => Element69,
70 => Element70,
71 => Element71,
72 => Element72,
73 => Element73,
74 => Element74,
75 => Element75,
76 => Element76,
77 => Element77,
78 => Element78,
79 => Element79,
80 => Element80,
81 => Element81,
82 => Element82,
83 => Element83,
84 => Element84,
85 => Element85,
86 => Element86,
87 => Element87,
88 => Element88,
89 => Element89,
90 => Element90,
91 => Element91,
92 => Element92,
93 => Element93,
94 => Element94,
95 => Element95,
96 => Element96,
97 => Element97,
98 => Element98,
99 => Element99,
100 => Element100,
101 => Element101,
102 => Element102,
103 => Element103,
104 => Element104,
105 => Element105,
106 => Element106,
107 => Element107,
108 => Element108,
109 => Element109,
110 => Element110,
111 => Element111,
112 => Element112,
113 => Element113,
114 => Element114,
115 => Element115,
116 => Element116,
117 => Element117,
118 => Element118,
119 => Element119,
120 => Element120,
121 => Element121,
122 => Element122,
123 => Element123,
124 => Element124,
125 => Element125,
126 => Element126,
127 => Element127,
_ => Element0,
};
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private void SetElement(int index, GpuUInt128 value)
{
switch (index)
{
case 0:
Element0 = value;
return;
case 1:
Element1 = value;
return;
case 2:
Element2 = value;
return;
case 3:
Element3 = value;
return;
case 4:
Element4 = value;
return;
case 5:
Element5 = value;
return;
case 6:
Element6 = value;
return;
case 7:
Element7 = value;
return;
case 8:
Element8 = value;
return;
case 9:
Element9 = value;
return;
case 10:
Element10 = value;
return;
case 11:
Element11 = value;
return;
case 12:
Element12 = value;
return;
case 13:
Element13 = value;
return;
case 14:
Element14 = value;
return;
case 15:
Element15 = value;
return;
case 16:
Element16 = value;
return;
case 17:
Element17 = value;
return;
case 18:
Element18 = value;
return;
case 19:
Element19 = value;
return;
case 20:
Element20 = value;
return;
case 21:
Element21 = value;
return;
case 22:
Element22 = value;
return;
case 23:
Element23 = value;
return;
case 24:
Element24 = value;
return;
case 25:
Element25 = value;
return;
case 26:
Element26 = value;
return;
case 27:
Element27 = value;
return;
case 28:
Element28 = value;
return;
case 29:
Element29 = value;
return;
case 30:
Element30 = value;
return;
case 31:
Element31 = value;
return;
case 32:
Element32 = value;
return;
case 33:
Element33 = value;
return;
case 34:
Element34 = value;
return;
case 35:
Element35 = value;
return;
case 36:
Element36 = value;
return;
case 37:
Element37 = value;
return;
case 38:
Element38 = value;
return;
case 39:
Element39 = value;
return;
case 40:
Element40 = value;
return;
case 41:
Element41 = value;
return;
case 42:
Element42 = value;
return;
case 43:
Element43 = value;
return;
case 44:
Element44 = value;
return;
case 45:
Element45 = value;
return;
case 46:
Element46 = value;
return;
case 47:
Element47 = value;
return;
case 48:
Element48 = value;
return;
case 49:
Element49 = value;
return;
case 50:
Element50 = value;
return;
case 51:
Element51 = value;
return;
case 52:
Element52 = value;
return;
case 53:
Element53 = value;
return;
case 54:
Element54 = value;
return;
case 55:
Element55 = value;
return;
case 56:
Element56 = value;
return;
case 57:
Element57 = value;
return;
case 58:
Element58 = value;
return;
case 59:
Element59 = value;
return;
case 60:
Element60 = value;
return;
case 61:
Element61 = value;
return;
case 62:
Element62 = value;
return;
case 63:
Element63 = value;
return;
case 64:
Element64 = value;
return;
case 65:
Element65 = value;
return;
case 66:
Element66 = value;
return;
case 67:
Element67 = value;
return;
case 68:
Element68 = value;
return;
case 69:
Element69 = value;
return;
case 70:
Element70 = value;
return;
case 71:
Element71 = value;
return;
case 72:
Element72 = value;
return;
case 73:
Element73 = value;
return;
case 74:
Element74 = value;
return;
case 75:
Element75 = value;
return;
case 76:
Element76 = value;
return;
case 77:
Element77 = value;
return;
case 78:
Element78 = value;
return;
case 79:
Element79 = value;
return;
case 80:
Element80 = value;
return;
case 81:
Element81 = value;
return;
case 82:
Element82 = value;
return;
case 83:
Element83 = value;
return;
case 84:
Element84 = value;
return;
case 85:
Element85 = value;
return;
case 86:
Element86 = value;
return;
case 87:
Element87 = value;
return;
case 88:
Element88 = value;
return;
case 89:
Element89 = value;
return;
case 90:
Element90 = value;
return;
case 91:
Element91 = value;
return;
case 92:
Element92 = value;
return;
case 93:
Element93 = value;
return;
case 94:
Element94 = value;
return;
case 95:
Element95 = value;
return;
case 96:
Element96 = value;
return;
case 97:
Element97 = value;
return;
case 98:
Element98 = value;
return;
case 99:
Element99 = value;
return;
case 100:
Element100 = value;
return;
case 101:
Element101 = value;
return;
case 102:
Element102 = value;
return;
case 103:
Element103 = value;
return;
case 104:
Element104 = value;
return;
case 105:
Element105 = value;
return;
case 106:
Element106 = value;
return;
case 107:
Element107 = value;
return;
case 108:
Element108 = value;
return;
case 109:
Element109 = value;
return;
case 110:
Element110 = value;
return;
case 111:
Element111 = value;
return;
case 112:
Element112 = value;
return;
case 113:
Element113 = value;
return;
case 114:
Element114 = value;
return;
case 115:
Element115 = value;
return;
case 116:
Element116 = value;
return;
case 117:
Element117 = value;
return;
case 118:
Element118 = value;
return;
case 119:
Element119 = value;
return;
case 120:
Element120 = value;
return;
case 121:
Element121 = value;
return;
case 122:
Element122 = value;
return;
case 123:
Element123 = value;
return;
case 124:
Element124 = value;
return;
case 125:
Element125 = value;
return;
case 126:
Element126 = value;
return;
case 127:
Element127 = value;
return;
default:
// ILGPU kernels cannot throw exceptions, and callers guarantee the index range.
return;
}
}
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static int GetScalarBitLength(ulong value)
{
if (value == 0UL)
{
return 0;
}
return 64 - XMath.LeadingZeroCount(value);
}
private static int GetScalarBitLength(ulong value) => value == 0UL ? 0 : 64 - XMath.LeadingZeroCount(value);
public static readonly GpuUInt128 Zero = new();
public static readonly GpuUInt128 One = new(1UL);
@@ -743,23 +60,21 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public readonly int GetBitLength()
{
if (High != 0UL)
ulong temp = High;
if (temp != 0UL)
{
return 64 + (64 - BitOperations.LeadingZeroCount(High));
return 64 + (64 - BitOperations.LeadingZeroCount(temp));
}
ulong low = Low;
if (low == 0UL)
temp = Low;
if (temp == 0UL)
{
return 0;
}
return 64 - BitOperations.LeadingZeroCount(low);
return 64 - BitOperations.LeadingZeroCount(temp);
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static int GetBitLength(GpuUInt128 value) => value.GetBitLength();
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static implicit operator GpuUInt128(UInt128 value) => new(value);
@@ -770,6 +85,7 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
public static implicit operator UInt128(GpuUInt128 value) =>
((UInt128)value.High << 64) | value.Low;
// TODO: The operators modifying the state of left is intuitive and can easily lead to bugs. Change this back to return a new instance, but replace where possible with method calls, if we want to modify the state of the instance.
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static GpuUInt128 operator +(GpuUInt128 left, GpuUInt128 right)
{
@@ -809,16 +125,17 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
ulong high = value.High;
ulong low = value.Low;
int shiftedValue;
if (shift >= 64)
{
int longShift = shift - 64;
value.High = low << longShift;
shiftedValue = shift - 64;
value.High = low << shiftedValue;
value.Low = 0UL;
return value;
}
int inverseShift = 64 - shift;
value.High = (high << shift) | (low >> inverseShift);
shiftedValue = 64 - shift;
value.High = (high << shift) | (low >> shiftedValue);
value.Low = low << shift;
return value;
}
@@ -835,16 +152,17 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
ulong high = value.High;
ulong low = value.Low;
int shiftedValue;
if (shift >= 64)
{
int longShift = shift - 64;
value.Low = longShift == 0 ? high : high >> longShift;
shiftedValue = shift - 64;
value.Low = shiftedValue == 0 ? high : high >> shiftedValue;
value.High = 0UL;
return value;
}
int inverseShift = 64 - shift;
value.Low = (low >> shift) | (high << inverseShift);
shiftedValue = 64 - shift;
value.Low = (low >> shift) | (high << shiftedValue);
value.High = high >> shift;
return value;
}
@@ -913,17 +231,20 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
public void Add(GpuUInt128 other)
{
ulong originalLow = Low;
// We're reusing originalLow for carry to avoid an extra local.
ulong low = originalLow + other.Low;
ulong carry = low < originalLow ? 1UL : 0UL;
High = High + other.High + carry;
originalLow = low < originalLow ? 1UL : 0UL;
Low = low;
// We're reusing low for the final sum to avoid an extra local and to keep max stack frame at 3 instead of 4 with one statement.
low = High + other.High;
High = low + originalLow;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public void Add(ulong value)
{
ulong low = Low + value;
High += (low < Low ? 1UL : 0UL);
High += low < Low ? 1UL : 0UL;
Low = low;
}
@@ -962,10 +283,11 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static GpuUInt128 Pow2Minus1Mod(ulong exponent, GpuUInt128 modulus)
{
if (modulus.IsZero)
{
return Zero;
}
// This should never happen in production code
// if (modulus.IsZero)
// {
// return Zero;
// }
GpuUInt128 pow = Pow2Mod(exponent, modulus);
if (pow.IsZero)
@@ -1034,30 +356,34 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static ulong MulHigh(ulong x, ulong y)
{
// TODO: Review if we can reuse any other existing variables to reduce registry pressure.
ulong xLow = (uint)x;
ulong yLow = (uint)y;
ulong lowProduct = xLow * yLow;
ulong yHigh = y >> 32;
ulong cross = xLow * yHigh;
// We're reusing xLow for the cross product to avoid an extra local.
xLow *= yHigh;
ulong xHigh = x >> 32;
ulong result = xHigh * yHigh;
ulong temp = xHigh * yLow;
// We're reusing yHigh for the result to void an extra local.
yHigh *= xHigh;
// We're reusing yLow for the other cross product to avoid an extra local.
yLow *= xHigh;
// Keeping the wide partial sum in a dedicated local prevents the JIT from
// materialising it on the stack before the final carry propagation. The
// additional store looks redundant in C#, but it shortens the generated
// instruction sequence by avoiding an extra temporary and results in a
// measurable throughput win in the MulHigh benchmarks.
result += cross >> 32;
result += temp >> 32;
yHigh += (xLow >> 32);
// We've more instructions with this but the max method stack frame is 3 instead of 4.
yHigh += (yLow >> 32);
lowProduct >>= 32;
lowProduct += (uint)cross;
lowProduct += (uint)temp;
result += lowProduct >> 32;
return result;
lowProduct += (uint)xLow + (uint)yLow;
yHigh += lowProduct >> 32;
return yHigh;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
@@ -1099,23 +425,25 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static GpuUInt128 Pow2Mod(ulong exponent, GpuUInt128 modulus)
{
if (modulus.IsZero || modulus == One)
{
return new();
}
// This should never happen in production code.
// if (modulus.IsZero || modulus == One)
// {
// return new();
// }
if (exponent == 0UL)
{
return new GpuUInt128(1UL);
}
// This should never happen in production code.
// if (exponent == 0UL)
// {
// return new GpuUInt128(1UL);
// }
Pow2OddPowerTable oddPowers = default;
GpuUInt128 power = new GpuUInt128(1UL);
GpuUInt128[] oddPowers = new GpuUInt128[PerfectNumberConstants.MaxOddPowersCount];
GpuUInt128 power = new(1UL);
int oddIndex = 0;
for (int bit = 1; bit <= Pow2WindowMaxExponent; bit++)
{
power += power;
power.Add(power);
if (power.CompareTo(modulus) >= 0)
{
power.Sub(modulus);
@@ -1128,7 +456,7 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
}
}
GpuUInt128 result = new GpuUInt128(1UL);
GpuUInt128 result = GpuUInt128.One;
int bitLength = GetScalarBitLength(exponent);
int index = bitLength - 1;
@@ -2144,14 +1472,14 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
}
}
// TODO: Check if the TODO below is still relevant.
// TODO: Check if the TODO below is still relevant.
// TODO(MOD-OPT): Montgomery/Barrett integration plan
// - Introduce caches of modulus-dependent constants:
// * Montgomery: n' (-(n^{-1}) mod 2^64 or 2^128), R2 = (R^2 mod n)
// * Barrett: mu = floor(2^k / n) for k ∈ {128, 192, 256}
// - Add fast-path for 64-bit NTT primes (modulus.High == 0UL) using pure 64-bit ops.
// - Expose helpers to retrieve/calc constants once per modulus and reuse in kernels.
// - Wire these into MulMod and SquareMod hot paths under feature toggles.
// - Ensure ILGPU compatibility (no BigInteger, no % inside kernels).
// TODO(MOD-OPT): Montgomery/Barrett integration plan
// - Introduce caches of modulus-dependent constants:
// * Montgomery: n' (-(n^{-1}) mod 2^64 or 2^128), R2 = (R^2 mod n)
// * Barrett: mu = floor(2^k / n) for k ∈ {128, 192, 256}
// - Add fast-path for 64-bit NTT primes (modulus.High == 0UL) using pure 64-bit ops.
// - Expose helpers to retrieve/calc constants once per modulus and reuse in kernels.
// - Wire these into MulMod and SquareMod hot paths under feature toggles.
// - Ensure ILGPU compatibility (no BigInteger, no % inside kernels).