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Adding a vectorized implementation of TensorPrimitives.Log #92960

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Oct 3, 2023
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Adding a vectorized implementation of TensorPrimitives.Log #92960

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Adding a vectorized implementation of TensorPrimitives.Log
tannergooding Oct 3, 2023
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16 changes: 2 additions & 14 deletions src/libraries/System.Numerics.Tensors/src/System/Numerics/Tensors/TensorPrimitives.cs
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Expand Up @@ -563,20 +563,8 @@ public static unsafe int IndexOfMinMagnitude(ReadOnlySpan<float> x)
/// operating systems or architectures.
/// </para>
/// </remarks>
public static void Log(ReadOnlySpan<float> x, Span<float> destination)
{
if (x.Length > destination.Length)
{
ThrowHelper.ThrowArgument_DestinationTooShort();
}

ValidateInputOutputSpanNonOverlapping(x, destination);

for (int i = 0; i < x.Length; i++)
{
destination[i] = MathF.Log(x[i]);
}
}
public static void Log(ReadOnlySpan<float> x, Span<float> destination) =>
InvokeSpanIntoSpan<LogOperator>(x, destination);

/// <summary>Computes the element-wise base 2 logarithm of single-precision floating-point numbers in the specified tensor.</summary>
/// <param name="x">The tensor, represented as a span.</param>
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285 changes: 285 additions & 0 deletions ...libraries/System.Numerics.Tensors/src/System/Numerics/Tensors/TensorPrimitives.netcore.cs
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Expand Up @@ -2579,6 +2579,291 @@ public static Vector512<float> Invoke(Vector512<float> x, Vector512<float> y)
#endif
}

private readonly struct LogOperator : IUnaryOperator
{
// This code is based on `vrs4_logf` from amd/aocl-libm-ose
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// Copyright (C) 2018-2019 Advanced Micro Devices, Inc. All rights reserved.
//
// Licensed under the BSD 3-Clause "New" or "Revised" License
// See THIRD-PARTY-NOTICES.TXT for the full license text

// Spec:
// logf(x)
// = logf(x) if x ∈ F and x > 0
// = x if x = qNaN
// = 0 if x = 1
// = -inf if x = (-0, 0}
// = NaN otherwise
//
// Assumptions/Expectations
// - ULP is derived to be << 4 (always)
// - Some FPU Exceptions may not be available
// - Performance is at least 3x
//
// Implementation Notes:
// 1. Range Reduction:
// x = 2^n*(1+f) .... (1)
// where n is exponent and is an integer
// (1+f) is mantissa ∈ [1,2). i.e., 1 ≤ 1+f < 2 .... (2)
//
// From (1), taking log on both sides
// log(x) = log(2^n * (1+f))
// = log(2^n) + log(1+f)
// = n*log(2) + log(1+f) .... (3)
//
// let z = 1 + f
// log(z) = log(k) + log(z) - log(k)
// log(z) = log(kz) - log(k)
//
// From (2), range of z is [1, 2)
// by simply dividing range by 'k', z is in [1/k, 2/k) .... (4)
// Best choice of k is the one which gives equal and opposite values
// at extrema +- -+
// 1 | 2 |
// --- - 1 = - |--- - 1 |
// k | k | .... (5)
// +- -+
//
// Solving for k, k = 3/2,
// From (4), using 'k' value, range is therefore [-0.3333, 0.3333]
//
// 2. Polynomial Approximation:
// More information refer to tools/sollya/vrs4_logf.sollya
//
// 7th Deg - Error abs: 0x1.04c4ac98p-22 rel: 0x1.2216e6f8p-19
// 6th Deg - Error abs: 0x1.179e97d8p-19 rel: 0x1.db676c1p-17

private const uint V_MIN = 0x00800000;
private const uint V_MAX = 0x7F800000;
private const uint V_MASK = 0x007FFFFF;
private const uint V_OFF = 0x3F2AAAAB;

private const float V_LN2 = 0.6931472f;

private const float C0 = 0.0f;
private const float C1 = 1.0f;
private const float C2 = -0.5000001f;
private const float C3 = 0.33332965f;
private const float C4 = -0.24999046f;
private const float C5 = 0.20018855f;
private const float C6 = -0.16700386f;
private const float C7 = 0.13902695f;
private const float C8 = -0.1197452f;
private const float C9 = 0.14401625f;
private const float C10 = -0.13657966f;

public static float Invoke(float x) => MathF.Log(x);

public static Vector128<float> Invoke(Vector128<float> x)
{
Vector128<float> specialResult = x;

// x is subnormal or infinity or NaN
Vector128<uint> specialMask = Vector128.GreaterThanOrEqual(x.AsUInt32() - Vector128.Create(V_MIN), Vector128.Create(V_MAX - V_MIN));

if (specialMask != Vector128<uint>.Zero)
{
// float.IsZero(x) ? float.NegativeInfinity : x
Vector128<float> zeroMask = Vector128.Equals(x, Vector128<float>.Zero);

specialResult = Vector128.ConditionalSelect(
zeroMask,
Vector128.Create(float.NegativeInfinity),
specialResult
);

// (x < 0) ? float.NaN : x
Vector128<float> lessThanZeroMask = Vector128.LessThan(x, Vector128<float>.Zero);

specialResult = Vector128.ConditionalSelect(
lessThanZeroMask,
Vector128.Create(float.NaN),
specialResult
);

// float.IsZero(x) | (x < 0) | float.IsNaN(x) | float.IsPositiveInfinity(x)
Vector128<float> temp = zeroMask
| lessThanZeroMask
| ~Vector128.Equals(x, x)
| Vector128.Equals(x, Vector128.Create(float.PositiveInfinity));

// subnormal
Vector128<float> subnormalMask = Vector128.AndNot(specialMask.AsSingle(), temp);

x = Vector128.ConditionalSelect(
subnormalMask,
((x * 8388608.0f).AsUInt32() - Vector128.Create(23u << 23)).AsSingle(),
x
);

specialMask = temp.AsUInt32();
}

Vector128<uint> vx = x.AsUInt32() - Vector128.Create(V_OFF);
Vector128<float> n = Vector128.ConvertToSingle(Vector128.ShiftRightArithmetic(vx.AsInt32(), 23));

vx = (vx & Vector128.Create(V_MASK)) + Vector128.Create(V_OFF);

Vector128<float> r = vx.AsSingle() - Vector128.Create(1.0f);

Vector128<float> r2 = r * r;
Vector128<float> r4 = r2 * r2;
Vector128<float> r8 = r4 * r4;

Vector128<float> q = (Vector128.Create(C10) * r2 + (Vector128.Create(C9) * r + Vector128.Create(C8)))
* r8 + (((Vector128.Create(C7) * r + Vector128.Create(C6))
* r2 + (Vector128.Create(C5) * r + Vector128.Create(C4)))
* r4 + ((Vector128.Create(C3) * r + Vector128.Create(C2))
* r2 + (Vector128.Create(C1) * r + Vector128.Create(C0))));

return Vector128.ConditionalSelect(
specialMask.AsSingle(),
specialResult,
n * Vector128.Create(V_LN2) + q
);
}

public static Vector256<float> Invoke(Vector256<float> x)
{
Vector256<float> specialResult = x;

// x is subnormal or infinity or NaN
Vector256<uint> specialMask = Vector256.GreaterThanOrEqual(x.AsUInt32() - Vector256.Create(V_MIN), Vector256.Create(V_MAX - V_MIN));

if (specialMask != Vector256<uint>.Zero)
{
// float.IsZero(x) ? float.NegativeInfinity : x
Vector256<float> zeroMask = Vector256.Equals(x, Vector256<float>.Zero);

specialResult = Vector256.ConditionalSelect(
zeroMask,
Vector256.Create(float.NegativeInfinity),
specialResult
);

// (x < 0) ? float.NaN : x
Vector256<float> lessThanZeroMask = Vector256.LessThan(x, Vector256<float>.Zero);

specialResult = Vector256.ConditionalSelect(
lessThanZeroMask,
Vector256.Create(float.NaN),
specialResult
);

// float.IsZero(x) | (x < 0) | float.IsNaN(x) | float.IsPositiveInfinity(x)
Vector256<float> temp = zeroMask
| lessThanZeroMask
| ~Vector256.Equals(x, x)
| Vector256.Equals(x, Vector256.Create(float.PositiveInfinity));

// subnormal
Vector256<float> subnormalMask = Vector256.AndNot(specialMask.AsSingle(), temp);

x = Vector256.ConditionalSelect(
subnormalMask,
((x * 8388608.0f).AsUInt32() - Vector256.Create(23u << 23)).AsSingle(),
x
);

specialMask = temp.AsUInt32();
}

Vector256<uint> vx = x.AsUInt32() - Vector256.Create(V_OFF);
Vector256<float> n = Vector256.ConvertToSingle(Vector256.ShiftRightArithmetic(vx.AsInt32(), 23));

vx = (vx & Vector256.Create(V_MASK)) + Vector256.Create(V_OFF);

Vector256<float> r = vx.AsSingle() - Vector256.Create(1.0f);

Vector256<float> r2 = r * r;
Vector256<float> r4 = r2 * r2;
Vector256<float> r8 = r4 * r4;

Vector256<float> q = (Vector256.Create(C10) * r2 + (Vector256.Create(C9) * r + Vector256.Create(C8)))
* r8 + (((Vector256.Create(C7) * r + Vector256.Create(C6))
* r2 + (Vector256.Create(C5) * r + Vector256.Create(C4)))
* r4 + ((Vector256.Create(C3) * r + Vector256.Create(C2))
* r2 + (Vector256.Create(C1) * r + Vector256.Create(C0))));

return Vector256.ConditionalSelect(
specialMask.AsSingle(),
specialResult,
n * Vector256.Create(V_LN2) + q
);
}

#if NET8_0_OR_GREATER
public static Vector512<float> Invoke(Vector512<float> x)
{
Vector512<float> specialResult = x;

// x is subnormal or infinity or NaN
Vector512<uint> specialMask = Vector512.GreaterThanOrEqual(x.AsUInt32() - Vector512.Create(V_MIN), Vector512.Create(V_MAX - V_MIN));

if (specialMask != Vector512<uint>.Zero)
{
// float.IsZero(x) ? float.NegativeInfinity : x
Vector512<float> zeroMask = Vector512.Equals(x, Vector512<float>.Zero);

specialResult = Vector512.ConditionalSelect(
zeroMask,
Vector512.Create(float.NegativeInfinity),
specialResult
);

// (x < 0) ? float.NaN : x
Vector512<float> lessThanZeroMask = Vector512.LessThan(x, Vector512<float>.Zero);

specialResult = Vector512.ConditionalSelect(
lessThanZeroMask,
Vector512.Create(float.NaN),
specialResult
);

// float.IsZero(x) | (x < 0) | float.IsNaN(x) | float.IsPositiveInfinity(x)
Vector512<float> temp = zeroMask
| lessThanZeroMask
| ~Vector512.Equals(x, x)
| Vector512.Equals(x, Vector512.Create(float.PositiveInfinity));

// subnormal
Vector512<float> subnormalMask = Vector512.AndNot(specialMask.AsSingle(), temp);

x = Vector512.ConditionalSelect(
subnormalMask,
((x * 8388608.0f).AsUInt32() - Vector512.Create(23u << 23)).AsSingle(),
x
);

specialMask = temp.AsUInt32();
}

Vector512<uint> vx = x.AsUInt32() - Vector512.Create(V_OFF);
Vector512<float> n = Vector512.ConvertToSingle(Vector512.ShiftRightArithmetic(vx.AsInt32(), 23));

vx = (vx & Vector512.Create(V_MASK)) + Vector512.Create(V_OFF);

Vector512<float> r = vx.AsSingle() - Vector512.Create(1.0f);

Vector512<float> r2 = r * r;
Vector512<float> r4 = r2 * r2;
Vector512<float> r8 = r4 * r4;

Vector512<float> q = (Vector512.Create(C10) * r2 + (Vector512.Create(C9) * r + Vector512.Create(C8)))
* r8 + (((Vector512.Create(C7) * r + Vector512.Create(C6))
* r2 + (Vector512.Create(C5) * r + Vector512.Create(C4)))
* r4 + ((Vector512.Create(C3) * r + Vector512.Create(C2))
* r2 + (Vector512.Create(C1) * r + Vector512.Create(C0))));

return Vector512.ConditionalSelect(
specialMask.AsSingle(),
specialResult,
n * Vector512.Create(V_LN2) + q
);
}
#endif
}

private readonly struct Log2Operator : IUnaryOperator
{
// This code is based on `vrs4_log2f` from amd/aocl-libm-ose
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13 changes: 13 additions & 0 deletions ...aries/System.Numerics.Tensors/src/System/Numerics/Tensors/TensorPrimitives.netstandard.cs
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Expand Up @@ -923,6 +923,19 @@ public Vector<float> Invoke(Vector<float> x, Vector<float> y)
public Vector<float> Invoke(Vector<float> x) => Vector.Abs(x);
}

private readonly struct LogOperator : IUnaryOperator
{
public bool CanVectorize => false;

public float Invoke(float x) => MathF.Log(x);

public Vector<float> Invoke(Vector<float> x)
{
// Vectorizing requires shift right support, which is .NET 7 or later
throw new NotImplementedException();
}
}

private readonly struct Log2Operator : IUnaryOperator
{
public bool CanVectorize => false;
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35 changes: 35 additions & 0 deletions src/libraries/System.Numerics.Tensors/tests/TensorPrimitivesTests.cs
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Expand Up @@ -1006,6 +1006,41 @@ public static void Log_InPlace(int tensorLength)
}
}

[Theory]
[MemberData(nameof(TensorLengths))]
public static void Log_SpecialValues(int tensorLength)
{
using BoundedMemory<float> x = CreateAndFillTensor(tensorLength);
using BoundedMemory<float> destination = CreateTensor(tensorLength);

// NaN
x[s_random.Next(x.Length)] = float.NaN;

// +Infinity
x[s_random.Next(x.Length)] = float.PositiveInfinity;

// -Infinity
x[s_random.Next(x.Length)] = float.NegativeInfinity;

// +Zero
x[s_random.Next(x.Length)] = +0.0f;

// -Zero
x[s_random.Next(x.Length)] = -0.0f;

// +Epsilon
x[s_random.Next(x.Length)] = +float.Epsilon;

// -Epsilon
x[s_random.Next(x.Length)] = -float.Epsilon;

TensorPrimitives.Log(x, destination);
for (int i = 0; i < tensorLength; i++)
{
Assert.Equal(MathF.Log(x[i]), destination[i], Tolerance);
}
}

[Theory]
[MemberData(nameof(TensorLengths))]
public static void Log_ThrowsForTooShortDestination(int tensorLength)
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