public void RunBasicScenario_UnsafeRead()
{
TestLibrary.TestFramework.BeginScenario(nameof(RunBasicScenario_UnsafeRead));
var result = Avx.Divide(
Unsafe.Read <Vector256 <Single> >(_dataTable.inArray1Ptr),
Unsafe.Read <Vector256 <Single> >(_dataTable.inArray2Ptr)
);
Unsafe.Write(_dataTable.outArrayPtr, result);
ValidateResult(_dataTable.inArray1Ptr, _dataTable.inArray2Ptr, _dataTable.outArrayPtr);
}
public void RunClsVarScenario()
{
TestLibrary.TestFramework.BeginScenario(nameof(RunClsVarScenario));
var result = Avx.Divide(
_clsVar1,
_clsVar2
);
Unsafe.Write(_dataTable.outArrayPtr, result);
ValidateResult(_clsVar1, _clsVar2, _dataTable.outArrayPtr);
}
public void RunBasicScenario_LoadAligned()
{
TestLibrary.TestFramework.BeginScenario(nameof(RunBasicScenario_LoadAligned));
var result = Avx.Divide(
Avx.LoadAlignedVector256((Double *)(_dataTable.inArray1Ptr)),
Avx.LoadAlignedVector256((Double *)(_dataTable.inArray2Ptr))
);
Unsafe.Write(_dataTable.outArrayPtr, result);
ValidateResult(_dataTable.inArray1Ptr, _dataTable.inArray2Ptr, _dataTable.outArrayPtr);
}
public void RunStructLclFldScenario_Load()
{
TestLibrary.TestFramework.BeginScenario(nameof(RunStructLclFldScenario_Load));
var test = TestStruct.Create();
var result = Avx.Divide(
Avx.LoadVector256((Double *)(&test._fld1)),
Avx.LoadVector256((Double *)(&test._fld2))
);
Unsafe.Write(_dataTable.outArrayPtr, result);
ValidateResult(test._fld1, test._fld2, _dataTable.outArrayPtr);
}
public void RunStructFldScenario_Load(SimpleBinaryOpTest__DivideDouble testClass)
{
fixed(Vector256 <Double> *pFld1 = &_fld1)
fixed(Vector256 <Double> *pFld2 = &_fld2)
{
var result = Avx.Divide(
Avx.LoadVector256((Double *)(pFld1)),
Avx.LoadVector256((Double *)(pFld2))
);
Unsafe.Write(testClass._dataTable.outArrayPtr, result);
testClass.ValidateResult(_fld1, _fld2, testClass._dataTable.outArrayPtr);
}
}
public void RunClsVarScenario_Load()
{
TestLibrary.TestFramework.BeginScenario(nameof(RunClsVarScenario_Load));
fixed(Vector256 <Single> *pClsVar1 = &_clsVar1)
fixed(Vector256 <Single> *pClsVar2 = &_clsVar2)
{
var result = Avx.Divide(
Avx.LoadVector256((Single *)(pClsVar1)),
Avx.LoadVector256((Single *)(pClsVar2))
);
Unsafe.Write(_dataTable.outArrayPtr, result);
ValidateResult(_clsVar1, _clsVar2, _dataTable.outArrayPtr);
}
}
public void RunClassFldScenario_Load()
{
TestLibrary.TestFramework.BeginScenario(nameof(RunClassFldScenario_Load));
fixed(Vector256 <Double> *pFld1 = &_fld1)
fixed(Vector256 <Double> *pFld2 = &_fld2)
{
var result = Avx.Divide(
Avx.LoadVector256((Double *)(pFld1)),
Avx.LoadVector256((Double *)(pFld2))
);
Unsafe.Write(_dataTable.outArrayPtr, result);
ValidateResult(_fld1, _fld2, _dataTable.outArrayPtr);
}
}
public void RunClassLclFldScenario_Load()
{
TestLibrary.TestFramework.BeginScenario(nameof(RunClassLclFldScenario_Load));
var test = new SimpleBinaryOpTest__DivideDouble();
fixed(Vector256 <Double> *pFld1 = &test._fld1)
fixed(Vector256 <Double> *pFld2 = &test._fld2)
{
var result = Avx.Divide(
Avx.LoadVector256((Double *)(pFld1)),
Avx.LoadVector256((Double *)(pFld2))
);
Unsafe.Write(_dataTable.outArrayPtr, result);
ValidateResult(test._fld1, test._fld2, _dataTable.outArrayPtr);
}
}
public (double near, double far) IntersectAVX(Ray ray)
{
Vector256 <double> origin = (Vector256 <double>)ray.Origin;
Vector256 <double> direction = (Vector256 <double>)ray.Direction;
Vector256 <double> zeroes = new Vector256 <double>();
Vector256 <double> min = (Vector256 <double>)Minimum;
Vector256 <double> max = (Vector256 <double>)Maximum;
// Replace slabs that won't be checked (0 direction axis) with infinity so that NaN doesn't propagate
Vector256 <double> dirInfMask = Avx.And(
Avx.Compare(direction, zeroes, FloatComparisonMode.OrderedEqualNonSignaling),
Avx.And(
Avx.Compare(origin, min, FloatComparisonMode.OrderedGreaterThanOrEqualNonSignaling),
Avx.Compare(origin, max, FloatComparisonMode.OrderedLessThanOrEqualNonSignaling)));
min = Avx.BlendVariable(min, SIMDHelpers.BroadcastScalar4(double.NegativeInfinity), dirInfMask);
max = Avx.BlendVariable(max, SIMDHelpers.BroadcastScalar4(double.PositiveInfinity), dirInfMask);
// Flip slabs in direction axes that are negative (using direction as mask takes the most significant bit, the sign.. probably includes -0)
Vector256 <double> minMasked = Avx.BlendVariable(min, max, direction);
Vector256 <double> maxMasked = Avx.BlendVariable(max, min, direction);
direction = Avx.Divide(Vector256.Create(1D), direction);
Vector256 <double> near4 = Avx.Multiply(Avx.Subtract(minMasked, origin), direction);
Vector256 <double> far4 = Avx.Multiply(Avx.Subtract(maxMasked, origin), direction);
Vector128 <double> near2 = Sse2.Max(near4.GetLower(), near4.GetUpper());
near2 = Sse2.MaxScalar(near2, SIMDHelpers.Swap(near2));
Vector128 <double> far2 = Sse2.Min(far4.GetLower(), far4.GetUpper());
far2 = Sse2.MinScalar(far2, SIMDHelpers.Swap(far2));
if (Sse2.CompareScalarOrderedGreaterThan(near2, far2) | Sse2.CompareScalarOrderedLessThan(far2, new Vector128 <double>()))
{
return(double.NaN, double.NaN);
}
return(near2.ToScalar(), far2.ToScalar());
}
public static Vector256 <float> Digamma(Vector256 <float> x)
{
const float s3 = 1.0f / 12.0f;
const float s4 = 1.0f / 120.0f;
const float s5 = 1.0f / 252.0f;
const float s6 = 1.0f / 240.0f;
const float s7 = 1.0f / 132.0f;
const float half = 0.5f;
const float one = 1f;
var vone = Vector256.Create(one);
// note: 'Reciprocal' does not yield the same numerical results than 'Divide(1f, x)'
var result = Vector256 <float> .Zero;
for (var i = 0; i < 3; i++)
{
result = Avx.Subtract(result, Avx.Divide(vone, x));
x = Avx2.Add(x, vone);
}
var r = Avx.Divide(vone, x);
result = Avx.Add(result, Avx.Subtract(Log(x), Avx.Multiply(Vector256.Create(half), r)));
r = Avx.Multiply(r, r);
result = Avx.Subtract(result,
Avx.Multiply(r,
Avx.Subtract(Vector256.Create(s3),
Avx.Multiply(r,
Avx.Subtract(Vector256.Create(s4),
Avx.Multiply(r,
Avx.Subtract(Vector256.Create(s5),
Avx.Multiply(r,
Avx.Subtract(Vector256.Create(s6),
Avx.Multiply(r, Vector256.Create(s7)))))))))));
return(result);
}
public static Vector128 <float> GetBrucePsmeAbgrGrowthEffectiveAge(SiteConstants site, float timeStepInYears, Vector128 <float> treeHeight, out Vector128 <float> potentialHeightGrowth)
{
Vector128 <float> B1 = AvxExtensions.BroadcastScalarToVector128(site.B1);
Vector128 <float> B2 = AvxExtensions.BroadcastScalarToVector128(site.B2);
Vector128 <float> X2toB2 = AvxExtensions.BroadcastScalarToVector128(site.X2toB2);
Vector128 <float> siteIndexFromGround128 = AvxExtensions.BroadcastScalarToVector128(site.SiteIndexFromGround);
Vector128 <float> X1 = AvxExtensions.BroadcastScalarToVector128(site.X1);
Vector128 <float> XX1 = Avx.Add(Avx.Divide(MathV.Ln(Avx.Divide(treeHeight, siteIndexFromGround128)), B1), X2toB2);
Vector128 <float> xx1lessThanZero = Avx.CompareLessThanOrEqual(XX1, Vector128 <float> .Zero);
Vector128 <float> growthEffectiveAge = Avx.Subtract(MathV.Pow(XX1, Avx.Reciprocal(B2)), X1);
growthEffectiveAge = Avx.BlendVariable(growthEffectiveAge, AvxExtensions.BroadcastScalarToVector128(500.0F), xx1lessThanZero);
Vector128 <float> timeStepInYearsPlusX1 = AvxExtensions.BroadcastScalarToVector128(timeStepInYears + site.X1);
Vector128 <float> potentialHeightPower = Avx.Multiply(B1, Avx.Subtract(MathV.Pow(Avx.Add(growthEffectiveAge, timeStepInYearsPlusX1), B2), X2toB2));
Vector128 <float> potentialHeight = Avx.Multiply(siteIndexFromGround128, MathV.Exp(potentialHeightPower));
potentialHeightGrowth = Avx.Subtract(potentialHeight, treeHeight);
return(growthEffectiveAge);
}
public override ulong Run(CancellationToken cancellationToken)
{
if (!Avx.IsSupported)
{
return(0uL);
}
var randomFloatingSpan = new Span <float>(new[]
{
RANDOM_FLOAT, RANDOM_FLOAT, RANDOM_FLOAT, RANDOM_FLOAT, RANDOM_FLOAT, RANDOM_FLOAT, RANDOM_FLOAT,
RANDOM_FLOAT
});
var dst = new Span <float>(Enumerable.Repeat(float.MaxValue, 8).ToArray());
var iterations = 0uL;
unsafe
{
fixed(float *pdst = dst)
fixed(float *psrc = randomFloatingSpan)
{
var srcVector = Avx.LoadVector256(psrc);
var dstVector = Avx.LoadVector256(pdst);
while (!cancellationToken.IsCancellationRequested)
{
for (var j = 0; j < LENGTH; j++)
{
dstVector = Avx.Divide(dstVector, srcVector);
}
Avx.Store(pdst, dstVector);
iterations++;
}
}
}
return(iterations);
}
public static Vector256 <float> LogGamma(Vector256 <float> x)
{
const float one = 1f;
const float half = 0.5f;
// Numeric shift to improve accuracy (cost +1 'Log').
// logGamma(x) = logGamma(x + 1) - log(x)
var result = Log(x);
x = Avx.Add(x, Vector256.Create(one));
const float Ln2Pi_2 = 0.91893853320467274178032f;
// A & S eq. 6.1.48 (continuing fraction)
const float a0 = (float)(1.0 / 12);
const float a1 = (float)(1.0 / 30);
const float a2 = (float)(53.0 / 210);
const float a3 = (float)(195.0 / 371);
const float a4 = (float)(22999.0 / 22737);
const float a5 = (float)(29944523.0 / 19733142);
const float a6 = (float)(109535241009.0 / 48264275462);
var t6 = Avx.Divide(Vector256.Create(a6), x);
var t5 = Avx.Divide(Vector256.Create(a5), Avx.Add(x, t6));
var t4 = Avx.Divide(Vector256.Create(a4), Avx.Add(x, t5));
var t3 = Avx.Divide(Vector256.Create(a3), Avx.Add(x, t4));
var t2 = Avx.Divide(Vector256.Create(a2), Avx.Add(x, t3));
var t1 = Avx.Divide(Vector256.Create(a1), Avx.Add(x, t2));
var t0 = Avx.Divide(Vector256.Create(a0), Avx.Add(x, t1));
result = Avx.Subtract(
Avx.Add(
Avx.Add(Avx.Subtract(t0, x), Avx.Multiply(Avx.Subtract(x, Vector256.Create(half)), Log(x))),
Vector256.Create(Ln2Pi_2)),
result);
return(result);
}
public Intro()
{
var middleVector = Vector128.Create(1.0f); // middleVector = <1,1,1,1>
middleVector = Vector128.CreateScalar(-1.0f); // middleVector = <-1,0,0,0>
var floatBytes = Vector64.AsByte(Vector64.Create(1.0f, -1.0f)); // floatBytes = <0, 0, 128, 63, 0, 0, 128, 191>
if (Avx.IsSupported)
{
var left = Vector256.Create(-2.5f); // <-2.5, -2.5, -2.5, -2.5, -2.5, -2.5, -2.5, -2.5>
var right = Vector256.Create(5.0f); // <5, 5, 5, 5, 5, 5, 5, 5>
Vector256 <float> result = Avx.AddSubtract(left, right); // result = <-7.5, 2.5, -7.5, 2.5, -7.5, 2.5, -7.5, 2.5>xit
left = Vector256.Create(-1.0f, -2.0f, -3.0f, -4.0f, -50.0f, -60.0f, -70.0f, -80.0f);
right = Vector256.Create(0.0f, 2.0f, 3.0f, 4.0f, 50.0f, 60.0f, 70.0f, 80.0f);
result = Avx.UnpackHigh(left, right); // result = <-3, 3, -4, 4, -70, 70, -80, 80>
result = Avx.UnpackLow(left, right); // result = <-1, 1, -2, 2, -50, 50, -60, 60>
result = Avx.DotProduct(left, right, 0b1111_0001); // result = <-30, 0, 0, 0, -17400, 0, 0, 0>
bool testResult = Avx.TestC(left, right); // testResult = true
testResult = Avx.TestC(right, left); // testResult = false
Vector256 <float> result1 = Avx.Divide(left, right);
var plusOne = Vector256.Create(1.0f);
result = Avx.Compare(right, result1, FloatComparisonMode.OrderedGreaterThanNonSignaling);
result = Avx.Compare(right, result1, FloatComparisonMode.UnorderedNotLessThanNonSignaling);
left = Vector256.Create(0.0f, 3.0f, -3.0f, 4.0f, -50.0f, 60.0f, -70.0f, 80.0f);
right = Vector256.Create(0.0f, 2.0f, 3.0f, 2.0f, 50.0f, -60.0f, 70.0f, -80.0f);
Vector256 <float> nanInFirstPosition = Avx.Divide(left, right);
left = Vector256.Create(1.1f, 3.3333333f, -3.0f, 4.22f, -50.0f, 60.0f, -70.0f, 80.0f);
Vector256 <float> InfInFirstPosition = Avx.Divide(left, right);
left = Vector256.Create(-1.1f, 3.0f, 1.0f / 3.0f, MathF.PI, -50.0f, 60.0f, -70.0f, 80.0f);
right = Vector256.Create(0.0f, 2.0f, 3.1f, 2.0f, 50.0f, -60.0f, 70.0f, -80.0f);
Vector256 <float> compareResult = Avx.Compare(left, right, FloatComparisonMode.OrderedGreaterThanNonSignaling); // compareResult = <0, NaN, 0, NaN, 0, NaN, 0, NaN>
Vector256 <float> mixed = Avx.BlendVariable(left, right, compareResult); // mixed = <-1, 2, -3, 2, -50, -60, -70, -80>
//left = Vector256.Create(-1.0f, 1.0f, -1.0f, 1.0f, -1.0f, 1.0f, -1.0f, 1.0f);
//right = Vector256.Create(1.0f, 1.0f, -1.0f, 1.0f, 1.0f, 1.0f, -1.0f, 1.0f);
Vector256 <float> other = right = Vector256.Create(0.0f, 2.0f, 3.0f, 2.0f, 50.0f, -60.0f, 70.0f, -80.0f);
bool bRes = Avx.TestZ(plusOne, compareResult);
bool bRes2 = Avx.TestC(plusOne, compareResult);
bool allTrue = !Avx.TestZ(compareResult, compareResult);
compareResult = Avx.Compare(nanInFirstPosition, right, FloatComparisonMode.OrderedEqualNonSignaling); // compareResult = <0, NaN, 0, NaN, 0, NaN, 0, NaN>
compareResult = Avx.Compare(nanInFirstPosition, right, FloatComparisonMode.UnorderedEqualNonSignaling);
compareResult = Avx.Compare(InfInFirstPosition, right, FloatComparisonMode.UnorderedNotLessThanOrEqualNonSignaling);
compareResult = Avx.Compare(InfInFirstPosition, right, FloatComparisonMode.OrderedGreaterThanNonSignaling);
var left128 = Vector128.Create(1.0f, 2.0f, 3.0f, 4.0f);
var right128 = Vector128.Create(2.0f, 3.0f, 4.0f, 5.0f);
Vector128 <float> compResult128 = Sse.CompareGreaterThan(left128, right128); // compResult128 = <0, 0, 0, 0>
int res = Avx.MoveMask(compareResult);
if (Fma.IsSupported)
{
Vector256 <float> resultFma = Fma.MultiplyAdd(left, right, other); // = left * right + other for each element
resultFma = Fma.MultiplyAddNegated(left, right, other); // = -(left * right + other) for each element
resultFma = Fma.MultiplySubtract(left, right, other); // = left * right - other for each element
Fma.MultiplyAddSubtract(left, right, other); // even elements (0, 2, ...) like MultiplyAdd, odd elements like MultiplySubtract
}
result = Avx.DotProduct(left, right, 0b1010_0001); // result = <-20, 0, 0, 0, -10000, 0, 0, 0>
result = Avx.Floor(left); // result = <-3, -3, -3, -3, -3, -3, -3, -3>
result = Avx.Add(left, right); // result = <2.5, 2.5, 2.5, 2.5, 2.5, 2.5, 2.5, 2.5>
result = Avx.Ceiling(left); // result = <-2, -2, -2, -2, -2, -2, -2, -2>
result = Avx.Multiply(left, right); // result = <-12.5, -12.5, -12.5, -12.5, -12.5, -12.5, -12.5, -12.5>
result = Avx.HorizontalAdd(left, right); // result = <-5, -5, 10, 10, -5, -5, 10, 10>
result = Avx.HorizontalSubtract(left, right); // result = <0, 0, 0, 0, 0, 0, 0, 0>
double[] someDoubles = new double[] { 1.0, 3.0, -2.5, 7.5, 10.8, 0.33333 };
double[] someOtherDoubles = new double[] { 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 };
double[] someResult = new double[someDoubles.Length];
float[] someFloats = new float[] { 1, 2, 3, 4, 10, 20, 30, 40, 0 };
float[] someOtherFloats = new float[] { 1, 1, 1, 1, 1, 1, 1, 1 };
unsafe
{
fixed(double *ptr = &someDoubles[1])
{
fixed(double *ptr2 = &someResult[0])
{
Vector256 <double> res2 = Avx.LoadVector256(ptr); // res2 = <3, -2.5, 7.5, 10.8>
Avx.Store(ptr2, res2);
}
}
fixed(float *ptr = &someFloats[0])
{
fixed(float *ptr2 = &someOtherFloats[0])
{
Vector256 <float> res2 = Avx.DotProduct(Avx.LoadVector256(ptr), Avx.LoadVector256(ptr2), 0b0001_0001);
//Avx.Store(ptr2, res2);
}
}
}
}
}
public static f32 Div(f32 lhs, f32 rhs) => Avx.Divide(lhs, rhs);
// Element-wise division.
public static IEnumerable <Vector256 <double> > Div(
this IEnumerable <Vector256 <double> > @this,
IEnumerable <Vector256 <double> > other)
=> @this.Zip(other).Select(ab => Avx.Divide(ab.First, ab.Second));
public static Vector256 <float> op_Division(Vector256 <float> left, Vector256 <float> right) => Avx.Divide(left, right);
public static Vector256 <float> op_Division(Vector256 <float> vector, float scalar) => Avx.Divide(vector, Vector256.Create(scalar));
public static Vector256 <double> op_Division(Vector256 <double> left, Vector256 <double> right) => Avx.Divide(left, right);
public unsafe override double[] Applay(double[] values, int halfWindow)
{
var windowSize = 2 * halfWindow + 1;
var resultSize = values.Length - windowSize + 1;
if (resultSize == 0)
{
return(null);
}
var a = new double[resultSize];
var sum = 0d;
fixed(double *valueStart = values, aStart = a)
{
var valueCurrent = valueStart;
var valueEndwindowSize = valueCurrent + windowSize;
while (valueCurrent < valueEndwindowSize)
{
sum += *valueCurrent;
valueCurrent++;
}
var aCurrent = aStart + 1;
var aEnd = aStart + resultSize;
var aUnrolledEnd = aStart + (((resultSize - 1) >> 4) << 4);
valueCurrent = valueStart;
var valueWindowSize = valueStart + windowSize;
var vWindowSize = Vector256.Create(
(double)windowSize,
(double)windowSize,
(double)windowSize,
(double)windowSize);
while (aCurrent < aUnrolledEnd)
{
#region 1
Avx.Store(
aCurrent,
Avx.Divide(
Avx.Subtract(
Avx.LoadVector256(valueWindowSize),
Avx.LoadVector256(valueCurrent)),
vWindowSize
)
);
#endregion
#region 2
Avx.Store(
aCurrent + 4,
Avx.Divide(
Avx.Subtract(
Avx.LoadVector256(valueWindowSize + 4),
Avx.LoadVector256(valueCurrent + 4)),
vWindowSize
)
);
#endregion
#region 3
Avx.Store(
aCurrent + 8,
Avx.Divide(
Avx.Subtract(
Avx.LoadVector256(valueWindowSize + 8),
Avx.LoadVector256(valueCurrent + 8)),
vWindowSize
)
);
#endregion
#region 4
Avx.Store(
aCurrent + 12,
Avx.Divide(
Avx.Subtract(
Avx.LoadVector256(valueWindowSize + 12),
Avx.LoadVector256(valueCurrent + 12)),
vWindowSize
)
);
#endregion
valueWindowSize += 16;
valueCurrent += 16;
aCurrent += 16;
}
while (aCurrent < aEnd)
{
*aCurrent = (*valueWindowSize - *valueCurrent) / windowSize;
aCurrent++;
valueCurrent++;
valueWindowSize++;
}
var aPrev = aStart;
aCurrent = aStart + 1;
aEnd = aStart + resultSize;
*aPrev = sum / windowSize;
aUnrolledEnd = aStart + (((resultSize - 1) >> 2) << 2);
while (aCurrent < aUnrolledEnd)
{
#region 1
*aCurrent += *aPrev;
aCurrent++;
aPrev++;
#endregion
#region 2
*aCurrent += *aPrev;
aCurrent++;
aPrev++;
#endregion
#region 3
*aCurrent += *aPrev;
aCurrent++;
aPrev++;
#endregion
#region 4
*aCurrent += *aPrev;
aCurrent++;
aPrev++;
#endregion
}
while (aCurrent < aEnd)
{
*aCurrent += *aPrev;
aCurrent++;
aPrev++;
}
}
return(a);
}
public unsafe override double[] Applay(double[] values, int halfWindow)
{
var windowSize = 2 * halfWindow + 1;
var resultSize = values.Length - windowSize + 1;
if (resultSize == 0)
{
return(null);
}
var a = new double[resultSize];
var sum = 0d;
fixed(double *valueStart = values, aStart = a)
{
var valueCurrent = valueStart;
var valueEndwindowSize = valueCurrent + windowSize;
while (valueCurrent < valueEndwindowSize)
{
sum += *valueCurrent;
valueCurrent++;
}
var aCurrent = aStart + 1;
var aEnd = aStart + resultSize;
var aUnrolledEnd = aStart + (((resultSize - 1) >> 4) << 4);
valueCurrent = valueStart;
var valueWindowSize = valueStart + windowSize;
var vWindowSize = Vector256.Create((double)windowSize);
var vCurrent = Vector256.Create(
(ulong)aCurrent,
(ulong)aCurrent + 4 * sizeof(double),
(ulong)aCurrent + 8 * sizeof(double),
(ulong)aCurrent + 12 * sizeof(double));
var vValueCurrent = Vector256.Create(
(ulong)valueCurrent,
(ulong)valueCurrent + 4 * sizeof(double),
(ulong)valueCurrent + 8 * sizeof(double),
(ulong)valueCurrent + 12 * sizeof(double));
var vValueWindowSize = Vector256.Create(
(ulong)valueWindowSize,
(ulong)valueWindowSize + 4 * sizeof(double),
(ulong)valueWindowSize + 8 * sizeof(double),
(ulong)valueWindowSize + 12 * sizeof(double));
var vShiftIndex1 = Vector256.Create(16ul * sizeof(double));
while (aCurrent < aUnrolledEnd)
{
#region 1
Avx.Store(
aCurrent,
Avx.Divide(
Avx.Subtract(
Avx.LoadVector256((double *)vValueWindowSize.GetElement(0)),
Avx.LoadVector256((double *)vValueCurrent.GetElement(0))),
vWindowSize
)
);
#endregion
#region 2
Avx.Store(
(double *)vCurrent.GetElement(1),
Avx.Divide(
Avx.Subtract(
Avx.LoadVector256((double *)vValueWindowSize.GetElement(1)),
Avx.LoadVector256((double *)vValueCurrent.GetElement(1))),
vWindowSize
)
);
#endregion
#region 3
Avx.Store(
(double *)vCurrent.GetElement(2),
Avx.Divide(
Avx.Subtract(
Avx.LoadVector256((double *)vValueWindowSize.GetElement(2)),
Avx.LoadVector256((double *)vValueCurrent.GetElement(2))),
vWindowSize
)
);
#endregion
#region 4
Avx.Store(
(double *)vCurrent.GetElement(3),
Avx.Divide(
Avx.Subtract(
Avx.LoadVector256((double *)vValueWindowSize.GetElement(3)),
Avx.LoadVector256((double *)vValueCurrent.GetElement(3))),
vWindowSize
)
);
#endregion
vCurrent = Avx.Add(vCurrent.AsDouble(), vShiftIndex1.AsDouble()).AsUInt64();
vValueCurrent = Avx.Add(vValueCurrent.AsDouble(), vShiftIndex1.AsDouble()).AsUInt64();
vValueWindowSize = Avx.Add(vValueWindowSize.AsDouble(), vShiftIndex1.AsDouble()).AsUInt64();
aCurrent = (double *)vCurrent.GetElement(0);
}
valueWindowSize = (double *)vValueWindowSize.GetElement(0);
valueCurrent = (double *)vValueCurrent.GetElement(0);
while (aCurrent < aEnd)
{
*aCurrent = (*valueWindowSize - *valueCurrent) / windowSize;
aCurrent++;
valueCurrent++;
valueWindowSize++;
}
var aPrev = aStart;
aCurrent = aStart + 1;
aEnd = aStart + resultSize;
*aPrev = sum / windowSize;
aUnrolledEnd = aStart + (((resultSize - 1) >> 2) << 2);
vCurrent = Vector256.Create(
(ulong)aCurrent,
(ulong)aCurrent + sizeof(double),
(ulong)aCurrent + 2 * sizeof(double),
(ulong)aCurrent + 3 * sizeof(double));
var vPrev = Vector256.Create(
(ulong)aPrev,
(ulong)aPrev + sizeof(double),
(ulong)aPrev + 2 * sizeof(double),
(ulong)aPrev + 3 * sizeof(double));
var vShiftIndex = Vector256.Create(4ul * sizeof(double));
while (aCurrent < aUnrolledEnd)
{
#region 1
*aCurrent += *(double *)vPrev.GetElement(0);
#endregion
#region 2
*(double *)vCurrent.GetElement(1) += *(double *)vPrev.GetElement(1);
#endregion
#region 3
*(double *)vCurrent.GetElement(2) += *(double *)vPrev.GetElement(2);
#endregion
#region 4
*(double *)vCurrent.GetElement(3) += *(double *)vPrev.GetElement(3);
#endregion
vCurrent = Avx.Add(vCurrent.AsDouble(), vShiftIndex.AsDouble()).AsUInt64();
vPrev = Avx.Add(vPrev.AsDouble(), vShiftIndex.AsDouble()).AsUInt64();
aCurrent = (double *)vCurrent.GetElement(0);
}
aPrev = (double *)vPrev.GetElement(0);
while (aCurrent < aEnd)
{
*aCurrent += *aPrev;
aCurrent++;
aPrev++;
}
}
return(a);
}
public static Vector256 <double> op_Division(Vector256 <double> vector, double scalar) => Avx.Divide(vector, Vector256.Create(scalar));
protected override unsafe double CalculateImpl(double x, double stepThreshold, int maxN)
{
if (!Avx.IsSupported)
{
Status = TaylorSeriesStatus.NotSupported;
return(Double.NaN);
}
const int vectorSize = 256 / 8 / sizeof(double);
// v8888 <- (8, 8, 8, 8)
var value8 = 8.0;
var v8888 = Avx.BroadcastScalarToVector256(&value8);
// xPow8 <- (x^8, x^8, x^8, x^8)
var xPow8 = Avx.BroadcastScalarToVector256(&x);
xPow8 = Avx.Multiply(xPow8, xPow8);
xPow8 = Avx.Multiply(xPow8, xPow8);
xPow8 = Avx.Multiply(xPow8, xPow8);
// up <- (x^(-1), x^(-3), x^(-5), x^(-7))
var upSa = stackalloc double[vectorSize];
var xDiv2iPlus1 = 1 / x;
for (var i = 0; i < vectorSize; i++)
{
upSa[i] = xDiv2iPlus1;
xDiv2iPlus1 /= x * x;
}
var up = Avx.LoadVector256(upSa);
// down <- (1, 3, 5, 7)
var downSa = stackalloc double[vectorSize] {
1, 3, 5, 7
};
var down = Avx.LoadVector256(downSa);
// sum <- (0, 0, 0, 0)
var sum = Vector256 <double> .Zero;
N = 0;
while (N < maxN)
{
// div <- up / down
var div = Avx.Divide(up, down);
// sum <- sum + div
sum = Avx.Add(sum, div);
// div = (x1, x2, x3, last)
var last = div.GetElement(vectorSize - 1);
N += vectorSize;
if (Math.Abs(last) < stepThreshold)
{
break;
}
// up <- up / (x^8, x^8, x^8, x^8)
up = Avx.Divide(up, xPow8);
// down <- down + (8, 8, 8, 8)
down = Avx.Add(down, v8888);
}
var resultSa = stackalloc double[vectorSize];
Avx.Store(resultSa, sum);
Status = N >= maxN ? TaylorSeriesStatus.TooManyIterations : TaylorSeriesStatus.Success;
return(resultSa[0] + resultSa[1] + resultSa[2] + resultSa[3]);
}
}
public static unsafe float GetScribnerBoardFeetPerAcre(Trees trees)
{
// for now, assume all trees are of the same species
if (trees.Species != FiaCode.PseudotsugaMenziesii)
{
throw new NotSupportedException();
}
if (trees.Units != Units.English)
{
throw new NotSupportedException();
}
// Douglas-fir
#if DEBUG
Vector128 <float> v6p8 = AvxExtensions.BroadcastScalarToVector128(6.8F);
Vector128 <float> v10k = AvxExtensions.BroadcastScalarToVector128(10.0F * 1000.0F);
#endif
// constants
Vector128 <float> forestersEnglish = AvxExtensions.BroadcastScalarToVector128(Constant.ForestersEnglish);
Vector128 <float> one = AvxExtensions.BroadcastScalarToVector128(1.0F);
Vector128 <float> six = AvxExtensions.BroadcastScalarToVector128(6.0F);
Vector128 <float> vm3p21809 = AvxExtensions.BroadcastScalarToVector128(-3.21809F); // b4
Vector128 <float> v0p04948 = AvxExtensions.BroadcastScalarToVector128(0.04948F);
Vector128 <float> vm0p15664 = AvxExtensions.BroadcastScalarToVector128(-0.15664F);
Vector128 <float> v2p02132 = AvxExtensions.BroadcastScalarToVector128(2.02132F);
Vector128 <float> v1p63408 = AvxExtensions.BroadcastScalarToVector128(1.63408F);
Vector128 <float> vm0p16184 = AvxExtensions.BroadcastScalarToVector128(-0.16184F);
Vector128 <float> v1p033 = AvxExtensions.BroadcastScalarToVector128(1.033F);
Vector128 <float> v1p382937 = AvxExtensions.BroadcastScalarToVector128(1.382937F);
Vector128 <float> vm0p4015292 = AvxExtensions.BroadcastScalarToVector128(-0.4015292F);
Vector128 <float> v0p087266 = AvxExtensions.BroadcastScalarToVector128(0.087266F);
Vector128 <float> vm0p174533 = AvxExtensions.BroadcastScalarToVector128(-0.174533F);
Vector128 <float> vm0p6896598794 = AvxExtensions.BroadcastScalarToVector128(-0.6896598794F); // rc6-rs632
Vector128 <float> v0p993 = AvxExtensions.BroadcastScalarToVector128(0.993F);
Vector128 <float> v0p174439 = AvxExtensions.BroadcastScalarToVector128(0.174439F);
Vector128 <float> v0p117594 = AvxExtensions.BroadcastScalarToVector128(0.117594F);
Vector128 <float> vm8p210585 = AvxExtensions.BroadcastScalarToVector128(-8.210585F);
Vector128 <float> v0p236693 = AvxExtensions.BroadcastScalarToVector128(0.236693F);
Vector128 <float> v0p00001345 = AvxExtensions.BroadcastScalarToVector128(0.00001345F);
Vector128 <float> v0p00001937 = AvxExtensions.BroadcastScalarToVector128(0.00001937F);
Vector128 <float> v1p001491 = AvxExtensions.BroadcastScalarToVector128(1.001491F);
Vector128 <float> vm6p924097 = AvxExtensions.BroadcastScalarToVector128(-6.924097F);
Vector128 <float> v0p912733 = AvxExtensions.BroadcastScalarToVector128(0.912733F);
Vector128 <float> v0p00001351 = AvxExtensions.BroadcastScalarToVector128(0.00001351F);
fixed(float *dbh = &trees.Dbh[0], expansionFactors = &trees.LiveExpansionFactor[0], height = &trees.Height[0])
{
Vector128 <float> standBoardFeetPerAcre = Vector128 <float> .Zero;
for (int treeIndex = 0; treeIndex < trees.Count; treeIndex += Constant.Simd128x4.Width)
{
Vector128 <float> dbhInInches = Avx.LoadVector128(dbh + treeIndex);
Vector128 <float> heightInFeet = Avx.LoadVector128(height + treeIndex);
Vector128 <float> logDbhInInches = MathV.Log10(dbhInInches);
Vector128 <float> logHeightInFeet = MathV.Log10(heightInFeet);
// FiaCode.PseudotsugaMenziesii => -3.21809F + 0.04948F * logHeightInFeet * logDbhInInches - 0.15664F * logDbhInInches * logDbhInInches +
// 2.02132F * logDbhInInches + 1.63408F * logHeightInFeet - 0.16184F * logHeightInFeet * logHeightInFeet,
Vector128 <float> cvtsl = Avx.Add(vm3p21809, Avx.Multiply(v0p04948, Avx.Multiply(logHeightInFeet, logDbhInInches)));
cvtsl = Avx.Add(cvtsl, Avx.Multiply(vm0p15664, Avx.Multiply(logDbhInInches, logDbhInInches)));
cvtsl = Avx.Add(cvtsl, Avx.Multiply(v2p02132, logDbhInInches));
cvtsl = Avx.Add(cvtsl, Avx.Multiply(v1p63408, logHeightInFeet));
cvtsl = Avx.Add(cvtsl, Avx.Multiply(vm0p16184, Avx.Multiply(logHeightInFeet, logHeightInFeet)));
Vector128 <float> cubicFeet = MathV.Exp10(cvtsl);
Vector128 <float> dbhSquared = Avx.Multiply(dbhInInches, dbhInInches); // could be consolidated by merging other scaling constants with Forester's constant for basal area
Vector128 <float> basalAreaInSquareFeet = Avx.Multiply(forestersEnglish, dbhSquared);
// b4 = cubicFeet / (1.033F * (1.0F + 1.382937F * MathV.Exp(-4.015292F * dbhInInches / 10.0F)) * (basalAreaInSquareFeet + 0.087266F) - 0.174533F);
Vector128 <float> b4 = Avx.Divide(cubicFeet, Avx.Add(Avx.Multiply(v1p033,
Avx.Multiply(Avx.Add(one, Avx.Multiply(v1p382937,
MathV.Exp(Avx.Multiply(vm0p4015292,
dbhInInches)))),
Avx.Add(basalAreaInSquareFeet, v0p087266))),
vm0p174533));
Vector128 <float> cv4 = Avx.Multiply(b4, Avx.Subtract(basalAreaInSquareFeet, v0p087266));
// conversion to Scribner volumes for 32 foot trees
// Waddell 2014:32
// rc6 = 0.993F * (1.0F - MathF.Pow(0.62F, dbhInInches - 6.0F));
Vector128 <float> rc6 = Avx.Multiply(v0p993, Avx.Subtract(one, MathV.Exp(Avx.Multiply(vm0p6896598794, Avx.Subtract(dbhInInches, six))))); // log2(0.62) = -0.6896598794
Vector128 <float> cv6 = Avx.Multiply(rc6, cv4);
Vector128 <float> logB4 = MathV.Log10(b4);
// float rs616 = MathF.Pow(10.0F, 0.174439F + 0.117594F * logDbhInInches * logB4 - 8.210585F / (dbhInInches * dbhInInches) + 0.236693F * logB4 - 0.00001345F * b4 * b4 - 0.00001937F * dbhInInches * dbhInInches);
Vector128 <float> rs616l = Avx.Add(v0p174439, Avx.Multiply(v0p117594, Avx.Multiply(logDbhInInches, logB4)));
rs616l = Avx.Add(rs616l, Avx.Divide(vm8p210585, dbhSquared));
rs616l = Avx.Add(rs616l, Avx.Multiply(v0p236693, logB4));
rs616l = Avx.Subtract(rs616l, Avx.Multiply(v0p00001345, Avx.Multiply(b4, b4)));
rs616l = Avx.Subtract(rs616l, Avx.Multiply(v0p00001937, dbhSquared));
Vector128 <float> rs616 = MathV.Exp10(rs616l);
Vector128 <float> sv616 = Avx.Multiply(rs616, cv6); // Scribner board foot volume to a 6 inch top for 16 foot logs
// float rs632 = 1.001491F - 6.924097F / tarif + 0.00001351F * dbhInInches * dbhInInches;
Vector128 <float> rs632 = Avx.Add(v1p001491, Avx.Divide(vm6p924097, Avx.Multiply(v0p912733, b4)));
rs632 = Avx.Add(rs632, Avx.Multiply(v0p00001351, dbhSquared));
Vector128 <float> zeroVolumeMask = Avx.CompareLessThanOrEqual(dbhInInches, six);
Vector128 <float> sv632 = Avx.Multiply(rs632, sv616); // Scribner board foot volume to a 6 inch top for 32 foot logs
sv632 = Avx.BlendVariable(sv632, Vector128 <float> .Zero, zeroVolumeMask);
#if DEBUG
DebugV.Assert(Avx.CompareGreaterThanOrEqual(Avx.BlendVariable(rc6, Vector128 <float> .Zero, zeroVolumeMask), Vector128 <float> .Zero));
DebugV.Assert(Avx.CompareLessThanOrEqual(rc6, one));
DebugV.Assert(Avx.CompareGreaterThanOrEqual(Avx.BlendVariable(rs616, one, zeroVolumeMask), one));
DebugV.Assert(Avx.CompareLessThanOrEqual(Avx.BlendVariable(rs616, Vector128 <float> .Zero, zeroVolumeMask), v6p8));
DebugV.Assert(Avx.CompareGreaterThanOrEqual(Avx.BlendVariable(rs632, Vector128 <float> .Zero, zeroVolumeMask), Vector128 <float> .Zero));
DebugV.Assert(Avx.CompareLessThanOrEqual(Avx.BlendVariable(rs632, Vector128 <float> .Zero, zeroVolumeMask), one));
DebugV.Assert(Avx.CompareGreaterThanOrEqual(Avx.BlendVariable(sv632, Vector128 <float> .Zero, zeroVolumeMask), Vector128 <float> .Zero));
DebugV.Assert(Avx.CompareLessThanOrEqual(Avx.BlendVariable(sv632, Vector128 <float> .Zero, zeroVolumeMask), v10k));
#endif
Vector128 <float> expansionFactor = Avx.LoadVector128(expansionFactors + treeIndex);
standBoardFeetPerAcre = Avx.Add(standBoardFeetPerAcre, Avx.Multiply(expansionFactor, sv632));
}
standBoardFeetPerAcre = Avx.HorizontalAdd(standBoardFeetPerAcre, standBoardFeetPerAcre);
standBoardFeetPerAcre = Avx.HorizontalAdd(standBoardFeetPerAcre, standBoardFeetPerAcre);
return(standBoardFeetPerAcre.ToScalar());
}
}
