public static Vector128 <float> MaskExp(Vector128 <float> power, int exponentMask)
{
Vector128 <float> restrictedPower = Avx.Blend(power, AvxExtensions.BroadcastScalarToVector128(1.0F), (byte)exponentMask);
Vector128 <float> exponent = Avx.Blend(MathV.Exp(restrictedPower), Vector128 <float> .Zero, (byte)exponentMask);
return(exponent);
}
public unsafe static Vector128 <float> Exp2(Vector128 <float> power)
{
Debug.Assert(Avx.MoveMask(Avx.And(Avx.CompareGreaterThan(power, AvxExtensions.BroadcastScalarToVector128(MathV.FloatMaximumPower)), Avx.CompareOrdered(power, power))) == 0);
byte zeroMask = (byte)Avx.MoveMask(Avx.CompareLessThan(power, AvxExtensions.BroadcastScalarToVector128(-MathV.FloatMaximumPower)));
Vector128 <float> integerPart = Avx.RoundToNearestInteger(power);
Vector128 <float> integerExponent = Avx.ShiftLeftLogical(Avx.Add(Avx.ConvertToVector128Int32(integerPart), MathV.FloatMantissaZero128), MathV.FloatMantissaBits).AsSingle();
// evaluate polynomial
Vector128 <float> beta1 = AvxExtensions.BroadcastScalarToVector128(MathV.Exp2Beta1);
Vector128 <float> beta2 = AvxExtensions.BroadcastScalarToVector128(MathV.Exp2Beta2);
Vector128 <float> beta3 = AvxExtensions.BroadcastScalarToVector128(MathV.Exp2Beta3);
Vector128 <float> beta4 = AvxExtensions.BroadcastScalarToVector128(MathV.Exp2Beta4);
Vector128 <float> x = Avx.Subtract(power, integerPart); // fractional part
Vector128 <float> fractionalExponent = AvxExtensions.BroadcastScalarToVector128(MathV.One);
fractionalExponent = Avx.Add(fractionalExponent, Avx.Multiply(beta1, x));
Vector128 <float> x2 = Avx.Multiply(x, x);
fractionalExponent = Avx.Add(fractionalExponent, Avx.Multiply(beta2, x2));
Vector128 <float> x3 = Avx.Multiply(x2, x);
fractionalExponent = Avx.Add(fractionalExponent, Avx.Multiply(beta3, x3));
Vector128 <float> x4 = Avx.Multiply(x3, x);
fractionalExponent = Avx.Add(fractionalExponent, Avx.Multiply(beta4, x4));
// form exponent
Vector128 <float> exponent = Avx.Multiply(integerExponent, fractionalExponent);
// suppress exponent overflows by truncating values less than 2^-127 to zero
if (zeroMask != 0)
{
exponent = Avx.Blend(exponent, Vector128 <float> .Zero, zeroMask);
}
return(exponent);
}
public unsafe static Vector128 <float> Log2(Vector128 <float> value)
{
// split value into exponent and mantissa parts
Vector128 <float> one = AvxExtensions.BroadcastScalarToVector128(MathV.One);
Vector128 <int> integerValue = value.AsInt32();
Vector128 <float> exponent = Avx.ConvertToVector128Single(Avx.Subtract(Avx.ShiftRightLogical(Avx.And(integerValue, MathV.FloatExponentMask128),
MathV.FloatMantissaBits),
MathV.FloatMantissaZero128));
Vector128 <float> mantissa = Avx.Or(Avx.And(integerValue, MathV.FloatMantissaMask128).AsSingle(), one);
// evaluate mantissa polynomial
Vector128 <float> beta1 = AvxExtensions.BroadcastScalarToVector128(MathV.Log2Beta1);
Vector128 <float> beta2 = AvxExtensions.BroadcastScalarToVector128(MathV.Log2Beta2);
Vector128 <float> beta3 = AvxExtensions.BroadcastScalarToVector128(MathV.Log2Beta3);
Vector128 <float> beta4 = AvxExtensions.BroadcastScalarToVector128(MathV.Log2Beta4);
Vector128 <float> beta5 = AvxExtensions.BroadcastScalarToVector128(MathV.Log2Beta5);
Vector128 <float> x = Avx.Subtract(mantissa, one);
Vector128 <float> polynomial = Avx.Multiply(beta1, x);
Vector128 <float> x2 = Avx.Multiply(x, x);
polynomial = Avx.Add(polynomial, Avx.Multiply(beta2, x2));
Vector128 <float> x3 = Avx.Multiply(x2, x);
polynomial = Avx.Add(polynomial, Avx.Multiply(beta3, x3));
Vector128 <float> x4 = Avx.Multiply(x3, x);
polynomial = Avx.Add(polynomial, Avx.Multiply(beta4, x4));
Vector128 <float> x5 = Avx.Multiply(x4, x);
polynomial = Avx.Add(polynomial, Avx.Multiply(beta5, x5));
// form logarithm
return(Avx.Add(exponent, polynomial));
}
public unsafe static Vector128 <float> Exp(Vector128 <float> power)
{
return(MathV.Exp2(Avx.Multiply(AvxExtensions.BroadcastScalarToVector128(MathV.ExpToExp2), power)));
}
public unsafe static Vector128 <float> Log10(Vector128 <float> value)
{
return(Avx.Multiply(AvxExtensions.BroadcastScalarToVector128(MathV.Log2ToLog10), MathV.Log2(value)));
}
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());
}
}
