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);
}
/// <summary>
/// Find cubic volume of tree per hectare.
/// </summary>
/// <param name="trees">Trees in stand.</param>
/// <param name="treeIndex">Tree.</param>
/// <returns>Cubic volume including top and stump in m³/ha.</returns>
public static float GetCubicVolume(Trees trees, int treeIndex)
{
float dbhInCm = trees.Dbh[treeIndex];
float heightInM = trees.Height[treeIndex];
float expansionFactor = trees.LiveExpansionFactor[treeIndex];
if (trees.Units == Units.English)
{
dbhInCm *= Constant.CentimetersPerInch;
heightInM *= Constant.MetersPerFoot;
expansionFactor *= Constant.AcresPerHectare;
}
if (dbhInCm <= 0.0F)
{
Debug.Assert(dbhInCm == 0.0F);
return(0.0F);
}
float cvtsPerTreeInCubicM = trees.Species switch
{
// Poudel K, Temesgen H, Gray AN. 2018. Estimating upper stem diameters and volume of Douglas-fir and Western hemlock
// trees in the Pacific northwest. Forest Ecosystems 5:16. https://doi.org/10.1186/s40663-018-0134-2
// Table 8
FiaCode.PseudotsugaMenziesii => MathV.Exp(-9.70405F + 1.61812F * MathV.Ln(dbhInCm) + 1.21071F * MathV.Ln(heightInM)),
FiaCode.TsugaHeterophylla => MathV.Exp(-9.98200F + 1.37228F * MathV.Ln(dbhInCm) + 1.57319F * MathV.Ln(heightInM)),
_ => throw Trees.CreateUnhandledSpeciesException(trees.Species),
};
return(expansionFactor * cvtsPerTreeInCubicM);
}
/// <summary>
/// Find cubic volume of tree.
/// </summary>
/// <param name="trees">Trees in stand.</param>
/// <param name="treeIndex">Tree.</param>
/// <returns>Tree's volume including top and stump in ft³.</returns>
public static float GetCubicFeet(Trees trees, int treeIndex)
{
if (trees.Units != Units.English)
{
throw new NotSupportedException();
}
float dbhInInches = trees.Dbh[treeIndex];
if (dbhInInches < Constant.InchesPerCentimeter * Constant.Bucking.MinimumScalingDiameter4Saw)
{
return(0.0F);
}
float logDbhInInches = MathV.Log10(dbhInInches);
float heightInFeet = trees.Height[treeIndex];
float logHeightInFeet = MathV.Log10(heightInFeet);
float cvtsl = trees.Species switch
{
// Waddell K, Campbell K, Kuegler O, Christensen G. 2014. FIA Volume Equation documentation updated on 9-19-2014:
// Volume estimation for PNW Databases NIMS and FIADB. https://ww3.arb.ca.gov/cc/capandtrade/offsets/copupdatereferences/qm_volume_equations_pnw_updated_091914.pdf
// Equation 1: western Oregon and Washington (Brackett 1973)
FiaCode.PseudotsugaMenziesii => - 3.21809F + 0.04948F * logHeightInFeet * logDbhInInches - 0.15664F * logDbhInInches * logDbhInInches +
2.02132F * logDbhInInches + 1.63408F * logHeightInFeet - 0.16184F * logHeightInFeet * logHeightInFeet,
// FIA Equation 6: all of Oregon and California (Chambers 1979)
FiaCode.TsugaHeterophylla => - 2.72170F + 2.00857F * logDbhInInches + 1.08620F * logHeightInFeet - 0.00568F * dbhInInches,
_ => throw Trees.CreateUnhandledSpeciesException(trees.Species)
};
return(MathV.Exp10(cvtsl));
}
public static float Pow(float x, float y)
{
if (x < 0.0F)
{
throw new ArgumentOutOfRangeException(nameof(x));
}
if (x == 0.0F)
{
if (y <= 0.0F)
{
throw new ArgumentOutOfRangeException(nameof(y));
}
return(0.0F);
}
return(MathV.Exp2(MathV.Log2(x) * y));
}
/// <summary>
/// Get cubic volume to a 10 centimeter (four inch) top.
/// </summary>
/// <param name="trees">Trees in stand.</param>
/// <param name="treeIndex">Tree.</param>
/// <returns>Tree's volume in m³.</returns>
public static float GetMerchantableCubicFeet(Trees trees, int treeIndex)
{
if (trees.Units != Units.English)
{
throw new NotSupportedException();
}
float dbhInInches = trees.Dbh[treeIndex];
if (dbhInInches < Constant.InchesPerCentimeter * Constant.Bucking.MinimumScalingDiameter4Saw)
{
// CV4 regression goes negative, unsurprisingly, for trees less than four inches in diameter
return(0.0F);
}
float cvts = FiaVolume.GetCubicFeet(trees, treeIndex);
if (cvts <= 0.0)
{
return(0.0F);
}
float basalAreaInSquareFeet = Constant.ForestersEnglish * dbhInInches * dbhInInches;
float tarif = trees.Species switch
{
// Waddell K, Campbell K, Kuegler O, Christensen G. 2014. FIA Volume Equation documentation updated on 9-19-2014:
// Volume estimation for PNW Databases NIMS and FIADB. https://ww3.arb.ca.gov/cc/capandtrade/offsets/copupdatereferences/qm_volume_equations_pnw_updated_091914.pdf
// Douglas-fir and western hemlock use the same tarif and CV4 regressions
// FIA Equation 1: western Oregon and Washington (Brackett 1973)
// FIA Equation 6: all of Oregon and California (Chambers 1979)
FiaCode.PseudotsugaMenziesii or
FiaCode.TsugaHeterophylla =>
0.912733F *cvts / (1.033F * (1.0F + 1.382937F * MathV.Exp(-4.015292F * dbhInInches / 10.0F)) * (basalAreaInSquareFeet + 0.087266F) - 0.174533F),
_ => throw Trees.CreateUnhandledSpeciesException(trees.Species)
};
return(tarif * (basalAreaInSquareFeet - 0.087266F) / 0.912733F);
}
public unsafe static Vector128 <float> Exp(Vector128 <float> power)
{
return(MathV.Exp2(Avx.Multiply(AvxExtensions.BroadcastScalarToVector128(MathV.ExpToExp2), power)));
}
public static float Exp(float power)
{
return(MathV.Exp2(MathV.ExpToExp2 * power));
}
public static Vector128 <float> Pow(Vector128 <float> x, Vector128 <float> y)
{
return(MathV.Exp2(Avx.Multiply(MathV.Log2(x), y)));
}
public unsafe static Vector128 <float> Log10(Vector128 <float> value)
{
return(Avx.Multiply(AvxExtensions.BroadcastScalarToVector128(MathV.Log2ToLog10), MathV.Log2(value)));
}
public static float Log10(float value)
{
return(MathV.Log2ToLog10 * MathV.Log2(value));
}
public static float Ln(float value)
{
return(MathV.Log2ToNaturalLog * 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());
}
}
/// <summary>
/// Get Scribner board foot volume for 32 foot logs to a six inch top.
/// </summary>
/// <param name="trees">Trees in stand.</param>
/// <param name="treeIndex">Tree.</param>
/// <returns>Tree's volume in Scribner board feet</returns>
public static float GetScribnerBoardFeet(Trees trees, int treeIndex)
{
if (trees.Units != Units.English)
{
throw new NotSupportedException();
}
// repeat code of GetCubicFeet() as this provides about a 6% speedup
float dbhInInches = trees.Dbh[treeIndex];
if (dbhInInches < 6.0F)
{
return(0.0F);
}
float logDbhInInches = MathV.Log10(dbhInInches);
float heightInFeet = trees.Height[treeIndex];
float logHeightInFeet = MathV.Log10(heightInFeet);
float cvtsl = trees.Species switch
{
// Waddell K, Campbell K, Kuegler O, Christensen G. 2014. FIA Volume Equation documentation updated on 9-19-2014:
// Volume estimation for PNW Databases NIMS and FIADB. https://ww3.arb.ca.gov/cc/capandtrade/offsets/copupdatereferences/qm_volume_equations_pnw_updated_091914.pdf
// Equation 1: western Oregon and Washington (Brackett 1973)
FiaCode.PseudotsugaMenziesii => - 3.21809F + 0.04948F * logHeightInFeet * logDbhInInches - 0.15664F * logDbhInInches * logDbhInInches +
2.02132F * logDbhInInches + 1.63408F * logHeightInFeet - 0.16184F * logHeightInFeet * logHeightInFeet,
// FIA Equation 6: all of Oregon and California (Chambers 1979)
FiaCode.TsugaHeterophylla => - 2.72170F + 2.00857F * logDbhInInches + 1.08620F * logHeightInFeet - 0.00568F * dbhInInches,
_ => throw Trees.CreateUnhandledSpeciesException(trees.Species)
};
float cubicFeet = MathV.Exp10(cvtsl);
float basalAreaInSquareFeet = Constant.ForestersEnglish * dbhInInches * dbhInInches;
float tarif = trees.Species switch
{
// Waddell K, Campbell K, Kuegler O, Christensen G. 2014. FIA Volume Equation documentation updated on 9-19-2014:
// Volume estimation for PNW Databases NIMS and FIADB. https://ww3.arb.ca.gov/cc/capandtrade/offsets/copupdatereferences/qm_volume_equations_pnw_updated_091914.pdf
// Douglas-fir and western hemlock use the same tarif and CV4 regressions
// FIA Equation 1: western Oregon and Washington (Brackett 1973)
// FIA Equation 6: all of Oregon and California (Chambers 1979)
FiaCode.PseudotsugaMenziesii or
FiaCode.TsugaHeterophylla =>
0.912733F *cubicFeet / (1.033F * (1.0F + 1.382937F * MathV.Exp(-4.015292F * dbhInInches / 10.0F)) * (basalAreaInSquareFeet + 0.087266F) - 0.174533F),
_ => throw Trees.CreateUnhandledSpeciesException(trees.Species)
};
float cv4 = tarif * (basalAreaInSquareFeet - 0.087266F) / 0.912733F;
// conversion to Scribner volumes for 32 foot trees
// Waddell 2014:32
// float rc6 = 0.993F * (1.0F - MathF.Pow(0.62F, dbhInInches - 6.0F));
float rc6 = 0.993F * (1.0F - MathV.Exp(-0.6896598794F * (dbhInInches - 6.0F))); // log2(0.62) = -0.6896598794
float cv6 = rc6 * cv4;
float b4 = tarif / 0.912733F;
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);
float rs616 = MathV.Exp10(0.174439F + 0.117594F * logDbhInInches * logB4 - 8.210585F / (dbhInInches * dbhInInches) + 0.236693F * logB4 - 0.00001345F * b4 * b4 - 0.00001937F * dbhInInches * dbhInInches);
float sv616 = 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;
float sv632 = rs632 * sv616; // Scribner board foot volume to a 6 inch top for 32 foot logs
Debug.Assert(rc6 >= 0.0F);
Debug.Assert(rc6 <= 1.0F);
Debug.Assert(rs616 >= 1.0F);
Debug.Assert(rs616 <= 6.8F);
Debug.Assert(rs632 >= 0.0F);
Debug.Assert(rs632 <= 1.0F);
Debug.Assert(sv632 >= 0.0F);
Debug.Assert(sv632 <= 10.0 * 1000.0F);
return(sv632);
}
}
}
