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mXparser is a super easy, rich, fast and highly flexible math expression parser library (parser and evaluator of mathematical expressions / formulas provided as plain text / string). Software delivers easy to use API for JAVA, Android and C# .NET/MONO (Common Language Specification compliant: F#, Visual Basic, C++/CLI). *** If you find the software useful donation is something you might consider: https://mathparser.org/donate/ *** Scalar Scientific Calculator, Charts and Scripts, Scalar Lite: https://play.google.com/store/apps/details?id=org.mathparser.scalar.lite *** Scalar Pro: https://play.google.com/store/apps/details?id=org.mathparser.scalar.pro *** ScalarMath.org: https://scalarmath.org/ *** MathSpace.pl: https://mathspace.pl/ ***
/*
* @(#)MathFunctions.java 4.4.3 2022-05-28
*
* MathParser.org-mXparser DUAL LICENSE AGREEMENT as of date 2022-05-22
* The most up-to-date license is available at the below link:
* - https://mathparser.org/mxparser-license
*
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*
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* PRODUCT: MathParser.org-mXparser SOFTWARE
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package org.mariuszgromada.math.mxparser.mathcollection;
import java.math.BigDecimal;
import java.math.MathContext;
import java.math.RoundingMode;
import org.mariuszgromada.math.mxparser.mXparser;
/**
* MathFunctions - the most popular math functions. Many of function implemented by this class
* could be found in java Math package (in fact functions from MathFunctions typically calls
* original functions from the Math package). The reason why it was "re-implemented" is:
* if you decide to implement your own function you do not need to change anything in the parser,
* jut modify function implementation in this class.
*
* @author Mariusz Gromada
* [email protected]
* MathSpace.pl
* MathParser.org - mXparser project page
* mXparser on GitHub
* mXparser on SourceForge
* mXparser on Bitbucket
* mXparser on CodePlex
* Janet Sudoku - project web page
* Janet Sudoku on GitHub
* Janet Sudoku on CodePlex
* Janet Sudoku on SourceForge
* Janet Sudoku on BitBucket
* Scalar Free
* Scalar Pro
* ScalarMath.org
*
* @version 4.4.2
*/
public final class MathFunctions {
/**
* Addition a + b applying canonical rounding if canonical
* rounding is enabled
*
* @param a The a parameter
* @param b The b parameter
* @return The result of addition
*/
public static final double plus(double a, double b) {
if (Double.isNaN(a)) return Double.NaN;
if (Double.isNaN(b)) return Double.NaN;
if (!mXparser.checkIfCanonicalRounding()) return a + b;
if (Double.isInfinite(a)) return a + b;
if (Double.isInfinite(b)) return a + b;
BigDecimal da = BigDecimal.valueOf(a);
BigDecimal db = BigDecimal.valueOf(b);
return da.add(db).doubleValue();
}
/**
* Subtraction a - b applying canonical rounding if canonical
* rounding is enabled
*
* @param a The a parameter
* @param b The b parameter
* @return The result of subtraction
*/
public static final double minus(double a, double b) {
if (Double.isNaN(a)) return Double.NaN;
if (Double.isNaN(b)) return Double.NaN;
if (!mXparser.checkIfCanonicalRounding()) return a - b;
if (Double.isInfinite(a)) return a - b;
if (Double.isInfinite(b)) return a - b;
BigDecimal da = BigDecimal.valueOf(a);
BigDecimal db = BigDecimal.valueOf(b);
return da.subtract(db).doubleValue();
}
/**
* Multiplication a * b applying canonical rounding if canonical
* rounding is enabled
*
* @param a The a parameter
* @param b The b parameter
* @return The result of multiplication
*/
public static final double multiply(double a, double b) {
if (Double.isNaN(a)) return Double.NaN;
if (Double.isNaN(b)) return Double.NaN;
if (!mXparser.checkIfCanonicalRounding()) return a * b;
if (Double.isInfinite(a)) return a * b;
if (Double.isInfinite(b)) return a * b;
BigDecimal da = BigDecimal.valueOf(a);
BigDecimal db = BigDecimal.valueOf(b);
return da.multiply(db).doubleValue();
}
/**
* Division a / b applying canonical rounding if canonical
* rounding is enabled
*
* @param a The a parameter
* @param b The b parameter
* @return The result of division
*/
public static final double div(double a, double b) {
if (b == 0) return Double.NaN;
if (Double.isNaN(a)) return Double.NaN;
if (Double.isNaN(b)) return Double.NaN;
if (!mXparser.checkIfCanonicalRounding()) return a / b;
if (Double.isInfinite(a)) return a / b;
if (Double.isInfinite(b)) return a / b;
BigDecimal da = BigDecimal.valueOf(a);
BigDecimal db = BigDecimal.valueOf(b);
return da.divide(db, MathContext.DECIMAL128).doubleValue();
}
/**
* Bell Numbers
*
* @param n the n
*
* @return if n >= 0 returns Bell numbers,
* otherwise returns Double.NaN.
*/
public static final double bellNumber(int n) {
double result = Double.NaN;
if (n > 1) {
n -= 1;
if ( (n+1)*(n+1) >= Integer.MAX_VALUE ) return Double.NaN;
long[][] bellTriangle = new long[n+1][n+1];
bellTriangle[0][0] = 1;
bellTriangle[1][0] = 1;
for (int r = 1; r <= n; r++) {
for (int k = 0; k < r; k++)
bellTriangle[r][k+1] = bellTriangle[r-1][k] + bellTriangle[r][k];
if (r < n)
bellTriangle[r+1][0] = bellTriangle[r][r];
if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
}
result = bellTriangle[n][n];
} else if (n >= 0)
result = 1;
return result;
}
/**
* Bell number
* @param n the n
*
* @return if n <> Double.NaN return bellNumber( (int)Math.round(n) ),
* otherwise return Double.NaN.
*/
public static final double bellNumber(double n) {
if (Double.isNaN(n))
return Double.NaN;
return bellNumber( (int)Math.round(n) );
}
/**
* Euler numbers
*
* @param n the n function param
* @param k the k function param
*
* @return if n >=0 returns Euler number,
* otherwise return Double.NaN.
*/
public static final double eulerNumber(int n, int k) {
if ( n < 0)
return Double.NaN;
if (k < 0)
return 0;
if (n == 0)
if (k == 0)
return 1;
else
return 0;
if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
return (k+1) * eulerNumber(n-1, k) + (n-k) * eulerNumber(n-1, k-1);
}
/**
* Euler numbers
*
* @param n the n function param
* @param k the k function param
*
* @return if n, k <> Double.NaN returns eulerNumber( (int)Math.round(n), (int)Math.round(k) ),
* otherwise return Double.NaN.
*/
public static final double eulerNumber(double n, double k) {
if (Double.isNaN(n) || Double.isNaN(k))
return Double.NaN;
return eulerNumber( (int)Math.round(n), (int)Math.round(k) );
}
/**
* Factorial
*
* @param n the n function parameter
*
* @return Factorial if n >=0, otherwise returns Double.NaN.
*/
public static final double factorial(int n) {
double f = Double.NaN;
if (n >= 0)
if (n < 2) f = 1;
else {
f = 1;
for (int i = 1; i <= n; i++) {
f = f*i;
if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
}
}
return f;
}
/**
* Factorial
*
* @param n the n function parameter
*
* @return if n <> Double.NaN return factorial( (int)Math.round(n) ),
* otherwise returns Double.NaN.
*/
public static final double factorial(double n) {
if (Double.isNaN(n))
return Double.NaN;
return factorial( (int)Math.round(n) );
}
/**
* Generalized binomial coefficient
*
* @param n the n function parameter
* @param k k the k function parameter
*
* @return Generalized binomial coefficient, if
* n = Double.NaN or k < 0 returns Double.NaN.
*/
public static final double binomCoeff(double n, long k) {
if (Double.isNaN(n))
return Double.NaN;
double result = Double.NaN;
if ( k >= 0 ){
double numerator = 1;
if (k > 0 )
for (long i = 0; i <= k-1; i++) {
numerator*=(n-i);
if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
}
double denominator = 1;
if ( k > 1 )
for (long i = 1; i <= k; i++) {
denominator *= i;
if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
}
result = numerator / denominator;
}
return result;
}
/**
* Generalized binomial coefficient
*
* @param n the n function parameter
* @param k the k function parameter
*
* @return if n, k <> Double.NaN returns binomCoeff(n, (int)Math.round(k) ),
* otherwise returns Double.NaN.
*/
public static final double binomCoeff(double n, double k) {
if (Double.isNaN(n) || Double.isNaN(k))
return Double.NaN;
return binomCoeff(n, (long)Math.round(k) );
}
/**
* Generalized coefficient returning number of k permutations
* that can be drawn for n elements set.
*
* @param n the n function parameter
* @param k the k function parameter
*
* @return For k greater than 0 return number of permutations, otherwise
* returns Double.NaN
*/
public static final double numberOfPermutations(double n, long k) {
if (Double.isNaN(n))
return Double.NaN;
double result = Double.NaN;
if ( k >= 0 ){
double numerator = 1;
if (k > 0 )
for (long i = 0; i <= k-1; i++) {
numerator*=(n-i);
if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
}
result = numerator;
}
return result;
}
/**
* Generalized coefficient returning number of k permutations
* that can be drawn for n elements set.
*
* @param n the n function parameter
* @param k the k function parameter
*
* @return For k greater than 0 return number of permutations, otherwise
* returns Double.NaN
*/
public static final double numberOfPermutations(double n, double k) {
if (Double.isNaN(n) || Double.isNaN(k))
return Double.NaN;
return numberOfPermutations(n, (long)Math.round(k) );
}
/**
* Bernoulli numbers
*
* @param m the m function parameter
* @param n the n function parameter
*
* @return if n, m >= 0 returns Bernoulli number,
* otherwise returns Double.NaN.
*/
public static final double bernoulliNumber(int m, int n) {
double result = Double.NaN;
if ( (m >= 0) && (n >= 0) ) {
result = 0;
for (int k = 0; k <= m; k++)
for (int v = 0; v <= k; v++) {
result += Math.pow(-1, v) * binomCoeff(k, v)
* ( Math.pow(n + v, m) / (k + 1) );
if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
}
}
return result;
}
/**
* Bernoulli numbers
*
* @param m the m function parameter
* @param n the n function parameter
*
* @return if n, m <> Double.NaN returns bernoulliNumber( (int)Math.round(m), (int)Math.round(n) ),
* otherwise returns Double.NaN.
*/
public static final double bernoulliNumber(double m, double n) {
if (Double.isNaN(m) || Double.isNaN(n))
return Double.NaN;
return bernoulliNumber( (int)Math.round(m), (int)Math.round(n) );
}
/**
* Stirling numbers of the first kind
*
* @param n the n function parameter
* @param k the k function parameter
*
* @return Stirling numbers of the first kind
*/
public static final double Stirling1Number(int n, int k) {
if (k > n)
return 0;
if (n == 0)
if (k == 0)
return 1;
else
return 0;
if (k == 0)
if (n == 0)
return 1;
else
return 0;
if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
return (n-1) * Stirling1Number(n-1, k) + Stirling1Number(n-1, k-1);
}
/**
* Stirling numbers of the first kind
*
* @param n the n function parameter
* @param k the k function parameter
*
* @return if n, k <> Doube.NaN returns Stirling1Number( (int)Math.round(n), (int)Math.round(k) ),
* otherwise returns Double.NaN.
*/
public static final double Stirling1Number(double n, double k) {
if (Double.isNaN(n) || Double.isNaN(k))
return Double.NaN;
return Stirling1Number( (int)Math.round(n), (int)Math.round(k) );
}
/**
* Stirling numbers of the second kind
*
* @param n the n function parameter
* @param k the k function parameter
*
* @return Stirling numbers of the second kind
*/
public static final double Stirling2Number(int n, int k) {
if (k > n)
return 0;
if (n == 0)
if (k == 0)
return 1;
else
return 0;
if (k == 0)
if (n == 0)
return 1;
else
return 0;
if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
return k * Stirling2Number(n-1, k) + Stirling2Number(n-1, k-1);
}
/**
* Stirling numbers of the second kind
*
* @param n the n function parameter
* @param k the k function parameter
*
* @return if n, k <> Doube.NaN returns Stirling2Number( (int)Math.round(n), (int)Math.round(k) ),
* otherwise returns Double.NaN.
*/
public static final double Stirling2Number(double n, double k) {
if (Double.isNaN(n) || Double.isNaN(k))
return Double.NaN;
return Stirling2Number( (int)Math.round(n), (int)Math.round(k) );
}
/**
* Worpitzky numbers
*
* @param n the n function parameter
* @param k the k function parameter
*
* @return if n,k >= 0 and k <= n return Worpitzky number,
* otherwise return Double.NaN.
*/
public static final double worpitzkyNumber(int n, int k) {
double result = Double.NaN;
if ( (n >= 0) && (k >= 0) && (k <= n) ){
result = 0;
for (int v = 0; v <= k; v++) {
result += Math.pow(-1, v+k) * Math.pow(v+1, n) * binomCoeff(k, v);
if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
}
}
return result;
}
/**
* Worpitzky numbers
*
* @param n the n function parameter
* @param k the k function parameter
*
* @return if n,k <> Double.NaN returns worpitzkyNumber( (int)Math.round(n), (int)Math.round(k) ),
* otherwise return Double.NaN.
*/
public static final double worpitzkyNumber(double n, double k) {
if (Double.isNaN(n) || Double.isNaN(k))
return Double.NaN;
return worpitzkyNumber( (int)Math.round(n), (int)Math.round(k) );
}
/**
* Harmonic numer
*
* @param n the n function parameter
*
* @return if n > 0 returns harmonic number, otherwise returns 0
* (empty summation operator)
*/
public static final double harmonicNumber(int n) {
if (n <= 0)
return 0;
if (n == 1)
return 1;
double h = 1;
for (double k = 2.0; k <= n; k++) {
h += 1.0 / k;
if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
}
return h;
}
/**
* Harmonic number
*
* @param n the n function parameter
*
* @return if n <> Double.NaN returns harmonicNumber( (int)Math.round(n) ),
* otherwise returns Double.NaN
*/
public static final double harmonicNumber(double n) {
if (Double.isNaN(n))
return Double.NaN;
return harmonicNumber( (int)Math.round(n) );
}
/**
* Harmonic number 1/1 + 1/2^x + ... + 1/n^x
*
* @param x the x function parameter
* @param n the n function parameter
*
* @return if x <> Double.NaN and x >= 0 Harmonic number,
* otherwise returns Double.NaN.
*/
public static final double harmonicNumber(double x, int n) {
if ( (Double.isNaN(x)) || (x < 0) )
return Double.NaN;
if (n <= 0)
return 0;
if (n == 1)
return x;
double h = 1;
for (double k = 2.0; k <= n; k++) {
h += 1 / power(k, x);
if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
}
return h;
}
/**
* Harmonic number 1/1 + 1/2^x + ... + 1/n^x
*
* @param x the x function parameter
* @param n the n function parameter
*
* @return if x,n <> Double.NaN returns harmonicNumber( x, (int)Math.round(n) ),
* otherwise returns Double.NaN.
*/
public static final double harmonicNumber(double x, double n) {
if ( (Double.isNaN(x)) || (Double.isNaN(n)) )
return Double.NaN;
return harmonicNumber( x, (int)Math.round(n) );
}
/**
* Catalan numbers
*
* @param n the n function parameter
*
* @return Catalan numbers
*/
public static final double catalanNumber(int n) {
return binomCoeff(2*n, n) * div(1, n+1);
}
/**
* Catalan numbers
*
* @param n the n function parameter
*
* @return if n <> Double.NaN returns catalanNumber( (int)Math.round(n) ),
* otherwise returns Double.NaN.
*/
public static final double catalanNumber(double n) {
if (Double.isNaN(n))
return Double.NaN;
return catalanNumber( (int)Math.round(n) );
}
/**
* Fibonacci numbers
*
* @param n the n function parameter
*
* @return if n >= 0 returns fibonacci numbers,
* otherwise returns Double.NaN.
*/
public final static double fibonacciNumber(int n) {
if (n < 0 )
return Double.NaN;
if (n == 0)
return 0;
if (n == 1)
return 1;
if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
return fibonacciNumber(n-1) + fibonacciNumber(n-2);
}
/**
* Fibonacci numbers
*
* @param n the n function parameter
*
* @return if n <> Double.NaN returns fibonacciNumber( (int)Math.round(n) ),
* otherwise returns Double.NaN.
*/
public final static double fibonacciNumber(double n) {
if (Double.isNaN(n))
return Double.NaN;
return fibonacciNumber( (int)Math.round(n) );
}
/**
* Lucas numebrs
*
* @param n the n function parameter
*
* @return if n >= 0 returns Lucas numbers,
* otherwise returns Double.NaN.
*/
public final static double lucasNumber(int n) {
if (n < 0 )
return Double.NaN;
if (n == 0)
return 2;
if (n == 1)
return 1;
if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
return lucasNumber(n-1) + lucasNumber(n-2);
}
/**
* Lucas numebrs
*
* @param n the n function parameter
*
* @return if n <> Double.NaN returns lucasNumber( (int)Math.round(n) ),
* otherwise returns Double.NaN.
*/
public final static double lucasNumber(double n) {
if (Double.isNaN(n))
return Double.NaN;
return lucasNumber( (int)Math.round(n) );
}
/**
* Kronecker delta
*
* @param i the i function parameter
* @param j the j function parameter
*
* @return if i,j <> Double.NaN returns Kronecker delta,
* otherwise returns Double.NaN.
*/
public static final double kroneckerDelta(double i, double j) {
if (Double.isNaN(i) || Double.isNaN(j))
return Double.NaN;
if (i == j)
return 1;
else
return 0;
}
/**
* Kronecker delta
*
* @param i the i function parameter
* @param j the j function parameter
*
* @return Kronecker delta
*/
public static final double kroneckerDelta(int i, int j) {
if (i == j)
return 1;
else
return 0;
}
/**
* Continued fraction
*
* @param sequence the numbers
*
* @return if each number form the sequence <> Double.NaN and
* there is no division by 0 while computing returns continued fraction
* value, otherwise returns Double.NaN.
*/
public static final double continuedFraction(double... sequence) {
if (sequence == null) return Double.NaN;
if (sequence.length == 0) return Double.NaN;
double cf = 0;
double a;
if (sequence.length == 1)
return sequence[0];
int lastIndex = sequence.length-1;
for(int i = lastIndex; i >= 0; i--) {
a = sequence[i];
if (Double.isNaN(a))
return Double.NaN;
if (i == lastIndex) {
cf = a;
} else {
if (cf == 0)
return Double.NaN;
cf = a + 1.0 / cf;
}
if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
}
return cf;
}
/**
* Private function calculating continued polynomial
* recursively.
*
* @param n the polynomial order
* @param x the x values
*
* @return continued polynomial value
*/
private static final double continuedPolynomial(int n, double[] x) {
if (x == null) return Double.NaN;
if (x.length == 0) return Double.NaN;
if (n == 0)
return 1;
if (n == 1)
return x[0];
if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
return x[n-1] * continuedPolynomial(n-1, x) + continuedPolynomial(n-2, x);
}
/**
* Continued polynomial
*
* @param x the x values
*
* @return if each number for x is different the Double.NaN
* returns continued polynomial, otherwise returns
* Double.NaN.
*/
public static final double continuedPolynomial(double... x) {
if (x == null) return Double.NaN;
if (x.length == 0) return Double.NaN;
for (double d : x) {
if (Double.isNaN(d))
return Double.NaN;
if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
}
return continuedPolynomial(x.length, x);
}
/**
* Euler polynomial
*
* @param m the m parameter
* @param x the x parameter
*
* @return if x <> Double.NaN and m >= 0 returns polynomial value,
* otherwise returns Double.NaN.
*/
public static final double eulerPolynomial(int m, double x) {
if (Double.isNaN(x))
return Double.NaN;
double result = Double.NaN;
if (m >= 0) {
result = 0;
for (int n = 0; n <= m; n++) {
for (int k = 0; k <= n; k++) {
result += Math.pow(-1, k) * binomCoeff(n, k) * Math.pow(x+k, m);
if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
}
result /= Math.pow(2, n);
}
}
return result;
}
/**
* Euler polynomial
*
* @param m the m parameter
* @param x the x parameter
*
* @return if x,m <> Double.NaN returns eulerPolynomial( (int)Math.round(m), (int)Math.round(x) ),
* otherwise returns Double.NaN.
*/
public static final double eulerPolynomial(double m, double x) {
if (Double.isNaN(m) || Double.isNaN(x))
return Double.NaN;
return eulerPolynomial( (int)Math.round(m), (int)Math.round(x) );
}
/**
* Characteristic function x in (a,b)
*
* @param x the x value
* @param a the left (lower) limit
* @param b the right (upper) limit
*
* @return if x, a, b <> Double.NaN returns
* characteristic function value on the (a,b) range.
*/
public static final double chi(double x, double a, double b) {
if (Double.isNaN(x) || Double.isNaN(a) || Double.isNaN(b))
return Double.NaN;
double result = Double.NaN;
if ( (!Double.isNaN(x)) && (!Double.isNaN(a)) && (!Double.isNaN(b)) )
if ( (x > a) && (x < b) )
result = 1;
else
result = 0;
return result;
}
/**
* Characteristic function x in [a,b]
*
* @param x the x value
* @param a the left (lower) limit
* @param b the right (upper) limit
*
* @return if x, a, b <> Double.NaN returns
* characteristic function value on the [a,b] range.
*/
public static final double chi_LR(double x, double a, double b) {
if (Double.isNaN(x) || Double.isNaN(a) || Double.isNaN(b))
return Double.NaN;
double result = Double.NaN;
if ( (!Double.isNaN(x)) && (!Double.isNaN(a)) && (!Double.isNaN(b)) )
if ( (x >= a) && (x <= b) )
result = 1;
else
result = 0;
return result;
}
/**
* Characteristic function x in [a,b)
*
* @param x the x value
* @param a the left (lower) limit
* @param b the right (upper) limit
*
* @return if x, a, b <> Double.NaN returns
* characteristic function value on the [a,b) range.
*/
public static final double chi_L(double x, double a, double b) {
if (Double.isNaN(x) || Double.isNaN(a) || Double.isNaN(b))
return Double.NaN;
double result = Double.NaN;
if ( (!Double.isNaN(x)) && (!Double.isNaN(a)) && (!Double.isNaN(b)) )
if ( (x >= a) && (x < b) )
result = 1;
else
result = 0;
return result;
}
/**
* Characteristic function x in (a,b]
*
* @param x the x value
* @param a the left (lower) limit
* @param b the right (upper) limit
*
* @return if x, a, b <> Double.NaN returns
* characteristic function value on the (a,b] range.
*/
public static final double chi_R(double x, double a, double b) {
if (Double.isNaN(x) || Double.isNaN(a) || Double.isNaN(b))
return Double.NaN;
double result = Double.NaN;
if ( (!Double.isNaN(x)) && (!Double.isNaN(a)) && (!Double.isNaN(b)) )
if ( (x > a) && (x <= b) )
result = 1;
else
result = 0;
return result;
}
/**
* Verifies whether provided number is almost integer
*
* @see BinaryRelations#DEFAULT_COMPARISON_EPSILON
*
* @param a The number to be verified
* @return True if the number is almost integer according to the default epsilon,
* otherwise returns false.
*/
public static final boolean isAlmostInt(double a) {
double aint = Math.round(a);
if (abs(a - aint) <= BinaryRelations.DEFAULT_COMPARISON_EPSILON) return true;
else return false;
}
/**
* Applies the integer exponent to the base a
*
* @param a The base
* @param n The integer exponent
* @return Return a to the power of n, if canonical rounding is enable, the it operates on big numbers
*/
private static final double powInt(double a, int n) {
if (Double.isNaN(a)) return Double.NaN;
if (Double.isInfinite(a)) Math.pow(a, n);
if (a == 0) return Math.pow(a, n);
if (n == 0) return 1;
if (n == 1) return a;
if (mXparser.checkIfCanonicalRounding()) {
BigDecimal da = BigDecimal.valueOf(a);
if (n >= 0) return da.pow(n).doubleValue();
else return BigDecimal.ONE.divide(da, MathContext.DECIMAL128).pow(-n).doubleValue();
} else {
return Math.pow(a, n);
}
}
/**
* Power function a^b
*
* @param a the a function parameter
* @param b the b function parameter
*
* @return if a,b <> Double.NaN returns Math.pow(a, b),
* otherwise returns Double.NaN.
*/
public static final double power(double a, double b) {
if (Double.isNaN(a) || Double.isNaN(b))
return Double.NaN;
if (Double.isInfinite(a)) Math.pow(a, b);
if (Double.isInfinite(b)) Math.pow(a, b);
double babs = Math.abs(b);
double bint = Math.round(babs);
if ( MathFunctions.abs(babs - bint) <= BinaryRelations.DEFAULT_COMPARISON_EPSILON ) {
if (b >= 0) return powInt(a, (int)bint);
else return powInt(a, -(int)bint);
} else if (a >= 0)
return Math.pow(a, b);
else if (abs(b) >= 1)
return Math.pow(a, b);
else if (b == 0)
return Math.pow(a, b);
else {
double ndob = 1.0 / abs(b);
double nint = Math.round(ndob);
if ( MathFunctions.abs(ndob-nint) <= BinaryRelations.DEFAULT_COMPARISON_EPSILON ) {
long n = (long)nint;
if (n % 2 == 1)
if (b > 0)
return -Math.pow( abs(a), 1.0 / ndob);
else
return -Math.pow( abs(a), -1.0 / ndob);
else
return Double.NaN;
} else return Double.NaN;
}
}
/**
* Nth order root of a number
*
* @param n Root order
* @param x Number
* @return Returns root of a number. If calculation is not possible Double.NaN is returned.
*/
public static final double root(double n, double x) {
if (Double.isNaN(n) || Double.isNaN(n)) return Double.NaN;
if (Double.isInfinite(n) || Double.isInfinite(n)) return Double.NaN;
if (n < -BinaryRelations.DEFAULT_COMPARISON_EPSILON) return Double.NaN;
if (abs(n) <= BinaryRelations.DEFAULT_COMPARISON_EPSILON) {
if (abs(x) <= BinaryRelations.DEFAULT_COMPARISON_EPSILON) return 0;
else if (abs(x-1) <= BinaryRelations.DEFAULT_COMPARISON_EPSILON) return 1;
else return Double.NaN;
}
long nint = (long)floor(n);
if (nint == 1) return x;
if (nint == 2) return sqrt(x);
if (nint % 2 == 1) {
if ( x >= 0) return Math.pow(x, 1.0 / nint);
else return -Math.pow( abs(x), 1.0 / nint);
} else {
if ( x >= 0) return Math.pow(x, 1.0 / nint);
else return Double.NaN;
}
}
/**
* Tetration, exponential power, power series
*
* @param a base
* @param n exponent
* @return Tetration result.
*/
public static final double tetration(double a, double n) {
if (Double.isNaN(a)) return Double.NaN;
if (Double.isNaN(n)) return Double.NaN;
if (n == Double.POSITIVE_INFINITY) {
if (abs(a - MathConstants.EXP_MINUS_E) <= BinaryRelations.DEFAULT_COMPARISON_EPSILON)
return MathConstants.EXP_MINUS_1;
if (abs(a - MathConstants.EXP_1_OVER_E) <= BinaryRelations.DEFAULT_COMPARISON_EPSILON)
return MathConstants.E;
if ((a > MathConstants.EXP_MINUS_E) && (a < MathConstants.EXP_1_OVER_E))
return SpecialFunctions.lambertW( -MathFunctions.ln(a), 0) / ( -MathFunctions.ln(a) );
if (a > MathConstants.EXP_1_OVER_E) return Double.POSITIVE_INFINITY;
if (a < MathConstants.EXP_MINUS_E) return Double.NaN;
}
if (n < -BinaryRelations.DEFAULT_COMPARISON_EPSILON) return Double.NaN;
if (abs(n) <= BinaryRelations.DEFAULT_COMPARISON_EPSILON) {
if (abs(a) > BinaryRelations.DEFAULT_COMPARISON_EPSILON)
return 1;
else
return Double.NaN;
}
n = floor(n);
if (n == 0) {
if (abs(a) > BinaryRelations.DEFAULT_COMPARISON_EPSILON)
return 1;
else
return Double.NaN;
}
if (abs(a) <= BinaryRelations.DEFAULT_COMPARISON_EPSILON) return 0;
if (n == 1) return a;
double r = a;
for (double i = 2; i <= n; i++) {
r = Math.pow(a, r);
if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
}
return r;
}
/**
* Modulo operator a % b
*
* @param a the a function parameter
* @param b the b function parameter
*
* @return if a,b <> Double.NaN returns a % b.
*/
public static final double mod(double a, double b) {
if (Double.isNaN(a) || Double.isNaN(b))
return Double.NaN;
return a % b;
}
/**
* Division a/b
*
* @param a the a function parameter
* @param b the b function parameter
*
* @return if a,b <> Double.NaN and b <> 0 returns a/b,
* otherwise return Double.NaN.
*/
/*
public static final double div(double a, double b) {
if (Double.isNaN(a) || Double.isNaN(b))
return Double.NaN;
double result = Double.NaN;
if (b != 0)
result = a / b;
return result;
}
*/
/**
* Sine trigonometric function
*
* @param a the a function parameter
*
* @return if a <> Double.NaN return Math.sin(a),
* otherwise return Double.NaN.
*/
public static final double sin(double a) {
if (Double.isNaN(a))
return Double.NaN;
if (mXparser.checkIfDegreesMode())
a = a * Units.DEGREE_ARC;
SpecialValueTrigonometric sv = SpecialValueTrigonometric.getSpecialValueTrigonometric(a);
if (sv != null)
return sv.sin;
return Math.sin(a);
}
/**
* Cosine trigonometric function
*
* @param a the a function parameter
*
* @return if a <> Double.NaN returns Math.cos(a),
* otherwise returns Double.NaN.
*/
public static final double cos(double a) {
if (Double.isNaN(a))
return Double.NaN;
if (mXparser.checkIfDegreesMode())
a = a * Units.DEGREE_ARC;
SpecialValueTrigonometric sv = SpecialValueTrigonometric.getSpecialValueTrigonometric(a);
if (sv != null)
return sv.cos;
return Math.cos(a);
}
/**
* Tangent trigonometric function
*
* @param a the a function parameter
*
* @return if a <> Double.NaN returns Math.tan(a),
* otherwise returns Double.NaN.
*/
public static final double tan(double a) {
if (Double.isNaN(a))
return Double.NaN;
if (mXparser.checkIfDegreesMode())
a = a * Units.DEGREE_ARC;
SpecialValueTrigonometric sv = SpecialValueTrigonometric.getSpecialValueTrigonometric(a);
if (sv != null)
return sv.tan;
return Math.tan(a);
}
/**
* Cotangent trigonometric function
*
* @param a the a function parameter
*
* @return if a <> Double.NaN and tan(a) <> 0 returns 1 / Math.tan(a),
* otherwise returns Double.NaN.
*/
public static final double ctan(double a) {
if (Double.isNaN(a))
return Double.NaN;
if (mXparser.checkIfDegreesMode())
a = a * Units.DEGREE_ARC;
SpecialValueTrigonometric sv = SpecialValueTrigonometric.getSpecialValueTrigonometric(a);
if (sv != null)
return sv.ctan;
double result = Double.NaN;
double tg = Math.tan(a);
if (tg != 0)
result = 1.0 / tg;
return result;
}
/**
* Secant trigonometric function
*
* @param a the a function parameter
*
* @return if a <> Double.NaN and cos(a) <> 0 returns 1 / Math.cos(a),
* otherwise returns Double.NaN.
*/
public static final double sec(double a) {
if (Double.isNaN(a))
return Double.NaN;
if (mXparser.checkIfDegreesMode())
a = a * Units.DEGREE_ARC;
SpecialValueTrigonometric sv = SpecialValueTrigonometric.getSpecialValueTrigonometric(a);
if (sv != null)
return sv.sec;
double result = Double.NaN;
double cos = Math.cos(a);
if (cos != 0)
result = 1.0 / cos;
return result;
}
/**
* Cosecant trigonometric function
*
* @param a the a function parameter
*
* @return if a <> Double.NaN and sin(a) <> 0 returns 1 / Math.sin(a),
* otherwise returns Double.NaN.
*/
public static final double cosec(double a) {
if (Double.isNaN(a))
return Double.NaN;
if (mXparser.checkIfDegreesMode())
a = a * Units.DEGREE_ARC;
SpecialValueTrigonometric sv = SpecialValueTrigonometric.getSpecialValueTrigonometric(a);
if (sv != null)
return sv.csc;
double result = Double.NaN;
double sin = Math.sin(a);
if (sin != 0)
result = 1.0 / sin;
return result;
}
/**
* If double is almost integer returns the closes integer, otherwise original value
* @param val Parameter
* @return f double is almost integer returns the closest integer, otherwise original value
*/
private static final double intIfAlmostIntOtherwiseOrig(double val) {
double valint = Math.round(val);
if ( Math.abs(val-valint) <= BinaryRelations.DEFAULT_COMPARISON_EPSILON ) return valint;
return val;
}
/**
* Arcus sine - inverse trigonometric sine function
*
* @param a the a function parameter
*
* @return if a <> Double.NaN returns Math.asin(a),
* otherwise returns Double.NaN.
*/
public static final double asin(double a) {
if (Double.isNaN(a))
return Double.NaN;
SpecialValue sv = SpecialValueTrigonometric.getSpecialValueAsin(a);
double r;
if (sv != null) r = sv.fv;
else r = Math.asin(a);
if (mXparser.checkIfDegreesMode()) {
if (sv != null) return sv.fvdeg;
return intIfAlmostIntOtherwiseOrig(r / Units.DEGREE_ARC);
} else return r;
}
/**
* Arcus cosine - inverse trigonometric cosine function
*
* @param a the a function parameter
*
* @return if a <> Double.NaN returns Math.acos(a),
* otherwise returns Double.NaN.
*/
public static final double acos(double a) {
if (Double.isNaN(a))
return Double.NaN;
SpecialValue sv = SpecialValueTrigonometric.getSpecialValueAcos(a);
double r;
if (sv != null) r = sv.fv;
else r = Math.acos(a);
if (mXparser.checkIfDegreesMode()) {
if (sv != null) return sv.fvdeg;
return intIfAlmostIntOtherwiseOrig(r / Units.DEGREE_ARC);
} else return r;
}
/**
* Arcus tangent - inverse trigonometric tangent function
*
* @param a the a function parameter
*
* @return if a <> Double.NaN returns Math.atan(a),
* otherwise returns Double.NaN.
*/
public static final double atan(double a) {
if (Double.isNaN(a))
return Double.NaN;
SpecialValue sv = SpecialValueTrigonometric.getSpecialValueAtan(a);
double r;
if (sv != null) r = sv.fv;
else r = Math.atan(a);
if (mXparser.checkIfDegreesMode()) {
if (sv != null) return sv.fvdeg;
return intIfAlmostIntOtherwiseOrig(r / Units.DEGREE_ARC);
}
else return r;
}
/**
* Arcus cotangent - inverse trigonometric cotangent function
*
* @param a the a function parameter
*
* @return if a <> Double.NaN and a <> 0 returns Math.atan(1/a),
* otherwise returns Double.NaN.
*/
public static final double actan(double a) {
if (Double.isNaN(a))
return Double.NaN;
SpecialValue sv = SpecialValueTrigonometric.getSpecialValueActan(a);
double r;
if (sv != null) r = sv.fv;
else {
if (a > 0) r = Math.atan(1/a);
else if (a < 0) r = Math.atan(1/a) + MathConstants.PI;
else r = Double.NaN;
}
if (mXparser.checkIfDegreesMode()) {
if (sv != null) return sv.fvdeg;
return intIfAlmostIntOtherwiseOrig(r / Units.DEGREE_ARC);
}
else return r;
}
/**
* Arcus secant - inverse trigonometric secant function
*
* @param a the a function parameter
* @return Inverse trigonometric secant function
*/
public static final double asec(double a) {
if (Double.isNaN(a))
return Double.NaN;
SpecialValue sv = SpecialValueTrigonometric.getSpecialValueAsec(a);
double r;
if (sv != null) r = sv.fv;
else r = Math.acos(1/a);
if (mXparser.checkIfDegreesMode()) {
if (sv != null) return sv.fvdeg;
return intIfAlmostIntOtherwiseOrig(r / Units.DEGREE_ARC);
}
else return r;
}
/**
* Arcus cosecant - inverse trigonometric cosecant function
*
* @param a the a function parameter
* @return Inverse trigonometric cosecant function
*/
public static final double acosec(double a) {
if (Double.isNaN(a))
return Double.NaN;
SpecialValue sv = SpecialValueTrigonometric.getSpecialValueAcsc(a);
double r;
if (sv != null) r = sv.fv;
else r = Math.asin(1/a);
if (mXparser.checkIfDegreesMode()) {
if (sv != null) return sv.fvdeg;
return intIfAlmostIntOtherwiseOrig(r / Units.DEGREE_ARC);
}
else return r;
}
/**
* Natural logarithm
*
* @param a the a function parameter
*
* @return if a <> Double.NaN returns Math.log(1/a),
* otherwise returns Double.NaN.
*/
public static final double ln(double a) {
if (Double.isNaN(a))
return Double.NaN;
return Math.log(a);
}
/**
* Binary logarithm
*
* @param a the a function parameter
*
* @return if a <> Double.NaN returns Math.log(a)/Math.log(2.0),
* otherwise returns Double.NaN.
*/
public static final double log2(double a) {
if (Double.isNaN(a))
return Double.NaN;
return Math.log(a)/Math.log(2.0);
}
/**
* Common logarithm
*
* @param a the a function parameter
*
* @return if a <> Double.NaN returns Math.log10(a),
* otherwise returns Double.NaN.
*/
public static final double log10(double a) {
if (Double.isNaN(a))
return Double.NaN;
return Math.log10(a);
}
/**
* Degrees to radius translation.
*
* @param a the a function parameter
*
* @return if a <> Double.NaN returns Math.toRadians(a),
* otherwise returns Double.NaN.
*/
public static final double rad(double a) {
if (Double.isNaN(a))
return Double.NaN;
return Math.toRadians(a);
}
/**
* Exponential function.
*
* @param a the a function parameter
*
* @return if a <> Double.NaN returns Math.exp(a),
* otherwise returns Double.NaN.
*/
public static final double exp(double a) {
if (Double.isNaN(a))
return Double.NaN;
return Math.exp(a);
}
/**
* Square root.
*
* @param a the a function parameter
*
* @return if a <> Double.NaN returns Math.sqrt(a),
* otherwise returns Double.NaN.
*/
public static final double sqrt(double a) {
if (Double.isNaN(a))
return Double.NaN;
return Math.sqrt(a);
}
/**
* Hyperbolic sine function.
*
* @param a the a function parameter
*
* @return if a <> Double.NaN returns Math.sinh(a),
* otherwise returns Double.NaN.
*/
public static final double sinh(double a) {
if (Double.isNaN(a))
return Double.NaN;
return Math.sinh(a);
}
/**
* Hyperbolic cosine function.
*
* @param a the a function parameter
*
* @return if a <> Double.NaN returns Math.cosh(a),
* otherwise returns Double.NaN.
*/
public static final double cosh(double a) {
if (Double.isNaN(a))
return Double.NaN;
return Math.cosh(a);
}
/**
* Hyperbolic tangent function.
*
* @param a the a function parameter
*
* @return if a <> Double.NaN returns Math.tanh(a),
* otherwise returns Double.NaN.
*/
public static final double tanh(double a) {
if (Double.isNaN(a))
return Double.NaN;
return Math.tanh(a);
}
/**
* Hyperbolic cotangent function.
*
* @param a the a function parameter
*
* @return if a <> Double.NaN and tanh(a) <> 0 returns 1 / Math.tanh(a),
* otherwise returns Double.NaN.
*/
public static final double coth(double a) {
if (Double.isNaN(a))
return Double.NaN;
double result = Double.NaN;
double tanh = Math.tanh(a);
if (tanh != 0)
result = 1.0 / tanh;
return result;
}
/**
* Hyperbolic secant function.
*
* @param a the a function parameter
*
* @return if a <> Double.NaN and cosh(a) <> 0 returns 1 / Math.cosh(a),
* otherwise returns Double.NaN.
*/
public static final double sech(double a) {
if (Double.isNaN(a))
return Double.NaN;
double result = Double.NaN;
double cosh = Math.cosh(a);
if (cosh != 0)
result = 1.0 / cosh;
return result;
}
/**
* Hyperbolic cosecant function.
*
* @param a the a function parameter
*
* @return if a <> Double.NaN and sinh(a) <> 0 returns 1 / Math.sinh(a),
* otherwise returns Double.NaN.
*/
public static final double csch(double a) {
if (Double.isNaN(a))
return Double.NaN;
double result = Double.NaN;
double sinh = Math.sinh(a);
if (sinh != 0)
result = 1.0 / sinh;
return result;
}
/**
* Radius to degrees translation.
*
* @param a the a function parameter
*
* @return if a <> Double.NaN returns Math.toDegrees(a),
* otherwise returns Double.NaN.
*/
public static final double deg(double a) {
if (Double.isNaN(a))
return Double.NaN;
return Math.toDegrees(a);
}
/**
* Absolute value.
*
* @param a the a function parameter
*
* @return if a <> Double.NaN returns Math.abs(a),
* otherwise returns Double.NaN.
*/
public static final double abs(double a) {
if (Double.isNaN(a))
return Double.NaN;
return Math.abs(a);
}
/**
* Signum function.
*
* @param a the a function parameter
*
* @return if a <> Double.NaN returns Math.signum(a),
* otherwise returns Double.NaN.
*/
public static final double sgn(double a) {
if (Double.isNaN(a))
return Double.NaN;
return Math.signum(a);
}
/**
* Floor function.
*
* @param a the a function parameter
*
* @return if a <> Double.NaN returns Math.floor(a),
* otherwise returns Double.NaN.
*/
public static final double floor(double a) {
if (Double.isNaN(a))
return Double.NaN;
return Math.floor(a);
}
/**
* Ceiling function.
*
* @param a the a function parameter
*
* @return if a <> Double.NaN returns Math.ceil(a),
* otherwise returns Double.NaN.
*/
public static final double ceil(double a) {
if (Double.isNaN(a))
return Double.NaN;
return Math.ceil(a);
}
/**
* Arcus hyperbolic sine - inverse hyperbolic sine function.
*
* @param a the a function parameter
*
* @return if a <> Double.NaN returns Math.log(a + Math.sqrt(a*a+1)),
* otherwise returns Double.NaN.
*/
public static final double arsinh(double a) {
if (Double.isNaN(a))
return Double.NaN;
return Math.log(a + Math.sqrt(a*a+1));
}
/**
* Arcus hyperbolic cosine - inverse hyperbolic cosine function.
*
* @param a the a function parameter
*
* @return if a <> Double.NaN returns Math.log(a + Math.sqrt(a*a-1)),
* otherwise returns Double.NaN.
*/
public static final double arcosh(double a) {
if (Double.isNaN(a))
return Double.NaN;
return Math.log(a + Math.sqrt(a*a-1));
}
/**
* Arcus hyperbolic tangent - inverse hyperbolic tangent function.
*
* @param a the a function parameter
*
* @return if a <> Double.NaN and 1-a <> 0 returns 0.5*Math.log( (1+a)/(1-a) ),
* otherwise returns Double.NaN.
*/
public static final double artanh(double a) {
if (Double.isNaN(a))
return Double.NaN;
double result = Double.NaN;
if (1-a != 0)
result = 0.5*Math.log( (1+a)/(1-a) );
return result;
}
/**
* Arcus hyperbolic tangent - inverse hyperbolic tangent function.
*
* @param a the a function parameter
*
* @return if a <> Double.NaN and a-1 <> 0 returns 0.5*Math.log( (a+1)/(a-1) );,
* otherwise returns Double.NaN.
*/
public static final double arcoth(double a) {
if (Double.isNaN(a))
return Double.NaN;
double result = Double.NaN;
if (a-1 != 0)
result = 0.5*Math.log( (a+1)/(a-1) );
return result;
}
/**
* Arcus hyperbolic secant - inverse hyperbolic secant function.
*
* @param a the a function parameter
*
* @return if a <> Double.NaN and a <> 0 returns Math.log( (1+Math.sqrt(1-a*a))/a);,
* otherwise returns Double.NaN.
*/
public static final double arsech(double a) {
if (Double.isNaN(a))
return Double.NaN;
double result = Double.NaN;
if (a != 0)
result = Math.log( (1+Math.sqrt(1-a*a))/a);
return result;
}
/**
* Arcus hyperbolic cosecant - inverse hyperbolic cosecant function.
*
* @param a the a function parameter
*
* @return if a <> Double.NaN and a <> 0 returns Math.log( (1+Math.sqrt(1-a*a))/a);,
* otherwise returns Double.NaN.
*/
public static final double arcsch(double a) {
if (Double.isNaN(a))
return Double.NaN;
double result = Double.NaN;
if (a != 0)
result = Math.log( 1/a + Math.sqrt(1+a*a)/Math.abs(a) );
return result;
}
/**
* Normalized sinc function.
*
* @param a the a function parameter
*
* @return if a <> Double.NaN and a <> 0 returns Math.sin(PI*a) / (PI*a);,
* otherwise returns Double.NaN.
*/
public static final double sa(double a) {
if (Double.isNaN(a))
return Double.NaN;
double x = MathConstants.PI * a;
double result = Double.NaN;
if (x != 0)
result = Math.sin(x) / (x);
else
result = 1.0;
return result;
}
/**
* Sinc function.
*
* @param a the a function parameter
*
* @return if a <> Double.NaN and a <> 0 returns Math.sin(a) / (a),
* otherwise returns Double.NaN.
*/
public static final double sinc(double a) {
if (Double.isNaN(a))
return Double.NaN;
double result = Double.NaN;
if (a != 0)
if (mXparser.checkIfDegreesMode())
result = Math.sin(a * Units.DEGREE_ARC) / (a);
else
result = Math.sin(a) / (a);
else
result = 1.0;
return result;
}
/**
* General logarithm.
*
* @param a the a function parameter (base)
* @param b the b function parameter (number)
*
* @return if a,b <> Double.NaN and log(b) <> 0 returns Math.log(a) / Math.log(b),
* otherwise returns Double.NaN.
*/
public static final double log(double a, double b) {
if (Double.isNaN(a) || Double.isNaN(b))
return Double.NaN;
double result = Double.NaN;
double logb = Math.log(b);
if (logb != 0)
result = Math.log(a) / logb;
return result;
}
/**
* Double rounding
*
* @param value double value to be rounded
* @param places decimal places
* @return Rounded value
*/
public static final double round(double value, int places) {
if (Double.isNaN(value)) return Double.NaN;
if (Double.isInfinite(value)) return value;
if (places < 0) return Double.NaN;
BigDecimal bd = new BigDecimal(Double.toString(value));
bd = bd.setScale(places, RoundingMode.HALF_UP);
return bd.doubleValue();
}
/**
* Double half up rounding
*
* @param value double value to be rounded
* @param places decimal places
* @return Rounded value
*/
public static final double roundHalfUp(double value, int places) {
if (Double.isNaN(value)) return Double.NaN;
if (places < 0) return Double.NaN;
if (value == Double.NEGATIVE_INFINITY) return Double.NEGATIVE_INFINITY;
if (value == Double.POSITIVE_INFINITY) return Double.POSITIVE_INFINITY;
if (value == 0) return 0;
double sign = 1;
double origValue = value;
if (value < 0) {
sign = -1;
value = -value;
}
int ulpPosition = MathFunctions.ulpDecimalDigitsBefore(value);
if (ulpPosition <= 0) return sign * Math.floor(value);
if (places > ulpPosition) return origValue;
double multiplier = 1;
for (int place = 0; place < places; place++) {
multiplier = Math.floor(multiplier * 10);
if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
}
double valueMultiplied = value * multiplier;
double valueFloor = Math.floor(valueMultiplied);
if (Math.abs(valueMultiplied - valueFloor) >= 0.5) valueFloor = Math.floor(valueFloor + 1);
return Math.floor(sign * valueFloor) / multiplier;
}
/**
* Double down rounding
*
* @param value double value to be rounded
* @param places decimal places
* @return Rounded value
*/
public static final double roundDown(double value, int places) {
if (Double.isNaN(value)) return Double.NaN;
if (places < 0) return Double.NaN;
if (value == Double.NEGATIVE_INFINITY) return Double.NEGATIVE_INFINITY;
if (value == Double.POSITIVE_INFINITY) return Double.POSITIVE_INFINITY;
if (value == 0) return 0;
double sign = 1;
double origValue = value;
if (value < 0) {
sign = -1;
value = -value;
}
int ulpPosition = MathFunctions.ulpDecimalDigitsBefore(value);
if (ulpPosition <= 0) return sign * Math.floor(value);
if (places > ulpPosition) return origValue;
double multiplier = 1;
for (int place = 0; place < places; place++) {
multiplier = Math.floor(multiplier * 10);
if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
}
double valueMultiplied = value * multiplier;
double valueFloor = Math.floor(valueMultiplied);
return Math.floor(sign * valueFloor) / multiplier;
}
/**
* Unit in the last place rounding, see
* 0.1 + 0.1 + 0.1 vs roundUlp(0.1 + 0.1 + 0.1)
*
* @param number Double number that is to be rounded
*
* @return Double number with rounded ulp
*
* @see MathFunctions#decimalDigitsBefore(double)
* @see MathFunctions#ulp(double)
*/
public static final double roundUlp(double number) {
if ( (Double.isNaN(number) ) || (Double.isInfinite(number)) || (number == 0) )
return number;
else {
int precision = MathFunctions.ulpDecimalDigitsBefore(number);
if (precision >= 1)
return MathFunctions.round(number, precision-5);
else if (precision == 0)
return MathFunctions.round(number, 0);
else return number;
}
}
/**
* Returns integer part of a double value.
* @param x Number
* @return For non- negative x returns Math.floor(x),
* otherwise returns -Math.floor(-x)
*/
public static final double integerPart(double x) {
if (x > 0) return Math.floor(x);
else if (x < 0) return -Math.floor(-x);
else return 0;
}
/**
* For very small number returns the position of
* first significant digit, ie 0.1 = 1, 0.01 = 2
*
* @param value Double value, small one.
* @return Number of digits, number of places.
*/
public static final int decimalDigitsBefore(double value) {
if (value == 0) return -1;
if (value <= 1e-322) return 322;
else if (value <= 1e-321) return 321;
else if (value <= 1e-320) return 320;
else if (value <= 1e-319) return 319;
else if (value <= 1e-318) return 318;
else if (value <= 1e-317) return 317;
else if (value <= 1e-316) return 316;
else if (value <= 1e-315) return 315;
else if (value <= 1e-314) return 314;
else if (value <= 1e-313) return 313;
else if (value <= 1e-312) return 312;
else if (value <= 1e-311) return 311;
else if (value <= 1e-310) return 310;
else if (value <= 1e-309) return 309;
else if (value <= 1e-308) return 308;
else if (value <= 1e-307) return 307;
else if (value <= 1e-306) return 306;
else if (value <= 1e-305) return 305;
else if (value <= 1e-304) return 304;
else if (value <= 1e-303) return 303;
else if (value <= 1e-302) return 302;
else if (value <= 1e-301) return 301;
else if (value <= 1e-300) return 300;
else if (value <= 1e-299) return 299;
else if (value <= 1e-298) return 298;
else if (value <= 1e-297) return 297;
else if (value <= 1e-296) return 296;
else if (value <= 1e-295) return 295;
else if (value <= 1e-294) return 294;
else if (value <= 1e-293) return 293;
else if (value <= 1e-292) return 292;
else if (value <= 1e-291) return 291;
else if (value <= 1e-290) return 290;
else if (value <= 1e-289) return 289;
else if (value <= 1e-288) return 288;
else if (value <= 1e-287) return 287;
else if (value <= 1e-286) return 286;
else if (value <= 1e-285) return 285;
else if (value <= 1e-284) return 284;
else if (value <= 1e-283) return 283;
else if (value <= 1e-282) return 282;
else if (value <= 1e-281) return 281;
else if (value <= 1e-280) return 280;
else if (value <= 1e-279) return 279;
else if (value <= 1e-278) return 278;
else if (value <= 1e-277) return 277;
else if (value <= 1e-276) return 276;
else if (value <= 1e-275) return 275;
else if (value <= 1e-274) return 274;
else if (value <= 1e-273) return 273;
else if (value <= 1e-272) return 272;
else if (value <= 1e-271) return 271;
else if (value <= 1e-270) return 270;
else if (value <= 1e-269) return 269;
else if (value <= 1e-268) return 268;
else if (value <= 1e-267) return 267;
else if (value <= 1e-266) return 266;
else if (value <= 1e-265) return 265;
else if (value <= 1e-264) return 264;
else if (value <= 1e-263) return 263;
else if (value <= 1e-262) return 262;
else if (value <= 1e-261) return 261;
else if (value <= 1e-260) return 260;
else if (value <= 1e-259) return 259;
else if (value <= 1e-258) return 258;
else if (value <= 1e-257) return 257;
else if (value <= 1e-256) return 256;
else if (value <= 1e-255) return 255;
else if (value <= 1e-254) return 254;
else if (value <= 1e-253) return 253;
else if (value <= 1e-252) return 252;
else if (value <= 1e-251) return 251;
else if (value <= 1e-250) return 250;
else if (value <= 1e-249) return 249;
else if (value <= 1e-248) return 248;
else if (value <= 1e-247) return 247;
else if (value <= 1e-246) return 246;
else if (value <= 1e-245) return 245;
else if (value <= 1e-244) return 244;
else if (value <= 1e-243) return 243;
else if (value <= 1e-242) return 242;
else if (value <= 1e-241) return 241;
else if (value <= 1e-240) return 240;
else if (value <= 1e-239) return 239;
else if (value <= 1e-238) return 238;
else if (value <= 1e-237) return 237;
else if (value <= 1e-236) return 236;
else if (value <= 1e-235) return 235;
else if (value <= 1e-234) return 234;
else if (value <= 1e-233) return 233;
else if (value <= 1e-232) return 232;
else if (value <= 1e-231) return 231;
else if (value <= 1e-230) return 230;
else if (value <= 1e-229) return 229;
else if (value <= 1e-228) return 228;
else if (value <= 1e-227) return 227;
else if (value <= 1e-226) return 226;
else if (value <= 1e-225) return 225;
else if (value <= 1e-224) return 224;
else if (value <= 1e-223) return 223;
else if (value <= 1e-222) return 222;
else if (value <= 1e-221) return 221;
else if (value <= 1e-220) return 220;
else if (value <= 1e-219) return 219;
else if (value <= 1e-218) return 218;
else if (value <= 1e-217) return 217;
else if (value <= 1e-216) return 216;
else if (value <= 1e-215) return 215;
else if (value <= 1e-214) return 214;
else if (value <= 1e-213) return 213;
else if (value <= 1e-212) return 212;
else if (value <= 1e-211) return 211;
else if (value <= 1e-210) return 210;
else if (value <= 1e-209) return 209;
else if (value <= 1e-208) return 208;
else if (value <= 1e-207) return 207;
else if (value <= 1e-206) return 206;
else if (value <= 1e-205) return 205;
else if (value <= 1e-204) return 204;
else if (value <= 1e-203) return 203;
else if (value <= 1e-202) return 202;
else if (value <= 1e-201) return 201;
else if (value <= 1e-200) return 200;
else if (value <= 1e-199) return 199;
else if (value <= 1e-198) return 198;
else if (value <= 1e-197) return 197;
else if (value <= 1e-196) return 196;
else if (value <= 1e-195) return 195;
else if (value <= 1e-194) return 194;
else if (value <= 1e-193) return 193;
else if (value <= 1e-192) return 192;
else if (value <= 1e-191) return 191;
else if (value <= 1e-190) return 190;
else if (value <= 1e-189) return 189;
else if (value <= 1e-188) return 188;
else if (value <= 1e-187) return 187;
else if (value <= 1e-186) return 186;
else if (value <= 1e-185) return 185;
else if (value <= 1e-184) return 184;
else if (value <= 1e-183) return 183;
else if (value <= 1e-182) return 182;
else if (value <= 1e-181) return 181;
else if (value <= 1e-180) return 180;
else if (value <= 1e-179) return 179;
else if (value <= 1e-178) return 178;
else if (value <= 1e-177) return 177;
else if (value <= 1e-176) return 176;
else if (value <= 1e-175) return 175;
else if (value <= 1e-174) return 174;
else if (value <= 1e-173) return 173;
else if (value <= 1e-172) return 172;
else if (value <= 1e-171) return 171;
else if (value <= 1e-170) return 170;
else if (value <= 1e-169) return 169;
else if (value <= 1e-168) return 168;
else if (value <= 1e-167) return 167;
else if (value <= 1e-166) return 166;
else if (value <= 1e-165) return 165;
else if (value <= 1e-164) return 164;
else if (value <= 1e-163) return 163;
else if (value <= 1e-162) return 162;
else if (value <= 1e-161) return 161;
else if (value <= 1e-160) return 160;
else if (value <= 1e-159) return 159;
else if (value <= 1e-158) return 158;
else if (value <= 1e-157) return 157;
else if (value <= 1e-156) return 156;
else if (value <= 1e-155) return 155;
else if (value <= 1e-154) return 154;
else if (value <= 1e-153) return 153;
else if (value <= 1e-152) return 152;
else if (value <= 1e-151) return 151;
else if (value <= 1e-150) return 150;
else if (value <= 1e-149) return 149;
else if (value <= 1e-148) return 148;
else if (value <= 1e-147) return 147;
else if (value <= 1e-146) return 146;
else if (value <= 1e-145) return 145;
else if (value <= 1e-144) return 144;
else if (value <= 1e-143) return 143;
else if (value <= 1e-142) return 142;
else if (value <= 1e-141) return 141;
else if (value <= 1e-140) return 140;
else if (value <= 1e-139) return 139;
else if (value <= 1e-138) return 138;
else if (value <= 1e-137) return 137;
else if (value <= 1e-136) return 136;
else if (value <= 1e-135) return 135;
else if (value <= 1e-134) return 134;
else if (value <= 1e-133) return 133;
else if (value <= 1e-132) return 132;
else if (value <= 1e-131) return 131;
else if (value <= 1e-130) return 130;
else if (value <= 1e-129) return 129;
else if (value <= 1e-128) return 128;
else if (value <= 1e-127) return 127;
else if (value <= 1e-126) return 126;
else if (value <= 1e-125) return 125;
else if (value <= 1e-124) return 124;
else if (value <= 1e-123) return 123;
else if (value <= 1e-122) return 122;
else if (value <= 1e-121) return 121;
else if (value <= 1e-120) return 120;
else if (value <= 1e-119) return 119;
else if (value <= 1e-118) return 118;
else if (value <= 1e-117) return 117;
else if (value <= 1e-116) return 116;
else if (value <= 1e-115) return 115;
else if (value <= 1e-114) return 114;
else if (value <= 1e-113) return 113;
else if (value <= 1e-112) return 112;
else if (value <= 1e-111) return 111;
else if (value <= 1e-110) return 110;
else if (value <= 1e-109) return 109;
else if (value <= 1e-108) return 108;
else if (value <= 1e-107) return 107;
else if (value <= 1e-106) return 106;
else if (value <= 1e-105) return 105;
else if (value <= 1e-104) return 104;
else if (value <= 1e-103) return 103;
else if (value <= 1e-102) return 102;
else if (value <= 1e-101) return 101;
else if (value <= 1e-100) return 100;
else if (value <= 1e-99) return 99;
else if (value <= 1e-98) return 98;
else if (value <= 1e-97) return 97;
else if (value <= 1e-96) return 96;
else if (value <= 1e-95) return 95;
else if (value <= 1e-94) return 94;
else if (value <= 1e-93) return 93;
else if (value <= 1e-92) return 92;
else if (value <= 1e-91) return 91;
else if (value <= 1e-90) return 90;
else if (value <= 1e-89) return 89;
else if (value <= 1e-88) return 88;
else if (value <= 1e-87) return 87;
else if (value <= 1e-86) return 86;
else if (value <= 1e-85) return 85;
else if (value <= 1e-84) return 84;
else if (value <= 1e-83) return 83;
else if (value <= 1e-82) return 82;
else if (value <= 1e-81) return 81;
else if (value <= 1e-80) return 80;
else if (value <= 1e-79) return 79;
else if (value <= 1e-78) return 78;
else if (value <= 1e-77) return 77;
else if (value <= 1e-76) return 76;
else if (value <= 1e-75) return 75;
else if (value <= 1e-74) return 74;
else if (value <= 1e-73) return 73;
else if (value <= 1e-72) return 72;
else if (value <= 1e-71) return 71;
else if (value <= 1e-70) return 70;
else if (value <= 1e-69) return 69;
else if (value <= 1e-68) return 68;
else if (value <= 1e-67) return 67;
else if (value <= 1e-66) return 66;
else if (value <= 1e-65) return 65;
else if (value <= 1e-64) return 64;
else if (value <= 1e-63) return 63;
else if (value <= 1e-62) return 62;
else if (value <= 1e-61) return 61;
else if (value <= 1e-60) return 60;
else if (value <= 1e-59) return 59;
else if (value <= 1e-58) return 58;
else if (value <= 1e-57) return 57;
else if (value <= 1e-56) return 56;
else if (value <= 1e-55) return 55;
else if (value <= 1e-54) return 54;
else if (value <= 1e-53) return 53;
else if (value <= 1e-52) return 52;
else if (value <= 1e-51) return 51;
else if (value <= 1e-50) return 50;
else if (value <= 1e-49) return 49;
else if (value <= 1e-48) return 48;
else if (value <= 1e-47) return 47;
else if (value <= 1e-46) return 46;
else if (value <= 1e-45) return 45;
else if (value <= 1e-44) return 44;
else if (value <= 1e-43) return 43;
else if (value <= 1e-42) return 42;
else if (value <= 1e-41) return 41;
else if (value <= 1e-40) return 40;
else if (value <= 1e-39) return 39;
else if (value <= 1e-38) return 38;
else if (value <= 1e-37) return 37;
else if (value <= 1e-36) return 36;
else if (value <= 1e-35) return 35;
else if (value <= 1e-34) return 34;
else if (value <= 1e-33) return 33;
else if (value <= 1e-32) return 32;
else if (value <= 1e-31) return 31;
else if (value <= 1e-30) return 30;
else if (value <= 1e-29) return 29;
else if (value <= 1e-28) return 28;
else if (value <= 1e-27) return 27;
else if (value <= 1e-26) return 26;
else if (value <= 1e-25) return 25;
else if (value <= 1e-24) return 24;
else if (value <= 1e-23) return 23;
else if (value <= 1e-22) return 22;
else if (value <= 1e-21) return 21;
else if (value <= 1e-20) return 20;
else if (value <= 1e-19) return 19;
else if (value <= 1e-18) return 18;
else if (value <= 1e-17) return 17;
else if (value <= 1e-16) return 16;
else if (value <= 1e-15) return 15;
else if (value <= 1e-14) return 14;
else if (value <= 1e-13) return 13;
else if (value <= 1e-12) return 12;
else if (value <= 1e-11) return 11;
else if (value <= 1e-10) return 10;
else if (value <= 1e-9) return 9;
else if (value <= 1e-8) return 8;
else if (value <= 1e-7) return 7;
else if (value <= 1e-6) return 6;
else if (value <= 1e-5) return 5;
else if (value <= 1e-4) return 4;
else if (value <= 1e-3) return 3;
else if (value <= 1e-2) return 2;
else if (value <= 1e-1) return 1;
else if (value <= 1e-0) return 0;
else return -1;
}
/**
* Unit in the last place(ULP) for double
* @param value Double number
* @return ULP for a given double.
*/
public static final double ulp(double value) {
return Math.ulp(value);
}
/**
* Unit in The Last Place - number of decimal digits before
* @param value Double number
* @return Positive number of digits N for ulp = 1e-{N+1},
* if ulp is > 1 then -1 is returned.
* Returned proper value is always between -1 and +322.
* If value is NaN then -2 is returned.
*/
public static final int ulpDecimalDigitsBefore(double value) {
if (Double.isNaN(value)) return -2;
double u = ulp(value);
return decimalDigitsBefore(u);
}
/**
* Returns the first non-NaN value
*
* @param values List of values
* @return Returns the first non-NaN value, if list is null
* then returns Double.NaN, if list contains no elements
* then returns Double.NaN.
*/
public static final double coalesce(double[] values) {
if (values == null) return Double.NaN;
if (values.length == 0) return Double.NaN;
for (double v : values) {
if (!Double.isNaN(v)) return v;
if (mXparser.isCurrentCalculationCancelled()) return Double.NaN;
}
return Double.NaN;
}
/**
* Check whether double value is almost integer.
* @param x Number
* @return True if double value is almost integer, otherwise false.
* {@link BinaryRelations#DEFAULT_COMPARISON_EPSILON}
*
* @see BinaryRelations#DEFAULT_COMPARISON_EPSILON
*/
public static final boolean isInteger(double x) {
if (Double.isNaN(x)) return false;
if (x == Double.POSITIVE_INFINITY) return false;
if (x == Double.NEGATIVE_INFINITY) return false;
if (x < 0) x = -x;
double round = Math.round(x);
if (Math.abs(x - round) < BinaryRelations.DEFAULT_COMPARISON_EPSILON) return true;
else return false;
}
/**
* Check whether two double values are almost equal.
* @param a First number
* @param b Second number
* @return True if double values are almost equal, otherwise false.
* {@link BinaryRelations#DEFAULT_COMPARISON_EPSILON}
*
* @see BinaryRelations#DEFAULT_COMPARISON_EPSILON
*/
public static final boolean almostEqual(double a, double b) {
if (Double.isNaN(a)) return false;
if (Double.isNaN(b)) return false;
if (a == b) return true;
if (Math.abs(a - b) <= BinaryRelations.DEFAULT_COMPARISON_EPSILON) return true;
return false;
}
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