Examples with BigFraction org.hipparchus.fraction.BigFraction used on opensource projects

Example 1 with BigFraction

use of org.hipparchus.fraction.BigFraction in project symja_android_library by axkr.

the class AbstractFractionSym method valueOfExact.

/**
 * Rationalizes the given double value exactly.
 * <p>
 * This methods returns an {@link IExpr} that, when being evaluated to a double value (using
 * {@link IExpr#evalDouble()}), results to the exact same value (per bit) as the given one.
 * <p>
 * Although it is not possible to express all real numbers as a fraction of two integers, it is
 * possible for all finite floating-point numbers to be expressed as fraction with exact same
 * value, because floating-point numbers are finite in their representation and therefore cannot
 * express all real numbers exactly. But this allows the exact representation as a fraction.<br>
 * Nevertheless this may lead to unexpected results. For example the value {@code 0.7} is
 * rationalized to {@code 3152519739159347/4503599627370496} and not the expected {@code 7/10}.
 * </p>
 * </p>
 * There is no guarantee made about the specific type of the returned expression. Not all possible
 * values of a double, especially small ones, can be expressed as {@link IFraction} in such way
 * that it evaluates to the same double value. In such cases the value is expressed by
 * {@code  mantissa * 2 ^ power}.
 *
 * @param value the double value to convert
 * @return an IExpr that evaluates to the exact same double value
 */
public static IExpr valueOfExact(double value) {
    IExpr ii = getInfiniteOrInteger(value);
    if (ii != null) {
        return ii;
    }
    // computes exact fraction representation
    BigFraction exactFraction = new BigFraction(value);
    int denominatorExponent2 = exactFraction.getDenominator().bitLength() - 1;
    if (denominatorExponent2 <= Double.MAX_EXPONENT) {
        return valueOf(exactFraction);
    }
    // The fractions denominator cannot be expressed as double value and would lead to an infinite
    // denominator double-value this has the consequence that the fraction will become return zero
    // when evaluated to double. Instead express the value as mantissa2 * 2 ^ exp2
    int exp2 = Math.getExponent(value);
    double mantissa2 = value * Math.pow(2, -exp2);
    // try shortcut
    IExpr mantissaFraction = getInfiniteOrInteger(mantissa2);
    if (mantissaFraction == null) {
        mantissaFraction = valueOf(new BigFraction(mantissa2));
    }
    return F.Times(mantissaFraction, F.Power(F.C2, F.ZZ(exp2)));
}

Example 2 with BigFraction

use of org.hipparchus.fraction.BigFraction in project symja_android_library by axkr.

the class BigFractionSym method add.

/**
 * Return a new rational representing <code>this + other</code>.
 *
 * @param other Rational to add.
 * @return Sum of <code>this</code> and <code>other</code>.
 */
@Override
public IFraction add(IFraction other) {
    if (other.isZero()) {
        return this;
    }
    if (other instanceof BigFractionSym) {
        BigFraction res = fFraction.add(((BigFractionSym) other).toBigFraction());
        return valueOf(res);
    }
    BigInteger tdenom = toBigDenominator();
    BigInteger odenom = other.toBigDenominator();
    if (tdenom.equals(odenom)) {
        return valueOf(toBigNumerator().add(other.toBigNumerator()), tdenom);
    }
    BigInteger gcd = tdenom.gcd(odenom);
    BigInteger tdenomgcd = tdenom.divide(gcd);
    BigInteger odenomgcd = odenom.divide(gcd);
    BigInteger newnum = toBigNumerator().multiply(odenomgcd).add(other.toBigNumerator().multiply(tdenomgcd));
    BigInteger newdenom = tdenom.multiply(odenomgcd);
    return valueOf(newnum, newdenom);
}

Example 3 with BigFraction

use of org.hipparchus.fraction.BigFraction in project symja_android_library by axkr.

the class BigFractionSym method compareTo.

@Override
public int compareTo(IExpr expr) {
    if (expr instanceof IRational) {
        if (expr instanceof IFraction) {
            BigInteger valthis = toBigNumerator().multiply(((IFraction) expr).toBigDenominator());
            BigInteger valo = ((IFraction) expr).toBigNumerator().multiply(toBigDenominator());
            return valthis.compareTo(valo);
        }
        if (expr instanceof IInteger) {
            return fFraction.compareTo(new BigFraction(((IInteger) expr).toBigNumerator(), BigInteger.ONE));
        }
    }
    if (expr.isReal()) {
        return Double.compare(fFraction.doubleValue(), ((ISignedNumber) expr).doubleValue());
    }
    return -1;
// return super.compareTo(expr);
}

Example 4 with BigFraction

use of org.hipparchus.fraction.BigFraction in project symja_android_library by axkr.

the class PolynomialsUtils method computeUpToDegree.

/**
 * Compute polynomial coefficients up to a given degree.
 *
 * @param degree maximal degree
 * @param maxDegree current maximal degree
 * @param generator recurrence coefficients generator
 * @param coefficients list where the computed coefficients should be appended
 */
private static void computeUpToDegree(final int degree, final int maxDegree, final RecurrenceCoefficientsGenerator generator, final List<BigFraction> coefficients) {
    int startK = (maxDegree - 1) * maxDegree / 2;
    for (int k = maxDegree; k < degree; ++k) {
        // start indices of two previous polynomials Pk(X) and Pk-1(X)
        int startKm1 = startK;
        startK += k;
        // Pk+1(X) = (a[0] + a[1] X) Pk(X) - a[2] Pk-1(X)
        BigFraction[] ai = generator.generate(k);
        BigFraction ck = coefficients.get(startK);
        BigFraction ckm1 = coefficients.get(startKm1);
        // degree 0 coefficient
        coefficients.add(ck.multiply(ai[0]).subtract(ckm1.multiply(ai[2])));
        // degree 1 to degree k-1 coefficients
        for (int i = 1; i < k; ++i) {
            final BigFraction ckPrev = ck;
            ck = coefficients.get(startK + i);
            ckm1 = coefficients.get(startKm1 + i);
            coefficients.add(ck.multiply(ai[0]).add(ckPrev.multiply(ai[1])).subtract(ckm1.multiply(ai[2])));
            if (coefficients.size() > Config.MAX_AST_SIZE) {
                ASTElementLimitExceeded.throwIt(coefficients.size());
            }
        }
        // degree k coefficient
        final BigFraction ckPrev = ck;
        ck = coefficients.get(startK + k);
        coefficients.add(ck.multiply(ai[0]).add(ckPrev.multiply(ai[1])));
        // degree k+1 coefficient
        coefficients.add(ck.multiply(ai[1]));
        if (coefficients.size() > Config.MAX_AST_SIZE) {
            ASTElementLimitExceeded.throwIt(coefficients.size());
        }
    }
}

Example 5 with BigFraction

use of org.hipparchus.fraction.BigFraction in project symja_android_library by axkr.

the class TeXFormFactory method convert.

public void convert(final StringBuffer buf, final Object o, final int precedence) {
    if (o instanceof IExpr) {
        IExpr expr = (IExpr) o;
        String str = CONSTANT_EXPRS.get(expr);
        if (str != null) {
            buf.append(str);
            return;
        }
    }
    if (o instanceof IAST) {
        final IAST f = ((IAST) o);
        IExpr h = f.head();
        if (h.isSymbol()) {
            IConverter converter = reflection(((ISymbol) h).getSymbolName());
            if ((converter != null) && (converter.convert(buf, f, precedence))) {
                return;
            }
        }
        convertAST(buf, f);
        return;
    }
    if (o instanceof IInteger) {
        convertInteger(buf, (IInteger) o, precedence);
        return;
    }
    if (o instanceof IFraction) {
        convertFraction(buf, (IFraction) o, precedence);
        return;
    }
    if (o instanceof INum) {
        convertDouble(buf, (INum) o, precedence);
        return;
    }
    if (o instanceof IComplexNum) {
        convertDoubleComplex(buf, (IComplexNum) o, precedence);
        return;
    }
    if (o instanceof IComplex) {
        convertComplex(buf, (IComplex) o, precedence);
        return;
    }
    if (o instanceof ISymbol) {
        convertSymbol(buf, (ISymbol) o);
        return;
    }
    if (o instanceof BigFraction) {
        convertFraction(buf, (BigFraction) o, precedence);
        return;
    }
    convertString(buf, o.toString());
}