Examples of org.apache.commons.math3.dfp.Dfp

org.apache.commons.math3.dfp.Dfp
Decimal floating point library for Java
Another floating point class. This one is built using radix 10000 which is 10⁴, so its almost decimal.

The design goals here are:
1. Decimal math, or close to it
2. Settable precision (but no mix between numbers using different settings)
3. Portability. Code should be kept as portable as possible.
4. Performance
5. Accuracy - Results should always be +/- 1 ULP for basic algebraic operation
6. Comply with IEEE 854-1987 as much as possible. (See IEEE 854-1987 notes below)
Trade offs:
1. Memory foot print. I'm using more memory than necessary to represent numbers to get better performance.
2. Digits are bigger, so rounding is a greater loss. So, if you really need 12 decimal digits, better use 4 base 10000 digits there can be one partially filled.
Numbers are represented in the following form:
```
 n  =  sign × mant × (radix)^exp;
 
```
where sign is ±1, mantissa represents a fractional number between zero and one. mant[0] is the least significant digit. exp is in the range of -32767 to 32768

IEEE 854-1987 Notes and differences

IEEE 854 requires the radix to be either 2 or 10. The radix here is 10000, so that requirement is not met, but it is possible that a subclassed can be made to make it behave as a radix 10 number. It is my opinion that if it looks and behaves as a radix 10 number then it is one and that requirement would be met.

The radix of 10000 was chosen because it should be faster to operate on 4 decimal digits at once instead of one at a time. Radix 10 behavior can be realized by adding an additional rounding step to ensure that the number of decimal digits represented is constant.

The IEEE standard specifically leaves out internal data encoding, so it is reasonable to conclude that such a subclass of this radix 10000 system is merely an encoding of a radix 10 system.

IEEE 854 also specifies the existence of "sub-normal" numbers. This class does not contain any such entities. The most significant radix 10000 digit is always non-zero. Instead, we support "gradual underflow" by raising the underflow flag for numbers less with exponent less than expMin, but don't flush to zero until the exponent reaches MIN_EXP-digits. Thus the smallest number we can represent would be: 1E(-(MIN_EXP-digits-1)*4), eg, for digits=5, MIN_EXP=-32767, that would be 1e-131092.

IEEE 854 defines that the implied radix point lies just to the right of the most significant digit and to the left of the remaining digits. This implementation puts the implied radix point to the left of all digits including the most significant one. The most significant digit here is the one just to the right of the radix point. This is a fine detail and is really only a matter of definition. Any side effects of this can be rendered invisible by a subclass.
@see DfpField @version $Id: Dfp.java 1244107 2012-02-14 16:17:55Z erans $ @since 2.2

                return false;
            }
            final int    n = FastMath.max(1, (int) FastMath.ceil(FastMath.abs(dt) / maxCheckInterval));
            final double h = dt / n;


            final UnivariateFunction f = new UnivariateFunction() {
                public double value(final double t) throws LocalMaxCountExceededException {
                    try {
                        interpolator.setInterpolatedTime(t);
                        return handler.g(t, getCompleteState(interpolator));
                    } catch (MaxCountExceededException mcee) {
                        throw new LocalMaxCountExceededException(mcee);
                    }
                }
            };


            double ta = t0;
            double ga = g0;
            for (int i = 0; i < n; ++i) {


                // evaluate handler value at the end of the substep
                final double tb = t0 + (i + 1) * h;
                interpolator.setInterpolatedTime(tb);
                final double gb = handler.g(tb, getCompleteState(interpolator));


                // check events occurrence
                if (g0Positive ^ (gb >= 0)) {
                    // there is a sign change: an event is expected during this step


                    // variation direction, with respect to the integration direction
                    increasing = gb >= ga;


                    // find the event time making sure we select a solution just at or past the exact root
                    final double root;
                    if (solver instanceof BracketedUnivariateSolver<?>) {
                        @SuppressWarnings("unchecked")
                        BracketedUnivariateSolver<UnivariateFunction> bracketing =
                                (BracketedUnivariateSolver<UnivariateFunction>) solver;
                        root = forward ?
                               bracketing.solve(maxIterationCount, f, ta, tb, AllowedSolution.RIGHT_SIDE) :
                               bracketing.solve(maxIterationCount, f, tb, ta, AllowedSolution.LEFT_SIDE);
                    } else {
                        final double baseRoot = forward ?
                                                solver.solve(maxIterationCount, f, ta, tb) :
                                                solver.solve(maxIterationCount, f, tb, ta);
                        final int remainingEval = maxIterationCount - solver.getEvaluations();
                        BracketedUnivariateSolver<UnivariateFunction> bracketing =
                                new PegasusSolver(solver.getRelativeAccuracy(), solver.getAbsoluteAccuracy());
                        root = forward ?
                               UnivariateSolverUtils.forceSide(remainingEval, f, bracketing,
                                                                   baseRoot, ta, tb, AllowedSolution.RIGHT_SIDE) :
                               UnivariateSolverUtils.forceSide(remainingEval, f, bracketing,
                                                                   baseRoot, tb, ta, AllowedSolution.LEFT_SIDE);
                    }


                    if ((!Double.isNaN(previousEventTime)) &&
                        (FastMath.abs(root - ta) <= convergence) &&
                        (FastMath.abs(root - previousEventTime) <= convergence)) {
                        // we have either found nothing or found (again ?) a past event,
                        // retry the substep excluding this value, and taking care to have the
                        // required sign in case the g function is noisy around its zero and
                        // crosses the axis several times
                        do {
                            ta = forward ? ta + convergence : ta - convergence;
                            ga = f.value(ta);
                        } while ((g0Positive ^ (ga >= 0)) && (forward ^ (ta >= tb)));
                        --i;
                    } else if (Double.isNaN(previousEventTime) ||
                               (FastMath.abs(previousEventTime - root) > convergence)) {
                        pendingEventTime = root;

View Full Code Here

                        final double baseRoot = forward ?
                                                solver.solve(maxIterationCount, f, ta, tb) :
                                                solver.solve(maxIterationCount, f, tb, ta);
                        final int remainingEval = maxIterationCount - solver.getEvaluations();
                        BracketedUnivariateSolver<UnivariateFunction> bracketing =
                                new PegasusSolver(solver.getRelativeAccuracy(), solver.getAbsoluteAccuracy());
                        root = forward ?
                               UnivariateSolverUtils.forceSide(remainingEval, f, bracketing,
                                                                   baseRoot, ta, tb, AllowedSolution.RIGHT_SIDE) :
                               UnivariateSolverUtils.forceSide(remainingEval, f, bracketing,
                                                                   baseRoot, tb, ta, AllowedSolution.LEFT_SIDE);

View Full Code Here

            double y = generator.nextDouble() - 0.5;
            // double x = (generator.nextDouble() * 20.0) - 10.0;
            // double x = ((generator.nextDouble() * 2.0) - 1.0) * generator.nextDouble();
            /* double x = 3.0 / 512.0 * i - 3.0; */
            double tst = FastMath.atan2(y, x);
            Dfp refdfp = DfpMath.atan(field.newDfp(y)
                .divide(field.newDfp(x)));
            /* Make adjustments for sign */
            if (x < 0.0) {
                if (y > 0.0)
                    refdfp = field.getPi().add(refdfp);
                else
                    refdfp = refdfp.subtract(field.getPi());
            }


            double ref = refdfp.toDouble();
            double err = (tst - ref) / ref;


            if (err != 0) {
                double ulp = Math.abs(ref -
                                      Double.longBitsToDouble((Double

View Full Code Here

      if (x.lessThan(field.getZero())) {
          negative = true;
          x = x.negate();
      }


      Dfp y = DfpMath.pow(x, field.getOne().divide(3));


      if (negative) {
          y = y.negate();
      }


      return y;
    }

View Full Code Here

    @Test
    public void testIntPow() {
        final int maxExp = 300;
        DfpField field = new DfpField(40);
        final double base = 1.23456789;
        Dfp baseDfp = field.newDfp(base);
        Dfp dfpPower = field.getOne();
        for (int i = 0; i < maxExp; i++) {
            Assert.assertEquals("exp=" + i, dfpPower.toDouble(), FastMath.pow(base, i),
                                0.6 * FastMath.ulp(dfpPower.toDouble()));
            dfpPower = dfpPower.multiply(baseDfp);
        }
    }

View Full Code Here

            double y = generator.nextDouble() - 0.5;
            // double x = (generator.nextDouble() * 20.0) - 10.0;
            // double x = ((generator.nextDouble() * 2.0) - 1.0) * generator.nextDouble();
            /* double x = 3.0 / 512.0 * i - 3.0; */
            double tst = FastMath.atan2(y, x);
            Dfp refdfp = DfpMath.atan(field.newDfp(y)
                .divide(field.newDfp(x)));
            /* Make adjustments for sign */
            if (x < 0.0) {
                if (y > 0.0)
                    refdfp = field.getPi().add(refdfp);
                else
                    refdfp = refdfp.subtract(field.getPi());
            }


            double ref = refdfp.toDouble();
            double err = (tst - ref) / ref;


            if (err != 0) {
                double ulp = Math.abs(ref -
                                      Double.longBitsToDouble((Double

View Full Code Here

      if (x.lessThan(field.getZero())) {
          negative = true;
          x = x.negate();
      }


      Dfp y = DfpMath.pow(x, field.getOne().divide(3));


      if (negative) {
          y = y.negate();
      }


      return y;
    }

View Full Code Here

    @Test
    public void testIntPow() {
        final int maxExp = 300;
        DfpField field = new DfpField(40);
        final double base = 1.23456789;
        Dfp baseDfp = field.newDfp(base);
        Dfp dfpPower = field.getOne();
        for (int i = 0; i < maxExp; i++) {
            Assert.assertEquals("exp=" + i, dfpPower.toDouble(), FastMath.pow(base, i),
                                0.6 * FastMath.ulp(dfpPower.toDouble()));
            dfpPower = dfpPower.multiply(baseDfp);
        }
    }

View Full Code Here

            double y = generator.nextDouble() - 0.5;
            // double x = (generator.nextDouble() * 20.0) - 10.0;
            // double x = ((generator.nextDouble() * 2.0) - 1.0) * generator.nextDouble();
            /* double x = 3.0 / 512.0 * i - 3.0; */
            double tst = FastMath.atan2(y, x);
            Dfp refdfp = DfpMath.atan(field.newDfp(y)
                .divide(field.newDfp(x)));
            /* Make adjustments for sign */
            if (x < 0.0) {
                if (y > 0.0)
                    refdfp = field.getPi().add(refdfp);
                else
                    refdfp = refdfp.subtract(field.getPi());
            }


            double ref = refdfp.toDouble();
            double err = (tst - ref) / ref;


            if (err != 0) {
                double ulp = Math.abs(ref -
                                      Double.longBitsToDouble((Double

View Full Code Here

      if (x.lessThan(field.getZero())) {
          negative = true;
          x = x.negate();
      }


      Dfp y = DfpMath.pow(x, field.getOne().divide(3));


      if (negative) {
          y = y.negate();
      }


      return y;
    }

View Full Code Here

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org.apache.commons.math3.analysis.differentiation.DerivativeStructure

org.apache.commons.math3.analysis.differentiation.MultivariateDifferentiableVectorFunction

org.apache.commons.math3.analysis.function.HarmonicOscillator

org.apache.commons.math3.analysis.function.Sin

org.apache.commons.math3.analysis.function.Sinc

org.apache.commons.math3.analysis.function.SincTest

org.apache.commons.math3.analysis.interpolation.FieldHermiteInterpolatorTest

org.apache.commons.math3.analysis.MultivariateFunction

org.apache.commons.math3.analysis.QuinticFunction

org.apache.commons.math3.analysis.solvers.BrentSolver

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