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pub    858FC4C4F43856A3
uid    J. Daniel Kulp <dan@kulp.com>

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Version: BCPG v1.68

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//	    | L1*s +...+L7*s    -  R(z) | <= 2
//	    |                             |
//	Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
//	In order to guarantee error in log below 1ulp, we compute log by
//		log(1+f) = f - s*(f - R)		(if f is not too large)
//		log(1+f) = f - (hfsq - s*(hfsq+R)).	(better accuracy)
//
//	3. Finally,  log(x) = k*Ln2 + log(1+f).

//          | Lp1*s +...+Lp7*s    -  R(z) | <= 2
//          |                             |
//      Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
//      In order to guarantee error in log below 1ulp, we compute log
//      by
//              log1p(f) = f - (hfsq - s*(hfsq+R)).
//
//   3. Finally, log1p(x) = k*ln2 + log1p(f).
//                        = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))

}

func roundShortest(d *decimal, x *Float) {
	// if the mantissa is zero, the number is zero - stop now
	if len(d.mant) == 0 {
		return
	}

	// Approach: All numbers in the interval [x - 1/2ulp, x + 1/2ulp]
	// (possibly exclusive) round to x for the given precision of x.
	// Compute the lower and upper bound in decimal form and find the
	// shortest decimal number d such that lower <= d <= upper.

    @Override
    Map<String, Versions> getPluginsToValidate() {
        [
            // Grunt and Gulp plugins are not properly published on the plugin portal
            //'com.moowork.grunt': TestedVersions.node,
            //'com.moowork.gulp': TestedVersions.node,
            'com.moowork.node': TestedVersions.node,
            'com.github.node-gradle.node': TestedVersions.newNode
        ]

//   3. Final rounding
//      After generating the 53 bits result, we compute one more bit.
//      Together with the remainder, we can decide whether the
//      result is exact, bigger than 1/2ulp, or less than 1/2ulp
//      (it will never equal to 1/2ulp).
//      The rounding mode can be detected by checking whether
//      huge + tiny is equal to huge, and whether huge - tiny is
//      equal to huge for some floating point number "huge" and "tiny".

    }
  }

  @GwtIncompatible // #trueLog2, Math.ulp
  public void testLog2Accuracy() {
    for (double d : POSITIVE_FINITE_DOUBLE_CANDIDATES) {
      double dmLog2 = DoubleMath.log2(d);
      double trueLog2 = trueLog2(d);
      assertTrue(Math.abs(dmLog2 - trueLog2) <= Math.ulp(trueLog2));
    }
  }

  public void testLog2SemiMonotonic() {

	// Table 14: Stress Inputs for Conversion to 24-bit Binary, <1/2 ULP
	"5e-20",
	"67e+14",
	"985e+15",
	"7693e-42",
	"55895e-16",
	"996622e-44",
	"7038531e-32",
	"60419369e-46",
	"702990899e-20",
	"6930161142e-48",
	"25933168707e+13",
	"596428896559e+20",

	// Table 15: Stress Inputs for Conversion to 24-bit Binary, >1/2 ULP
	"3e-23",
	"57e+18",
	"789e-35",
	"2539e-18",

// and include err.Num = s.
//
// If s is not syntactically well-formed, ParseComplex returns err.Err = ErrSyntax.
//
// If s is syntactically well-formed but either component is more than 1/2 ULP
// away from the largest floating point number of the given component's size,
// ParseComplex returns err.Err = ErrRange and c = ±Inf for the respective component.
func ParseComplex(s string, bitSize int) (complex128, error) {

   * </ul>
   *
   * <p>The computed result is within 1 ulp of the exact result.
   *
   * <p>If the result of this method will be immediately rounded to an {@code int}, {@link
   * #log2(double, RoundingMode)} is faster.
   */
  public static double log2(double x) {
    return log(x) / LN_2; // surprisingly within 1 ulp according to tests
  }

  /**