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@ -93,7 +93,7 @@ public class BigDecimalMath {
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* Euler-Stieltjes as shown in Dilcher, Aequat Math 48 (1) (1994)
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* 55-85
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*/
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MathContext mcloc = new MathContext(2 + mc.getPrecision());
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MathContext mcloc = SafeMathContext.newMathContext(2 + mc.getPrecision());
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BigDecimal resul = BigDecimal.ONE;
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resul = resul.add(log(2, mcloc));
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resul = resul.subtract(log(3, mcloc));
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@ -105,7 +105,7 @@ public class BigDecimalMath {
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* Log(2) is 0.7
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*/
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final int kmax = (int) ((Math.log(eps / 0.7) - 2.) / 4.);
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mcloc = new MathContext(1 + err2prec(1.2, eps / kmax));
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mcloc = SafeMathContext.newMathContext(1 + err2prec(1.2, eps / kmax));
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for (int n = 1;; n++) {
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/*
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* zeta is close to 1. Division of zeta-1 through
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@ -146,7 +146,7 @@ public class BigDecimalMath {
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final BigDecimal half = new BigDecimal("2");
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/* increase the local accuracy by 2 digits */
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final MathContext locmc = new MathContext(mc.getPrecision() + 2, mc.getRoundingMode());
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final MathContext locmc = SafeMathContext.newMathContext(mc.getPrecision() + 2, mc.getRoundingMode());
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/*
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* relative accuracy requested is 10^(-precision)
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@ -242,7 +242,7 @@ public class BigDecimalMath {
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* slightly larger than what is demanded by 'eps' below.
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*/
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final BigDecimal xhighpr = scalePrec(x, 2);
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final MathContext mc = new MathContext(2 + x.precision());
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final MathContext mc = SafeMathContext.newMathContext(2 + x.precision());
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/*
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* Relative accuracy of the result is eps.
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@ -257,14 +257,14 @@ public class BigDecimalMath {
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*/
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BigDecimal c = xhighpr.divide(s.pow(n - 1), mc);
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c = s.subtract(c);
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final MathContext locmc = new MathContext(c.precision());
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final MathContext locmc = SafeMathContext.newMathContext(c.precision());
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c = c.divide(nth, locmc);
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s = s.subtract(c);
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if (Math.abs(c.doubleValue() / s.doubleValue()) < eps) {
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break;
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}
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}
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return s.round(new MathContext(err2prec(eps)));
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return s.round(SafeMathContext.newMathContext(err2prec(eps)));
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} /* BigDecimalMath.root */
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/**
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@ -291,7 +291,7 @@ public class BigDecimalMath {
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* digits.
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*/
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final BigDecimal zerr = x.abs().multiply(x.ulp()).add(y.abs().multiply(y.ulp()));
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MathContext mc = new MathContext(2 + err2prec(z, zerr));
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MathContext mc = SafeMathContext.newMathContext(2 + err2prec(z, zerr));
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/* Pull square root */
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z = sqrt(z.round(mc));
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@ -300,7 +300,7 @@ public class BigDecimalMath {
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* Final rounding. Absolute error in the square root is
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* (y*yerr+x*xerr)/z, where zerr holds 2*(x*xerr+y*yerr).
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*/
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mc = new MathContext(err2prec(z.doubleValue(), 0.5 * zerr.doubleValue() / z.doubleValue()));
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mc = SafeMathContext.newMathContext(err2prec(z.doubleValue(), 0.5 * zerr.doubleValue() / z.doubleValue()));
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return z.round(mc);
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} /* BigDecimalMath.hypot */
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@ -330,7 +330,7 @@ public class BigDecimalMath {
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* so this feature does not harm.
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*/
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final double zerr = x.doubleValue() * x.ulp().doubleValue();
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MathContext mc = new MathContext(2 + err2prec(z.doubleValue(), zerr));
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MathContext mc = SafeMathContext.newMathContext(2 + err2prec(z.doubleValue(), zerr));
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/* Pull square root */
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z = sqrt(z.round(mc));
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@ -339,7 +339,7 @@ public class BigDecimalMath {
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* Final rounding. Absolute error in the square root is x*xerr/z, where
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* zerr holds 2*x*xerr.
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*/
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mc = new MathContext(err2prec(z.doubleValue(), 0.5 * zerr / z.doubleValue()));
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mc = SafeMathContext.newMathContext(err2prec(z.doubleValue(), 0.5 * zerr / z.doubleValue()));
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return z.round(mc);
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} /* BigDecimalMath.hypot */
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@ -375,7 +375,7 @@ public class BigDecimalMath {
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* errror in invx.
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* This is used to define the precision of the result.
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*/
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final MathContext mc = new MathContext(invx.precision());
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final MathContext mc = SafeMathContext.newMathContext(invx.precision());
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return BigDecimal.ONE.divide(invx, mc);
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} else if (x.compareTo(BigDecimal.ZERO) == 0) {
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/*
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@ -420,7 +420,7 @@ public class BigDecimalMath {
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* add noise beyond
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* what's already in x.
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*/
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final MathContext mcTay = new MathContext(err2prec(1., xUlpDbl / TAYLOR_NTERM));
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final MathContext mcTay = SafeMathContext.newMathContext(err2prec(1., xUlpDbl / TAYLOR_NTERM));
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for (int i = 1; i <= TAYLOR_NTERM; i++) {
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ifac = ifac.multiply(new BigInteger("" + i));
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xpowi = xpowi.multiply(x);
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@ -435,7 +435,7 @@ public class BigDecimalMath {
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* relative error
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* in the result equals the absolute error in the argument.
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*/
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final MathContext mc = new MathContext(err2prec(xUlpDbl / 2.));
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final MathContext mc = SafeMathContext.newMathContext(err2prec(xUlpDbl / 2.));
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return resul.round(mc);
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} else {
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/*
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@ -454,7 +454,7 @@ public class BigDecimalMath {
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* binomial expansion).
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* This looses one digit.
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*/
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final MathContext mc = new MathContext(expxby10.precision() - exSc);
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final MathContext mc = SafeMathContext.newMathContext(expxby10.precision() - exSc);
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/*
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* Rescaling the powers of 10 is done in chunks of a maximum of
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* 8 to avoid an invalid operation
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@ -463,7 +463,7 @@ public class BigDecimalMath {
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while (exSc > 0) {
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int exsub = Math.min(8, exSc);
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exSc -= exsub;
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final MathContext mctmp = new MathContext(expxby10.precision() - exsub + 2);
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final MathContext mctmp = SafeMathContext.newMathContext(expxby10.precision() - exsub + 2);
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int pex = 1;
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while (exsub-- > 0) {
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pex *= 10;
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@ -539,7 +539,7 @@ public class BigDecimalMath {
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break;
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}
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}
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final MathContext mc = new MathContext(err2prec(resul.doubleValue(), eps));
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final MathContext mc = SafeMathContext.newMathContext(err2prec(resul.doubleValue(), eps));
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return resul.round(mc);
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} else {
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final double xDbl = x.doubleValue();
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@ -573,7 +573,7 @@ public class BigDecimalMath {
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* in the result equals the relative error in the input,
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* xUlpDbl/xDbl .
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*/
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final MathContext mc = new MathContext(err2prec(resul.doubleValue(), xUlpDbl / xDbl));
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final MathContext mc = SafeMathContext.newMathContext(err2prec(resul.doubleValue(), xUlpDbl / xDbl));
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return resul.round(mc);
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}
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} /* BigDecimalMath.log */
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@ -610,7 +610,7 @@ public class BigDecimalMath {
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* S(2,-5,...).
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*/
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final int[] a = { 2, -5, -2, -7, -2, -5, 2, -3 };
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BigDecimal S = broadhurstBBP(2, 1, a, new MathContext(1 + mc.getPrecision()));
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BigDecimal S = broadhurstBBP(2, 1, a, SafeMathContext.newMathContext(1 + mc.getPrecision()));
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S = S.multiply(new BigDecimal(8));
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S = sqrt(divideRound(S, 3));
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return S.round(mc);
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@ -625,7 +625,7 @@ public class BigDecimalMath {
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* so k>= precision/1.87.
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*/
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final int kmax = (int) (mc.getPrecision() / 1.87);
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MathContext mcloc = new MathContext(mc.getPrecision() + 1 + (int) (Math.log10(kmax * 0.693 / 1.098)));
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MathContext mcloc = SafeMathContext.newMathContext(mc.getPrecision() + 1 + (int) (Math.log10(kmax * 0.693 / 1.098)));
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BigDecimal log3 = multiplyRound(log(2, mcloc), 19);
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/*
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@ -646,7 +646,7 @@ public class BigDecimalMath {
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/*
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* how many digits of tmp do we need in the sum?
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*/
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mcloc = new MathContext(err2prec(tmp.doubleValue(), eps));
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mcloc = SafeMathContext.newMathContext(err2prec(tmp.doubleValue(), eps));
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final BigDecimal c = pk.divide(k).BigDecimalValue(mcloc);
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if (k % 2 != 0) {
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log3 = log3.add(c);
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@ -667,7 +667,7 @@ public class BigDecimalMath {
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* so k>= precision/1.33.
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*/
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final int kmax = (int) (mc.getPrecision() / 1.33);
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MathContext mcloc = new MathContext(mc.getPrecision() + 1 + (int) (Math.log10(kmax * 0.693 / 1.609)));
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MathContext mcloc = SafeMathContext.newMathContext(mc.getPrecision() + 1 + (int) (Math.log10(kmax * 0.693 / 1.609)));
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BigDecimal log5 = multiplyRound(log(2, mcloc), 14);
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/*
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@ -688,7 +688,7 @@ public class BigDecimalMath {
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/*
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* how many digits of tmp do we need in the sum?
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*/
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mcloc = new MathContext(err2prec(tmp.doubleValue(), eps));
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mcloc = SafeMathContext.newMathContext(err2prec(tmp.doubleValue(), eps));
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final BigDecimal c = pk.divide(k).BigDecimalValue(mcloc);
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log5 = log5.subtract(c);
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pk = pk.multiply(r);
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@ -705,7 +705,7 @@ public class BigDecimalMath {
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* so k>= precision/0.903.
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*/
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final int kmax = (int) (mc.getPrecision() / 0.903);
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MathContext mcloc = new MathContext(mc.getPrecision() + 1 + (int) (Math.log10(kmax * 3 * 0.693 / 1.098)));
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MathContext mcloc = SafeMathContext.newMathContext(mc.getPrecision() + 1 + (int) (Math.log10(kmax * 3 * 0.693 / 1.098)));
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BigDecimal log7 = multiplyRound(log(2, mcloc), 3);
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/*
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@ -723,7 +723,7 @@ public class BigDecimalMath {
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/*
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* how many digits of tmp do we need in the sum?
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*/
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mcloc = new MathContext(err2prec(tmp.doubleValue(), eps));
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mcloc = SafeMathContext.newMathContext(err2prec(tmp.doubleValue(), eps));
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final BigDecimal c = pk.divide(k).BigDecimalValue(mcloc);
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log7 = log7.subtract(c);
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pk = pk.multiply(r);
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@ -753,7 +753,7 @@ public class BigDecimalMath {
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* Convert this absolute requirement of error in n to a relative
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* error in n
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*/
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final MathContext mcloc = new MathContext(1 + err2prec(n, eps));
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final MathContext mcloc = SafeMathContext.newMathContext(1 + err2prec(n, eps));
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/*
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* Padd n with a number of zeros to trigger the required accuracy in
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* the standard signature method
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@ -796,7 +796,7 @@ public class BigDecimalMath {
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* in r, given that
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* epsr/r is also the relative precision of r. Add one safety digit.
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*/
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final MathContext mcloc = new MathContext(1 + err2prec(eps));
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final MathContext mcloc = SafeMathContext.newMathContext(1 + err2prec(eps));
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final BigDecimal resul = log(r.BigDecimalValue(mcloc));
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@ -834,7 +834,7 @@ public class BigDecimalMath {
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* |log(x)*err(y)|+|y*err(x)/x|
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*/
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final double errR = Math.abs(logx.doubleValue() * y.ulp().doubleValue() / 2.) + Math.abs(y.doubleValue() * x.ulp().doubleValue() / 2. / x.doubleValue());
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final MathContext mcR = new MathContext(err2prec(1.0, errR));
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final MathContext mcR = SafeMathContext.newMathContext(err2prec(1.0, errR));
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return resul.round(mcR);
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}
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} /* BigDecimalMath.pow */
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@ -867,7 +867,7 @@ public class BigDecimalMath {
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* Since the standard BigDecimal.pow can only handle positive n, we
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* split the algorithm.
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*/
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final MathContext mc = new MathContext(x.precision() - (int) Math.log10((Math.abs(n))));
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final MathContext mc = SafeMathContext.newMathContext(x.precision() - (int) Math.log10((Math.abs(n))));
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if (n > 0) {
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return x.pow(n, mc);
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} else {
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@ -991,7 +991,7 @@ public class BigDecimalMath {
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*/
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eps = nu.divide(de, MathContext.DECIMAL32);
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} else {
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final MathContext mc = new MathContext(precDiv);
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final MathContext mc = SafeMathContext.newMathContext(precDiv);
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eps = nu.divide(de, mc);
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}
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@ -1006,7 +1006,7 @@ public class BigDecimalMath {
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* delete the bits of extra precision kept in this
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* working copy.
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*/
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final MathContext mc = new MathContext(err2prec(reserr.doubleValue()));
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final MathContext mc = SafeMathContext.newMathContext(err2prec(reserr.doubleValue()));
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return res.round(mc);
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}
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}
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@ -1019,7 +1019,7 @@ public class BigDecimalMath {
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* Delta(q)/q << Delta(x)/x/log(x) .
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*/
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final int precq = 3 + err2prec((x.ulp().divide(x, MathContext.DECIMAL64)).doubleValue() / Math.log(x.doubleValue()));
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final MathContext mc = new MathContext(precq);
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final MathContext mc = SafeMathContext.newMathContext(precq);
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/*
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* Perform the actual calculation as exponentiation of two
|
|
|
|
@ -1051,9 +1051,9 @@ public class BigDecimalMath {
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|
|
|
*/
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|
|
|
|
final BigDecimal res = mod2pi(x);
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|
|
|
|
final double errpi = 0.5 * Math.abs(x.ulp().doubleValue());
|
|
|
|
|
MathContext mc = new MathContext(2 + err2prec(3.14159, errpi));
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|
|
|
|
MathContext mc = SafeMathContext.newMathContext(2 + err2prec(3.14159, errpi));
|
|
|
|
|
final BigDecimal p = pi(mc);
|
|
|
|
|
mc = new MathContext(x.precision());
|
|
|
|
|
mc = SafeMathContext.newMathContext(x.precision());
|
|
|
|
|
if (res.compareTo(p) > 0) {
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|
|
|
|
/*
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|
* pi<x<=2pi: sin(x)= - sin(x-pi)
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|
@ -1102,7 +1102,7 @@ public class BigDecimalMath {
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|
* 2k*(-log10(x)) > x.precision; 2k*log10(1/x) > x.precision
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|
|
|
*/
|
|
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|
|
final int k = (int) (res.precision() / Math.log10(1.0 / res.doubleValue())) / 2;
|
|
|
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|
final MathContext mcTay = new MathContext(err2prec(res.doubleValue(), xUlpDbl / k));
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|
|
|
final MathContext mcTay = SafeMathContext.newMathContext(err2prec(res.doubleValue(), xUlpDbl / k));
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|
|
|
|
for (int i = 1;; i++) {
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|
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|
|
/*
|
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|
|
* TBD: at which precision will 2*i or 2*i+1 overflow?
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|
@ -1119,7 +1119,7 @@ public class BigDecimalMath {
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|
/*
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|
* The error in the result is set by the error in x itself.
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|
*/
|
|
|
|
|
mc = new MathContext(res.precision());
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|
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|
mc = SafeMathContext.newMathContext(res.precision());
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|
return resul.round(mc);
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}
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|
}
|
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|
@ -1146,9 +1146,9 @@ public class BigDecimalMath {
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|
*/
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|
|
final BigDecimal res = mod2pi(x);
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|
|
final double errpi = 0.5 * Math.abs(x.ulp().doubleValue());
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|
|
|
MathContext mc = new MathContext(2 + err2prec(3.14159, errpi));
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|
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|
MathContext mc = SafeMathContext.newMathContext(2 + err2prec(3.14159, errpi));
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|
|
final BigDecimal p = pi(mc);
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|
|
mc = new MathContext(x.precision());
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|
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|
mc = SafeMathContext.newMathContext(x.precision());
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|
|
if (res.compareTo(p) > 0) {
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|
|
/*
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|
|
* pi<x<=2pi: cos(x)= - cos(x-pi)
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|
@ -1198,7 +1198,7 @@ public class BigDecimalMath {
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|
* x^(2k) < xUlpDbl; (2k)*log(x) < log(xUlpDbl);
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|
|
*/
|
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|
|
final int k = (int) (Math.log(xUlpDbl) / Math.log(res.doubleValue())) / 2;
|
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|
|
|
final MathContext mcTay = new MathContext(err2prec(1., xUlpDbl / k));
|
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|
|
|
final MathContext mcTay = SafeMathContext.newMathContext(err2prec(1., xUlpDbl / k));
|
|
|
|
|
for (int i = 1;; i++) {
|
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|
|
/*
|
|
|
|
|
* TBD: at which precision will 2*i-1 or 2*i overflow?
|
|
|
|
@ -1216,7 +1216,7 @@ public class BigDecimalMath {
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|
|
|
|
* The error in the result is governed by the error in x
|
|
|
|
|
* itself.
|
|
|
|
|
*/
|
|
|
|
|
mc = new MathContext(err2prec(resul.doubleValue(), xUlpDbl));
|
|
|
|
|
mc = SafeMathContext.newMathContext(err2prec(resul.doubleValue(), xUlpDbl));
|
|
|
|
|
return resul.round(mc);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
@ -1252,7 +1252,7 @@ public class BigDecimalMath {
|
|
|
|
|
if (xDbl > 0.8) {
|
|
|
|
|
/* tan(x) = 1/cot(x) */
|
|
|
|
|
final BigDecimal co = cot(x);
|
|
|
|
|
final MathContext mc = new MathContext(err2prec(1. / co.doubleValue(), eps));
|
|
|
|
|
final MathContext mc = SafeMathContext.newMathContext(err2prec(1. / co.doubleValue(), eps));
|
|
|
|
|
return BigDecimal.ONE.divide(co, mc);
|
|
|
|
|
} else {
|
|
|
|
|
final BigDecimal xhighpr = scalePrec(res, 2);
|
|
|
|
@ -1282,7 +1282,7 @@ public class BigDecimalMath {
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
final MathContext mc = new MathContext(err2prec(resul.doubleValue(), eps));
|
|
|
|
|
final MathContext mc = SafeMathContext.newMathContext(err2prec(resul.doubleValue(), eps));
|
|
|
|
|
return resul.round(mc);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
@ -1318,7 +1318,7 @@ public class BigDecimalMath {
|
|
|
|
|
final BigDecimal xhighpr = scalePrec(res, 2);
|
|
|
|
|
final BigDecimal xhighprSq = multiplyRound(xhighpr, xhighpr);
|
|
|
|
|
|
|
|
|
|
MathContext mc = new MathContext(err2prec(xhighpr.doubleValue(), eps));
|
|
|
|
|
MathContext mc = SafeMathContext.newMathContext(err2prec(xhighpr.doubleValue(), eps));
|
|
|
|
|
BigDecimal resul = BigDecimal.ONE.divide(xhighpr, mc);
|
|
|
|
|
|
|
|
|
|
/* x^(2i-1) */
|
|
|
|
@ -1348,7 +1348,7 @@ public class BigDecimalMath {
|
|
|
|
|
fourn = fourn.shiftLeft(2);
|
|
|
|
|
xpowi = multiplyRound(xpowi, xhighprSq);
|
|
|
|
|
}
|
|
|
|
|
mc = new MathContext(err2prec(resul.doubleValue(), eps));
|
|
|
|
|
mc = SafeMathContext.newMathContext(err2prec(resul.doubleValue(), eps));
|
|
|
|
|
return resul.round(mc);
|
|
|
|
|
}
|
|
|
|
|
} /* BigDecimalMath.cot */
|
|
|
|
@ -1371,7 +1371,7 @@ public class BigDecimalMath {
|
|
|
|
|
* arcsin(1) = pi/2
|
|
|
|
|
*/
|
|
|
|
|
final double errpi = Math.sqrt(x.ulp().doubleValue());
|
|
|
|
|
final MathContext mc = new MathContext(err2prec(3.14159, errpi));
|
|
|
|
|
final MathContext mc = SafeMathContext.newMathContext(err2prec(3.14159, errpi));
|
|
|
|
|
return pi(mc).divide(new BigDecimal(2));
|
|
|
|
|
} else if (x.compareTo(BigDecimal.ZERO) < 0) {
|
|
|
|
|
return asin(x.negate()).negate();
|
|
|
|
@ -1417,10 +1417,10 @@ public class BigDecimalMath {
|
|
|
|
|
xpowi = sqrt(xhighpr.multiply(new BigDecimal(2)));
|
|
|
|
|
resul = multiplyRound(xpowi, resul);
|
|
|
|
|
|
|
|
|
|
MathContext mc = new MathContext(resul.precision());
|
|
|
|
|
MathContext mc = SafeMathContext.newMathContext(resul.precision());
|
|
|
|
|
final BigDecimal pihalf = pi(mc).divide(new BigDecimal(2));
|
|
|
|
|
|
|
|
|
|
mc = new MathContext(err2prec(resul.doubleValue(), eps));
|
|
|
|
|
mc = SafeMathContext.newMathContext(err2prec(resul.doubleValue(), eps));
|
|
|
|
|
return pihalf.subtract(resul, mc);
|
|
|
|
|
} else {
|
|
|
|
|
/*
|
|
|
|
@ -1453,7 +1453,7 @@ public class BigDecimalMath {
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
final MathContext mc = new MathContext(err2prec(resul.doubleValue(), eps));
|
|
|
|
|
final MathContext mc = SafeMathContext.newMathContext(err2prec(resul.doubleValue(), eps));
|
|
|
|
|
return resul.round(mc);
|
|
|
|
|
}
|
|
|
|
|
} /* BigDecimalMath.asin */
|
|
|
|
@ -1475,7 +1475,7 @@ public class BigDecimalMath {
|
|
|
|
|
BigDecimal resul = asin(xhighpr);
|
|
|
|
|
double eps = resul.ulp().doubleValue() / 2.;
|
|
|
|
|
|
|
|
|
|
MathContext mc = new MathContext(err2prec(3.14159, eps));
|
|
|
|
|
MathContext mc = SafeMathContext.newMathContext(err2prec(3.14159, eps));
|
|
|
|
|
final BigDecimal pihalf = pi(mc).divide(new BigDecimal(2));
|
|
|
|
|
resul = pihalf.subtract(resul);
|
|
|
|
|
|
|
|
|
@ -1486,7 +1486,7 @@ public class BigDecimalMath {
|
|
|
|
|
final double xUlpDbl = x.ulp().doubleValue() / 2.;
|
|
|
|
|
eps = xUlpDbl / 2. / Math.sqrt(1. - Math.pow(xDbl, 2.));
|
|
|
|
|
|
|
|
|
|
mc = new MathContext(err2prec(resul.doubleValue(), eps));
|
|
|
|
|
mc = SafeMathContext.newMathContext(err2prec(resul.doubleValue(), eps));
|
|
|
|
|
return resul.round(mc);
|
|
|
|
|
|
|
|
|
|
} /* BigDecimalMath.acos */
|
|
|
|
@ -1524,7 +1524,7 @@ public class BigDecimalMath {
|
|
|
|
|
* of the ulp.
|
|
|
|
|
*/
|
|
|
|
|
final double eps = x.ulp().doubleValue() / (2.0 * Math.hypot(1.0, x.doubleValue()));
|
|
|
|
|
final MathContext mc = new MathContext(err2prec(resul.doubleValue(), eps));
|
|
|
|
|
final MathContext mc = SafeMathContext.newMathContext(err2prec(resul.doubleValue(), eps));
|
|
|
|
|
return resul.round(mc);
|
|
|
|
|
} else if (x.doubleValue() < 0.71) {
|
|
|
|
|
/* Taylor expansion around x=0; Abramowitz-Stegun 4.4.42 */
|
|
|
|
@ -1552,7 +1552,7 @@ public class BigDecimalMath {
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
final MathContext mc = new MathContext(err2prec(resul.doubleValue(), eps));
|
|
|
|
|
final MathContext mc = SafeMathContext.newMathContext(err2prec(resul.doubleValue(), eps));
|
|
|
|
|
return resul.round(mc);
|
|
|
|
|
} else {
|
|
|
|
|
/* Taylor expansion around x=infinity; Abramowitz-Stegun 4.4.42 */
|
|
|
|
@ -1567,7 +1567,7 @@ public class BigDecimalMath {
|
|
|
|
|
* start with the term pi/2; gather its precision relative to the
|
|
|
|
|
* expected result
|
|
|
|
|
*/
|
|
|
|
|
MathContext mc = new MathContext(2 + err2prec(3.1416, eps));
|
|
|
|
|
MathContext mc = SafeMathContext.newMathContext(2 + err2prec(3.1416, eps));
|
|
|
|
|
final BigDecimal onepi = pi(mc);
|
|
|
|
|
BigDecimal resul = onepi.divide(new BigDecimal(2));
|
|
|
|
|
|
|
|
|
@ -1586,7 +1586,7 @@ public class BigDecimalMath {
|
|
|
|
|
}
|
|
|
|
|
xpowi = multiplyRound(xpowi, xhighprSq);
|
|
|
|
|
}
|
|
|
|
|
mc = new MathContext(err2prec(resul.doubleValue(), eps));
|
|
|
|
|
mc = SafeMathContext.newMathContext(err2prec(resul.doubleValue(), eps));
|
|
|
|
|
return resul.round(mc);
|
|
|
|
|
}
|
|
|
|
|
} /* BigDecimalMath.atan */
|
|
|
|
@ -1644,7 +1644,7 @@ public class BigDecimalMath {
|
|
|
|
|
* the absolute value will give a safe relative error estimate
|
|
|
|
|
* for the indivdual terms
|
|
|
|
|
*/
|
|
|
|
|
final MathContext mcTay = new MathContext(err2prec(1., xUlpDbl / k));
|
|
|
|
|
final MathContext mcTay = SafeMathContext.newMathContext(err2prec(1., xUlpDbl / k));
|
|
|
|
|
for (int i = 1;; i++) {
|
|
|
|
|
/*
|
|
|
|
|
* TBD: at which precision will 2*i-1 or 2*i overflow?
|
|
|
|
@ -1661,7 +1661,7 @@ public class BigDecimalMath {
|
|
|
|
|
/*
|
|
|
|
|
* The error in the result is governed by the error in x itself.
|
|
|
|
|
*/
|
|
|
|
|
final MathContext mc = new MathContext(err2prec(resul.doubleValue(), xUlpDbl));
|
|
|
|
|
final MathContext mc = SafeMathContext.newMathContext(err2prec(resul.doubleValue(), xUlpDbl));
|
|
|
|
|
return resul.round(mc);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
@ -1698,7 +1698,7 @@ public class BigDecimalMath {
|
|
|
|
|
* coth(x)*errx = errx/tanh(x)
|
|
|
|
|
*/
|
|
|
|
|
final double eps = Math.tanh(x.doubleValue());
|
|
|
|
|
final MathContext mc = new MathContext(err2prec(0.5 * x.ulp().doubleValue() / eps));
|
|
|
|
|
final MathContext mc = SafeMathContext.newMathContext(err2prec(0.5 * x.ulp().doubleValue() / eps));
|
|
|
|
|
return resul.round(mc);
|
|
|
|
|
} else {
|
|
|
|
|
final BigDecimal xhighpr = scalePrec(x, 2);
|
|
|
|
@ -1727,7 +1727,7 @@ public class BigDecimalMath {
|
|
|
|
|
* 2k*(-log10(x)) > x.precision; 2k*log10(1/x) > x.precision
|
|
|
|
|
*/
|
|
|
|
|
final int k = (int) (x.precision() / Math.log10(1.0 / xhighpr.doubleValue())) / 2;
|
|
|
|
|
final MathContext mcTay = new MathContext(err2prec(x.doubleValue(), xUlpDbl / k));
|
|
|
|
|
final MathContext mcTay = SafeMathContext.newMathContext(err2prec(x.doubleValue(), xUlpDbl / k));
|
|
|
|
|
for (int i = 1;; i++) {
|
|
|
|
|
/*
|
|
|
|
|
* TBD: at which precision will 2*i or 2*i+1 overflow?
|
|
|
|
@ -1744,7 +1744,7 @@ public class BigDecimalMath {
|
|
|
|
|
/*
|
|
|
|
|
* The error in the result is set by the error in x itself.
|
|
|
|
|
*/
|
|
|
|
|
final MathContext mc = new MathContext(x.precision());
|
|
|
|
|
final MathContext mc = SafeMathContext.newMathContext(x.precision());
|
|
|
|
|
return resul.round(mc);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
@ -1776,7 +1776,7 @@ public class BigDecimalMath {
|
|
|
|
|
* The error in tanh x is err(x)/cosh^2(x).
|
|
|
|
|
*/
|
|
|
|
|
final double eps = 0.5 * x.ulp().doubleValue() / Math.pow(Math.cosh(x.doubleValue()), 2.0);
|
|
|
|
|
final MathContext mc = new MathContext(err2prec(Math.tanh(x.doubleValue()), eps));
|
|
|
|
|
final MathContext mc = SafeMathContext.newMathContext(err2prec(Math.tanh(x.doubleValue()), eps));
|
|
|
|
|
return BigDecimal.ONE.subtract(exp2x).divide(BigDecimal.ONE.add(exp2x), mc);
|
|
|
|
|
}
|
|
|
|
|
} /* BigDecimalMath.tanh */
|
|
|
|
@ -1806,7 +1806,7 @@ public class BigDecimalMath {
|
|
|
|
|
*/
|
|
|
|
|
final double xDbl = x.doubleValue();
|
|
|
|
|
final double eps = 0.5 * x.ulp().doubleValue() / Math.hypot(1., xDbl);
|
|
|
|
|
final MathContext mc = new MathContext(err2prec(logx.doubleValue(), eps));
|
|
|
|
|
final MathContext mc = SafeMathContext.newMathContext(err2prec(logx.doubleValue(), eps));
|
|
|
|
|
return logx.round(mc);
|
|
|
|
|
}
|
|
|
|
|
} /* BigDecimalMath.asinh */
|
|
|
|
@ -1838,7 +1838,7 @@ public class BigDecimalMath {
|
|
|
|
|
*/
|
|
|
|
|
final double xDbl = x.doubleValue();
|
|
|
|
|
final double eps = 0.5 * x.ulp().doubleValue() / Math.sqrt(xDbl * xDbl - 1.);
|
|
|
|
|
final MathContext mc = new MathContext(err2prec(logx.doubleValue(), eps));
|
|
|
|
|
final MathContext mc = SafeMathContext.newMathContext(err2prec(logx.doubleValue(), eps));
|
|
|
|
|
return logx.round(mc);
|
|
|
|
|
}
|
|
|
|
|
} /* BigDecimalMath.acosh */
|
|
|
|
@ -1876,7 +1876,7 @@ public class BigDecimalMath {
|
|
|
|
|
* add intermediately 2 digits to the partial sum accumulation
|
|
|
|
|
*/
|
|
|
|
|
z = scalePrec(z, 2);
|
|
|
|
|
MathContext mcloc = new MathContext(z.precision());
|
|
|
|
|
MathContext mcloc = SafeMathContext.newMathContext(z.precision());
|
|
|
|
|
|
|
|
|
|
/*
|
|
|
|
|
* measure of the absolute error is the relative error in the first,
|
|
|
|
@ -1901,7 +1901,7 @@ public class BigDecimalMath {
|
|
|
|
|
* absolute error in z)
|
|
|
|
|
*/
|
|
|
|
|
BigDecimal c = divideRound(z.pow(n, mcloc), n);
|
|
|
|
|
MathContext m = new MathContext(err2prec(n * z.ulp().doubleValue() / 2. / z.doubleValue()));
|
|
|
|
|
MathContext m = SafeMathContext.newMathContext(err2prec(n * z.ulp().doubleValue() / 2. / z.doubleValue()));
|
|
|
|
|
c = c.round(m);
|
|
|
|
|
|
|
|
|
|
/*
|
|
|
|
@ -1917,9 +1917,9 @@ public class BigDecimalMath {
|
|
|
|
|
* of the order of 1.
|
|
|
|
|
*/
|
|
|
|
|
if (eps / 100. / c.doubleValue() < 0.01) {
|
|
|
|
|
m = new MathContext(err2prec(eps / 100. / c.doubleValue()));
|
|
|
|
|
m = SafeMathContext.newMathContext(err2prec(eps / 100. / c.doubleValue()));
|
|
|
|
|
} else {
|
|
|
|
|
m = new MathContext(2);
|
|
|
|
|
m = SafeMathContext.newMathContext(2);
|
|
|
|
|
}
|
|
|
|
|
/* zeta(n) -1 */
|
|
|
|
|
final BigDecimal zetm1 = zeta(n, m).subtract(BigDecimal.ONE);
|
|
|
|
@ -1946,7 +1946,7 @@ public class BigDecimalMath {
|
|
|
|
|
*/
|
|
|
|
|
final double zdbl = z.doubleValue();
|
|
|
|
|
eps = psi(zdbl) * x.ulp().doubleValue() / 2.;
|
|
|
|
|
mcloc = new MathContext(err2prec(eps));
|
|
|
|
|
mcloc = SafeMathContext.newMathContext(err2prec(eps));
|
|
|
|
|
return exp(resul).round(mcloc);
|
|
|
|
|
}
|
|
|
|
|
} /* BigDecimalMath.gamma */
|
|
|
|
@ -2003,7 +2003,7 @@ public class BigDecimalMath {
|
|
|
|
|
final double qdbl = q.doubleValue();
|
|
|
|
|
final double deltx = 5. * Math.pow(10., -mc.getPrecision()) / psi(qdbl);
|
|
|
|
|
|
|
|
|
|
final MathContext mcx = new MathContext(err2prec(qdbl, deltx));
|
|
|
|
|
final MathContext mcx = SafeMathContext.newMathContext(err2prec(qdbl, deltx));
|
|
|
|
|
final BigDecimal x = q.BigDecimalValue(mcx);
|
|
|
|
|
|
|
|
|
|
/* forward calculation to the general floating point case */
|
|
|
|
@ -2047,10 +2047,10 @@ public class BigDecimalMath {
|
|
|
|
|
for (int i = 1; i < n; i++) {
|
|
|
|
|
eps += 0.5 * xUlpDbl / Math.abs(xDbl + i);
|
|
|
|
|
resul = resul.multiply(xhighpr.add(new BigDecimal(i)));
|
|
|
|
|
final MathContext mcloc = new MathContext(4 + err2prec(eps));
|
|
|
|
|
final MathContext mcloc = SafeMathContext.newMathContext(4 + err2prec(eps));
|
|
|
|
|
resul = resul.round(mcloc);
|
|
|
|
|
}
|
|
|
|
|
return resul.round(new MathContext(err2prec(eps)));
|
|
|
|
|
return resul.round(SafeMathContext.newMathContext(err2prec(eps)));
|
|
|
|
|
}
|
|
|
|
|
} /* BigDecimalMath.pochhammer */
|
|
|
|
|
|
|
|
|
@ -2084,7 +2084,7 @@ public class BigDecimalMath {
|
|
|
|
|
} else {
|
|
|
|
|
err2pi = 0.5 * Math.abs(x.ulp().doubleValue());
|
|
|
|
|
}
|
|
|
|
|
MathContext mc = new MathContext(2 + err2prec(6.283, err2pi));
|
|
|
|
|
MathContext mc = SafeMathContext.newMathContext(2 + err2prec(6.283, err2pi));
|
|
|
|
|
final BigDecimal twopi = pi(mc).multiply(new BigDecimal(2));
|
|
|
|
|
|
|
|
|
|
/*
|
|
|
|
@ -2101,7 +2101,7 @@ public class BigDecimalMath {
|
|
|
|
|
* The actual precision is set by the input value, its absolute value of
|
|
|
|
|
* x.ulp()/2.
|
|
|
|
|
*/
|
|
|
|
|
mc = new MathContext(err2prec(res.doubleValue(), x.ulp().doubleValue() / 2.));
|
|
|
|
|
mc = SafeMathContext.newMathContext(err2prec(res.doubleValue(), x.ulp().doubleValue() / 2.));
|
|
|
|
|
return res.round(mc);
|
|
|
|
|
} /* mod2pi */
|
|
|
|
|
|
|
|
|
@ -2135,7 +2135,7 @@ public class BigDecimalMath {
|
|
|
|
|
} else {
|
|
|
|
|
errpi = 0.5 * Math.abs(x.ulp().doubleValue());
|
|
|
|
|
}
|
|
|
|
|
MathContext mc = new MathContext(2 + err2prec(3.1416, errpi));
|
|
|
|
|
MathContext mc = SafeMathContext.newMathContext(2 + err2prec(3.1416, errpi));
|
|
|
|
|
final BigDecimal onepi = pi(mc);
|
|
|
|
|
final BigDecimal pihalf = onepi.divide(new BigDecimal(2));
|
|
|
|
|
|
|
|
|
@ -2155,7 +2155,7 @@ public class BigDecimalMath {
|
|
|
|
|
* The actual precision is set by the input value, its absolute value of
|
|
|
|
|
* x.ulp()/2.
|
|
|
|
|
*/
|
|
|
|
|
mc = new MathContext(err2prec(res.doubleValue(), x.ulp().doubleValue() / 2.));
|
|
|
|
|
mc = SafeMathContext.newMathContext(err2prec(res.doubleValue(), x.ulp().doubleValue() / 2.));
|
|
|
|
|
return res.round(mc);
|
|
|
|
|
} /* modpi */
|
|
|
|
|
|
|
|
|
@ -2195,7 +2195,7 @@ public class BigDecimalMath {
|
|
|
|
|
* Need one more digit in pi if n=10, two digits if n=100 etc, and
|
|
|
|
|
* add one extra digit.
|
|
|
|
|
*/
|
|
|
|
|
final MathContext mcpi = new MathContext(mc.getPrecision() + (int) (Math.log10(10.0 * n)));
|
|
|
|
|
final MathContext mcpi = SafeMathContext.newMathContext(mc.getPrecision() + (int) (Math.log10(10.0 * n)));
|
|
|
|
|
final BigDecimal piton = pi(mcpi).pow(n, mc);
|
|
|
|
|
return multiplyRound(piton, b);
|
|
|
|
|
} else if (n == 3) {
|
|
|
|
@ -2225,9 +2225,9 @@ public class BigDecimalMath {
|
|
|
|
|
final int[] a51 = { 31, -1614, -31, -6212, -31, -1614, 31, 74552 };
|
|
|
|
|
final int[] a53 = { 173, 284, -173, -457, -173, 284, 173, -111 };
|
|
|
|
|
final int[] a55 = { 1, 0, -1, -1, -1, 0, 1, 1 };
|
|
|
|
|
BigDecimal S51 = broadhurstBBP(5, 1, a51, new MathContext(2 + mc.getPrecision()));
|
|
|
|
|
BigDecimal S53 = broadhurstBBP(5, 3, a53, new MathContext(2 + mc.getPrecision()));
|
|
|
|
|
BigDecimal S55 = broadhurstBBP(5, 5, a55, new MathContext(1 + mc.getPrecision()));
|
|
|
|
|
BigDecimal S51 = broadhurstBBP(5, 1, a51, SafeMathContext.newMathContext(2 + mc.getPrecision()));
|
|
|
|
|
BigDecimal S53 = broadhurstBBP(5, 3, a53, SafeMathContext.newMathContext(2 + mc.getPrecision()));
|
|
|
|
|
BigDecimal S55 = broadhurstBBP(5, 5, a55, SafeMathContext.newMathContext(1 + mc.getPrecision()));
|
|
|
|
|
S51 = S51.multiply(new BigDecimal(18432));
|
|
|
|
|
S53 = S53.multiply(new BigDecimal(14336));
|
|
|
|
|
S55 = S55.multiply(new BigDecimal(1511424));
|
|
|
|
@ -2258,7 +2258,7 @@ public class BigDecimalMath {
|
|
|
|
|
* and the precision
|
|
|
|
|
* requested for 2*pi is in absolute terms adjusted.
|
|
|
|
|
*/
|
|
|
|
|
final MathContext mcloc = new MathContext(2 + mc.getPrecision() + (int) (Math.log10((n))));
|
|
|
|
|
final MathContext mcloc = SafeMathContext.newMathContext(2 + mc.getPrecision() + (int) (Math.log10((n))));
|
|
|
|
|
BigDecimal ftrm = pi(mcloc).multiply(new BigDecimal(2));
|
|
|
|
|
ftrm = ftrm.pow(n);
|
|
|
|
|
ftrm = multiplyRound(ftrm, betsum.BigDecimalValue(mcloc));
|
|
|
|
@ -2286,7 +2286,7 @@ public class BigDecimalMath {
|
|
|
|
|
* The absolute error is
|
|
|
|
|
* 4*exp(2pi)*err(pi)/(exp(2pi)-1)^2=0.0075*err(pi)
|
|
|
|
|
*/
|
|
|
|
|
BigDecimal exp2p = pi(new MathContext(3 + err2prec(3.14, eps / 0.0075)));
|
|
|
|
|
BigDecimal exp2p = pi(SafeMathContext.newMathContext(3 + err2prec(3.14, eps / 0.0075)));
|
|
|
|
|
exp2p = exp(exp2p.multiply(new BigDecimal(2)));
|
|
|
|
|
BigDecimal c = exp2p.subtract(BigDecimal.ONE);
|
|
|
|
|
exps = divideRound(1, c);
|
|
|
|
@ -2319,7 +2319,7 @@ public class BigDecimalMath {
|
|
|
|
|
* The absolute error is 0.017*err(pi) at k=9, 0.013*err(pi) at
|
|
|
|
|
* k=13, 0.012 at k=17
|
|
|
|
|
*/
|
|
|
|
|
BigDecimal twop = pi(new MathContext(3 + err2prec(3.14, eps / 0.017)));
|
|
|
|
|
BigDecimal twop = pi(SafeMathContext.newMathContext(3 + err2prec(3.14, eps / 0.017)));
|
|
|
|
|
twop = twop.multiply(new BigDecimal(2));
|
|
|
|
|
final BigDecimal exp2p = exp(twop);
|
|
|
|
|
BigDecimal c = exp2p.subtract(BigDecimal.ONE);
|
|
|
|
@ -2378,7 +2378,7 @@ public class BigDecimalMath {
|
|
|
|
|
* in relative units is higher, because zeta is around 1.
|
|
|
|
|
*/
|
|
|
|
|
final double eps = 1.e-18 * Math.pow(2., (-n));
|
|
|
|
|
final MathContext mc = new MathContext(err2prec(eps));
|
|
|
|
|
final MathContext mc = SafeMathContext.newMathContext(err2prec(eps));
|
|
|
|
|
return zeta(n, mc).subtract(BigDecimal.ONE).doubleValue();
|
|
|
|
|
}
|
|
|
|
|
} /* zeta */
|
|
|
|
@ -2506,7 +2506,7 @@ public class BigDecimalMath {
|
|
|
|
|
if (Math.abs(r.doubleValue()) < eps) {
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
final MathContext mcloc = new MathContext(1 + err2prec(r.doubleValue(), eps));
|
|
|
|
|
final MathContext mcloc = SafeMathContext.newMathContext(1 + err2prec(r.doubleValue(), eps));
|
|
|
|
|
res = res.add(r.BigDecimalValue(mcloc));
|
|
|
|
|
}
|
|
|
|
|
return res.round(mc);
|
|
|
|
@ -2547,7 +2547,7 @@ public class BigDecimalMath {
|
|
|
|
|
if (err2prec < 0) {
|
|
|
|
|
err2prec = 0;
|
|
|
|
|
}
|
|
|
|
|
final MathContext mc = new MathContext(err2prec);
|
|
|
|
|
final MathContext mc = SafeMathContext.newMathContext(err2prec);
|
|
|
|
|
return resul.round(mc);
|
|
|
|
|
} /* addRound */
|
|
|
|
|
|
|
|
|
@ -2599,7 +2599,7 @@ public class BigDecimalMath {
|
|
|
|
|
* |err(y)|+|err(x)|
|
|
|
|
|
*/
|
|
|
|
|
final double errR = Math.abs(y.ulp().doubleValue() / 2.) + Math.abs(x.ulp().doubleValue() / 2.);
|
|
|
|
|
final MathContext mc = new MathContext(err2prec(resul.doubleValue(), errR));
|
|
|
|
|
final MathContext mc = SafeMathContext.newMathContext(err2prec(resul.doubleValue(), errR));
|
|
|
|
|
return resul.round(mc);
|
|
|
|
|
} /* subtractRound */
|
|
|
|
|
|
|
|
|
@ -2636,7 +2636,7 @@ public class BigDecimalMath {
|
|
|
|
|
* relative
|
|
|
|
|
* errors |err(y)/y|+|err(x)/x|
|
|
|
|
|
*/
|
|
|
|
|
final MathContext mc = new MathContext(Math.min(x.precision(), y.precision()));
|
|
|
|
|
final MathContext mc = SafeMathContext.newMathContext(Math.min(x.precision(), y.precision()));
|
|
|
|
|
return resul.round(mc);
|
|
|
|
|
} /* multiplyRound */
|
|
|
|
|
|
|
|
|
@ -2689,7 +2689,7 @@ public class BigDecimalMath {
|
|
|
|
|
/*
|
|
|
|
|
* Convert the rational value with two digits of extra precision
|
|
|
|
|
*/
|
|
|
|
|
final MathContext mc = new MathContext(2 + x.precision());
|
|
|
|
|
final MathContext mc = SafeMathContext.newMathContext(2 + x.precision());
|
|
|
|
|
final BigDecimal fbd = f.BigDecimalValue(mc);
|
|
|
|
|
|
|
|
|
|
/*
|
|
|
|
@ -2715,7 +2715,7 @@ public class BigDecimalMath {
|
|
|
|
|
/*
|
|
|
|
|
* The estimation of the absolute error in the result is |n*err(x)|
|
|
|
|
|
*/
|
|
|
|
|
final MathContext mc = new MathContext(n != 0 ? x.precision() : 0);
|
|
|
|
|
final MathContext mc = SafeMathContext.newMathContext(n != 0 ? x.precision() : 0);
|
|
|
|
|
return resul.round(mc);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
@ -2734,7 +2734,7 @@ public class BigDecimalMath {
|
|
|
|
|
/*
|
|
|
|
|
* The estimation of the absolute error in the result is |n*err(x)|
|
|
|
|
|
*/
|
|
|
|
|
final MathContext mc = new MathContext(n.compareTo(BigInteger.ZERO) != 0 ? x.precision() : 0);
|
|
|
|
|
final MathContext mc = SafeMathContext.newMathContext(n.compareTo(BigInteger.ZERO) != 0 ? x.precision() : 0);
|
|
|
|
|
return resul.round(mc);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
@ -2753,7 +2753,7 @@ public class BigDecimalMath {
|
|
|
|
|
* The estimation of the relative error in the result is
|
|
|
|
|
* |err(y)/y|+|err(x)/x|
|
|
|
|
|
*/
|
|
|
|
|
final MathContext mc = new MathContext(Math.min(x.precision(), y.precision()));
|
|
|
|
|
final MathContext mc = SafeMathContext.newMathContext(Math.min(x.precision(), y.precision()));
|
|
|
|
|
final BigDecimal resul = x.divide(y, mc);
|
|
|
|
|
/*
|
|
|
|
|
* If x and y are precise integer values that may have common factors,
|
|
|
|
@ -2777,13 +2777,13 @@ public class BigDecimalMath {
|
|
|
|
|
/*
|
|
|
|
|
* In this case with vanishing Im(x), the result is simply 1/Re z.
|
|
|
|
|
*/
|
|
|
|
|
final MathContext mc = new MathContext(z.re.precision());
|
|
|
|
|
final MathContext mc = SafeMathContext.newMathContext(z.re.precision());
|
|
|
|
|
return new BigComplex(BigDecimal.ONE.divide(z.re, mc));
|
|
|
|
|
} else if (z.re.compareTo(BigDecimal.ZERO) == 0) {
|
|
|
|
|
/*
|
|
|
|
|
* In this case with vanishing Re(z), the result is simply -i/Im z
|
|
|
|
|
*/
|
|
|
|
|
final MathContext mc = new MathContext(z.im.precision());
|
|
|
|
|
final MathContext mc = SafeMathContext.newMathContext(z.im.precision());
|
|
|
|
|
return new BigComplex(BigDecimal.ZERO, BigDecimal.ONE.divide(z.im, mc).negate());
|
|
|
|
|
} else {
|
|
|
|
|
/*
|
|
|
|
@ -2791,9 +2791,9 @@ public class BigDecimalMath {
|
|
|
|
|
*/
|
|
|
|
|
BigDecimal R = addRound(z.re, divideRound(multiplyRound(z.im, z.im), z.re));
|
|
|
|
|
BigDecimal I = addRound(z.im, divideRound(multiplyRound(z.re, z.re), z.im));
|
|
|
|
|
MathContext mc = new MathContext(1 + R.precision());
|
|
|
|
|
MathContext mc = SafeMathContext.newMathContext(1 + R.precision());
|
|
|
|
|
R = BigDecimal.ONE.divide(R, mc);
|
|
|
|
|
mc = new MathContext(1 + I.precision());
|
|
|
|
|
mc = SafeMathContext.newMathContext(1 + I.precision());
|
|
|
|
|
I = BigDecimal.ONE.divide(I, mc);
|
|
|
|
|
return new BigComplex(R, I.negate());
|
|
|
|
|
}
|
|
|
|
@ -2827,7 +2827,7 @@ public class BigDecimalMath {
|
|
|
|
|
/*
|
|
|
|
|
* The estimation of the relative error in the result is |err(x)/x|
|
|
|
|
|
*/
|
|
|
|
|
final MathContext mc = new MathContext(x.precision());
|
|
|
|
|
final MathContext mc = SafeMathContext.newMathContext(x.precision());
|
|
|
|
|
return x.divide(new BigDecimal(n), mc);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
@ -2845,7 +2845,7 @@ public class BigDecimalMath {
|
|
|
|
|
/*
|
|
|
|
|
* The estimation of the relative error in the result is |err(x)/x|
|
|
|
|
|
*/
|
|
|
|
|
final MathContext mc = new MathContext(x.precision());
|
|
|
|
|
final MathContext mc = SafeMathContext.newMathContext(x.precision());
|
|
|
|
|
return x.divide(new BigDecimal(n), mc);
|
|
|
|
|
} /* divideRound */
|
|
|
|
|
|
|
|
|
@ -2863,7 +2863,7 @@ public class BigDecimalMath {
|
|
|
|
|
/*
|
|
|
|
|
* The estimation of the relative error in the result is |err(x)/x|
|
|
|
|
|
*/
|
|
|
|
|
final MathContext mc = new MathContext(x.precision());
|
|
|
|
|
final MathContext mc = SafeMathContext.newMathContext(x.precision());
|
|
|
|
|
return new BigDecimal(n).divide(x, mc);
|
|
|
|
|
} /* divideRound */
|
|
|
|
|
|
|
|
|
@ -2910,7 +2910,7 @@ public class BigDecimalMath {
|
|
|
|
|
/*
|
|
|
|
|
* The estimation of the relative error in the result is |err(x)/x|
|
|
|
|
|
*/
|
|
|
|
|
final MathContext mc = new MathContext(x.precision());
|
|
|
|
|
final MathContext mc = SafeMathContext.newMathContext(x.precision());
|
|
|
|
|
return new BigDecimal(n).divide(x, mc);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|