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Added Sine block

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Andrea Cavalli 2017-06-25 00:23:49 +02:00
parent b194f19092
commit 0277af9eca
13 changed files with 299 additions and 173 deletions
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194
src/main/java/org/nevec/rjm/BigDecimalMath.java
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@ -93,7 +93,7 @@ public class BigDecimalMath {
* Euler-Stieltjes as shown in Dilcher, Aequat Math 48 (1) (1994) * Euler-Stieltjes as shown in Dilcher, Aequat Math 48 (1) (1994)
* 55-85 * 55-85
*/ */
MathContext mcloc = new MathContext(2 + mc.getPrecision()); MathContext mcloc = SafeMathContext.newMathContext(2 + mc.getPrecision());
BigDecimal resul = BigDecimal.ONE; BigDecimal resul = BigDecimal.ONE;
resul = resul.add(log(2, mcloc)); resul = resul.add(log(2, mcloc));
resul = resul.subtract(log(3, mcloc)); resul = resul.subtract(log(3, mcloc));
@ -105,7 +105,7 @@ public class BigDecimalMath {
* Log(2) is 0.7 * Log(2) is 0.7
*/ */
final int kmax = (int) ((Math.log(eps / 0.7) - 2.) / 4.); final int kmax = (int) ((Math.log(eps / 0.7) - 2.) / 4.);
mcloc = new MathContext(1 + err2prec(1.2, eps / kmax)); mcloc = SafeMathContext.newMathContext(1 + err2prec(1.2, eps / kmax));
for (int n = 1;; n++) { for (int n = 1;; n++) {
/* /*
* zeta is close to 1. Division of zeta-1 through * zeta is close to 1. Division of zeta-1 through
@ -146,7 +146,7 @@ public class BigDecimalMath {
final BigDecimal half = new BigDecimal("2"); final BigDecimal half = new BigDecimal("2");
/* increase the local accuracy by 2 digits */ /* increase the local accuracy by 2 digits */
final MathContext locmc = new MathContext(mc.getPrecision() + 2, mc.getRoundingMode()); final MathContext locmc = SafeMathContext.newMathContext(mc.getPrecision() + 2, mc.getRoundingMode());
/* /*
* relative accuracy requested is 10^(-precision) * relative accuracy requested is 10^(-precision)
@ -242,7 +242,7 @@ public class BigDecimalMath {
* slightly larger than what is demanded by 'eps' below. * slightly larger than what is demanded by 'eps' below.
*/ */
final BigDecimal xhighpr = scalePrec(x, 2); final BigDecimal xhighpr = scalePrec(x, 2);
final MathContext mc = new MathContext(2 + x.precision()); final MathContext mc = SafeMathContext.newMathContext(2 + x.precision());
/* /*
* Relative accuracy of the result is eps. * Relative accuracy of the result is eps.
@ -257,14 +257,14 @@ public class BigDecimalMath {
*/ */
BigDecimal c = xhighpr.divide(s.pow(n - 1), mc); BigDecimal c = xhighpr.divide(s.pow(n - 1), mc);
c = s.subtract(c); c = s.subtract(c);
final MathContext locmc = new MathContext(c.precision()); final MathContext locmc = SafeMathContext.newMathContext(c.precision());
c = c.divide(nth, locmc); c = c.divide(nth, locmc);
s = s.subtract(c); s = s.subtract(c);
if (Math.abs(c.doubleValue() / s.doubleValue()) < eps) { if (Math.abs(c.doubleValue() / s.doubleValue()) < eps) {
break; break;
} }
} }
return s.round(new MathContext(err2prec(eps))); return s.round(SafeMathContext.newMathContext(err2prec(eps)));
} /* BigDecimalMath.root */ } /* BigDecimalMath.root */
/** /**
@ -291,7 +291,7 @@ public class BigDecimalMath {
* digits. * digits.
*/ */
final BigDecimal zerr = x.abs().multiply(x.ulp()).add(y.abs().multiply(y.ulp())); final BigDecimal zerr = x.abs().multiply(x.ulp()).add(y.abs().multiply(y.ulp()));
MathContext mc = new MathContext(2 + err2prec(z, zerr)); MathContext mc = SafeMathContext.newMathContext(2 + err2prec(z, zerr));
/* Pull square root */ /* Pull square root */
z = sqrt(z.round(mc)); z = sqrt(z.round(mc));
@ -300,7 +300,7 @@ public class BigDecimalMath {
* Final rounding. Absolute error in the square root is * Final rounding. Absolute error in the square root is
* (y*yerr+x*xerr)/z, where zerr holds 2*(x*xerr+y*yerr). * (y*yerr+x*xerr)/z, where zerr holds 2*(x*xerr+y*yerr).
*/ */
mc = new MathContext(err2prec(z.doubleValue(), 0.5 * zerr.doubleValue() / z.doubleValue())); mc = SafeMathContext.newMathContext(err2prec(z.doubleValue(), 0.5 * zerr.doubleValue() / z.doubleValue()));
return z.round(mc); return z.round(mc);
} /* BigDecimalMath.hypot */ } /* BigDecimalMath.hypot */
@ -330,7 +330,7 @@ public class BigDecimalMath {
* so this feature does not harm. * so this feature does not harm.
*/ */
final double zerr = x.doubleValue() * x.ulp().doubleValue(); final double zerr = x.doubleValue() * x.ulp().doubleValue();
MathContext mc = new MathContext(2 + err2prec(z.doubleValue(), zerr)); MathContext mc = SafeMathContext.newMathContext(2 + err2prec(z.doubleValue(), zerr));
/* Pull square root */ /* Pull square root */
z = sqrt(z.round(mc)); z = sqrt(z.round(mc));
@ -339,7 +339,7 @@ public class BigDecimalMath {
* Final rounding. Absolute error in the square root is x*xerr/z, where * Final rounding. Absolute error in the square root is x*xerr/z, where
* zerr holds 2*x*xerr. * zerr holds 2*x*xerr.
*/ */
mc = new MathContext(err2prec(z.doubleValue(), 0.5 * zerr / z.doubleValue())); mc = SafeMathContext.newMathContext(err2prec(z.doubleValue(), 0.5 * zerr / z.doubleValue()));
return z.round(mc); return z.round(mc);
} /* BigDecimalMath.hypot */ } /* BigDecimalMath.hypot */
@ -375,7 +375,7 @@ public class BigDecimalMath {
* errror in invx. * errror in invx.
* This is used to define the precision of the result. * This is used to define the precision of the result.
*/ */
final MathContext mc = new MathContext(invx.precision()); final MathContext mc = SafeMathContext.newMathContext(invx.precision());
return BigDecimal.ONE.divide(invx, mc); return BigDecimal.ONE.divide(invx, mc);
} else if (x.compareTo(BigDecimal.ZERO) == 0) { } else if (x.compareTo(BigDecimal.ZERO) == 0) {
/* /*
@ -420,7 +420,7 @@ public class BigDecimalMath {
* add noise beyond * add noise beyond
* what's already in x. * what's already in x.
*/ */
final MathContext mcTay = new MathContext(err2prec(1., xUlpDbl / TAYLOR_NTERM)); final MathContext mcTay = SafeMathContext.newMathContext(err2prec(1., xUlpDbl / TAYLOR_NTERM));
for (int i = 1; i <= TAYLOR_NTERM; i++) { for (int i = 1; i <= TAYLOR_NTERM; i++) {
ifac = ifac.multiply(new BigInteger("" + i)); ifac = ifac.multiply(new BigInteger("" + i));
xpowi = xpowi.multiply(x); xpowi = xpowi.multiply(x);
@ -435,7 +435,7 @@ public class BigDecimalMath {
* relative error * relative error
* in the result equals the absolute error in the argument. * in the result equals the absolute error in the argument.
*/ */
final MathContext mc = new MathContext(err2prec(xUlpDbl / 2.)); final MathContext mc = SafeMathContext.newMathContext(err2prec(xUlpDbl / 2.));
return resul.round(mc); return resul.round(mc);
} else { } else {
/* /*
@ -454,7 +454,7 @@ public class BigDecimalMath {
* binomial expansion). * binomial expansion).
* This looses one digit. * This looses one digit.
*/ */
final MathContext mc = new MathContext(expxby10.precision() - exSc); final MathContext mc = SafeMathContext.newMathContext(expxby10.precision() - exSc);
/* /*
* Rescaling the powers of 10 is done in chunks of a maximum of * Rescaling the powers of 10 is done in chunks of a maximum of
* 8 to avoid an invalid operation * 8 to avoid an invalid operation
@ -463,7 +463,7 @@ public class BigDecimalMath {
while (exSc > 0) { while (exSc > 0) {
int exsub = Math.min(8, exSc); int exsub = Math.min(8, exSc);
exSc -= exsub; exSc -= exsub;
final MathContext mctmp = new MathContext(expxby10.precision() - exsub + 2); final MathContext mctmp = SafeMathContext.newMathContext(expxby10.precision() - exsub + 2);
int pex = 1; int pex = 1;
while (exsub-- > 0) { while (exsub-- > 0) {
pex *= 10; pex *= 10;
@ -539,7 +539,7 @@ public class BigDecimalMath {
break; break;
} }
} }
final MathContext mc = new MathContext(err2prec(resul.doubleValue(), eps)); final MathContext mc = SafeMathContext.newMathContext(err2prec(resul.doubleValue(), eps));
return resul.round(mc); return resul.round(mc);
} else { } else {
final double xDbl = x.doubleValue(); final double xDbl = x.doubleValue();
@ -573,7 +573,7 @@ public class BigDecimalMath {
* in the result equals the relative error in the input, * in the result equals the relative error in the input,
* xUlpDbl/xDbl . * xUlpDbl/xDbl .
*/ */
final MathContext mc = new MathContext(err2prec(resul.doubleValue(), xUlpDbl / xDbl)); final MathContext mc = SafeMathContext.newMathContext(err2prec(resul.doubleValue(), xUlpDbl / xDbl));
return resul.round(mc); return resul.round(mc);
} }
} /* BigDecimalMath.log */ } /* BigDecimalMath.log */
@ -610,7 +610,7 @@ public class BigDecimalMath {
* S(2,-5,...). * S(2,-5,...).
*/ */
final int[] a = { 2, -5, -2, -7, -2, -5, 2, -3 }; final int[] a = { 2, -5, -2, -7, -2, -5, 2, -3 };
BigDecimal S = broadhurstBBP(2, 1, a, new MathContext(1 + mc.getPrecision())); BigDecimal S = broadhurstBBP(2, 1, a, SafeMathContext.newMathContext(1 + mc.getPrecision()));
S = S.multiply(new BigDecimal(8)); S = S.multiply(new BigDecimal(8));
S = sqrt(divideRound(S, 3)); S = sqrt(divideRound(S, 3));
return S.round(mc); return S.round(mc);
@ -625,7 +625,7 @@ public class BigDecimalMath {
* so k>= precision/1.87. * so k>= precision/1.87.
*/ */
final int kmax = (int) (mc.getPrecision() / 1.87); final int kmax = (int) (mc.getPrecision() / 1.87);
MathContext mcloc = new MathContext(mc.getPrecision() + 1 + (int) (Math.log10(kmax * 0.693 / 1.098))); MathContext mcloc = SafeMathContext.newMathContext(mc.getPrecision() + 1 + (int) (Math.log10(kmax * 0.693 / 1.098)));
BigDecimal log3 = multiplyRound(log(2, mcloc), 19); BigDecimal log3 = multiplyRound(log(2, mcloc), 19);
/* /*
@ -646,7 +646,7 @@ public class BigDecimalMath {
/* /*
* how many digits of tmp do we need in the sum? * how many digits of tmp do we need in the sum?
*/ */
mcloc = new MathContext(err2prec(tmp.doubleValue(), eps)); mcloc = SafeMathContext.newMathContext(err2prec(tmp.doubleValue(), eps));
final BigDecimal c = pk.divide(k).BigDecimalValue(mcloc); final BigDecimal c = pk.divide(k).BigDecimalValue(mcloc);
if (k % 2 != 0) { if (k % 2 != 0) {
log3 = log3.add(c); log3 = log3.add(c);
@ -667,7 +667,7 @@ public class BigDecimalMath {
* so k>= precision/1.33. * so k>= precision/1.33.
*/ */
final int kmax = (int) (mc.getPrecision() / 1.33); final int kmax = (int) (mc.getPrecision() / 1.33);
MathContext mcloc = new MathContext(mc.getPrecision() + 1 + (int) (Math.log10(kmax * 0.693 / 1.609))); MathContext mcloc = SafeMathContext.newMathContext(mc.getPrecision() + 1 + (int) (Math.log10(kmax * 0.693 / 1.609)));
BigDecimal log5 = multiplyRound(log(2, mcloc), 14); BigDecimal log5 = multiplyRound(log(2, mcloc), 14);
/* /*
@ -688,7 +688,7 @@ public class BigDecimalMath {
/* /*
* how many digits of tmp do we need in the sum? * how many digits of tmp do we need in the sum?
*/ */
mcloc = new MathContext(err2prec(tmp.doubleValue(), eps)); mcloc = SafeMathContext.newMathContext(err2prec(tmp.doubleValue(), eps));
final BigDecimal c = pk.divide(k).BigDecimalValue(mcloc); final BigDecimal c = pk.divide(k).BigDecimalValue(mcloc);
log5 = log5.subtract(c); log5 = log5.subtract(c);
pk = pk.multiply(r); pk = pk.multiply(r);
@ -705,7 +705,7 @@ public class BigDecimalMath {
* so k>= precision/0.903. * so k>= precision/0.903.
*/ */
final int kmax = (int) (mc.getPrecision() / 0.903); final int kmax = (int) (mc.getPrecision() / 0.903);
MathContext mcloc = new MathContext(mc.getPrecision() + 1 + (int) (Math.log10(kmax * 3 * 0.693 / 1.098))); MathContext mcloc = SafeMathContext.newMathContext(mc.getPrecision() + 1 + (int) (Math.log10(kmax * 3 * 0.693 / 1.098)));
BigDecimal log7 = multiplyRound(log(2, mcloc), 3); BigDecimal log7 = multiplyRound(log(2, mcloc), 3);
/* /*
@ -723,7 +723,7 @@ public class BigDecimalMath {
/* /*
* how many digits of tmp do we need in the sum? * how many digits of tmp do we need in the sum?
*/ */
mcloc = new MathContext(err2prec(tmp.doubleValue(), eps)); mcloc = SafeMathContext.newMathContext(err2prec(tmp.doubleValue(), eps));
final BigDecimal c = pk.divide(k).BigDecimalValue(mcloc); final BigDecimal c = pk.divide(k).BigDecimalValue(mcloc);
log7 = log7.subtract(c); log7 = log7.subtract(c);
pk = pk.multiply(r); pk = pk.multiply(r);
@ -753,7 +753,7 @@ public class BigDecimalMath {
* Convert this absolute requirement of error in n to a relative * Convert this absolute requirement of error in n to a relative
* error in n * error in n
*/ */
final MathContext mcloc = new MathContext(1 + err2prec(n, eps)); final MathContext mcloc = SafeMathContext.newMathContext(1 + err2prec(n, eps));
/* /*
* Padd n with a number of zeros to trigger the required accuracy in * Padd n with a number of zeros to trigger the required accuracy in
* the standard signature method * the standard signature method
@ -796,7 +796,7 @@ public class BigDecimalMath {
* in r, given that * in r, given that
* epsr/r is also the relative precision of r. Add one safety digit. * epsr/r is also the relative precision of r. Add one safety digit.
*/ */
final MathContext mcloc = new MathContext(1 + err2prec(eps)); final MathContext mcloc = SafeMathContext.newMathContext(1 + err2prec(eps));
final BigDecimal resul = log(r.BigDecimalValue(mcloc)); final BigDecimal resul = log(r.BigDecimalValue(mcloc));
@ -834,7 +834,7 @@ public class BigDecimalMath {
* |log(x)*err(y)|+|y*err(x)/x| * |log(x)*err(y)|+|y*err(x)/x|
*/ */
final double errR = Math.abs(logx.doubleValue() * y.ulp().doubleValue() / 2.) + Math.abs(y.doubleValue() * x.ulp().doubleValue() / 2. / x.doubleValue()); final double errR = Math.abs(logx.doubleValue() * y.ulp().doubleValue() / 2.) + Math.abs(y.doubleValue() * x.ulp().doubleValue() / 2. / x.doubleValue());
final MathContext mcR = new MathContext(err2prec(1.0, errR)); final MathContext mcR = SafeMathContext.newMathContext(err2prec(1.0, errR));
return resul.round(mcR); return resul.round(mcR);
} }
} /* BigDecimalMath.pow */ } /* BigDecimalMath.pow */
@ -867,7 +867,7 @@ public class BigDecimalMath {
* Since the standard BigDecimal.pow can only handle positive n, we * Since the standard BigDecimal.pow can only handle positive n, we
* split the algorithm. * split the algorithm.
*/ */
final MathContext mc = new MathContext(x.precision() - (int) Math.log10((Math.abs(n)))); final MathContext mc = SafeMathContext.newMathContext(x.precision() - (int) Math.log10((Math.abs(n))));
if (n > 0) { if (n > 0) {
return x.pow(n, mc); return x.pow(n, mc);
} else { } else {
@ -991,7 +991,7 @@ public class BigDecimalMath {
*/ */
eps = nu.divide(de, MathContext.DECIMAL32); eps = nu.divide(de, MathContext.DECIMAL32);
} else { } else {
final MathContext mc = new MathContext(precDiv); final MathContext mc = SafeMathContext.newMathContext(precDiv);
eps = nu.divide(de, mc); eps = nu.divide(de, mc);
} }
@ -1006,7 +1006,7 @@ public class BigDecimalMath {
* delete the bits of extra precision kept in this * delete the bits of extra precision kept in this
* working copy. * working copy.
*/ */
final MathContext mc = new MathContext(err2prec(reserr.doubleValue())); final MathContext mc = SafeMathContext.newMathContext(err2prec(reserr.doubleValue()));
return res.round(mc); return res.round(mc);
} }
} }
@ -1019,7 +1019,7 @@ public class BigDecimalMath {
* Delta(q)/q << Delta(x)/x/log(x) . * Delta(q)/q << Delta(x)/x/log(x) .
*/ */
final int precq = 3 + err2prec((x.ulp().divide(x, MathContext.DECIMAL64)).doubleValue() / Math.log(x.doubleValue())); final int precq = 3 + err2prec((x.ulp().divide(x, MathContext.DECIMAL64)).doubleValue() / Math.log(x.doubleValue()));
final MathContext mc = new MathContext(precq); final MathContext mc = SafeMathContext.newMathContext(precq);
/* /*
* Perform the actual calculation as exponentiation of two * Perform the actual calculation as exponentiation of two
@ -1051,9 +1051,9 @@ public class BigDecimalMath {
*/ */
final BigDecimal res = mod2pi(x); final BigDecimal res = mod2pi(x);
final double errpi = 0.5 * Math.abs(x.ulp().doubleValue()); final double errpi = 0.5 * Math.abs(x.ulp().doubleValue());
MathContext mc = new MathContext(2 + err2prec(3.14159, errpi)); MathContext mc = SafeMathContext.newMathContext(2 + err2prec(3.14159, errpi));
final BigDecimal p = pi(mc); final BigDecimal p = pi(mc);
mc = new MathContext(x.precision()); mc = SafeMathContext.newMathContext(x.precision());
if (res.compareTo(p) > 0) { if (res.compareTo(p) > 0) {
/* /*
* pi<x<=2pi: sin(x)= - sin(x-pi) * pi<x<=2pi: sin(x)= - sin(x-pi)
@ -1102,7 +1102,7 @@ public class BigDecimalMath {
* 2k*(-log10(x)) > x.precision; 2k*log10(1/x) > x.precision * 2k*(-log10(x)) > x.precision; 2k*log10(1/x) > x.precision
*/ */
final int k = (int) (res.precision() / Math.log10(1.0 / res.doubleValue())) / 2; final int k = (int) (res.precision() / Math.log10(1.0 / res.doubleValue())) / 2;
final MathContext mcTay = new MathContext(err2prec(res.doubleValue(), xUlpDbl / k)); final MathContext mcTay = SafeMathContext.newMathContext(err2prec(res.doubleValue(), xUlpDbl / k));
for (int i = 1;; i++) { for (int i = 1;; i++) {
/* /*
* TBD: at which precision will 2*i or 2*i+1 overflow? * TBD: at which precision will 2*i or 2*i+1 overflow?
@ -1119,7 +1119,7 @@ public class BigDecimalMath {
/* /*
* The error in the result is set by the error in x itself. * The error in the result is set by the error in x itself.
*/ */
mc = new MathContext(res.precision()); mc = SafeMathContext.newMathContext(res.precision());
return resul.round(mc); return resul.round(mc);
} }
} }
@ -1146,9 +1146,9 @@ public class BigDecimalMath {
*/ */
final BigDecimal res = mod2pi(x); final BigDecimal res = mod2pi(x);
final double errpi = 0.5 * Math.abs(x.ulp().doubleValue()); final double errpi = 0.5 * Math.abs(x.ulp().doubleValue());
MathContext mc = new MathContext(2 + err2prec(3.14159, errpi)); MathContext mc = SafeMathContext.newMathContext(2 + err2prec(3.14159, errpi));
final BigDecimal p = pi(mc); final BigDecimal p = pi(mc);
mc = new MathContext(x.precision()); mc = SafeMathContext.newMathContext(x.precision());
if (res.compareTo(p) > 0) { if (res.compareTo(p) > 0) {
/* /*
* pi<x<=2pi: cos(x)= - cos(x-pi) * pi<x<=2pi: cos(x)= - cos(x-pi)
@ -1198,7 +1198,7 @@ public class BigDecimalMath {
* x^(2k) < xUlpDbl; (2k)*log(x) < log(xUlpDbl); * x^(2k) < xUlpDbl; (2k)*log(x) < log(xUlpDbl);
*/ */
final int k = (int) (Math.log(xUlpDbl) / Math.log(res.doubleValue())) / 2; final int k = (int) (Math.log(xUlpDbl) / Math.log(res.doubleValue())) / 2;
final MathContext mcTay = new MathContext(err2prec(1., xUlpDbl / k)); final MathContext mcTay = SafeMathContext.newMathContext(err2prec(1., xUlpDbl / k));
for (int i = 1;; i++) { for (int i = 1;; i++) {
/* /*
* TBD: at which precision will 2*i-1 or 2*i overflow? * TBD: at which precision will 2*i-1 or 2*i overflow?
@ -1216,7 +1216,7 @@ public class BigDecimalMath {
* The error in the result is governed by the error in x * The error in the result is governed by the error in x
* itself. * itself.
*/ */
mc = new MathContext(err2prec(resul.doubleValue(), xUlpDbl)); mc = SafeMathContext.newMathContext(err2prec(resul.doubleValue(), xUlpDbl));
return resul.round(mc); return resul.round(mc);
} }
} }
@ -1252,7 +1252,7 @@ public class BigDecimalMath {
if (xDbl > 0.8) { if (xDbl > 0.8) {
/* tan(x) = 1/cot(x) */ /* tan(x) = 1/cot(x) */
final BigDecimal co = 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); return BigDecimal.ONE.divide(co, mc);
} else { } else {
final BigDecimal xhighpr = scalePrec(res, 2); final BigDecimal xhighpr = scalePrec(res, 2);
@ -1282,7 +1282,7 @@ public class BigDecimalMath {
break; break;
} }
} }
final MathContext mc = new MathContext(err2prec(resul.doubleValue(), eps)); final MathContext mc = SafeMathContext.newMathContext(err2prec(resul.doubleValue(), eps));
return resul.round(mc); return resul.round(mc);
} }
} }
@ -1318,7 +1318,7 @@ public class BigDecimalMath {
final BigDecimal xhighpr = scalePrec(res, 2); final BigDecimal xhighpr = scalePrec(res, 2);
final BigDecimal xhighprSq = multiplyRound(xhighpr, xhighpr); 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); BigDecimal resul = BigDecimal.ONE.divide(xhighpr, mc);
/* x^(2i-1) */ /* x^(2i-1) */
@ -1348,7 +1348,7 @@ public class BigDecimalMath {
fourn = fourn.shiftLeft(2); fourn = fourn.shiftLeft(2);
xpowi = multiplyRound(xpowi, xhighprSq); xpowi = multiplyRound(xpowi, xhighprSq);
} }
mc = new MathContext(err2prec(resul.doubleValue(), eps)); mc = SafeMathContext.newMathContext(err2prec(resul.doubleValue(), eps));
return resul.round(mc); return resul.round(mc);
} }
} /* BigDecimalMath.cot */ } /* BigDecimalMath.cot */
@ -1371,7 +1371,7 @@ public class BigDecimalMath {
* arcsin(1) = pi/2 * arcsin(1) = pi/2
*/ */
final double errpi = Math.sqrt(x.ulp().doubleValue()); 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)); return pi(mc).divide(new BigDecimal(2));
} else if (x.compareTo(BigDecimal.ZERO) < 0) { } else if (x.compareTo(BigDecimal.ZERO) < 0) {
return asin(x.negate()).negate(); return asin(x.negate()).negate();
@ -1417,10 +1417,10 @@ public class BigDecimalMath {
xpowi = sqrt(xhighpr.multiply(new BigDecimal(2))); xpowi = sqrt(xhighpr.multiply(new BigDecimal(2)));
resul = multiplyRound(xpowi, resul); 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)); 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); return pihalf.subtract(resul, mc);
} else { } else {
/* /*
@ -1453,7 +1453,7 @@ public class BigDecimalMath {
break; break;
} }
} }
final MathContext mc = new MathContext(err2prec(resul.doubleValue(), eps)); final MathContext mc = SafeMathContext.newMathContext(err2prec(resul.doubleValue(), eps));
return resul.round(mc); return resul.round(mc);
} }
} /* BigDecimalMath.asin */ } /* BigDecimalMath.asin */
@ -1475,7 +1475,7 @@ public class BigDecimalMath {
BigDecimal resul = asin(xhighpr); BigDecimal resul = asin(xhighpr);
double eps = resul.ulp().doubleValue() / 2.; 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)); final BigDecimal pihalf = pi(mc).divide(new BigDecimal(2));
resul = pihalf.subtract(resul); resul = pihalf.subtract(resul);
@ -1486,7 +1486,7 @@ public class BigDecimalMath {
final double xUlpDbl = x.ulp().doubleValue() / 2.; final double xUlpDbl = x.ulp().doubleValue() / 2.;
eps = xUlpDbl / 2. / Math.sqrt(1. - Math.pow(xDbl, 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); return resul.round(mc);
} /* BigDecimalMath.acos */ } /* BigDecimalMath.acos */
@ -1524,7 +1524,7 @@ public class BigDecimalMath {
* of the ulp. * of the ulp.
*/ */
final double eps = x.ulp().doubleValue() / (2.0 * Math.hypot(1.0, x.doubleValue())); 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); return resul.round(mc);
} else if (x.doubleValue() < 0.71) { } else if (x.doubleValue() < 0.71) {
/* Taylor expansion around x=0; Abramowitz-Stegun 4.4.42 */ /* Taylor expansion around x=0; Abramowitz-Stegun 4.4.42 */
@ -1552,7 +1552,7 @@ public class BigDecimalMath {
break; break;
} }
} }
final MathContext mc = new MathContext(err2prec(resul.doubleValue(), eps)); final MathContext mc = SafeMathContext.newMathContext(err2prec(resul.doubleValue(), eps));
return resul.round(mc); return resul.round(mc);
} else { } else {
/* Taylor expansion around x=infinity; Abramowitz-Stegun 4.4.42 */ /* 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 * start with the term pi/2; gather its precision relative to the
* expected result * 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); final BigDecimal onepi = pi(mc);
BigDecimal resul = onepi.divide(new BigDecimal(2)); BigDecimal resul = onepi.divide(new BigDecimal(2));
@ -1586,7 +1586,7 @@ public class BigDecimalMath {
} }
xpowi = multiplyRound(xpowi, xhighprSq); xpowi = multiplyRound(xpowi, xhighprSq);
} }
mc = new MathContext(err2prec(resul.doubleValue(), eps)); mc = SafeMathContext.newMathContext(err2prec(resul.doubleValue(), eps));
return resul.round(mc); return resul.round(mc);
} }
} /* BigDecimalMath.atan */ } /* BigDecimalMath.atan */
@ -1644,7 +1644,7 @@ public class BigDecimalMath {
* the absolute value will give a safe relative error estimate * the absolute value will give a safe relative error estimate
* for the indivdual terms * 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++) { for (int i = 1;; i++) {
/* /*
* TBD: at which precision will 2*i-1 or 2*i overflow? * 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. * 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); return resul.round(mc);
} }
} }
@ -1698,7 +1698,7 @@ public class BigDecimalMath {
* coth(x)*errx = errx/tanh(x) * coth(x)*errx = errx/tanh(x)
*/ */
final double eps = Math.tanh(x.doubleValue()); 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); return resul.round(mc);
} else { } else {
final BigDecimal xhighpr = scalePrec(x, 2); final BigDecimal xhighpr = scalePrec(x, 2);
@ -1727,7 +1727,7 @@ public class BigDecimalMath {
* 2k*(-log10(x)) > x.precision; 2k*log10(1/x) > x.precision * 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 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++) { for (int i = 1;; i++) {
/* /*
* TBD: at which precision will 2*i or 2*i+1 overflow? * 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. * 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); return resul.round(mc);
} }
} }
@ -1776,7 +1776,7 @@ public class BigDecimalMath {
* The error in tanh x is err(x)/cosh^2(x). * 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 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); return BigDecimal.ONE.subtract(exp2x).divide(BigDecimal.ONE.add(exp2x), mc);
} }
} /* BigDecimalMath.tanh */ } /* BigDecimalMath.tanh */
@ -1806,7 +1806,7 @@ public class BigDecimalMath {
*/ */
final double xDbl = x.doubleValue(); final double xDbl = x.doubleValue();
final double eps = 0.5 * x.ulp().doubleValue() / Math.hypot(1., xDbl); 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); return logx.round(mc);
} }
} /* BigDecimalMath.asinh */ } /* BigDecimalMath.asinh */
@ -1838,7 +1838,7 @@ public class BigDecimalMath {
*/ */
final double xDbl = x.doubleValue(); final double xDbl = x.doubleValue();
final double eps = 0.5 * x.ulp().doubleValue() / Math.sqrt(xDbl * xDbl - 1.); 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); return logx.round(mc);
} }
} /* BigDecimalMath.acosh */ } /* BigDecimalMath.acosh */
@ -1876,7 +1876,7 @@ public class BigDecimalMath {
* add intermediately 2 digits to the partial sum accumulation * add intermediately 2 digits to the partial sum accumulation
*/ */
z = scalePrec(z, 2); 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, * measure of the absolute error is the relative error in the first,
@ -1901,7 +1901,7 @@ public class BigDecimalMath {
* absolute error in z) * absolute error in z)
*/ */
BigDecimal c = divideRound(z.pow(n, mcloc), n); 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); c = c.round(m);
/* /*
@ -1917,9 +1917,9 @@ public class BigDecimalMath {
* of the order of 1. * of the order of 1.
*/ */
if (eps / 100. / c.doubleValue() < 0.01) { if (eps / 100. / c.doubleValue() < 0.01) {
m = new MathContext(err2prec(eps / 100. / c.doubleValue())); m = SafeMathContext.newMathContext(err2prec(eps / 100. / c.doubleValue()));
} else { } else {
m = new MathContext(2); m = SafeMathContext.newMathContext(2);
} }
/* zeta(n) -1 */ /* zeta(n) -1 */
final BigDecimal zetm1 = zeta(n, m).subtract(BigDecimal.ONE); final BigDecimal zetm1 = zeta(n, m).subtract(BigDecimal.ONE);
@ -1946,7 +1946,7 @@ public class BigDecimalMath {
*/ */
final double zdbl = z.doubleValue(); final double zdbl = z.doubleValue();
eps = psi(zdbl) * x.ulp().doubleValue() / 2.; eps = psi(zdbl) * x.ulp().doubleValue() / 2.;
mcloc = new MathContext(err2prec(eps)); mcloc = SafeMathContext.newMathContext(err2prec(eps));
return exp(resul).round(mcloc); return exp(resul).round(mcloc);
} }
} /* BigDecimalMath.gamma */ } /* BigDecimalMath.gamma */
@ -2003,7 +2003,7 @@ public class BigDecimalMath {
final double qdbl = q.doubleValue(); final double qdbl = q.doubleValue();
final double deltx = 5. * Math.pow(10., -mc.getPrecision()) / psi(qdbl); 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); final BigDecimal x = q.BigDecimalValue(mcx);
/* forward calculation to the general floating point case */ /* forward calculation to the general floating point case */
@ -2047,10 +2047,10 @@ public class BigDecimalMath {
for (int i = 1; i < n; i++) { for (int i = 1; i < n; i++) {
eps += 0.5 * xUlpDbl / Math.abs(xDbl + i); eps += 0.5 * xUlpDbl / Math.abs(xDbl + i);
resul = resul.multiply(xhighpr.add(new BigDecimal(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); resul = resul.round(mcloc);
} }
return resul.round(new MathContext(err2prec(eps))); return resul.round(SafeMathContext.newMathContext(err2prec(eps)));
} }
} /* BigDecimalMath.pochhammer */ } /* BigDecimalMath.pochhammer */
@ -2084,7 +2084,7 @@ public class BigDecimalMath {
} else { } else {
err2pi = 0.5 * Math.abs(x.ulp().doubleValue()); 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)); 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 * The actual precision is set by the input value, its absolute value of
* x.ulp()/2. * 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); return res.round(mc);
} /* mod2pi */ } /* mod2pi */
@ -2135,7 +2135,7 @@ public class BigDecimalMath {
} else { } else {
errpi = 0.5 * Math.abs(x.ulp().doubleValue()); 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 onepi = pi(mc);
final BigDecimal pihalf = onepi.divide(new BigDecimal(2)); 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 * The actual precision is set by the input value, its absolute value of
* x.ulp()/2. * 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); return res.round(mc);
} /* modpi */ } /* modpi */
@ -2195,7 +2195,7 @@ public class BigDecimalMath {
* Need one more digit in pi if n=10, two digits if n=100 etc, and * Need one more digit in pi if n=10, two digits if n=100 etc, and
* add one extra digit. * 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); final BigDecimal piton = pi(mcpi).pow(n, mc);
return multiplyRound(piton, b); return multiplyRound(piton, b);
} else if (n == 3) { } else if (n == 3) {
@ -2225,9 +2225,9 @@ public class BigDecimalMath {
final int[] a51 = { 31, -1614, -31, -6212, -31, -1614, 31, 74552 }; final int[] a51 = { 31, -1614, -31, -6212, -31, -1614, 31, 74552 };
final int[] a53 = { 173, 284, -173, -457, -173, 284, 173, -111 }; final int[] a53 = { 173, 284, -173, -457, -173, 284, 173, -111 };
final int[] a55 = { 1, 0, -1, -1, -1, 0, 1, 1 }; final int[] a55 = { 1, 0, -1, -1, -1, 0, 1, 1 };
BigDecimal S51 = broadhurstBBP(5, 1, a51, new MathContext(2 + mc.getPrecision())); BigDecimal S51 = broadhurstBBP(5, 1, a51, SafeMathContext.newMathContext(2 + mc.getPrecision()));
BigDecimal S53 = broadhurstBBP(5, 3, a53, new MathContext(2 + mc.getPrecision())); BigDecimal S53 = broadhurstBBP(5, 3, a53, SafeMathContext.newMathContext(2 + mc.getPrecision()));
BigDecimal S55 = broadhurstBBP(5, 5, a55, new MathContext(1 + mc.getPrecision())); BigDecimal S55 = broadhurstBBP(5, 5, a55, SafeMathContext.newMathContext(1 + mc.getPrecision()));
S51 = S51.multiply(new BigDecimal(18432)); S51 = S51.multiply(new BigDecimal(18432));
S53 = S53.multiply(new BigDecimal(14336)); S53 = S53.multiply(new BigDecimal(14336));
S55 = S55.multiply(new BigDecimal(1511424)); S55 = S55.multiply(new BigDecimal(1511424));
@ -2258,7 +2258,7 @@ public class BigDecimalMath {
* and the precision * and the precision
* requested for 2*pi is in absolute terms adjusted. * 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)); BigDecimal ftrm = pi(mcloc).multiply(new BigDecimal(2));
ftrm = ftrm.pow(n); ftrm = ftrm.pow(n);
ftrm = multiplyRound(ftrm, betsum.BigDecimalValue(mcloc)); ftrm = multiplyRound(ftrm, betsum.BigDecimalValue(mcloc));
@ -2286,7 +2286,7 @@ public class BigDecimalMath {
* The absolute error is * The absolute error is
* 4*exp(2pi)*err(pi)/(exp(2pi)-1)^2=0.0075*err(pi) * 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))); exp2p = exp(exp2p.multiply(new BigDecimal(2)));
BigDecimal c = exp2p.subtract(BigDecimal.ONE); BigDecimal c = exp2p.subtract(BigDecimal.ONE);
exps = divideRound(1, c); 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 * The absolute error is 0.017*err(pi) at k=9, 0.013*err(pi) at
* k=13, 0.012 at k=17 * 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)); twop = twop.multiply(new BigDecimal(2));
final BigDecimal exp2p = exp(twop); final BigDecimal exp2p = exp(twop);
BigDecimal c = exp2p.subtract(BigDecimal.ONE); BigDecimal c = exp2p.subtract(BigDecimal.ONE);
@ -2378,7 +2378,7 @@ public class BigDecimalMath {
* in relative units is higher, because zeta is around 1. * in relative units is higher, because zeta is around 1.
*/ */
final double eps = 1.e-18 * Math.pow(2., (-n)); 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(); return zeta(n, mc).subtract(BigDecimal.ONE).doubleValue();
} }
} /* zeta */ } /* zeta */
@ -2506,7 +2506,7 @@ public class BigDecimalMath {
if (Math.abs(r.doubleValue()) < eps) { if (Math.abs(r.doubleValue()) < eps) {
break; 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)); res = res.add(r.BigDecimalValue(mcloc));
} }
return res.round(mc); return res.round(mc);
@ -2547,7 +2547,7 @@ public class BigDecimalMath {
if (err2prec < 0) { if (err2prec < 0) {
err2prec = 0; err2prec = 0;
} }
final MathContext mc = new MathContext(err2prec); final MathContext mc = SafeMathContext.newMathContext(err2prec);
return resul.round(mc); return resul.round(mc);
} /* addRound */ } /* addRound */
@ -2599,7 +2599,7 @@ public class BigDecimalMath {
* |err(y)|+|err(x)| * |err(y)|+|err(x)|
*/ */
final double errR = Math.abs(y.ulp().doubleValue() / 2.) + Math.abs(x.ulp().doubleValue() / 2.); 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); return resul.round(mc);
} /* subtractRound */ } /* subtractRound */
@ -2636,7 +2636,7 @@ public class BigDecimalMath {
* relative * relative
* errors |err(y)/y|+|err(x)/x| * 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); return resul.round(mc);
} /* multiplyRound */ } /* multiplyRound */
@ -2689,7 +2689,7 @@ public class BigDecimalMath {
/* /*
* Convert the rational value with two digits of extra precision * 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); 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)| * 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); return resul.round(mc);
} }
@ -2734,7 +2734,7 @@ public class BigDecimalMath {
/* /*
* The estimation of the absolute error in the result is |n*err(x)| * 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); return resul.round(mc);
} }
@ -2753,7 +2753,7 @@ public class BigDecimalMath {
* The estimation of the relative error in the result is * The estimation of the relative error in the result is
* |err(y)/y|+|err(x)/x| * |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); final BigDecimal resul = x.divide(y, mc);
/* /*
* If x and y are precise integer values that may have common factors, * 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. * 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)); return new BigComplex(BigDecimal.ONE.divide(z.re, mc));
} else if (z.re.compareTo(BigDecimal.ZERO) == 0) { } else if (z.re.compareTo(BigDecimal.ZERO) == 0) {
/* /*
* In this case with vanishing Re(z), the result is simply -i/Im z * 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()); return new BigComplex(BigDecimal.ZERO, BigDecimal.ONE.divide(z.im, mc).negate());
} else { } else {
/* /*
@ -2791,9 +2791,9 @@ public class BigDecimalMath {
*/ */
BigDecimal R = addRound(z.re, divideRound(multiplyRound(z.im, z.im), z.re)); 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)); 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); R = BigDecimal.ONE.divide(R, mc);
mc = new MathContext(1 + I.precision()); mc = SafeMathContext.newMathContext(1 + I.precision());
I = BigDecimal.ONE.divide(I, mc); I = BigDecimal.ONE.divide(I, mc);
return new BigComplex(R, I.negate()); 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| * 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); 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| * 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); return x.divide(new BigDecimal(n), mc);
} /* divideRound */ } /* divideRound */
@ -2863,7 +2863,7 @@ public class BigDecimalMath {
/* /*
* The estimation of the relative error in the result is |err(x)/x| * 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); return new BigDecimal(n).divide(x, mc);
} /* divideRound */ } /* divideRound */
@ -2910,7 +2910,7 @@ public class BigDecimalMath {
/* /*
* The estimation of the relative error in the result is |err(x)/x| * 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); return new BigDecimal(n).divide(x, mc);
} }

26
src/main/java/org/nevec/rjm/SafeMathContext.java Normal file
View File

@ -0,0 +1,26 @@
package org.nevec.rjm;
import java.math.MathContext;
import java.math.RoundingMode;
import org.warp.picalculator.Utils;
public final class SafeMathContext {
public static MathContext newMathContext(int precision) {
if (precision <= 0) {
Utils.out.print(Utils.OUTPUTLEVEL_DEBUG_MIN, "Warning! MathContext precision is <= 0 ("+precision+")");
precision = 1;
}
return new MathContext(precision);
}
public static MathContext newMathContext(int precision, RoundingMode roundingMode) {
if (precision <= 0) {
Utils.out.print(Utils.OUTPUTLEVEL_DEBUG_MIN, "Warning! MathContext precision is <= 0 ("+precision+")");
precision = 1;
}
return new MathContext(precision, roundingMode);
}
}

74
src/main/java/org/warp/picalculator/gui/expression/blocks/BlockParenthesis.java
View File

@ -9,79 +9,9 @@ import org.warp.picalculator.math.MathContext;
import org.warp.picalculator.math.parser.features.FeatureParenthesis; import org.warp.picalculator.math.parser.features.FeatureParenthesis;
import org.warp.picalculator.math.parser.features.interfaces.Feature; import org.warp.picalculator.math.parser.features.interfaces.Feature;
public class BlockParenthesis extends Block { public class BlockParenthesis extends BlockParenthesisAbstract {
private final BlockContainer containerNumber;
private int chw;
private int chh;
public BlockParenthesis() { public BlockParenthesis() {
containerNumber = new BlockContainer(false); super();
recomputeDimensions();
}
@Override
public void draw(GraphicEngine ge, Renderer r, int x, int y, Caret caret) {
BlockContainer.getDefaultFont(small).use(ge);
r.glColor(BlockContainer.getDefaultColor());
r.glDrawCharLeft(x, y, '╭');
r.glDrawCharLeft(x, y+height-chh, '╰');
r.glFillColor(x+3, y+6, 2, height-6*2);
r.glFillColor(x+width-5, y+6, 2, height-6*2);
r.glDrawCharLeft(x+width-chw, y, '╮');
r.glDrawCharLeft(x+width-chw, y+height-chh, '╯');
containerNumber.draw(ge, r, x+chw, y, caret);
}
@Override
public boolean putBlock(Caret caret, Block newBlock) {
boolean added = false;
added = added | containerNumber.putBlock(caret, newBlock);
if (added) {
recomputeDimensions();
}
return added;
}
@Override
public boolean delBlock(Caret caret) {
boolean removed = false;
removed = removed | containerNumber.delBlock(caret);
if (removed) {
recomputeDimensions();
}
return removed;
}
@Override
public Block getBlock(Caret caret) {
return containerNumber.getBlock(caret);
}
@Override
public void recomputeDimensions() {
chw = BlockContainer.getDefaultCharWidth(small);
chh = BlockContainer.getDefaultCharHeight(small);
width = containerNumber.getWidth() + chw * 2 + 3;
height = containerNumber.getHeight();
line = containerNumber.getLine();
}
@Override
public void setSmall(boolean small) {
this.small = small;
containerNumber.setSmall(small);
recomputeDimensions();
}
public BlockContainer getNumberContainer() {
return containerNumber;
}
@Override
public int computeCaretMaxBound() {
return containerNumber.computeCaretMaxBound();
} }
@Override @Override

107
src/main/java/org/warp/picalculator/gui/expression/blocks/BlockParenthesisAbstract.java Normal file
View File

@ -0,0 +1,107 @@
package org.warp.picalculator.gui.expression.blocks;
import org.warp.picalculator.Error;
import org.warp.picalculator.gui.expression.Caret;
import org.warp.picalculator.gui.graphicengine.GraphicEngine;
import org.warp.picalculator.gui.graphicengine.Renderer;
import org.warp.picalculator.math.Function;
import org.warp.picalculator.math.MathContext;
import org.warp.picalculator.math.parser.features.FeatureParenthesis;
import org.warp.picalculator.math.parser.features.interfaces.Feature;
public abstract class BlockParenthesisAbstract extends Block {
private final BlockContainer containerNumber;
private final String prefix;
private int prw;
private int chw;
private int chh;
protected BlockParenthesisAbstract(String prefix) {
containerNumber = new BlockContainer(false);
this.prefix = prefix;
recomputeDimensions();
}
public BlockParenthesisAbstract() {
containerNumber = new BlockContainer(false);
this.prefix = null;
recomputeDimensions();
}
@Override
public void draw(GraphicEngine ge, Renderer r, int x, int y, Caret caret) {
BlockContainer.getDefaultFont(small).use(ge);
r.glColor(BlockContainer.getDefaultColor());
if (prefix != null) {
r.glDrawStringLeft(x+1, y+line-chh/2, prefix);
}
r.glDrawCharLeft(x+prw, y, '╭');
r.glDrawCharLeft(x+prw, y+height-chh, '╰');
r.glFillColor(x+prw+3, y+6, 2, height-6*2);
r.glFillColor(x+width-5, y+6, 2, height-6*2);
r.glDrawCharLeft(x+width-chw, y, '╮');
r.glDrawCharLeft(x+width-chw, y+height-chh, '╯');
containerNumber.draw(ge, r, x+prw+chw, y, caret);
}
@Override
public boolean putBlock(Caret caret, Block newBlock) {
boolean added = false;
added = added | containerNumber.putBlock(caret, newBlock);
if (added) {
recomputeDimensions();
}
return added;
}
@Override
public boolean delBlock(Caret caret) {
boolean removed = false;
removed = removed | containerNumber.delBlock(caret);
if (removed) {
recomputeDimensions();
}
return removed;
}
@Override
public Block getBlock(Caret caret) {
return containerNumber.getBlock(caret);
}
@Override
public void recomputeDimensions() {
if (prefix == null) {
prw=0;
} else {
prw = 1+BlockContainer.getDefaultCharWidth(small)*prefix.length()+2;
}
chw = BlockContainer.getDefaultCharWidth(small);
chh = BlockContainer.getDefaultCharHeight(small);
width = prw + chw + containerNumber.getWidth() + chw + 3;
height = containerNumber.getHeight();
line = containerNumber.getLine();
}
@Override
public void setSmall(boolean small) {
this.small = small;
containerNumber.setSmall(small);
recomputeDimensions();
}
public BlockContainer getNumberContainer() {
return containerNumber;
}
@Override
public int computeCaretMaxBound() {
return containerNumber.computeCaretMaxBound();
}
public abstract Feature toFeature(MathContext context) throws Error;
}

20
src/main/java/org/warp/picalculator/gui/expression/blocks/BlockSine.java Normal file
View File

@ -0,0 +1,20 @@
package org.warp.picalculator.gui.expression.blocks;
import org.warp.picalculator.Error;
import org.warp.picalculator.math.Function;
import org.warp.picalculator.math.MathContext;
import org.warp.picalculator.math.parser.features.FeatureParenthesis;
import org.warp.picalculator.math.parser.features.FeatureSine;
import org.warp.picalculator.math.parser.features.interfaces.Feature;
public class BlockSine extends BlockParenthesisAbstract {
public BlockSine() {
super("SIN");
}
@Override
public Feature toFeature(MathContext context) throws Error {
final Function cont = getNumberContainer().toFunction(context);
return new FeatureSine(cont);
}
}

2
src/main/java/org/warp/picalculator/gui/expression/containers/InlineInputContainer.java
View File

@ -31,6 +31,6 @@ public class InlineInputContainer extends InputContainer {
@Override @Override
public Block parseChar(char c) { public Block parseChar(char c) {
return new BlockChar(MathematicalSymbols.DIVISION); return new BlockChar(c);
} }
} }

3
src/main/java/org/warp/picalculator/gui/expression/containers/NormalInputContainer.java
View File

@ -6,6 +6,7 @@ import org.warp.picalculator.gui.expression.blocks.BlockChar;
import org.warp.picalculator.gui.expression.blocks.BlockDivision; import org.warp.picalculator.gui.expression.blocks.BlockDivision;
import org.warp.picalculator.gui.expression.blocks.BlockParenthesis; import org.warp.picalculator.gui.expression.blocks.BlockParenthesis;
import org.warp.picalculator.gui.expression.blocks.BlockPower; import org.warp.picalculator.gui.expression.blocks.BlockPower;
import org.warp.picalculator.gui.expression.blocks.BlockSine;
import org.warp.picalculator.gui.expression.blocks.BlockSquareRoot; import org.warp.picalculator.gui.expression.blocks.BlockSquareRoot;
import org.warp.picalculator.gui.expression.blocks.BlockVariable; import org.warp.picalculator.gui.expression.blocks.BlockVariable;
import org.warp.picalculator.math.MathematicalSymbols; import org.warp.picalculator.math.MathematicalSymbols;
@ -63,6 +64,8 @@ public class NormalInputContainer extends InputContainer {
case '8': case '8':
case '9': case '9':
return new BlockChar(c); return new BlockChar(c);
case MathematicalSymbols.SINE:
return new BlockSine();
default: default:
for (char v : MathematicalSymbols.variables) { for (char v : MathematicalSymbols.variables) {
if (c == v) { if (c == v) {

3
src/main/java/org/warp/picalculator/gui/graphicengine/cpu/CPUEngine.java
View File

@ -5,6 +5,9 @@ import java.awt.GraphicsEnvironment;
import java.awt.image.BufferedImage; import java.awt.image.BufferedImage;
import java.io.IOException; import java.io.IOException;
import javax.swing.UIManager;
import javax.swing.UnsupportedLookAndFeelException;
import org.warp.picalculator.Main; import org.warp.picalculator.Main;
import org.warp.picalculator.Utils; import org.warp.picalculator.Utils;
import org.warp.picalculator.gui.DisplayManager; import org.warp.picalculator.gui.DisplayManager;

2
src/main/java/org/warp/picalculator/gui/graphicengine/cpu/SwingWindow.java
View File

@ -14,6 +14,8 @@ import java.awt.image.DataBufferInt;
import javax.swing.JFrame; import javax.swing.JFrame;
import javax.swing.JPanel; import javax.swing.JPanel;
import javax.swing.UIManager;
import javax.swing.UnsupportedLookAndFeelException;
import org.warp.picalculator.Utils; import org.warp.picalculator.Utils;
import org.warp.picalculator.device.Keyboard; import org.warp.picalculator.device.Keyboard;

16
src/main/java/org/warp/picalculator/math/functions/trigonometry/Sine.java
View File

@ -3,6 +3,9 @@ package org.warp.picalculator.math.functions.trigonometry;
import org.nevec.rjm.BigDecimalMath; import org.nevec.rjm.BigDecimalMath;
import org.warp.picalculator.Error; import org.warp.picalculator.Error;
import org.warp.picalculator.gui.expression.blocks.Block; import org.warp.picalculator.gui.expression.blocks.Block;
import org.warp.picalculator.gui.expression.blocks.BlockContainer;
import org.warp.picalculator.gui.expression.blocks.BlockParenthesis;
import org.warp.picalculator.gui.expression.blocks.BlockSine;
import org.warp.picalculator.math.AngleMode; import org.warp.picalculator.math.AngleMode;
import org.warp.picalculator.math.Function; import org.warp.picalculator.math.Function;
import org.warp.picalculator.math.FunctionSingle; import org.warp.picalculator.math.FunctionSingle;
@ -60,8 +63,17 @@ public class Sine extends FunctionSingle {
@Override @Override
public ObjectArrayList<Block> toBlock(MathContext context) throws Error { public ObjectArrayList<Block> toBlock(MathContext context) throws Error {
// TODO Auto-generated method stub ObjectArrayList<Block> result = new ObjectArrayList<>();
return null; ObjectArrayList<Block> sub = getParameter(0).toBlock(context);
BlockSine bs = new BlockSine();
BlockContainer bpc = bs.getNumberContainer();
for (Block b : sub) {
bpc.appendBlockUnsafe(b);
}
bpc.recomputeDimensions();
bs.recomputeDimensions();
result.add(bs);
return result;
} }
} }

4
src/main/java/org/warp/picalculator/math/parser/MathParser.java
View File

@ -12,6 +12,7 @@ import org.warp.picalculator.math.MathematicalSymbols;
import org.warp.picalculator.math.functions.Expression; import org.warp.picalculator.math.functions.Expression;
import org.warp.picalculator.math.functions.Variable.V_TYPE; import org.warp.picalculator.math.functions.Variable.V_TYPE;
import org.warp.picalculator.math.parser.features.FeatureChar; import org.warp.picalculator.math.parser.features.FeatureChar;
import org.warp.picalculator.math.parser.features.FeatureDivision;
import org.warp.picalculator.math.parser.features.FeatureMultiplication; import org.warp.picalculator.math.parser.features.FeatureMultiplication;
import org.warp.picalculator.math.parser.features.FeatureNumber; import org.warp.picalculator.math.parser.features.FeatureNumber;
import org.warp.picalculator.math.parser.features.FeatureSum; import org.warp.picalculator.math.parser.features.FeatureSum;
@ -164,6 +165,9 @@ public class MathParser {
case MathematicalSymbols.MULTIPLICATION: case MathematicalSymbols.MULTIPLICATION:
result = new FeatureMultiplication(null, null); result = new FeatureMultiplication(null, null);
break; break;
case MathematicalSymbols.DIVISION:
result = new FeatureDivision(null, null);
break;
} }
for (char var : MathematicalSymbols.variables) { for (char var : MathematicalSymbols.variables) {

19
src/main/java/org/warp/picalculator/math/parser/features/FeatureSine.java Normal file
View File

@ -0,0 +1,19 @@
package org.warp.picalculator.math.parser.features;
import org.warp.picalculator.Error;
import org.warp.picalculator.math.Function;
import org.warp.picalculator.math.MathContext;
import org.warp.picalculator.math.functions.trigonometry.Sine;
public class FeatureSine extends FeatureSingleImpl {
public FeatureSine(Object child) {
super(child);
}
@Override
public Function toFunction(MathContext context) throws Error {
return new Sine(context, this.getFunction1());
}
}

2
src/main/java/org/warp/picalculator/math/parser/steps/JoinNumberAndVariables.java
View File

@ -21,7 +21,7 @@ public class JoinNumberAndVariables implements MathParserStep {
@Override @Override
public boolean eval(IntegerObj curIndex, Function lastFunction, Function currentFunction, ObjectArrayList<Function> functionsList) { public boolean eval(IntegerObj curIndex, Function lastFunction, Function currentFunction, ObjectArrayList<Function> functionsList) {
if (currentFunction instanceof Number | currentFunction instanceof Variable) { if (currentFunction instanceof Number | currentFunction instanceof Variable) {
if (lastFunction instanceof Variable | lastFunction instanceof Number | lastFunction instanceof Multiplication) { if (lastFunction instanceof Variable | lastFunction instanceof Number | (lastFunction instanceof Multiplication && ((Multiplication)lastFunction).getParameter2() != null)) {
final Function var = lastFunction; final Function var = lastFunction;
final Function numb = currentFunction; final Function numb = currentFunction;
functionsList.set(curIndex.i, new Multiplication(context, numb, var)); functionsList.set(curIndex.i, new Multiplication(context, numb, var));