return Li2_series(x, prec);
}
+
/** Numeric evaluation of Dilogarithm. The domain is the entire complex plane,
* the branch cut lies along the positive real axis, starting at 1 and
* continuous with quadrant IV.
*
* @return arbitrary precision numerical Li2(x). */
-const numeric Li2(const numeric &x)
+const cln::cl_N Li2_(const cln::cl_N& value)
{
- if (x.is_zero())
- return *_num0_p;
+ if (zerop(value))
+ return 0;
// what is the desired float format?
// first guess: default format
cln::float_format_t prec = cln::default_float_format;
- const cln::cl_N value = x.to_cl_N();
// second guess: the argument's format
- if (!x.real().is_rational())
+ if (!instanceof(realpart(value), cln::cl_RA_ring))
prec = cln::float_format(cln::the<cln::cl_F>(cln::realpart(value)));
- else if (!x.imag().is_rational())
+ else if (!instanceof(imagpart(value), cln::cl_RA_ring))
prec = cln::float_format(cln::the<cln::cl_F>(cln::imagpart(value)));
if (value==1) // may cause trouble with log(1-x)
- cln::zeta(2, prec)
- Li2_projection(cln::recip(value), prec));
else
- return Li2_projection(x.to_cl_N(), prec);
+ return Li2_projection(value, prec);
+}
+
+const numeric Li2(const numeric &x)
+{
+ const cln::cl_N x_ = x.to_cl_N();
+ if (zerop(x_))
+ return *_num0_p;
+ const cln::cl_N result = Li2_(x_);
+ return numeric(result);
}
if (x.is_real()) {
const int aux = (int)(cln::double_approx(cln::the<cln::cl_R>(x.to_cl_N())));
if (cln::zerop(x.to_cl_N()-aux))
- return cln::zeta(aux);
+ return numeric(cln::zeta(aux));
}
throw dunno();
}
coeffs[3].swap(coeffs_120);
}
+static const cln::float_format_t guess_precision(const cln::cl_N& x)
+{
+ cln::float_format_t prec = cln::default_float_format;
+ if (!instanceof(realpart(x), cln::cl_RA_ring))
+ prec = cln::float_format(cln::the<cln::cl_F>(realpart(x)));
+ if (!instanceof(imagpart(x), cln::cl_RA_ring))
+ prec = cln::float_format(cln::the<cln::cl_F>(imagpart(x)));
+ return prec;
+}
/** The Gamma function.
* Use the Lanczos approximation. If the coefficients used here are not
* sufficiently many or sufficiently accurate, more can be calculated
* using the program doc/examples/lanczos.cpp. In that case, be sure to
* read the comments in that file. */
-const numeric lgamma(const numeric &x)
+const cln::cl_N lgamma(const cln::cl_N &x)
{
+ cln::float_format_t prec = guess_precision(x);
lanczos_coeffs lc;
- if (lc.sufficiently_accurate(Digits)) {
- cln::cl_N pi_val = cln::pi(cln::default_float_format);
- if (x.real() < 0.5)
- return log(pi_val) - log(sin(pi_val*x.to_cl_N()))
- - lgamma(numeric(1).sub(x));
- cln::cl_N A = lc.calc_lanczos_A(x.to_cl_N());
- cln::cl_N temp = x.to_cl_N() + lc.get_order() - cln::cl_N(1)/2;
+ if (lc.sufficiently_accurate(prec)) {
+ cln::cl_N pi_val = cln::pi(prec);
+ if (realpart(x) < 0.5)
+ return cln::log(pi_val) - cln::log(sin(pi_val*x))
+ - lgamma(1 - x);
+ cln::cl_N A = lc.calc_lanczos_A(x);
+ cln::cl_N temp = x + lc.get_order() - cln::cl_N(1)/2;
cln::cl_N result = log(cln::cl_I(2)*pi_val)/2
- + (x.to_cl_N()-cln::cl_N(1)/2)*log(temp)
+ + (x-cln::cl_N(1)/2)*log(temp)
- temp
+ log(A);
return result;
throw dunno();
}
-const numeric tgamma(const numeric &x)
+const numeric lgamma(const numeric &x)
{
+ const cln::cl_N x_ = x.to_cl_N();
+ const cln::cl_N result = lgamma(x_);
+ return numeric(result);
+}
+
+const cln::cl_N tgamma(const cln::cl_N &x)
+{
+ cln::float_format_t prec = guess_precision(x);
lanczos_coeffs lc;
- if (lc.sufficiently_accurate(Digits)) {
- cln::cl_N pi_val = cln::pi(cln::default_float_format);
- if (x.real() < 0.5)
- return pi_val/(sin(pi_val*x))/(tgamma(numeric(1).sub(x)).to_cl_N());
- cln::cl_N A = lc.calc_lanczos_A(x.to_cl_N());
- cln::cl_N temp = x.to_cl_N() + lc.get_order() - cln::cl_N(1)/2;
+ if (lc.sufficiently_accurate(prec)) {
+ cln::cl_N pi_val = cln::pi(prec);
+ if (realpart(x) < 0.5)
+ return pi_val/(cln::sin(pi_val*x))/tgamma(1 - x);
+ cln::cl_N A = lc.calc_lanczos_A(x);
+ cln::cl_N temp = x + lc.get_order() - cln::cl_N(1)/2;
cln::cl_N result
- = sqrt(cln::cl_I(2)*pi_val) * expt(temp, x.to_cl_N()-cln::cl_N(1)/2)
+ = sqrt(cln::cl_I(2)*pi_val) * expt(temp, x - cln::cl_N(1)/2)
* exp(-temp) * A;
return result;
}
throw dunno();
}
+const numeric tgamma(const numeric &x)
+{
+ const cln::cl_N x_ = x.to_cl_N();
+ const cln::cl_N result = tgamma(x_);
+ return numeric(result);
+}
/** The psi function (aka polygamma function).
* This is only a stub! */
next_r = 4;
}
if (n<next_r)
- return results[n/2-1];
+ return numeric(results[n/2-1]);
results.reserve(n/2);
for (unsigned p=next_r; p<=n; p+=2) {
results.push_back(-b/(p+1));
}
next_r = n+2;
- return results[n/2-1];
+ return numeric(results[n/2-1]);
}
if (n.is_even())
// Here we don't use the squaring formula because one multiplication
// is cheaper than two squarings.
- return u * ((v << 1) - u);
+ return numeric(u * ((v << 1) - u));
else
- return cln::square(u) + cln::square(v);
+ return numeric(cln::square(u) + cln::square(v));
}
/** Absolute value. */
const numeric abs(const numeric& x)
{
- return cln::abs(x.to_cl_N());
+ return numeric(cln::abs(x.to_cl_N()));
}
const numeric mod(const numeric &a, const numeric &b)
{
if (a.is_integer() && b.is_integer())
- return cln::mod(cln::the<cln::cl_I>(a.to_cl_N()),
- cln::the<cln::cl_I>(b.to_cl_N()));
+ return numeric(cln::mod(cln::the<cln::cl_I>(a.to_cl_N()),
+ cln::the<cln::cl_I>(b.to_cl_N())));
else
return *_num0_p;
}
{
if (a.is_integer() && b.is_integer()) {
const cln::cl_I b2 = cln::ceiling1(cln::the<cln::cl_I>(b.to_cl_N()) >> 1) - 1;
- return cln::mod(cln::the<cln::cl_I>(a.to_cl_N()) + b2,
- cln::the<cln::cl_I>(b.to_cl_N())) - b2;
+ return numeric(cln::mod(cln::the<cln::cl_I>(a.to_cl_N()) + b2,
+ cln::the<cln::cl_I>(b.to_cl_N())) - b2);
} else
return *_num0_p;
}
if (b.is_zero())
throw std::overflow_error("numeric::irem(): division by zero");
if (a.is_integer() && b.is_integer())
- return cln::rem(cln::the<cln::cl_I>(a.to_cl_N()),
- cln::the<cln::cl_I>(b.to_cl_N()));
+ return numeric(cln::rem(cln::the<cln::cl_I>(a.to_cl_N()),
+ cln::the<cln::cl_I>(b.to_cl_N())));
else
return *_num0_p;
}
if (a.is_integer() && b.is_integer()) {
const cln::cl_I_div_t rem_quo = cln::truncate2(cln::the<cln::cl_I>(a.to_cl_N()),
cln::the<cln::cl_I>(b.to_cl_N()));
- q = rem_quo.quotient;
- return rem_quo.remainder;
+ q = numeric(rem_quo.quotient);
+ return numeric(rem_quo.remainder);
} else {
q = *_num0_p;
return *_num0_p;
if (b.is_zero())
throw std::overflow_error("numeric::iquo(): division by zero");
if (a.is_integer() && b.is_integer())
- return cln::truncate1(cln::the<cln::cl_I>(a.to_cl_N()),
- cln::the<cln::cl_I>(b.to_cl_N()));
+ return numeric(cln::truncate1(cln::the<cln::cl_I>(a.to_cl_N()),
+ cln::the<cln::cl_I>(b.to_cl_N())));
else
return *_num0_p;
}
if (a.is_integer() && b.is_integer()) {
const cln::cl_I_div_t rem_quo = cln::truncate2(cln::the<cln::cl_I>(a.to_cl_N()),
cln::the<cln::cl_I>(b.to_cl_N()));
- r = rem_quo.remainder;
- return rem_quo.quotient;
+ r = numeric(rem_quo.remainder);
+ return numeric(rem_quo.quotient);
} else {
r = *_num0_p;
return *_num0_p;
const numeric gcd(const numeric &a, const numeric &b)
{
if (a.is_integer() && b.is_integer())
- return cln::gcd(cln::the<cln::cl_I>(a.to_cl_N()),
- cln::the<cln::cl_I>(b.to_cl_N()));
+ return numeric(cln::gcd(cln::the<cln::cl_I>(a.to_cl_N()),
+ cln::the<cln::cl_I>(b.to_cl_N())));
else
return *_num1_p;
}
const numeric lcm(const numeric &a, const numeric &b)
{
if (a.is_integer() && b.is_integer())
- return cln::lcm(cln::the<cln::cl_I>(a.to_cl_N()),
- cln::the<cln::cl_I>(b.to_cl_N()));
+ return numeric(cln::lcm(cln::the<cln::cl_I>(a.to_cl_N()),
+ cln::the<cln::cl_I>(b.to_cl_N())));
else
return a.mul(b);
}
* where imag(x)>0. */
const numeric sqrt(const numeric &x)
{
- return cln::sqrt(x.to_cl_N());
+ return numeric(cln::sqrt(x.to_cl_N()));
}
if (x.is_integer()) {
cln::cl_I root;
cln::isqrt(cln::the<cln::cl_I>(x.to_cl_N()), &root);
- return root;
+ return numeric(root);
} else
return *_num0_p;
}
git://www.ginac.de / ginac.git / blobdiff