// archiving
//////////
-numeric::numeric(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
+/**
+ * Construct a floating point number from sign, mantissa, and exponent
+ */
+static const cln::cl_F make_real_float(const cln::cl_idecoded_float& dec)
{
- cln::cl_N ctorval = 0;
+ cln::cl_F x = cln::cl_float(dec.mantissa, cln::default_float_format);
+ x = cln::scale_float(x, dec.exponent);
+ cln::cl_F sign = cln::cl_float(dec.sign, cln::default_float_format);
+ x = cln::float_sign(sign, x);
+ return x;
+}
+
+/**
+ * Read serialized floating point number
+ */
+static const cln::cl_F read_real_float(std::istream& s)
+{
+ cln::cl_idecoded_float dec;
+ s >> dec.sign >> dec.mantissa >> dec.exponent;
+ const cln::cl_F x = make_real_float(dec);
+ return x;
+}
+numeric::numeric(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
+{
+ value = 0;
+
// Read number as string
std::string str;
if (n.find_string("number", str)) {
std::istringstream s(str);
- cln::cl_idecoded_float re, im;
+ cln::cl_R re, im;
char c;
s.get(c);
switch (c) {
- case 'R': // Integer-decoded real number
- s >> re.sign >> re.mantissa >> re.exponent;
- ctorval = re.sign * re.mantissa * cln::expt(cln::cl_float(2.0, cln::default_float_format), re.exponent);
+ case 'R':
+ // real FP (floating point) number
+ re = read_real_float(s);
+ value = re;
+ break;
+ case 'C':
+ // both real and imaginary part are FP numbers
+ re = read_real_float(s);
+ im = read_real_float(s);
+ value = cln::complex(re, im);
+ break;
+ case 'H':
+ // real part is a rational number,
+ // imaginary part is a FP number
+ s >> re;
+ im = read_real_float(s);
+ value = cln::complex(re, im);
break;
- case 'C': // Integer-decoded complex number
- s >> re.sign >> re.mantissa >> re.exponent;
- s >> im.sign >> im.mantissa >> im.exponent;
- ctorval = cln::complex(re.sign * re.mantissa * cln::expt(cln::cl_float(2.0, cln::default_float_format), re.exponent),
- im.sign * im.mantissa * cln::expt(cln::cl_float(2.0, cln::default_float_format), im.exponent));
+ case 'J':
+ // real part is a FP number,
+ // imaginary part is a rational number
+ re = read_real_float(s);
+ s >> im;
+ value = cln::complex(re, im);
break;
- default: // Ordinary number
+ default:
+ // both real and imaginary parts are rational
s.putback(c);
- s >> ctorval;
+ s >> value;
break;
}
}
- value = ctorval;
setflag(status_flags::evaluated | status_flags::expanded);
}
+static void write_real_float(std::ostream& s, const cln::cl_R& n)
+{
+ const cln::cl_idecoded_float dec = cln::integer_decode_float(cln::the<cln::cl_F>(n));
+ s << dec.sign << ' ' << dec.mantissa << ' ' << dec.exponent;
+}
+
void numeric::archive(archive_node &n) const
{
inherited::archive(n);
// Write number as string
+
+ const cln::cl_R re = cln::realpart(value);
+ const cln::cl_R im = cln::imagpart(value);
+ const bool re_rationalp = cln::instanceof(re, cln::cl_RA_ring);
+ const bool im_rationalp = cln::instanceof(im, cln::cl_RA_ring);
+
+ // Non-rational numbers are written in an integer-decoded format
+ // to preserve the precision
std::ostringstream s;
- if (this->is_crational())
+ if (re_rationalp && im_rationalp)
s << value;
- else {
- // Non-rational numbers are written in an integer-decoded format
- // to preserve the precision
- if (this->is_real()) {
- cln::cl_idecoded_float re = cln::integer_decode_float(cln::the<cln::cl_F>(value));
- s << "R";
- s << re.sign << " " << re.mantissa << " " << re.exponent;
- } else {
- cln::cl_idecoded_float re = cln::integer_decode_float(cln::the<cln::cl_F>(cln::realpart(cln::the<cln::cl_N>(value))));
- cln::cl_idecoded_float im = cln::integer_decode_float(cln::the<cln::cl_F>(cln::imagpart(cln::the<cln::cl_N>(value))));
- s << "C";
- s << re.sign << " " << re.mantissa << " " << re.exponent << " ";
- s << im.sign << " " << im.mantissa << " " << im.exponent;
- }
+ else if (zerop(im)) {
+ // real FP (floating point) number
+ s << 'R';
+ write_real_float(s, re);
+ } else if (re_rationalp) {
+ s << 'H'; // just any unique character
+ // real part is a rational number,
+ // imaginary part is a FP number
+ s << re << ' ';
+ write_real_float(s, im);
+ } else if (im_rationalp) {
+ s << 'J';
+ // real part is a FP number,
+ // imaginary part is a rational number
+ write_real_float(s, re);
+ s << ' ' << im;
+ } else {
+ // both real and imaginary parts are floating point
+ s << 'C';
+ write_real_float(s, re);
+ s << ' ';
+ write_real_float(s, im);
}
n.add_string("number", s.str());
}
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));
}
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 = numeric(rem_quo.remainder);
- return rem_quo.quotient;
+ return numeric(rem_quo.quotient);
} else {
r = *_num0_p;
return *_num0_p;
git://www.ginac.de / ginac.git / blobdiff