* of special functions or implement the interface to the bignum package. */
/*
- * GiNaC Copyright (C) 1999-2008 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2015 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
+#ifdef HAVE_CONFIG_H
#include "config.h"
-
-#include <vector>
-#include <stdexcept>
-#include <string>
-#include <sstream>
-#include <limits>
+#endif
#include "numeric.h"
#include "ex.h"
#include "operators.h"
#include "archive.h"
-#include "tostring.h"
#include "utils.h"
+#include <limits>
+#include <sstream>
+#include <stdexcept>
+#include <string>
+#include <vector>
+
// CLN should pollute the global namespace as little as possible. Hence, we
// include most of it here and include only the part needed for properly
// declaring cln::cl_number in numeric.h. This can only be safely done in
//////////
/** default ctor. Numerically it initializes to an integer zero. */
-numeric::numeric() : basic(&numeric::tinfo_static)
+numeric::numeric()
{
value = cln::cl_I(0);
setflag(status_flags::evaluated | status_flags::expanded);
// public
-numeric::numeric(int i) : basic(&numeric::tinfo_static)
+numeric::numeric(int i)
{
// Not the whole int-range is available if we don't cast to long
// first. This is due to the behaviour of the cl_I-ctor, which
}
-numeric::numeric(unsigned int i) : basic(&numeric::tinfo_static)
+numeric::numeric(unsigned int i)
{
// Not the whole uint-range is available if we don't cast to ulong
// first. This is due to the behaviour of the cl_I-ctor, which
}
-numeric::numeric(long i) : basic(&numeric::tinfo_static)
+numeric::numeric(long i)
{
value = cln::cl_I(i);
setflag(status_flags::evaluated | status_flags::expanded);
}
-numeric::numeric(unsigned long i) : basic(&numeric::tinfo_static)
+numeric::numeric(unsigned long i)
{
value = cln::cl_I(i);
setflag(status_flags::evaluated | status_flags::expanded);
/** Constructor for rational numerics a/b.
*
* @exception overflow_error (division by zero) */
-numeric::numeric(long numer, long denom) : basic(&numeric::tinfo_static)
+numeric::numeric(long numer, long denom)
{
if (!denom)
throw std::overflow_error("division by zero");
}
-numeric::numeric(double d) : basic(&numeric::tinfo_static)
+numeric::numeric(double d)
{
// We really want to explicitly use the type cl_LF instead of the
// more general cl_F, since that would give us a cl_DF only which
/** ctor from C-style string. It also accepts complex numbers in GiNaC
* notation like "2+5*I". */
-numeric::numeric(const char *s) : basic(&numeric::tinfo_static)
+numeric::numeric(const char *s)
{
cln::cl_N ctorval = 0;
// parse complex numbers (functional but not completely safe, unfortunately
// E to lower case
term = term.replace(term.find("E"),1,"e");
// append _<Digits> to term
- term += "_" + ToString((unsigned)Digits);
+ term += "_" + std::to_string((unsigned)Digits);
// construct float using cln::cl_F(const char *) ctor.
if (imaginary)
ctorval = ctorval + cln::complex(cln::cl_I(0),cln::cl_F(term.c_str()));
/** Ctor from CLN types. This is for the initiated user or internal use
* only. */
-numeric::numeric(const cln::cl_N &z) : basic(&numeric::tinfo_static)
+numeric::numeric(const cln::cl_N &z)
{
value = z;
setflag(status_flags::evaluated | status_flags::expanded);
// 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;
+}
+
+void numeric::read_archive(const archive_node &n, lst &sym_lst)
+{
+ inherited::read_archive(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);
}
+GINAC_BIND_UNARCHIVER(numeric);
+
+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());
}
-DEFAULT_UNARCHIVE(numeric)
-
//////////
// functions overriding virtual functions from base classes
//////////
{
if (cln::instanceof(x, cln::cl_I_ring)) {
- int dst;
- // fixnum
- if (coerce(dst, cln::the<cln::cl_I>(x))) {
- // can be converted to native int
- if (dst < 0)
- c.s << "(-" << dst << ")";
- else
- c.s << dst;
- } else {
- // bignum
- c.s << "cln::cl_I(\"";
- print_real_number(c, x);
- c.s << "\")";
- }
+ int dst;
+ // fixnum
+ if (coerce(dst, cln::the<cln::cl_I>(x))) {
+ // can be converted to native int
+ if (dst < 0)
+ c.s << "(-" << dst << ")";
+ else
+ c.s << dst;
+ } else {
+ // bignum
+ c.s << "cln::cl_I(\"";
+ print_real_number(c, x);
+ c.s << "\")";
+ }
} else if (cln::instanceof(x, cln::cl_RA_ring)) {
// Rational number
case info_flags::negative:
return is_negative();
case info_flags::nonnegative:
- return !is_negative();
+ return is_zero() || is_positive();
case info_flags::posint:
return is_pos_integer();
case info_flags::negint:
if (cln::instanceof(r, cln::cl_RA_ring) && cln::instanceof(i, cln::cl_RA_ring)) {
const cln::cl_I s = cln::lcm(cln::denominator(r), cln::denominator(i));
return numeric(cln::complex(cln::numerator(r)*(cln::exquo(s,cln::denominator(r))),
- cln::numerator(i)*(cln::exquo(s,cln::denominator(i)))));
+ cln::numerator(i)*(cln::exquo(s,cln::denominator(i)))));
}
}
// at least one float encountered
return *_num0_p;
if (x.is_real() && y.is_real())
return numeric(cln::atan(cln::the<cln::cl_R>(x.to_cl_N()),
- cln::the<cln::cl_R>(y.to_cl_N())));
+ cln::the<cln::cl_R>(y.to_cl_N())));
// Compute -I*log((x+I*y)/sqrt(x^2+y^2))
// == -I*log((x+I*y)/sqrt((x+I*y)*(x-I*y)))
{
cln::cl_N A = (*current_vector)[0];
int size = current_vector->size();
- for (int i=1; i<size; ++i)
- A = A + (*current_vector)[i]/(x+cln::cl_I(-1+i));
+ for (int i=1; i<size; ++i)
+ A = A + (*current_vector)[i]/(x+cln::cl_I(-1+i));
return A;
}
* 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 cln::cl_N lgamma_(const cln::cl_N &x)
+const cln::cl_N lgamma(const cln::cl_N &x)
{
cln::float_format_t prec = guess_precision(x);
lanczos_coeffs lc;
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);
+ - 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-cln::cl_N(1)/2)*log(temp)
- - temp
- + log(A);
- return result;
+ cln::cl_N result = log(cln::cl_I(2)*pi_val)/2
+ + (x-cln::cl_N(1)/2)*log(temp)
+ - temp
+ + log(A);
+ return result;
}
else
throw dunno();
const numeric lgamma(const numeric &x)
{
const cln::cl_N x_ = x.to_cl_N();
- const cln::cl_N result = lgamma_(x_);
+ const cln::cl_N result = lgamma(x_);
return numeric(result);
}
-const cln::cl_N tgamma_(const cln::cl_N &x)
+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(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);
+ 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 - cln::cl_N(1)/2)
- * exp(-temp) * A;
- return result;
+ cln::cl_N result = sqrt(cln::cl_I(2)*pi_val)
+ * expt(temp, x - cln::cl_N(1)/2)
+ * exp(-temp) * A;
+ return result;
}
else
throw dunno();
const numeric tgamma(const numeric &x)
{
const cln::cl_N x_ = x.to_cl_N();
- const cln::cl_N result = tgamma_(x_);
+ const cln::cl_N result = tgamma(x_);
return numeric(result);
}
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) {
c = cln::exquo((c * (p+3-2*k)) * (p/2-k+1), cln::cl_I(2*k-1)*k);
b = b + c*results[k-1];
}
- }
+ }
results.push_back(-b/(p+1));
}
next_r = n+2;
- return results[n/2-1];
+ return numeric(results[n/2-1]);
}
// F(2n+2) = F(n+1)*(2*F(n) + F(n+1))
if (n.is_zero())
return *_num0_p;
- if (n.is_negative())
- if (n.is_even())
+ if (n.is_negative()) {
+ if (n.is_even()) {
return -fibonacci(-n);
- else
+ }
+ else {
return fibonacci(-n);
+ }
+ }
cln::cl_I u(0);
cln::cl_I v(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));
}
/** Modulus (in symmetric representation).
- * Equivalent to Maple's mods.
*
- * @return a mod b in the range [-iquo(abs(b)-1,2), iquo(abs(b),2)]. */
-const numeric smod(const numeric &a, const numeric &b)
-{
- 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 numeric(cln::mod(cln::the<cln::cl_I>(a.to_cl_N()) + b2,
- cln::the<cln::cl_I>(b.to_cl_N())) - b2);
+ * @return a mod b in the range [-iquo(abs(b),2), iquo(abs(b),2)]. */
+const numeric smod(const numeric &a_, const numeric &b_)
+{
+ if (a_.is_integer() && b_.is_integer()) {
+ const cln::cl_I a = cln::the<cln::cl_I>(a_.to_cl_N());
+ const cln::cl_I b = cln::the<cln::cl_I>(b_.to_cl_N());
+ const cln::cl_I b2 = b >> 1;
+ const cln::cl_I m = cln::mod(a, b);
+ const cln::cl_I m_b = m - b;
+ const cln::cl_I ret = m > b2 ? m_b : m;
+ return numeric(ret);
} else
return *_num0_p;
}
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;
cln::default_float_format = cln::float_format(prec);
// call registered callbacks
- std::vector<digits_changed_callback>::const_iterator it = callbacklist.begin(), end = callbacklist.end();
- for (; it != end; ++it) {
- (*it)(digitsdiff);
+ for (auto it : callbacklist) {
+ (it)(digitsdiff);
}
return *this;
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