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290 lines
8.6 KiB
290 lines
8.6 KiB
/*
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* include/dd_real.h
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*
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* This work was supported by the Director, Office of Science, Division
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* of Mathematical, Information, and Computational Sciences of the
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* U.S. Department of Energy under contract number DE-AC03-76SF00098.
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*
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* Copyright (c) 2000-2007
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*
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* Double-double precision (>= 106-bit significand) floating point
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* arithmetic package based on David Bailey's Fortran-90 double-double
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* package, with some changes. See
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*
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* http://www.nersc.gov/~dhbailey/mpdist/mpdist.html
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*
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* for the original Fortran-90 version.
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*
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* Overall structure is similar to that of Keith Brigg's C++ double-double
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* package. See
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*
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* http://www-epidem.plansci.cam.ac.uk/~kbriggs/doubledouble.html
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*
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* for more details. In particular, the fix for x86 computers is borrowed
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* from his code.
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*
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* Yozo Hida
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*/
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#ifndef _QD_DD_REAL_H
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#define _QD_DD_REAL_H
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#include <cmath>
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#include <iostream>
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#include <string>
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#include <limits>
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#include <qd/qd_config.h>
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#include <qd/fpu.h>
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// Some compilers define isnan, isfinite, and isinf as macros, even for
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// C++ codes, which cause havoc when overloading these functions. We undef
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// them here.
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#ifdef isnan
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#undef isnan
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#endif
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#ifdef isfinite
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#undef isfinite
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#endif
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#ifdef isinf
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#undef isinf
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#endif
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#ifdef max
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#undef max
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#endif
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#ifdef min
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#undef min
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#endif
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struct QD_API dd_real {
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double x[2];
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dd_real(double hi, double lo) { x[0] = hi; x[1] = lo; }
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dd_real() {x[0] = 0.0; x[1] = 0.0; }
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dd_real(double h) { x[0] = h; x[1] = 0.0; }
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dd_real(int h) {
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x[0] = (static_cast<double>(h));
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x[1] = 0.0;
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}
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dd_real (const char *s);
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explicit dd_real (const double *d) {
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x[0] = d[0]; x[1] = d[1];
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}
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static void error(const char *msg);
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double _hi() const { return x[0]; }
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double _lo() const { return x[1]; }
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static const dd_real _2pi;
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static const dd_real _pi;
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static const dd_real _3pi4;
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static const dd_real _pi2;
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static const dd_real _pi4;
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static const dd_real _e;
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static const dd_real _log2;
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static const dd_real _log10;
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static const dd_real _nan;
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static const dd_real _inf;
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static const double _eps;
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static const double _min_normalized;
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static const dd_real _max;
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static const dd_real _safe_max;
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static const int _ndigits;
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bool isnan() const { return QD_ISNAN(x[0]) || QD_ISNAN(x[1]); }
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bool isfinite() const { return QD_ISFINITE(x[0]); }
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bool isinf() const { return QD_ISINF(x[0]); }
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static dd_real add(double a, double b);
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static dd_real ieee_add(const dd_real &a, const dd_real &b);
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static dd_real sloppy_add(const dd_real &a, const dd_real &b);
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dd_real &operator+=(double a);
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dd_real &operator+=(const dd_real &a);
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static dd_real sub(double a, double b);
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dd_real &operator-=(double a);
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dd_real &operator-=(const dd_real &a);
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dd_real operator-() const;
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static dd_real mul(double a, double b);
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dd_real &operator*=(double a);
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dd_real &operator*=(const dd_real &a);
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static dd_real div(double a, double b);
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static dd_real sloppy_div(const dd_real &a, const dd_real &b);
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static dd_real accurate_div(const dd_real &a, const dd_real &b);
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dd_real &operator/=(double a);
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dd_real &operator/=(const dd_real &a);
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dd_real &operator=(double a);
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dd_real &operator=(const char *s);
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dd_real operator^(int n);
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static dd_real sqr(double d);
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static dd_real sqrt(double a);
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bool is_zero() const;
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bool is_one() const;
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bool is_positive() const;
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bool is_negative() const;
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static dd_real rand(void);
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void to_digits(char *s, int &expn, int precision = _ndigits) const;
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void write(char *s, int len, int precision = _ndigits,
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bool showpos = false, bool uppercase = false) const;
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std::string to_string(int precision = _ndigits, int width = 0,
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std::ios_base::fmtflags fmt = static_cast<std::ios_base::fmtflags>(0),
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bool showpos = false, bool uppercase = false, char fill = ' ') const;
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int read(const char *s, dd_real &a);
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/* Debugging Methods */
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void dump(const std::string &name = "", std::ostream &os = std::cerr) const;
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void dump_bits(const std::string &name = "",
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std::ostream &os = std::cerr) const;
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static dd_real debug_rand();
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};
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namespace std {
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template <>
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class numeric_limits<dd_real> : public numeric_limits<double> {
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public:
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inline static double epsilon() { return dd_real::_eps; }
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inline static dd_real max() { return dd_real::_max; }
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inline static dd_real safe_max() { return dd_real::_safe_max; }
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inline static double min() { return dd_real::_min_normalized; }
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static const int digits = 104;
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static const int digits10 = 31;
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};
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}
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QD_API dd_real ddrand(void);
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QD_API dd_real sqrt(const dd_real &a);
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QD_API dd_real polyeval(const dd_real *c, int n, const dd_real &x);
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QD_API dd_real polyroot(const dd_real *c, int n,
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const dd_real &x0, int max_iter = 32, double thresh = 0.0);
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QD_API inline bool isnan(const dd_real &a) { return a.isnan(); }
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QD_API inline bool isfinite(const dd_real &a) { return a.isfinite(); }
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QD_API inline bool isinf(const dd_real &a) { return a.isinf(); }
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/* Computes dd * d where d is known to be a power of 2. */
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QD_API dd_real mul_pwr2(const dd_real &dd, double d);
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QD_API dd_real operator+(const dd_real &a, double b);
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QD_API dd_real operator+(double a, const dd_real &b);
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QD_API dd_real operator+(const dd_real &a, const dd_real &b);
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QD_API dd_real operator-(const dd_real &a, double b);
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QD_API dd_real operator-(double a, const dd_real &b);
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QD_API dd_real operator-(const dd_real &a, const dd_real &b);
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QD_API dd_real operator*(const dd_real &a, double b);
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QD_API dd_real operator*(double a, const dd_real &b);
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QD_API dd_real operator*(const dd_real &a, const dd_real &b);
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QD_API dd_real operator/(const dd_real &a, double b);
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QD_API dd_real operator/(double a, const dd_real &b);
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QD_API dd_real operator/(const dd_real &a, const dd_real &b);
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QD_API dd_real inv(const dd_real &a);
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QD_API dd_real rem(const dd_real &a, const dd_real &b);
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QD_API dd_real drem(const dd_real &a, const dd_real &b);
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QD_API dd_real divrem(const dd_real &a, const dd_real &b, dd_real &r);
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QD_API dd_real pow(const dd_real &a, int n);
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QD_API dd_real pow(const dd_real &a, const dd_real &b);
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QD_API dd_real npwr(const dd_real &a, int n);
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QD_API dd_real sqr(const dd_real &a);
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QD_API dd_real sqrt(const dd_real &a);
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QD_API dd_real nroot(const dd_real &a, int n);
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QD_API bool operator==(const dd_real &a, double b);
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QD_API bool operator==(double a, const dd_real &b);
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QD_API bool operator==(const dd_real &a, const dd_real &b);
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QD_API bool operator<=(const dd_real &a, double b);
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QD_API bool operator<=(double a, const dd_real &b);
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QD_API bool operator<=(const dd_real &a, const dd_real &b);
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QD_API bool operator>=(const dd_real &a, double b);
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QD_API bool operator>=(double a, const dd_real &b);
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QD_API bool operator>=(const dd_real &a, const dd_real &b);
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QD_API bool operator<(const dd_real &a, double b);
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QD_API bool operator<(double a, const dd_real &b);
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QD_API bool operator<(const dd_real &a, const dd_real &b);
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QD_API bool operator>(const dd_real &a, double b);
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QD_API bool operator>(double a, const dd_real &b);
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QD_API bool operator>(const dd_real &a, const dd_real &b);
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QD_API bool operator!=(const dd_real &a, double b);
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QD_API bool operator!=(double a, const dd_real &b);
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QD_API bool operator!=(const dd_real &a, const dd_real &b);
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QD_API dd_real nint(const dd_real &a);
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QD_API dd_real floor(const dd_real &a);
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QD_API dd_real ceil(const dd_real &a);
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QD_API dd_real aint(const dd_real &a);
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QD_API dd_real ddrand(void);
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double to_double(const dd_real &a);
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int to_int(const dd_real &a);
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QD_API dd_real exp(const dd_real &a);
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QD_API dd_real ldexp(const dd_real &a, int exp);
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QD_API dd_real log(const dd_real &a);
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QD_API dd_real log10(const dd_real &a);
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QD_API dd_real sin(const dd_real &a);
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QD_API dd_real cos(const dd_real &a);
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QD_API dd_real tan(const dd_real &a);
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QD_API void sincos(const dd_real &a, dd_real &sin_a, dd_real &cos_a);
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QD_API dd_real asin(const dd_real &a);
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QD_API dd_real acos(const dd_real &a);
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QD_API dd_real atan(const dd_real &a);
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QD_API dd_real atan2(const dd_real &y, const dd_real &x);
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QD_API dd_real sinh(const dd_real &a);
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QD_API dd_real cosh(const dd_real &a);
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QD_API dd_real tanh(const dd_real &a);
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QD_API void sincosh(const dd_real &a,
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dd_real &sinh_a, dd_real &cosh_a);
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QD_API dd_real asinh(const dd_real &a);
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QD_API dd_real acosh(const dd_real &a);
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QD_API dd_real atanh(const dd_real &a);
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QD_API dd_real fabs(const dd_real &a);
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QD_API dd_real abs(const dd_real &a); /* same as fabs */
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QD_API dd_real fmod(const dd_real &a, const dd_real &b);
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QD_API std::ostream& operator<<(std::ostream &s, const dd_real &a);
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QD_API std::istream& operator>>(std::istream &s, dd_real &a);
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#ifdef QD_INLINE
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#include <qd/dd_inline.h>
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#endif
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#endif /* _QD_DD_REAL_H */
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