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637 lines
26 KiB
637 lines
26 KiB
// Public real number operations.
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#ifndef _CL_REAL_H
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#define _CL_REAL_H
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#include "cln/number.h"
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#include "cln/real_class.h"
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#include "cln/rational_class.h"
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#include "cln/integer_class.h"
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#include "cln/float.h"
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#include "cln/floatformat.h"
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#include "cln/random.h"
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namespace cln {
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CL_DEFINE_AS_CONVERSION(cl_R)
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// zerop(x) testet, ob (= x 0).
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extern bool zerop (const cl_R& x);
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// minusp(x) testet, ob (< x 0).
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extern bool minusp (const cl_R& x);
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// plusp(x) testet, ob (> x 0).
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extern bool plusp (const cl_R& x);
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// R_to_SF(x) wandelt eine reelle Zahl x in ein Short-Float um.
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// < ergebnis: (coerce x 'short-float)
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extern const cl_SF cl_R_to_SF (const cl_R& x);
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// R_to_FF(x) wandelt eine reelle Zahl x in ein Single-Float um.
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// < ergebnis: (coerce x 'single-float)
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extern const cl_FF cl_R_to_FF (const cl_R& x);
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// R_to_DF(x) wandelt eine reelle Zahl x in ein Double-Float um.
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// < ergebnis: (coerce x 'double-float)
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extern const cl_DF cl_R_to_DF (const cl_R& x);
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// R_to_LF(x,len) wandelt eine reelle Zahl x in ein Long-Float mit len Digits um.
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// > uintC len: gewünschte Anzahl Digits, >=LF_minlen
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// < ergebnis: (coerce x `(long-float ,len))
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extern const cl_LF cl_R_to_LF (const cl_R& x, uintC len);
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// cl_float(x,y) wandelt eine reelle Zahl x in das Float-Format des
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// Floats y um und rundet dabei nötigenfalls.
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// > x: eine reelle Zahl
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// > y: ein Float
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// < ergebnis: (float x y)
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extern const cl_F cl_float (const cl_R& x, const cl_F& y);
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// cl_float(x,f) wandelt eine reelle Zahl x in das Float-Format f um
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// und rundet dabei nötigenfalls.
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// > x: eine reelle Zahl
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// > f: eine Float-Format-Spezifikation
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// < ergebnis: (float x f)
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extern const cl_F cl_float (const cl_R& x, float_format_t f);
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// cl_float(x) wandelt eine reelle Zahl x in ein Float um
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// und rundet dabei nötigenfalls.
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// > x: eine reelle Zahl
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// < ergebnis: (float x)
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// Abhängig von default_float_format.
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extern const cl_F cl_float (const cl_R& x);
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// Liefert (- x), wo x eine reelle Zahl ist.
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extern const cl_R operator- (const cl_R& x);
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// Liefert (+ x y), wo x und y reelle Zahlen sind.
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extern const cl_R operator+ (const cl_R& x, const cl_R& y);
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// Spezialfall: x oder y Float -> Ergebnis Float
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inline const cl_F operator+ (const cl_R& x, const cl_F& y)
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{ return The(cl_F)(x + The(cl_R)(y)); }
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inline const cl_F operator+ (const cl_F& x, const cl_R& y)
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{ return The(cl_F)(The(cl_R)(x) + y); }
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// Dem C++-Compiler muß man nun auch das Folgende sagen:
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inline const cl_R operator+ (const int x, const cl_R& y)
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{ return cl_I(x) + y; }
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inline const cl_R operator+ (const unsigned int x, const cl_R& y)
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{ return cl_I(x) + y; }
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inline const cl_R operator+ (const long x, const cl_R& y)
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{ return cl_I(x) + y; }
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inline const cl_R operator+ (const unsigned long x, const cl_R& y)
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{ return cl_I(x) + y; }
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#ifdef HAVE_LONGLONG
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inline const cl_R operator+ (const long long x, const cl_R& y)
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{ return cl_I(x) + y; }
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inline const cl_R operator+ (const unsigned long long x, const cl_R& y)
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{ return cl_I(x) + y; }
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#endif
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inline const cl_F operator+ (const float x, const cl_R& y)
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{ return The(cl_F)(cl_R(x) + y); }
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inline const cl_F operator+ (const double x, const cl_R& y)
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{ return The(cl_F)(cl_R(x) + y); }
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inline const cl_R operator+ (const cl_R& x, const int y)
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{ return x + cl_I(y); }
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inline const cl_R operator+ (const cl_R& x, const unsigned int y)
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{ return x + cl_I(y); }
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inline const cl_R operator+ (const cl_R& x, const long y)
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{ return x + cl_I(y); }
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inline const cl_R operator+ (const cl_R& x, const unsigned long y)
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{ return x + cl_I(y); }
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#ifdef HAVE_LONGLONG
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inline const cl_R operator+ (const cl_R& x, const long long y)
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{ return x + cl_I(y); }
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inline const cl_R operator+ (const cl_R& x, const unsigned long long y)
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{ return x + cl_I(y); }
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#endif
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inline const cl_F operator+ (const cl_R& x, const float y)
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{ return The(cl_F)(x + cl_R(y)); }
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inline const cl_F operator+ (const cl_R& x, const double y)
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{ return The(cl_F)(x + cl_R(y)); }
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// Liefert (- x y), wo x und y reelle Zahlen sind.
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extern const cl_R operator- (const cl_R& x, const cl_R& y);
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// Spezialfall: x oder y Float -> Ergebnis Float
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inline const cl_F operator- (const cl_R& x, const cl_F& y)
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{ return The(cl_F)(x - The(cl_R)(y)); }
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inline const cl_F operator- (const cl_F& x, const cl_R& y)
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{ return The(cl_F)(The(cl_R)(x) - y); }
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// Dem C++-Compiler muß man nun auch das Folgende sagen:
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inline const cl_R operator- (const int x, const cl_R& y)
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{ return cl_I(x) - y; }
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inline const cl_R operator- (const unsigned int x, const cl_R& y)
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{ return cl_I(x) - y; }
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inline const cl_R operator- (const long x, const cl_R& y)
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{ return cl_I(x) - y; }
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inline const cl_R operator- (const unsigned long x, const cl_R& y)
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{ return cl_I(x) - y; }
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#ifdef HAVE_LONGLONG
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inline const cl_R operator- (const long long x, const cl_R& y)
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{ return cl_I(x) - y; }
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inline const cl_R operator- (const unsigned long long x, const cl_R& y)
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{ return cl_I(x) - y; }
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#endif
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inline const cl_F operator- (const float x, const cl_R& y)
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{ return The(cl_F)(cl_R(x) - y); }
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inline const cl_F operator- (const double x, const cl_R& y)
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{ return The(cl_F)(cl_R(x) - y); }
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inline const cl_R operator- (const cl_R& x, const int y)
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{ return x - cl_I(y); }
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inline const cl_R operator- (const cl_R& x, const unsigned int y)
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{ return x - cl_I(y); }
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inline const cl_R operator- (const cl_R& x, const long y)
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{ return x - cl_I(y); }
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inline const cl_R operator- (const cl_R& x, const unsigned long y)
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{ return x - cl_I(y); }
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#ifdef HAVE_LONGLONG
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inline const cl_R operator- (const cl_R& x, const long long y)
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{ return x - cl_I(y); }
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inline const cl_R operator- (const cl_R& x, const unsigned long long y)
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{ return x - cl_I(y); }
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#endif
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inline const cl_F operator- (const cl_R& x, const float y)
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{ return The(cl_F)(x - cl_R(y)); }
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inline const cl_F operator- (const cl_R& x, const double y)
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{ return The(cl_F)(x - cl_R(y)); }
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// Liefert (* x y), wo x und y reelle Zahlen sind.
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extern const cl_R operator* (const cl_R& x, const cl_R& y);
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// Dem C++-Compiler muß man auch das Folgende sagen (wg. `int * cl_F' u.ä.):
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inline const cl_R operator* (const int x, const cl_R& y)
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{ return cl_I(x) * y; }
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inline const cl_R operator* (const unsigned int x, const cl_R& y)
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{ return cl_I(x) * y; }
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inline const cl_R operator* (const long x, const cl_R& y)
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{ return cl_I(x) * y; }
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inline const cl_R operator* (const unsigned long x, const cl_R& y)
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{ return cl_I(x) * y; }
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#ifdef HAVE_LONGLONG
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inline const cl_R operator* (const long long x, const cl_R& y)
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{ return cl_I(x) * y; }
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inline const cl_R operator* (const unsigned long long x, const cl_R& y)
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{ return cl_I(x) * y; }
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#endif
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inline const cl_R operator* (const float x, const cl_R& y)
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{ return cl_R(x) * y; }
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inline const cl_R operator* (const double x, const cl_R& y)
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{ return cl_R(x) * y; }
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inline const cl_R operator* (const cl_R& x, const int y)
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{ return x * cl_I(y); }
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inline const cl_R operator* (const cl_R& x, const unsigned int y)
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{ return x * cl_I(y); }
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inline const cl_R operator* (const cl_R& x, const long y)
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{ return x * cl_I(y); }
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inline const cl_R operator* (const cl_R& x, const unsigned long y)
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{ return x * cl_I(y); }
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#ifdef HAVE_LONGLONG
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inline const cl_R operator* (const cl_R& x, const long long y)
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{ return x * cl_I(y); }
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inline const cl_R operator* (const cl_R& x, const unsigned long long y)
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{ return x * cl_I(y); }
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#endif
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inline const cl_R operator* (const cl_R& x, const float y)
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{ return x * cl_R(y); }
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inline const cl_R operator* (const cl_R& x, const double y)
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{ return x * cl_R(y); }
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// Liefert (* x x), wo x eine reelle Zahl ist.
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extern const cl_R square (const cl_R& x);
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// Liefert (/ x y), wo x und y reelle Zahlen sind.
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extern const cl_R operator/ (const cl_R& x, const cl_R& y);
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// Spezialfall: x Float -> Ergebnis Float
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inline const cl_F operator/ (const cl_F& x, const cl_R& y)
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{ return The(cl_F)(The(cl_R)(x) / y); }
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// Dem C++-Compiler muß man auch das Folgende sagen (wg. `int / cl_F' u.ä.):
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inline const cl_R operator/ (const int x, const cl_R& y)
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{ return cl_I(x) / y; }
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inline const cl_R operator/ (const unsigned int x, const cl_R& y)
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{ return cl_I(x) / y; }
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inline const cl_R operator/ (const long x, const cl_R& y)
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{ return cl_I(x) / y; }
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inline const cl_R operator/ (const unsigned long x, const cl_R& y)
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{ return cl_I(x) / y; }
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#ifdef HAVE_LONGLONG
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inline const cl_R operator/ (const long long x, const cl_R& y)
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{ return cl_I(x) / y; }
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inline const cl_R operator/ (const unsigned long long x, const cl_R& y)
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{ return cl_I(x) / y; }
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#endif
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inline const cl_F operator/ (const float x, const cl_R& y)
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{ return The(cl_F)(cl_R(x) / y); }
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inline const cl_F operator/ (const double x, const cl_R& y)
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{ return The(cl_F)(cl_R(x) / y); }
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inline const cl_R operator/ (const cl_R& x, const int y)
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{ return x / cl_I(y); }
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inline const cl_R operator/ (const cl_R& x, const unsigned int y)
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{ return x / cl_I(y); }
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inline const cl_R operator/ (const cl_R& x, const long y)
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{ return x / cl_I(y); }
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inline const cl_R operator/ (const cl_R& x, const unsigned long y)
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{ return x / cl_I(y); }
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#ifdef HAVE_LONGLONG
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inline const cl_R operator/ (const cl_R& x, const long long y)
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{ return x / cl_I(y); }
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inline const cl_R operator/ (const cl_R& x, const unsigned long long y)
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{ return x / cl_I(y); }
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#endif
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inline const cl_R operator/ (const cl_R& x, const float y)
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{ return x / cl_R(y); }
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inline const cl_R operator/ (const cl_R& x, const double y)
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{ return x / cl_R(y); }
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// Liefert (abs x), wo x eine reelle Zahl ist.
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extern const cl_R abs (const cl_R& x);
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// recip(x) liefert (/ x), wo x eine reelle Zahl ist.
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extern const cl_R recip (const cl_R& x);
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// (1+ x), wo x eine reelle Zahl ist.
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extern const cl_R plus1 (const cl_R& x);
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// (1- x), wo x eine reelle Zahl ist.
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extern const cl_R minus1 (const cl_R& x);
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// Return type for rounding operators.
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// x / y --> (q,r) with x = y*q+r.
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struct cl_R_div_t {
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cl_I quotient;
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cl_R remainder;
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// Constructor.
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cl_R_div_t () {}
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cl_R_div_t (const cl_I& q, const cl_R& r) : quotient(q), remainder(r) {}
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cl_R_div_t (const struct cl_I_div_t &);
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cl_R_div_t (const struct cl_RA_div_t &);
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cl_R_div_t (const struct cl_F_div_t &);
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};
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// floor2(x) liefert (floor x), wo x eine reelle Zahl ist.
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extern const cl_R_div_t floor2 (const cl_R& x);
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extern const cl_I floor1 (const cl_R& x);
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// ceiling2(x) liefert (ceiling x), wo x eine reelle Zahl ist.
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extern const cl_R_div_t ceiling2 (const cl_R& x);
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extern const cl_I ceiling1 (const cl_R& x);
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// truncate2(x) liefert (truncate x), wo x eine reelle Zahl ist.
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extern const cl_R_div_t truncate2 (const cl_R& x);
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extern const cl_I truncate1 (const cl_R& x);
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// round2(x) liefert (round x), wo x eine reelle Zahl ist.
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extern const cl_R_div_t round2 (const cl_R& x);
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extern const cl_I round1 (const cl_R& x);
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// floor2(x,y) liefert (floor x y), wo x und y reelle Zahlen sind.
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extern const cl_R_div_t floor2 (const cl_R& x, const cl_R& y);
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extern const cl_I floor1 (const cl_R& x, const cl_R& y);
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// ceiling2(x,y) liefert (ceiling x y), wo x und y reelle Zahlen sind.
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extern const cl_R_div_t ceiling2 (const cl_R& x, const cl_R& y);
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extern const cl_I ceiling1 (const cl_R& x, const cl_R& y);
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// truncate2(x,y) liefert (truncate x y), wo x und y reelle Zahlen sind.
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extern const cl_R_div_t truncate2 (const cl_R& x, const cl_R& y);
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extern const cl_I truncate1 (const cl_R& x, const cl_R& y);
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// round2(x,y) liefert (round x y), wo x und y reelle Zahlen sind.
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extern const cl_R_div_t round2 (const cl_R& x, const cl_R& y);
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extern const cl_I round1 (const cl_R& x, const cl_R& y);
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// Return type for frounding operators.
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// x / y --> (q,r) with x = y*q+r.
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struct cl_R_fdiv_t {
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cl_F quotient;
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cl_R remainder;
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// Constructor.
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cl_R_fdiv_t () {}
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cl_R_fdiv_t (const cl_F& q, const cl_R& r) : quotient(q), remainder(r) {}
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cl_R_fdiv_t (const struct cl_F_fdiv_t &);
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};
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// ffloor2(x) liefert (ffloor x), wo x eine reelle Zahl ist.
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extern const cl_R_fdiv_t ffloor2 (const cl_R& x);
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extern const cl_F ffloor (const cl_R& x);
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// fceiling2(x) liefert (fceiling x), wo x eine reelle Zahl ist.
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extern const cl_R_fdiv_t fceiling2 (const cl_R& x);
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extern const cl_F fceiling (const cl_R& x);
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// ftruncate2(x) liefert (ftruncate x), wo x eine reelle Zahl ist.
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extern const cl_R_fdiv_t ftruncate2 (const cl_R& x);
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extern const cl_F ftruncate (const cl_R& x);
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// fround2(x) liefert (fround x), wo x eine reelle Zahl ist.
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extern const cl_R_fdiv_t fround2 (const cl_R& x);
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extern const cl_F fround (const cl_R& x);
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// ffloor2(x,y) liefert (ffloor x y), wo x und y reelle Zahlen sind.
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extern const cl_R_fdiv_t ffloor2 (const cl_R& x, const cl_R& y);
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extern const cl_F ffloor (const cl_R& x, const cl_R& y);
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// fceiling2(x,y) liefert (fceiling x y), wo x und y reelle Zahlen sind.
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extern const cl_R_fdiv_t fceiling2 (const cl_R& x, const cl_R& y);
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extern const cl_F fceiling (const cl_R& x, const cl_R& y);
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// ftruncate2(x,y) liefert (ftruncate x y), wo x und y reelle Zahlen sind.
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extern const cl_R_fdiv_t ftruncate2 (const cl_R& x, const cl_R& y);
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extern const cl_F ftruncate (const cl_R& x, const cl_R& y);
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// fround2(x,y) liefert (fround x y), wo x und y reelle Zahlen sind.
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extern const cl_R_fdiv_t fround2 (const cl_R& x, const cl_R& y);
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extern const cl_F fround (const cl_R& x, const cl_R& y);
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// mod(x,y) = (mod x y), wo x und y reelle Zahlen sind.
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extern const cl_R mod (const cl_R& x, const cl_R& y);
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// rem(x,y) = (rem x y), wo x und y reelle Zahlen sind.
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extern const cl_R rem (const cl_R& x, const cl_R& y);
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// rational(x) liefert (rational x), wo x eine reelle Zahl ist.
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extern const cl_RA rational (const cl_R& x);
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// Spezialfall:
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inline const cl_RA rational (const cl_RA& x) { return x; }
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// equal(x,y) vergleicht zwei reelle Zahlen x und y auf Gleichheit.
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extern bool equal (const cl_R& x, const cl_R& y);
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// equal_hashcode(x) liefert einen equal-invarianten Hashcode für x.
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extern uint32 equal_hashcode (const cl_R& x);
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// compare(x,y) vergleicht zwei reelle Zahlen x und y.
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// Ergebnis: 0 falls x=y, +1 falls x>y, -1 falls x<y.
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extern cl_signean compare (const cl_R& x, const cl_R& y);
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inline bool operator== (const cl_R& x, const cl_R& y)
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{ return equal(x,y); }
|
|
inline bool operator!= (const cl_R& x, const cl_R& y)
|
|
{ return !equal(x,y); }
|
|
inline bool operator<= (const cl_R& x, const cl_R& y)
|
|
{ return compare(x,y)<=0; }
|
|
inline bool operator< (const cl_R& x, const cl_R& y)
|
|
{ return compare(x,y)<0; }
|
|
inline bool operator>= (const cl_R& x, const cl_R& y)
|
|
{ return compare(x,y)>=0; }
|
|
inline bool operator> (const cl_R& x, const cl_R& y)
|
|
{ return compare(x,y)>0; }
|
|
|
|
// max(x,y) liefert (max x y), wo x und y reelle Zahlen sind.
|
|
extern const cl_R max (const cl_R& x, const cl_R& y);
|
|
|
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// min(x,y) liefert (min x y), wo x und y reelle Zahlen sind.
|
|
extern const cl_R min (const cl_R& x, const cl_R& y);
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|
|
|
// signum(x) liefert (signum x), wo x eine reelle Zahl ist.
|
|
extern const cl_R signum (const cl_R& x);
|
|
|
|
// sqrt(x) = (sqrt x) zieht die Wurzel aus einer reellen Zahl x >=0.
|
|
extern const cl_R sqrt (const cl_R& x);
|
|
// sqrt(x) = (sqrt x) zieht die Wurzel aus einer rationalen Zahl x >=0.
|
|
extern const cl_R sqrt (const cl_RA& x);
|
|
|
|
// (expt x y), wo x eine reelle Zahl und y ein Integer ist.
|
|
extern const cl_R expt (const cl_R& x, sintL y);
|
|
extern const cl_R expt (const cl_R& x, const cl_I& y);
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|
|
|
// rationalize(x) liefert (rationalize x), wo x eine reelle Zahl ist.
|
|
extern const cl_RA rationalize (const cl_R& x);
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|
|
// Konversion zu einem C "float".
|
|
extern float float_approx (const cl_R& x);
|
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|
|
// Konversion zu einem C "double".
|
|
extern double double_approx (const cl_R& x);
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|
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// Transcendental functions
|
|
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// atan(x,y) liefert zu zwei reellen Zahlen x, y den Winkel von (x,y)
|
|
// in Polarkoordinaten. Ergebnis rational nur, wenn x>0 und y=0.
|
|
extern const cl_R atan (const cl_R& x, const cl_R& y);
|
|
// Spezialfall: y Float -> Ergebnis Float
|
|
inline const cl_F atan (const cl_R& x, const cl_F& y)
|
|
{ return The(cl_F)(atan(x,The(cl_R)(y))); }
|
|
// Dem C++-Compiler muß man nun auch das Folgende sagen:
|
|
inline const cl_R atan (const cl_R& x, const int y)
|
|
{ return atan(x,cl_I(y)); }
|
|
inline const cl_R atan (const cl_R& x, const unsigned int y)
|
|
{ return atan(x,cl_I(y)); }
|
|
inline const cl_R atan (const cl_R& x, const long y)
|
|
{ return atan(x,cl_I(y)); }
|
|
inline const cl_R atan (const cl_R& x, const unsigned long y)
|
|
{ return atan(x,cl_I(y)); }
|
|
|
|
// atan(x) liefert den Arctan einer reellen Zahl x.
|
|
// Ergebnis rational nur, wenn x=0.
|
|
extern const cl_R atan (const cl_R& x);
|
|
// Spezialfall: x Float -> Ergebnis Float
|
|
inline const cl_F atan (const cl_F& x) { return The(cl_F)(atan(The(cl_R)(x))); }
|
|
// Dem C++-Compiler muß man nun auch das Folgende sagen:
|
|
inline const cl_R atan (const int x) { return atan(cl_I(x)); }
|
|
inline const cl_R atan (const unsigned int x) { return atan(cl_I(x)); }
|
|
inline const cl_R atan (const long x) { return atan(cl_I(x)); }
|
|
inline const cl_R atan (const unsigned long x) { return atan(cl_I(x)); }
|
|
|
|
// sin(x) liefert den Sinus (sin x) einer reellen Zahl x.
|
|
extern const cl_R sin (const cl_R& x);
|
|
// Dem C++-Compiler muß man nun auch das Folgende sagen:
|
|
inline const cl_R sin (const int x) { return sin(cl_I(x)); }
|
|
inline const cl_R sin (const unsigned int x) { return sin(cl_I(x)); }
|
|
inline const cl_R sin (const long x) { return sin(cl_I(x)); }
|
|
inline const cl_R sin (const unsigned long x) { return sin(cl_I(x)); }
|
|
|
|
// cos(x) liefert den Cosinus (cos x) einer reellen Zahl x.
|
|
extern const cl_R cos (const cl_R& x);
|
|
// Dem C++-Compiler muß man nun auch das Folgende sagen:
|
|
inline const cl_R cos (const int x) { return cos(cl_I(x)); }
|
|
inline const cl_R cos (const unsigned int x) { return cos(cl_I(x)); }
|
|
inline const cl_R cos (const long x) { return cos(cl_I(x)); }
|
|
inline const cl_R cos (const unsigned long x) { return cos(cl_I(x)); }
|
|
|
|
// cos_sin(x) liefert ((cos x),(sin x)), beide Werte.
|
|
extern const cos_sin_t cos_sin (const cl_R& x);
|
|
|
|
// tan(x) liefert den Tangens (tan x) einer reellen Zahl x.
|
|
extern const cl_R tan (const cl_R& x);
|
|
// Dem C++-Compiler muß man nun auch das Folgende sagen:
|
|
inline const cl_R tan (const int x) { return tan(cl_I(x)); }
|
|
inline const cl_R tan (const unsigned int x) { return tan(cl_I(x)); }
|
|
inline const cl_R tan (const long x) { return tan(cl_I(x)); }
|
|
inline const cl_R tan (const unsigned long x) { return tan(cl_I(x)); }
|
|
|
|
// ln(x) liefert zu einer reellen Zahl x>0 die Zahl ln(x).
|
|
extern const cl_R ln (const cl_R& x);
|
|
// Dem C++-Compiler muß man nun auch das Folgende sagen:
|
|
inline const cl_R ln (const int x) { return ln(cl_I(x)); }
|
|
inline const cl_R ln (const unsigned int x) { return ln(cl_I(x)); }
|
|
inline const cl_R ln (const long x) { return ln(cl_I(x)); }
|
|
inline const cl_R ln (const unsigned long x) { return ln(cl_I(x)); }
|
|
|
|
// log(a,b) liefert zu reellen Zahlen a>0, b>0 die Zahl
|
|
// log(a,b)=ln(a)/ln(b).
|
|
// Ergebnis rational nur, wenn a=1 oder a und b rational.
|
|
extern const cl_R log (const cl_R& a, const cl_R& b);
|
|
|
|
// exp(x) liefert zu einer reellen Zahl x die Zahl exp(x).
|
|
extern const cl_R exp (const cl_R& x);
|
|
// Dem C++-Compiler muß man nun auch das Folgende sagen:
|
|
inline const cl_R exp (const int x) { return exp(cl_I(x)); }
|
|
inline const cl_R exp (const unsigned int x) { return exp(cl_I(x)); }
|
|
inline const cl_R exp (const long x) { return exp(cl_I(x)); }
|
|
inline const cl_R exp (const unsigned long x) { return exp(cl_I(x)); }
|
|
|
|
// sinh(x) liefert zu einer reellen Zahl x die Zahl sinh(x).
|
|
extern const cl_R sinh (const cl_R& x);
|
|
// Dem C++-Compiler muß man nun auch das Folgende sagen:
|
|
inline const cl_R sinh (const int x) { return sinh(cl_I(x)); }
|
|
inline const cl_R sinh (const unsigned int x) { return sinh(cl_I(x)); }
|
|
inline const cl_R sinh (const long x) { return sinh(cl_I(x)); }
|
|
inline const cl_R sinh (const unsigned long x) { return sinh(cl_I(x)); }
|
|
|
|
// cosh(x) liefert zu einer reellen Zahl x die Zahl cosh(x).
|
|
extern const cl_R cosh (const cl_R& x);
|
|
// Dem C++-Compiler muß man nun auch das Folgende sagen:
|
|
inline const cl_R cosh (const int x) { return cosh(cl_I(x)); }
|
|
inline const cl_R cosh (const unsigned int x) { return cosh(cl_I(x)); }
|
|
inline const cl_R cosh (const long x) { return cosh(cl_I(x)); }
|
|
inline const cl_R cosh (const unsigned long x) { return cosh(cl_I(x)); }
|
|
|
|
// cosh_sinh(x) liefert ((cosh x),(sinh x)), beide Werte.
|
|
extern const cosh_sinh_t cosh_sinh (const cl_R& x);
|
|
|
|
// tanh(x) liefert zu einer reellen Zahl x die Zahl tanh(x).
|
|
extern const cl_R tanh (const cl_R& x);
|
|
// Dem C++-Compiler muß man nun auch das Folgende sagen:
|
|
inline const cl_R tanh (const int x) { return tanh(cl_I(x)); }
|
|
inline const cl_R tanh (const unsigned int x) { return tanh(cl_I(x)); }
|
|
inline const cl_R tanh (const long x) { return tanh(cl_I(x)); }
|
|
inline const cl_R tanh (const unsigned long x) { return tanh(cl_I(x)); }
|
|
|
|
|
|
// random_R(randomstate,n) liefert zu einer reellen Zahl n>0 eine Zufallszahl
|
|
// x mit 0 <= x < n.
|
|
extern const cl_R random_R (random_state& randomstate, const cl_R& n);
|
|
|
|
inline const cl_R random_R (const cl_R& n)
|
|
{ return random_R(default_random_state,n); }
|
|
|
|
|
|
// This could be optimized to use in-place operations.
|
|
inline cl_R& operator+= (cl_R& x, const cl_R& y) { return x = x + y; }
|
|
inline cl_F& operator+= (cl_F& x, const cl_R& y) { return x = x + y; }
|
|
inline cl_F& operator+= (cl_F& x, const cl_RA& y) { return x = x + y; }
|
|
inline cl_F& operator+= (cl_F& x, const cl_I& y) { return x = x + y; }
|
|
inline cl_R& operator+= (cl_R& x, const int y) { return x = x + y; }
|
|
inline cl_R& operator+= (cl_R& x, const unsigned int y) { return x = x + y; }
|
|
inline cl_R& operator+= (cl_R& x, const long y) { return x = x + y; }
|
|
inline cl_R& operator+= (cl_R& x, const unsigned long y) { return x = x + y; }
|
|
#ifdef HAVE_LONGLONG
|
|
inline cl_R& operator+= (cl_R& x, const long long y) { return x = x + y; }
|
|
inline cl_R& operator+= (cl_R& x, const unsigned long long y) { return x = x + y; }
|
|
#endif
|
|
inline cl_F& operator+= (cl_R& x, const float y) { return static_cast<cl_F&>(x = x + y); }
|
|
inline cl_F& operator+= (cl_R& x, const double y) { return static_cast<cl_F&>(x = x + y); }
|
|
inline cl_F& operator+= (cl_F& x, const int y) { return x = x + y; }
|
|
inline cl_F& operator+= (cl_F& x, const unsigned int y) { return x = x + y; }
|
|
inline cl_F& operator+= (cl_F& x, const long y) { return x = x + y; }
|
|
inline cl_F& operator+= (cl_F& x, const unsigned long y) { return x = x + y; }
|
|
#ifdef HAVE_LONGLONG
|
|
inline cl_F& operator+= (cl_F& x, const long long y) { return x = x + y; }
|
|
inline cl_F& operator+= (cl_F& x, const unsigned long long y) { return x = x + y; }
|
|
#endif
|
|
inline cl_R& operator++ /* prefix */ (cl_R& x) { return x = plus1(x); }
|
|
inline void operator++ /* postfix */ (cl_R& x, int dummy) { (void)dummy; x = plus1(x); }
|
|
inline cl_R& operator-= (cl_R& x, const cl_R& y) { return x = x - y; }
|
|
inline cl_F& operator-= (cl_F& x, const cl_R& y) { return x = x - y; }
|
|
inline cl_F& operator-= (cl_F& x, const cl_RA& y) { return x = x - y; }
|
|
inline cl_F& operator-= (cl_F& x, const cl_I& y) { return x = x - y; }
|
|
inline cl_R& operator-= (cl_R& x, const int y) { return x = x - y; }
|
|
inline cl_R& operator-= (cl_R& x, const unsigned int y) { return x = x - y; }
|
|
inline cl_R& operator-= (cl_R& x, const long y) { return x = x - y; }
|
|
inline cl_R& operator-= (cl_R& x, const unsigned long y) { return x = x - y; }
|
|
#ifdef HAVE_LONGLONG
|
|
inline cl_R& operator-= (cl_R& x, const long long y) { return x = x - y; }
|
|
inline cl_R& operator-= (cl_R& x, const unsigned long long y) { return x = x - y; }
|
|
#endif
|
|
inline cl_F& operator-= (cl_R& x, const float y) { return static_cast<cl_F&>(x = x - y); }
|
|
inline cl_F& operator-= (cl_R& x, const double y) { return static_cast<cl_F&>(x = x - y); }
|
|
inline cl_F& operator-= (cl_F& x, const int y) { return x = x - y; }
|
|
inline cl_F& operator-= (cl_F& x, const unsigned int y) { return x = x - y; }
|
|
inline cl_F& operator-= (cl_F& x, const long y) { return x = x - y; }
|
|
inline cl_F& operator-= (cl_F& x, const unsigned long y) { return x = x - y; }
|
|
#ifdef HAVE_LONGLONG
|
|
inline cl_F& operator-= (cl_F& x, const long long y) { return x = x - y; }
|
|
inline cl_F& operator-= (cl_F& x, const unsigned long long y) { return x = x - y; }
|
|
#endif
|
|
inline cl_R& operator-- /* prefix */ (cl_R& x) { return x = minus1(x); }
|
|
inline void operator-- /* postfix */ (cl_R& x, int dummy) { (void)dummy; x = minus1(x); }
|
|
inline cl_R& operator*= (cl_R& x, const cl_R& y) { return x = x * y; }
|
|
inline cl_R& operator*= (cl_R& x, const int y) { return x = x * y; }
|
|
inline cl_R& operator*= (cl_R& x, const unsigned int y) { return x = x * y; }
|
|
inline cl_R& operator*= (cl_R& x, const long y) { return x = x * y; }
|
|
inline cl_R& operator*= (cl_R& x, const unsigned long y) { return x = x * y; }
|
|
#ifdef HAVE_LONGLONG
|
|
inline cl_R& operator*= (cl_R& x, const long long y) { return x = x * y; }
|
|
inline cl_R& operator*= (cl_R& x, const unsigned long long y) { return x = x * y; }
|
|
#endif
|
|
inline cl_R& operator*= (cl_R& x, const float y) { return x = x * y; }
|
|
inline cl_R& operator*= (cl_R& x, const double y) { return x = x * y; }
|
|
inline cl_R& operator/= (cl_R& x, const cl_R& y) { return x = x / y; }
|
|
inline cl_F& operator/= (cl_F& x, const cl_R& y) { return x = x / y; }
|
|
inline cl_F& operator/= (cl_F& x, const cl_RA& y) { return x = x / y; }
|
|
inline cl_F& operator/= (cl_F& x, const cl_I& y) { return x = x / y; }
|
|
inline cl_R& operator/= (cl_R& x, const int y) { return x = x / y; }
|
|
inline cl_R& operator/= (cl_R& x, const unsigned int y) { return x = x / y; }
|
|
inline cl_R& operator/= (cl_R& x, const long y) { return x = x / y; }
|
|
inline cl_R& operator/= (cl_R& x, const unsigned long y) { return x = x / y; }
|
|
#ifdef HAVE_LONGLONG
|
|
inline cl_R& operator/= (cl_R& x, const long long y) { return x = x / y; }
|
|
inline cl_R& operator/= (cl_R& x, const unsigned long long y) { return x = x / y; }
|
|
#endif
|
|
inline cl_R& operator/= (cl_R& x, const float y) { return x = x / y; }
|
|
inline cl_R& operator/= (cl_R& x, const double y) { return x = x / y; }
|
|
inline cl_F& operator/= (cl_F& x, const int y) { return x = x / y; }
|
|
inline cl_F& operator/= (cl_F& x, const unsigned int y) { return x = x / y; }
|
|
inline cl_F& operator/= (cl_F& x, const long y) { return x = x / y; }
|
|
inline cl_F& operator/= (cl_F& x, const unsigned long y) { return x = x / y; }
|
|
#ifdef HAVE_LONGLONG
|
|
inline cl_F& operator/= (cl_F& x, const long long y) { return x = x / y; }
|
|
inline cl_F& operator/= (cl_F& x, const unsigned long long y) { return x = x / y; }
|
|
#endif
|
|
|
|
|
|
// Complex operations, trivial for reals
|
|
|
|
inline const cl_R realpart (const cl_R& x)
|
|
{
|
|
return x;
|
|
}
|
|
inline const cl_R imagpart (const cl_R& x)
|
|
{
|
|
(void)x; // unused x
|
|
return 0;
|
|
}
|
|
inline const cl_R conjugate (const cl_R& x)
|
|
{
|
|
return x;
|
|
}
|
|
|
|
|
|
// Debugging support.
|
|
#ifdef CL_DEBUG
|
|
extern int cl_R_debug_module;
|
|
CL_FORCE_LINK(cl_R_debug_dummy, cl_R_debug_module)
|
|
#endif
|
|
|
|
} // namespace cln
|
|
|
|
#endif /* _CL_REAL_H */
|