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433 lines
14 KiB
433 lines
14 KiB
// Public long float operations.
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#ifndef _CL_LFLOAT_H
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#define _CL_LFLOAT_H
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#include "cln/number.h"
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#include "cln/lfloat_class.h"
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#include "cln/integer_class.h"
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#include "cln/float.h"
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namespace cln {
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CL_DEFINE_AS_CONVERSION(cl_LF)
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// Liefert zu einem Long-Float x : (- x), ein LF.
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extern const cl_LF operator- (const cl_LF& x);
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// compare(x,y) vergleicht zwei Long-Floats 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_LF& x, const cl_LF& 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_LF& x);
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inline bool operator== (const cl_LF& x, const cl_LF& y)
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{ return compare(x,y)==0; }
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inline bool operator!= (const cl_LF& x, const cl_LF& y)
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{ return compare(x,y)!=0; }
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inline bool operator<= (const cl_LF& x, const cl_LF& y)
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{ return compare(x,y)<=0; }
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inline bool operator< (const cl_LF& x, const cl_LF& y)
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{ return compare(x,y)<0; }
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inline bool operator>= (const cl_LF& x, const cl_LF& y)
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{ return compare(x,y)>=0; }
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inline bool operator> (const cl_LF& x, const cl_LF& y)
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{ return compare(x,y)>0; }
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// minusp(x) == (< x 0)
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extern bool minusp (const cl_LF& x);
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// zerop(x) stellt fest, ob ein Long-Float x = 0.0 ist.
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extern bool zerop (const cl_LF& x);
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// plusp(x) == (> x 0)
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extern bool plusp (const cl_LF& x);
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// Liefert zu zwei Long-Float x und y : (+ x y), ein LF.
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extern const cl_LF operator+ (const cl_LF& x, const cl_LF& y);
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// Liefert zu zwei Long-Float x und y : (- x y), ein LF.
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extern const cl_LF operator- (const cl_LF& x, const cl_LF& y);
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// Liefert zu zwei Long-Float x und y : (* x y), ein LF.
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extern const cl_LF operator* (const cl_LF& x, const cl_LF& y);
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// Spezialfall x oder y Integer oder rationale Zahl.
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inline const cl_R operator* (const cl_LF& x, const cl_I& y)
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{
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extern const cl_R cl_LF_I_mul (const cl_LF&, const cl_I&);
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return cl_LF_I_mul(x,y);
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}
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inline const cl_R operator* (const cl_I& x, const cl_LF& y)
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{
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extern const cl_R cl_LF_I_mul (const cl_LF&, const cl_I&);
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return cl_LF_I_mul(y,x);
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}
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inline const cl_R operator* (const cl_LF& x, const cl_RA& y)
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{
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extern const cl_R cl_LF_RA_mul (const cl_LF&, const cl_RA&);
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return cl_LF_RA_mul(x,y);
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}
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inline const cl_R operator* (const cl_RA& x, const cl_LF& y)
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{
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extern const cl_R cl_LF_RA_mul (const cl_LF&, const cl_RA&);
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return cl_LF_RA_mul(y,x);
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}
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// Dem C++-Compiler muß man auch das Folgende sagen (wg. `int * cl_LF' u.ä.):
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inline const cl_R operator* (const int x, const cl_LF& 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_LF& y)
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{ return cl_I(x) * y; }
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inline const cl_R operator* (const long x, const cl_LF& 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_LF& 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_LF& 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_LF& 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 cl_LF& x, const int y)
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{ return x * cl_I(y); }
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inline const cl_R operator* (const cl_LF& 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_LF& x, const long y)
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{ return x * cl_I(y); }
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inline const cl_R operator* (const cl_LF& 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_LF& 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_LF& x, const unsigned long long y)
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{ return x * cl_I(y); }
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#endif
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// Spezialfall x = y.
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// Liefert zu einem Long-Float x : (* x x), ein LF.
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extern const cl_LF square (const cl_LF& x);
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// Liefert zu zwei Long-Float x und y : (/ x y), ein LF.
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extern const cl_LF operator/ (const cl_LF& x, const cl_LF& y);
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// Spezialfall x oder y Integer oder rationale Zahl.
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inline const cl_LF operator/ (const cl_LF& x, const cl_I& y)
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{
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extern const cl_LF cl_LF_I_div (const cl_LF& x, const cl_I& y);
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return cl_LF_I_div(x,y);
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}
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inline const cl_R operator/ (const cl_I& x, const cl_LF& y)
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{
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extern const cl_R cl_I_LF_div (const cl_I& x, const cl_LF& y);
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return cl_I_LF_div(x,y);
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}
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inline const cl_LF operator/ (const cl_LF& x, const cl_RA& y)
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{
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extern const cl_LF cl_LF_RA_div (const cl_LF& x, const cl_RA& y);
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return cl_LF_RA_div(x,y);
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}
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inline const cl_R operator/ (const cl_RA& x, const cl_LF& y)
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{
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extern const cl_R cl_RA_LF_div (const cl_RA& x, const cl_LF& y);
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return cl_RA_LF_div(x,y);
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}
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// Dem C++-Compiler muß man nun auch das Folgende sagen:
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inline const cl_LF operator/ (const cl_LF& x, const int y)
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{ return x / cl_I(y); }
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inline const cl_LF operator/ (const cl_LF& x, const unsigned int y)
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{ return x / cl_I(y); }
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inline const cl_LF operator/ (const cl_LF& x, const long y)
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{ return x / cl_I(y); }
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inline const cl_LF operator/ (const cl_LF& 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_LF operator/ (const cl_LF& x, const long long y)
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{ return x / cl_I(y); }
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inline const cl_LF operator/ (const cl_LF& 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 int x, const cl_LF& 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_LF& y)
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{ return cl_I(x) / y; }
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inline const cl_R operator/ (const long x, const cl_LF& 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_LF& 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_LF& 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_LF& y)
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{ return cl_I(x) / y; }
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#endif
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// Liefert zu einem Long-Float x>=0 : (sqrt x), ein LF.
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extern const cl_LF sqrt (const cl_LF& x);
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// recip(x) liefert (/ x), wo x ein Long-Float ist.
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extern const cl_LF recip (const cl_LF& x);
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// abs(x) liefert (abs x), wo x ein Long-Float ist.
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extern const cl_LF abs (const cl_LF& x);
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// (1+ x), wo x ein Long-Float ist.
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extern const cl_LF plus1 (const cl_LF& x);
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// (1- x), wo x ein Long-Float ist.
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extern const cl_LF minus1 (const cl_LF& x);
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// ffloor(x) liefert (ffloor x), wo x ein LF ist.
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extern const cl_LF ffloor (const cl_LF& x);
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// fceiling(x) liefert (fceiling x), wo x ein LF ist.
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extern const cl_LF fceiling (const cl_LF& x);
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// ftruncate(x) liefert (ftruncate x), wo x ein LF ist.
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extern const cl_LF ftruncate (const cl_LF& x);
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// fround(x) liefert (fround x), wo x ein LF ist.
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extern const cl_LF fround (const cl_LF& x);
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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_LF_fdiv_t {
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cl_LF quotient;
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cl_LF remainder;
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// Constructor.
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cl_LF_fdiv_t () {}
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cl_LF_fdiv_t (const cl_LF& q, const cl_LF& r) : quotient(q), remainder(r) {}
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};
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// ffloor2(x) liefert (ffloor x), wo x ein LF ist.
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inline const cl_LF_fdiv_t ffloor2 (const cl_LF& x)
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{
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extern const cl_LF LF_LF_minus_LF (const cl_LF&, const cl_LF&);
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cl_LF q = ffloor(x);
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return cl_LF_fdiv_t(q,LF_LF_minus_LF(x,q));
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}
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// fceiling2(x) liefert (fceiling x), wo x ein LF ist.
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inline const cl_LF_fdiv_t fceiling2 (const cl_LF& x)
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{
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extern const cl_LF LF_LF_minus_LF (const cl_LF&, const cl_LF&);
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cl_LF q = fceiling(x);
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return cl_LF_fdiv_t(q,LF_LF_minus_LF(x,q));
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}
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// ftruncate2(x) liefert (ftruncate x), wo x ein LF ist.
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inline const cl_LF_fdiv_t ftruncate2 (const cl_LF& x)
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{
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extern const cl_LF LF_LF_minus_LF (const cl_LF&, const cl_LF&);
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cl_LF q = ftruncate(x);
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return cl_LF_fdiv_t(q,LF_LF_minus_LF(x,q));
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}
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// fround2(x) liefert (fround x), wo x ein LF ist.
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inline const cl_LF_fdiv_t fround2 (const cl_LF& x)
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{
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extern const cl_LF LF_LF_minus_LF (const cl_LF&, const cl_LF&);
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cl_LF q = fround(x);
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return cl_LF_fdiv_t(q,LF_LF_minus_LF(x,q));
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}
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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_LF_div_t {
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cl_I quotient;
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cl_LF remainder;
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// Constructor.
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cl_LF_div_t () {}
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cl_LF_div_t (const cl_I& q, const cl_LF& r) : quotient(q), remainder(r) {}
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};
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// floor2(x) liefert (floor x), wo x ein LF ist.
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inline const cl_LF_div_t floor2 (const cl_LF& x)
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{
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extern const cl_LF LF_LF_minus_LF (const cl_LF&, const cl_LF&);
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extern const cl_I cl_LF_to_I (const cl_LF& x);
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cl_LF q = ffloor(x);
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return cl_LF_div_t(cl_LF_to_I(q),LF_LF_minus_LF(x,q));
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}
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inline const cl_I floor1 (const cl_LF& x)
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{
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extern const cl_I cl_LF_to_I (const cl_LF& x);
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return cl_LF_to_I(ffloor(x));
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}
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// ceiling2(x) liefert (ceiling x), wo x ein LF ist.
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inline const cl_LF_div_t ceiling2 (const cl_LF& x)
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{
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extern const cl_LF LF_LF_minus_LF (const cl_LF&, const cl_LF&);
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extern const cl_I cl_LF_to_I (const cl_LF& x);
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cl_LF q = fceiling(x);
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return cl_LF_div_t(cl_LF_to_I(q),LF_LF_minus_LF(x,q));
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}
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inline const cl_I ceiling1 (const cl_LF& x)
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{
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extern const cl_I cl_LF_to_I (const cl_LF& x);
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return cl_LF_to_I(fceiling(x));
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}
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// truncate2(x) liefert (truncate x), wo x ein LF ist.
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inline const cl_LF_div_t truncate2 (const cl_LF& x)
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{
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extern const cl_LF LF_LF_minus_LF (const cl_LF&, const cl_LF&);
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extern const cl_I cl_LF_to_I (const cl_LF& x);
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cl_LF q = ftruncate(x);
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return cl_LF_div_t(cl_LF_to_I(q),LF_LF_minus_LF(x,q));
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}
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inline const cl_I truncate1 (const cl_LF& x)
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{
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extern const cl_I cl_LF_to_I (const cl_LF& x);
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return cl_LF_to_I(ftruncate(x));
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}
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// round2(x) liefert (round x), wo x ein LF ist.
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inline const cl_LF_div_t round2 (const cl_LF& x)
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{
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extern const cl_LF LF_LF_minus_LF (const cl_LF&, const cl_LF&);
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extern const cl_I cl_LF_to_I (const cl_LF& x);
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cl_LF q = fround(x);
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return cl_LF_div_t(cl_LF_to_I(q),LF_LF_minus_LF(x,q));
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}
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inline const cl_I round1 (const cl_LF& x)
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{
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extern const cl_I cl_LF_to_I (const cl_LF& x);
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return cl_LF_to_I(fround(x));
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}
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// floor2(x,y) liefert (floor x y).
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extern const cl_LF_div_t floor2 (const cl_LF& x, const cl_LF& y);
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inline const cl_I floor1 (const cl_LF& x, const cl_LF& y) { return floor1(x/y); }
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// ceiling2(x,y) liefert (ceiling x y).
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extern const cl_LF_div_t ceiling2 (const cl_LF& x, const cl_LF& y);
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inline const cl_I ceiling1 (const cl_LF& x, const cl_LF& y) { return ceiling1(x/y); }
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// truncate2(x,y) liefert (truncate x y).
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extern const cl_LF_div_t truncate2 (const cl_LF& x, const cl_LF& y);
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inline const cl_I truncate1 (const cl_LF& x, const cl_LF& y) { return truncate1(x/y); }
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// round2(x,y) liefert (round x y).
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extern const cl_LF_div_t round2 (const cl_LF& x, const cl_LF& y);
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inline const cl_I round1 (const cl_LF& x, const cl_LF& y) { return round1(x/y); }
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// cl_float(x,y) returns a long float if y is a long float.
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inline const cl_LF cl_float (const cl_F& x, const cl_LF& y)
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{
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extern const cl_F cl_float (const cl_F& x, const cl_F& y);
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return The(cl_LF)(cl_float(x,(const cl_F&)y));
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}
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inline const cl_LF cl_float (const cl_I& x, const cl_LF& y)
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{
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extern const cl_F cl_float (const cl_I& x, const cl_F& y);
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return The(cl_LF)(cl_float(x,(const cl_F&)y));
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}
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inline const cl_LF cl_float (const cl_RA& x, const cl_LF& y)
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{
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extern const cl_F cl_float (const cl_RA& x, const cl_F& y);
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return The(cl_LF)(cl_float(x,(const cl_F&)y));
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}
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inline const cl_LF cl_float (int x, const cl_LF& y)
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{ return cl_float(cl_I(x),y); }
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inline const cl_LF cl_float (unsigned int x, const cl_LF& y)
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{ return cl_float(cl_I(x),y); }
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// Return type for decode_float:
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struct decoded_lfloat {
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cl_LF mantissa;
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cl_I exponent;
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cl_LF sign;
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// Constructor.
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decoded_lfloat () {}
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decoded_lfloat (const cl_LF& m, const cl_I& e, const cl_LF& s) : mantissa(m), exponent(e), sign(s) {}
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};
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// decode_float(x) liefert zu einem Float x: (decode-float x).
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// x = 0.0 liefert (0.0, 0, 1.0).
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// x = (-1)^s * 2^e * m liefert ((-1)^0 * 2^0 * m, e als Integer, (-1)^s).
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extern const decoded_lfloat decode_float (const cl_LF& x);
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// float_exponent(x) liefert zu einem Float x:
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// den Exponenten von (decode-float x).
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// x = 0.0 liefert 0.
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// x = (-1)^s * 2^e * m liefert e.
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extern sintE float_exponent (const cl_LF& x);
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// float_radix(x) liefert (float-radix x), wo x ein Float ist.
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inline sintL float_radix (const cl_LF& x)
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{
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(void)x; // unused x
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return 2;
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}
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// float_sign(x) liefert (float-sign x), wo x ein Float ist.
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extern const cl_LF float_sign (const cl_LF& x);
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// float_digits(x) liefert (float-digits x), wo x ein Float ist.
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// < ergebnis: ein uintC >0
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extern uintC float_digits (const cl_LF& x);
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// float_precision(x) liefert (float-precision x), wo x ein Float ist.
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// < ergebnis: ein uintC >=0
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extern uintC float_precision (const cl_LF& x);
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// integer_decode_float(x) liefert zu einem Float x: (integer-decode-float x).
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// x = 0.0 liefert (0, 0, 1).
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// x = (-1)^s * 2^e * m bei Float-Precision p liefert
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// (Mantisse 2^p * m als Integer, e-p als Integer, (-1)^s als Fixnum).
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extern const cl_idecoded_float integer_decode_float (const cl_LF& x);
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// scale_float(x,delta) liefert x*2^delta, wo x ein LF ist.
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extern const cl_LF scale_float (const cl_LF& x, sintC delta);
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extern const cl_LF scale_float (const cl_LF& x, const cl_I& delta);
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// max(x,y) liefert (max x y), wo x und y Floats sind.
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extern const cl_LF max (const cl_LF& x, const cl_LF& y);
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// min(x,y) liefert (min x y), wo x und y Floats sind.
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extern const cl_LF min (const cl_LF& x, const cl_LF& y);
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// signum(x) liefert (signum x), wo x ein Float ist.
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extern const cl_LF signum (const cl_LF& x);
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// Konversion zu einem C "float".
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extern float float_approx (const cl_LF& x);
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// Konversion zu einem C "double".
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extern double double_approx (const cl_LF& x);
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// This could be optimized to use in-place operations.
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inline cl_LF& operator+= (cl_LF& x, const cl_LF& y) { return x = x + y; }
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inline cl_LF& operator++ /* prefix */ (cl_LF& x) { return x = plus1(x); }
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inline void operator++ /* postfix */ (cl_LF& x, int dummy) { (void)dummy; x = plus1(x); }
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inline cl_LF& operator-= (cl_LF& x, const cl_LF& y) { return x = x - y; }
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inline cl_LF& operator-- /* prefix */ (cl_LF& x) { return x = minus1(x); }
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inline void operator-- /* postfix */ (cl_LF& x, int dummy) { (void)dummy; x = minus1(x); }
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inline cl_LF& operator*= (cl_LF& x, const cl_LF& y) { return x = x * y; }
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inline cl_LF& operator/= (cl_LF& x, const cl_LF& y) { return x = x / y; }
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// Runtime typing support.
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extern cl_class cl_class_lfloat;
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// Debugging support.
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#ifdef CL_DEBUG
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extern int cl_LF_debug_module;
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CL_FORCE_LINK(cl_LF_debug_dummy, cl_LF_debug_module)
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#endif
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} // namespace cln
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#endif /* _CL_LFLOAT_H */
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