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329 lines
10 KiB
329 lines
10 KiB
// Public double float operations.
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#ifndef _CL_DFLOAT_H
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#define _CL_DFLOAT_H
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#include "cln/number.h"
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#include "cln/dfloat_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_DF)
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// Liefert zu einem Double-Float x : (- x), ein DF.
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extern const cl_DF operator- (const cl_DF& x);
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// compare(x,y) vergleicht zwei Double-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_DF& x, const cl_DF& 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_DF& x);
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inline bool operator== (const cl_DF& x, const cl_DF& y)
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{ return compare(x,y)==0; }
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inline bool operator!= (const cl_DF& x, const cl_DF& y)
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{ return compare(x,y)!=0; }
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inline bool operator<= (const cl_DF& x, const cl_DF& y)
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{ return compare(x,y)<=0; }
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inline bool operator< (const cl_DF& x, const cl_DF& y)
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{ return compare(x,y)<0; }
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inline bool operator>= (const cl_DF& x, const cl_DF& y)
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{ return compare(x,y)>=0; }
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inline bool operator> (const cl_DF& x, const cl_DF& 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_DF& x);
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// zerop(x) stellt fest, ob ein Double-Float x = 0.0 ist.
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extern bool zerop (const cl_DF& x);
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// plusp(x) == (> x 0)
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extern bool plusp (const cl_DF& x);
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// Liefert zu zwei Double-Float x und y : (+ x y), ein DF.
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extern const cl_DF operator+ (const cl_DF& x, const cl_DF& y);
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// The C++ compiler may hesitate to do these conversions of its own:
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inline const cl_DF operator+ (const cl_DF& x, const double y)
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{ return x + cl_DF(y); }
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inline const cl_DF operator+ (const double x, const cl_DF& y)
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{ return cl_DF(x) + y; }
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// Liefert zu zwei Double-Float x und y : (- x y), ein DF.
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extern const cl_DF operator- (const cl_DF& x, const cl_DF& y);
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// The C++ compiler may hesitate to do these conversions of its own:
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inline const cl_DF operator- (const cl_DF& x, const double y)
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{ return x - cl_DF(y); }
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inline const cl_DF operator- (const double x, const cl_DF& y)
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{ return cl_DF(x) - y; }
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// Liefert zu zwei Double-Float x und y : (* x y), ein DF.
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extern const cl_DF operator* (const cl_DF& x, const cl_DF& y);
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// The C++ compiler may hesitate to do these conversions of its own:
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inline const cl_DF operator* (const cl_DF& x, const double y)
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{ return x * cl_DF(y); }
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inline const cl_DF operator* (const double x, const cl_DF& y)
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{ return cl_DF(x) * y; }
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// Liefert zu einem Double-Float x : (* x x), ein DF.
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inline const cl_DF square (const cl_DF& x) { return x*x; }
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// Liefert zu zwei Double-Float x und y : (/ x y), ein DF.
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extern const cl_DF operator/ (const cl_DF& x, const cl_DF& y);
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// The C++ compiler may hesitate to do these conversions of its own:
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inline const cl_DF operator/ (const cl_DF& x, const double y)
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{ return x / cl_DF(y); }
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inline const cl_DF operator/ (const double x, const cl_DF& y)
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{ return cl_DF(x) / y; }
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// Liefert zu einem Double-Float x>=0 : (sqrt x), ein DF.
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extern const cl_DF sqrt (const cl_DF& x);
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// recip(x) liefert (/ x), wo x ein Double-Float ist.
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extern const cl_DF recip (const cl_DF& x);
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// abs(x) liefert (abs x), wo x ein Double-Float ist.
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extern const cl_DF abs (const cl_DF& x);
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// (1+ x), wo x ein Double-Float ist.
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inline const cl_DF plus1 (const cl_DF& x)
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{
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extern const cl_DF cl_I_to_DF (const cl_I&);
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return x + cl_I_to_DF(cl_I(1));
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}
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// (1- x), wo x ein Double-Float ist.
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inline const cl_DF minus1 (const cl_DF& x)
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{
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extern const cl_DF cl_I_to_DF (const cl_I&);
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return x + cl_I_to_DF(cl_I(-1));
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}
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// ffloor(x) liefert (ffloor x), wo x ein DF ist.
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extern const cl_DF ffloor (const cl_DF& x);
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// fceiling(x) liefert (fceiling x), wo x ein DF ist.
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extern const cl_DF fceiling (const cl_DF& x);
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// ftruncate(x) liefert (ftruncate x), wo x ein DF ist.
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extern const cl_DF ftruncate (const cl_DF& x);
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// fround(x) liefert (fround x), wo x ein DF ist.
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extern const cl_DF fround (const cl_DF& 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_DF_fdiv_t {
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cl_DF quotient;
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cl_DF remainder;
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// Constructor.
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cl_DF_fdiv_t () {}
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cl_DF_fdiv_t (const cl_DF& q, const cl_DF& r) : quotient(q), remainder(r) {}
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};
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// ffloor2(x) liefert (ffloor x), wo x ein DF ist.
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inline const cl_DF_fdiv_t ffloor2 (const cl_DF& x)
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{ cl_DF q = ffloor(x); return cl_DF_fdiv_t(q,x-q); }
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// fceiling2(x) liefert (fceiling x), wo x ein DF ist.
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inline const cl_DF_fdiv_t fceiling2 (const cl_DF& x)
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{ cl_DF q = fceiling(x); return cl_DF_fdiv_t(q,x-q); }
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// ftruncate2(x) liefert (ftruncate x), wo x ein DF ist.
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inline const cl_DF_fdiv_t ftruncate2 (const cl_DF& x)
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{ cl_DF q = ftruncate(x); return cl_DF_fdiv_t(q,x-q); }
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// fround2(x) liefert (fround x), wo x ein DF ist.
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inline const cl_DF_fdiv_t fround2 (const cl_DF& x)
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{ cl_DF q = fround(x); return cl_DF_fdiv_t(q,x-q); }
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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_DF_div_t {
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cl_I quotient;
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cl_DF remainder;
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// Constructor.
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cl_DF_div_t () {}
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cl_DF_div_t (const cl_I& q, const cl_DF& r) : quotient(q), remainder(r) {}
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};
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// floor2(x) liefert (floor x), wo x ein DF ist.
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inline const cl_DF_div_t floor2 (const cl_DF& x)
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{
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extern const cl_I cl_DF_to_I (const cl_DF& x);
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cl_DF q = ffloor(x);
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return cl_DF_div_t(cl_DF_to_I(q),x-q);
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}
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inline const cl_I floor1 (const cl_DF& x)
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{
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extern const cl_I cl_DF_to_I (const cl_DF& x);
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return cl_DF_to_I(ffloor(x));
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}
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// ceiling2(x) liefert (ceiling x), wo x ein DF ist.
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inline const cl_DF_div_t ceiling2 (const cl_DF& x)
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{
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extern const cl_I cl_DF_to_I (const cl_DF& x);
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cl_DF q = fceiling(x);
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return cl_DF_div_t(cl_DF_to_I(q),x-q);
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}
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inline const cl_I ceiling1 (const cl_DF& x)
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{
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extern const cl_I cl_DF_to_I (const cl_DF& x);
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return cl_DF_to_I(fceiling(x));
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}
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// truncate2(x) liefert (truncate x), wo x ein DF ist.
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inline const cl_DF_div_t truncate2 (const cl_DF& x)
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{
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extern const cl_I cl_DF_to_I (const cl_DF& x);
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cl_DF q = ftruncate(x);
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return cl_DF_div_t(cl_DF_to_I(q),x-q);
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}
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inline const cl_I truncate1 (const cl_DF& x)
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{
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extern const cl_I cl_DF_to_I (const cl_DF& x);
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return cl_DF_to_I(ftruncate(x));
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}
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// round2(x) liefert (round x), wo x ein DF ist.
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inline const cl_DF_div_t round2 (const cl_DF& x)
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{
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extern const cl_I cl_DF_to_I (const cl_DF& x);
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cl_DF q = fround(x);
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return cl_DF_div_t(cl_DF_to_I(q),x-q);
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}
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inline const cl_I round1 (const cl_DF& x)
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{
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extern const cl_I cl_DF_to_I (const cl_DF& x);
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return cl_DF_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_DF_div_t floor2 (const cl_DF& x, const cl_DF& y);
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inline const cl_I floor1 (const cl_DF& x, const cl_DF& y) { return floor1(x/y); }
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// ceiling2(x,y) liefert (ceiling x y).
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extern const cl_DF_div_t ceiling2 (const cl_DF& x, const cl_DF& y);
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inline const cl_I ceiling1 (const cl_DF& x, const cl_DF& y) { return ceiling1(x/y); }
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// truncate2(x,y) liefert (truncate x y).
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extern const cl_DF_div_t truncate2 (const cl_DF& x, const cl_DF& y);
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inline const cl_I truncate1 (const cl_DF& x, const cl_DF& y) { return truncate1(x/y); }
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// round2(x,y) liefert (round x y).
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extern const cl_DF_div_t round2 (const cl_DF& x, const cl_DF& y);
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inline const cl_I round1 (const cl_DF& x, const cl_DF& y) { return round1(x/y); }
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// Return type for decode_float:
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struct decoded_dfloat {
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cl_DF mantissa;
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cl_I exponent;
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cl_DF sign;
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// Constructor.
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decoded_dfloat () {}
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decoded_dfloat (const cl_DF& m, const cl_I& e, const cl_DF& 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_dfloat decode_float (const cl_DF& 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_DF& 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_DF& 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_DF float_sign (const cl_DF& 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_DF& 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_DF& 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_DF& x);
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// scale_float(x,delta) liefert x*2^delta, wo x ein DF ist.
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extern const cl_DF scale_float (const cl_DF& x, sintC delta);
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extern const cl_DF scale_float (const cl_DF& 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_DF max (const cl_DF& x, const cl_DF& 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_DF min (const cl_DF& x, const cl_DF& y);
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// signum(x) liefert (signum x), wo x ein Float ist.
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extern const cl_DF signum (const cl_DF& x);
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// Konversion zu einem C "float".
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extern float float_approx (const cl_DF& x);
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// Konversion zu einem C "double".
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extern double double_approx (const cl_DF& x);
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#ifdef WANT_OBFUSCATING_OPERATORS
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// This could be optimized to use in-place operations.
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inline cl_DF& operator+= (cl_DF& x, const cl_DF& y) { return x = x + y; }
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inline cl_DF& operator+= (cl_DF& x, const double y) { return x = x + y; }
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inline cl_DF& operator++ /* prefix */ (cl_DF& x) { return x = plus1(x); }
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inline void operator++ /* postfix */ (cl_DF& x, int dummy) { (void)dummy; x = plus1(x); }
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inline cl_DF& operator-= (cl_DF& x, const cl_DF& y) { return x = x - y; }
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inline cl_DF& operator-= (cl_DF& x, const double y) { return x = x - y; }
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inline cl_DF& operator-- /* prefix */ (cl_DF& x) { return x = minus1(x); }
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inline void operator-- /* postfix */ (cl_DF& x, int dummy) { (void)dummy; x = minus1(x); }
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inline cl_DF& operator*= (cl_DF& x, const cl_DF& y) { return x = x * y; }
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inline cl_DF& operator*= (cl_DF& x, const double y) { return x = x * y; }
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inline cl_DF& operator/= (cl_DF& x, const cl_DF& y) { return x = x / y; }
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inline cl_DF& operator/= (cl_DF& x, const double y) { return x = x / y; }
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#endif
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/* */
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CL_REQUIRE(cl_ieee)
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// Runtime typing support.
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extern cl_class cl_class_dfloat;
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// Debugging support.
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#ifdef CL_DEBUG
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extern int cl_DF_debug_module;
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CL_FORCE_LINK(cl_DF_debug_dummy, cl_DF_debug_module)
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#endif
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} // namespace cln
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#endif /* _CL_DFLOAT_H */
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