39 #ifndef _CXSC_LX_REAL_HPP_INCLUDED 40 #define _CXSC_LX_REAL_HPP_INCLUDED 42 #include <l_imath.hpp> 49 const real Max_Int_R = 9007199254740991.0;
50 const real Max_Int_N = -9007199254738891.0;
70 lx_real(
void) throw() {}
72 lx_real(
const real& n,
const l_real &a)
throw()
75 cxscthrow(REAL_NOT_ALLOWED(
"lx_real(const real&, const l_real&)"));
83 lx_real(
const real& n,
const real &a)
throw()
86 cxscthrow(REAL_NOT_ALLOWED(
"lx_real(const real&, const real&)"));
94 explicit lx_real(
const l_real &a)
throw() : ex(0), lr(a) { }
96 explicit lx_real(
const real &a)
throw() : ex(0), lr(a) { }
98 lx_real(
const real&,
const string&) throw();
104 inline lx_real & operator = (const lx_real &) throw();
106 inline lx_real & operator = (const l_real &) throw();
108 inline lx_real & operator = (const real &) throw();
113 friend inline
int StagPrec(const lx_real&) throw();
115 friend inline real expo(const lx_real&) throw();
117 friend inline
int sign(const lx_real&) throw();
119 friend inline l_real lr_part(const lx_real&) throw();
121 friend inline lx_real
abs(const lx_real&) throw();
123 friend
void scale_up (lx_real &) throw();
125 friend
void scale_down(lx_real &) throw();
127 friend inline lx_real adjust(const lx_real &) throw();
130 friend inline
bool eq_zero (const lx_real &a) throw();
132 friend inline
bool gr_zero (const lx_real &a) throw();
134 friend inline
bool ge_zero (const lx_real &a) throw();
136 friend inline
bool sm_zero (const lx_real &a) throw();
138 friend inline
bool se_zero (const lx_real &a) throw();
141 friend inline
void times2pown(lx_real &, const real &) throw();
143 friend inline
void times2pown_neg(lx_real& a, const real& n) throw();
145 friend inline
bool operator ! (const lx_real &) throw();
147 friend inline lx_real operator -(const lx_real &) throw();
157 friend std::
string & operator << (std::
string &s, const lx_real& a)
168 inline
int StagPrec(const lx_real&) throw();
169 inline real expo(const lx_real&) throw();
170 inline
int sign(const lx_real&) throw();
171 inline l_real lr_part(const lx_real&) throw();
172 inline lx_real
abs(const lx_real&) throw();
173 inline lx_real adjust(const lx_real &) throw();
174 inline
void times2pown_neg(lx_real&, const real&) throw();
176 void scale_up (lx_real&) throw();
177 void scale_down(lx_real &a) throw();
179 inline
bool eq_zero (const lx_real &a) throw();
180 inline
bool gr_zero (const lx_real &a) throw();
181 inline
bool ge_zero (const lx_real &a) throw();
182 inline
bool sm_zero (const lx_real &a) throw();
183 inline
bool se_zero (const lx_real &a) throw();
185 inline
void times2pown(lx_real &, const real &) throw();
186 inline
bool operator ! (const lx_real &) throw();
188 inline lx_real operator -(const lx_real &) throw();
193 string & operator >> (
string &s, lx_real &a) throw();
195 void operator >> (const
string &s, lx_real &a) throw();
197 void operator >> (const
char *s, lx_real&) throw();
199 std::istream & operator >> (std::istream &s, lx_real &a) throw();
203 std::
string & operator << (std::
string &s, const lx_real& a)
208 inline std::
string & operator << (std::
string &s, const lx_real& a)
216 inline real
add_real(const real &a, const real &b) throw();
219 inline real
sub_real(const real &a, const real &b) throw();
222 lx_real
upper_bnd(const lx_real& x) throw();
225 lx_real
lower_bnd(const lx_real& x) throw();
227 inline lx_real operator +(const lx_real &) throw();
230 lx_real operator + (const lx_real &, const lx_real &) throw();
232 inline lx_real operator + (const lx_real&, const l_real &) throw();
234 inline lx_real operator + (const l_real&, const lx_real &) throw();
236 inline lx_real operator + (const lx_real&, const real &) throw();
238 inline lx_real operator + (const real&, const lx_real &) throw();
241 inline lx_real & operator +=(lx_real &, const lx_real &) throw();
243 inline lx_real & operator +=(lx_real &, const l_real &) throw();
245 inline lx_real & operator +=(lx_real &, const real &) throw();
248 inline lx_real operator - (const lx_real &, const lx_real &) throw();
250 inline lx_real operator - (const lx_real &, const l_real &) throw();
252 inline lx_real operator - (const l_real &, const lx_real &) throw();
254 inline lx_real operator - (const lx_real &, const real &) throw();
256 inline lx_real operator - (const real &, const lx_real &) throw();
259 inline lx_real & operator -=(lx_real &, const lx_real &) throw();
261 inline lx_real & operator -=(lx_real &, const l_real &) throw();
263 inline lx_real & operator -=(lx_real &, const real &) throw();
266 lx_real operator * (const lx_real &, const lx_real &) throw();
268 inline lx_real operator * (const lx_real&, const l_real &) throw();
270 inline lx_real operator * (const l_real&, const lx_real &) throw();
272 inline lx_real operator * (const lx_real&, const real &) throw();
274 inline lx_real operator * (const real&, const lx_real &) throw();
277 inline lx_real & operator *=(lx_real &, const lx_real &) throw();
279 inline lx_real & operator *=(lx_real &, const l_real &) throw();
281 inline lx_real & operator *=(lx_real &, const real &) throw();
284 lx_real operator / (const lx_real &, const lx_real &) throw(DIV_BY_ZERO);
286 inline lx_real operator / (const lx_real&, const l_real &) throw();
288 inline lx_real operator / (const l_real&, const lx_real &) throw();
290 inline lx_real operator / (const lx_real&, const real &) throw();
292 inline lx_real operator / (const real&, const lx_real &) throw();
295 inline lx_real & operator /=(lx_real &, const lx_real &) throw();
297 inline lx_real & operator /=(lx_real &, const l_real &) throw();
299 inline lx_real & operator /=(lx_real &, const real &) throw();
302 bool operator == (const lx_real &, const lx_real &) throw();
304 inline
bool operator == (const lx_real &, const l_real &) throw();
306 inline
bool operator == (const l_real &, const lx_real &) throw();
308 inline
bool operator == (const lx_real &, const real &) throw();
310 inline
bool operator == (const real &, const lx_real &) throw();
313 inline
bool operator != (const lx_real &, const lx_real &) throw();
315 inline
bool operator != (const lx_real &, const l_real &) throw();
317 inline
bool operator != (const l_real &, const lx_real &) throw();
319 inline
bool operator != (const lx_real &, const real &) throw();
321 inline
bool operator != (const real &, const lx_real &) throw();
324 bool operator > (const lx_real &, const lx_real &) throw();
327 inline
bool operator <= (const lx_real &, const lx_real &) throw();
329 inline
bool operator < (const lx_real &, const lx_real &) throw();
331 inline
bool operator >= (const lx_real &, const lx_real &) throw();
334 inline
bool operator > (const real &, const lx_real &) throw();
336 inline
bool operator <= (const real &, const lx_real &) throw();
338 inline
bool operator < (const real &, const lx_real &) throw();
340 inline
bool operator >= (const real &, const lx_real &) throw();
343 inline
bool operator > (const lx_real &, const real &) throw();
345 inline
bool operator <= (const lx_real &, const real &) throw();
347 inline
bool operator < (const lx_real &, const real &) throw();
349 inline
bool operator >= (const lx_real &, const real &) throw();
352 inline
bool operator > (const l_real &, const lx_real &) throw();
354 inline
bool operator <= (const l_real &, const lx_real &) throw();
356 inline
bool operator < (const l_real &, const lx_real &) throw();
358 inline
bool operator >= (const l_real &, const lx_real &) throw();
361 inline
bool operator > (const lx_real &, const l_real &) throw();
363 inline
bool operator <= (const lx_real &, const l_real &) throw();
365 inline
bool operator < (const lx_real &, const l_real &) throw();
367 inline
bool operator >= (const lx_real &, const l_real &) throw();
370 inline lx_real max(const lx_real&, const lx_real&);
372 inline lx_real min(const lx_real&, const lx_real&);
375 inline real
cutint(const real& x) throw();
464 const real ln_N[180] =
465 {6243314768165359.0 / 9007199254740992.0,
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644 5852987323223851.0 / 1125899906842624.0};
651 lx_real
sqrt(
const lx_real&) throw();
653 lx_real
sqr(const lx_real&) throw();
655 lx_real
ln(const lx_real &) throw();
657 lx_real
log2(const lx_real &) throw();
659 lx_real
log10(const lx_real &) throw();
661 lx_real
lnp1(const lx_real &) throw();
663 lx_real
exp(const lx_real &) throw();
665 lx_real
exp2(const lx_real &) throw();
667 lx_real
exp10(const lx_real &) throw();
669 lx_real
expm1(const lx_real &x) throw();
671 lx_real
power(const lx_real &, const real &) throw();
673 lx_real
pow(const lx_real &, const lx_real &) throw();
675 lx_real
xp1_pow_y(const lx_real &, const lx_real &) throw();
677 lx_real
sin(const lx_real &)throw();
679 lx_real
sin_n(const lx_real &x, const real& n) throw();
681 lx_real
cos(const lx_real &) throw();
683 lx_real
cos_n(const lx_real &x, const real& n) throw();
685 lx_real
tan(const lx_real &) throw();
687 lx_real
cot(const lx_real &) throw();
689 lx_real
sqrt1px2(const lx_real &) throw();
691 lx_real
atan(const lx_real &) throw();
693 lx_real
sqrt1mx2(const lx_real &) throw();
695 lx_real
sqrtx2m1(const lx_real &) throw();
697 lx_real
asin(const lx_real & ) throw();
699 lx_real
acos(const lx_real &) throw();
701 lx_real
acot(const lx_real &) throw();
703 lx_real
sinh(const lx_real &) throw();
705 lx_real
cosh(const lx_real &) throw();
707 lx_real
tanh(const lx_real &) throw();
709 lx_real
coth(const lx_real &) throw();
711 lx_real
sqrtp1m1(const lx_real &) throw();
713 lx_real
asinh(const lx_real &) throw();
715 lx_real
acosh(const lx_real &) throw();
717 lx_real
acoshp1(const lx_real &) throw();
719 lx_real
atanh(const lx_real &) throw();
721 lx_real
atanh1m(const lx_real &) throw();
723 lx_real
atanhm1p(const lx_real &) throw();
725 lx_real
acoth(const lx_real &) throw();
727 lx_real
acothp1(const lx_real &) throw();
729 lx_real
acothm1m(const lx_real &) throw();
731 lx_real
sqrtx2y2(const lx_real &, const lx_real &) throw();
733 lx_real
ln_sqrtx2y2(const lx_real &, const lx_real &) throw();
735 lx_real
sqrt(const lx_real &,
int) throw();
739 #include "lx_real.inl" 741 #endif // _CXSC_LX_REAL_HPP_INCLUDED cinterval sqrtx2m1(const cinterval &z)
Calculates .
cinterval sqrt1px2(const cinterval &z)
Calculates .
lx_real lower_bnd(const lx_real &x)
Returns a rather great lower bound of x.
cinterval log2(const cinterval &z)
Calculates .
lx_real EpPid4_lx_real()
lx_real approximation for
interval sqrtx2y2(const interval &x, const interval &y)
Calculates .
real cutint(const real &x)
Returns the truncated integer part of x.
cinterval ln(const cinterval &z)
Calculates .
cinterval sin(const cinterval &z)
Calculates .
lx_real EpPid2_lx_real()
lx_real approximation for
lx_real EpPi_lx_real()
lx_real approximation for
cinterval cot(const cinterval &z)
Calculates .
The namespace cxsc, providing all functionality of the class library C-XSC.
interval ln_sqrtx2y2(const interval &x, const interval &y)
Calculates .
cinterval acot(const cinterval &z)
Calculates .
lx_real E_lx_real()
lx_real approximation for
cinterval atan(const cinterval &z)
Calculates .
cinterval acos(const cinterval &z)
Calculates .
cinterval sqr(const cinterval &z)
Calculates .
lx_real Pid2_lx_real()
lx_real approximation for
lx_real One_p_lx_real()
lx_real approximation for
lx_real sqrt5_lx_real()
lx_real approximation for
cinterval expm1(const cinterval &z)
Calculates .
lx_interval cos_n(const lx_interval &x, const real &n)
Calculates .
lx_real Sqrt2_lx_real()
lx_real approximation for
lx_real Sqrt3d2_lx_real()
lx_real approximation for
real add_real(const real &a, const real &b)
Returns a,b must be integers with .
cinterval tanh(const cinterval &z)
Calculates .
cinterval asinh(const cinterval &z)
Calculates .
cinterval log10(const cinterval &z)
Calculates .
lx_real EulerGamma_lx_real()
lx_real approximation for
cinterval sqrt1mx2(const cinterval &z)
Calculates .
interval acoshp1(const interval &x)
Calculates .
lx_real SqrtPi_lx_real()
lx_real approximation for
cinterval lnp1(const cinterval &z)
Calculates .
lx_real Er_lx_real()
lx_real approximation for
lx_real Catalan_lx_real()
lx_real approximation for
lx_real Ln2Pi_lx_real()
lx_real approximation for
lx_real Pid3_lx_real()
lx_real approximation for
real sub_real(const real &a, const real &b)
Returns a,b must be integers with .
lx_real upper_bnd(const lx_real &x)
Returns a rather small upper bound of x.
lx_real Pip2_lx_real()
lx_real approximation for
cinterval sqrt(const cinterval &z)
Calculates .
lx_real Sqrt2Pi_lx_real()
lx_real approximation for
lx_interval atanh1m(const lx_interval &x)
Calculates .
lx_real sqrt7_lx_real()
lx_real approximation for
lx_interval sin_n(const lx_interval &x, const real &n)
Calculates .
cinterval cos(const cinterval &z)
Calculates .
lx_real LnPi_lx_real()
lx_real approximation for
cinterval atanh(const cinterval &z)
Calculates .
lx_interval atanhm1p(const lx_interval &x)
Calculates .
lx_real Sqrt3_lx_real()
lx_real approximation for
cinterval exp10(const cinterval &z)
Calculates .
void times2pown(cinterval &x, int n)
Fast multiplication of reference parameter [z] with .
cinterval sqrtp1m1(const cinterval &z)
Calculates .
lx_real Pi2_lx_real()
lx_real approximation for
cinterval exp(const cinterval &z)
Calculates .
lx_interval acothp1(const lx_interval &x)
Calculates .
lx_interval xp1_pow_y(const lx_interval &x, const lx_interval &y)
Calculates .
lx_real Ln2_lx_real()
lx_real approximation for
cinterval cosh(const cinterval &z)
Calculates .
lx_real Pir_lx_real()
lx_real approximation for
lx_real Ln2r_lx_real()
lx_real approximation for
cinterval tan(const cinterval &z)
Calculates .
cinterval sinh(const cinterval &z)
Calculates .
lx_real Sqrt2Pir_lx_real()
lx_real approximation for
lx_interval acothm1m(const lx_interval &x)
Calculates .
cinterval exp2(const cinterval &z)
Calculates .
lx_real Ep2_lx_real()
lx_real approximation for
lx_real Ep2r_lx_real()
lx_real approximation for
lx_real Ep2Pi_lx_real()
lx_real approximation for
cinterval asin(const cinterval &z)
Calculates .
cinterval acoth(const cinterval &z)
Calculates .
lx_real Ln10r_lx_real()
lx_real approximation for
lx_real Sqrt2r_lx_real()
lx_real approximation for
lx_real SqrtPir_lx_real()
lx_real approximation for
cinterval coth(const cinterval &z)
Calculates .
lx_real Sqrt3r_lx_real()
lx_real approximation for
cinterval pow(const cinterval &z, const interval &p)
Calculates .
lx_real One_m_lx_real()
lx_real approximation for
cinterval power(const cinterval &z, int n)
Calculates .
lx_real Pid4_lx_real()
lx_real approximation for
bool Is_Integer(const real &x)
Returns 1 if x is an integer value and if .
lx_real Ln10_lx_real()
lx_real approximation for
lx_real Pi_lx_real()
lx_real approximation for
ivector abs(const cimatrix_subv &mv)
Returns the absolute value of the matrix.
cinterval acosh(const cinterval &z)
Calculates .
lx_real Pi2r_lx_real()
lx_real approximation for