39 #ifndef _CXSC_LX_INTERVAL_HPP_INCLUDED
40 #define _CXSC_LX_INTERVAL_HPP_INCLUDED
42 #include <l_imath.hpp>
43 #include <lx_real.hpp>
63 lx_interval(
void) noexcept {}
66 lx_interval(
const real& n,
const l_interval& a) noexcept
69 cxscthrow(REAL_NOT_ALLOWED(
"lx_interval(const real&, const l_interval&)"));
77 lx_interval(
const real& n,
const l_real& a) noexcept
80 cxscthrow(REAL_NOT_ALLOWED(
"lx_interval(const real& n, const l_real& a)"));
88 lx_interval(
const real& n,
const interval& a) noexcept
91 cxscthrow(REAL_NOT_ALLOWED(
"lx_interval(const real&, const interval&)"));
99 explicit lx_interval(
const real& n,
const real& a) noexcept
102 cxscthrow(REAL_NOT_ALLOWED(
"lx_interval(const real&, const real&)"));
109 explicit lx_interval(
const l_interval& a) noexcept : ex(0), li(a) { }
111 explicit lx_interval(
const l_real& a) noexcept : ex(0), li(a) { }
113 lx_interval(
const l_real& a,
const l_real& b) noexcept : ex(0),li(a,b) { }
115 explicit lx_interval(
const interval& a) noexcept : ex(0), li(a) { }
117 explicit lx_interval(
const real& a) noexcept : ex(0), li(a) { }
119 lx_interval(
const lx_real&,
const lx_real&) noexcept;
121 explicit lx_interval(
const lx_real& a)
122 noexcept : ex(expo(a)), li(lr_part(a)) { }
124 lx_interval(
const real&,
const string&) noexcept;
129 inline lx_interval & operator = (
const lx_interval & a) noexcept;
131 inline lx_interval & operator = (
const l_interval & a) noexcept;
133 inline lx_interval & operator = (
const l_real & a) noexcept;
135 inline lx_interval & operator = (
const real & a) noexcept;
137 inline lx_interval & operator = (
const interval & a) noexcept;
139 inline lx_interval & operator = (
const lx_real & a) noexcept;
150 friend inline int StagPrec(
const lx_interval&) noexcept;
152 friend inline real expo(
const lx_interval&) noexcept;
154 friend inline l_interval li_part(
const lx_interval&) noexcept;
156 friend void scale_down(lx_interval &a);
158 friend void scale_up (lx_interval &a);
161 friend inline lx_interval adjust(
const lx_interval &) noexcept;
163 friend inline lx_interval
abs(
const lx_interval &) noexcept;
165 friend inline bool point_intv(
const lx_interval &);
167 friend inline bool operator ! (
const lx_interval &) noexcept;
169 friend inline bool IsEmpty(
const lx_interval &) noexcept;
171 friend inline void times2pown(lx_interval &,
const real &) noexcept;
173 friend inline lx_interval
Blow(
const lx_interval &) noexcept;
175 friend inline void times2pown_neg(lx_interval &,
const real&) noexcept;
177 friend inline lx_real
RelDiam(
const lx_interval &);
179 friend inline lx_real
diam(
const lx_interval &) noexcept;
181 friend inline lx_real
mid(
const lx_interval &) noexcept;
183 friend inline lx_real Inf(
const lx_interval &) noexcept;
185 friend inline lx_real Sup(
const lx_interval &) noexcept;
190 friend inline lx_interval operator-(
const lx_interval & a) noexcept;
196 friend std::ostream& operator << (std::ostream&,
const lx_interval&)
200 friend std::string & operator << (std::string&,
const lx_interval&)
210 inline int StagPrec(
const lx_interval &a) noexcept;
211 inline real expo(
const lx_interval &a) noexcept;
212 inline l_interval li_part(
const lx_interval &a) noexcept;
214 void scale_down(lx_interval &);
215 void scale_up (lx_interval &);
216 inline bool point_intv(
const lx_interval &);
217 inline bool IsEmpty(
const lx_interval &) noexcept;
218 inline void times2pown(lx_interval &,
const real &) noexcept;
219 inline lx_interval
Blow(
const lx_interval &) noexcept;
220 inline void times2pown_neg(lx_interval &,
const real&) noexcept;
221 inline lx_real
RelDiam(
const lx_interval &);
222 inline lx_real Inf(
const lx_interval &) noexcept;
223 inline lx_real Sup(
const lx_interval &) noexcept;
224 inline lx_interval
abs(
const lx_interval &) noexcept;
225 inline lx_interval adjust(
const lx_interval &) noexcept;
226 inline lx_real
diam(
const lx_interval &) noexcept;
227 inline lx_real
mid(
const lx_interval &) noexcept;
232 std::string & operator >> (std::string &s, lx_interval &a) noexcept;
234 void operator >> (
const std::string &s, lx_interval &a) noexcept;
236 void operator >> (
const char *s, lx_interval&) noexcept;
239 std::istream & operator >> (std::istream&, lx_interval&) noexcept;
243 std::ostream& operator << (std::ostream& s,
const lx_interval& a) noexcept;
248 std::string & operator << (std::string &s,
const lx_interval& a) noexcept;
257 void Bin2Dec(
const lx_interval& a, real& p, l_interval& m);
260 lx_interval
expo2zero(
const lx_interval &);
262 inline int Disjoint(
const lx_interval &,
const lx_interval &);
264 inline int in (
const lx_interval&,
const lx_interval&);
266 inline int in (
const l_interval&,
const lx_interval&);
268 inline int in (
const interval&,
const lx_interval&);
271 inline int in (
const lx_real&,
const lx_interval&);
273 inline int in (
const l_real&,
const lx_interval&);
275 inline int in (
const real&,
const lx_interval&);
278 inline lx_interval
Blow(
const lx_interval&,
const real& );
280 inline lx_real
AbsMin (
const lx_interval&);
282 inline lx_real
AbsMax (
const lx_interval&);
291 inline bool operator < (
const lx_interval&,
const lx_interval&) noexcept;
293 inline bool operator <= (
const lx_interval&,
const lx_interval&) noexcept;
295 inline bool operator > (
const lx_interval&,
const lx_interval&) noexcept;
297 inline bool operator >= (
const lx_interval&,
const lx_interval&) noexcept;
302 inline bool operator < (
const lx_interval&,
const l_interval&) noexcept;
304 inline bool operator <= (
const lx_interval&,
const l_interval&) noexcept;
306 inline bool operator < (
const l_interval&,
const lx_interval&) noexcept;
308 inline bool operator <= (
const l_interval&,
const lx_interval&) noexcept;
310 inline bool operator > (
const lx_interval&,
const l_interval&) noexcept;
311 inline bool operator >= (
const lx_interval&,
const l_interval&) noexcept;
313 inline bool operator > (
const l_interval&,
const lx_interval&) noexcept;
315 inline bool operator >= (
const l_interval&,
const lx_interval&) noexcept;
320 inline bool operator < (
const lx_interval&,
const interval&) noexcept;
322 inline bool operator <= (
const lx_interval&,
const interval&) noexcept;
324 inline bool operator < (
const interval&,
const lx_interval&) noexcept;
326 inline bool operator <= (
const interval&,
const lx_interval&) noexcept;
328 inline bool operator > (
const lx_interval&,
const interval&) noexcept;
330 inline bool operator >= (
const lx_interval&,
const interval&) noexcept;
332 inline bool operator > (
const interval&,
const lx_interval&) noexcept;
334 inline bool operator >= (
const interval&,
const lx_interval&) noexcept;
339 inline bool operator < (
const real &,
const lx_interval &) noexcept;
341 inline bool operator <= (
const real &,
const lx_interval &) noexcept;
343 inline bool operator > (
const lx_interval &,
const real &) noexcept;
345 inline bool operator >= (
const lx_interval &,
const real &) noexcept;
350 inline bool operator < (
const l_real &,
const lx_interval &) noexcept;
352 inline bool operator <= (
const l_real &,
const lx_interval &) noexcept;
354 inline bool operator > (
const lx_interval &,
const l_real &) noexcept;
356 inline bool operator >= (
const lx_interval &,
const l_real &) noexcept;
361 inline bool operator < (
const lx_real &,
const lx_interval &) noexcept;
363 inline bool operator <= (
const lx_real &,
const lx_interval &) noexcept;
365 inline bool operator > (
const lx_interval &,
const lx_real &) noexcept;
367 inline bool operator >= (
const lx_interval &,
const lx_real &) noexcept;
373 inline bool operator ! (
const lx_interval &) noexcept;
376 inline bool operator == (
const lx_interval &,
const lx_interval &) noexcept;
378 inline bool operator == (
const lx_interval &,
const l_interval &) noexcept;
380 inline bool operator == (
const l_interval &,
const lx_interval &) noexcept;
382 inline bool operator == (
const lx_interval &,
const interval &) noexcept;
384 inline bool operator == (
const interval &,
const lx_interval &) noexcept;
386 inline bool operator == (
const lx_interval &,
const real &) noexcept;
388 inline bool operator == (
const real &,
const lx_interval &) noexcept;
390 inline bool operator == (
const lx_interval &,
const l_real &) noexcept;
392 inline bool operator == (
const l_real &,
const lx_interval &) noexcept;
394 inline bool operator == (
const lx_interval &,
const lx_real &) noexcept;
396 inline bool operator == (
const lx_real &,
const lx_interval &) noexcept;
399 inline bool operator != (
const lx_interval &,
const lx_interval &) noexcept;
401 inline bool operator != (
const lx_interval &,
const l_interval &) noexcept;
403 inline bool operator != (
const l_interval &,
const lx_interval &) noexcept;
405 inline bool operator != (
const lx_interval &,
const interval &) noexcept;
407 inline bool operator != (
const interval &,
const lx_interval &) noexcept;
409 inline bool operator != (
const lx_interval &,
const real &) noexcept;
411 inline bool operator != (
const real &,
const lx_interval &) noexcept;
413 inline bool operator != (
const lx_interval &,
const l_real &) noexcept;
415 inline bool operator != (
const l_real &,
const lx_interval &) noexcept;
417 inline bool operator != (
const lx_interval &,
const lx_real &) noexcept;
419 inline bool operator != (
const lx_real &,
const lx_interval &) noexcept;
422 inline lx_interval operator+(
const lx_interval &) noexcept;
424 inline lx_interval operator-(
const lx_interval &) noexcept;
427 lx_interval operator + (
const lx_interval &,
const lx_interval &) noexcept;
430 inline lx_interval operator + (
const lx_interval &,
const l_interval &)
433 inline lx_interval operator + (
const l_interval &,
const lx_interval &)
436 inline lx_interval operator + (
const lx_interval &,
const l_real &)
439 inline lx_interval operator + (
const l_real &,
const lx_interval &)
442 inline lx_interval operator + (
const lx_interval &,
const lx_real &)
445 inline lx_interval operator + (
const lx_real &,
const lx_interval &)
448 inline lx_interval operator + (
const lx_interval &,
const real &)
451 inline lx_interval operator + (
const real &,
const lx_interval &)
454 inline lx_interval operator + (
const lx_interval &,
const interval &)
457 inline lx_interval operator + (
const interval &,
const lx_interval &)
461 inline lx_interval &
operator +=(lx_interval &,
const lx_interval &) noexcept;
463 inline lx_interval &
operator +=(lx_interval &,
const l_interval &) noexcept;
465 inline lx_interval &
operator +=(lx_interval &,
const l_real &) noexcept;
467 inline lx_interval &
operator +=(lx_interval &,
const lx_real &) noexcept;
469 inline lx_interval &
operator +=(lx_interval &,
const real &) noexcept;
471 inline lx_interval &
operator +=(lx_interval &,
const interval &) noexcept;
474 inline lx_interval operator - (
const lx_interval &,
const lx_interval &)
477 inline lx_interval operator - (
const lx_interval &,
const l_interval &)
480 inline lx_interval operator - (
const l_interval &,
const lx_interval &)
483 inline lx_interval operator - (
const lx_interval &,
const l_real &)
486 inline lx_interval operator - (
const l_real &,
const lx_interval &)
489 inline lx_interval operator - (
const lx_interval &,
const lx_real &)
492 inline lx_interval operator - (
const lx_real &,
const lx_interval &)
495 inline lx_interval operator - (
const lx_interval &,
const real &)
498 inline lx_interval operator - (
const real &,
const lx_interval &)
501 inline lx_interval operator - (
const lx_interval &,
const interval &)
504 inline lx_interval operator - (
const interval &,
const lx_interval &)
508 inline lx_interval & operator -=(lx_interval &,
const lx_interval &) noexcept;
510 inline lx_interval & operator -=(lx_interval &,
const l_interval &) noexcept;
512 inline lx_interval & operator -=(lx_interval &,
const l_real &) noexcept;
514 inline lx_interval & operator -=(lx_interval &,
const lx_real &) noexcept;
516 inline lx_interval & operator -=(lx_interval &,
const real &) noexcept;
518 inline lx_interval & operator -=(lx_interval &,
const interval &) noexcept;
521 lx_interval
operator * (
const lx_interval &,
const lx_interval &)
525 inline lx_interval
operator * (
const lx_interval &,
const l_interval &)
528 inline lx_interval
operator * (
const l_interval &,
const lx_interval &)
531 inline lx_interval
operator * (
const lx_interval &,
const l_real &)
534 inline lx_interval
operator * (
const l_real &,
const lx_interval &)
537 inline lx_interval
operator * (
const lx_interval &,
const lx_real &)
540 inline lx_interval
operator * (
const lx_real &,
const lx_interval &)
543 inline lx_interval
operator * (
const lx_interval &,
const real &)
546 inline lx_interval
operator * (
const real &,
const lx_interval &)
549 inline lx_interval
operator * (
const lx_interval &,
const interval &)
552 inline lx_interval
operator * (
const interval &,
const lx_interval &)
556 inline lx_interval &
operator *=(lx_interval &,
const lx_interval &) noexcept;
558 inline lx_interval &
operator *=(lx_interval &,
const l_interval &) noexcept;
560 inline lx_interval &
operator *=(lx_interval &,
const l_real &) noexcept;
562 inline lx_interval &
operator *=(lx_interval &,
const lx_real &) noexcept;
564 inline lx_interval &
operator *=(lx_interval &,
const real &) noexcept;
566 inline lx_interval &
operator *=(lx_interval &,
const interval &) noexcept;
569 lx_interval
operator / (
const lx_interval &,
const lx_interval &)
573 inline lx_interval
operator / (
const lx_interval &,
const l_interval &)
576 inline lx_interval
operator / (
const l_interval &,
const lx_interval &)
579 inline lx_interval
operator / (
const lx_interval &,
const l_real &)
582 inline lx_interval
operator / (
const l_real &,
const lx_interval &)
585 inline lx_interval
operator / (
const lx_interval &,
const real &)
588 inline lx_interval
operator / (
const real &,
const lx_interval &)
591 inline lx_interval
operator / (
const lx_interval &,
const interval &)
594 inline lx_interval
operator / (
const interval &,
const lx_interval &)
597 inline lx_interval
operator / (
const lx_interval &,
const lx_real &)
600 inline lx_interval
operator / (
const lx_real &,
const lx_interval &)
604 inline lx_interval &
operator /=(lx_interval &,
const lx_interval &) noexcept;
606 inline lx_interval &
operator /=(lx_interval &,
const l_interval &) noexcept;
608 inline lx_interval &
operator /=(lx_interval &,
const l_real &) noexcept;
610 inline lx_interval &
operator /=(lx_interval &,
const lx_real &) noexcept;
612 inline lx_interval &
operator /=(lx_interval &,
const real &) noexcept;
614 inline lx_interval &
operator /=(lx_interval &,
const interval &) noexcept;
619 inline lx_interval operator | (
const lx_interval&,
const lx_interval&)
622 inline lx_interval operator | (
const lx_interval&,
const l_interval&)
625 inline lx_interval operator | (
const l_interval&,
const lx_interval&)
628 inline lx_interval operator | (
const lx_interval&,
const interval&)
631 inline lx_interval operator | (
const interval&,
const lx_interval&)
634 inline lx_interval & operator |= (lx_interval&,
const lx_interval&)
637 inline lx_interval & operator |= (lx_interval&,
const l_interval&)
640 inline lx_interval & operator |= (lx_interval&,
const interval&)
643 inline lx_interval operator | (
const lx_real&,
const lx_interval&)
646 inline lx_interval operator | (
const real&,
const lx_interval&)
649 inline lx_interval operator | (
const lx_interval&,
const lx_real&)
652 inline lx_interval operator | (
const lx_interval&,
const real&)
655 inline lx_interval operator | (
const lx_interval&,
const l_real&)
658 inline lx_interval operator | (
const l_real&,
const lx_interval&)
661 inline lx_interval & operator |= (lx_interval&,
const real&)
664 inline lx_interval & operator |= (lx_interval&,
const l_real&)
667 inline lx_interval & operator |= (lx_interval&,
const lx_real&)
670 inline lx_interval operator | (
const lx_real&,
const lx_real&)
676 inline lx_interval operator & (
const lx_interval&,
const lx_interval&)
679 inline lx_interval operator & (
const lx_interval&,
const l_interval&)
682 inline lx_interval & operator &= (lx_interval&,
const l_interval&)
685 inline lx_interval operator & (
const l_interval&,
const lx_interval&)
688 inline lx_interval operator & (
const lx_interval&,
const interval&)
691 inline lx_interval & operator &= (lx_interval &a,
const interval &b)
694 inline lx_interval operator & (
const interval&,
const lx_interval&)
697 inline lx_interval & operator &= (lx_interval&,
const lx_interval&)
700 inline lx_interval operator & (
const lx_interval&,
const lx_real&)
703 inline lx_interval operator & (
const lx_interval&,
const l_real&)
706 inline lx_interval operator & (
const lx_interval&,
const real&)
709 inline lx_interval operator & (
const lx_real&,
const lx_interval&)
712 inline lx_interval operator & (
const l_real&,
const lx_interval&)
715 inline lx_interval operator & (
const real&,
const lx_interval&)
718 inline lx_interval & operator &= (lx_interval&,
const lx_real&)
721 inline lx_interval & operator &= (lx_interval&,
const l_real&)
724 inline lx_interval & operator &= (lx_interval&,
const real&)
730 inline lx_interval & SetInf(lx_interval&,
const lx_real&)
733 inline lx_interval & SetInf(lx_interval&,
const l_real&)
736 inline lx_interval & SetInf(lx_interval&,
const real&)
740 inline lx_interval & SetSup(lx_interval&,
const lx_real&)
743 inline lx_interval & SetSup(lx_interval&,
const l_real&)
746 inline lx_interval & SetSup(lx_interval&,
const real&)
860 lx_interval
sqrt(const lx_interval&) noexcept;
862 lx_interval
sqr(const lx_interval&) noexcept;
864 lx_interval
ln(const lx_interval &) noexcept;
866 lx_interval
log2(const lx_interval &) noexcept;
868 lx_interval
log10(const lx_interval &) noexcept;
870 lx_interval
lnp1(const lx_interval &) noexcept;
872 lx_interval
exp(const lx_interval &) noexcept;
874 lx_interval
exp2(const lx_interval &) noexcept;
876 lx_interval
exp10(const lx_interval &) noexcept;
878 lx_interval
expm1(const lx_interval &x) noexcept;
880 lx_interval
power(const lx_interval &, const real &) noexcept;
882 lx_interval
pow(const lx_interval &, const lx_interval &) noexcept;
884 lx_interval
xp1_pow_y(const lx_interval &, const lx_interval &) noexcept;
886 lx_interval
sin(const lx_interval &)throw();
888 lx_interval
sin_n(const lx_interval &x, const real& n) noexcept;
890 lx_interval
cos(const lx_interval &) noexcept;
892 lx_interval
cos_n(const lx_interval &x, const real& n) noexcept;
894 lx_interval
tan(const lx_interval &) noexcept;
896 lx_interval
cot(const lx_interval &) noexcept;
898 lx_interval
sqrt1px2(const lx_interval &) noexcept;
900 lx_interval
atan(const lx_interval &) noexcept;
902 lx_interval
sqrt1mx2(const lx_interval &) noexcept;
904 lx_interval
sqrtx2m1(const lx_interval &) noexcept;
906 lx_interval
asin(const lx_interval & ) noexcept;
908 lx_interval
acos(const lx_interval &) noexcept;
910 lx_interval
acot(const lx_interval &) noexcept;
912 lx_interval
sinh(const lx_interval &) noexcept;
914 lx_interval
cosh(const lx_interval &) noexcept;
916 lx_interval
tanh(const lx_interval &) noexcept;
918 lx_interval
coth(const lx_interval &) noexcept;
920 lx_interval
sqrtp1m1(const lx_interval &) noexcept;
922 lx_interval
asinh(const lx_interval &) noexcept;
924 lx_interval
acosh(const lx_interval &) noexcept;
926 lx_interval
acoshp1(const lx_interval &) noexcept;
928 lx_interval
atanh(const lx_interval &) noexcept;
930 lx_interval
atanh1m(const lx_interval &) noexcept;
932 lx_interval
atanhm1p(const lx_interval &) noexcept;
934 lx_interval
acoth(const lx_interval &) noexcept;
936 lx_interval
acothp1(const lx_interval &) noexcept;
938 lx_interval
acothm1m(const lx_interval &) noexcept;
940 lx_interval
sqrtx2y2(const lx_interval &, const lx_interval &) noexcept;
942 lx_interval
ln_sqrtx2y2(const lx_interval &, const lx_interval &) noexcept;
944 lx_interval
sqrt(const lx_interval &,
int) noexcept;
948 #include "lx_interval.inl"
The namespace cxsc, providing all functionality of the class library C-XSC.
lx_interval Sqrt2Pi_lx_interval() noexcept
Enclosure-Interval for .
l_interval wide_max(void)
Returns a wide interval with maximum exponent 1020.
lx_interval Er_lx_interval() noexcept
Enclosure-Interval for .
cinterval sqrtp1m1(const cinterval &z) noexcept
Calculates .
lx_interval Catalan_lx_interval() noexcept
Enclosure-Interval for .
cinterval exp2(const cinterval &z) noexcept
Calculates .
cinterval sqrt1mx2(const cinterval &z) noexcept
Calculates .
cinterval asinh(const cinterval &z) noexcept
Calculates .
lx_interval SqrtPi_lx_interval() noexcept
Enclosure-Interval for .
l_interval point_max(void)
Returns a point interval with maximum exponent 1020.
cinterval coth(const cinterval &z) noexcept
Calculates .
lx_interval expo2zero(const lx_interval &a)
b = expo2zero(a) returns with
cinterval log2(const cinterval &z) noexcept
Calculates .
lx_interval Sqrt2r_lx_interval() noexcept
Enclosure-Interval for .
cinterval power(const cinterval &z, int n) noexcept
Calculates .
cinterval log10(const cinterval &z) noexcept
Calculates .
lx_interval Ln10r_lx_interval() noexcept
Enclosure-Interval for .
lx_interval EpPid4_lx_interval() noexcept
Enclosure-Interval for .
lx_interval cos_n(const lx_interval &x, const real &n) noexcept
Calculates .
lx_interval Pir_lx_interval() noexcept
Enclosure-Interval for .
int Disjoint(const interval &a, const interval &b)
Checks arguments for disjointness.
cinterval ln(const cinterval &z) noexcept
Calculates .
lx_interval E_lx_interval() noexcept
Enclosure-Interval for .
lx_interval Pi2r_lx_interval() noexcept
Enclosure-Interval for .
lx_interval acothp1(const lx_interval &x) noexcept
Calculates .
lx_interval Sqrt2_lx_interval() noexcept
Enclosure-Interval for .
bool Is_Integer(const real &x)
Returns 1 if x is an integer value and if .
civector operator/(const cimatrix_subv &rv, const cinterval &s) noexcept
Implementation of division operation.
lx_interval Sqrt3_lx_interval() noexcept
Enclosure-Interval for .
lx_interval Ln2_lx_interval() noexcept
Enclosure-Interval for .
lx_interval Sqrt2Pir_lx_interval() noexcept
Enclosure-Interval for .
lx_interval Pid4_lx_interval() noexcept
Enclosure-Interval for .
lx_interval sqrt7_lx_interval() noexcept
Enclosure-Interval for .
cvector diam(const cimatrix_subv &mv) noexcept
Returns the diameter of the matrix.
lx_interval LnPi_lx_interval() noexcept
Enclosure-Interval for .
lx_interval Ln2Pi_lx_interval() noexcept
Enclosure-Interval for .
cinterval pow(const cinterval &z, const interval &p) noexcept
Calculates .
lx_interval EpPi_lx_interval() noexcept
Enclosure-Interval for .
lx_interval Sqrt3d2_lx_interval() noexcept
Enclosure-Interval for .
real RelDiam(const interval &x)
Computes the relative diameter .
lx_interval Ln10_lx_interval() noexcept
Enclosure-Interval for .
lx_interval EpPid2_lx_interval() noexcept
Enclosure-Interval for .
cinterval sinh(const cinterval &z) noexcept
Calculates .
lx_interval atanh1m(const lx_interval &x) noexcept
Calculates .
cinterval asin(const cinterval &z) noexcept
Calculates .
interval acoshp1(const interval &x)
Calculates .
cinterval tan(const cinterval &z) noexcept
Calculates .
lx_interval sqrt5_lx_interval() noexcept
Enclosure-Interval for .
cinterval exp10(const cinterval &z) noexcept
Calculates .
int in(const cinterval &x, const cinterval &y)
Checks if first argument is part of second argument.
lx_interval Sqrt3r_lx_interval() noexcept
Enclosure-Interval for .
cinterval acos(const cinterval &z) noexcept
Calculates .
cinterval sqrtx2m1(const cinterval &z) noexcept
Calculates .
cinterval acosh(const cinterval &z) noexcept
Calculates .
lx_interval sin_n(const lx_interval &x, const real &n) noexcept
Calculates .
l_interval wide_any(int n)
Returns a wide interval with exponent n, .
lx_interval Ep2r_lx_interval() noexcept
Enclosure-Interval for .
lx_interval SqrtPir_lx_interval() noexcept
Enclosure-Interval for .
cinterval cosh(const cinterval &z) noexcept
Calculates .
cinterval cos(const cinterval &z) noexcept
Calculates .
lx_interval Ln2r_lx_interval() noexcept
Enclosure-Interval for .
lx_interval Ep2_lx_interval() noexcept
Enclosure-Interval for .
lx_interval One_p_lx_interval() noexcept
Enclosure-Interval for .
cdotprecision & operator+=(cdotprecision &cd, const l_complex &lc) noexcept
Implementation of standard algebraic addition and allocation operation.
cinterval sqrt1px2(const cinterval &z) noexcept
Calculates .
cinterval exp(const cinterval &z) noexcept
Calculates .
lx_interval Pi_lx_interval() noexcept
Enclosure-Interval for .
cinterval tanh(const cinterval &z) noexcept
Calculates .
interval ln_sqrtx2y2(const interval &x, const interval &y) noexcept
Calculates .
cimatrix & operator*=(cimatrix &m, const cinterval &c) noexcept
Implementation of multiplication and allocation operation.
lx_interval Pid2_lx_interval() noexcept
Enclosure-Interval for .
real AbsMax(const interval &x)
Computes the greatest absolute value .
cinterval expm1(const cinterval &z) noexcept
Calculates .
cinterval cot(const cinterval &z) noexcept
Calculates .
lx_interval Ep2Pi_lx_interval() noexcept
Enclosure-Interval for .
ivector abs(const cimatrix_subv &mv) noexcept
Returns the absolute value of the matrix.
cinterval sqrt(const cinterval &z) noexcept
Calculates .
cinterval acot(const cinterval &z) noexcept
Calculates .
void times2pown(cinterval &x, int n) noexcept
Fast multiplication of reference parameter [z] with .
lx_interval Pid3_lx_interval() noexcept
Enclosure-Interval for .
cinterval sqr(const cinterval &z) noexcept
Calculates .
lx_interval atanhm1p(const lx_interval &x) noexcept
Calculates .
cinterval lnp1(const cinterval &z) noexcept
Calculates .
cvector mid(const cimatrix_subv &mv) noexcept
Returns the middle of the matrix.
civector operator*(const cimatrix_subv &rv, const cinterval &s) noexcept
Implementation of multiplication operation.
cinterval atan(const cinterval &z) noexcept
Calculates .
cinterval atanh(const cinterval &z) noexcept
Calculates .
lx_interval acothm1m(const lx_interval &x) noexcept
Calculates .
l_interval point_any(int n)
Returns a point interval with exponent n.
cinterval acoth(const cinterval &z) noexcept
Calculates .
lx_interval Pi2_lx_interval() noexcept
Enclosure-Interval for .
interval sqrtx2y2(const interval &x, const interval &y) noexcept
Calculates .
lx_interval One_m_lx_interval() noexcept
Enclosure-Interval for .
lx_interval xp1_pow_y(const lx_interval &x, const lx_interval &y) noexcept
Calculates .
lx_interval Pip2_lx_interval() noexcept
Enclosure-Interval for .
cinterval sin(const cinterval &z) noexcept
Calculates .
cinterval Blow(cinterval x, const real &eps)
Performs an epsilon inflation.
real AbsMin(const interval &x)
Computes the smallest absolute value .
cimatrix & operator/=(cimatrix &m, const cinterval &c) noexcept
Implementation of division and allocation operation.
lx_interval EulerGamma_lx_interval() noexcept
Enclosure-Interval for .