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SCIP Doxygen Documentation: intervalarith.c Source File

35#define _USE_MATH_DEFINES 50#if defined(__INTEL_COMPILER) || defined(_MSC_VER) 51#pragma fenv_access (on) 52#elif defined(__GNUC__) && !defined(__clang__) 53#pragma STDC FENV_ACCESS ON 63#if defined(__GNUC__) && !defined(__INTEL_COMPILER) 65#pragma clang optimize off 67#pragma GCC optimize ("O0"

)

74#ifdef SCIP_ROUNDING_FE 83#define SCIP_ROUND_DOWNWARDS FE_DOWNWARD 84#define SCIP_ROUND_UPWARDS FE_UPWARD 85#define SCIP_ROUND_NEAREST FE_TONEAREST 86#define SCIP_ROUND_ZERO FE_TOWARDZERO 103 if

( fesetround(roundmode) != 0 )

109

(void) fesetround(roundmode);

126#ifdef SCIP_ROUNDING_FP 135#define SCIP_ROUND_DOWNWARDS FP_RND_RM 136#define SCIP_ROUND_UPWARDS FP_RND_RP 137#define SCIP_ROUND_NEAREST FP_RND_RN 138#define SCIP_ROUND_ZERO FP_RND_RZ 155 if

( write_rnd(roundmode) != 0 )

161

(void) write_rnd(roundmode);

178#ifdef SCIP_ROUNDING_MS 187#define SCIP_ROUND_DOWNWARDS RC_DOWN 188#define SCIP_ROUND_UPWARDS RC_UP 189#define SCIP_ROUND_NEAREST RC_NEAR 190#define SCIP_ROUND_ZERO RC_CHOP 207 if

( (_controlfp(roundmode, _MCW_RC) & _MCW_RC) != roundmode )

213

(void) _controlfp(roundmode, _MCW_RC);

223 return

_controlfp(0, 0) & _MCW_RC;

233#define SCIP_ROUND_DOWNWARDS 0 234#define SCIP_ROUND_UPWARDS 1 235#define SCIP_ROUND_NEAREST 2 236#define SCIP_ROUND_ZERO 3 252 SCIPerrorMessage

(

"setting rounding mode not available - interval arithmetic is invalid!\n"

);

283#if defined(__GNUC__) && (defined(__i386__) || defined(__x86_64__)) 297

__asm

volatile

(

"fldl %1; fchs; fstpl %0"

:

"=m"

(

x

) :

"m"

(

x

));

304#elif defined(_MSC_VER) && (defined(__INTEL_COMPILER) || !defined(_M_X64)) 393#undef SCIPintervalGetInf 394#undef SCIPintervalGetSup 395#undef SCIPintervalSet 396#undef SCIPintervalSetBounds 397#undef SCIPintervalSetEmpty 398#undef SCIPintervalIsEmpty 399#undef SCIPintervalSetEntire 400#undef SCIPintervalIsEntire 401#undef SCIPintervalIsPositiveInfinity 402#undef SCIPintervalIsNegativeInfinity 409 return

interval.

;

417 return

interval.

;

426

assert(resultant !=

);

428

resultant->

= value;

429

resultant->

= value;

439

assert(resultant !=

);

442

resultant->

= inf;

443

resultant->

= sup;

451

assert(resultant !=

);

453

resultant->

= 1.0;

454

resultant->

= -1.0;

466 return

operand.

< operand.

;

475

assert(resultant !=

);

516 if

( operand1.

> operand1.

)

520 if

( operand2.

> operand2.

)

533 return

(operand1.

< operand2.

) || (operand2.

< operand1.

);

547 if

( operand1.

< operand2.

)

550 if

( operand1.

> operand2.

)

563

assert(resultant !=

);

585

assert(resultant !=

);

588 if

( operand1.

< operand2.

)

596 else if

( operand1.

> operand2.

)

615

assert(resultant !=

);

617 if

( operand1.

> operand1.

)

620

*resultant = operand2;

624 if

( operand2.

> operand2.

)

627

*resultant = operand1;

644

assert(resultant !=

);

658

resultant->

= operand1.

+ operand2.

;

671

assert(resultant !=

);

685

resultant->

= operand1.

+ operand2.

;

699

assert(resultant !=

);

726

assert(resultant !=

);

744

resultant->

= operand1.

+ operand2;

760

resultant->

= operand1.

+ operand2;

782 for

( i = 0; i < length; ++i )

788 for

( i = 0; i < length; ++i )

806

assert(resultant !=

);

824

resultant->

= operand1.

- operand2.

;

838

resultant->

= operand1.

- operand2.

;

863

assert(resultant !=

);

907

cand1 = operand1.

* operand2.

;

908

cand2 = operand1.

* operand2.

;

909

cand3 = operand1.

* operand2.

;

910

cand4 = operand1.

* operand2.

;

911

resultant->

=

(

(cand1, cand2),

(cand3, cand4));

923

assert(resultant !=

);

967

cand1 = operand1.

* operand2.

;

968

cand2 = operand1.

* operand2.

;

969

cand3 = operand1.

* operand2.

;

970

cand4 = operand1.

* operand2.

;

971

resultant->

=

(

(cand1, cand2),

(cand3, cand4));

985

assert(resultant !=

);

1011

assert(resultant !=

);

1017 if

( operand1.

> 0 )

1019 else if

( operand1.

< 0 )

1022

resultant->

= 0.0;

1027 if

( operand1.

> 0 )

1029 else if

( operand1.

< 0 )

1032

resultant->

= 0.0;

1034 else if

( operand2 == 0.0 )

1036

resultant->

= 0.0;

1038 else if

( operand2 > 0.0 )

1045

resultant->

= operand1.

* operand2;

1054

resultant->

= operand1.

* operand2;

1067

assert(resultant !=

);

1073 if

( operand1.

> 0 )

1075 else if

( operand1.

< 0 )

1078

resultant->

= 0.0;

1083 if

( operand1.

> 0 )

1085 else if

( operand1.

< 0 )

1088

resultant->

= 0.0;

1090 else if

( operand2 == 0.0 )

1092

resultant->

= 0.0;

1094 else if

( operand2 > 0.0 )

1101

resultant->

= operand1.

* operand2;

1110

resultant->

= operand1.

* operand2;

1124

assert(resultant !=

);

1127 if

( operand2 == 1.0 )

1129

*resultant = operand1;

1133 if

( operand2 == -1.0 )

1135

resultant->

= -operand1.

;

1136

resultant->

= -operand1.

;

1164

assert(resultant !=

);

1168 if

( operand2.

<= 0.0 && operand2.

>= 0.0 )

1175 if

( operand1.

== 0.0 && operand1.

== 0.0 )

1191

intmed.

= 1.0 / operand2.

;

1200

intmed.

= 1.0 / operand2.

;

1217

assert(resultant !=

);

1225

resultant->

= 0.0;

1226

resultant->

= 0.0;

1228 else if

( operand2 > 0.0 )

1240

resultant->

= operand1.

/ operand2;

1253

resultant->

= operand1.

/ operand2;

1256 else if

( operand2 < 0.0 )

1268

resultant->

= operand1.

/ operand2;

1281

resultant->

= operand1.

/ operand2;

1286 if

( operand1.

>= 0 )

1292 else if

( operand1.

<= 0 )

1325

resultant->

= 0.0;

1326

resultant->

= 0.0;

1330 for

( i = 0; i < length && resultant->

> -

; ++i )

1336

assert(resultant->

== 0.0);

1340 for

( i = 0; i < length && resultant->

<

; ++i )

1364

resultant->

= 0.0;

1368 for

( i = 0; i < length && resultant->

> -

; ++i )

1390

resultant->

= 0.0;

1394 for

( i = 0; i < length && resultant->

<

; ++i )

1415

resultant->

= 0.0;

1416

resultant->

= 0.0;

1421

assert(resultant->

== 0.0);

1439

assert(resultant !=

);

1444 if

( operand.

<= 0.0 )

1451

resultant->

= operand.

* operand.

;

1459

resultant->

= operand.

* operand.

;

1462 else if

( operand.

>= 0.0 )

1469

resultant->

= operand.

* operand.

;

1477

resultant->

= operand.

* operand.

;

1482

resultant->

= 0.0;

1491 x

= operand.

* operand.

;

1492 y

= operand.

* operand.

;

1509

assert(resultant !=

);

1512 if

( operand.

< 0.0 )

1518 if

( operand.

== operand.

)

1530

tmp = sqrt(operand.

);

1538 if

( operand.

<= 0.0 )

1539

resultant->

= 0.0;

1571

assert(resultant !=

);

1575 if

( operand2.

== operand2.

)

1584 if

( operand1.

== 0.0 )

1586 if

( operand2.

<= 0.0 && operand2.

>= 0.0 )

1618

assert(operand1 >= 0.0);

1620 if

( operand1 == 0.0 )

1622

assert(operand2 >= 0);

1623 if

( operand2 == 0 )

1630 if

( operand1 == 1.0 || operand2 == 0 )

1637

assert(result != 0.0);

1641

result = 1.0 / result;

1652

n = (

unsigned

int)operand2;

1671

result = result * z;

1701

assert(operand1 >= 0.0);

1703 if

( operand1 == 0.0 )

1705

assert(operand2 >= 0);

1706 if

( operand2 == 0 )

1713 if

( operand1 == 1.0 || operand2 == 0 )

1720

assert(result != 0.0);

1724

result = 1.0 / result;

1735

n = (

unsigned

int)operand2;

1746

result = result * z;

1776

assert(operand1 >= 0.0);

1778 if

( operand1 == 0.0 )

1780

assert(operand2 >= 0);

1781 if

( operand2 == 0 )

1794 if

( operand1 == 1.0 || operand2 == 0 )

1804

assert(resultant->

> 0.0 || resultant->

< 0.0);

1821

n = (

unsigned

int)operand2;

1834

result_sup = result_sup * z_sup;

1842

z_sup = z_sup * z_sup;

1848

resultant->

= result_inf;

1849

resultant->

= result_sup;

1850

assert(resultant->

<= resultant->

);

1868

assert(resultant !=

);

1870 if

( operand1 == 0.0 )

1872

assert(operand2 >= 0);

1873 if

( operand2 == 0 )

1886 if

( operand1 == 1.0 || operand2 == 0 )

1893

result = pow(operand1, operand2);

1912

assert(resultant !=

);

1921 if

( operand1.

< 0.0 )

1924

resultant->

= 0.0;

1925 if

( operand1.

> 0.0 )

1928

resultant->

= 0.0;

1932 if

( operand2 == 0.0 )

1934 if

( operand1.

== 0.0 && operand1.

== 0.0 )

1936

resultant->

= 0.0;

1937

resultant->

= 0.0;

1939 else if

( operand1.

<= 0.0 || operand1.

>= 0.0 )

1941

resultant->

= 0.0;

1942

resultant->

= 1.0;

1946

resultant->

= 1.0;

1947

resultant->

= 1.0;

1952 if

( operand2 == 1.0 )

1955

*resultant = operand1;

1959

op2isint = (ceil(operand2) == operand2);

1961 if

( !op2isint && operand1.

< 0.0 )

1963

operand1.

= 0.0;

1964 if

( operand1.

< operand1.

)

1971 if

( operand1.

>= 0.0 )

1973 if

( operand2 >= 0.0 )

1978 else if

( operand1.

> 0.0 )

1984

resultant->

= 0.0;

1988 else if

( operand1.

> 0.0 )

1994

resultant->

= 0.0;

1999

resultant->

= 0.0;

2000 else if

( operand1.

== 0.0 )

2004 if

( ceil(operand2/2) == operand2/2 )

2016 if

( operand1.

== 0.0 )

2025 else if

( operand1.

<= 0.0 )

2028 if

( operand2 >= 0.0 && ceil(operand2/2) == operand2/2 )

2042 else if

( operand2 <= 0.0 && ceil(operand2/2) != operand2/2 )

2047

resultant->

= 0.0;

2048 else if

( operand1.

== 0.0 )

2056

resultant->

= 0.0;

2057 else if

( operand1.

== 0.0 )

2063 else if

( operand2 >= 0.0 )

2080

resultant->

= 0.0;

2081 else if

( operand1.

== 0.0 )

2088

resultant->

= 0.0;

2089 else if

( operand1.

== 0.0 )

2100 if

( operand2 >= 0.0 && operand2/2 == ceil(operand2/2) )

2103

resultant->

= 0.0;

2109 else if

( operand2 <= 0.0 && ceil(operand2/2) == operand2/2 )

2114

resultant->

= 0.0;

2118 else if

( operand2 >= 0.0 )

2163

assert(resultant !=

);

2164

assert(image.

<= image.

);

2165

assert(basedomain.

<= basedomain.

);

2167 if

( exponent == 0.0 )

2170 if

( image.

<= 1.0 && image.

>= 1.0 )

2173

*resultant = basedomain;

2175 else if

( image.

<= 0.0 && image.

>= 0.0 )

2199 if

( image.

>= 0.0 )

2203 if

( basedomain.

<= -resultant->

&&

(exponent, 0.0) && (

int

)exponent % 2 == 0 )

2205 if

( basedomain.

< resultant->

)

2217 if

( image.

< 0.0 && basedomain.

< 0.0 &&

(exponent, 0.0) && ((

int

)exponent % 2 != 0) )

2241

assert(resultant !=

);

2244

assert(operand2 >= 0.0);

2252 if

( operand1.

< 0.0 )

2255

resultant->

= 0.0;

2256 if

( operand1.

> 0.0 )

2259

resultant->

= 0.0;

2263 if

( operand2 == 0.0 )

2266 if

( operand1.

< 0.0 )

2267

resultant->

= -1.0;

2268 else if

( operand1.

== 0.0 )

2269

resultant->

= 0.0;

2271

resultant->

= 1.0;

2273 if

( operand1.

< 0.0 )

2274

resultant->

= -1.0;

2275 else if

( operand1.

== 0.0 )

2276

resultant->

= 0.0;

2278

resultant->

= 1.0;

2283 if

( operand2 == 1.0 )

2285

*resultant = operand1;

2291 if

( operand2 == 2.0 )

2301 else if

( operand1.

> 0.0 )

2304

resultant->

= operand1.

* operand1.

;

2321 else if

( operand1.

> 0.0 )

2324

resultant->

= operand1.

* operand1.

;

2332

assert(resultant->

<= resultant->

);

2334 else if

( operand2 == 0.5 )

2340 else if

( operand1.

>= 0.0 )

2355 else if

( operand1.

> 0.0 )

2365

assert(resultant->

<= resultant->

);

2373 else if

( operand1.

> 0.0 )

2388 else if

( operand1.

> 0.0 )

2413

assert(resultant !=

);

2416 if

( operand.

== 0.0 && operand.

== 0.0 )

2425 if

( operand.

>= 0.0 )

2428

resultant->

= 0.0;

2432

resultant->

= 1.0 / operand.

;

2436

resultant->

= 0.0;

2437 else if

( operand.

== 0.0 )

2442

resultant->

= 1.0 / operand.

;

2447 else if

( operand.

<= 0.0 )

2450

resultant->

= 0.0;

2451 else if

( operand.

== 0.0 )

2456

resultant->

= 1.0 / operand.

;

2464

resultant->

= 1.0 / operand.

;

2484

assert(resultant !=

);

2489

resultant->

= 0.0;

2490

resultant->

= 0.0;

2501 if

( operand.

== operand.

)

2503 if

( operand.

== 0.0 )

2505

resultant->

= 1.0;

2506

resultant->

= 1.0;

2513

tmp = exp(operand.

);

2515

assert(resultant->

>= 0.0);

2524

resultant->

= 0.0;

2526 else if

( operand.

== 0.0 )

2528

resultant->

= 1.0;

2535

tmp = exp(operand.

);

2546 else if

( operand.

== 0.0 )

2548

resultant->

= 1.0;

2568

assert(resultant !=

);

2574 if

( operand.

<= 0.0 )

2580 if

( operand.

== operand.

)

2582 if

( operand.

== 1.0 )

2584

resultant->

= 0.0;

2585

resultant->

= 0.0;

2592

tmp = log(operand.

);

2600 if

( operand.

<= 0.0 )

2604 else if

( operand.

== 1.0 )

2606

resultant->

= 0.0;

2618 else if

( operand.

== 1.0 )

2620

resultant->

= 0.0;

2637

assert(resultant !=

);

2641

resultant->

=

(operand1.

, operand2.

);

2642

resultant->

=

(operand1.

, operand2.

);

2653

assert(resultant !=

);

2657

resultant->

=

(operand1.

, operand2.

);

2658

resultant->

=

(operand1.

, operand2.

);

2668

assert(resultant !=

);

2671 if

( operand.

<= 0.0 && operand.

>= 0.0)

2673

resultant->

= 0.0;

2676 else if

( operand.

> 0.0 )

2678

*resultant = operand;

2682

resultant->

= -operand.

;

2683

resultant->

= -operand.

;

2692static const double pi_d_l

= (3373259426.0 + 273688.0 / (1<<21)) / (1<<30);

2693static const double pi_d_u

= (3373259426.0 + 273689.0 / (1<<21)) / (1<<30);

2695#define pi_d_l ((3373259426.0 + 273688.0 / (1<<21)) / (1<<30)) 2696#define pi_d_u ((3373259426.0 + 273689.0 / (1<<21)) / (1<<30)) 2724

tmp = -resultant->

;

2725

resultant->

= -resultant->

;

2726

resultant->

= tmp;

2736

resultant->

= 0.0;

2737 else if

( operand.

== 0.0 && operand.

> -

)

2738

resultant->

= 0.0;

2762

assert(resultant !=

);

2767 if

( operand.

== operand.

)

2772

tmp = cos(operand.

);

2781 if

( operand.

> 1e12 || operand.

< -1e12 )

2791

negwidth = operand.

- operand.

;

2792 if

( -negwidth >= 2.0*

)

2811

assert(operand.

>= 0.0);

2822

resultant->

=

(-1.0, resultant->

);

2823 if

( operand.

== 0.0 )

2824

resultant->

= 1.0;

2828

resultant->

=

( 1.0, resultant->

);

2835

resultant->

= -1.0;

2836 if

( operand.

== 0.0 )

2837

resultant->

= 1.0;

2843

cinf = cos(operand.

);

2844

csup = cos(operand.

);

2846

resultant->

=

(1.0, resultant->

);

2856 if

( fmod(k, 2.0) != 0.0 )

2859

resultant->

= -resultant->

;

2860

resultant->

= tmp;

2864

assert(resultant->

>= -1.0);

2865

assert(resultant->

<= 1.0);

2875

assert(resultant !=

);

2878 if

( operand.

< 0.0 )

2880

resultant->

= -1.0;

2881

resultant->

= -1.0;

2883 else if

( operand.

>= 0.0 )

2885

resultant->

= 1.0;

2886

resultant->

= 1.0;

2890

resultant->

= -1.0;

2891

resultant->

= 1.0;

2912

assert(resultant !=

);

2916 if

( operand.

< 0.0 )

2923 if

( operand.

== 0.0 )

2933 if

( operand.

> 0.0 )

2935

loginf = log(operand.

);

2942

logsup = log(operand.

);

2951 if

( operand.

> 0.0 )

2976

inf =

(infcand1, infcand2);

2979 if

( operand.

<= extr && extr <= operand.

)

2982

sup =

(supcand1, supcand2, extr);

2985

sup =

(supcand1, supcand2);

3028

cand1 = b_.

*

x

.inf;

3029

cand2 = b_.

*

x

.sup;

3030

cand3 = b_.

*

x

.inf;

3031

cand4 = b_.

*

x

.sup;

3032

u =

(

(cand1, cand2),

(cand3, cand4));

3040 if

(

x

.sup <= 0.0 )

3052 if

(

x

.inf >= 0.0 )

3063

u =

(

x

.inf * (

a

*

x

.inf +

b

),

x

.sup * (

a

*

x

.sup +

b

));

3066 if

( t >

x

.inf &&

(2*

a

)*

x

.sup >

b

&& s*t > u )

3077

assert(

x

.inf < 0.0 &&

x

.sup > 0);

3083 return MAX

(cand1, cand2);

3105 if

( sqrcoeff == 0.0 )

3113

tmp = lincoeff.

;

3114

lincoeff.

= -lincoeff.

;

3115

lincoeff.

= -tmp;

3118

assert(resultant->

>= resultant->

);

3134

assert(resultant !=

);

3139

resultant->

= 0.0;

3145 SCIPdebugMessage

(

"solve %g*x^2 + %g*x >= %g gives [%.20f, %.20f]\n"

, -sqrcoeff.

, -lincoeff.

, -rhs.

, resultant->

, resultant->

);

3187

tmp = lincoeff.

;

3188

lincoeff.

= -lincoeff.

;

3189

lincoeff.

= -tmp;

3192

xbnds.

= -xbnds.

;

3197

tmp = resultant->

;

3198

resultant->

= -resultant->

;

3199

resultant->

= -tmp;

3222

assert(resultant !=

);

3226 if

( sqrcoeff == 0.0 )

3239 if

( lincoeff <= 0.0 && rhs > 0.0 )

3245 if

( lincoeff >= 0.0 && rhs <= 0.0 )

3248

resultant->

=

(0.0, xbnds.

);

3249

resultant->

= xbnds.

;

3255 if

( lincoeff < 0.0 && rhs <= 0.0 )

3258

resultant->

=

(0.0, xbnds.

);

3261

resultant->

= rhs / lincoeff;

3262 if

( xbnds.

< resultant->

)

3263

resultant->

= xbnds.

;

3267

assert(lincoeff > 0.0);

3273

resultant->

= rhs / lincoeff;

3274 if

( resultant->

< xbnds.

)

3275

resultant->

= xbnds.

;

3277

resultant->

= xbnds.

;

3285

resultant->

= 0.0;

3296 if

( lincoeff >= 0.0 )

3301

delta =

b

*

b

+ sqrcoeff*rhs;

3313 if

( sqrcoeff < 0.0 )

3314

resultant->

= z /

(sqrcoeff);

3319 if

( sqrcoeff < 0.0 )

3322

delta =

b

*

b

+ sqrcoeff*rhs;

3327

resultant->

= z /

(sqrcoeff);

3335 if

( sqrcoeff > 0.0 )

3338

delta =

b

*

b

+ sqrcoeff*rhs;

3343

resultant->

= z / sqrcoeff;

3353

delta =

b

*

b

+ sqrcoeff * rhs;

3367 if

( sqrcoeff > 0.0 )

3376 if

( xbnds.

< zdiva )

3380 else if

( xbnds.

> resultant->

)

3383

resultant->

= zdiva;

3424

assert(resultant !=

);

3433 if

( sqrcoeff.

== 0.0 && sqrcoeff.

== 0.0 && (lincoeff.

> 0.0 || lincoeff.

< 0.0) )

3437 SCIPdebugMessage

(

"solving [%g,%g]*x = [%g,%g] for x in [%g,%g] gives [%g,%g]\n"

, lincoeff.

, lincoeff.

, rhs.

, rhs.

, xbnds.

, xbnds.

, resultant->

, resultant->

);

3441 SCIPdebugMessage

(

"solving [%g,%g]*x^2 + [%g,%g]*x = [%g,%g] for x in [%g,%g]\n"

, sqrcoeff.

, sqrcoeff.

, lincoeff.

, lincoeff.

, rhs.

, rhs.

, xbnds.

, xbnds.

);

3444 if

( xbnds.

>= 0 )

3447 SCIPdebugMessage

(

" solutions of [%g,%g]*x^2 + [%g,%g]*x in [%g,%g] for x in [%g,%g] are [%.15g,%.15g]\n"

,

3448

sqrcoeff.

, sqrcoeff.

, lincoeff.

, lincoeff.

, rhs.

, rhs.

,

(xbnds.

, 0.0), xbnds.

, xpos.

, xpos.

);

3456 if

( xbnds.

<= 0.0 )

3459 SCIPdebugMessage

(

" solutions of [%g,%g]*x^2 + [%g,%g]*x in [%g,%g] for x in [%g,%g] are [%g,%g]\n"

,

3460

sqrcoeff.

, sqrcoeff.

, lincoeff.

, lincoeff.

, rhs.

, rhs.

, xbnds.

,

(xbnds.

, 0.0), xneg.

, xneg.

);

3498

assert(resultant !=

);

3499

assert(xbnds.

<= xbnds.

);

3500

assert(ybnds.

<= ybnds.

);

3524

denom = 4.0 * ax * ay - axy * axy;

3527 x

= (axy * by - 2.0 * ay * bx) / denom;

3528 y

= (axy * bx - 2.0 * ax * by) / denom;

3529 if

( xbnds.

<=

x

&&

x

<= xbnds.

&& ybnds.

<=

y

&&

y

<= ybnds.

)

3531

val = (axy * bx * by - ay * bx * bx - ax * by * by) / denom;

3532

minval =

(val, minval);

3533

maxval =

(val, maxval);

3536 else if

(

(2.0 * ay * bx - axy * by) <= 1e-9 )

3544

val = -ay * bx * bx / (axy * axy);

3545

minval =

(val, minval);

3546

maxval =

(val, maxval);

3557 else if

( ax < 0.0 )

3559 else if

( ax == 0.0 )

3565 else if

( bx + axy * ybnds.

< 0.0 )

3569

minval =

(val, minval);

3570

maxval =

(val, maxval);

3574 else if

( bx + axy * ybnds.

< 0.0 )

3578

minval =

(val, minval);

3579

maxval =

(val, maxval);

3591

minval =

(tmp.

, minval);

3592

maxval =

(tmp.

, maxval);

3600 else if

( ax < 0.0 )

3602 else if

( ax == 0.0 )

3608 else if

( bx + axy * ybnds.

> 0.0 )

3612

minval =

(val, minval);

3613

maxval =

(val, maxval);

3617 else if

( bx + axy * ybnds.

> 0.0 )

3621

minval =

(val, minval);

3622

maxval =

(val, maxval);

3634

minval =

(tmp.

, minval);

3635

maxval =

(tmp.

, maxval);

3643 else if

( ay < 0.0 )

3645 else if

( ay == 0.0 )

3651 else if

( by + axy * xbnds.

< 0.0 )

3655

minval =

(val, minval);

3656

maxval =

(val, maxval);

3660 else if

( by + axy * xbnds.

< 0.0 )

3664

minval =

(val, minval);

3665

maxval =

(val, maxval);

3677

minval =

(tmp.

, minval);

3678

maxval =

(tmp.

, maxval);

3686 else if

( ay < 0.0 )

3688 else if

( ay == 0.0 )

3694 else if

( by + axy * xbnds.

> 0.0 )

3698

minval =

(val, minval);

3699

maxval =

(val, maxval);

3703 else if

( by + axy * xbnds.

> 0.0 )

3707

minval =

(val, minval);

3708

maxval =

(val, maxval);

3720

minval =

(tmp.

, minval);

3721

maxval =

(tmp.

, maxval);

3724

minval -= 1e-10 *

(minval);

3725

maxval += 1e-10 *

(maxval);

3728 SCIPdebugMessage

(

"range for %gx^2 + %gy^2 + %gxy + %gx + %gy = [%g, %g] for x = [%g, %g], y=[%g, %g]\n"

,

3729

ax, ay, axy, bx, by, minval, maxval, xbnds.

, xbnds.

, ybnds.

, ybnds.

);

3755

assert(resultant !=

);

3773 if

( xbnds.

>= 0.0 )

3782 if

( xbnds.

< 0.0 )

3864

rcoef_y = axy * bx / (2.0*ax) - by;

3865

rcoef_yy = axy * axy / (4.0*ax) - ay;

3866

rcoef_const = bx * bx / (4.0*ax);

3868#define CALCB(y) ((bx + axy * (y)) / (2.0 * sqrtax)) 3869#define CALCR(c,y) (rcoef_const + (c) + (rcoef_y + rcoef_yy * (y)) * (y)) 3880 if

(

(ub, 1e-9) )

3885 else if

( ub < 0.0 )

3891

rhs.

+= -2.0*ub;

3920 if

( !

(ay, 1e-9) && axy * axy >= 4.0 * ax * ay )

3941 else if

( !

(ay, 1e-9) )

3948

minvalleft = -by / 2.0;

3949

maxvalleft = -by / 2.0;

3970

minvalleft =

(-sqrtc -

b

, minvalleft);

3971

maxvalright =

( sqrtc -

b

, maxvalright);

3984

maxvalleft =

(-sqrtc -

b

, maxvalleft);

3985

minvalright =

( sqrtc -

b

, minvalright);

3994 if

( !

(ay, 1e-9) && axy * axy >= 4.0 * ax * ay )

4015 else if

( !

(ay, 1e-9) )

4024

minvalright =

(minvalright, -by / 2.0);

4025

maxvalright =

(maxvalright, -by / 2.0);

4044

minvalleft =

(-sqrtc -

b

, minvalleft);

4045

maxvalright =

( sqrtc -

b

, maxvalright);

4058

maxvalleft =

(-sqrtc -

b

, maxvalleft);

4059

minvalright =

( sqrtc -

b

, minvalright);

4066 if

( !

(ay, 1e-9) )

4068 if

(

(axy*axy - 4.0*ax*ay) > 1e-9 )

4074

sqrtterm = axy * axy * ay * (ay * bx * bx - axy * bx * by + ax * by * by - axy * axy * rhs.

+ 4.0 * ax * ay * rhs.

);

4075 if

( !

(sqrtterm, 1e-9) )

4077

sqrtterm = sqrt(

(sqrtterm, 0.0));

4079

ymin = axy * ay * bx - 2.0 * ax * ay * by - sqrtterm;

4081

ymin /= 4.0 * ax * ay - axy * axy;

4083 if

( ymin > ybnds.

&& ymin < ybnds.

)

4096

minvalleft =

(-sqrtc -

b

, minvalleft);

4097

maxvalright =

( sqrtc -

b

, maxvalright);

4102

ymin = axy * ay * bx - 2.0 * ax * ay * by + sqrtterm;

4104

ymin /= 4.0 * ax * ay - axy * axy;

4106 if

( ymin > ybnds.

&& ymin < ybnds.

)

4119

minvalleft =

(-sqrtc -

b

, minvalleft);

4120

maxvalright =

( sqrtc -

b

, maxvalright);

4128

sqrtterm = axy * axy * ay * (ay * bx * bx - axy * bx * by + ax * by * by - axy * axy * rhs.

+ 4.0 * ax * ay * rhs.

);

4129 if

( !

(sqrtterm, 1e-9) )

4131

sqrtterm = sqrt(

(sqrtterm, 0.0));

4133

ymin = axy * ay * bx - 2.0 * ax * ay * by - sqrtterm;

4135

ymin /= 4.0 * ax * ay - axy * axy;

4137 if

( ymin > ybnds.

&& ymin < ybnds.

)

4150

maxvalleft =

(-sqrtc -

b

, maxvalleft);

4151

minvalright =

( sqrtc -

b

, minvalright);

4156

ymin = axy * ay * bx - 2.0 * ax * ay * by + sqrtterm;

4158

ymin /= 4.0 * ax * ay - axy * axy;

4160 if

( ymin > ybnds.

&& ymin < ybnds.

)

4173

maxvalleft =

(-sqrtc -

b

, maxvalleft);

4174

minvalright =

( sqrtc -

b

, minvalright);

4180 else if

(

(2.0 * ay * bx - axy * by) > 1e-9 )

4184

ymin = - (4.0 * ay * bx * by - axy * by * by + 4.0 * axy * ay * rhs.

);

4186

ymin /= 2.0 * ay * bx - axy * by;

4188 if

( ymin > ybnds.

&& ymin < ybnds.

)

4201

minvalleft =

(-sqrtc -

b

, minvalleft);

4202

maxvalright =

( sqrtc -

b

, maxvalright);

4209

ymin = - (4.0 * ay * bx * by - axy * by * by + 4.0 * axy * ay * rhs.

);

4211

ymin /= 2.0 * ay * bx - axy * by;

4213 if

( ymin > ybnds.

&& ymin < ybnds.

)

4226

maxvalleft =

(-sqrtc -

b

, maxvalleft);

4227

minvalright =

( sqrtc -

b

, minvalright);

4258 if

( ybnds.

>= 0.0 )

4265

assert(ypos.

>= 0.0);

4267

minvalleft =

(minvalleft, -

b

);

4268

maxvalleft =

(maxvalleft, -

b

);

4269

minvalright =

(minvalright, -

b

);

4270

maxvalright =

(maxvalright, -

b

);

4275

minvalleft =

(minvalleft, -

b

);

4276

maxvalleft =

(maxvalleft, -

b

);

4277

minvalright =

(minvalright, -

b

);

4278

maxvalright =

(maxvalright, -

b

);

4301 if

( ybnds.

< 0.0 )

4311

minvalleft =

(minvalleft, -

b

);

4312

maxvalleft =

(maxvalleft, -

b

);

4313

minvalright =

(minvalright, -

b

);

4314

maxvalright =

(maxvalright, -

b

);

4331

assert(yneg.

<= 0.0);

4333

minvalleft =

(minvalleft, -

b

);

4334

maxvalleft =

(maxvalleft, -

b

);

4335

minvalright =

(minvalright, -

b

);

4336

maxvalright =

(maxvalright, -

b

);

4345

assert(

(minvalright, minvalleft, 1e-9));

4366

assert(

(maxvalleft, maxvalright, 1e-9));

4400 if

(

(-bx / axy, ybnds.

, 1e-9) &&

(-bx / axy, ybnds.

, 1e-9) )

4410 if

( xbnds.

< 0.0 && xbnds.

> 0.0 )

4428 if

( lincoef.

== 0.0 && lincoef.

== 0.0 )

4431 if

( myrhs.

<= 0.0 && myrhs.

>= 0.0 )

4436 else if

( xbnds.

>= 0.0 )

4449

assert(xbnds.

<= 0.0);

4467 if

( bx + axy * (axy > 0.0 ? ybnds.

: ybnds.

) > 0.0 )

4477 if

(

(ay, 1e-9) )

4479 else if

( ay * axy < 0.0 )

4484

val = (c - ay * ybnds.

* ybnds.

- by * ybnds.

) / (bx + axy * ybnds.

);

4485

minval =

(val, minval);

4491 if

(

(ay, 1e-9) )

4492

minval =

(minval, -by / axy);

4493 else if

( ay * axy > 0.0 )

4498

val = (c - ay * ybnds.

* ybnds.

- by * ybnds.

) / (bx + axy * ybnds.

);

4499

minval =

(val, minval);

4502 if

( !

(ay, 1e-9) )

4504

d = ay * (ay * bx * bx - axy * (bx * by + axy * c));

4505 if

( !

(d, 1e-9) )

4507

ymin = -ay * bx + sqrt(

(d, 0.0));

4510 if

( ymin > ybnds.

&& ymin < ybnds.

)

4512

assert(bx + axy * ymin != 0.0);

4514

val = (c - ay * ymin * ymin - by * ymin) / (bx + axy * ymin);

4515

minval =

(val, minval);

4518

ymin = -ay * bx - sqrt(

(d, 0.0));

4521 if

(ymin > ybnds.

&& ymin < ybnds.

)

4523

assert(bx + axy * ymin != 0.0);

4525

val = (c - ay * ymin * ymin - by * ymin) / (bx + axy * ymin);

4526

minval =

(val, minval);

4537 if

( bx + axy * (axy > 0.0 ? ybnds.

: ybnds.

) > 0.0 )

4547 if

(

(ay, 1e-9) )

4549 else if

( ay * axy > 0.0 )

4554

val = (c - ay * ybnds.

* ybnds.

- by * ybnds.

) / (bx + axy * ybnds.

);

4555

maxval =

(val, maxval);

4561 if

(

(ay, 1e-9) )

4562

maxval =

(maxval, -by / axy);

4563 else if

( ay * axy < 0.0 )

4568

val = (c - ay * ybnds.

* ybnds.

- by * ybnds.

) / (bx + axy * ybnds.

);

4569

maxval =

(val, maxval);

4572 if

( !

(ay, 1e-9) )

4574

d = ay * (ay * bx * bx - axy * (bx * by + axy * c));

4575 if

( !

(d, 1e-9) )

4577

ymin = ay * bx + sqrt(

(d, 0.0));

4580 if

( ymin > ybnds.

&& ymin < ybnds.

)

4582

assert(bx + axy * ymin != 0.0);

4583

val = (c - ay * ymin * ymin - by * ymin) / (bx + axy * ymin);

4584

maxval =

(val, maxval);

4587

ymin = ay * bx - sqrt(

(d, 0.0));

4590 if

( ymin > ybnds.

&& ymin < ybnds.

)

4592

assert(bx + axy * ymin != 0.0);

4593

val = (c - ay * ymin * ymin - by * ymin) / (bx + axy * ymin);

4594

maxval =

(val, maxval);

4605

resultant->

= minval - 1e-10 *

(minval);

4609

resultant->

= maxval + 1e-10 *

(maxval);

4640 int

minlinactivityinf;

4641 int

maxlinactivityinf;

4642 int

nreductions = 0;

4645

assert(noperands > 0);

4646

assert(operands !=

);

4647

assert(weights !=

);

4648

assert(resultants !=

);

4649

assert(infeasible !=

);

4651

*infeasible =

;

4660

minlinactivity = constant;

4661

maxlinactivity = -constant;

4662

minlinactivityinf = 0;

4663

maxlinactivityinf = 0;

4665 SCIPdebugMessage

(

"reverse prop with %d children: %.20g"

, noperands, constant);

4670 for

( c = 0; c < noperands; ++c )

4672

childbounds = operands[c];

4677

*infeasible =

;

4684 if

( resultants[c].sup >=

)

4685

++maxlinactivityinf;

4688

assert(resultants[c].sup > -

);

4689

maxlinactivity -= resultants[c].

;

4692 if

( resultants[c].inf <= -

)

4693

++minlinactivityinf;

4696

assert(resultants[c].inf <

);

4697

minlinactivity += resultants[c].

;

4700

maxlinactivity = -maxlinactivity;

4703

minlinactivityinf ? -

: minlinactivity,

4704

maxlinactivityinf ?

: maxlinactivity,

4708 if

( (minlinactivityinf >= 2 || rhs.

>=

) && (maxlinactivityinf >= 2 || rhs.

<= -

) )

4714 for

( c = 0; c < noperands; ++c )

4724 if

( resultants[c].inf <= -

&& minlinactivityinf <= 1 )

4726

assert(minlinactivityinf == 1);

4729 else if

( minlinactivityinf == 0 )

4741 if

( resultants[c].sup >=

&& maxlinactivityinf <= 1 )

4743

assert(maxlinactivityinf == 1);

4744

childbounds.

= rhs.

- maxlinactivity;

4746 else if

( maxlinactivityinf == 0 )

4748

childbounds.

= rhs.

- maxlinactivity + resultants[c].

;

4752 SCIPdebugMessage

(

"child %d: %.20g*x in [%.20g,%.20g]"

, c, weights[c], childbounds.

, childbounds.

);

4761

*infeasible =

;

4775

*infeasible =

;

4780 if

( resultants[c].inf != operands[c].inf || resultants[c].sup != operands[c].sup )

4787 if

( c < noperands )

common defines and data types used in all packages of SCIP

SCIP_Real SCIPnextafter(SCIP_Real from, SCIP_Real to)

SCIP_Real SCIPrelDiff(SCIP_Real val1, SCIP_Real val2)

void SCIPintervalMulSup(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void SCIPintervalSetRoundingModeUpwards(void)

void SCIPintervalIntersectEps(SCIP_INTERVAL *resultant, SCIP_Real eps, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void SCIPintervalAddSup(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void SCIPintervalMulScalarInf(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)

void SCIPintervalSetRoundingModeDownwards(void)

SCIP_Real SCIPintervalGetInf(SCIP_INTERVAL interval)

SCIP_Real SCIPintervalQuadUpperBound(SCIP_Real infinity, SCIP_Real a, SCIP_INTERVAL b_, SCIP_INTERVAL x)

SCIP_Bool SCIPintervalIsEntire(SCIP_Real infinity, SCIP_INTERVAL operand)

void SCIPintervalScalprodScalarsInf(SCIP_Real infinity, SCIP_INTERVAL *resultant, int length, SCIP_INTERVAL *operand1, SCIP_Real *operand2)

void SCIPintervalSub(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void SCIPintervalSetEntire(SCIP_Real infinity, SCIP_INTERVAL *resultant)

SCIP_Bool SCIPintervalIsPositiveInfinity(SCIP_Real infinity, SCIP_INTERVAL operand)

SCIP_Real SCIPintervalPowerScalarIntegerSup(SCIP_Real operand1, int operand2)

void SCIPintervalSquareRoot(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)

void SCIPintervalMulInf(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void SCIPintervalScalprodScalarsSup(SCIP_Real infinity, SCIP_INTERVAL *resultant, int length, SCIP_INTERVAL *operand1, SCIP_Real *operand2)

SCIP_ROUNDMODE SCIPintervalGetRoundingMode(void)

void SCIPintervalSetRoundingModeToNearest(void)

void SCIPintervalPower(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void SCIPintervalSolveUnivariateQuadExpression(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL sqrcoeff, SCIP_INTERVAL lincoeff, SCIP_INTERVAL rhs, SCIP_INTERVAL xbnds)

void SCIPintervalSignPowerScalar(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)

SCIP_Real SCIPintervalPowerScalarIntegerInf(SCIP_Real operand1, int operand2)

void SCIPintervalSetRoundingMode(SCIP_ROUNDMODE roundmode)

void SCIPintervalScalprodScalars(SCIP_Real infinity, SCIP_INTERVAL *resultant, int length, SCIP_INTERVAL *operand1, SCIP_Real *operand2)

void SCIPintervalUnify(SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void SCIPintervalAbs(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)

void SCIPintervalSubScalar(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)

void SCIPintervalSetRoundingModeTowardsZero(void)

void SCIPintervalCos(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)

void SCIPintervalSolveBivariateQuadExpressionAllScalar(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_Real ax, SCIP_Real ay, SCIP_Real axy, SCIP_Real bx, SCIP_Real by, SCIP_INTERVAL rhs, SCIP_INTERVAL xbnds, SCIP_INTERVAL ybnds)

void SCIPintervalMax(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void SCIPintervalIntersect(SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void SCIPintervalSquare(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)

void SCIPintervalSet(SCIP_INTERVAL *resultant, SCIP_Real value)

SCIP_Bool SCIPintervalIsSubsetEQ(SCIP_Real infinity, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

SCIP_Bool SCIPintervalIsEmpty(SCIP_Real infinity, SCIP_INTERVAL operand)

void SCIPintervalPowerScalarInverse(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL basedomain, SCIP_Real exponent, SCIP_INTERVAL image)

SCIP_Bool SCIPintervalHasRoundingControl(void)

void SCIPintervalSin(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)

void SCIPintervalSolveUnivariateQuadExpressionPositive(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL sqrcoeff, SCIP_INTERVAL lincoeff, SCIP_INTERVAL rhs, SCIP_INTERVAL xbnds)

void SCIPintervalSetBounds(SCIP_INTERVAL *resultant, SCIP_Real inf, SCIP_Real sup)

void SCIPintervalAddInf(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void SCIPintervalMin(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void SCIPintervalAddVectors(SCIP_Real infinity, SCIP_INTERVAL *resultant, int length, SCIP_INTERVAL *operand1, SCIP_INTERVAL *operand2)

SCIP_Bool SCIPintervalIsNegativeInfinity(SCIP_Real infinity, SCIP_INTERVAL operand)

void SCIPintervalMulScalar(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)

void SCIPintervalReciprocal(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)

void SCIPintervalPowerScalarInteger(SCIP_INTERVAL *resultant, SCIP_Real operand1, int operand2)

void SCIPintervalEntropy(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)

void SCIPintervalMul(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void SCIPintervalDiv(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void SCIPintervalPowerScalarScalar(SCIP_INTERVAL *resultant, SCIP_Real operand1, SCIP_Real operand2)

void SCIPintervalQuad(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_Real sqrcoeff, SCIP_INTERVAL lincoeff, SCIP_INTERVAL xrng)

void SCIPintervalSign(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)

void SCIPintervalPowerScalar(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)

void SCIPintervalLog(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)

void SCIPintervalAddScalar(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)

void SCIPintervalMulScalarSup(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)

void SCIPintervalDivScalar(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_Real operand2)

SCIP_Bool SCIPintervalAreDisjointEps(SCIP_Real eps, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void SCIPintervalSolveUnivariateQuadExpressionNegative(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL sqrcoeff, SCIP_INTERVAL lincoeff, SCIP_INTERVAL rhs, SCIP_INTERVAL xbnds)

SCIP_Real SCIPintervalGetSup(SCIP_INTERVAL interval)

void SCIPintervalSolveUnivariateQuadExpressionPositiveAllScalar(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_Real sqrcoeff, SCIP_Real lincoeff, SCIP_Real rhs, SCIP_INTERVAL xbnds)

void SCIPintervalQuadBivar(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_Real ax, SCIP_Real ay, SCIP_Real axy, SCIP_Real bx, SCIP_Real by, SCIP_INTERVAL xbnds, SCIP_INTERVAL ybnds)

SCIP_Real SCIPintervalNegateReal(SCIP_Real x)

SCIP_Bool SCIPintervalAreDisjoint(SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

int SCIPintervalPropagateWeightedSum(SCIP_Real infinity, int noperands, SCIP_INTERVAL *operands, SCIP_Real *weights, SCIP_Real constant, SCIP_INTERVAL rhs, SCIP_INTERVAL *resultants, SCIP_Bool *infeasible)

void SCIPintervalExp(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand)

void SCIPintervalAdd(SCIP_Real infinity, SCIP_INTERVAL *resultant, SCIP_INTERVAL operand1, SCIP_INTERVAL operand2)

void SCIPintervalScalprod(SCIP_Real infinity, SCIP_INTERVAL *resultant, int length, SCIP_INTERVAL *operand1, SCIP_INTERVAL *operand2)

void SCIPintervalSetEmpty(SCIP_INTERVAL *resultant)

static const double pi_d_l

#define SCIP_ROUND_NEAREST

static SCIP_Real negate(SCIP_Real x)

static SCIP_ROUNDMODE intervalGetRoundingMode(void)

#define SCIP_ROUND_UPWARDS

static const double pi_d_u

#define SCIP_ROUND_DOWNWARDS

static void intervalSetRoundingMode(SCIP_ROUNDMODE roundmode)

interval arithmetics for provable bounds

#define BMScopyMemoryArray(ptr, source, num)

SCIP_Real SCIPnegateReal(SCIP_Real x)

internal miscellaneous methods

public methods for message output

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