{2==X*X},solve(X). Wrong Answer

Hi, ridgeworks. I use windows 10. When I run examples, it didn't work as expected.

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?- use_module(library(clpBNR)).
% *** clpBNR v0.9.7alpha ***.
true.

?- {2==X*X},solve(X).
X:: 1.414213562373095... .

?- {2==X*X}.
X::real(-1.4142135623730951, 1.4142135623730951).

?- {2==X*X, X < 0}.
false.

When I run?- {2==X*X},solve(X)., X has only one result. I didn't have a choice to type ;. When I run?- {2==X*X}., it worked as expected. When I run?- {2==X*X, X < 0}., I got a false. When I runbetween(1,100,X),{X == Y*Y},findall(Y, solve(Y),List),length(List,Len),writeln([X,Len,List]),fail.,

[1,2,[-1,1]]
[2,1,[_8118{real(1.414213562373095,1.4142135623730951)}]]
[3,1,[_8118{real(1.7320508075688772,1.7320508075688774)}]]
[4,2,[-2,2]]
[5,1,[_8118{real(2.2360679774997894,2.23606797749979)}]]
[6,2,[_8198{real(-2.4494897427831783,-2.449489742783178)},_8118{real(2.449489742783178,2.4494897427831783)}]]
[7,1,[_8118{real(2.6457513110645903,2.6457513110645907)}]]
[8,1,[_8118{real(2.82842712474619,2.8284271247461903)}]]
[9,2,[-3,3]]
[10,1,[_8118{real(3.162277660168379,3.1622776601683795)}]]
[11,2,[_8198{real(-3.3166247903554003,-3.3166247903554)},_8118{real(3.3166247903554,3.3166247903554003)}]]
[12,1,[_8118{real(3.4641016151377544,3.464101615137755)}]]
[13,2,[_8198{real(-3.6055512754639896,-3.605551275463989)},_8118{real(3.605551275463989,3.6055512754639896)}]]
[14,2,[_8198{real(-3.7416573867739418,-3.7416573867739413)},_8118{real(3.7416573867739413,3.7416573867739418)}]]
[15,1,[_8118{real(3.8729833462074166,3.872983346207417)}]]
[16,2,[-4,4]]
[17,1,[_8118{real(4.12310562561766,4.123105625617661)}]]
[18,2,[_8198{real(-4.242640687119286,-4.242640687119285)},_8118{real(4.242640687119285,4.242640687119286)}]]
[19,2,[_8198{real(-4.358898943540674,-4.358898943540673)},_8118{real(4.358898943540673,4.358898943540674)}]]
[20,1,[_8118{real(4.472135954999579,4.47213595499958)}]]
[21,2,[_8198{real(-4.582575694955841,-4.58257569495584)},_8118{real(4.58257569495584,4.582575694955841)}]]
[22,1,[_8118{real(4.690415759823429,4.69041575982343)}]]
[23,2,[_8198{real(-4.79583152331272,-4.795831523312719)},_8118{real(4.795831523312719,4.79583152331272)}]]
[24,2,[_8198{real(-4.898979485566357,-4.898979485566356)},_8118{real(4.898979485566356,4.898979485566357)}]]
[25,2,[-5,5]]
[26,2,[_8198{real(-5.099019513592785,-5.0990195135927845)},_8118{real(5.0990195135927845,5.099019513592785)}]]
[27,1,[_8118{real(5.196152422706631,5.196152422706632)}]]
[28,1,[_8118{real(5.2915026221291805,5.291502622129181)}]]
[29,2,[_8198{real(-5.385164807134505,-5.385164807134504)},_8118{real(5.385164807134504,5.385164807134505)}]]
[30,1,[_8118{real(5.47722557505166,5.477225575051661)}]]
[31,2,[_8198{real(-5.567764362830022,-5.5677643628300215)},_8118{real(5.5677643628300215,5.567764362830022)}]]
[32,1,[_8118{real(5.65685424949238,5.656854249492381)}]]
[33,2,[_8198{real(-5.7445626465380295,-5.744562646538029)},_8118{real(5.744562646538029,5.7445626465380295)}]]
[34,1,[_8118{real(5.8309518948453,5.830951894845301)}]]
[35,1,[_8118{real(5.916079783099615,5.916079783099616)}]]
[36,2,[-6,6]]
[37,1,[_8118{real(6.082762530298219,6.08276253029822)}]]
[38,1,[_8118{real(6.164414002968976,6.164414002968977)}]]
[39,1,[_8118{real(6.244997998398397,6.244997998398398)}]]
[40,1,[_8118{real(6.324555320336758,6.324555320336759)}]]
[41,2,[_8198{real(-6.403124237432849,-6.4031242374328485)},_8118{real(6.4031242374328485,6.403124237432849)}]]
[42,1,[_8118{real(6.4807406984078595,6.48074069840786)}]]
[43,2,[_8198{real(-6.557438524302001,-6.557438524302)},_8118{real(6.557438524302,6.557438524302001)}]]
[44,2,[_8198{real(-6.6332495807108005,-6.6332495807108)},_8118{real(6.6332495807108,6.6332495807108005)}]]
[45,1,[_8118{real(6.7082039324993685,6.708203932499369)}]]
[46,2,[_8198{real(-6.782329983125269,-6.782329983125268)},_8118{real(6.782329983125268,6.782329983125269)}]]
[47,2,[_8198{real(-6.855654600401045,-6.855654600401044)},_8118{real(6.855654600401044,6.855654600401045)}]]
[48,1,[_8118{real(6.928203230275509,6.92820323027551)}]]
[49,2,[-7,7]]
[50,1,[_8118{real(7.071067811865475,7.0710678118654755)}]]
[51,1,[_8118{real(7.1414284285428495,7.14142842854285)}]]
[52,2,[_8198{real(-7.211102550927979,-7.211102550927978)},_8118{real(7.211102550927978,7.211102550927979)}]]
[53,2,[_8198{real(-7.280109889280519,-7.280109889280518)},_8118{real(7.280109889280518,7.280109889280519)}]]
[54,1,[_8118{real(7.348469228349534,7.3484692283495345)}]]
[55,1,[_8118{real(7.416198487095662,7.416198487095663)}]]
[56,2,[_8198{real(-7.4833147735478835,-7.483314773547883)},_8118{real(7.483314773547883,7.4833147735478835)}]]
[57,1,[_8118{real(7.549834435270749,7.54983443527075)}]]
[58,1,[_8118{real(7.615773105863908,7.615773105863909)}]]
[59,2,[_8198{real(-7.681145747868609,-7.681145747868608)},_8118{real(7.681145747868608,7.681145747868609)}]]
[60,1,[_8118{real(7.745966692414833,7.745966692414834)}]]
[61,2,[_8198{real(-7.810249675906655,-7.810249675906654)},_8118{real(7.810249675906654,7.810249675906655)}]]
[62,1,[_8118{real(7.87400787401181,7.874007874011811)}]]
[63,1,[_8118{real(7.937253933193771,7.937253933193772)}]]
[64,2,[-8,8]]
[65,2,[_8198{real(-8.062257748298551,-8.06225774829855)},_8118{real(8.06225774829855,8.062257748298551)}]]
[66,1,[_8118{real(8.124038404635959,8.12403840463596)}]]
[67,1,[_8118{real(8.185352771872449,8.18535277187245)}]]
[68,1,[_8118{real(8.24621125123532,8.246211251235321)}]]
[69,1,[_8118{real(8.306623862918073,8.306623862918075)}]]
[70,1,[_8118{real(8.366600265340754,8.366600265340756)}]]
[71,1,[_8118{real(8.426149773176357,8.426149773176359)}]]
[72,2,[_8198{real(-8.485281374238571,-8.48528137423857)},_8118{real(8.48528137423857,8.485281374238571)}]]
[73,2,[_8198{real(-8.544003745317532,-8.54400374531753)},_8118{real(8.54400374531753,8.544003745317532)}]]
[74,2,[_8198{real(-8.602325267042628,-8.602325267042627)},_8118{real(8.602325267042627,8.602325267042628)}]]
[75,2,[_8198{real(-8.660254037844387,-8.660254037844386)},_8118{real(8.660254037844386,8.660254037844387)}]]
[76,2,[_8198{real(-8.717797887081348,-8.717797887081346)},_8118{real(8.717797887081346,8.717797887081348)}]]
[77,1,[_8118{real(8.77496438739212,8.774964387392123)}]]
[78,2,[_8198{real(-8.831760866327848,-8.831760866327846)},_8118{real(8.831760866327846,8.831760866327848)}]]
[79,2,[_8198{real(-8.88819441731559,-8.888194417315589)},_8118{real(8.888194417315589,8.88819441731559)}]]
[80,1,[_8118{real(8.944271909999157,8.94427190999916)}]]
[81,2,[-9,9]]
[82,1,[_8118{real(9.055385138137416,9.055385138137417)}]]
[83,1,[_8118{real(9.110433579144297,9.1104335791443)}]]
[84,2,[_8198{real(-9.165151389911681,-9.16515138991168)},_8118{real(9.16515138991168,9.165151389911681)}]]
[85,2,[_8198{real(-9.219544457292889,-9.219544457292887)},_8118{real(9.219544457292887,9.219544457292889)}]]
[86,1,[_8118{real(9.273618495495702,9.273618495495704)}]]
[87,1,[_8118{real(9.327379053088814,9.327379053088816)}]]
[88,1,[_8118{real(9.380831519646858,9.38083151964686)}]]
[89,2,[_8198{real(-9.433981132056605,-9.433981132056603)},_8118{real(9.433981132056603,9.433981132056605)}]]
[90,1,[_8118{real(9.486832980505136,9.486832980505138)}]]
[91,2,[_8198{real(-9.539392014169458,-9.539392014169456)},_8118{real(9.539392014169456,9.539392014169458)}]]
[92,2,[_8198{real(-9.59166304662544,-9.591663046625438)},_8118{real(9.591663046625438,9.59166304662544)}]]
[93,2,[_8198{real(-9.643650760992957,-9.643650760992955)},_8118{real(9.643650760992955,9.643650760992957)}]]
[94,1,[_8118{real(9.695359714832657,9.695359714832659)}]]
[95,2,[_8198{real(-9.746794344808965,-9.746794344808963)},_8118{real(9.746794344808963,9.746794344808965)}]]
[96,2,[_8198{real(-9.797958971132713,-9.797958971132712)},_8118{real(9.797958971132712,9.797958971132713)}]]
[97,2,[_8198{real(-9.848857801796106,-9.848857801796104)},_8118{real(9.848857801796104,9.848857801796106)}]]
[98,1,[_8118{real(9.899494936611664,9.899494936611665)}]]
[99,2,[_8198{real(-9.949874371066201,-9.9498743710662)},_8118{real(9.9498743710662,9.949874371066201)}]]
[100,2,[-10,10]]
false.

In some cases it cannot find the negative result .

Thanks for the bug report. There's definitely a problem with rounding precise values (integers) in the power primitive that I need to fix, but it's a bit tricky since the underlying C libraries provide no guarantees this operation obeys the IEEE rounding mode setting. A fix is in work but may take a while to properly regression test it.

Note that float values don't exhibit the same problem:

?- {2.0==X*X},solve(X).
X:: -1.41421356237309... ;
X:: 1.41421356237309... .

?- between(1,100,Xi),X is float(Xi),{X == Y*Y},findall(Y, solve(Y),List),length(List,Len),writeln([X,Len,List]),fail.
[1.0,2,[_35520{real(-1.0000000000000007,-0.9999999999999997)},_35398{real(0.9999999999999997,1.0000000000000007)}]]
[2.0,2,[_35520{real(-1.4142135623730956,-1.4142135623730945)},_35398{real(1.4142135623730945,1.4142135623730956)}]]
[3.0,2,[_35520{real(-1.732050807568878,-1.7320508075688765)},_35398{real(1.7320508075688765,1.732050807568878)}]]
[4.0,2,[_35520{real(-2.0000000000000013,-1.9999999999999993)},_35398{real(1.9999999999999993,2.0000000000000013)}]]
[5.0,2,[_35520{real(-2.236067977499791,-2.2360679774997885)},_35398{real(2.2360679774997885,2.236067977499791)}]]
[6.0,2,[_35520{real(-2.449489742783179,-2.449489742783177)},_35398{real(2.449489742783177,2.449489742783179)}]]
[7.0,2,[_35520{real(-2.645751311064592,-2.6457513110645894)},_35398{real(2.6457513110645894,2.645751311064592)}]]
[8.0,2,[_35520{real(-2.828427124746191,-2.828427124746189)},_35398{real(2.828427124746189,2.828427124746191)}]]
[9.0,2,[_35520{real(-3.0000000000000013,-2.9999999999999987)},_35398{real(2.9999999999999987,3.0000000000000013)}]]
[10.0,2,[_35520{real(-3.162277660168381,-3.1622776601683777)},_35398{real(3.1622776601683777,3.162277660168381)}]]
[11.0,2,[_35520{real(-3.316624790355401,-3.3166247903553985)},_35398{real(3.3166247903553985,3.316624790355401)}]]
[12.0,2,[_35520{real(-3.464101615137756,-3.464101615137753)},_35398{real(3.464101615137753,3.464101615137756)}]]
[13.0,2,[_35520{real(-3.6055512754639905,-3.605551275463988)},_35398{real(3.605551275463988,3.6055512754639905)}]]
[14.0,2,[_35520{real(-3.7416573867739427,-3.74165738677394)},_35398{real(3.74165738677394,3.7416573867739427)}]]
[15.0,2,[_35520{real(-3.8729833462074184,-3.8729833462074157)},_35398{real(3.8729833462074157,3.8729833462074184)}]]
[16.0,2,[_35520{real(-4.000000000000003,-3.9999999999999987)},_35398{real(3.9999999999999987,4.000000000000003)}]]
[17.0,2,[_35520{real(-4.123105625617663,-4.123105625617658)},_35398{real(4.123105625617658,4.123105625617663)}]]
[18.0,2,[_35520{real(-4.242640687119287,-4.242640687119282)},_35398{real(4.242640687119282,4.242640687119287)}]]
[19.0,2,[_35520{real(-4.358898943540676,-4.358898943540671)},_35398{real(4.358898943540671,4.358898943540676)}]]
[20.0,2,[_35520{real(-4.472135954999582,-4.472135954999577)},_35398{real(4.472135954999577,4.472135954999582)}]]
[21.0,2,[_35520{real(-4.5825756949558425,-4.582575694955837)},_35398{real(4.582575694955837,4.5825756949558425)}]]
[22.0,2,[_35520{real(-4.690415759823432,-4.690415759823427)},_35398{real(4.690415759823427,4.690415759823432)}]]
[23.0,2,[_35520{real(-4.795831523312722,-4.795831523312717)},_35398{real(4.795831523312717,4.795831523312722)}]]
[24.0,2,[_35520{real(-4.898979485566358,-4.898979485566354)},_35398{real(4.898979485566354,4.898979485566358)}]]
[25.0,2,[_35520{real(-5.000000000000003,-4.999999999999997)},_35398{real(4.999999999999997,5.000000000000003)}]]
[26.0,2,[_35520{real(-5.099019513592787,-5.099019513592782)},_35398{real(5.099019513592782,5.099019513592787)}]]
[27.0,2,[_35520{real(-5.196152422706635,-5.196152422706629)},_35398{real(5.196152422706629,5.196152422706635)}]]
[28.0,2,[_35520{real(-5.291502622129184,-5.291502622129179)},_35398{real(5.291502622129179,5.291502622129184)}]]
[29.0,2,[_35520{real(-5.385164807134506,-5.385164807134501)},_35398{real(5.385164807134501,5.385164807134506)}]]
[30.0,2,[_35520{real(-5.477225575051664,-5.4772255750516585)},_35398{real(5.4772255750516585,5.477225575051664)}]]
[31.0,2,[_35520{real(-5.567764362830024,-5.56776436283002)},_35398{real(5.56776436283002,5.567764362830024)}]]
[32.0,2,[_35520{real(-5.656854249492382,-5.656854249492378)},_35398{real(5.656854249492378,5.656854249492382)}]]
[33.0,2,[_35520{real(-5.744562646538031,-5.744562646538026)},_35398{real(5.744562646538026,5.744562646538031)}]]
[34.0,2,[_35520{real(-5.830951894845303,-5.830951894845298)},_35398{real(5.830951894845298,5.830951894845303)}]]
[35.0,2,[_35520{real(-5.916079783099619,-5.9160797830996135)},_35398{real(5.9160797830996135,5.916079783099619)}]]
[36.0,2,[_35520{real(-6.000000000000003,-5.999999999999997)},_35398{real(5.999999999999997,6.000000000000003)}]]
[37.0,2,[_35520{real(-6.082762530298223,-6.082762530298217)},_35398{real(6.082762530298217,6.082762530298223)}]]
[38.0,2,[_35520{real(-6.16441400296898,-6.164414002968973)},_35398{real(6.164414002968973,6.16441400296898)}]]
[39.0,2,[_35520{real(-6.244997998398401,-6.244997998398396)},_35398{real(6.244997998398396,6.244997998398401)}]]
[40.0,2,[_35520{real(-6.324555320336762,-6.3245553203367555)},_35398{real(6.3245553203367555,6.324555320336762)}]]
[41.0,2,[_35520{real(-6.403124237432851,-6.403124237432846)},_35398{real(6.403124237432846,6.403124237432851)}]]
[42.0,2,[_35520{real(-6.480740698407863,-6.480740698407858)},_35398{real(6.480740698407858,6.480740698407863)}]]
[43.0,2,[_35520{real(-6.557438524302003,-6.557438524301998)},_35398{real(6.557438524301998,6.557438524302003)}]]
[44.0,2,[_35520{real(-6.633249580710802,-6.633249580710797)},_35398{real(6.633249580710797,6.633249580710802)}]]
[45.0,2,[_35520{real(-6.708203932499372,-6.708203932499367)},_35398{real(6.708203932499367,6.708203932499372)}]]
[46.0,2,[_35520{real(-6.782329983125271,-6.7823299831252655)},_35398{real(6.7823299831252655,6.782329983125271)}]]
[47.0,2,[_35520{real(-6.855654600401047,-6.855654600401041)},_35398{real(6.855654600401041,6.855654600401047)}]]
[48.0,2,[_35520{real(-6.928203230275512,-6.928203230275506)},_35398{real(6.928203230275506,6.928203230275512)}]]
[49.0,2,[_35520{real(-7.000000000000003,-6.999999999999997)},_35398{real(6.999999999999997,7.000000000000003)}]]
[50.0,2,[_35520{real(-7.071067811865478,-7.071067811865473)},_35398{real(7.071067811865473,7.071067811865478)}]]
[51.0,2,[_35520{real(-7.141428428542853,-7.141428428542847)},_35398{real(7.141428428542847,7.141428428542853)}]]
[52.0,2,[_35520{real(-7.211102550927981,-7.211102550927976)},_35398{real(7.211102550927976,7.211102550927981)}]]
[53.0,2,[_35520{real(-7.280109889280521,-7.280109889280515)},_35398{real(7.280109889280515,7.280109889280521)}]]
[54.0,2,[_35520{real(-7.348469228349537,-7.348469228349532)},_35398{real(7.348469228349532,7.348469228349537)}]]
[55.0,2,[_35520{real(-7.416198487095666,-7.41619848709566)},_35398{real(7.41619848709566,7.416198487095666)}]]
[56.0,2,[_35520{real(-7.483314773547885,-7.48331477354788)},_35398{real(7.48331477354788,7.483314773547885)}]]
[57.0,2,[_35520{real(-7.5498344352707525,-7.549834435270747)},_35398{real(7.549834435270747,7.5498344352707525)}]]
[58.0,2,[_35520{real(-7.615773105863911,-7.615773105863906)},_35398{real(7.615773105863906,7.615773105863911)}]]
[59.0,2,[_35520{real(-7.6811457478686105,-7.681145747868605)},_35398{real(7.681145747868605,7.6811457478686105)}]]
[60.0,2,[_35520{real(-7.745966692414837,-7.745966692414831)},_35398{real(7.745966692414831,7.745966692414837)}]]
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[90.0,2,[_35520{real(-9.486832980505143,-9.486832980505133)},_35398{real(9.486832980505133,9.486832980505143)}]]
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[93.0,2,[_35520{real(-9.64365076099296,-9.64365076099295)},_35398{real(9.64365076099295,9.64365076099296)}]]
[94.0,2,[_35520{real(-9.695359714832664,-9.695359714832653)},_35398{real(9.695359714832653,9.695359714832664)}]]
[95.0,2,[_35520{real(-9.746794344808968,-9.74679434480896)},_35398{real(9.74679434480896,9.746794344808968)}]]
[96.0,2,[_35520{real(-9.797958971132717,-9.797958971132708)},_35398{real(9.797958971132708,9.797958971132717)}]]
[97.0,2,[_35520{real(-9.84885780179611,-9.8488578017961)},_35398{real(9.8488578017961,9.84885780179611)}]]
[98.0,2,[_35520{real(-9.89949493661167,-9.89949493661166)},_35398{real(9.89949493661166,9.89949493661167)}]]
[99.0,2,[_35520{real(-9.949874371066205,-9.949874371066194)},_35398{real(9.949874371066194,9.949874371066205)}]]
[100.0,2,[_35520{real(-10.000000000000005,-9.999999999999995)},_35398{real(9.999999999999995,10.000000000000005)}]]
false.

ridgeworks / clpBNR

{2==X*X},solve(X). Wrong Answer #11