:- module(test_rint, [test_rint/0]).

:- use_module(library(plunit)).
:- use_module(library(debug)).
:- use_module(library(rint)).

test_rint :-
    run_tests([r, assignment, binom, normal, t, chisq]).

:- begin_tests(r).

test(r1) :-
    A is 1,
    interval(<-(x, A), _),
    interval(r(x), Res),
    Res = A.

test(r2) :-
    interval(r(1 + 1) + 2...3, Res),
    Res = 4...5.

test(r3) :-
    interval(dbinom(1...2, 10, 0.7), L1...U1),
    interval(r(dbinom(1...2, 10, 0.7)), L2...U2),
    L1 =:= L2,
    U1 =:= U2.

:- end_tests(r).

:- begin_tests(assignment).

test(assign1) :-
    A = 1,
    interval(a <- A, _Res),
    interval(r(a), Res),
    Res =:= A.

test(assign2) :-
    A = 1...2,
    interval(a <- A, _Res),
    interval(r(a), Res),
    Res = A.

:- end_tests(assignment).

:- begin_tests(binom).

test(dbinom1) :-
    interval(dbinom(11, 20, 0.6), Res),
    equal(Res, 0.1597...0.1598).

test(dbinom2) :-
    interval(dbinom(11...12, 20, 0.6...0.7), Res),
    equal(Res, 0.0653...0.1798).

test(dbinom3) :-
    interval(dbinom(11...12, 20, 0.6), Res),
    equal(Res, 0.1597...0.1798).

test(dbinom4) :-
    interval(dbinom(11...12, 20...21, 0.6...0.7), Res),
    equal(Res, 0.0411...0.1798).

% left to X / N
test(dbinom5) :- 
    interval(dbinom(10...11, 20...21, 0.6...0.7), Res),
    equal(Res, 0.0176...0.1598).

% right to X / N
test(dbinom6) :- 
    interval(dbinom(15...16, 20...21, 0.6...0.7), Res),
    equal(Res, 0.0349...0.1879).

test(qbinom1) :-
    interval(qbinom(0.6, 20, 0.3), Res),
    Res = 6.0.

test(qbinom2) :-
    interval(qbinom(0.6, 20, 0.3, false), Res),
    Res = 5.0.

test(qbinom3) :-
    interval(qbinom(0.5...0.6, 20...21, 0.6...0.7), Res),
    equal(Res, 12...15).

test(qbinom4) :-
    interval(qbinom(0.5...0.6, 20...21, 0.6...0.7, false), Res),
    equal(Res, 11...15).

test(pbinom1) :-
    interval(pbinom(10, 20, 0.6), Res),
    equal(Res, 0.2446...0.2447).

test(pbinom2) :-
    interval(pbinom(10, 20, 0.6, false), Res),
    equal(Res, 0.7553...0.7554).

test(pbinom3) :-
    interval(pbinom(10, 20, 0.6...0.7), Res),
    equal(Res, 0.0479...0.2447).

test(pbinom4) :-
    interval(pbinom(10, 20, 0.6...0.7, false), Res),
    equal(Res, 0.7553...0.9521).

:- end_tests(binom).

:- begin_tests(normal).

test(pnorm1) :-
    interval(pnorm(0.5), Res),
    interval(round(Res, 4), L...U),
    L = 0.6914,
    U = 0.6915.

test(pnorm2) :-
    interval(pnorm(90, 100, 10), Res),
    interval(round(Res, 4), L...U),
    L = 0.1586,
    U = 0.1587.

test(pnorm3) :-
    interval(pnorm(90, 100, 10, false), Res),
    interval(round(Res, 4), L...U),
    L = 0.8413,
    U = 0.8414.

test(pnorm4) :-
    interval(pnorm(0.5...0.7), Res),
    equal(Res, 0.6914...0.7581).

test(pnorm5) :-
    interval(pnorm(90...91, 100...101, 10...11), Res),
    equal(Res, 0.1356...0.2067).

test(pnorm5) :-
    interval(pnorm(90...91, 100...101, 10...11, false), Res),
    equal(Res, 0.7933...0.8644).

test(qnorm1) :-
    interval(qnorm(0.6), Res),
    interval(round(Res, 4), L...U),
    L = 0.2533,
    U = 0.2534.

test(qnorm2) :-
    interval(qnorm(0.6, 100, 10), Res),
    interval(round(Res, 4), L...U),
    L = 102.5334,
    U = 102.5335.

test(qnorm3) :-
    interval(qnorm(0.6, 100, 10, false), Res),
    interval(round(Res, 4), L...U),
    L = 97.4665,
    U = 97.4666.

test(qnorm4) :-
    interval(qnorm(0.6...0.7), Res),
    equal(Res, 0.2533...0.5245).

test(qnorm5) :-
    interval(qnorm(0.6...0.7, 100...101, 10...11), Res),
    equal(Res, 102.5334...106.7685).

test(qnorm6) :-
    interval(qnorm(0.6...0.7, 100...101, 10...11, false), Res),
    equal(Res, 94.2315...98.4666).

test(dnorm1) :-
    interval(dnorm(0.5), Res),
    equal(Res, 0.3520...0.3521).

test(dnorm2) :-
    interval(dnorm(90, 100, 10), Res),
    equal(Res, 0.0241...0.0242).

test(dnorm3) :-
    interval(dnorm(0.5...0.6), Res),
    equal(Res, 0.3332...0.3521).

test(dnorm4) :-
    interval(dnorm(90...91, 100...101, 10...11), Res),
    equal(Res, 0.0198...0.0286).

test(dnorm5) :-
    interval(dnorm(110...111, 100...101, 10...11), Res),
    equal(Res, 0.0198...0.0286).

test(dnorm6) :-
    interval(dnorm(99...102, 100...101, 10...11), Res),
    equal(Res, 0.0355...0.0399).

:- end_tests(normal).

:- begin_tests(t).

test(pt1) :-
    interval(pt(-0.5, 5), Res),
    equal(Res, 0.3191...0.3192).

test(pt2) :-
    interval(pt(-0.5, 5, false), Res),
    equal(Res, 0.6808...0.6809).

test(pt3) :-
    interval(pt(-0.5... -0.2, 5), Res),
    equal(Res, 0.3191...0.4247).

test(pt4) :-
    interval(pt(-0.5... -0.2, 5...6), Res),
    equal(Res, 0.3191...0.4241).

test(pt5) :-
    interval(pt(-0.5... -0.2, 5, false), Res),
    equal(Res, 0.5753...0.6809).

test(pt6) :-
    interval(pt(0.5...1, 2...5, false), Res),
    equal(Res, 0.1816...0.3334).

test(qt1) :-
    interval(qt(0.4, 5), Res),
    interval(round(Res, 4), -0.2672... -0.2671).

test(qt2) :-
    interval(qt(0.4, 5, false), Res),
    interval(round(Res, 4), 0.2671...0.2672).
    
test(qt3) :-
    interval(qt(0.4...0.7, 5), Res),
    equal(Res, -0.2672...0.5595).

test(qt4) :-
    interval(qt(0.4...0.7, 5, false), Res),
    equal(Res, -0.5595...0.2672).

test(qt5) :-
    interval(qt(0.4...0.6, 2...5), Res),
    equal(Res, -0.2672...0.2887).

test(dt1) :-
    interval(dt(-0.5, 5), Res),
    equal(Res, 0.3279...0.3280).

test(d2) :-
    interval(dt(-0.5... -0.4, 5), Res),
    equal(Res, 0.3279...0.3454).

test(dt3) :-
    interval(dt(0.4...0.5, 5), Res),
    equal(Res, 0.3279...0.3454).

test(dt4) :-
    interval(dt(-0.4... 0.5, 5), Res),
    equal(Res, 0.3279...0.3797).

test(dt5) :-
    interval(dt(-0.5... -0.4, 2...5), Res),
    equal(Res, 0.2962...0.3454).

:- end_tests(t).

:- begin_tests(chisq).

test(pchisq1) :-
    interval(pchisq(0.3, 5), Res),
    equal(Res, 0.0023...0.0024).

test(pchisq2) :-
    interval(pchisq(0.3, 5, false), Res),
    equal(Res, 0.9976...0.9977).

test(pchisq3) :-
    interval(pchisq(0.3...0.4, 5), Res),
    equal(Res, 0.0023...0.0047).

test(pchisq4) :-
    interval(pchisq(0.3...0.4, 5, false), Res),
    equal(Res, 0.9953...0.9977).

test(qchisq1) :-
    interval(qchisq(0.3, 5), Res),
    equal(Res, 2.9999...3).

test(qchisq2) :-
    interval(qchisq(0.3, 5, false), Res),
    equal(Res, 6.0644...6.0645).

test(qchisq3) :-
    interval(qchisq(0.3...0.4, 5), Res),
    equal(Res, 2.9999...3.6555).
    
test(qchisq4) :-
    interval(qchisq(0.3...0.4, 5, false), Res),
    equal(Res, 5.1318...6.0645).

test(dchisq1) :-
    interval(dchisq(0.3, 2), Res),
    equal(Res, 0.4303...0.4304).

test(dchisq2) :-
    interval(dchisq(0.3...0.4, 2), Res),
    equal(Res, 0.4093...0.4304).

test(dchisq3) :-
    interval(dchisq(1.3...1.4, 4), Res),
    equal(Res, 0.1696...0.1739).

test(dchisq4) :-
    interval(dchisq(1.3...1.4, 3), Res),
    equal(Res, 0.2344...0.2375).

test(dchisq5) :-
    interval(dchisq(0.9...1.1, 3), Res),
    equal(Res, 0.2413...0.2420).

:- end_tests(chisq).

% Helper predicate to check equality
equal(Res0, Res) :-
    interval(round(Res0, 4), Res).