-- tests basic methods (e.g., arithmetic operations) for RRi implementation FF := RRi_1000 assert(precision FF===1000) I := interval(1,3) assert not (I===interval(3,1)) assert isEmpty interval(3,1) assert (I===span(3,1)) assert (I===interval[1,3]) assert (precision ring I === 53) assert (precision interval(1,3_(RR_1000))==1000) assert (precision interval(Precision=>1000,1,3) == 1000) assert (precision interval(1_(RR_1000),2_(RR_2000)) == 1000) assert (precision (interval(Precision=>100,1,3)+interval(Precision=>200,2,4)) == 100) assert (precision toRRi(300,2,2) == 300) assert (precision toRRi(30) == 53) assert (precision toRRi(10_(RR_100)) == 100) assert (toRRi(4) == interval(4)) assert(toString FF === "RRi_1000") assert(expression FF === new Subscript from {symbol RRi,1000}) assert(left I === 1_(RR_53)) assert(right I === 3_(RR_53)) assert(midpoint I === 2_(RR_53)) J := toRRi 2 assert not(I<J or I>J or I==J or I>=J or I<=J) assert isSubset(J,I) assert (J <= J) assert not(I <= I) assert (I==I) assert (J==J) assert (I===I) assert (I==interval(1,3)) assert (0<I) assert (I<=interval(3,5)) assert (J<interval(3,5)) assert(left sin J <= sin 2.0) assert(right sin J >= sin 2.0) assert(left sin J != right sin J) assert(I+J===J+I) assert(I*J===J*I) K := interval(-2,3) assert(not (K*K===K^2)) assert(diameter sqrt I < 1) assert(right sqrt I > sqrt 3) -- this has to do with different rounding directions (mpfi vs mpfr) assert(right log exp interval 1 > 1) assert(left log exp interval 1 < 1) assert (abs(K)===interval(0,3)) assert (midpoint(I) == J) assert (diameter(I) == 2) assert isMember(numeric_100 pi,numericInterval_100 pi) L = interval(-2/3,1.5_(RR_53)) M = interval(-4,2.7) assert (L+M===interval(-14/3,4.2)) assert isSubset(interval(-10.1/3,5.5),L-M) assert isSubset(interval(-6,4.05),L*M) assert isSubset(K^2,K*K) assert not isSubset(K*K,K^2) assert (L/I===L) assert (L^2===interval(0,2.25)) assert isSubset(interval(-8/27,3.375),L^3) assert isSubset(sin(L),interval(-1,1)) assert isFinite(I) assert not isFinite(I/K) assert isANumber(I) assert isANumber(I/K) assert not isInfinite(I) assert isInfinite(I/K) assert isMember(numeric_100 pi,acos cos(numericInterval_100 pi)) assert (left atan I == atan 1) assert (right atan I == atan 3) assert (left sinh I == sinh 1) assert (acosh(I) >= 0) --- TO FIX: --------------------------------------------- -* sqrt K -- produce a different error? *- -* Ok to divide by 0, gives infinity. Ok to take log of 0 (-infinity), just not negative values. Can't take arc-trig of inappropriate intervals. Some of these functions (like contains) should be isSubset *- -* debug Core errorDepth = 0 FF[x] -- start with... rawToRRi in d/interface.dd *-

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