Laboratoire de l'Informatique et du Parallélisme » Pobyso

        ##### Prepare for results.

        intervalResultsList = []

        intervalResultsList.append((lb, ub))

        #### Check roots.

        rootsResultsList = []

        rootsComputationTime        = cputime()

        for root in reducedPolynomialsRootsSet:

            specificRootResultsList = []

            failingBounds = []

            intIntPdivN = intIntP(root[0], root[1]) / N

            if int(intIntPdivN) != intIntPdivN:

                continue # Next root

            # Root qualifies for modular equation, test it for hardness to round.

            hardToRoundCaseAsFloat = RRR((icAsInt + root[0]) / toIntegerFactor)

            #print "Before unscaling:", hardToRoundCaseAsFloat.n(prec=precision)

            #print scalingFunction

            scaledHardToRoundCaseAsFloat = \

                scalingFunction(hardToRoundCaseAsFloat) 

            print "Candidate HTRNc at x =", \

                scaledHardToRoundCaseAsFloat.n().str(base=2),

            if slz_is_htrn(scaledHardToRoundCaseAsFloat,

                           f,

                           2^-(targetHardnessToRound),

                           RRR):

                print hardToRoundCaseAsFloat, "is HTRN case."

                if lb <= hardToRoundCaseAsFloat and hardToRoundCaseAsFloat <= ub:

                    print "Found in interval."

                else:

                    print "Found out of interval."

                specificRootResultsList.append(hardToRoundCaseAsFloat.n().str(base=2))

                # Check the root is in the bounds

                if abs(root[0]) > iBound or abs(root[1]) > tBound:

                    print "Root", root, "is out of bounds."

                    if abs(root[0]) > iBound:

                        print "root[0]:", root[0]

                        print "i bound:", iBound

                        failingBounds.append('i')

                        failingBounds.append(root[0])

                        failingBounds.append(iBound)

                    if abs(root[1]) > tBound:

                        print "root[1]:", root[1]

                        print "t bound:", tBound

                        failingBounds.append('t')

                        failingBounds.append(root[1])

                        failingBounds.append(tBound)

                if len(failingBounds) > 0:

                    specificRootResultsList.append(failingBounds)

            else: # From slz_is_htrn...

                print "is not an HTRN case."

            if len(specificRootResultsList) > 0:

                rootsResultsList.append(specificRootResultsList)

        rootsComputationsFullTime       =   cputime(rootsComputationTime)

        rootsComputationsCount          +=  1

        if len(rootsResultsList) > 0:

            intervalResultsList.append(rootsResultsList)

        #### An intervalResultsList has at least the bounds.

        globalResultsList.append(intervalResultsList)   

            inputLowerBound = 6/16, 

            inputUpperBound = 7/16, 

#inputUpperBound = RRR(1/2) - RRR(1/4).ulp(),