Laboratoire de l'Informatique et du Parallélisme » Pobyso

def slz_check_htr_value(function, htrValue, lowerBound, upperBound, precision, \

                        degree, targetHardnessToRound, alpha):

    """

    Check an Hard-to-round value.

    TODO::

    Full rewriting: this is hardly a draft.

    """

    polyApproxPrec = targetHardnessToRound + 1

    polyTargetHardnessToRound = targetHardnessToRound + 1

    internalSollyaPrec = ceil((RR('1.5') * targetHardnessToRound) / 64) * 64

    RRR = htrValue.parent()

    #

    ## Compute the scaled function.

    fff = slz_compute_scaled_function(f, lowerBound, upperBound, precision)[0]

    print "Scaled function:", fff

    #

    ## Compute the scaling.

    boundsIntervalRifSa = RealIntervalField(precision)

    domainBoundsInterval = boundsIntervalRifSa(lowerBound, upperBound)

    scalingExpressions = \

        slz_interval_scaling_expression(domainBoundsInterval, i)

    #

    ## Get the polynomials, bounds, etc. for all the interval.

    resultListOfTuplesOfSo = \

        slz_get_intervals_and_polynomials(f, degree, lowerBound, upperBound, \

                                          precision, internalSollyaPrec,\

                                          2^-(polyApproxPrec))

    #

    ## We only want one interval.

    if len(resultListOfTuplesOfSo) > 1:

        print "Too many intervals! Aborting!"

        exit

    #

    ## Get the first tuple of Sollya objects as Sage objects. 

    firstTupleSa = \

        slz_interval_and_polynomial_to_sage(resultListOfTuplesOfSo[0])

    pobyso_set_canonical_on()

    #

    print "Floatting point polynomial:", firstTupleSa[0]

    print "with coefficients precision:", firstTupleSa[0].base_ring().prec()

    #

    ## From a polynomial over a real ring, create a polynomial over the 

    #  rationals ring.

    rationalPolynomial = \

        slz_float_poly_of_float_to_rat_poly_of_rat(firstTupleSa[0])

    print "Rational polynomial:", rationalPolynomial

    #

    ## Create a polynomial over the rationals that will take integer 

    # variables instead of rational. 

    rationalPolynomialOfIntegers = \

        slz_rat_poly_of_rat_to_rat_poly_of_int(rationalPolynomial, precision)

    print "Type:", type(rationalPolynomialOfIntegers)

    print "Rational polynomial of integers:", rationalPolynomialOfIntegers

    #

    ## Check the rational polynomial of integers variables.

    # (check against the scaled function).

    toIntegerFactor = 2^(precision-1)

    intervalCenterAsIntegerSa = int(firstTupleSa[3] * toIntegerFactor)

    print "Interval center as integer:", intervalCenterAsIntegerSa

    lowerBoundAsIntegerSa = int(firstTupleSa[2].endpoints()[0] * \

                                toIntegerFactor) - intervalCenterAsIntegerSa

    upperBoundAsIntegerSa = int(firstTupleSa[2].endpoints()[1] * \

                                toIntegerFactor) - intervalCenterAsIntegerSa

    print "Lower bound as integer:", lowerBoundAsIntegerSa

    print "Upper bound as integer:", upperBoundAsIntegerSa

    print "Image of the lower bound by the scaled function", \

            fff(firstTupleSa[2].endpoints()[0])

    print "Image of the lower bound by the approximation polynomial of ints:", \

            RRR(rationalPolynomialOfIntegers(lowerBoundAsIntegerSa))

    print "Image of the center by the scaled function", fff(firstTupleSa[3])

    print "Image of the center by the approximation polynomial of ints:", \

            RRR(rationalPolynomialOfIntegers(0))

    print "Image of the upper bound by the scaled function", \

            fff(firstTupleSa[2].endpoints()[1])

    print "Image of the upper bound by the approximation polynomial of ints:", \

            RRR(rationalPolynomialOfIntegers(upperBoundAsIntegerSa))

# End slz_check_htr_value.