Laboratoire de l'Informatique et du Parallélisme » Pobyso

def slz_compute_binade(number):

    """"

    For a given number, compute the "binade" that is integer m such that

    2^m <= number < 2^(m+1). If number == 0 return None.

    """

    # Checking the parameter.

    # The exception construction is used to detect if numbre is a RealNumber

    # since not all numbers have

    # the mro() method. sage.rings.real_mpfr.RealNumber do.

    try:

        classTree = [number.__class__] + number.mro()

        # If the number is not a RealNumber (of offspring thereof) try

        # to transform it.

        if not sage.rings.real_mpfr.RealNumber in classTree:

            numberAsRR = RR(number)

        else:

            numberAsRR = number

    except AttributeError:

        return None

    # Zero special case.

    if numberAsRR == 0:

        return RR(-infinity)

    else:

        return floor(numberAsRR.abs().log2())

# End slz_compute_binade

    # The exception construction is necessary since not all objects have

    # Regular case cont'd.

    If the interval spans more than one binade, result is wrong since

    scaling is only based on the lower bound.

    # The "one of the bounds is 0" special case. Here we consider

    # the interval as the subnormals binade.

    if boundsInterval.endpoints()[0] == 0 or boundsInterval.endpoints()[1] == 0:

        # The upper bound is (or should be) positive.

        if boundsInterval.endpoints()[0] == 0:

            if boundsInterval.endpoints()[1] == 0:

                return None

            binade = slz_compute_binade(boundsInterval.endpoints()[1])

            l2     = boundsInterval.endpoints()[1].abs().log2()

            # The upper bound is a power of two

            if binade == l2:

                scalingCoeff    = 2^(-binade)

                invScalingCoeff = 2^(binade)

                scalingOffset   = 1

                return((scalingCoeff * expVar + scalingOffset),\

                       ((expVar - scalingOffset) * invScalingCoeff))

            else:

                scalingCoeff    = 2^(-binade-1)

                invScalingCoeff = 2^(binade+1)

                scalingOffset   = 1

                return((scalingCoeff * expVar + scalingOffset),\

                    ((expVar - scalingOffset) * invScalingCoeff))

        # The lower bound is (or should be) negative.

        if boundsInterval.endpoints()[1] == 0:

            if boundsInterval.endpoints()[0] == 0:

                return None

            binade = slz_compute_binade(boundsInterval.endpoints()[0])

            l2     = boundsInterval.endpoints()[0].abs().log2()

            # The upper bound is a power of two

            if binade == l2:

                scalingCoeff    = -2^(-binade)

                invScalingCoeff = -2^(binade)

                scalingOffset   = 1

                return((scalingCoeff * expVar + scalingOffset),\

                    ((expVar - scalingOffset) * invScalingCoeff))

            else:

                scalingCoeff    = -2^(-binade-1)

                invScalingCoeff = -2^(binade+1)

                scalingOffset   = 1

                return((scalingCoeff * expVar + scalingOffset),\

                   ((expVar - scalingOffset) * invScalingCoeff))

    # General case

    lbBinade = slz_compute_binade(boundsInterval.endpoints()[0])

    ubBinade = slz_compute_binade(boundsInterval.endpoints()[1])

    # We allow for a single exception in binade spanning is when the

    # "outward bound" is a power of 2 and its binade is that of the

    # "inner bound" + 1.

    if boundsInterval.endpoints()[0] > 0:

        ubL2 = boundsInterval.endpoints()[1].abs().log2()

        if lbBinade != ubBinade:

            print "Different binades."

            if ubL2 != ubBinade:

                print "Not a power of 2."

                return None

            elif abs(ubBinade - lbBinade) > 1:

                print "Too large span:", abs(ubBinade - lbBinade)

                return None

    else:

        lbL2 = boundsInterval.endpoints()[0].abs().log2()

        if lbBinade != ubBinade:

            print "Different binades."

            if lbL2 != lbBinade:

                print "Not a power of 2."

                return None

            elif abs(ubBinade - lbBinade) > 1:

                print "Too large span:", abs(ubBinade - lbBinade)

                return None

    #print "Lower bound binade:", binade

    if boundsInterval.endpoints()[0] > 0:

        return((2^(-lbBinade) * expVar),(2^(lbBinade) * expVar))

    else:

        return((-(2^(-lbBinade+1)) * expVar),(-(2^(lbBinade-1)) * expVar))

"""

    # Code sent to attic. Should be the base for a 

    # "slz_interval_translate_expression" rather than scale.

    # Extra control and special cases code  added in  

    # slz_interval_scaling_expression could (should ?) be added to

    # this new function.

"""