Laboratoire de l'Informatique et du Parallélisme » Pobyso

    domainBoundsIntervalSa = boundsIntervalRifSa(lowerBoundSa, upperBoundSa)

    (domainScalingExpressionSa, invDomainScalingExpressionSa) = \

        slz_interval_scaling_expression(domainBoundsIntervalSa, x)

    print "f: ", f

    ff = f.subs({x : domainScalingExpressionSa})

    #ff = f.subs_expr(x==domainScalingExpressionSa)

    domainScalingFunction(x) = invDomainScalingExpressionSa

    print 'ff:', ff, "- Domain:", scaledLowerBoundSa, scaledUpperBoundSa

    #

    # Scalling the image -> [1,2[.

    if flbSa <= fubSa: # Increasing

        imageBinadeBottomSa = floor(flbSa.log2())

    else: # Decreasing

    imageBoundsIntervalSa = boundsIntervalRifSa(flbSa, fubSa)

    (imageScalingExpressionSa, invImageScalingExpressionSa) = \

        slz_interval_scaling_expression(imageBoundsIntervalSa, x)

    iis = invImageScalingExpressionSa.function(x)

    fff = iis.subs({x:ff})

    print "fff:", fff,

    print " - Image:", fff(scaledLowerBoundSa), fff(scaledUpperBoundSa)

    return([fff, scaledLowerBoundSa, scaledUpperBoundSa, \

            fff(scaledLowerBoundSa), fff(scaledUpperBoundSa)])

def slz_float_poly_of_float_to_rat_poly_of_rat(polyOfFloat):

    # Create a polynomial over the rationals.

                                              upperBoundSa.parent().precision()))

    boundsSa = pobyso_range_to_interval_so_sa(boundsSo, realIntervalField)

    errorSa = pobyso_get_constant_as_rn_with_rf_so_sa(maxErrorSo)

    # If the error and interval are OK a the first try, just return.

    if boundsSa.endpoints()[1] >= scaledUpperBoundSa:

        # Change variable stuff in Sollya x -> x0-x.

def slz_interval_scaling_expression(boundsInterval, expVar):

    """

    a single binade to [1, 2) and the inverse expression as well.

    Not very sure that the transformation makes sense for negative numbers.

    """

    # The scaling offset is only used for negative numbers.

    if abs(boundsInterval.endpoints()[0]) < 1:

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

            scalingCoeff = 2^floor(boundsInterval.endpoints()[0].log2())

            #scalingOffset = 0

            return((scalingCoeff * expVar + scalingOffset,

                    1/scalingCoeff * expVar + 3))

def slz_interval_and_polynomial_to_sage(polyRangeCenterErrorSo):

    """

print "\t...sageSLZ loaded"