Laboratoire de l'Informatique et du Parallélisme » Pobyso

# This file was *autogenerated* from the file ./runSLZ-06.sage

from sage.all_cmdline import *   # import sage library

# @file runSLZ-05.sage

#from scipy.constants.codata import precision

def initialize_env():

    """

    Load all necessary modules.

    """

    if not 'mpfi' in sage.misc.cython.standard_libs:

        sage.misc.cython.standard_libs.append('mpfi')

    load("/home/storres/recherche/arithmetique/pobysoPythonSage/src/sollya_lib.sage")

    load("/home/storres/recherche/arithmetique/pobysoPythonSage/src/pobyso.py")

    load("/home/storres/recherche/arithmetique/pobysoPythonSage/src/sageSLZ/sageSLZ.sage")

    load("/home/storres/recherche/arithmetique/pobysoPythonSage/src/sageSLZ/sageNumericalOperations.sage")

print "Running SLZ..."

initialize_env()

x = var('x')

__tmp__=var("x"); func = symbolic_expression(exp(x)).function(x)

RRR = RealField(precision)

icUlp               = intervalCenter.ulp()

intervalRadius      = RRR(_sage_const_2 **(-_sage_const_35 ))          

                precision               = precision, 

                debug                   = True)

#

def slz_compute_polynomial_and_interval_02(functionSo, degreeSo, lowerBoundSa, 

                                        upperBoundSa, approxAccurSa, 

    """

    Under the assumptions listed for slz_get_intervals_and_polynomials, compute

    a polynomial that approximates the function on a an interval starting

    - the center of the interval;

    - the maximum error in the approximation of the input functionSo by the

      output polynomial ; this error <= approxAccurSaS.

    """

    print"In slz_compute_polynomial_and_interval..."

    ## Superficial argument check.

    ## Change Sollya precision, if requested.

    sollyaPrecChanged = False

    (initialSollyaPrecSo, initialSollyaPrecSa) = pobyso_get_prec_so_so_sa()

        sollyaPrecSa = initialSollyaPrecSa

    else:

        if sollyaPrecSa <= 2:

    currentRangeSo = pobyso_bounds_to_range_sa_so(lowerBoundSa, upperBoundSa)

    currentUpperBoundSa = upperBoundSa

    currentLowerBoundSa = lowerBoundSa

    (polySo, intervalCenterSo, maxErrorSo) = \

        pobyso_taylor_expansion_no_change_var_so_so(functionSo, degreeSo, 

                                                    currentRangeSo, 

                                                    absoluteErrorTypeSo)

    maxErrorSa = pobyso_get_constant_as_rn_with_rf_so_sa(maxErrorSo)

    while maxErrorSa > approxAccurSa:

        print "++Approximation error:", maxErrorSa.n()

        sollya_lib_clear_obj(polySo)

    """

    Load all necessary modules.

    """

    if not 'mpfi' in sage.misc.cython.standard_libs:

        sage.misc.cython.standard_libs.append('mpfi')

    load("/home/storres/recherche/arithmetique/pobysoPythonSage/src/sollya_lib.sage")

    load("/home/storres/recherche/arithmetique/pobysoPythonSage/src/pobyso.py")

    load("/home/storres/recherche/arithmetique/pobysoPythonSage/src/sageSLZ/sageSLZ.sage")

    load("/home/storres/recherche/arithmetique/pobysoPythonSage/src/sageSLZ/sageNumericalOperations.sage")

print "Running SLZ..."

initialize_env()

x = var('x')

func(x) = exp(x)

RRR = RealField(precision)

icUlp               = intervalCenter.ulp()

intervalRadius      = RRR(2^(-35))          

                precision               = precision, 

                debug                   = True)

#

        2- once a non null resultant is found, check for roots;

        3- constant resultant == no root.

    """

    if debug:

        print "Function                :", inputFunction

        print "Lower bound             :", inputLowerBound

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

    if internalSollyaPrec < 192:

        internalSollyaPrec = 192

    pobyso_set_prec_sa_so(internalSollyaPrec)

    print "Sollya internal precision:", internalSollyaPrec

    targetPlusOnePrecRF       = RealField(RRR.prec()+1)

        iterCount += 1

        print "[", lb, ",", ub, "]", ((ub - lb) / intervalUlp).log2().n(), \

            "log2(numbers)." 

        ### Compute a Sollya polynomial that will honor the Taylor condition.

                                                        degreeSo,

                                                        lb,

                                                        ub,

                                                        polyApproxAccur,

                                                        debug=True)

        if debug:

        ### Convert back the data into Sage space.                         

        (floatP, floatPcv, intvl, ic, terr) = \

    Get the current default precision in Sollya.

    The return value is Sage/Python int.

    """

    sollya_lib_clear_obj(precSo)

# End pobyso_get_prec_so_sa.

def pobyso_get_prec_so_so_sa():

    Sage integer as hybrid tuple.

    To avoid multiple calls for precision manipulations. 

    """

def pobyso_get_prec_of_constant(ctExpSo):

    """ Legacy function. See pobyso_get_prec_of_constant_so_sa. """

    pobyso_set_prec_sa_so(p)

def pobyso_set_prec_sa_so(p):

    #precSo = c_void_p(sollya_lib_constant_from_int(a))

    sollya_lib_set_prec(precSo)

    sollya_lib_clear_obj(precSo)

# End pobyso_set_prec_sa_so.

    x -> x-intervalCenter.

    """

    # Change internal Sollya precision, if needed.

    sollyaPrecChanged = False

    if sollyaPrecSo is None:

        pass

    pobyso_clear_taylorform_sa_so(taylorFormListSaSo)

    if absMaxErrorSa > absMinErrorSa:

        sollya_lib_clear_obj(absMinErrorSo)

    else:

        sollya_lib_clear_obj(absMaxErrorSo)

# end pobyso_taylor_expansion_no_change_var_so_so

def pobyso_taylor_expansion_with_change_var_so_so(functionSo, degreeSo, \