@defun
def adaptive_extrapolation(ctx, update, emfun, kwargs):
    option = kwargs.get
    if ctx._fixed_precision:
        tol = option('tol', ctx.eps*2**10)
    else:
        tol = option('tol', ctx.eps/2**10)
    verbose = option('verbose', False)
    maxterms = option('maxterms', ctx.dps*10)
    method = set(option('method', 'r+s').split('+'))
    skip = option('skip', 0)
    steps = iter(option('steps', xrange(10, 10**9, 10)))
    strict = option('strict')
    #steps = (10 for i in xrange(1000))
    summer=[]
    if 'd' in method or 'direct' in method:
        TRY_RICHARDSON = TRY_SHANKS = TRY_EULER_MACLAURIN = False
    else:
        TRY_RICHARDSON = ('r' in method) or ('richardson' in method)
        TRY_SHANKS = ('s' in method) or ('shanks' in method)
        TRY_EULER_MACLAURIN = ('e' in method) or \
            ('euler-maclaurin' in method)

        def init_levin(m):
            variant = kwargs.get("levin_variant", "u")
            if isinstance(variant, str):
                if variant == "all":
                    variant = ["u", "v", "t"]
                else:
                    variant = [variant]
            for s in variant:
                L = levin_class(method = m, variant = s)
                L.ctx = ctx
                L.name = m + "(" + s + ")"
                summer.append(L)

        if ('l' in method) or ('levin' in method):
            init_levin("levin")

        if ('sidi' in method):
            init_levin("sidi")

        if ('a' in method) or ('alternating' in method):
            L = cohen_alt_class()
            L.ctx = ctx
            L.name = "alternating"
            summer.append(L)

    last_richardson_value = 0
    shanks_table = []
    index = 0
    step = 10
    partial = []
    best = ctx.zero
    orig = ctx.prec
    try:
        if 'workprec' in kwargs:
            ctx.prec = kwargs['workprec']
        elif TRY_RICHARDSON or TRY_SHANKS or len(summer)!=0:
            ctx.prec = (ctx.prec+10) * 4
        else:
            ctx.prec += 30
        while 1:
            if index >= maxterms:
                break

            # Get new batch of terms
            try:
                step = next(steps)
            except StopIteration:
                pass
            if verbose:
                print("-"*70)
                print("Adding terms #%i-#%i" % (index, index+step))
            update(partial, xrange(index, index+step))
            index += step

            # Check direct error
            best = partial[-1]
            error = abs(best - partial[-2])
            if verbose:
                print("Direct error: %s" % ctx.nstr(error))
            if error <= tol:
                return best

            # Check each extrapolation method
            if TRY_RICHARDSON:
                value, maxc = ctx.richardson(partial)
                # Convergence
                richardson_error = abs(value - last_richardson_value)
                if verbose:
                    print("Richardson error: %s" % ctx.nstr(richardson_error))
                # Convergence
                if richardson_error <= tol:
                    return value
                last_richardson_value = value
                # Unreliable due to cancellation
                if ctx.eps*maxc > tol:
                    if verbose:
                        print("Ran out of precision for Richardson")
                    TRY_RICHARDSON = False
                if richardson_error < error:
                    error = richardson_error
                    best = value
            if TRY_SHANKS:
                shanks_table = ctx.shanks(partial, shanks_table, randomized=True)
                row = shanks_table[-1]
                if len(row) == 2:
                    est1 = row[-1]
                    shanks_error = 0
                else:
                    est1, maxc, est2 = row[-1], abs(row[-2]), row[-3]
                    shanks_error = abs(est1-est2)
                if verbose:
                    print("Shanks error: %s" % ctx.nstr(shanks_error))
                if shanks_error <= tol:
                    return est1
                if ctx.eps*maxc > tol:
                    if verbose:
                        print("Ran out of precision for Shanks")
                    TRY_SHANKS = False
                if shanks_error < error:
                    error = shanks_error
                    best = est1
            for L in summer:
                est, lerror = L.update_psum(partial)
                if verbose:
                    print("%s error: %s" % (L.name, ctx.nstr(lerror)))
                if lerror <= tol:
                    return est
                if lerror < error:
                    error = lerror
                    best = est
            if TRY_EULER_MACLAURIN:
                if ctx.mpc(ctx.sign(partial[-1]) / ctx.sign(partial[-2])).ae(-1):
                    if verbose:
                        print ("NOT using Euler-Maclaurin: the series appears"
                            " to be alternating, so numerical\n quadrature"
                            " will most likely fail")
                    TRY_EULER_MACLAURIN = False
                else:
                    value, em_error = emfun(index, tol)
                    value += partial[-1]
                    if verbose:
                        print("Euler-Maclaurin error: %s" % ctx.nstr(em_error))
                    if em_error <= tol:
                        return value
                    if em_error < error:
                        best = value
    finally:
        ctx.prec = orig
    if strict:
        raise ctx.NoConvergence
    if verbose:
        print("Warning: failed to converge to target accuracy")
    return best
dataset/ETHPy150Open fredrik-johansson/mpmath/mpmath/calculus/extrapolation.py/adaptive_extrapolation/original