"""Deterministic integer-order and randomized Shannon entropy-rate intervals."""
from fractions import Fraction as Q
import random
from .arithmetic import positive_int
from .numerics import log_bounds, spectral_bounds, sqrt_upper
from .compiler import collision_matrix, target_mass


def renyi_interval(source,depth,order,relative_precision=Q(1,10**10),max_states=500000):
    matrix,diagnostics=collision_matrix(source,depth,order,max_states)
    root=spectral_bounds(matrix,relative_precision)
    a=log_bounds(root["lower"])[0]
    b=log_bounds(root["upper"])[1]
    divisor=depth*(order-1)
    spectral_lo,spectral_hi=-b/divisor,-a/divisor
    split=source.split_bound(depth)
    error=log_bounds(source.states*split)[1]/depth
    # Edge alphabet size bounds the number of n-edge histories.
    beta_upper=source.field.embeddings(128)[3].hi
    ceiling=min(log_bounds(len(source.edges))[1],source.kmax*log_bounds(beta_upper)[1])
    lo=max(Q(0),spectral_lo-error)
    hi=min(ceiling,spectral_hi)
    if lo>hi:
        raise ArithmeticError("inconsistent certified bounds")
    return {"order":order,"depth":depth,"interval_nats_per_branch":(lo,hi),
            "width":hi-lo,"spectral_proxy_interval":(spectral_lo,spectral_hi),
            "split_bound":split,"boundary_fibre_log_error":error,
            "moment_matrix":matrix,"spectral_radius":root,"diagnostics":diagnostics,
            "probabilistic":False,"source_stationary":source.stationary}


def shannon_interval(source,depth,samples,confidence=Q(99,100),seed=None,
                     numerical_width=Q(1,10**8),max_states=500000,rng=None):
    positive_int(depth,"depth");positive_int(samples,"samples")
    if not source.stationary:
        raise ValueError("the Shannon finite-block bracket requires an exactly stationary source")
    confidence,numerical_width=Q(confidence),Q(numerical_width)
    if not 0<confidence<1 or numerical_width<=0:
        raise ValueError("invalid confidence or numerical width")
    if seed is not None and rng is not None:
        raise ValueError("supply a seed or a random oracle, not both")
    mode=("seeded pseudorandom demonstration" if seed is not None else
          "supplied random-integer oracle" if rng is not None else "SystemRandom sampling")
    rng=rng if rng is not None else random.Random(seed) if seed is not None else random.SystemRandom()
    minp=min(e.probability for e in source.edges)
    B=max(Q(1),log_bounds(1/minp)[1])
    logtail=log_bounds(2/(1-confidence))[1]
    # Choose square-root precision from requested numerical width, not a fixed floor.
    bits=max(80,numerical_width.denominator.bit_length()-numerical_width.numerator.bit_length()+8)
    margin=sqrt_upper(B*B*logtail/(2*samples),bits)
    lower=upper=Q(0)
    widths=[]
    for _ in range(samples):
        start,path,end=source.sample_path(depth,rng)
        mass,diag=target_mass(source,path,max_states,start=start,end=end)
        if mass<=0:
            raise ArithmeticError("sampled endpoint has zero mass")
        lo,hi=log_bounds(1/mass,depth*numerical_width)
        lower+=lo/depth;upper+=hi/depth
        widths.append(diag["max_layer_states"])
    lower/=samples;upper/=samples
    bias=log_bounds(source.states*source.split_bound(depth))[1]/depth
    beta_upper=source.field.embeddings(128)[3].hi
    ceiling=min(log_bounds(len(source.edges))[1],source.kmax*log_bounds(beta_upper)[1])
    lo=max(Q(0),lower-margin-bias)
    hi=min(ceiling,upper+margin)
    if lo>hi:
        # Bad concentration events can in principle create an empty intersection.
        # Report failure rather than inventing a valid confidence interval.
        return {"failure":True,"reason":"empty confidence/bound intersection","sampling_mode":mode}
    return {"order":1,"depth":depth,"samples":samples,"confidence":confidence,
            "interval_nats_per_branch":(lo,hi),"width":hi-lo,
            "sampling_mode":mode,"independent_exact_draws_required":True,
            "sampled_quantity":"H(X_n,Z_n | Z_0)/n",
            "surprisal_range_upper":B,"hoeffding_margin":margin,
            "finite_block_bias_upper":bias,"mean_surprisal_interval":(lower,upper),
            "maximum_fibre_layer_states":max(widths),"probabilistic":True}