# TODO: technically incorrect on 0 robustness since conflates < and >

from functools import singledispatch

import sympy as sym
from numpy import arange
from funcy import pairwise

import stl.ast
from stl.ast import t_sym
from stl.robustness import op_lookup

@singledispatch
def smooth_robustness(stl, L, h, eps, depth):
    raise NotImplementedError

@smooth_robustness.register(stl.And)
@smooth_robustness.register(stl.G)
def _(stl, L, H, eps):
    raise NotImplementedError("Call canonicalization function")

def eps_to_base(eps, N):
    return N**(1/eps)

def soft_max(rs, eps=0.1):
    N = len(rs)
    B = eps_to_base(eps, N)
    return sym.log(sum(B**r for r in rs), B)


def LSE(rs, eps=0.1):
    N = len(rs)
    B = eps_to_base(eps, N)
    return soft_max(rs) - sym.log(N, B)


@smooth_robustness.register(stl.Or)
def _(stl, L, h, eps, depth=0):
    rl, rh = list(zip(
        *[smooth_robustness(arg, L, h, eps=eps/2, depth=depth+1)
          for arg in stl.args]))
    return soft_max(rl, eps=eps/2), LSE(rh, eps=eps/2)


def soft_max2(r, eps, lo, hi, L, H, depth):
    N = sym.ceiling((hi - lo) / H)
    B = eps_to_base(eps, N)
    i = sym.Symbol("i_{}".format(depth))
    x_ij = (L*H + r.subs({t_sym: t_sym+i}) + r.subs({t_sym: t_sym+i+1}))/2
    return sym.log(sym.summation(B**x_ij, (i, lo, hi)), B)

def LSE2(r, eps, lo, hi, H, depth):
    N = sym.ceiling((hi - lo) / H)
    B = eps_to_base(eps, N)
    i = sym.Symbol("i_{}".format(depth))
    x_i = r.subs({t_sym: t_sym+i})
    return sym.log(sym.summation(B**x_i, (i, lo, hi))/N, B)



@smooth_robustness.register(stl.F)
def _(stl, L, H, eps, depth=0):
    lo, hi = stl.interval
    times = arange(lo, hi, H)
    rl, rh = smooth_robustness(stl.arg, L, H, eps=eps/2, depth=depth+1)
    return (LSE2(rl, eps/2, lo, hi, H, depth), 
            soft_max2(rh, eps/2, lo, hi, L, H, depth))


@smooth_robustness.register(stl.Neg)
def _(stl, L, H, eps, depth=0):
    rl, rh = smooth_robustness(arg, L, H, eps, depth=depth+1)
    return -rh, -rl


@smooth_robustness.register(stl.LinEq)
def _(stl, L, H, eps, depth=0):
    op = op_lookup[stl.op]
    retval = op(eval_terms(stl), stl.const)
    return retval, retval


def eval_terms(lineq):
    return sum(map(eval_term, lineq.terms))


def eval_term(term):
    return term.coeff*sym.Function(term.id.name)(t_sym)