code: def separate_zeros_in_block(
      ctx, zero_number_block, T, V, limitloop=None, fp_tolerance=None
  ):
      """Separate the zeros contained in the block T, limitloop
      determines how long one must search"""
      if limitloop is None:
          limitloop = ctx.inf
      loopnumber = 0
      variations = count_variations(V)
      while (variations < zero_number_block) and (
          loopnumber < limitloop
      ):
          a = T[0]
          v = V[0]
          newT = [a]
          newV = [v]
          variations = 0
          for n in range(1, len(T)):
              b2 = T[n]
              u = V[n]
              if u * v > 0:
                  alpha = ctx.sqrt(u / v)
                  b = (alpha * a + b2) / (alpha + 1)
              else:
                  b = (a + b2) / 2
              if fp_tolerance < 10:
                  w = ctx._fp.siegelz(b)
                  if abs(w) < fp_tolerance:
                      w = ctx.siegelz(b)
              else:
                  w = ctx.siegelz(b)
              if v * w < 0:
                  variations += 1
              newT.append(b)
              newV.append(w)
              u = V[n]
              if u * w < 0:
                  variations += 1
              newT.append(b2)
              newV.append(u)
              a = b2
              v = u
          T = newT
          V = newV
          loopnumber += 1
          if (
              (limitloop > ITERATION_LIMIT)
              and (loopnumber > 2)
              and (variations + 2 == zero_number_block)
          ):
              dtMax = 0
              dtSec = 0
              kMax = 0
              for k1 in range(1, len(T)):
                  dt = T[k1] - T[k1 - 1]
                  if dt > dtMax:
                      kMax = k1
                      dtSec = dtMax
                      dtMax = dt
                  elif (dt < dtMax) and (dt > dtSec):
                      dtSec = dt
              if dtMax > 3 * dtSec:
                  f = lambda x: ctx.rs_z(x, derivative=1)
                  t0 = T[kMax - 1]
                  t1 = T[kMax]
                  t = ctx.findroot(
                      f,
                      (t0, t1),
                      solver="illinois",
                      verify=False,
                      verbose=False,
                  )
                  v = ctx.siegelz(t)
                  if (t0 < t) and (t < t1) and (v * V[kMax] < 0):
                      T.insert(kMax, t)
                      V.insert(kMax, v)
          variations = count_variations(V)
      if variations == zero_number_block:
          separated = True
      else:
          separated = False
      return (T, V, separated)
  
file_path: catboost/contrib/python/mpmath/py3/mpmath/functions/zetazeros.py
imports: from .functions import defun, defun_wrapped
label_desc: Use image node_id 3 for calling a global function with example usage: separate_zeros_in_block(ctx, zero_number_block, T, V, limitloop, fp_tolerance) and returns: T,  V,  separated