code: def nzeros(ctx, t):
      r"""
      Computes the number of zeros of the Riemann zeta function in
      `(0,1) \times (0,t]`, usually denoted by `N(t)`.
  
      **Examples**
  
      The first zero has imaginary part between 14 and 15::
  
          >>> from mpmath import *
          >>> mp.dps = 15; mp.pretty = True
          >>> nzeros(14)
          0
          >>> nzeros(15)
          1
          >>> zetazero(1)
          (0.5 + 14.1347251417347j)
  
      Some closely spaced zeros::
  
          >>> nzeros(10**7)
          21136125
          >>> zetazero(21136125)
          (0.5 + 9999999.32718175j)
          >>> zetazero(21136126)
          (0.5 + 10000000.2400236j)
          >>> nzeros(545439823.215)
          1500000001
          >>> zetazero(1500000001)
          (0.5 + 545439823.201985j)
          >>> zetazero(1500000002)
          (0.5 + 545439823.325697j)
  
      This confirms the data given by J. van de Lune,
      H. J. J. te Riele and D. T. Winter in 1986.
      """
      if t < 14.1347251417347:
          return 0
      x = gram_index(ctx, t)
      k = int(ctx.floor(x))
      wpinitial = ctx.prec
      wpz, fp_tolerance = comp_fp_tolerance(ctx, k)
      ctx.prec = wpz
      a = ctx.siegelz(t)
      if k == -1 and a < 0:
          return 0
      elif k == -1 and a > 0:
          return 1
      if k + 2 < 400000000:
          Rblock = find_rosser_block_zero(ctx, k + 2)
      else:
          Rblock = search_supergood_block(ctx, k + 2, fp_tolerance)
      n1, n2 = Rblock[1]
      if n2 - n1 == 1:
          b = Rblock[3][0]
          if a * b > 0:
              ctx.prec = wpinitial
              return k + 1
          else:
              ctx.prec = wpinitial
              return k + 2
      my_zero_number, block, T, V = Rblock
      zero_number_block = n2 - n1
      T, V, separated = separate_zeros_in_block(
          ctx,
          zero_number_block,
          T,
          V,
          limitloop=ctx.inf,
          fp_tolerance=fp_tolerance,
      )
      n = count_to(ctx, t, T, V)
      ctx.prec = wpinitial
      return n + n1 + 1
  
file_path: catboost/contrib/python/mpmath/py3/mpmath/functions/zetazeros.py
imports: from .functions import defun, defun_wrapped
label_desc: Use image node_id 14 for calling a global function with example usage: nzeros(ctx, t) and returns: unknown, int, int, int, unknown, unknown