tensorflow_privacy/privacy/analysis/rdp_accountant.py [99:155]:
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def _log_comb(n, k):
  return (special.gammaln(n + 1) - special.gammaln(k + 1) -
          special.gammaln(n - k + 1))


def _compute_log_a_int(q, sigma, alpha):
  """Compute log(A_alpha) for integer alpha. 0 < q < 1."""
  assert isinstance(alpha, int)

  # Initialize with 0 in the log space.
  log_a = -np.inf

  for i in range(alpha + 1):
    log_coef_i = (
        _log_comb(alpha, i) + i * math.log(q) + (alpha - i) * math.log(1 - q))

    s = log_coef_i + (i * i - i) / (2 * (sigma**2))
    log_a = _log_add(log_a, s)

  return float(log_a)


def _compute_log_a_frac(q, sigma, alpha):
  """Compute log(A_alpha) for fractional alpha. 0 < q < 1."""
  # The two parts of A_alpha, integrals over (-inf,z0] and [z0, +inf), are
  # initialized to 0 in the log space:
  log_a0, log_a1 = -np.inf, -np.inf
  i = 0

  z0 = sigma**2 * math.log(1 / q - 1) + .5

  while True:  # do ... until loop
    coef = special.binom(alpha, i)
    log_coef = math.log(abs(coef))
    j = alpha - i

    log_t0 = log_coef + i * math.log(q) + j * math.log(1 - q)
    log_t1 = log_coef + j * math.log(q) + i * math.log(1 - q)

    log_e0 = math.log(.5) + _log_erfc((i - z0) / (math.sqrt(2) * sigma))
    log_e1 = math.log(.5) + _log_erfc((z0 - j) / (math.sqrt(2) * sigma))

    log_s0 = log_t0 + (i * i - i) / (2 * (sigma**2)) + log_e0
    log_s1 = log_t1 + (j * j - j) / (2 * (sigma**2)) + log_e1

    if coef > 0:
      log_a0 = _log_add(log_a0, log_s0)
      log_a1 = _log_add(log_a1, log_s1)
    else:
      log_a0 = _log_sub(log_a0, log_s0)
      log_a1 = _log_sub(log_a1, log_s1)

    i += 1
    if max(log_s0, log_s1) < -30:
      break

  return _log_add(log_a0, log_a1)
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tensorflow_privacy/privacy/analysis/rdp_privacy_accountant.py [69:126]:
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def _log_comb(n, k):
  """Computes log of binomial coefficient."""
  return (special.gammaln(n + 1) - special.gammaln(k + 1) -
          special.gammaln(n - k + 1))


def _compute_log_a_int(q, sigma, alpha):
  """Computes log(A_alpha) for integer alpha, 0 < q < 1."""
  assert isinstance(alpha, int)

  # Initialize with 0 in the log space.
  log_a = -np.inf

  for i in range(alpha + 1):
    log_coef_i = (
        _log_comb(alpha, i) + i * math.log(q) + (alpha - i) * math.log(1 - q))

    s = log_coef_i + (i * i - i) / (2 * (sigma**2))
    log_a = _log_add(log_a, s)

  return float(log_a)


def _compute_log_a_frac(q, sigma, alpha):
  """Computes log(A_alpha) for fractional alpha, 0 < q < 1."""
  # The two parts of A_alpha, integrals over (-inf,z0] and [z0, +inf), are
  # initialized to 0 in the log space:
  log_a0, log_a1 = -np.inf, -np.inf
  i = 0

  z0 = sigma**2 * math.log(1 / q - 1) + .5

  while True:  # do ... until loop
    coef = special.binom(alpha, i)
    log_coef = math.log(abs(coef))
    j = alpha - i

    log_t0 = log_coef + i * math.log(q) + j * math.log(1 - q)
    log_t1 = log_coef + j * math.log(q) + i * math.log(1 - q)

    log_e0 = math.log(.5) + _log_erfc((i - z0) / (math.sqrt(2) * sigma))
    log_e1 = math.log(.5) + _log_erfc((z0 - j) / (math.sqrt(2) * sigma))

    log_s0 = log_t0 + (i * i - i) / (2 * (sigma**2)) + log_e0
    log_s1 = log_t1 + (j * j - j) / (2 * (sigma**2)) + log_e1

    if coef > 0:
      log_a0 = _log_add(log_a0, log_s0)
      log_a1 = _log_add(log_a1, log_s1)
    else:
      log_a0 = _log_sub(log_a0, log_s0)
      log_a1 = _log_sub(log_a1, log_s1)

    i += 1
    if max(log_s0, log_s1) < -30:
      break

  return _log_add(log_a0, log_a1)
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