# 二分法の例
awk '
BEGIN {
  print find_zero(0, 3)
  exit 0
}
# 区間 a <= x <= b で測定値が 0 になる x を探す
function find_zero(a, b) {
  fa = meas(a)
  fb = meas(b)
  for (i = 0; i < 100; i++) {
	if ((b - a) / (a + b) < 5e-3)
		break
	c = (a + b) * 0.5
	fc = meas(c)
	if (fc * fa > 0.0) {
		a = c
		fa = c
	}
	else {
		b = c
		fb = fc
	}
  }
  if (i == 100)
	print "Retry over." >"/dev/stderr"
  return (a + b) * 0.5
}
# 変数 x に対する測定値
function meas(x) {
  return cos(x)
}
'