fastinvsqrt.vim

function! s:fastinvsqrt(x)
  let x = str2float(string(a:x))
  let s = x < 0
  if s
    let x = x * -1
  endif
  let exp = float2nr(log(x) / 0.6931471805599453 + 127.0)
  let frac = float2nr(x * pow(2, 150.0 - exp))
  let b = ''
  while frac > 0
    let b = (float2nr(frac) % 2) . b
    let frac = frac / 2
  endwhile
  let fb = b
  let b = ''
  while exp > 0
    let b = (float2nr(exp) % 2) . b
    let exp = exp / 2
  endwhile
  let eb = ("000000000" . b)[-8:]
  let fb .= repeat('0', 30-len(eb)-len(fb))
  let fb = fb[-23:]
  let fb = ((s ? '1' : '0') . eb) . fb
  let r = '0b' . fb + 0
  let r = 0x5f3759df - (r / 2)
  let b = ''
  while r > 0
    let b = (float2nr(r) % 2) . b
    let r = r / 2
  endwhile
  let b = repeat('0', 31-len(b)) . b
  let b = (r > 0 ? '1' : '0') . b
  let s = b[0]
  let exp = ('0b' . b[1:8]) - 127.0
  let frac = eval('0b' . b[9:])
  let y = eval('1.' . frac) * pow(2.0, exp)
  return y * (1.5 - 0.5 * x * y * y)
endfunction

echo s:fastinvsqrt(100)
echo s:fastinvsqrt(10)
echo s:fastinvsqrt(1)
echo s:fastinvsqrt(0.1)
echo s:fastinvsqrt(0.01)
echo s:fastinvsqrt(0.0025)