include Math

# 2を底にした対数を取り切り捨てる
def log2(x)
  (log(x)/log(2)).floor
end

# 16ビットの浮動小数点形式への変換
# 大きさ3の配列で
# [符号(0: 正, 1: 負), 指数部(0-63), 仮数部(0-1023)]
# 指数部が63の時はNaN(Not a Number 表現できる範囲外の数)
# 指数部が0の時は0
def toFloat16(f)
  if f<0
    sign=1
    f=-f;
  else
    sign=0
  end
  if f==0
    [0,0,0]
  else
    exp=log2(f)
    if(exp+31<=0)
      [sign,0,0]
    elsif(exp+31>=63)
      [sign,63,0]
    else
      f=f/2**exp
      [sign,exp+31,(f* 2**10).floor-1024]
    end
  end
end
# NaNに対応する定数
NAN=0.0/0.0
# 16ビットの浮動小数点形式からの変換
def fromFloat16(x)
  if(x[1]==0)
    (1-2*x[0])*0.0
  elsif(x[1]==63)
    NAN
  else
    (1-2*x[0])* 2.0**(x[1]-31) * (x[2]+1024) * 2.0**-10
  end
end
# Float16同士の加算
def add(x,y)
  toFloat16(fromFloat16(x)+fromFloat16(y))
end
# Float16同士の減算
def sub(x,y)
  toFloat16(fromFloat16(x)-fromFloat16(y))
end
# Float16同士の積算
def mul(x,y)
  toFloat16(fromFloat16(x)*fromFloat16(y))
end
# Float16同士の除算
def div(x,y)
  toFloat16(fromFloat16(x)/fromFloat16(y))
end