python求pi的方法

#_*_ coding=utf-8 *_*
## {{{ http://code.activestate.com/recipes/578130/ (r5)
def pi(places=10):
 """Computes pi to given number of decimal places
 参数places表示要返回的pi的小数点后位数 
 方法：先整体扩大10**8（10的八次方）倍，然后计算完成后再缩小10的八次方倍
 """
 
 # 3 + 3*(1/24) + 3*(1/24)*(9/80) + 3*(1/24)*(9/80)*(25/168)
 # The numerators 1, 9, 25, ... are given by (2x + 1) ^ 2
 # The denominators 24, 80, 168 are given by (16x^2 -24x + 8)
 extra = 8
 one = 10 ** (places+extra)
 t, c, n, na, d, da = 3*one, 3*one, 1, 0, 0, 24
 #这里的n 和d 分别为每一项的分子与分母 ,na 和 da 分别为分子和分分母后一项比前一项增加的数值
 #这里的//可不是C++中的注释,而是除的意思
 while t > 1: 
 n, na, d, da = n+na, na+8, d+da, da+32
 t = t * n // d
 c += t
 return c // (10 ** extra)

def picirc(radius, aspect_ratio=5):
 """Display the digit of pi in a circle of given radius
 radius:显示的半径
 aspect_ratio：调节显示的比率参数
 """
 #display_width为各行的显示长度
 display_width = int(radius * aspect_ratio + 10)
 pi_str = repr(pi(int(2 * radius ** 2 * aspect_ratio)))
 pos = 0
 #cols为每一行中要显示的数字个数
 for i in range(2 * radius):
 cols = int(0.5 + aspect_ratio * (radius**2 - (radius-(i+0.5))**2) ** 0.5)
 print(pi_str[pos:pos+cols].center(display_width)) #将产生的pi数值生成的文本列表中相应的位数取出来显示在当前行
 pos += cols

if __name__ == '__main__':
 
 picirc(16)
## end of http://code.activestate.com/recipes/578130/ }}}

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