使用MicroPython计算任意位数圆周率

计算任意精度的圆周率是个有趣的主题，得益于python的强大计算能力，我们在MicroPython可以轻松的计算pi。
下面是一个使用MicroPython计算的程序。我们将它复制到STM32F7DISC中（STM32F7DISC已经下载了MicroPython固件，在其它系统中结果是一样的，只是计算速度有区别），然后测试一下计算速度。

"""
文件：pi.py
说明：用MicroPython计算任意精度圆周率计算
作者：未知
修改：邵子扬
"""
import time

def pi(places=10):
  # 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

  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 pi_t(n=10):
    t1=time.ticks_us()
    t=pi(n)
    t2=time.ticks_us()
    print('elapsed: ', time.ticks_diff(t2,t1)/1000000, 's')
    return t

def pi2(n=10):
    r=6*(10**n)*1000
    p=0
    k=0
    c=r//2
    d=c//(2*k+1)
    while d>0:
        p=p+d
        k=k+1
        k2=2*k
        c=c*(k2-1)//(4*k2)
        d=c//(k2+1)
    return p//1000

def pi2_t(n=10):
    t1=time.ticks_us()
    t=pi2(n)
    t2=time.ticks_us()
    print('elapsed: ', time.ticks_diff(t1,t2)/1000000, 's')
    return t

MicroPython v1.8 on 2016-05-15; F7DISC with STM32F746
Type “help()” for more information.
>>> import pi
>>> npi=pi.pi_t(1000)
elapsed: 0.221486 s
>>> npi=pi.pi_t(2000)
elapsed: 0.793141 s
>>> npi=pi.pi_t(5000)
elapsed: 4.981964 s
>>> npi=pi.pi_t(10000)
elapsed: 21.02012 s
>>>

从运行结果可以看出，虽然不是很快，但是考虑到STM32的资源和性能，结果已经出乎预料了，毕竟计算函数还不到10行代码，没有做深度优化。最后打印出1000位的圆周率，大家可以和标准结果比较看看。
>>> pi.pi(1000)
31415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989
>>>

via