与えられた小数に近い整数比を生成するジェネレータ ref: http://qiita.com/unau/items/46a98043557729db45be

file1.txt

>>> import rasi
>>> for i in rasi.rasi(0.315): print "%d/%d = %g : %g" % i
... 
1/1 = 1 : 0.685
1/2 = 0.5 : 0.185
1/3 = 0.333333 : 0.0183333
3/10 = 0.3 : 0.015
4/13 = 0.307692 : 0.00730769
5/16 = 0.3125 : 0.0025
6/19 = 0.315789 : 0.000789474
11/35 = 0.314286 : 0.000714286
17/54 = 0.314815 : 0.000185185
23/73 = 0.315068 : 6.84932e-05
40/127 = 0.314961 : 3.93701e-05
63/200 = 0.315 : 0

file2.txt

>>> for i in rasi.rasi(math.pi): print "%d/%d = %g : %g" % i
... 
1/1 = 1 : 2.14159
2/1 = 2 : 1.14159
3/1 = 3 : 0.141593
13/4 = 3.25 : 0.108407
16/5 = 3.2 : 0.0584073
19/6 = 3.16667 : 0.025074
22/7 = 3.14286 : 0.00126449
179/57 = 3.14035 : 0.00124178
201/64 = 3.14062 : 0.000967654
223/71 = 3.14085 : 0.000747583
245/78 = 3.14103 : 0.000567013
267/85 = 3.14118 : 0.000416183
289/92 = 3.1413 : 0.000288306
311/99 = 3.14141 : 0.000178512
333/106 = 3.14151 : 8.32196e-05
355/113 = 3.14159 : 2.66764e-07
52163/16604 = 3.14159 : 2.66213e-07
...

rasi.py

def rasi(target):
    a, b = 1, 1
    min_error = -1
    while True:
        ratio = float(b) / a
        diff = target - ratio
        error = abs(diff)
        if min_error < 0 or min_error > error:
            min_error = error
            yield (b, a, ratio, error)
            if error == 0:
                return
        if diff > 0:
            b += 1
        else:
            a += 1