import pandas as pd
from cStringIO import StringIO
import random
from decimal import Decimal
import numpy as np
import matplotlib.pyplot as plt

def xstrtod(s):
    return pd.read_csv(StringIO(s), header=None)[0][0]

def randnum():
    s = '0.'
    for i in range(20):
        s += random.choice('0123456789')
    return s

def ulp(s):
    num = Decimal(s)
    f = np.float64(s)
    a = f.view((np.uint8, 8))
    if Decimal(f) < num:
        a[0] += 1
    elif Decimal(f) > num:
        a[0] -= 1
    f2 = a.view(np.float64)[0]
    return abs(f2 - f)

y = []
good_vals = 0

for i in range(10000):
    val = randnum()
    guess = xstrtod(val)
    ulp_diff = abs(Decimal(val) - Decimal(guess)) / Decimal(ulp(val))
    y.append(float(ulp_diff))
    if float(ulp_diff) < 1.0:
        good_vals += 1

print('{0}% of values within 1.0 ULP'.format(good_vals * 100.0 / 10000))
plt.hist(y, bins=20)
plt.show()