In [1]:
import pandas as pd
from cStringIO import StringIO
import random
from decimal import Decimal
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
In [2]:
def xstrtod(s):
return pd.read_csv(StringIO(s), header=None)[0][0]
In [3]:
def randnum(length):
s = '1.'
for i in range(length):
s += random.choice('0123456789')
return s
In [4]:
def ulp(s):
num = Decimal(s)
f = np.float64(s)
a = f.view((np.uint8, 8))
# Since this is uint8 make sure the result doesn't accidentally wrap
if a[0] == 0:
a[0] = 1
elif a[0] == 255:
a[0] = 254
elif Decimal(f) < num:
a[0] += 1
elif Decimal(f) > num:
a[0] -= 1
f2 = a.view(np.float64)[0]
return abs(f2 - f)
In [5]:
def test_conversion(sig_figs):
y = []
diffs = []
great_vals = 0
good_vals = 0
for i in range(1000):
val = randnum(sig_figs)
guess = xstrtod(val)
decimal_diff = abs(Decimal(val) - Decimal(guess))
ulp_diff = decimal_diff / Decimal(ulp(val))
y.append(float(ulp_diff))
diffs.append(float(decimal_diff))
if float(ulp_diff) < 1.0:
good_vals += 1
if float(ulp_diff) < 0.5:
great_vals += 1
return (great_vals, good_vals, y, diffs)
In [6]:
def graph_results(sig_figs):
great_vals, good_vals, y, diffs = test_conversion(sig_figs)
print('{0}% of values within 0.5 ULP'.format(great_vals * 100.0 / 1000))
print('{0}% of values within 1.0 ULP'.format(good_vals * 100.0 / 1000))
plt.hist(y, bins=30, log=True)
plt.xlabel('Conversion error in ULP')
plt.ylabel('Logarithm of frequency')
plt.show()
plt.hist(diffs, bins=50, log=True)
plt.xlabel('Decimal conversion error')
plt.ylabel('Logarithm of frequency')
plt.show()
In [7]:
graph_results(5)
In [8]:
graph_results(10)
In [9]:
graph_results(15)
In [10]:
graph_results(20)
In [11]:
graph_results(45)
In [12]:
graph_results(100)