Tuesday, September 30, 2008
"Frequently Forgotten Fundamental Facts about Software Engineering"
This has good rules of thumb about software production.
Thursday, September 25, 2008
Tuesday, September 23, 2008
Python Fractions issue.
There
seems to be a problem/difference in calculating with the new fractions
module when comparing Python 26rc2 and 30rc1
I was
reading the paper " href="http://conference.scipy.org/proceedings/SciPy2008/paper_3/full_text.pdf">Interval
Arithmetic: Python Implementation and Applications" and
thought to try the first example function f(x,y), which needs more
precision than Python floating point provides (on my Windows PC), to
calculate a sensible answer.
Ahah, I thought, lets
try this with Fractions - so I first installed Python 30rc1, typed in
the Function - saw the rubbish result, then used Fractions and got the
'right' result.
I then wondered if fractions had been
back-ported to Python 2.6rc2, found that it had, but got different
results.
As you can see from the table, Python
2.6rc2 has a problem calculating t3 = F(11,2) * y**8 + x/(2*y), where F
is Fraction.
I wonder where the problem
lies?
style="text-align: left; margin-left: auto; margin-right: auto; font-family: monospace;"
border="4" cellpadding="2" cellspacing="2"> style="white-space: nowrap; text-align: left; vertical-align: top;">Python
3.0rc1 (r30rc1:66507, Sep 18 2008, 14:47:08) [MSC v.1500 32 bit (Intel)]
on
win32
Type "help", "copyright", "credits" or "license" for
more information.
>>> from fractions
import Fraction as F
>>>
def f(x,y):
... return
(
...
(333.75 - x**2)* y**6 + x**2 *
...
(11* x**2 * y**2 - 121 * y**4 - 2)
...
+ 5.5 * y**8 + x/(2*y))
...
>>>
f(77617.0, 33096.0)
1.1726039400531787
>>>
def f2(x,y):
...
return (
...
(333 + F(3,4) - x**2)* y**6 + x**2 *
...
(11* x**2 * y**2 - 121 * y**4 - 2)
...
+ F(11,2) * y**8 + x/(2*y))
...
>>>
f2(77617.0, 33096.0)
1.1726039400531787
>>>
f2(77617, 33096)
-0.82739605994682131
>>>
x,y = 77617, 33096
>>> t1 = (333 + F(3,4)
- x**2)* y**6 + x**2
>>> t1
Fraction(-7917110903377385049079188231255750815,
1)
>>> t2 = (11* x**2 * y**2 - 121 * y**4
- 2)
>>> t2
-72586759091903445314
>>>
t3 = F(11,2) * y**8 + x/(2*y)
>>> t3
7.9171113406689609e+36
>>> style="white-space: nowrap; text-align: left; vertical-align: top; width: 50%;">Python
2.6rc2 (r26rc2:66507, Sep 18 2008, 14:27:33) [MSC v.1500 32 bit
(Intel)] on win32
Type "copyright", "credits" or "license()"
for more information.
IDLE
2.6rc2
>>>
from fractions import Fraction as F
>>>
def f(x,y):
return (
(333.75 - x**2)* y**6 + x**2 *
(11* x**2 * y**2 - 121 * y**4 - 2)
+ 5.5 * y**8 + x/(2*y))
>>>
f(77617.0, 33096.0)
1.1726039400531787
>>>
def f2(x,y):
return (
(333 + F(3,4) - x**2)* y**6 + x**2 *
(11* x**2 * y**2 - 121 * y**4 - 2)
+ F(11,2) * y**8 + x/(2*y))
>>>
f2(77617.0, 33096.0)
1.1726039400531787
>>>
f2(77617, 33096)
style="background-color: rgb(255, 102, 102); font-weight: bold;">Fraction(-1,
1)
>>> x,y = 77617, 33096
>>>
t1 = (333 + F(3,4) - x**2)* y**6 + x**2
>>>
t1
Fraction(-7917110903377385049079188231255750815, 1)
>>>
t2 = (11* x**2 * y**2 - 121 * y**4 - 2)
>>>
t2
-72586759091903445314L
>>> t3
= F(11,2) * y**8 + x/(2*y)
>>> t3
style="background-color: rgb(255, 102, 102); font-weight: bold;">Fraction(7917111340668961361101134701524942849,
1)
>>>
seems to be a problem/difference in calculating with the new fractions
module when comparing Python 26rc2 and 30rc1
I was
reading the paper " href="http://conference.scipy.org/proceedings/SciPy2008/paper_3/full_text.pdf">Interval
Arithmetic: Python Implementation and Applications" and
thought to try the first example function f(x,y), which needs more
precision than Python floating point provides (on my Windows PC), to
calculate a sensible answer.
Ahah, I thought, lets
try this with Fractions - so I first installed Python 30rc1, typed in
the Function - saw the rubbish result, then used Fractions and got the
'right' result.
I then wondered if fractions had been
back-ported to Python 2.6rc2, found that it had, but got different
results.
As you can see from the table, Python
2.6rc2 has a problem calculating t3 = F(11,2) * y**8 + x/(2*y), where F
is Fraction.
I wonder where the problem
lies?
border="4" cellpadding="2" cellspacing="2">
3.0rc1 (r30rc1:66507, Sep 18 2008, 14:47:08) [MSC v.1500 32 bit (Intel)]
on
win32
Type "help", "copyright", "credits" or "license" for
more information.
>>> from fractions
import Fraction as F
>>>
def f(x,y):
... return
(
...
(333.75 - x**2)* y**6 + x**2 *
...
(11* x**2 * y**2 - 121 * y**4 - 2)
...
+ 5.5 * y**8 + x/(2*y))
...
>>>
f(77617.0, 33096.0)
1.1726039400531787
>>>
def f2(x,y):
...
return (
...
(333 + F(3,4) - x**2)* y**6 + x**2 *
...
(11* x**2 * y**2 - 121 * y**4 - 2)
...
+ F(11,2) * y**8 + x/(2*y))
...
>>>
f2(77617.0, 33096.0)
1.1726039400531787
>>>
f2(77617, 33096)
-0.82739605994682131
>>>
x,y = 77617, 33096
>>> t1 = (333 + F(3,4)
- x**2)* y**6 + x**2
>>> t1
Fraction(-7917110903377385049079188231255750815,
1)
>>> t2 = (11* x**2 * y**2 - 121 * y**4
- 2)
>>> t2
-72586759091903445314
>>>
t3 = F(11,2) * y**8 + x/(2*y)
>>> t3
7.9171113406689609e+36
>>>
2.6rc2 (r26rc2:66507, Sep 18 2008, 14:27:33) [MSC v.1500 32 bit
(Intel)] on win32
Type "copyright", "credits" or "license()"
for more information.
IDLE
2.6rc2
>>>
from fractions import Fraction as F
>>>
def f(x,y):
return (
(333.75 - x**2)* y**6 + x**2 *
(11* x**2 * y**2 - 121 * y**4 - 2)
+ 5.5 * y**8 + x/(2*y))
>>>
f(77617.0, 33096.0)
1.1726039400531787
>>>
def f2(x,y):
return (
(333 + F(3,4) - x**2)* y**6 + x**2 *
(11* x**2 * y**2 - 121 * y**4 - 2)
+ F(11,2) * y**8 + x/(2*y))
>>>
f2(77617.0, 33096.0)
1.1726039400531787
>>>
f2(77617, 33096)
style="background-color: rgb(255, 102, 102); font-weight: bold;">Fraction(-1,
1)
>>> x,y = 77617, 33096
>>>
t1 = (333 + F(3,4) - x**2)* y**6 + x**2
>>>
t1
Fraction(-7917110903377385049079188231255750815, 1)
>>>
t2 = (11* x**2 * y**2 - 121 * y**4 - 2)
>>>
t2
-72586759091903445314L
>>> t3
= F(11,2) * y**8 + x/(2*y)
>>> t3
style="background-color: rgb(255, 102, 102); font-weight: bold;">Fraction(7917111340668961361101134701524942849,
1)
>>>