Issue 247 in mpmath: Trig and equality

[mpm...@googlecode.com]

Status: New
Owner: ----

New issue 247 by GavinBra...@gmail.com: Trig and equality
http://code.google.com/p/mpmath/issues/detail?id=247

What steps will reproduce the problem?
I'm running this:

import unittest
from mpmath import *

class Test(unittest.TestCase):

def testBasicMaths(self):
assert (sqrt(3) * sin(acos(1/sqrt(3))) * sin(pi/4)).ae('1')
print( sqrt(3) * sin(acos(1/sqrt(3))) * sin(pi/4))
assert sqrt(3) * sin(acos(1/sqrt(3))) * sin(pi/4) == 1.0

if __name__ == "__main__":
#import sys;sys.argv = ['', 'Test.testName']
unittest.main()

What is the expected output? What do you see instead?
I expect this:
Finding files... done.
Importing test modules ... done.

1.0
----------------------------------------------------------------------
Ran 1 test in 0.000s

OK

I get this:
Finding files... done.
Importing test modules ... done.

1.0
======================================================================
FAIL: testBasicMaths (Coordinates.Test1.Test)
----------------------------------------------------------------------
Traceback (most recent call last):
File "H:\git\StarClash\Space Clash - Client\src\Coordinates\Test1.py",
line 14, in testBasicMaths
assert sqrt(3) * sin(acos(1/sqrt(3))) * sin(pi/4) == 1.0
AssertionError

----------------------------------------------------------------------
Ran 1 test in 0.010s

FAILED (failures=1)

For some reason 1.0 even though its very very close to 1, its just not
quite close enough to give not fail the test.

What version of the product are you using? On what operating system?
0.18 on Python 3.3 on Windows 7

Please provide any additional information below.



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[mpm...@googlecode.com]

Comment #1 on issue 247 by GavinBra...@gmail.com: Trig and equality
http://code.google.com/p/mpmath/issues/detail?id=247

One thing, if I set mp.dps=156 then it starts working (although 156 decimal
places seems a little over the top).

[mpm...@googlecode.com]

Comment #2 on issue 247 by fredrik....@gmail.com: Trig and equality
http://code.google.com/p/mpmath/issues/detail?id=247

This is not a bug. You can generally only expect the result of a
floating-point calculation to be an approximation of the mathematically
exact result, and the print function deliberately discards a couple of
digits to hide the effects of small rounding errors (just as it does for
Python's built-in floats). To see that the number is different from 1.0,
use repr() instead:

>>> repr(sqrt(3) * sin(acos(1/sqrt(3))) * sin(pi/4))
"mpf('0.99999999999999978')"

[mpm...@googlecode.com]

Comment #3 on issue 247 by GavinBra...@gmail.com: Trig and equality
http://code.google.com/p/mpmath/issues/detail?id=247

Yeah, that's also what I had worked out - I'd read about repr, but
forgotten about it.

Weirdly, this calculation appears to be dependent on the precision as to
whether it equates to 1, or very very nearly 1 (but not quite).

For example, I've found that setting mp.dps=8 make this work.
A higher level of precision changes it into 0.999<other bits>
Then it turns back into 1.0 at mp.dps=156

I guess I'll have to choose a level of precision I am happy with, and
potentially use the ae functionality for checks rather than

[mpm...@googlecode.com]

Comment #4 on issue 247 by fredrik....@gmail.com: Trig and equality
http://code.google.com/p/mpmath/issues/detail?id=247

The result will be a pseudorandom number close to 1. So by random chance,
it will be slightly smaller than 1 at some precisions, slightly larger than
1 at some precisions, and exactly equal to 1 at some precisions. Choosing a
precision where it just happens to work is not a reliable solution. The
correct solution is to check that the result is close to 1 (for example
using ae()).

[mpm...@googlecode.com]

Comment #5 on issue 247 by GavinBra...@gmail.com: Trig and equality
http://code.google.com/p/mpmath/issues/detail?id=247

OK, I accept that.
Can you close the ticket please?

[mpm...@googlecode.com]

Updates:
Status: Invalid

Comment #6 on issue 247 by fredrik....@gmail.com: Trig and equality
http://code.google.com/p/mpmath/issues/detail?id=247

Sure. Thanks for the feedback.