Bugs item #1725899, was opened at 2007-05-25 19:52
Message generated for change (Comment added) made by facundobatista
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Category: Python Library
Group: Python 2.5
>Status: Closed
>Resolution: Fixed
Priority: 5
Private: No
Submitted By: Mark Dickinson (marketdickinson)
Assigned to: Facundo Batista (facundobatista)
Summary: decimal sqrt method doesn't use round-half-even
Initial Comment:
According to version 1.66 of Cowlishaw's `General Decimal Arithmetic
Specification' the square-root operation in the decimal module should
round using the round-half-even algorithm (regardless of the rounding
setting in the current context). It doesn't appear to do so:
>>> from decimal import *
>>> getcontext().prec = 6
>>> Decimal(9123455**2).sqrt()
Decimal("9.12345E+6")
The exact value of this square root is exactly halfway between two
representable Decimals, so using round-half-even with 6 digits I'd
expect the answer to be rounded to the neighboring representable
Decimal with *even* last digit---that is,
Decimal("9.12346E+6")
This bug only seems to occur when the number of significant digits in
the argument exceeds the current precision (indeed, if the number of
sig. digits in the argument is less than or equal to the current
precision then it's impossible for the square root to be halfway
between two representable floats).
It seems to me that this is a minor bug that will occur rarely and is
unlikely to have any serious effect even when it does occur; however,
it does seem to be a deviation from the specification.
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>Comment By: Facundo Batista (facundobatista)
Date: 2007-08-02 00:15
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Fixed in the revisions 56654 to 56656, in the decimal-branch, using
patches generated by Mark, thanks!
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Comment By: Mark Dickinson (marketdickinson)
Date: 2007-06-22 15:57
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See patch 1741308. I'll contact Mike Cowlishaw to verify that the
reference implementation really is buggy.
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Comment By: Tim Peters (tim_one)
Date: 2007-06-22 13:06
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Of course you're right, the spec does say inputs shouldn't be rounded.
And that last example is horrendous: sqrt should definitely be monotonic
(a floating function f is "monotonic" if it guarantees f(x) >= f(y)
whenever x >= y; you found x and y such that x > y but sqrt(x) < sqrt(y) --
ouch!).
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Comment By: Mark Dickinson (marketdickinson)
Date: 2007-06-22 03:35
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One more result. This is definitely getting suspicious now--I'll submit my
patch.
>>> from decimal import *
>>> getcontext().prec = 3
>>> Decimal(11772).sqrt()
Decimal("109")
>>> Decimal(11774).sqrt()
Decimal("108")
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Comment By: Mark Dickinson (marketdickinson)
Date: 2007-06-22 03:16
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Some more strange results for sqrt(): with Emax = 9, Emin = -9 and prec =
3:
1. In the following, should the Subnormal and Underflow flags be set? The
result before rounding is subnormal, even though the post-rounding result
is not, and the spec seems to say that those flags should be set in this
situation. But Cowlishaw's reference implementation (version 3.50) doesn't
set these flags. (If 9.998 is replaced by 9.99 then the flags *are* set,
which seems inconsistent.)
>>> Decimal("9.998E-19").sqrt()
Decimal("1.00E-9")
>>> getcontext()
Context(prec=3, rounding=ROUND_HALF_EVEN, Emin=-9, Emax=9, capitals=1,
flags=[Rounded, Inexact], traps=[DivisionByZero, Overflow,
InvalidOperation])
2. As I understand the spec, the following result is incorrect:
>>> Decimal("1.12E-19").sqrt()
Decimal("3.4E-10")
(The true value of the square root is 3.34664...e-10, which should surely
be rounded to 3.3E-10, not 3.4E-10?).
But again, Cowlishaw's reference implementation also gives 3.4E-10.
3. Similarly for the following
>>> Decimal("4.21E-20").sqrt()
Decimal("2.0E-10")
The answer should, I think, be 2.1E-10; here the reference implementation
also gives 2.1E-10.
4. And I can't justify this one at all...
>>> Decimal("1.01001").sqrt()
Decimal("1.01")
Shouldn't this be 1.00? But again Python agrees with the reference
implementation.
Either all this is pretty mixed up, or I'm fundamentally misunderstanding
things. I have a patch that I think fixes all these bugs; if there's any
agreement that they really are bugs then I'll post it. Can anyone shed any
light on the above results?
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Comment By: Mark Dickinson (marketdickinson)
Date: 2007-05-25 20:30
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I don't think inputs should be rounded; note 1 near the start of the
`Arithmetic Operations' section of the specification says:
"Operands may have more than precision digits and are not rounded before
use."
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Comment By: Tim Peters (tim_one)
Date: 2007-05-25 20:24
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Doesn't the spec also require that /inputs/ get rounded to working
precision /before/ operations are performed? If so, the exact square
83237431137025 is rounded down to 83237400000000, and sqrt(83237400000000)
is 9.12345E+6 rounded to 6 digits.
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