============= Forewords =============
I investigated the numerical issues on my ARM build, and after much
poking around and searching, I found that I was chasing the dahu : the
tests were wrong, and the result were good.
Let's consider the numerical failures one by one :
============= 1/4 =============
File "/home/jpuydt/sage-4.8/devel/sage-main/sage/functions/other.py",
line 511:
sage: gamma1(float(6))
Expected:
120.0
Got:
119.99999999999997
Let's see how bad this is :
sage: res=gamma(float(6))
sage: res
119.99999999999997
sage: n(res,prec=57)
120.0000000000000
sage: n(res,prec=58)
119.99999999999997
============= 2/4 =============
File
"/home/jpuydt/sage-4.8/devel/sage-main/sage/symbolic/expression.pyx", line
6256:
sage: SR(10.0r).gamma()
Expected:
362880.0
Got:
362880.00000000047
Let's see how bad that is:
sage: res=SR(10.0r).gamma()
sage: res
362880.00000000047
sage: n(res,prec=54)
362880.000000000
sage: n(res,prec=55)
362880.0000000005
============= 3/4 =============
File
"/home/jpuydt/sage-4.8/devel/sage-main/sage/interfaces/maxima_abstract.py"
, line 1595:
sage: float(maxima("1.7e+17"))
Expected:
1.7e+17
Got:
1.6999999999999997e+17
Let's see how bad that is:
sage: res=float(maxima("1.7e17"))
sage: res
1.6999999999999997e+17
sage: n(res,prec=57)
1.700000000000000e17
sage: n(res,prec=58)
1.6999999999999997e17
============= 4/4 =============
File "/home/jpuydt/sage-4.8/devel/sage-main/sage/rings/arith.py", line 3061:
sage: binomial(0.5r, 5)
Expected:
0.02734375
Got:
0.02734375000000001
Let's see how bad that is:
sage: res=binomial(0.5r,5)
sage: res
0.02734375000000001
sage: n(res,prec=57)
0.02734375000000001
sage: n(res,prec=54)
0.0273437500000000
============= CONCLUSION =============
A double precision floating point number is supposed to have 53 digits,
according to the norm (http://en.wikipedia.org/wiki/IEEE_754-2008), and
the results are correct from that point of view.
So the tests should be modified not to depend on the specific
implementation : they're currently testing equality of floats!
I would provide a patch for the tests so they use n(..., prec=53), but
I'm hitting a problem in one of the cases ; see the mail I sent
yesterday for more about that.
Snark on #sagemath
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