[Maxima] bfloat on symbolic expressions
macrakis at alum.mit.edu
Tue Jan 16 17:15:09 CST 2007
Michel and I have discussed the interaction of bfloat and Levin
offline, and one of the issues seems to be this:
If you use bfloat on a symbolic expression, it normally converts all
included numbers into bfloats, e.g.
bfloat(9*(x-2/3)*(x+2/3)) => 9.0b0 (x - 6.6667b-1) (x + 6.6667b-1)
bfloat(3.4*x) => 3.4b0*x
bfloat(sin(x+%pi*6/7)) => sin(x + 2.6928b0)
But exponents are protected from this if the base is not a number:
bfloat(2^(x+2/3)) => 2.0b0^(x+6.6666667b-1)
bfloat(q^(x+2/3)) => q^(x+2/3)
bfloat(q^2.3) => q^2.3
This is presumably to avoid things like
bfloat(x^-1) => x^-1.0b0 (not current behavior)
bfloat(sqrt(x)) => x^0.5b0 (not current behavior)
But it seems as though it would be better to continue to convert all
*approximate* numbers (not integers and rationals) in the exponent
since they contain an implicit precision.
By the way, the behavior of 'float' is not entirely consistent with
that of bfloat in cases like this....
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