This is unfortunate:
sage: R256=RealField(256)
sage: R256('1.2')
1.200000000000000000000000000000000000000000000000000000000000000000000000000
sage: R256(1.2)
1.199999999999999955591079014993738383054733276367187500000000000000000000000
It's easy to see why this happens: the last input line preparses to
"R256(RealNumber('1.2'))", so the literal 1.2 gets first made into a
real number with default (53-bit) precision:
sage: RealNumber('1.2')
1.20000000000000
and that is then pushed into R256. Since 1.2 does not have a finite
binary expansion (it has 0011 recurring after the point) this makes a
difference: R256('1.2') is as accurate as possible (64 repeating
blocks of 0011 in the mantissa, or something close to that) while
R256(1.2) gets the first 53 bits right and then fills with 0s.
I'm not saying this is a bug; though if there was a way to get the
preparser to do the sensible thing with R256(1.2) that would be great.
But users need to be aware. (The same thing used to happen to me a
lot with C++ programming).
John
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