[Edu-sig] More re: Advanced or beginner?

[Tim Peters]

[Kirby Urner]
> ...
> Question:
>
> Why does float -> long work like this:
>
>     >>> long(1.0826786300000142e+045)
>     1082678630000014218353234260713996413124476928L
>
> and not like this?
>
>     >>> long(1.0826786300000142e+045)
>     1082678630000014200000000000000000000000000000L
>
> Kirby

Because your machine floating-point isn't decimal, it's binary:

>>> x = 2.**100
>>> print x
1.26765060023e+030
>>> print long(x)
1267650600228229401496703205376
>>> print 2L ** 100
1267650600228229401496703205376
>>>

So making long(2.**100)

1267650600230000000000000000000L

instead would be plain wrong.  The same thing happens in your example, but
is harder to picture because, offhand, I bet you don't know the exact
IEEE-754 bit pattern corresponding to 1.0826786300000142e+045 <wink>.

>>> x = 1.0826786300000142e+045
>>> import math
>>> mantissa, exponent = math.frexp(x)
>>> print mantissa
0.758577950788
>>> print exponent
150
>>> print math.ldexp(mantissa, 53)
6.832662753e+015
>>> mantissa_as_long = long(math.ldexp(mantissa, 53))
>>> mantissa_as_long
6832662753002049L
>>> print mantissa_as_long << (exponent-53)
1082678630000014218353234260713996413124476928
>>> print long(x)
1082678630000014218353234260713996413124476928
>>>

IOW, long(some_huge_integer_in_float_format) *does* have a large number of
trailing zeroes, but in base 2, not necessarily in base 10.

>>> print hex(long(x))
0x308C8A88868482000000000000000000000000L
>>>