Many thanks to John and Raul,
for simplicity I can summarise that
smallest is 2^_1074
just <1 is 0.9999999999999999 (which =(!.0) 0.99999999999999988898)
it only remains that the largest number needs a more complicated calculation.
John Randall wrote:
Raul Miller wrote:
On 4/10/07, John Randall <[EMAIL PROTECTED]> wrote:
NB. smallest positive
value 1 1 0
2.22507e_308
You did not consider denormalized numbers
_2{-:^:a: 1
4.94066e_324
You're right: my value function assumes normalization.
NB. largest positive
value 1,2046,#. 52#1
1.79769e308
That's what I got, too.
NB. largest less than 1
0j20": value 1 1022,#. 52#1
0.99999999999999988898
I got a different answer
0j20":_2{unq]1--:^:a: 1
0.99999999999999989000
But when I execute your expression I get yet another answer:
value 1 1022,#. 52#1
0.5
This is a difference between 32-bit and 64-bit J: #. 52 #1 is a valid
64-bit integer but not a valid 32-bit integer. The result I quoted was
done with J64: I get the same incorrect value in J32.
What I am trying to get at is the binary fraction .1111....1111 where
there are 53 1's. Unless I am misunderstanding the IEEE 754 standard,
this is the largest double not greater than 1.
Doing calculations rather than working with bit patterns may introduce
roundoff error. I was too lazy to manipulate the bits directly.
Best wishes,
John
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regards,
bill
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