26 Mar
2017
26 Mar
'17
2:03 p.m.
On 26/03/2017 17:43, Henry Baker wrote:
Basically, asinh numbers represent a real number x as the integer:
round(alpha*asinh(beta*x)) ... This means we can capture a brief segment of the integers within this representation, while also getting a logarithmic representation of numbers with very large absolute values.
In particular, if beta ~ 2^(-22) and we have a 32-bit asinh # representation, then all of the signed 16-bit integers are mapped 1-1, but the overall range is ~ +-10^228.
This has the drawback that essentially no integers other than 0 and +-1 are *exactly* represented, unless I'm missing something. I'm not sure how much that matters, but it would be quite a departure from conventional floating-point representations. -- g