[Tutor] Associate decimal values with an integer range

[Oscar Benjamin]

On 29 April 2013 22:03, eryksun <eryksun at gmail.com> wrote:
> On Mon, Apr 29, 2013 at 12:16 PM, Alan Gauld <alan.gauld at btinternet.com> wrote:
>>> I have to interpret a one-byte floating point number
>>
>> I'm curious, what does a one byte floating point number look like?
>> I've never come across such a beast, the smallest FP representation I've
>> come across is 16 bits or two bytes. But that wasn't in Python...
>
> For a maximum value of 240.0, an 8-bit floating point (as opposed to
> fixed point) format could use 1 sign bit, 4 exponent bits, and 3
> significand bits (plus 1 implicit bit). Emax is 7, so the maximum
> positive normal would be (2 - 2**-3) * 2**7 == 240.0. Emin is -6, so
> the minimum positive normal would be 2**-6. There's approximately 1
> decimal digit of precision, i.e. floor(log10(2**4)).
>
> There are 224 normal values in the range [-240.0, 240.0]. Of those, 96
> have a magnitude less than 1.0, and 128 have a magnitude in the range
> [1.0, 240.0]. There's also +/- zero, +/- infinity, 14 subnormal
> values, and 14 NaN (quiet and signaling) values:
>
>       +0: 0 0000 000
>       -0: 1 0000 000
>     +inf: 0 1111 000
>     -inf: 1 1111 000
>      sub: x 0000 non-zero
>      nan: x 1111 non-zero

Brilliant. I thought you were just making this up but here
http://mrob.com/pub/math/floatformats.html
I find that 8 bit floating point with values up to 240 is listed as a
floating point format. The link describes it as "Used in university
courses" so I guess it's not intended to be a practical format.


Oscar