Re:Why does e to pi i equal -1? (2015) [video]
by dnautics on Monday February 13, 2017 @05:31PM
(#13639425)
I wouldn't screw around too much with the sign bit. The way it's laid out is really kind of cool... Negation is simple two's complement.
In my software posit library (which is intentionally strictly binary and not backended by IEEE floats), (https://github.com/interplanetary-robot/SigmoidNumbers) I did everything by first inverting negative numbers and doing decode in the positive domain.
As I design the hardware, it's actually better to NOT do a two's complement inversion to do the decode, and keep the fraction as two's complement!
Also the 4 bit posit was just a simplification to help you understand the structure from a constructive point of view. posits can be of arbitrary length; they have a property I call isomorphic - so appending zeros exactly preserves the value of a short posit when increased in length; conversely, rounding a long posit to a shorter one reports the "nearest representable value".
In my software posit library (which is intentionally strictly binary and not backended by IEEE floats), (https://github.com/interplanetary-robot/SigmoidNumbers) I did everything by first inverting negative numbers and doing decode in the positive domain.
As I design the hardware, it's actually better to NOT do a two's complement inversion to do the decode, and keep the fraction as two's complement!
Also the 4 bit posit was just a simplification to help you understand the structure from a constructive point of view. posits can be of arbitrary length; they have a property I call isomorphic - so appending zeros exactly preserves the value of a short posit when increased in length; conversely, rounding a long posit to a shorter one reports the "nearest representable value".