Why does e to pi i equal -1? (2015) [video]

Re:Why does e to pi i equal -1? (2015) [video] by taw1 on Monday February 13, 2017 @08:02AM (#13634903)

Posits look too good to be true! Is there a reason why regime bits do not include the sign bit? Then both "0 0001" and "1 1110" could be interpreted as 4 regime bits. Even better we could include the last flipped bit as well and we would have 5 bits.

Edit: Well. I see it would result in losing the values 0 and 1. Another question: Since it is fixed length of 4 bits (for N=32) why don't we just extract the 4 bit value, then we could represent 2^4 regimes this time without losing 0 and 1.

[ Parent | on HN ]

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".

[ Parent | on HN ]

Re:Why does e to pi i equal -1? (2015) [video] by jacobolus on Monday February 13, 2017 @10:06AM (#13635730)

You need to be a lot more explicit about what you’re asking. Look at the slides, searching down for “At nbits = 5, fraction bits appear”. Notice that every possible bit pattern is used and meaningful.

http://web.stanford.edu/class/ee380/Abstracts/170201-slides....

[ Parent | on HN ]