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If scalar numbers could be called "1D", then could these `a + bi` numbers be called "2D"? ie, an ordered pair? ie, a vector? IFF I'm understanding the above
by daveloyall 11y ago
If scalar numbers could be called "1D", then could these `a + bi` numbers be called "2D"? ie, an ordered pair? ie, a vector?
IFF I'm understanding the above correctly, I have a question: does encoding scheme described in this system let you add/subtract vectors using the fast integer hardware in CPUs?
- jsprogrammer 11y agoPerhaps the theoretical idea of an `a + bi` number could be called 2D. However, this particular implementation, anyway, only represents scalar values (every number is just a binary string).
- eximius 11y agoTraditionally, complex numbers are on a 2D plane, yes. However, this method uses a subset of complex numbers strung out linearly. Conceptually, the visualization of Cantor's diagonalization argument is similar.
- yoklov 11y agoVector operations are already possible in hardware using the fast, well, vector hardware in the cpu. And ime the speed up from using integers is minor and often not the cost from conversion (to e.g 28.4 fixed or similar), since you often need floats in the end.