[math-fun] The end of the 32-bit computer?
Google's decision to end support for its browsers on 32-bit computers signals the end for 32-bit computers in general. If you can't run a browser, then you can't be a full-fledged computer in the 21st century. Most *serious* computer people have always considered 32 bits to be too small, and therefore a 32-bit computer was always a *mini* computer (at least DEC got this part right). Von Neumann's 1944 EDVAC computer had *44 bit* words, and was therefore a *real* computer: https://en.wikipedia.org/wiki/EDVAC At least 32-1=31 is prime; 64-1=63=3^2*7. 128-1=127 is again prime. But 257=2^8+1 is prime -- the next such after 17=2^4+1. --- Google to end updates, security bug fixes for Chrome on 32-bit Linux http://www.theregister.co.uk/2015/12/02/googles_chrome_32bit_linux/
Reasons I care about having 64-bits: - Broader range of unboxed immediate types in Lisp (even if our fixnums aren't a full 64-bits... though boxed IEEE-754 double floats is really annoying) - Easier to find large, sensible moduli for things like number theoretic transforms (e.g., ;; > (print-suitable-moduli (expt 2 53) 15);; [58,3] 180143985094819841 = 1 + 2^55 * 5;; [59,6] 459367161991790593 = 1 + 2^53 * 3 * 17;; [60,7] 855683929200394241 = 1 + 2^53 * 5 * 19;; [60,6] 882705526964617217 = 1 + 2^54 * 7^2;; [60,7] 891712726219358209 = 1 + 2^53 * 3^2 * 11;; [61,6] 1261007895663738881 = 1 + 2^55 * 5 * 7;; [61,8] 1288029493427961857 = 1 + 2^53 * 11 * 13;; [61,8] 1450159080013299713 = 1 + 2^53 * 7 * 23;; [61,5] 1945555039024054273 = 1 + 2^56 * 3^3;; [61,6] 2053641430080946177 = 1 + 2^55 * 3 * 19;; [61,8] 2098677426354651137 = 1 + 2^53 * 233;; [61,7] 2287828610704211969 = 1 + 2^54 * 127;; [62,9] 2422936599525326849 = 1 + 2^53 * 269;; [62,7] 2485986994308513793 = 1 + 2^55 * 3 * 23;; [62,9] 2747195772696002561 = 1 + 2^53 * 5 * 61
From the code: https://bitbucket.org/tarballs_are_good/lisp-random/raw/master/number-theore... )
Cheers! Robert On Wed, Dec 2, 2015 at 6:03 AM, Henry Baker <hbaker1@pipeline.com> wrote:
Google's decision to end support for its browsers on 32-bit computers signals the end for 32-bit computers in general. If you can't run a browser, then you can't be a full-fledged computer in the 21st century.
Most *serious* computer people have always considered 32 bits to be too small, and therefore a 32-bit computer was always a *mini* computer (at least DEC got this part right).
Von Neumann's 1944 EDVAC computer had *44 bit* words, and was therefore a *real* computer:
https://en.wikipedia.org/wiki/EDVAC
At least 32-1=31 is prime; 64-1=63=3^2*7. 128-1=127 is again prime.
But 257=2^8+1 is prime -- the next such after 17=2^4+1.
--- Google to end updates, security bug fixes for Chrome on 32-bit Linux
http://www.theregister.co.uk/2015/12/02/googles_chrome_32bit_linux/
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