About: Pete-3.c   Sponge Permalink

An Entity of Type : owl:Thing, within Data Space : dbkwik.org associated with source dataset(s)

pete-3.c is one of the nine entries an anonymous "Pete" submitted to Bignum Bakeoff, and the smallest entry that produces a large number. It uses the left shift operator <<, which in the fictional Bignum Bakeoff machine may be defined as \(a \ll b = a \cdot 2^b\) for nonnegative \(a\) and \(b\). (Its behavior is more complex in standard C implementations.)

AttributesValues
rdfs:label
  • Pete-3.c
rdfs:comment
  • pete-3.c is one of the nine entries an anonymous "Pete" submitted to Bignum Bakeoff, and the smallest entry that produces a large number. It uses the left shift operator <<, which in the fictional Bignum Bakeoff machine may be defined as \(a \ll b = a \cdot 2^b\) for nonnegative \(a\) and \(b\). (Its behavior is more complex in standard C implementations.)
dcterms:subject
dbkwik:googology/p...iPageUsesTemplate
abstract
  • pete-3.c is one of the nine entries an anonymous "Pete" submitted to Bignum Bakeoff, and the smallest entry that produces a large number. It uses the left shift operator <<, which in the fictional Bignum Bakeoff machine may be defined as \(a \ll b = a \cdot 2^b\) for nonnegative \(a\) and \(b\). (Its behavior is more complex in standard C implementations.) Presumably to save space, Pete did not use parentheses. Unfortunately, << is left-associative, and \(a \ll b\) grows much faster relative to \(b\) than to \(a\). So the returned value becomes \(9 \cdot (2^9)^{163} \cdot 2^{99} \approx 2.33 \cdot 10^{472}\), between a centillion and googolding. A large amount of space is therefore wasted on a number smaller than 1 << 1600. If the operator was instead right-to-left associative, the output would grow at a roughly tetrational rate with respect to the number of 9's. The full decimal expansion of this number is 23292479355228506120629103772205782521188556601365594768126262808438806540095385289219152367764951472483434579932913443405761122010738810864711712947727372583238365228030815708368105772248573097826643896491485324536255232791227961592036609194479127526553544504755505641588760449935355381277623598581929299236167791999017226178068796899131268137948410262725752057313568787813656536514657337239890061615130555787285358522635888992125632724527232536411274866890787299237298176.
Alternative Linked Data Views: ODE     Raw Data in: CXML | CSV | RDF ( N-Triples N3/Turtle JSON XML ) | OData ( Atom JSON ) | Microdata ( JSON HTML) | JSON-LD    About   
This material is Open Knowledge   W3C Semantic Web Technology [RDF Data] Valid XHTML + RDFa
OpenLink Virtuoso version 07.20.3217, on Linux (x86_64-pc-linux-gnu), Standard Edition
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2012 OpenLink Software