# chtab21.r                  September 2009, March 2010
 #
 # floating point representations using sprintf and "%a"
 #
 # list of interesting numbers
  onep <- 1 + 2**(-16)        # a little more than one
  full <- 2 - 2^(-52)         # biggest with zero exponent
 # internal representation
  cbind(c(onep,full),sprintf("%a",c(onep,full)))
  nums <- c(2,1,1/16,0,-15,2**53-1,     # exactly rep integer
                           2**53+1,     # no longer exact
                   2**(-1022)*onep,     # still normalized
                   2**(-1023)*onep,     # just denormalized
                   2**(-1058)*onep,     # very small positive
                   2**(-1074),          # smallest positive
                   2**(-1075)*onep,     # too small
                    (2**1023)*onep,     # almost biggest
                    (2**1023)*full,     # biggest
                    (2**1024)*onep)     # too big
  nums
 # names for those numbers
  names <- c("two","one","sixteenth","zero","neg fifteen",
         "exactly rep integer","no longer exact","still normalized",
         "just denormalized","very small positive","smallest positive",
         "too small", "almost biggest","biggest","too big")
 # internal representation
  internal <- sprintf("%a",nums)
  rbind(internal,nums,names)
  rm(list=ls())
  q()