R version 2.9.0 (2009-04-17)
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ISBN 3-900051-07-0

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>  # 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)))
     [,1]               [,2]                  
[1,] "1.00001525878906" "0x1.0001p+0"         
[2,] "2"                "0x1.fffffffffffffp+0"
>   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
 [1]   2.000000e+00   1.000000e+00   6.250000e-02   0.000000e+00  -1.500000e+01
 [6]   9.007199e+15   9.007199e+15  2.225108e-308  1.112554e-308  3.237958e-319
[11]  4.940656e-324   0.000000e+00  8.988603e+307  1.797693e+308            Inf
>  # 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)
         [,1]     [,2]     [,3]        [,4]     [,5]         
internal "0x1p+1" "0x1p+0" "0x1p-4"    "0x0p+0" "-0x1.ep+3"  
nums     "2"      "1"      "0.0625"    "0"      "-15"        
names    "two"    "one"    "sixteenth" "zero"   "neg fifteen"
         [,6]                    [,7]               [,8]                   
internal "0x1.fffffffffffffp+52" "0x1p+53"          "0x1.0001p-1022"       
nums     "9007199254740991"      "9007199254740992" "2.22510781043986e-308"
names    "exactly rep integer"   "no longer exact"  "still normalized"     
         [,9]                    [,10]                    
internal "0x0.80008p-1022"       "0x0.0000000010001p-1022"
nums     "1.11255390521993e-308" "3.23795802314978e-319"  
names    "just denormalized"     "very small positive"    
         [,11]                     [,12]       [,13]                 
internal "0x0.0000000000001p-1022" "0x0p+0"    "0x1.0001p+1023"      
nums     "4.94065645841247e-324"   "0"         "8.9886028274133e+307"
names    "smallest positive"       "too small" "almost biggest"      
         [,14]                     [,15]    
internal "0x1.fffffffffffffp+1023" "Inf"    
nums     "1.79769313486232e+308"   "Inf"    
names    "biggest"                 "too big"
>   rm(list=ls())
>   q()