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>  # macheps.s                         J F Monahan, June 2001
>  #                                   revised August 2007
>  # compute machine epsilon
>  #
> # first try some values to get in ballpark
> eps <- 2**(-56)
>  "2**(-56)"
[1] "2**(-56)"
> eps
[1] 1.387779e-17
>  "Is 1+eps bigger 1 for eps = j*2**(-56), j = 1 to 16"
[1] "Is 1+eps bigger 1 for eps = j*2**(-56), j = 1 to 16"
>  (1!=(1+eps*(1:16)))      # F if different, T if not 
 [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE
[13]  TRUE  TRUE  TRUE  TRUE
> #
> # at this point it's around 8*2**(-56) or 2**(-53)
> #  or ... 64*2**(-59), so try 60 to 70
>  "Is 1+eps bigger 1 for eps = j*2**(-59), j = 60 to 70"
[1] "Is 1+eps bigger 1 for eps = j*2**(-59), j = 60 to 70"
> eps <- 2**(-59)
>  (1!=(1+eps*(60:70)))
 [1] FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
> #
> # another try
>  eps <- 2**(-53)          # first guess + smaller
>  (1!=(1+eps*(1 + 2**(-1:-16))))
 [1]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE FALSE
[13] FALSE FALSE FALSE FALSE
> # this is different -- the real machine epsilon
>  "Is 1+eps bigger 1 for eps = 2**(-53) + 2**(-63)"
[1] "Is 1+eps bigger 1 for eps = 2**(-53) + 2**(-63)"
> eps <- 2**(-53) + 2**(-63)
> eps
[1] 1.111307e-16
>  (1!=(1+eps))
[1] TRUE
> #
> # this is the same -- just a hair too small
>  "Is 1+eps bigger 1 for eps = 2**(-53) + 2**(-64)"
[1] "Is 1+eps bigger 1 for eps = 2**(-53) + 2**(-64)"
> eps <- 2**(-53) + 2**(-64)
>  (1!=(1+eps))
[1] FALSE
> #
>  rm(list=ls())
>