OpenEuphoria

Re: Converting decimal number to carpenter's fractions

• Posted by bill May 06, 2012
• 2880 views

function carp(atom x) 
  integer u = floor(x) 
  integer n = floor((x-u) * 64 + 0.5) 
  -- boundary conditions 
  -- x-u >= 127/128 
  if n = 64 then 
	  return {u+1, 0, 1}  -- orginal function returned {u, 1, 1} 
  -- x-u < 1/128 
  elsif n = 0 then 
     return {u, 0, 1}    -- normal form 
  -- n in range 1-63 
  else 
    integer d = 64 
    while remainder(n, 2) = 0 do 
      n /= 2 
      d /= 2 
    end while 
    return {u, n, d} 
  end if 
end function 

results:

carp(0)       : {0,0,1} 
carp(1)       : {1,0,1} 
carp(0.625)   : {0,5,8} 
carp(2.314)   : {2,5,16} 
carp(127/128) : {1,0,1}  -- rounds up 
carp(1/128)   : {0,1,64} 

In the original code the normaisation loop went

d = 64 
while d > 1 do 
  if remainder(n, 2) = 1 then 
    exit 
  end if 
  n /= 2 
  d /= 2 
end while 

The only way this loop can normally terminate is if n started as 0 or 64.

Both conditions meet the test:

  remainder(n, 2) = 0 
 
the test d > 1 produces: 
  64  64      0 64 
  32  32      0 32 
  ......      .... 
   1   1      0  1 
<eucode> 
In the case n = 0, n doesn't change. 
 
In the case n = 64, the reduction shouldn't be 
applied as 64/64 is not a proper fraction. 
 
From a programming perspective 
<eucode> 
   while d > 1 do 

is a poor choice because it runs until d <= 1. It exits abnormally in almost all cases.

  while remainder(n, 2) = 0 

works properly because, *given n is in 0-63*, we know n reduces as d reduces and n must reduce to an odd number.