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Insignificant Digits

Consider the Fortran code

 program test 
   real :: x=100000.0, y=100000.1, z
   z = y-x
   print*, 'z=',z
 end program test
We would expect the output

but in fact the program prints (on Alpha ...)

Since single precision handles about 7 decimal digits, and the subtraction cancels the most significant 6, the result contains only one significant digit. The appended garbage 15625 are insignificant digits, coming from the inexact binary representation of x and y. Beware of convincing-looking results!

Adrian Sandu 2001-08-26