Precision Errors

Since real numbers are stored approximately:

• every operation yields a slight loss of accuracy,
• after many operations such 'round-off' errors build up,
• catastrophic accuracy loss can arise when values that are almost equal are subtracted, leading digits are cancelled and a rounding errors become visible.

Consider,

   x = 0.123456; y = 0.123446
   PRINT*, "x = ",x," y = ",y
   PRINT*, "x-y = ",x-y," should be 0.100d-4"

May produce:

   x = 0.123457  y = 0.123445
   x-y = 0.130d-4 should be 0.100d-4

which is 30% in error.

A whole branch of Numerical Analysis is dedicated to minimising this class of errors in algorithms. Be careful!

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