Significance Arithmetic for Fortran
Walter R. Burrus, B. W. Rust · NASA Technical Reports Server (NASA) · 1966
The FOIzllRAm statement X # 193./71.-2721./1001.has a true value of 0.00002814~. .-, but a single-precision FORTRAN computation (27 bit fraction) yields 0.281.333923-04(using an E14.8 output FORMAT) due to loss of Significance when subtracting.When the number of significant digits is questionable, the same problem may be run in both single and double precision.This is inconvenient because existing programs must be modified and because dou3le precision requires twice as much storage space.for keeping track of the amount of significance in floating-point numb q s by representing them in unnormalized form.in ordinary FORTRAN-IV, and the significance operations implemented by w e of the ALmR feature of the loader. of significance arithmetic are discussed. AWe have implemented a simple alternative due to Max Goldstein Programs may be written Some problems and applications w 0