KOTLER@USC-ECLB.ARPA (10/20/85)
The reason for the computation rules for the number of binary mantissa digits required to satisfy a particular decimal precision is somewhat subtle. The issue has been known to numerical analysys for quite some time. The original paper to treat this subject was "27 bits are not enough for 8-digit accuracy" by I.B. Glodberg[CACM 10,2, Feb. 1967 pp 105-106]. The most lucid contemporary description that I'm aware of is "Contributions to a Proposed Standard for Binary Floating-Point Arithmetic" by Jerome Coonen(PhD thesis, 1984, UC Berkeley). The basic problem has to do with the separation, or relative spacing of decimal fractions and binary fractions. In order to say that you have D digit arithmetic, one property that one might expect is that under conditions that rounding is well defin d , that if a D digits decimal number is converted to binary, and then converted back to decimal again, that we would get the same number. This however requires that between every D digit decimal fraction there is at least one B digit binary fraction, for otherwise one will have more than two D digit decimal numbers which can map to the same B digit binary number, and hence the conversion back to decimal will have converted at least one of our numbers to less than D digits precisely. This issue however is rather subtle and if fact was originally calculated incorrectly in earlier versions of the RM. The current definition in the RM came about as the result of an observation by the Ada Tokyo Study Group during the final reviews of Ada in 1982. Reed Kotler General Transformation Corp. (\ee issue oweverhawhen you caare ateveed, pederm haArithmetic~rte}imporary -------