2020-08-18 v 0.0.1 first draft posted on comp.lang.forth

2020-08-21 v 0.0.2 revised to introduce essential word for defining double-precision IEEE floating point value.

2020-08-22 v 0.0.3 fix code formatting and add references

The IEEE 754-2008 standard for floating point arithmetic [1] provides numerous advantages for those who write numerical floating point programs [2], including standardized floating point number formats which have been widely adopted for several decades, as well as a significantly simpler approach to dealing with exceptions in floating point arithmetic. Although significant parts of an optional IEEE floating point word set for Forth have been developed as RfD's since 2009, the proposal(s) [3] have languished now for 11 years without any progress towards including their features within a standard. This RfD takes the view that the lack of progress is primarily a result of two factors:

<p>Even in language standards which have adopted many of the IEEE 754 arithmetic features, support is often incomplete. One such example is the C99 standard, which specifies extensions for features such as setting the rounding modes and masking floating point exceptions, but does not specify a way to enable and disable floating point exception traps.

<p>Several Forth systems [4] have already extended their floating point capabilities to include IEEE 754 features such as special binary values representing signed infinity (+/-INF) and "not a number" (NAN) values, with possibly different names.

<p>Instead of a more or less comprehensive proposal, specifying words to provide most of the functionality within the IEEE 754 standard, we propose the formal inclusion within the standard of the "optional IEEE 754 binary floating-point word set", initially containing a minimal set of words to allow creating IEEE binary floating point values with bit-level precision. Further functionality provided by the IEEE 754-2008 standard may be added by subsequent proposals.

<p>In this proposal, in addition to the inclusion of the "optional IEEE 754 binary floating-point word set", also adding the word MAKE-IEEE-DFLOAT which permits the creation of any recognized double precision floating point value. It will allow definition of special IEEE 754 floating point values which are returned by default upon certain arithmetic exceptions (+/-INF, NAN), and are useful for detecting an arithmetic exception. The IEEE 754 standard also provides other mechanisms for detecting and dealing with floating point arithmetic exceptions.

<p>Subsequent proposals can incrementally add IEEE 754-2008 or IEEE 754-2019 functionality to the standard optional word set. For example, another proposal can add standardized named constants for special binary values returned upon arithmetic exceptions. Another proposal may formally update the specifications for existing floating point arithmetic words for consistency with the IEEE 754 standard, and yet another proposal may add words for exception detection by providing access to the exception flags of the floating point unit. Such changes may be introduced individually so that the problem of providing consistent floating point arithmetic consistent with the IEEE 754 standard can be tackled in pieces rather than all at once. Given the substantial amount of work already done towards such an optional word set [2], the problem can be reduced to identifying groups of words which may be added separately to provide enhanced capabilities.

<p>The adoption of an "optional IEEE 754 binary floating-point word set" into the Forth 20xx standard, initially with minimal provisions, will be immediately useful for practitioners of numerical floating-point computation in Forth. The proposed addition to the new word set is

which will return an IEEE 754 double precision floating point value from the specified bit fields for the sign, binary fraction, and exponent. It will also validate the binary fraction and exponent fields for consistency with the IEEE binary format and return a error value on the data stack, 0 for no error and non-zero values to indicate the type of failure. The least significant bit of the signbit value represents the sign of the floating point value (0 is positive, 1 is negative), the lower 32-bits of each cell value of udfraction are concatenated to provide the binary fraction bits of the mantissa, and uexp provides the binary representation of the exponent.

HEX
0 54442D18 921FB 1 MAKE-IEEE-DFLOAT fconstant pi

<p>

1. Adopt the Optional IEEE 754 binary floating point word set into the Forth 20xx standard.

2. The new word set will provide the word MAKE-IEEE-DFLOAT with the specifications given above.

HEX
\ Make an IEEE 754 double precision floating point value from
\ the specified bits for the sign, binary fraction, and exponent.
\ Return the fp value and error code with the following meaning:
\   0  no error
\   1  exponent out of range
\   2  fraction out of range
fvariable temp

: MAKE-IEEE-DFLOAT ( signbit udfraction uexp -- r nerror )
    dup 800 u< invert IF 2drop 2drop F=ZERO 1 EXIT THEN
    14 lshift 3 pick 1F lshift or >r
    dup 100000 u< invert IF
    r> 2drop 2drop F=ZERO 2 EXIT
 THEN
 r> or [ temp cell+ ] literal ! temp !
 drop temp df@ 0 ;

References

1. IEEE, 754-2008 - IEEE Standard for Floating-Point Arithmetic - Redline, https://ieeexplore.ieee.org/document/5976968 (2008).
2. W. Kahan, Lecture Notes on the Status of IEEE Standard 754 for Binary Floating-Point Arithmetic, https://people.eecs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF (1997).
3. D. N. Williams, Proposal for an Optional IEEE 754 Binary Floating-Point Word Set, v 0.5.4, http://www.forth200x.org/ieee-fp.txt (2009); Also, see older and more recent versions of this draft proposal and another proposal for supporting IEEE 754 exceptions and exception handling at http://www-personal.umich.edu/~williams/archive/forth/ieeefp-drafts/.
4. Based on discussions in comp.lang.forth during August 2020, the following systems appear to be able to output IEEE 754 values for signed INF: iForth gforth, lxf, kForth-32. Only iForth appears to support an intrinsic definition of fp values for +/-INF.

2020-08-23 v 0.0.4 fix reference

<p>Subsequent proposals can incrementally add IEEE 754-2008 or IEEE 754-2019 functionality to the standard optional word set. For example, another proposal can add standardized named constants for special binary values returned upon arithmetic exceptions. Another proposal may formally update the specifications for existing floating point arithmetic words for consistency with the IEEE 754 standard, and yet another proposal may add words for exception detection by providing access to the exception flags of the floating point unit. Such changes may be introduced individually so that the problem of providing consistent floating point arithmetic consistent with the IEEE 754 standard can be tackled in pieces rather than all at once. Given the substantial amount of work already done towards such an optional word set [3], the problem can be reduced to identifying groups of words which may be added separately to provide enhanced capabilities.