🚀 go-pugleaf

"Glen Herrmannsfeldt" <gah@ugcs.caltech.edu> writes: > An article by W. Kahan titled "How Java's Floating-Point Hurts Everyone
> Everywhere" (and which describes much more than Java)  includes a discussion
> about the results of floating point multiply.
> 
> 
> According to his description, until 1963 IBM Fortran compilers would
> generate double precision results for floating point multiply of two single
> precision numbers, at least when it was being summed into a double precision
> variable.  He then explains that IBM changed this in IBSYS 13, anticipating
> S/360.
> 
> As far as I can tell, the Fortran-66 standard requires a single precision
> product when multiplying single precision numbers, though I don't know how
> much impact IBM had on Fortran-66.
> 
> The reason why this comment is surprising to me is that S/360 (along with
> S/370 and ESA/390) do not have a single precision multipy instruction with a
> single precision product.  The product is always double precision.

While this is true, it is also true that subsequent single-precision
operations using the result will use only the single-precision
product.

Furthermore, storing the result into a single-precision variable
will store only the single-precision product.
To store a double-precision product, an STE will do,
followed by a MVC STE+4(4),=F'0', or
SDR 0,0
LER 0,4
STD 0, result
The sequence
SDR 0,0
LE  0,4
will convert the DP FPR 4 to single prec. for subsequent use with DP
operands.

>  I have
> checked the code generated by both the G and H compilers, and both, after
> generating the multiply instruction generate at least two more instructions
> to truncate the product to single precision.
> 
> It, then, seems unlikely to me that the change was made to accomodate S/360,
> when the S/360 hardware had exactly the opposite effect.   I don't know what
> the status of Fortran-66 was in 1963, though, and what influence that may
> have had.
> 
> As far as I know, Fortran still requires floating point multiply to generate
> a result with no more precision than the arguments that went into it.

The intrinsic DPROD will generate a DP product from SP arguments.

> W.Kahan describes well the advantage of summing a double precision product
> of single precision arguments, yet the Fortran standard doesn't seem to
> follow it.  (Someone with a more recent standard can comment on this.)
> 
> PL/I has the MULTIPLY function where one can specify the desired result
> precision.  At least one compiler I know of expands both operands before
> doing a double precision multiply when double precision is desired.
> 
> If someone wanted to comment about other hardware or compilers in use in the
> 1960's and 1970's, that might also be useful.
> 
> I would, in the end, like to thank W.Kahan for his unceasing drive to
> improve the results of floating point hardware and software, and hope for
> only constructive discussion of this problem.
> 
> -- glen