double.txt

With version 4.6 it is now possible to use a floating-point "double"
as the underlying type used to store the digits of a multi-precision number.
This is fully supported by the "config" utility.

Some new processors implement integer multiplication using the floating-point 
multiplier. On processors like these it may be advantageous to 
work directly with doubles. Other processors support Floating point 
multiplication, but not integer multiplication.

In many cases however this approach will NOT be optimal, and using an integer 
type as the underlying type is still recommended for the majority of cases.

To properly use a double type, the program must ideally be able to control the 
"rounding" behaviour of the floating-point processor. By default this may 
implement "round to nearest" which is wrong for integer arithmetic where 
"round to zero" is appropriate. Since no standard C constructs exist to 
control rounding, a small bit of assembly language may be required - see the 
function mr_invert() in the module mrarth1.c. Note however that some compilers 
like GNU C do allow control of rounding via functions declared in ieeefp.h

The compiler must properly support the Ansi Standard "long double" type. It 
should also implement the standard "modfl()" function for truncation to an 
integer.

In mirdef.h MR_FP is defined if a double type is to be used. MR_FP_ROUNDING is 
defined if rounding control can be exercised.

On the Pentium using a double is potentially optimal. See the experimental 
code in mr87f.c and mr87v.c, which can be used with the Borland C 
compiler/TASM macro assember combination. The floating point fmul instruction 
can be executed in just 1 cycle under ideal circumstances, but it requires 
some very complex code ordering to fully leverage this advantage.

See the ZMODEXP and NISTP224 programs by D. J. Bernstein at 
http://cr.yp.to/software.html for more optimal examples of this approach.

Note that GF(2^m) arithmetic, which requires bit shifting, and logical 
operations like XOR and AND, would be hopelessly inefficient using floating-
point, and so it is not supported with a double underlying type.

See mrmuldv.any for assembly language support...