Re: Using the GNU GMP Library for Bignums in Emacs

[Paul Eggert]

On 04/23/2018 12:22 PM, Helmut Eller wrote:
> If I read the code in in data.c correctly, than Emacs uses the
> INT_MULTIPLY_WRAPV macro which boils down to the __builtin_mul_overflow.
> Which indeed produces nice machine code.  But the original question was
> about ANSI C, which seems to require a division and 3 conditional jumps
> for the range check (with gcc 6).

Yes, in general INT_MULTIPLY_WRAPV does require a division on platforms 
that do not support overflow-checking builtins. In practice, though, 
this tends to not be an issue, as the major compilers are moving in the 
direction of supporting such builtins.

> Does INT_MULTIPLY_WRAPV macro even perform fixnum overflow tests?

No, it checks only for machine-level overflow. We could come up with a 
variant that does both machine-level and fixnum-level checking 
simultaneously; I'm not sure it's worth the trouble, though, as most 
arithmetic operations are addition and subtraction and for these, 
fixnum-level checking suffixes.

> Anyway, I find it curios that the following two expression yield
> different values:
>
> (* (* most-positive-fixnum 2) 1.0) => -2.0
>
> (* most-positive-fixnum 2 1.0) => 4.611686018427388e+18

Cool, huh? That's done on purpose; see this Emacs commit:

https://git.savannah.gnu.org/cgit/emacs.git/commit/?id=0ae6bdee0085b05028108325b0a4ce979eadb24e

The idea is to produce a floating-point answer that is more 
mathematically-correct, while sticking to Common Lisp-style rules for 
contagion and argument processing.