mpz_div_2exp function

[Niels Möller]

leif <not.really at online.de> writes:

> FWIW, in 5.1.1 there's
>
> /usr/include/gmp.h:#define mpz_div_2exp	mpz_fdiv_q_2exp

Ah, there it is. And fdiv means floor, i.e, rounding towards -infinity,
*not* towards zero. It works as an arithmetic right shift, if one thinks
about negative numbers as using two's complement representation.

So, e.g, -5 (decimal) divided by 2 gives -3. In signed-magnitude binary,
that's

  -101 >> 1 == -11

which might look strange. But in two's complement (with infinitely many
ones to the left), it's

  ...11111011 >> 1 == ...11111101 

which is a plain arithmetic right shift.

BTW, using >> in C for signed numbers is implementation defined, IIRC,
but at least on my platform it seems to be compiled to an arithmetic
right shift, i.e., rounding towards -infinity. Unlike the division
operator, which rounds towards zero. The following test program,

  #include <stdio.h>
  
  int
  main (int argc, char **argv)
  {
    int x = -5;
    printf ("%d >> 1 == %d\n", x, x >> 1);
    printf ("%d / 2 == %d\n", x, x / 2);
    return 0;
  }

prints

  -5 >> 1 == -3
  -5 / 2 == -2

Not sure if this makes the GMP behaviour more or less confusing...

Regards,
/Niels

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