Improved algorithms for mpq_class multiply/divide with (un)signed long integers

[Douglas Boffey]

Sirs,

I have rewritten the class members (see the attached patch file) for:

static void__gmp_binary_multiplies::eval(mpq_ptr, mpq_srcptr, unsigned long int)
static void__gmp_binary_multiplies::eval(mpq_ptr, unsigned long int, mpq_srcptr)
static void__gmp_binary_multiplies::eval(mpq_ptr, mpq_srcptr, signed long int)
static void__gmp_binary_multiplies::eval(mpq_ptr, signed long int, mpq_srcptr)
static void__gmp_binary_divides::eval(mpq_ptr, mpq_srcptr, unsigned long int)

static void__gmp_binary_divides::eval(mpq_ptr, unsigned long int, mpq_srcptr)
static void__gmp_binary_divides::eval(mpq_ptr, mpq_srcptr, signed long int)
static void__gmp_binary_divides::eval(mpq_ptr, signed long int, mpq_srcptr)

In each case, the mp operations involved (apart from trivial sign changes, etc.) are:

one  gcd (N x 1)
one integer div-exact (N x 1)
one integer multiply (N x 1)

instead of:

one gcd (M x N) for canonicalising
one integer multiply (N x 1), although only implicitly x 1 (I don't know whether there are any performance improvements of a _ui() over a non-_ui() function with a single limb in one argument.

Also, no temporaries are created.

Yours,

Douglas Boffey

p.s. I would be interested whether my patch is of any use or not.
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