Hey, the GMP 5 library now has a version of our mpn_mulmod_2expp1.
It's also undocumented I believe, but we can now use it in our timing.
That should give GMP a good speedup for this.
When this test was written, such a function did not exist in GMP.
The GMP 5 library is just a few days old. Give us a chance to catch up!
Bill.
2010/1/10 Gianrico Fini <gianrico.f...@gmail.com>:
> It didn't took me so much time as I feared to understand why the use
> of bench_two on GMP4.3 and MPIR1.3 (on my 32-bit CPU) gave so strange
> results...
> GMP4.3 was (slightly) faster than MPIR1.3 for all tests, expect two
> where it was terribly slower: fermat and mersenne. The overall score
> says:
>
> GMP4.3 => 136, 97.2
> MPIR1.3 => 145, 104
>
> I.e. the bench_two test I downloaded from mpir.org says that yes, for
> many application GMP is faster, but there are some (two) where it is
> by far slower... so, globally, MPIR is 6% better than GMP.
>
> It sounds strange, doesn't it?
>
> Well, go and look into the code, the tarball is available from the
> main page of MPIR, you can download it, unpack it and... before you
> use it, please READ THE CODE!
>
> The two very interesting test files are: fermat_prime_p.c,
> mersenne_prime_p.c .
>
> Let's start from the first one: fermat_prime_p.c
>
> At the beginning you can find:
> #ifndef __MPIR_VERSION
> // we are gmp
> #define NEED_MULMOD
> #elif __MPIR_VERSION < 1 || (__MPIR_VERSION == 1 &&
> __MPIR_VERSION_MINOR < 3)
> #define NEED_MULMOD
> #endif
>
> ...you will see, this means: if someone is testing GMP or a version of
> MPIR before 1.3, be _as_slow_as_possible_. The reason? This way MPIR
> will look like being fast :-D
>
> The "application" is very simple, it performs a "Pepin's Test for k"
> i.e. test if "3^((F_k-1)/2) == -1 mod F_k", where "F_k = 2^(2^k)+1".
>
> How would you write such an application? You would probably think you
> can use the documented function mpz_powm...
> The test doesn't do this, because this could be fast on libraries
> different from MPIR-1.3, and the goal is to be _slow_... so it will
> use a loop and the _undocumented_ function mpn_mulmod_2expp1. This is
> a test to see how the library perform with a typical application, and
> uses a function that NO application will use, for the simple fact that
> _it_is_NOT_documented!
> You can try:
> mpir-1.3.0$ grep -ri mulmod doc/mpir.*
>
> Nothing, no answer, it is not documented at all...And if you are not
> using MPIR-1.3? will the test use something different? NO! It will
> perform the computation using an _as_slow_as_possible_ substitute for
> that function.
>
> NO APPLICATION WILL EVER BE SO CRAZY, THIS IS NOT AN APPLICATION, IT'S
> A FAKE!!!
>
> I'll not analyse the ridicule "substitute", I'll do for the next
> "application", because it is absurd exactly in the same way!
>
> Next application: mersenne_prime_p.c
> Here the "application" uses the Lucas-Lehmer test on a Mersenne
> number, now the loop make sense, because it is not a simple
> exponentiation, but a sequence of squaring-subtract, to be performed
> modulo 2^p-1.
> How would you implement it? With some clever reduction using mpn_add_n
> or initialising the modulo once and then using it again and again...
>
> But here, again, the main goal of the person who wrote this code was
> to show that his mulmod function was giving a tremendous speed up, so,
> again, the fake-application uses an undocumented function. Let us look
> at the line where it is used:
> mpn_mulmod_2expm1 (rp, xp, xp, k, tp); // mpn_sqrmod_2expm1 would be
> faster
> Note the comment, using sqr can be faster! Then read the fake,
> as_slow_as_possible, implementation that is used if you are measuring
> speed of something different wrt MPIR-1.3:
>
> void mpn_mulmod_2expm1 (mp_ptr xp,mp_ptr yp,mp_ptr zp,mp_size_t
> k2,mp_ptr tp)
> {mpz_t x,y,z,m;mp_size_t n,tn;
> n=BITS_TO_LIMBS(k2);
> mpz_init2(y,k2);mpz_init2(z,k2);mpz_init2(m,k2);mpz_init2(x,2*k2);
> mpz_set_ui(m,1);mpz_mul_2exp(m,m,k2);mpz_sub_ui(m,m,1);
> MPN_COPY(y->_mp_d,yp,n);tn=n;MPN_NORMALIZE(y->_mp_d,tn);y-
>>_mp_size=tn;
> MPN_COPY(z->_mp_d,zp,n);tn=n;MPN_NORMALIZE(z->_mp_d,tn);z-
>>_mp_size=tn;
> mpz_mul(x,y,z);
> mpz_mod(x,x,m);tn=x->_mp_size;if(tn>n)tn=n;
> MPN_COPY(xp,x->_mp_d,tn);if(tn<n)MPN_ZERO(xp+tn,n-tn);
> mpz_clear(x);mpz_clear(y);mpz_clear(z);mpz_clear(m);
> return;}
>
> The guy who wrote this fake application decided to implement the
> needed sqrmod with the slowest possible strategy. Directly using mpn?
> no, there is the risk to be fast:
> - let's allocate four mpz on the fly (this means for every iteration!)
> - let's recompute the modulus in mpz on the fly (it is constant for
> the full run and it is recomputed every iteration!!!)
> we should exploit the fact that this function will always be called
> with yp==zp, but again we run the risk to be efficient, and the author
> did NON want that, because this function is used for other libraries,
> to be compared with MPIR... and they must be slowed down! So, you
> perfectly know (read the comment above) that yp==zp, but
> - copy the memory _twice_ in _two_different_ new locations...
> This way mpz_mul will see two different pointers and will _NOT_ use
> sqr! Clever way to avoid any possibly faster primitive!!!
> - copy back the result (the third copy, to be repeated for any cycle!)
> - free the memory...(for the same variables that will be used
> [recreated] again in the next step).
>
> It is quite obvious, if you read the code of this two functions that
> it was written with one goal in mind, show that any library without
> those two functions was slow... or, to be more exact, that any other
> library (i.e. not MPIR-1.3) was slow.
>
> BUT THIS IS A FAKE!
>
> As a conclusion, on my laptop, MPIR is able to be faster than GMP
> !!!!!!!!ONLY CHEATING!!!!!!!
>
> You guys are very funny!!!! :-D
> Because the cheating is so evident that when your library is slower on
> all operation, the fake application is 3-4 times faster with your
> funny-library... and your benchmark is so.... ingenuous .... to
> conclude that overall the funny-fake-library is faster!!!!
> RIDICULOUS!!!!!
>
> But now be serious, and confess... MPIR is not a library, it's a
> joke! :-D
>
> AH AH AH AH!!!!
> Adios!
>
> Gian.
>
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