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. > > -- > You received this message because you are subscribed to the Google Groups > "mpir-devel" group. > To post to this group, send email to mpir-de...@googlegroups.com. > To unsubscribe from this group, send email to > mpir-devel+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/mpir-devel?hl=en. > > > >
-- You received this message because you are subscribed to the Google Groups "mpir-devel" group. To post to this group, send email to mpir-de...@googlegroups.com. To unsubscribe from this group, send email to mpir-devel+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/mpir-devel?hl=en.