I don't know if there is a version of mpn_mulmod_2expm1 in GMP 5 or
not though. Does their p1 version allow negative values for n? I
didn't check.
Bill.
2010/1/11 Bill Hart <goodwillh...@googlemail.com>:
> 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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>>
>>
>
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