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Subject: [boost] performance of a linear algebra/matrix library
From: DE (satan66613_at_[hidden])
Date: 20100506 13:02:40
hi all
i work on a linear algebra library with an intent to propose it for
inclusion into boost collection of libs
so my question is: how fast such a lib should be to make everybody
happy?
i found that to increase the performance of a generic linear algebra
library one must complicate the implementation to a very high degree
(though this statement should be obvious to everyone)
i struggled with poor performance of matrix multiplication and finally
identified the bottleneck
i improved the implementation (seriosly complicating it, i'm afraid i
will forget how it works in a month) and now it performs some 33%
slower than C code for virtually any size of matrix
the C code is as follows:
typedef double type;
const size_t n = 42;
type
*a = new type[n*n],
*a1 = new type[n*n],
*a2 = new type[n*n];
//filling 'a1' and 'a2'
for (size_t i = 0; i<n; ++i)
{
type * const a_i = a + i*n;
for (size_t j = 0; j<n; ++j)
a_i[j] = 0.;
for (size_t k = 0; k<n; ++k)
{
type *a = a_i;
const type a1_ik = a1[i*n + k];
const type *a2_k = a2 + k*n;
for (size_t j = 0; j<n; ++j, ++a, ++a2_k)
*a += a1_ik*(*a2_k);
}
}
the C++ code is just
matrix<type> m(n, n), m1(n, n), m2(n, n);
//filling 'm1' and 'm2'
m.assign(m1, m2);
more detailed results:
'n' is the dimensions of matrices, 'ratio' is runtime of C++ code
divided by runtime of C code (time_cpp/time_c)
n  2  4  8  16  32  64  128  256  512  1024  2048
ratio  1,77  1,57  1,34  1,12  1,05  1,12  1,32  1,33  1,23  1,23  1,23
as you can see starting with 8 by 8 matices C++ code is roughly 33%
slower than C code
is that enough to make you (the reader) happy?
 Pavel
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