I think we should print pow using repeated multiplication. People
might not know about --ffast-math, not realize that we are using pow
and that it is needed, or not want other optimizations that it
provides.
Is there a reason to put a limit on the power (5 was suggested here,
10 on the pull request)?
Aaron Meurer
On Fri, Aug 29, 2014 at 9:38 AM, Jason Moore <[email protected]>
wrote:
Sorry, it wasn't merged. He found that the --fast-math flag in the
complier
takes care of this.
Jason
moorepants.info
+01 530-601-9791
On Fri, Aug 29, 2014 at 10:37 AM, Jason Moore <[email protected]>
wrote:
Here is some work on the pow issue:
https://github.com/sympy/sympy/pull/7519
Looks like it was merged so the ccode printer should print x*x*x...
for
less that 10 x's.
Jason
moorepants.info
+01 530-601-9791
On Fri, Aug 29, 2014 at 7:33 AM, Jason Moore <[email protected]>
wrote:
Jason
moorepants.info
+01 530-601-9791
On Fri, Aug 29, 2014 at 2:38 AM, James Crist <[email protected]>
wrote:
I was planning on going to bed, but ended up working on this
instead.
I
have no self control...
Anyway, I've uncovered some things:
1. Addition of the restrict keyword to tell the compiler we're
not
aliasing offers marginal gains. Gain a couple microseconds here
and
there.
This requires a c99 compiler, but it's 2014, everyone should have
one
by
now.
2. Inlining the function call resulted in smaller gains than 1,
but
still *slightly* measurable. I suspect that for larger expression
sizes this
will be negligible to none.
3. Here's the big one: For small powers, pow(c, n) is
considerably
slower than c*c*c*c... Changing the ccode Pow handler to print
all
pows less
than 5 (arbitrary number) out as multiplication I was able to
match/beat
(slightly) all of jason's benchmarks with the C + numpy ufuncs.
Oh yes! I knew that. In fact, I feel like I read in the current
code
somewhere. I forget, but that seems like a standard way we should
be
handling pows in C. Nice find!
On Thursday, August 28, 2014 1:38:30 PM UTC-5, Tim Lahey wrote:
On why Fortran is faster, Fortran semantics ensure that function
arguments never alias, this allows the optimizer to make
assumptions
about
the function and the arguments. This the main advantage of
Fortran
over C.
But, because of this, it can lead to more memory usage. I know
that
the
newer C++ standards have a keyword to mark arguments to indicate
that they
won't be aliased, but that requires that the code generator and
the
compiler
support them.
Cheers,
Tim.
On 2014-08-28, at 2:17 PM, Jason Moore <[email protected]>
wrote:
Jim and others,
Here are the benchmarks I made yesterday:
http://www.moorepants.info/blog/fast-matrix-eval.html
The working code is here:
https://gist.github.com/moorepants/6ef8ab450252789a1411
Any feedback is welcome.
Jason
moorepants.info
+01 530-601-9791
On Wed, Aug 27, 2014 at 11:44 PM, James Crist <[email protected]>
wrote:
I was wondering about that. I wasn't sure if the overhead from
looping through the inputs multiple times would outweigh
improvements from
fast C loops. Glad that in your case it does.
I've thrown a WIP PR up:
https://github.com/sympy/sympy/pull/7929
For some reason, creating the functions in python with numpy
calls
still seems to be faster (for micro-benchmarks). This probably
has
something
to do with function complexity (the example function above is
simple), but
I'd still think it'd be faster in pure C. I tried inlining the
call, which
was a small improvement, but it was still slower than the pure
numpy-python
version. Something to look into.
On Wed, Aug 27, 2014 at 10:28 PM, Jason Moore
<[email protected]>
wrote:
Yeh, but if you simply create a ufunc for each expression in a
matrix
you still get substantial speedups. I wrote a bunch of test
cases
that I'll
post to my blog tomorrow.
Jason
moorepants.info
+01 530-601-9791
On Wed, Aug 27, 2014 at 11:26 PM, James Crist <[email protected]>
wrote:
Not yet. I wrote it this morning during an extremely boring
meeting,
and haven't had a chance to clean it up. This doesn't solve
your
problem
about broadcasting a matrix calculation though...
On Wed, Aug 27, 2014 at 10:23 PM, Jason Moore
<[email protected]>
wrote:
Awesome. I was working on this today but it looks like you've
by
passed what I had working. Do you have a PR with this?
Jason
moorepants.info
+01 530-601-9791
On Wed, Aug 27, 2014 at 11:11 PM, Matthew Rocklin <
[email protected]>
wrote:
Cool
On Wed, Aug 27, 2014 at 8:07 PM, James Crist <[email protected]>
wrote:
I still need to do some cleanups and add tests, but I finally
have
this working and thought I'd share. I'm really happy with this:
In [1]: from sympy import *
In [2]: a, b, c = symbols('a, b, c')
In [3]: expr = (sin(a) + sqrt(b)*c**2)/2
In [4]: from sympy.utilities.autowrap import ufuncify
In [5]: func = ufuncify((a, b, c), expr)
In [6]: func(1, 2, 3)
Out[6]: 6.7846965230828769
In [7]: func([1, 2, 3, 4, 5], [6, 7, 8, 9, 10], 3)
Out[7]: array([ 11.44343933, 12.36052961, 12.79848207,
13.12159875, 13.75078733])
In [8]: from numpy import arange
In [9]: a = arange(10).reshape((2, 5))
In [10]: c = arange(10, 20).reshape((2, 5))
In [11]: b = 25
In [12]: func(a, b, c)
Out[12]:
array([[ 250. , 302.92073549, 360.45464871, 422.57056
,
489.62159875],
[ 562.02053786, 639.86029225, 722.8284933 ,
810.49467912,
902.70605924]])
In [13]: type(func)
Out[13]: numpy.ufunc
This now does everything a numpy `ufunc` does normally, as it
*is*
a
ufunc. Codegen is hooked up to numpy api. Type conversion and
broadcasting
are done automagically.
Caveats: only functions with a single output are accepted (this
could
be changed to accept multi-output without much effort though).
Also, as with
all unfuncs, input/outputs must all be scalars (no
matrix/Indexed
operations
allowed).
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