Switch standard 2D plotting from `fast_float` to `fast_callable`

[eviatarbach]

Switch the plot command to use fast_callable instead of fast_float. This will make commands like plot(abs(log(x)), x) work.

Component: graphics

Keywords: plot

Work Issues: compare patch with alternative by ppurka

Author: Eviatar Bach

Branch: 7a9e07a

Reviewer: Ralf Stephan

Issue created by migration from https://trac.sagemath.org/ticket/15030

[eviatarbach]

comment:1

Attachment: trac15030.patch.gz

The patch changes plot to use fast_callable. It doesn't fix contour_plot or plot3d, for example, since that seems to be more involved, and should be fixed in a future patch.

Patchbot apply trac15030.patch​

[tkluck]

comment:2

Thanks for looking into this important issue!

Did you check to see what the performance implications of your patch are? I assume that fast_float is faster than fast_callable, but that is not based on any data.

[eviatarbach]

comment:3

Yes, fast_float is slightly faster in my tests. However, I think the plan is to deprecate fast_float anyway; see #5572.

[ppurka]

comment:4

This doesn't really fix #13559. Do you have an idea why? I thought this change to fast_callable should take care of that other ticket too.

[eviatarbach]

comment:5

I think it's because plot (look at the function generate_plot_points in sage.plot.plot) generates float points, and

sage: exp(1e5r)
OverflowError: math range error

Maybe it should generate RealNumber points instead (I guess they should also be faster than floats for many functions, because MPFR functions are functions are fast)? In any case, that doesn't affect this ticket.

[ppurka]

comment:6

Hmm.. so, you are changing only the plots for symbolic expressions. This patch makes the symbolic expression plots about five times slower.

sage: timeit('plot(abs(log(x)), (x, -20, 20))') # with patch
25 loops, best of 3: 18.5 ms per loop

sage: timeit('plot(abs(log(x)), (x, -20, 20))') # without patch
125 loops, best of 3: 3.58 ms per loop

What do you think of the following change which introduces only a factor of two slowdown? The main problem seems to be that the fast float stuff does not handle complex numbers, and so we can explicitly specify the domain as CDF. I am not sure what is the default domain.

+        from sage.ext.fast_callable import fast_callable
+        from sage.rings.all import CDF
+        return fast_callable(self, vars=vars, expect_one_var=True,
+                             domain=CDF)

The timeit results are as follows:

sage: timeit('plot(abs(log(x)), (x, -20, 20))')
125 loops, best of 3: 6 ms per loop

A few doctests in expression.pyx fail, but they can be fixed (by changing their output).

[rwst]

Work Issues: compare patch with alternative by ppurka