Re: Same .m file: different results with different versions of Octave

[Judd Storrs]

I've started the attached program to test the accuracy and speed of
ctanh implementations.

One thing I realized is that the x=22 cutoff only applies to the real
component. Being eps from zero means nothing (doh) so I need to rework
the overflow of the denominator for the imaginary component.

The testing code uses MPFR and evaluates a grid (see top of file for
#defines to configure--sorry no fancyness). At each point it tests
whether the libm ctanh is within a multiple of eps from the MPFR
value. Compile with

c99 -o ctanh_test -lm -lmpfr ctanh_test.c

I intend to tests for the C99 special cases. Here are some results:

Original glibc:

 Error magn  Real part  Imag part  Both
 ----------- ---------- ---------- ---------
  >= 1 eps       11146       7376       6296
  >= 2 eps         296        290       2248
  >= 3 eps          48        150       1500
  >= 4 eps          24        128       1156
  >= 5 eps          32         86        952
  >= 6 eps           8         68        788
  >= 7 eps          36         64        692
  >= 8 eps          12         54        604
  >= 9 eps           8         56        544
  >=10 eps          12         52        472

 Grid size:                1025 x 1025
 Top Left corner:           -8.000000 + +8.000000 i
 Bottom Right corner:       +8.000000 + -8.000000 i
 Time to evaluate grid:     131.340000 (sec) [10000 loops]
 Internal inconsistencies:  0

This is a stripped down version of the Jaroslav's optimized version
(removing all branches for now):

 Error magn  Real part  Imag part  Both
 ----------- ---------- ---------- ---------
  >= 1 eps       12990      71680       6208
  >= 2 eps           0          4          0
  >= 3 eps           0          0          0
  >= 4 eps           0          0          0
  >= 5 eps           0          0          0
  >= 6 eps           0          0          0
  >= 7 eps           0          0          0
  >= 8 eps           0          0          0
  >= 9 eps           0          0          0
  >=10 eps           0          0          0

 Grid size:                1025 x 1025
 Top Left corner:           -8.000000 + +8.000000 i
 Bottom Right corner:       +8.000000 + -8.000000 i
 Time to evaluate grid:     134.570000 (sec) [10000 loops]
 Internal inconsistencies:  0


One thing you will notice is that the new code generates more total
errors but they are all small ~1eps. On the other hand, the old code
has quite a few errors greater than 10 eps. It could be that the
floating point rounding mode I chose for MPFR doesn't match what the
ieee doubles are doing. Also, notice that the change in cpu time is
very small with Jaroslav's optimizations.


--judd

ctanh_test.c
Description: Text Data