Evaluate pi_ and other constants as floats

vermaseren / form

The FORM project for symbolic manipulation of very big expressions

GNU General Public License v3.0

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Evaluate pi_ and other constants as floats #532

Open fllor opened 4 weeks ago

fllor commented 4 weeks ago

This PR addresses some issues discussed during the workshop.

Add Euler and Euler-Mascheroni constants as builtin symbols (ee_, em_)
Allow Evaluate statement to insert arbitrary precision floating point values for the three builtin constants (π, e, γ). The values are provided (and cached) by MPFR
Allow symbols as arguments to Evaluate statement, e.g. Evaluate pi_
Test cases are included for various expressions, such as pi_*sqrt_(3), sqrt_(pi_), pi_*ee_

Furthermore, this PR fixes a bug in the printing of floating point numbers, that could cause exponents to be truncated and memory errors that would be lead to warnings in valgrind.

coveralls commented 3 weeks ago

coverage: 50.581% (+0.6%) from 49.999% when pulling 6880a65c8187736ca0d1e0a640fb4eed75c80760 on fllor:master into 83e3d4185efca2e5938c665a6df9d67d6d9492ca on vermaseren:master.

fllor commented 3 weeks ago

It seems the failure of the 32-bit tests might be due to a bug somewhere in the floating point engine. The program

#StartFloat 64

Local X = 2/3;
Local Y = sqrt_(3);
Local Z = pi_;

ToFloat;
Evaluate;

Print;
.end

gives me

X = 6.66666666666666666667e-01;
Y = 1.73205080756887729352e+00;
Z = 3.14159265358979323846e+00;

on my laptop and

X = 6.66666666666666666666666666667e-;
Y = 1.7320508075688772935274463415e+0;
Z = 3.14159265358979323846264338328e+;

on the 32-bit containers.

For some reason, floats are evaluated to a different precision. Also, note that Y in the first case is not rounded correctly. In the second case the exponents are not printed properly.

I am not sure if this is a bug in Form or GMP/MPFR. The internal representations are already different in evaluate.c:668.

jodavies commented 3 weeks ago

There is a known problem with the truncation of trailing zeros and messing up the exponent (see #492) which looks to be also the cause of the valgrind failures in your tests. So that needs to be sorted out but I didn't re-check it yet.

Jos said in his slides that float mode is not expected to work properly in 32bit mode, and it seems that it will be removed/declared "unsupported" for v5 anyway.

Once the valgrind errors are resolved you could also move your tests to features.frm rather than user-tests.frm.

fllor commented 3 weeks ago

Printing of exponents and valgrind errors should be fixed now. 32-bit tests will probably still fail.