Named constants (pi)

[monadius]

Common mathematical constants should be supported in .dop files. The most important constant is pi. Internally, the best possible interval approximation should be used.

[keram88]

I will expose (some) of the internal GAOL constants:
two_pi
half_pi
pi_dn
pi_up
half_pi_dn
half_pi_up
ln2_dn
ln2_up
two_power_53
GAOL_NAN
GAOL_INFINITY
NaN (quiet)

I believe these are good approximations.
Gaol reference (attached for convenience)
gaol.pdf
page 49

[keram88]

I should also include e

[monadius]

For the constant e it is better to use a different name. For example, e_const.

[keram88]

Somehow I dropped pi from Gaol's constants.

[monadius]

Use intervals for two_pi, half_pi, pi (page 19 of gaol.pdf)

[keram88]

This is (partially) a front-end parser issue, so I'm assigning Ian.

[keram88]

I didn't notice that page 49 is about double versions. It looks like Gaol doesn't have e, so I'll need to get a good interval for it. I'll add it as a constant interval e_const = [down(e), up(e)].

[keram88]

For Ian's reference: Gaol's string constructor uses the tightest possible interval for pi. For now you can pass it straight through as a constant.

The width of the interval for the string "pi" is 1 ULP (in hex, [400921fb54442d18, 400921fb54442d19]), and the full decimal expansion of the lower bound is less than pi and the upper bound is greater than pi.

[keram88]

See #16 for a hint at the general strategy to implement this.

[keram88]

half_pi, two_pi, pi and e_const have been added. The constants are confirmed to be 1 ULP wide interval approximations.

[monadius]

I get the following error now:

bin/dop_gelpia benchmarks/classical_tests/1d/forrester.dop 
Traceback (most recent call last):
  File "bin/dop_gelpia", line 10, in <module>
   import argument_parser as ap
  File "/home/alexey/Work/Projects/gelpia/bin/argument_parser.py", line 11, in <module>
    from lexed_to_parsed import parse_function
  File "/home/alexey/Work/Projects/gelpia/bin/lexed_to_parsed.py", line 162
    t[0] = ["ConstantInterval", *SYMBOLIC_CONSTS[t[1]]]

My Python version is 3.4.4