Implement arbitrary-precision numerical data in (B)AGGs

[tturocy]

This implements a solution to #879, ensuring that numerical data in (Bayesian) action graph games are all stored with their original representation (as all other Gambit games).

This ensures no loss of precision if computing with rational numbers, or exporting to other game formats. (Even the export back to the AGG format actually lost precision!)

[Copilot]

Pull request overview

Adds exact rational storage and computation for AGG/BAGG numerical data while retaining double-precision solver paths.

Changes:

• Preserves original payoff and type-probability representations.
• Generalizes payoff convolution to double and Rational.
• Adds exactness fixtures and rational-solver tests.

Reviewed changes

Copilot reviewed 17 out of 17 changed files in this pull request and generated 8 comments.

Show a summary per file

File	Description
tests/test_nash.py	Documents rational AGG solver coverage.
tests/test_games/2x2_fraction_types.bagg	Adds fractional BAGG probabilities.
tests/test_games/2x2_fraction_payoffs.agg	Adds exact fractional/decimal payoffs.
tests/test_agg.py	Tests exact parsing and rational calculations.
src/solvers/gtracer/aggame.h	Adapts GameTracer declarations to typed distributions.
src/solvers/gtracer/aggame.cc	Keeps GameTracer computations double-based.
src/games/number.h	Adds original-text stream serialization.
src/games/gamebagg.h	Uses exact BAGG payoff extrema.
src/games/gamebagg.cc	Enables rational BAGG profiles and payoffs.
src/games/gameagg.h	Uses exact AGG payoff extrema.
src/games/gameagg.cc	Enables rational AGG profiles and payoffs.
src/games/agg/trie_map.imp	Makes constants compatible with templated values.
src/games/agg/trie_map.cc	Instantiates double and rational tries.
src/games/agg/bagg.h	Defines exact BAGG storage and APIs.
src/games/agg/bagg.cc	Implements exact BAGG parsing and computation.
src/games/agg/agg.h	Defines typed convolution state and exact tables.
src/games/agg/agg.cc	Implements exact AGG parsing, lookup, and convolution.

Suppressed comments (4)

src/games/agg/agg.cc:967

• The double branch has the same incomplete scan: only payoffs[0].begin() is considered for node 0, so this can return a value below the true maximum. Include node 0 in the loop.

    for (int i = 1; i < numActionNodes; i++) {

src/games/agg/agg.cc:981

• This omits every node-0 payoff except the first entry, so an exact minimum located elsewhere in exactPayoffs[0] is missed. Include node 0 in the scan.

    for (int i = 1; i < numActionNodes; i++) {

src/games/agg/agg.cc:990

• The double minimum scan also skips all but the first entry of node 0, which can return an incorrect minimum. Include node 0 in the loop.

    for (int i = 1; i < numActionNodes; i++) {

tests/test_agg.py:98

• There is no agg::AGG::getExactMixedPayoff; the exact engine is the getMixedPayoff<Rational> specialization. The docstring should name the real API.

    """AGG/BAGG mixed-strategy payoffs support exact (rational) computation: the convolution
    algorithm (agg::AGG::getMixedPayoff et al.) is generic in its numeric type, so it also runs
    with Rational arithmetic throughout (agg::AGG::getExactMixedPayoff), not just double.

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[tturocy]

@rahulsavani Those were good suggestions; I've pushed changes which address them, excepting the idea of the round-trip test. I rejected that originally because we don't yet expose (B)AGG writing and that's a whole piece of work in itself.

[Copilot]

Pull request overview

Copilot reviewed 17 out of 17 changed files in this pull request and generated no new comments.

Suppressed comments (2)

tests/test_agg.py:52

• This test never reads the 0.123456789012345 payoff: every assertion currently observes only 1/3, -10, or derived player extrema. A regression that still rounds long decimals would therefore pass despite the test name and fixture. Assert the (1, 1) contingency explicitly.

def test_agg_fraction_and_long_decimal_payoffs_parsed_exactly():
    """Payoffs written as a fraction ("1/3") or a decimal too precise for a double to round-trip
    are parsed into exact Rationals, not silently rounded through a bare double read.

    2x2_fraction_payoffs.agg is 2x2.agg with two of its four payoffs replaced: 35 -> 1/3 and
    95 -> 0.123456789012345.

src/games/agg/agg.h:251

• m_exactState eagerly constructs another numActionNodes × numPlayers matrix of trie_map objects for every AGG, and each empty trie_map heap-allocates a root. Thus double-only workflows—an important use case for large AGGs—now pay roughly twice the working-state allocations even if rational arithmetic is never requested. Please initialize the rational convolution state lazily on the first state<Rational>() call.

  ConvolutionState<double> m_state;
  ConvolutionState<Rational> m_exactState;