LMCAS::anonymous_namespace{calculus_continuity.cpp} 命名空间参考

函数
ContinuityResult	classify_continuity_point_value (const ExprPtr &limit, const ExprPtr &value, const FactsQuery &facts, ComputationContext &context)
ContinuityResult	continuity_from_limits (const ExprPtr &f, const std::string &var, const ExprPtr &point, const LimitOutcome &left, const LimitOutcome &right, ComputationContext &context)
Result< ExprPtr >	continuity_point_value (ExprPtr value, const FactsQuery &facts, ComputationContext &context)
ContinuityResult	continuity_with_limit (const ExprPtr &f, const std::string &var, const ExprPtr &point, const ExprPtr &limit, ComputationContext &context)
Result< detail::SymbolicNodePtr >	select_continuity_branch (const PiecewiseNode &piecewise, const FactsQuery &facts, const AssumptionContext &assumptions, ComputationContext &context)

函数说明

classify_continuity_point_value()

ContinuityResult LMCAS::anonymous_namespace{calculus_continuity.cpp}::classify_continuity_point_value	(	const ExprPtr &	limit,
		const ExprPtr &	value,
		const FactsQuery &	facts,
		ComputationContext &	context )

在文件 calculus_continuity.cpp 第 48 行定义.

                                                          {
    auto defined = detail::query_definedness(detail::node(value), facts, Domain::Real, context);
    if (!defined) { return ContinuityResult::failure(defined.error()); }
    if (defined.value() == Tribool::False) {
        return ContinuityResult::success(ContinuityType::Removable);
    }
    if (defined.value() != Tribool::True) {
        return ContinuityResult::failure(CasErrc::Inconclusive,
            "point-value definedness is unknown", "continuity_at");
    }
    auto same = detail::compare_pointwise_values(limit, value, context, Domain::Real);
    if (!same) { return ContinuityResult::failure(same.error()); }
    if (same.value() == Tribool::True) {
        return ContinuityResult::success(ContinuityType::Continuous);
    }
    if (same.value() == Tribool::False) {
        return ContinuityResult::success(ContinuityType::Removable);
    }
    return ContinuityResult::failure(CasErrc::Inconclusive,
        "point value could not be compared with the limit", "continuity_at");
}

引用了 classify_continuity_point_value(), LMCAS::detail::compare_pointwise_values(), LMCAS::context, LMCAS::Continuous, LMCAS::Result< ContinuityType >::failure(), LMCAS::False, LMCAS::Inconclusive, LMCAS::detail::node(), LMCAS::detail::query_definedness(), LMCAS::Real, LMCAS::Removable, LMCAS::Result< ContinuityType >::success(), LMCAS::True , 以及 LMCAS::value.

被这些函数引用 classify_continuity_point_value() , 以及 continuity_with_limit().

函数调用图:

这是这个函数的调用关系图:

continuity_from_limits()

ContinuityResult LMCAS::anonymous_namespace{calculus_continuity.cpp}::continuity_from_limits	(	const ExprPtr &	f,
		const std::string &	var,
		const ExprPtr &	point,
		const LimitOutcome &	left,
		const LimitOutcome &	right,
		ComputationContext &	context )

在文件 calculus_continuity.cpp 第 99 行定义.

                                                                                      {
    const auto* left_finite = std::get_if<FiniteLimit>(&left);
    const auto* right_finite = std::get_if<FiniteLimit>(&right);
    if (!left_finite || !right_finite) {
        return ContinuityResult::success(ContinuityType::Essential);
    }
    auto sides = detail::compare_pointwise_values(
        left_finite->value, right_finite->value, context, Domain::Real);
    if (!sides) { return ContinuityResult::failure(sides.error()); }
    if (sides.value() == Tribool::False) {
        return ContinuityResult::success(ContinuityType::Jump);
    }
    if (sides.value() != Tribool::True) {
        return ContinuityResult::failure(CasErrc::Inconclusive,
            "one-sided values could not be compared", "continuity_at");
    }
    return continuity_with_limit(f, var, point, left_finite->value, context);
}

引用了 LMCAS::detail::compare_pointwise_values(), LMCAS::context, continuity_from_limits(), continuity_with_limit(), LMCAS::Essential, LMCAS::Result< ContinuityType >::failure(), LMCAS::False, LMCAS::Inconclusive, LMCAS::Jump, LMCAS::point, LMCAS::Real, LMCAS::right, LMCAS::Result< ContinuityType >::success() , 以及 LMCAS::True.

被这些函数引用 continuity_from_limits().

函数调用图:

这是这个函数的调用关系图:

continuity_point_value()

Result< ExprPtr > LMCAS::anonymous_namespace{calculus_continuity.cpp}::continuity_point_value	(	ExprPtr	value,
		const FactsQuery &	facts,
		ComputationContext &	context )

在文件 calculus_continuity.cpp 第 35 行定义.

                                                                         {
    const AssumptionContext empty_assumptions;
    const auto& assumptions = context.assumptions() ? *context.assumptions() : empty_assumptions;
    while (const auto piecewise = std::dynamic_pointer_cast<const PiecewiseNode>(detail::node(value))) {
        auto selected = select_continuity_branch(*piecewise, facts, assumptions, context);
        if (!selected) { return Result<ExprPtr>::failure(selected.error()); }
        if (!selected.value()) { return ExprPtr{}; }
        value = detail::make_expression_ptr(selected.value());
    }
    return value;
}

引用了 LMCAS::context, continuity_point_value(), LMCAS::Result< T >::failure(), LMCAS::detail::make_expression_ptr(), LMCAS::detail::node(), select_continuity_branch() , 以及 LMCAS::value.

被这些函数引用 continuity_point_value() , 以及 continuity_with_limit().

函数调用图:

这是这个函数的调用关系图:

continuity_with_limit()

ContinuityResult LMCAS::anonymous_namespace{calculus_continuity.cpp}::continuity_with_limit	(	const ExprPtr &	f,
		const std::string &	var,
		const ExprPtr &	point,
		const ExprPtr &	limit,
		ComputationContext &	context )

在文件 calculus_continuity.cpp 第 72 行定义.

                                                           {
    detail::RewriteBudget transform_budget(context, (context).limits().max_recursion_depth,
                                            (context).limits().max_ast_nodes, "transform");
    auto value = detail::make_expression_ptr(detail::substitute_node(detail::node(f), var, detail::node(point), transform_budget));
    if (!value) {
        return ContinuityResult::failure(CasErrc::InternalInvariant,
            "substitution produced no value", "continuity_at");
    }
    std::optional<detail::AssumptionFacts> assumed;
    if (context.assumptions()) { assumed.emplace(*context.assumptions()); }
    const auto& facts = assumed ? static_cast<const FactsQuery&>(*assumed) : detail::no_facts();
    auto selected = continuity_point_value(value, facts, context);
    if (!selected) { return ContinuityResult::failure(selected.error()); }
    if (!selected.value()) { return ContinuityResult::success(ContinuityType::Removable); }
    return classify_continuity_point_value(limit, selected.value(), facts, context);
} catch (const CasError& error) {
    return ContinuityResult::failure(error);
} catch (const std::bad_alloc&) {
    return ContinuityResult::failure(CasErrc::ResourceLimit, "allocation failed", "continuity_with_limit");
} catch (const std::length_error& error) {
    return ContinuityResult::failure(CasErrc::ResourceLimit, error.what(), "continuity_with_limit");
} catch (const std::exception& error) {
    return ContinuityResult::failure(CasErrc::InternalInvariant, error.what(), "continuity_with_limit");
}

引用了 classify_continuity_point_value(), LMCAS::context, continuity_point_value(), continuity_with_limit(), LMCAS::Result< ContinuityType >::failure(), LMCAS::InternalInvariant, LMCAS::detail::make_expression_ptr(), LMCAS::detail::no_facts(), LMCAS::detail::node(), LMCAS::point, LMCAS::Removable, LMCAS::detail::substitute_node(), LMCAS::Result< ContinuityType >::success() , 以及 LMCAS::value.

被这些函数引用 continuity_from_limits() , 以及 continuity_with_limit().

函数调用图:

这是这个函数的调用关系图:

select_continuity_branch()

Result< detail::SymbolicNodePtr > LMCAS::anonymous_namespace{calculus_continuity.cpp}::select_continuity_branch	(	const PiecewiseNode &	piecewise,
		const FactsQuery &	facts,
		const AssumptionContext &	assumptions,
		ComputationContext &	context )

在文件 calculus_continuity.cpp 第 15 行定义.

                                                                       {
    for (const auto& branch : piecewise.branches()) {
        auto access = context.consume_steps(1, "continuity_at");
        if (!access) { return Result<detail::SymbolicNodePtr>::failure(access.error()); }
        auto defined = detail::query_definedness(branch.condition, facts, Domain::Real, context);
        if (!defined) { return Result<detail::SymbolicNodePtr>::failure(defined.error()); }
        const auto truth = defined.value() == Tribool::True
            ? assumptions.evaluate_condition(detail::expression_from_node(branch.condition))
            : Tribool::Unknown;
        if (truth == Tribool::Unknown) {
            return Result<detail::SymbolicNodePtr>::failure(CasErrc::Inconclusive,
                "point-value branch is undecided", "continuity_at");
        }
        if (truth == Tribool::True) { return branch.expression; }
    }
    return piecewise.default_expr();
}

引用了 LMCAS::PiecewiseNode::branches(), LMCAS::context, LMCAS::PiecewiseNode::default_expr(), LMCAS::detail::expression_from_node(), LMCAS::Result< T >::failure(), LMCAS::Inconclusive, LMCAS::detail::query_definedness(), LMCAS::Real, select_continuity_branch(), LMCAS::True , 以及 LMCAS::Unknown.

被这些函数引用 continuity_point_value() , 以及 select_continuity_branch().

函数调用图:

这是这个函数的调用关系图: