How to access class constants in Twig?

Just to save your time. If you need to access class constants under namespace, use

{{ constant('Acme\\DemoBundle\\Entity\\Demo::MY_CONSTANT') }}

{% if var == constant('Namespace\\Entity::TYPE_PERSON') %}
{# or #}
{% if var is constant('Namespace\\Entity::TYPE_PERSON') %}

See documentation for the constant function and the constant test.