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The octonion_test.cpp test program tests octonions specialisations for float, double and long double (sample output).
If you define the symbol BOOST_OCTONION_TEST_VERBOSE, you will get additional output (verbose output); this will only be helpful if you enable message output at the same time, of course (by uncommenting the relevant line in the test or by adding --log_level=messages to your command line,...). In that case, and if you are running interactively, you may in addition define the symbol BOOST_INTERACTIVE_TEST_INPUT_ITERATOR to interactively test the input operator with input of your choice from the standard input (instead of hard-coding it in the test).