This is a port of these two patches combined:

vim-patch:8.1.1524: tests are silently skipped

Problem:    Tests are silently skipped.
Solution:   Throw an exception for skipped tests in more places.
https://github.com/vim/vim/commit/b0f94c1ff34d27d33aa9f96204985ea29c2eb0a1

vim-patch:8.1.1544: some balloon tests don't run when they can

Problem:    Some balloon tests don't run when they can.
Solution:   Split GUI balloon tests off into a separate file. (Ozaki Kiichi,
            closes vim/vim#4538)  Change the feature check into a command for
            consistency.
https://github.com/vim/vim/commit/b46fecd3454399f8ebdc5055302e4bfc5a10f98b

Omit test_lua.vim: previous patches are N/A
Omit test_memory_usage.vim: previous patches are N/A
Omit test_textprop.vim: previous patches are N/A
Omit test_winbar.vim: previous patches are N/A
Omit test_termcodes.vim: mostly N/A
Skip Test_mouse_positon() because it uses test_setmouse().
Cannot throw error in a Test_nocatch_ test.
Use latest `CheckFeature clipboard_working` for test_quotestar.vim

Problem:    Some eval functionality is not covered by tests.
Solution:   Add a few more test cases. (Masato Nishihata, closes vim/vim#4374)
https://github.com/vim/vim/commit/17aca707f92235b6f962e637e8073162d18e6de2

Test_expand() changes are required for v8.1.1921.
Test_call() and Test_cindent_func() are already ported.

Problem:    More functions can be used as methods.
Solution:   Make float functions usable as a method.
https://github.com/vim/vim/commit/93cf85f9ef02931de3f8c8e536a137da0b48b7dc

Fix atan2() doc typo (patch referred to it as atan()).
Adjust Test_fmod() method test to expect "str2float('nan')".

Problem:    It is not easy to check for infinity.
Solution:   Add isinf(). (Ozaki Kiichi, closes vim/vim#3787)
https://github.com/vim/vim/commit/fda1bff39f89775b20a2d88ef3903656d52f66ad

Problem:    json_encode() does not handle NaN and inf properly. (David
            Barnett)
Solution:   For JSON turn them into "null".  For JS use "NaN" and "Infinity".
            Add isnan().
https://github.com/vim/vim/commit/f1b6ac72293e658bb6e68c5cfd926c405b1b6f34

Problem:    float2nr() is not exactly right.
Solution:   Make float2nr() more accurate.  Turn test64 into a new style test.
            (Hirohito Higashi, closes vim/vim#1688)

https://github.com/vim/vim/commit/863e80b4451b5102b41bebf9ddca3a420de746fa

Problem:    Still some float functionality is not covered by tests.
Solution:   Add more tests. (Dominique Pelle, closes vim/vim#1364)

https://github.com/vim/vim/commit/872004132f25cabe59352912889e042d6c7e6b4e

Problem:    str2nr() and str2float() do not always work with negative values.
Solution:   Be more flexible about handling signs. (LemonBoy, closes vim/vim#1332)
            Add more tests.

https://github.com/vim/vim/commit/08243d26d22ad44a857d02c90071578577b8a55d

Problem:    On MS-Windows some float functions return a different value when
            passed unusual values.  strtod() doesn't work for "inf" and "nan".
Solution:   Accept both results.  Fix str2float() for MS-Windows.  Also
            reorder assert function arguments.

https://github.com/vim/vim/commit/6247361101dcccc0c877e90ad67cd0cc83df7c68

Problem:    Several float functions are not covered by tests.
Solution:   Add float tests. (Dominique Pelle)

https://github.com/vim/vim/commit/453b576ee5d32e9b8e6876712748ae01f9be68dd