Is it possible to somehow(ajax/...) upload files larger than upload_max_filesize(128M) and post_max_filesize(128M)(and smaller than 1GB)? I've tried to google it but I haven't found nothing except changing php.ini configuration(I can't do that, I use shared webhosting).
I appreciate any clues
If you are supporting modern browsers you can use the FileReader API to slice the files. This allows you to slice your file into an arbitrary number of small slices. You'll never run into the upload_max_filesize or post_max_filesize.
You will need to add some logic to reassemble the slices server-side but this isn't very involved.
Maybe you could change the settings by ini_set. if the host did not disable the function ini_set in the global php.ini config.