First you have to decide how important keeping your job is.
If you need this job, I think you are better off figuring out how you can accept what is and learn how to not get so frustrated. You will need to repeat over and over until you really get it… “My boss is the way he is, not the way I want him to be.” Then you can use his abrasive ways to practice staying centered, loving, and good at attending to your job description, rather than getting caught in his awful style.
If you know in your heart you need to speak up and are willing to take a stand and risk getting terminated or paying consequences in terms of promotions, etc., then go ahead and figure out in advance what you need to say.
Before offering unsolicited feedback, you must ask and receive permission or else there will be little reception and you won’t attain the desired result.
When speaking follow Attitude Reconstruction’s 4 Rules of Communication — be specific, talk about yourself, and be kind, (that is, offer constructive suggestions), and lastly listen to what he might have to say.
Do some planning in advance so you get clear about specific issues and what you want to offer. Think about writing your suggestions out, since many people are initially reactive and defensive and not able to truly listen. When it’s written, your boss can go back to glean your message (if he or she is up to it), though you risk the possibility of your words backfiring.
In order to make your days smoother, ask for specifics about any tasks that are assigned so you can do them to the best of your ability. Focus on your job. Clarify assumptions so you don’t do extraneous tasks. Don’t join coworkers in swapping stories about what a horrible boss he is. Focus on the positive.
You can get enlightened if you remember how isolated, unhappy, and insecure this poor fellow probably is under his bluster and irrational behavior. Then you can stay in your flow rather than losing your balance due to your bosses’ own unexpressed fear, anger, and sadness.
Here are a few last radical thoughts. Make a friend. Invite him to lunch. Tell him it might be a tough job and see if he opens up. Appreciate what he does do well.