The only mention the Constitution actually makes of behavior resembling torture is found in the 8th Amendment which prohibits "cruel and unusual punishment." That's it, cruel and unusual punishment. It's the only form of torture that the Constitution specifically prohibits.
In other words, the Constitution prohibits torture when it's used as a form of punishment but, if you know where that bomb is hidden or where those kidnappers are hanging out, or we think you might know, trying to get some information from you is not 'punishment' and the Constitution is silent on what we can do to you.
Severe pain, electric shocks, waterboarding, whatever. Think it's immoral or unethical to do that kind of stuff? Well, ok. Think what you like but the Constitution doesn't prohibit it no matter what you've been told. It's almost as though the Constitution was written by folks who were thinking about what they would do if their own kids were taken or there was evidence that a bomb was going to be planted in their behinds.
And finally, while it is nevertheless true that virtually all international treaties continue to prohibit all forms of torture, it is also true that we can withdraw from these treaties a lot more easily than we can amend the Constitution. Maybe something to sit down...and think about some time..