clamping values

I'm looking at dot3 bumpmapping and at one point during the info I'm looking at it says that an integer between [0,255] must be clamped to [-1.0,1.0].

float clamp(unsigned char i)
{
	float temp;

	temp = (i / 255.0f);	// first, clamp the value to [0,1]
	temp *= 2;		// multiply by 2
	temp -= 1.0f;		// subtract 1

	return temp;
}

This is what I did, and it initially looks to be fine (works with values 0,65,127,191,255). I was wondering if there was a generalised forumla for clamping a value between [a,b] to [c,d]. I took a look on mathworld, but I'm not really sure what to search for.