glsl infinity constant

Like Nicol mentioned, there are no pre-defined constants.

However, from OpenGL 4.1 on, your solution is at least guaranteed to work and correctly generate an infinite value.

See for example in glsl 4.4:

4.7.1 Range and Precision

...

However, dividing a non-zero by 0 results in the appropriately signed IEEE Inf: If both positive and negative zeros are implemented, the correctly signed Inf will be generated, otherwise positive Inf is generated.

Be careful when you use an older version of OpenGL though:

For example in glsl 4.0 it says:

4.1.4 Floats

...

Similarly, treatment of conditions such as divide by 0 may lead to an unspecified result, but in no case should such a condition lead to the interruption or termination of processing.

There are no pre-defined constants for it, but there is the isinf function to test if something is infinity.

While I'm at it, are there constants for other things like FLT_MAX FLT_EPSILON etc the way there are in C?

No, there are not.

This might work?

const float pos_infinity = uintBitsToFloat(0x7F800000);
const float neg_infinity = uintBitsToFloat(0xFF800000);

"If the encoding of a floating point infinity is passed in parameter x, the resulting floating-point value is the corresponding (positive or negative) floating point infinity"