There are some ambiguities in your post that should be cleared up. First, a GL_SHORT type can hold negative values. It is not restricted to positive values. However, when converting an integer color value to a color of type GLclamp (the normal [0, 1] range for low dynamic range color), it maps integer 0 to 0.0,  and the maximum possible integer value to 1.0. So a GL_SHORT can only represent low dynamic range coor values in the range [0, 32k]. It can store negative values, but they are all mapped to color value 0.

So don't confuse clamped color values and GL_SHORT and its ability to store negative values.

The key here is to store color values in a format that is not clamped. I am not sure at the moment, but I think it is enought o change the internal format to either an integer format or a floating point format. For example, the internal format GL_RGBA32F should make a non-clamped RGBA floating point texture, or GL_RGBA16I for a 16-bit signed integer texture.

There are some ambiguities in your post that should be cleared up. First, a GL_SHORT type can hold negative values. It is not restricted to positive values. However, when converting an integer color value to a color of type GLclamp (the normal [0, 1] range for low dynamic range color), it maps integer 0 to 0.0,  and the maximum possible integer value to 1.0. So a GL_SHORT can only represent low dynamic range coor values in the range [0, 32k]. It can store negative values, but they are all mapped to color value 0.

So don't confuse clamped color values and GL_SHORT and its ability to store negative values.

The key here is to store color values in a format that is not clamped. I am not sure at the moment, but I think it is enought o change the internal format to either an integer format or a floating point format. For example, the internal format GL_RGBA32F should make a non-clamped RGBA floating point texture.