exponentiate a matrix

I have a rate matrix say Q. It has only real eigen values.
The trouble is: I want to exponentiate the matrix to a small power. In
other worlds, the Exp(Q*power) is very close to an Identity matrix in a
sense that the off diagonal are very close to zero, but diagonal is
very close 1.

I used the GNU Scientific library, but it occasionally gaves negative
entries when the powers are small. Exp(Q*power) is a transition
probability matrix, the entries shouldn't be negative.

Are there other packages in C that can deal with high precision
calculations in matrix?

Thanks for any comments

.

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