ASA109 is a FORTRAN90 library which "inverts" the incomplete Beta function, by Cran, Martin and Thomas.
Given a value of the incomplete Beta function, it can determine the argument that produced that value.
ASA109 is Applied Statistics Algorithm 109.
ASA109 is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.
ASA063, a FORTRAN90 library which evaluates the incomplete Beta function.
ASA226, a FORTRAN90 library which evaluates the CDF of the noncentral Beta distribution.
ASA310, a FORTRAN90 library which computes the CDF of the noncentral Beta distribution.
BETA_NC, a FORTRAN90 library which evaluates the CDF of the noncentral Beta distribution.
TEST_VALUES, a FORTRAN90 library which stores a few values of various mathematical functions.
TOMS179, a FORTRAN90 library which evaluates the incomplete Beta function.
TOMS708, a FORTRAN90 library which evaluates the incomplete Beta function.
Original FORTRAN77 version by GW Cran, KJ Martin, GE Thomas; FORTRAN90 version by John Burkardt.
You can go up one level to the FORTRAN90 source codes.