// Subroutine.
// Evaluates S = sum(N1 <= n < N2, a(n)/b(n) * (p(N1)...p(n))/(q(N1)...q(n)))
// and returns P = p(N1)...p(N2-1), Q = q(N1)...q(N2-1), B = B(N1)...B(N2-1)
// and T = B*Q*S (all integers). On entry N1 < N2.
// P will not be computed if a NULL pointer is passed.
// Subroutine.
// Evaluates S = sum(N1 <= n < N2, a(n)/b(n) * (p(N1)...p(n))/(q(N1)...q(n)))
// and returns P = p(N1)...p(N2-1), Q = q(N1)...q(N2-1), B = B(N1)...B(N2-1)
// and T = B*Q*S (all integers). On entry N1 < N2.
// P will not be computed if a NULL pointer is passed.