A bit less sophisticated than its advanced counterpart, the fx-4000P, the fx-3900P is nevertheless a capable programmable scientific calculator. Its 100-step program memory is a bit cramped, but its programming model is comprehensive, and it features the same full compliment of scientific functions as the fx-4000P.

Limited program memory means that the programmer needs to be innovative. For instance, if you wish to compute the Gamma function, an algorithm requiring a lot of constants will not do; constants take up memory, either in the form of program steps or using up number registers. Fortunately, I recently received an e-mail from Robert H. Windschitl who wrote about a compact approximation of Stirling's formula. With his algorithm, the following 100-step program computes the logarithm of the Gamma function to 9+ digits of accuracy across its entire domain, including negative arguments for which the function is defined. (Negative arguments require that you first place the calculator in radians mode in order to get the correct result.)

Ans→A:
Abs A→B:
1→C:
Lbl 1:
BC→C:
B+1→B:
9>B⇒Goto 1:
(ln (Bsinh B-1+1÷810÷B²²÷B²)÷2+ln B-1)B+ln (2π÷B)÷2-ln C→C:
0>A⇒ln (-π/A/sin πA)-C->C:
C