The CPU has onle accumulator which instructions act on. The argument is normally an address. The relevant instructions for this code snippet is:
AD - Add the value pointed to by the argument to the accumulator
TS - Transfer to storage. Write the accumulator to the argument
TCF - Transfer control to fixed memory. Jumps to an instruction in fixed storage
DOUBLE - Assembler macro compiling to AD A. I.e. double the accumulator.
XCH - This exchanges the value in the accumulator with the argument
INDEX - Adjust the address used in the next instruction by the argument
COM - Complements the accumulator. Note that the AGC uses one's complement arithmetic, so this negates the value.
EXTEND - Indicate that the next instruction is an extended instruction
MP - Multiply the accumulator with the argument
The final instruction is TS Q which jumps to the location stored in the Q register. This is the return address which is updated by the TS instruction. In other words, TS can be used both as a regular jump as well as being used as a function call, depending on what the destination does with the Q register.
I hope this helps you analyse the code further. I haven't spent much time looking at the code itself, so I am not going to attempt an analysis right now.
Of course, in many places in the code you need values outside of this range and the actual number represented is scaled by some factor. However, the CPU has no internal representation of the scale factor (i.e. the exponent bits in a floating point number) so the programmer had to manually manage this.
I can strongly recommend this book, if you're interested in the AGC: http://www.apolloguidancecomputer.com/
https://news.mit.edu/2016/scene-at-mit-margaret-hamilton-apo...
Scan of Luminary - Lunar Module source code https://archive.org/details/Luminary99001J2k60/page/n979/mod...