Episode 4: “A Rocket Ship That You Control”
In the last episode we put a rocketship on the screen, now it's time to add controls to its. Because, of course, this is one of the most compelling promises made by Computer Space. Also, some refinements…
For a beginning, we tweak the outline of the rocket ship, we already have, just a little bit. Essentially, we move up the last three rows of dots up by a grid unit to make it a bit bulkier. Also, we adjust the scaling (sadly, it's not just a fraction of a power of 2 of the unit vector and we've to add some components). Same applies for the offset of the tip, providing the perceptual pivoting point of our ship. Finally, we increase the brightness level of the rocket display, mostly for a larger dot size.
With this in place, we turn to the graphics of the exhaust flames of our litlle spaceship.
The thrust animation in Computer Space consists of just two pixels drawn alternately at the stern of the ship. Should be easy to implement, shouldn't it? — Not so, as may be guessed by this introduction: At a closer inspection of footage of the game, we're thrown back into the Heisenberg uncertainty of Computer Space graphics, once again, as shapes vary with rotation. (We may call this the Bushnell-Dabney Uncertainty of electronically generated visuals.)
As may be observed, the exhausts are much more accentuated at horizontal or diagonal rotational angles than in a close to vertical position of the ship, where they appear somewhat compressed and also closer to the vertical center of the rocket.
We settle for a compromise — and, of course, it's more on the prominent side, for effects. By this we arrive at the final form of our spaceship:
With the thrusting animation in place, we're ready to apply any player contolled dynamics to our little ship. As Computer Space has it's spaceship at a constant velocity, this is more or less about updating the values of delta x and delta y to a scaled amount of the unit vector (sine and cosine of the rotational angle) each time the player engages the thrust button. More or less — as there is more to this: Computer Space not only features a computer-like electronic device, but also a viscous space, where any newly applied dynamics just gradually come into effect.
We're facing two problems here: Constraining the velocity to a certain amount and implementing an accumulating acceleration. And, most important, we would like to avoid complex calculations, like square roots (as would be required for scaling a vector), for runtime's sake.
In order to do so, we come up with the following hack [ not by K.T. ;-) ]:
procedures: 1) scale the unit vector (sin for dx, cos for dy) to max velocity, store it. 2) scale this again for acceleration to be applied. 3) add old delta. 4) restrain the resulting components (for dx, dy) to the range of max velocity vector. (use the same method we've already used for the rotational angle.)
By this, we've arrived at a new value for
dy, respectively) that we can trust to not to exceed the maximum velocity. And this by a few shifts and additions/subtractions only! What's still missing, is a proper viscosity:
(cont.) 5) average with old delta (dx, dy) for viscosity. 6) store results (to be added as constant delta to position later).
With this in place, we are ready to actually burn some fuel and maneuver the ship accross the screen. Thanks to the method descibed above we arrive at a quite pleasing experience that isn't far from the original behavior.
As a final improvement, we put the scalings for max velocity and for the rocket's acceleration in a parameters table on top of our code for the ease of any adjustments, following Steve Russell's best practice (who did similar in Spacewar! 3.1).
▶ Experience the code live: www.masswerk.at/icss/.
The Dry Stuff — Implementation Details
Since the code has by now become a bit more complex, we wont go into verbose, descriptive details anymore, but rather refer any interested audiences to the comments in the code (see below).
However, it may be appropriate to introduce some more PDP-1 instructions for the benefit of the curious reader:
We're using a program flag (flag 5) to store, whether the ship is thrusting or not. (There are 6 program flags, 1–6, implemented in hardware. Flag 4 is also used for the console typewriter and we will avoid this one.) Instructions for setting and clearing flags are part of the operate group of instructions:
stf n ... set flag n (1...6) clf n ... clear flag n (1...6)
The operate group includes instruction to change the internal state of the CPU and it's registers, like:
cla ...... clear AC cma ...... complement AC cli ...... clear IO lat ...... load AC from testword switches hlt ...... halt nop ...... no operation opr ...... basic instruction code of operate group (syn. to nop)
Instructions of a group may be combined by microprogramming and will be executed in a single cycle. For this, we simply add the instruction codes (and substract the vale of the group,
opr, since only the 12 lower bits are used for microprogramming. The micro-sequence in which the instructions occur are hardwired into the CPU. Some of these microprogrammed instructions also enjoy a well known mnemonic:
clc = cma+cla-opr / clear AC and complement it (777777) cla stf 5 .... clear AC and set flag 5 at once
Another group of microprogrammable instructions is the skip group, used to branch on conditions:
sma ...... skip on minus AC (sign-bit set) spa ...... skip on plus AC sza ...... skip on zero AC spi ...... skip on plus IO szf n .... skip on flag n zero szs n0 .... skip sense switch n zero (n: 1...6) e.g., "zss 10" to skip on sense switch 1 zero
i-bit inverts the condition:
sza i .... skip on AC NOT zero szf i n ... skip on flag n set (not zero)
Again, skip conditions may be combined by microprogramming to form a union. Here, instruction "
szf" represents the basic instruction code of the group:
szm = sza sma-szf / skip on zero or minus AC
Having thus covered pretty much of the basic PDP-1 instructions, there are, we'll close our little PDP-1 101 for today.
And here's the code, so far:
ironic computer space 0.04 nl 2016-10-17 mul=mus div=dis define initialize A,B law B dap A term define index A,B,C idx A sas B jmp C term define swap rcl 9s rcl 9s term define load A,B lio (B dio A term define setup A,B law i B dac A term define count A,B isp A jmp B term /macros specific to the program define scale A,B,C lac A sar B dac C term define random lac ran rar 1s xor (355671 add (355671 dac ran term / Computer Space / Original arcade game by Nolan Bushnell and Ted Dabney, / Syzygy Engineering / Nutting Associates, 1971. /"A simulated space battle that pits / computer-guided saucers against / a rocket ship that you control." 3/ jmp sbf / ignore seq. break jmp a0 / start addr, use control boxes jmp a1 / alt. start addr, use testword controls /game parameters raa, 6, 2700 / rocket angular acceleration rvm, 7, sar 1s / scaling rocket max velocity rva, 10, sar 4s / scaling rocket acceleration ran, 11, 0 / random number /routine to flush sequence breaks, if they occur. sbf, tyi lio 2 lac 0 lsm jmp i 1 /sine-cosine subroutine - Adams associates /calling sequence= number in AC, jda sin or jdacos. /argument is between +/- +2 pi, with binary point to right of bit 3. /answer has binary point to right of bit 0. Time = 2.35-? ms. /changed for auto-multiply , ddp 1/19/63 cos, 0 dap csx lac (62210 add cos dac sin jmp .+4 sin, 0 dap csx lac sin spa si1, add (311040 sub (62210 sma jmp si2 add (62210 si3, ral 2s mul (242763 dac sin mul sin dac cos mul (756103 add (121312 mul cos add (532511 mul cos add (144417 mul sin scl 3s dac cos xor sin sma jmp csx-1 lac (377777 lio sin spi cma jmp csx lac cos csx, jmp . si2, cma add (62210 sma jmp si3 add (62210 spa jmp .+3 sub (62210 jmp si3 sub (62210 jmp si1 /subroutines for background display nos=77 /number of stars /table of stars coors (nos words, 9 bits x and 9 bits y) bst, . nos/ /setup (nos random coors starting at bst) bsi, dap bsx / deposit return address init bsc, bst / deposit first addr of bst in bsc bsl, random / get a new random number bsc, dac . / store it in current loc of st index bsc, (dac bst+nos, bsl / increment bsl, repeat at bgl for nos times bsx, jmp . / return /display background stars (displays every 2nd frame only) bg, dap bgx / deposit return address isp bgc / increment bgc, skip on positive bgx, jmp . / return law i 2 / load -2 into ac dac bgc / deposit in bgc to reset frame counter init bgl, bst / init bgl to first addr of stars table bgl, lac . / get coors of next star (x/y) cli / clear io scr 9s / shift low 9 bits in high 9 bits of io (x) sal 9s / move remaining 9 bits in ac in high part (y) add bgv / add vertical offset swap / swap contents of ac and io add bgh / add horizontal offset dpy-i / display a dot at coors in ac (x) and io (y) index bgl, (lac bst+nos, bgl / repeat the loop at bgl nos times jmp bgx / return bgc, 0 bgh, 0 bgv, 0 /here from start a0, law rcb /configure to read control boxes (sa 4) dap rcw jmp a2 a1, law rtw /configure to read testword (sa 5) dap rcw /start a new run a2, jsp bsi / initial setup of bg-stars dzm bgh / reset offsets of stars to zero dzm bgv /rocket reset ar, dzm \rth / rotational angle lac (-70000 dac \rpx / pos x cla dac \rpy / pos y dzm \rdx dzm \rdy /main loop fr0, load \ict, -4500 / initial instruction budget (delay) jsp bg / display background jsp rkt / rocket routine count \ict, . / use up rest of time of main loop jmp fr0 / next frame /player rocket routine rkt, dap rkx rcw, jsp . /read control word (ccw, cw, trust, fire) cla clf 5 -opr dio \cw /merge (or) spacewar player inputs rcr 4s ior \cw dac \cw lio \cw /parse and process rotation lac \rth /load angle spi /sign cleared in io? add raa /no, add angular acceleration ril 1s /next bit spi sub raa sma /normalize 0 >= angle >= 2Pi (311040) sub (311040 spa add (311040 dac \rth /update angle ril 1s /parse thrust input spi stf 5 /set flag 5 for thrust jda sin /get sin, store it in \sn dac \sn lac \rth jda cos /get cos, store it in \cs dac \cs szf i 5 /flag 5 set? update dx / dy jmp rp0 lac \sn /dx cma sar 7s xct rvm /apply scaling for max velocity dac \t1 xct rva /apply scaling for acceleration add \rdx /add old dx spa /is it positive? jmp . 6 /no, skip next 5 instr. sub \t1 /constrain positive vel. sma cla add \t1 jmp . 5 sub \t1 /constrain negative vel. spa cla add \t1 add \rdx /average with old dx for viscosity sar 1s dac \rdx /store updated dx lac \cs /same for dy sar 7s xct rvm dac \t1 xct rva add \rdy spa jmp . 6 sub \t1 sma cla add \t1 jmp . 5 sub \t1 spa cla add \t1 add \rdy sar 1s add \rdy rp0, scale \sn, 4s, \sn1 /get position of rocket tip sar 4s /offset x = (sin >> 4) - (sin >> 8) cma add \sn1 dac \sn1 scale \cs, 4s, \cn1 /offset y = (cos >> 4) - (cos >> 8) sar 4s cma add \cn1 dac \cn1 lac \rpx /update pos x (add dx) add \rdx dac \rpx sub \sn1 /subtract offset for tip, store it in \px dac \px lac \rpy /same for y add \rdy dac \rpy add \cn1 dac \py scale \sn, 7s, \sn4 /scaled sine 4 steps sar 1s add \sn4 dac \sn4 /sn4 = (sin >> 7) + (sin >> 8) dac \sm4 /sm4 for lateral offsets (will be complemented) sar 1s dac \sn2 /scaled sine 2 steps dac \sm2 sar 1s /scaled sine single step dac \sn1 dac \sm1 scale \cs, 7s, \cn4 /same for cosine sar 1s add \cn4 dac \cn4 dac \cm4 sar 1s dac \cn2 dac \cm2 sar 1s dac \cn1 dac \cm1 jsp rod /display it lac \ict /update instruction count add (1000 dac \ict rkx, jmp . /control word get routines /read control boxes rcb, dap rcx cli iot 11 rcx, jmp . /read testword rtw, dap rtx lat swap rtx, jmp . /rocket display / step rearwards - x add \sn1, y sub \cn1 / step outwards - x add \cm1, y add \sm1 / step inwards - x sub \cm1, y sub \sm1 define disp dpy-i 100 /display a dot at brightness level +1 term rod, dap rox stf 6 /set flag 6 lac \px lio \py disp rop, swap /y +3, x +3 sub \cn2 sub \cn1 add \sm2 add \sm1 swap add \sn2 add \sn1 add \cm2 add \cm1 disp swap /y +4, x +2 sub \cn4 add \sm2 swap add \sn4 add \cm2 disp swap /y +4, x +1 sub \cn4 add \sm1 swap add \sn4 add \cm1 disp swap /y +4, x -1 sub \cn4 sub \sm1 swap add \sn4 sub \cm1 disp swap /y +5, x +4 sub \cn4 sub \cn1 add \sm4 swap add \sn4 add \sn1 add \cm4 disp swap /y +1, x -6 sub \cn1 sub \sm4 sub \sm2 swap add \sn1 sub \cm4 sub \cm2 disp swap /y +4, x +3 sub \cn4 add \sm2 add \sm1 swap add \sn4 add \cm2 add \cm1 disp szf i 6 /flag 6 set? (skip on not zero) jmp rot clf 6 /clear flag 6 lac \cm1 /invert unit vector components cma dac \cm1 lac \sm1 cma dac \sm1 lac \cm2 cma dac \cm2 lac \sm2 cma dac \sm2 lac \cm4 cma dac \cm4 lac \sm4 cma dac \sm4 lac \px /load first pos lio \py jmp rop /second pass for other side rot, szf i 5 /no, flag 5 set? rox, jmp . /no, return swap /draw exhaust flame sub \sm4 /x -6 sub \sm2 swap sub \cm4 sub \cm2 dac \px /store position dio \py idx \rtc /increment a counter and check second least bit and (2 sza /is it zero? (state switch) jmp ro2 ro1, lac \py /state 1, display at y-1 add \cn1 swap lac \px sub \sn1 disp jmp rox ro2, lac \py /state 2, display at y+4 sub \cn4 swap lac \px add \sn4 disp jmp rox /jump to return constants variables start 4
That's all for this post.
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2016-10-17, Vienna, Austria
www.masswerk.at – contact me.
— This series is part of Retrochallenge 2016/10. —