GB disassembler takes in a 16 bit address internally as disassembly is expected to use System Bus for addressing (and using other domains typically makes no sense wrt addressing). I'm not quite sure if this is possible to fix per se, as disassembly would be expected to roll over at 0xFFFF -> 0x0000 for System Bus and addressing otherwise within the disassembly would be completely wrong unless System Bus is used (maybe disassembler allowing for multiple domains could be considered a misfeature here?).
memory.getmemorydomainsize("ROM")
--> 131072
emu.disassemble(0x1C000, "ROM")
--> "disasm": "C000: 5B ld e, e" "length": "1"Here's a problem I've been thinking about: ---- You start with a positive number N>1 and want to get down to 1 in a number of moves. Each move consists of going from the current number to a smaller positive number random based on uniform randomness. That is, from k, randomly go to a number 1, 2, ... , k-1 , each with equal probability. Keep doing this until you reach the number 1. For example, starting from 8, a sample three-move sequence is 8→5→2→1: Starting with 8, go from 8→5 (5 is chosen with probability 1/7), then from 5→2 (2 is chosen with probability 1/4), then from 2→1 (1 is chosen with probability 1). Starting from N, what is the expected number of moves to reach the number 1?
How the heck did they get literally every fact about us wrong?
Actually I wasn't sure about your intuitive answer since it wasn't so intuitive to me. But it works out somehow! (at least as an approximation)
This one looks like a simple optimization for me. Suppose you want to do it using n steps. You want to maximize a product of cosines whose argument sums to a given number. To do this you can apply Jensen's inequality for the function log(cos(x)). Since it's concave for 0 < x < pi/2, we find that cos(x/n)^n >= prod_n cos(x_n), when the sum of all x_n is x, and equality happens when each x_n = x/n. Essentially, what all this means is that to maximize the product of cosines given that all angles sum to some fixed amount, you must choose the arguments of the cosines to divide the interval evenly. So essentially you want to find the maximum of a^n*cos(pi/2n)^n, for a = 0,99. This sequence has a maximum because it's decreasing for large n.
Well, I must be doing something wrong then. I tested several games and simply get no input at all. Open a game - open Lua Console - load mouse2move script ...anything else I need to do? I can see on the Debugscreen that it produces inputs but no game receieves any. "Display Input" doesnt show anything. TAStudio doesnt record any inputs either.
"find a lower bound on the number of pollsters required".
Edit 3: After editing my post and refreshing Latest Posts, this instance of the glitch went away. I'm not sure whether refreshing the page or my edit had anything to do with it. Also, I'm using PageSize=30 to view the 30 most recent posts. Maybe that has something to do with it.I assume your actual question is why is the side HC the harmonic mean HM.
This seems especially difficult because radius r and line HC (the HM) don't appear to "communicate" with each other on the figure, nor do lines GC (the GM) and OH (AM minus HM). But maybe I'm missing something obvious.
(Of course, we can imagine max(a,b) as the "infinity-mean" and min(a,b) as the "-infinity-mean", naturally extending these definitions. Also, this isn't really a proof, but it does very quickly guide a viewer toward a proof.)
My question concerns the side HG, which is not labeled as any mean. We have two formulas for HG, evident from the figure:
HG^2 = r^2 - (AM-HM)^2
HG^2 = GM^2 - HM^2
Setting these two equal to each other yields the relation:
r^2 - (AM-HM)^2 = GM^2 - HM^2
which can be used as the last of seven equations relating the quantities. This is good enough on its own and requires no further explanation, but we can add those negative terms to both sides to make the equation more... "hypotenuse-like" (?):
r^2 + HM^2 = GM^2 + (AM-HM)^2
What I'm curious about, which may be very easy or very difficult (I'm not sure), is whether this new equation can be represented geometrically. Is there some way to swing these sides around on this figure such that the equation above is what is represented? It may be a silly question and may reveal how lazy I am, as it might be a simple step. I just don't see it immediately and don't care to rigorously investigate it.
Edit: Bonus points if you can provide a geometric justification for the version where we cancel HM^2 from both sides:
r^2 + 2*AM*HM = GM^2 + AM^2sorry if I am just too stupid. I can see how it works in the Debug mode and also think I get how all values work.. but, the game doesnt get any inputs. Do I have to check something first so that a Lua script is allowed to make inputs or something like that? Ive never used any script before :-/
Here's a link to the updated program. To cycle through the draw styles, press the D key. I've left the third draw style empty, but if you'd like to compare it with pixel by pixel, you can uncomment line 287. You can also display the magnetization and temperature by pressing space or enter, respectively.
The other minor update I have is to my fake words project. I had a "duhhhhhh!" moment and realized my method for adding new syllables was kind of ridiculous. The way they should be added, as far as my best guess, is to construct the network of syllables and add new syllables according to the product of their weights and total Huffman scores, the total number of bits used on those syllables. Unfortunately, I found editing my script rather confusing and I had to suppress a couple of errors so when I ran it for a few hours it only sort of worked. Some of the syllables it picked up were quite sensible: "abilitie", "ucle", "ously_", "ograph_", and "ologies_", for example. But the vast majority of the surviving syllables are just two characters in length, with only 56 (plus the original 27) being used at all, far too few to make me think that the program is working properly. Tons of other good syllables ("izations_", "ifying_", "super", "olog", "edly_", "ability_", "fulness", "ish_", etc.) are in my spreadsheet, but for some reason they have negative savings or zero instances. I've decided much of the program needs a rewrite. I'm planning on implementing an object oriented paradigm of data structures, which should be extremely well-suited to the directed graphs and Huffman trees involved in the project. If it works as well as I expect, I should be able to cut down significantly on the length of the program and make it much easier to debug. This is in addition to two or three other object oriented projects I have planned.
Edit: And I just now noticed that most individual letters pick up only ~200 instances, with some letters picking up 0. Yeah, this is broken.
Anyway, happy new year! I'm going to keep plugging away at these projects and I swear that I if I manage to follow through on them, you'll see some interesting results.Basically, I just copied all of the variables line-by-line. What I perhaps should have done instead was put both x and y values into a single table but... I didn't feel like it. Same request as above: run the script and tweak the parameters to your liking, then let me know what I should change.Language: lua-- The sign of a scalar. local function sign(x) return (x>0) and 1 or ((x<0) and -1 or 0) end -- Sums over a vector. local function sum(v) local total=0 for i=1,#v do total=total+v[i] end return total end -- Did we just press this key? local function justpressed(keys, last, button) return keys[button] and not(last[button]) end -- Inner product of two vectors. If not the same length, just uses the shorter of the two. To capture the most recent values, multiplies only the last elements. local function inner(v1, v2) local prod = {} for i=0,math.min(#v1, #v2)-1 do table.insert(prod, v1[#v1-i]*v2[#v2-i]) end return sum(prod) end -- Updates the mouse's history. local function updatemouse(history, axis) local curr=input.getmouse() table.remove(history, 1) table.insert(history, curr[axis]) return history end -- Returns the difference between adjacent x values, effectively the mouse velocity. local function getdeltas(history) local delta_x = {} for i=1,#history-1 do table.insert(delta_x, history[i+1]-history[i]) end return delta_x end -- Returns a sort of weighted average of the mouse's movement based on the window function. local function windowavg(v, window) local denom = sum(window) local num = inner(v, window) return num/denom end -- Makes a window function. Exponential with time. local function makewindow(length, lambda) local window={} for i=1,length do table.insert(window, math.exp(lambda*(i-length))) end return window end -- Updates the joypad input based on the threshold and its history. Also updates and returns the history. local function gameinput(threshold, mouseavg, joyhist, joyavg, buttons) local curr=false if math.abs(mouseavg)>threshold*(1+math.abs(joyavg)) then -- "1+math.abs(joyavg)" is just a guess. It maybe needs to be refined. curr=true end local lorr = sign(mouseavg) if curr then joypad.set({[buttons[lorr]]=curr}) end table.remove(joyhist, 1) table.insert(joyhist, curr and lorr or 0) return joyhist end -- Adjusts a single parameter according to whether we press some keys. local function adjustparam(param, keys, last, downkey, upkey, mini, maxi, interval, eps) eps=eps or 0.0001 if justpressed(keys, last, upkey) then param = (param>=maxi-eps) and maxi or param+interval elseif justpressed(keys, last, downkey) then param = (param<=mini+eps) and mini or param-interval end return param end local function updatevalues(last, mouselambda, joylambda, length, threshold, debugmode) local keys = input.get() mouselambda = adjustparam(mouselambda, keys, last, "Number6", "Number7", 0, 1, 0.1) joylambda = adjustparam(joylambda, keys, last, "Y", "U", 0, 1, 0.1) length = adjustparam(length, keys, last, "H", "J", 2, 10, 1) threshold = adjustparam(threshold, keys, last, "N", "M", 10, 50, 2) if justpressed(keys, last, "B") then gui.clearGraphics() debugmode = not(debugmode) end return keys, mouselambda, joylambda, length, threshold, debugmode end -- Initialization local last = input.get() local mouselambda = 0.2 local joylambda = 0.2 local length = 5 local threshold = 20 local mousestart = input.getmouse() local mousexhist, mouseyhist, joyxhist, joyyhist = {}, {}, {}, {} local buttonsx = {"Right", [-1]="Left"} local buttonsy = {"Down", [-1]="Up"} -- Inverted because the y coordinate is read from the top of the screen. local debugmode = false for i=1,10 do -- Keep a history of the last 10 mouse locations and joypad buttons. Changing length only changes the window. table.insert(mousexhist, mousestart.X) table.insert(mouseyhist, mousestart.Y) table.insert(joyxhist, 0) table.insert(joyyhist, 0) end while true do mousexhist = updatemouse(mousexhist, "X") mouseyhist = updatemouse(mouseyhist, "Y") delta_x = getdeltas(mousexhist) delta_y = getdeltas(mouseyhist) mousewindow = makewindow(length-1, mouselambda) local mousexavg = windowavg(delta_x, mousewindow) local mouseyavg = windowavg(delta_y, mousewindow) local joywindow = makewindow(length, joylambda) -- Note that the joypad window and mouse window are different lengths. I assume this either doesn't matter or makes very little difference. local joyxavg = windowavg(joyxhist, joywindow) local joyyavg = windowavg(joyyhist, joywindow) joyxhist = gameinput(threshold, mousexavg, joyxhist, joyxavg, buttonsx) joyyhist = gameinput(threshold, mouseyavg, joyyhist, joyyavg, buttonsy) emu.frameadvance() keys, mouselambda, joylambda, length, threshold, debugmode = updatevalues(keys, mouselambda, joylambda, length, threshold, debugmode) -- Print all the parameters and history for troubleshooting purposes. if debugmode then gui.drawRectangle(0,0,240,160,"gray","gray") gui.pixelText(180,20,mouselambda) gui.pixelText(180,28,joylambda) gui.pixelText(180,36,length) gui.pixelText(180,44,threshold) for i=1,length-1 do gui.pixelText(180,44+8*i,delta_x[i]) gui.pixelText(20,44+8*i,delta_y[i]) gui.pixelText(200,44+8*i,joyxhist[i]) gui.pixelText(40,44+8*i,joyyhist[i]) gui.pixelText(220,44+8*i,mousexhist[i]) gui.pixelText(60,44+8*i,mouseyhist[i]) end gui.pixelText(200,44+8*length,joyxhist[length]) gui.pixelText(40,44+8*length,joyyhist[length]) gui.pixelText(220,44+8*length,mousexhist[length]) gui.pixelText(60,44+8*length,mouseyhist[length]) end end
I've briefly run this in debug mode to verify that it is at least mostly working, but you'll want to tweak the parameters yourself. There are four main parameters: mouselambda, joylambda, length, and threshold.Language: lua-- The sign of a scalar. local function sign(x) return (x>0) and 1 or ((x<0) and -1 or 0) end -- Sums over a vector. local function sum(v) local total=0 for i=1,#v do total=total+v[i] end return total end -- Did we just press this key? local function justpressed(keys, last, button) return keys[button] and not(last[button]) end -- Inner product of two vectors. If not the same length, just uses the shorter of the two. To capture the most recent values, multiplies only the last elements. local function inner(v1, v2) local prod = {} for i=0,math.min(#v1, #v2)-1 do table.insert(prod, v1[#v1-i]*v2[#v2-i]) end return sum(prod) end -- Updates the mouse's history. local function updatemouse(history) local curr=input.getmouse() table.remove(history, 1) table.insert(history, curr.X) return history end -- Returns the difference between adjacent x values, effectively the mouse velocity. local function getdeltas(history) local delta_x = {} for i=1,#history-1 do table.insert(delta_x, history[i+1]-history[i]) end return delta_x end -- Returns a sort of weighted average of the mouse's movement based on the window function. local function windowavg(v, window) local denom = sum(window) local num = inner(v, window) return num/denom end -- Makes a window function. Exponential with time. local function makewindow(length, lambda) local window={} for i=1,length do table.insert(window, math.exp(lambda*(i-length))) end return window end -- Updates the joypad input based on the threshold and its history. Also updates and returns the history. local function gameinput(threshold, mouseavg, joyhist, joyavg) local curr=false if math.abs(mouseavg)>threshold*(1+math.abs(joyavg)) then -- "1+math.abs(joyavg)" is just a guess. It maybe needs to be refined. curr=true end local lorr = sign(mouseavg) local buttons = {"Right", [-1]="Left"} if curr then joypad.set({[buttons[lorr]]=curr}) end table.remove(joyhist, 1) table.insert(joyhist, curr and lorr or 0) return joyhist end -- Adjusts a single parameter according to whether we press some keys. local function adjustparam(param, keys, last, downkey, upkey, mini, maxi, interval, eps) eps=eps or 0.0001 if justpressed(keys, last, upkey) then param = (param>=maxi-eps) and maxi or param+interval elseif justpressed(keys, last, downkey) then param = (param<=mini+eps) and mini or param-interval end return param end local function updatevalues(last, mouselambda, joylambda, length, threshold, debugmode) local keys = input.get() mouselambda = adjustparam(mouselambda, keys, last, "Number6", "Number7", 0, 1, 0.1) joylambda = adjustparam(joylambda, keys, last, "Y", "U", 0, 1, 0.1) length = adjustparam(length, keys, last, "H", "J", 2, 10, 1) threshold = adjustparam(threshold, keys, last, "N", "M", 10, 50, 2) if justpressed(keys, last, "B") then gui.clearGraphics() debugmode = not(debugmode) end return keys, mouselambda, joylambda, length, threshold, debugmode end -- Initialization local last = input.get() local mouselambda = 0.2 local joylambda = 0.2 local length = 5 local threshold = 20 local mousestart = input.getmouse() mousestart=mousestart.X local mousehist, joyhist = {}, {} local debugmode = false for i=1,10 do -- Keep a history of the last 10 mouse locations and joypad buttons. Changing length only changes the window. table.insert(mousehist, mousestart) table.insert(joyhist, 0) end while true do mousehist = updatemouse(mousehist) delta_x = getdeltas(mousehist) mousewindow = makewindow(length-1, mouselambda) mouseavg = windowavg(delta_x, mousewindow) joywindow = makewindow(length, joylambda) -- Note that the joypad window and mouse window are different lengths. I assume this either doesn't matter or makes very little difference. joyavg = windowavg(joyhist, joywindow) joyhist = gameinput(threshold, mouseavg, joyhist, joyavg) emu.frameadvance() keys, mouselambda, joylambda, length, threshold, debugmode = updatevalues(keys, mouselambda, joylambda, length, threshold, debugmode) -- Print all the parameters and history for troubleshooting purposes. if debugmode then gui.drawRectangle(0,0,240,160,"gray","gray") gui.pixelText(180,20,mouselambda) gui.pixelText(180,28,joylambda) gui.pixelText(180,36,length) gui.pixelText(180,44,threshold) for i=1,length-1 do gui.pixelText(180,44+8*i,delta_x[i]) gui.pixelText(200,44+8*i,joyhist[i]) gui.pixelText(220,44+8*i,mousehist[i]) end gui.pixelText(200,44+8*length,joyhist[length]) gui.pixelText(220,44+8*length,mousehist[length]) end end