add draw/update stat readout

surprisingly, update is most of my problem

collisiontest.p8

@@ -0,0 +1,229 @@
+pico-8 cartridge // http://www.pico-8.com
+version 42
+__lua__
+bx0=0
+by0=0
+bx1=127
+by1=127
+lx0=0
+ly0=0
+lx1=127
+ly1=127
+
+-->8
+
+function collides()
+	local tmin,tmax=0,1
+	
+	local ldx,ldy=lx1-lx0,ly1-ly0
+	
+	
+	-- x
+	if ldx==0 then
+		if (lx0<bx0 or lx0>bx1) return
+	else
+ 	local tx0=(bx0-lx0)/ldx
+ 	local tx1=(bx1-lx0)/ldx
+ 	if (tx0 > tx1) tx0,tx1=tx1,tx0
+ 	if (tmin < tx0) tmin=tx0
+ 	if (tmax > tx1) tmax=tx1
+ end
+ 
+	if ldy==0 then
+		if (ly0<by0 or ly0>by1) return
+	else
+ 	local ty0=(by0-ly0)/ldy
+ 	local ty1=(by1-ly0)/ldy
+ 	if (ty0 > ty1) ty0,ty1=ty1,ty0
+ 	if (tmin < ty0) tmin=ty0
+ 	if (tmax > ty1) tmax=ty1
+ end 
+ 
+ if (tmax < tmin) return
+ return tmin,tmax
+end
+
+
+-->8
+function _init()
+	poke(0x5f2d,1) -- enable mouse
+end
+
+function _bounce_screen(x)
+ return _bounce(x*128,128)
+end
+function _bounce(x,mx)
+	x=x%(mx * 2)
+	if (x>=mx)return mx-(x-mx)
+	return x
+end
+
+function _to_halfopen(x0,x1)
+ -- turn two numbers into a
+ -- half-open integer range
+ x0=flr(x0)
+ x1=flr(x1)
+ local lo=min(x0,x1)
+ local hi=max(x0,x1)
+ if (hi==lo) return lo,hi
+ return lo,hi-1
+end
+
+function _update60()
+ local t=time()/16
+ 
+	local bx0_=_bounce_screen(t*1)
+	local by0_=_bounce_screen(t*2)
+	local bx1_=_bounce_screen(t*3)
+	local by1_=_bounce_screen(t*4)
+	
+	bx0,bx1=_to_halfopen(bx0_,bx1_)
+	by0,by1=_to_halfopen(by0_,by1_)
+	
+	update_line()
+	
+	--[[
+ local lx0_=_bounce_screen(t*1.5)
+ local ly0_=_bounce_screen(t*2.5)
+ local lx1_=_bounce_screen(t*3.5)
+ local ly1_=_bounce_screen(t*4.5)
+	
+	lx0,lx1=lx0_,lx1_
+	ly0,ly1=ly0_,ly1_
+	]]--
+end
+
+was_down=false
+last_mx,last_my=nil,nil
+
+function update_line()
+ local mx,my=stat(32),stat(33)
+ local is_down=stat(34)!=0
+
+ if is_down then
+  if was_down then
+   lx1,ly1=mx,my
+  else
+  	lx0,ly0=mx,my
+  end
+ end
+ was_down=is_down
+ last_mx,last_my=mx,my
+end
+-->8
+function _draw()
+ cls(0)
+	rect(bx0,by0,bx1,by1,6)
+	--quickzot(lx1,ly1,2,lx1-lx0,ly1-ly0,10,9,8)
+ linefill(lx0, ly0, lx1, ly1, 2, 9)
+	line(lx0,ly0,lx1,ly1,2)
+	local cmin, cmax = collides()
+	if cmin then
+	 local dx,dy=lx1-lx0,ly1-ly0
+	 line(lx0 + dx*cmin,
+	      ly0 + dy*cmin,
+	      lx0 + dx*cmax,
+	      ly0 + dy*cmax,
+	      11)
+	 pset(lx0 + dx*cmin,
+	      ly0 + dy*cmin,
+	      12)
+	end
+	
+	pset(last_mx,last_my,7)
+end
+-->8
+function zot_one(x, y, r, ir, dx, dy, hot, warm)
+ local x0, y0 = x-dx, y-dy
+ local rx,ry,irx,iry=r*sgn(dx),r*sgn(dy),ir*sgn(dx),ir*sgn(dy)
+ if warm then
+  line(x0+irx,y0-ry,x+rx,y-iry,warm)
+  line(x0-rx,y0+iry,x-irx,y+ry,warm)
+  --line(x0-rx,y0-ry,x+rx,y+ry,warm)
+ end
+ line(x0,y0,x+rx,y-iry,hot)
+ line(x0,y0,x-irx,y+ry,hot)
+ --line(x0,y0,x+rx,y+ry,hot)
+end
+
+function zot(x,y,r,dx,dy,hot,warm,cold)
+ local x0,y0,sdx,sdy=x-dx,y-dy,sgn(dx),sgn(dy)
+ local rx,ry=r*sdx,r*sdy
+ if cold then
+  rectfill(x0-rx,y0-ry,x0+rx,y0+ry,cold)
+  local sdxh,sdyh=sdx/2,sdy/2
+  line(x0-rx-sdxh,y0+ry+sdyh,x-rx,y+ry,cold)
+  line(x0+rx+sdxh,y0-ry-sdyh,x+rx,y-ry,cold)
+ end
+ for i=-r,r do
+  line(x0+i*sdx,y0-ry,x+rx,y-i*sdy,warm)
+  line(x0-rx,y0+i*sdy,x-i*sdx,y+ry,warm)
+ end
+ for i=-r,r do
+  line(x0,y0,x+rx,y-i*sdy,hot)
+  line(x0,y0,x-i*sdx,y+ry,hot)
+ end
+end
+
+function quickzot(x,y,r,dx,dy,hot,warm,cold)
+ local x0, y0, r2 = x-dx, y-dy, r/2
+ rectfill(x0-0.5-r2, y0-0.5-r2, x0+r2+0.5, y0+r2+0.5, cold)
+ local a = atan2(dx,dy)-0.25
+ local tdx,tdy=cos(a), sin(a)
+ for i=-r*0.65,r*0.65,0.65 do
+  line(x0+i*tdx, y0+i*tdy, x+i*tdx, y+i*tdy, warm)
+ end
+ rectfill(x-r2,y-r2,x+r2,y+r2,hot)
+end
+
+-- linefill x0 y0 x1 y1 r [col]
+-- draw a thicc line
+-- https://www.lexaloffle.com/bbs/?tid=39016
+function linefill(ax,ay,bx,by,r,c)
+ if(c) color(c)
+ local dx,dy=bx-ax,by-ay
+ -- avoid overflow
+ -- credits: https://www.lexaloffle.com/bbs/?tid=28999
+ local d,n = abs(dx),abs(dy)
+ if (d<n) d,n=n,d
+ n/=d
+ d*=sqrt(n*n+1)
+ if(d<0.001) return
+ local ca,sa=dx/d,-dy/d
+
+ -- polygon points
+ local s={
+  {0,-r},{d,-r},{d,r},{0,r}
+ }
+ local u,v,spans=s[4][1],s[4][2],{}
+ local x0,y0=ax+u*ca+v*sa,ay-u*sa+v*ca
+ for i=1,4 do
+  local u,v=unpack(s[i])
+  local x1,y1=ax+u*ca+v*sa,ay-u*sa+v*ca
+  local _x1,_y1=x1,y1
+  if(y0>y1) x0,y0,x1,y1=x1,y1,x0,y0
+  local dx=(x1-x0)/(y1-y0)
+  if(y0<0) x0-=y0*dx y0=-1
+  local cy0=y0\1+1
+  -- sub-pix shift
+  x0+=(cy0-y0)*dx
+  for y=y0\1+1,min(y1\1,127) do
+   -- open span?
+   local span=spans[y]
+   if span then
+       rectfill(x0,y,span,y)
+   else
+       spans[y]=x0
+   end
+   x0+=dx
+  end
+  x0,y0=_x1,_y1
+ end
+end
+__gfx__
+00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
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magnitest.p8

@@ -0,0 +1,245 @@
+pico-8 cartridge // http://www.pico-8.com
+version 42
+__lua__
+--magnitest.p8
+--accuracy and perf tests for
+--vector calculation logic
+
+-- profiler says 67 cycles
+-- 39 lua, 28 system
+function bbs28999alg(dx, dy)
+  local d = max(abs(dx),abs(dy))
+  local n = min(abs(dx),abs(dy)) / d
+  return sqrt(n*n + 1) * d
+end
+
+-- profiler says 56 cycles
+-- 24 lua, 32 system
+function bbs28999algopt(dx, dy)
+  local d,n=abs(dx),abs(dy)
+  if (d<n) d,n=n,d
+  n/=d
+  return (n*n + 1)^0.5 * d
+end
+
+-- profiler says 54 cycles
+-- 26 lua, 28 system
+function bbs28999algopt2(dx, dy)
+  local d,n=abs(dx),abs(dy)
+  if (d<n) d,n=n,d
+  n/=d
+  return sqrt(n*n + 1) * d
+end
+
+
+-- profiler says 18 cycles
+-- 18 lua, 0 system
+function trigalg(dx, dy)
+ local s = sin(atan2(dx,dy))
+ if (s==0) return abs(dx)
+ return abs(dy/s)
+end
+-->8
+function _init()
+ gdx,gdy=0,0
+ acc=1
+ magnitude = 1
+ tresult=0
+ bresult=0
+ delta=0
+ dp=0
+end
+
+function _update60()
+ if (btn(0)) gdx -= acc
+ if (btn(1)) gdx += acc
+ if (btn(2)) gdy -= acc
+ if (btn(3)) gdy += acc
+ if (btn(4) and btn(5)) gdx,gdy=0,0
+ gdx=mid(-16000,16000,gdx)
+ gdy=mid(-16000,16000,gdy)
+
+ if btn() == 0 or btn(4) then
+  acc = 1
+ elseif btn(5) then
+  acc *= 1.05
+ else
+  acc *= 1.02
+ end
+ if (acc > 1024) acc=1024
+
+ local a,b=abs(gdx),abs(gdy)
+ if (b>a) a,b=b,a
+ magnitude = 1
+ while magnitude < a/64 do
+  magnitude *= 2
+ end
+
+ bresult=bbs28999algopt2(gdx,gdy)
+ tresult=trigalg(gdx,gdy)
+ delta=tresult-bresult
+ dp=(2*abs(delta)/abs(abs(bresult)+abs(tresult)))*100
+ if (delta == 0) dp=0
+end
+
+cols = {
+ 6,7,
+ [4]=10,
+ [8]=9,
+ [16]=4,
+ [32]=14,
+ [64]=15,
+ [128]=11,
+ [256]=12,
+ [512]=13,
+ [1024]=8,
+}
+
+function _draw()
+ cls()
+ camera()
+ print("x: "..tostr(gdx).."  y: "..tostr(gdy).."\nbase: "..tostr(bresult).."\ntrig: "..tostr(tresult).."\n\ndiff: "..tostr(delta).."\n   %:"..tostr(dp),0,0,13)
+ print("⬆️⬇️⬅️➡️:move  ❎:fast 🅾️:slow\n❎+🅾️:reset position",0,117,12)
+ camera(-63,-63)
+ line(0,0,gdx/magnitude,gdy/magnitude,cols[magnitude] or 2)
+ rectfill(0,0,gdx/magnitude,0,5)
+ rectfill(0,0,0,gdy/magnitude,5)
+end
+
+__gfx__
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profiling.p8

@@ -0,0 +1,501 @@
+pico-8 cartridge // http://www.pico-8.com
+version 42
+__lua__
+-- prof: cpu cycle counter v1.4
+--  BY PANCELOR
+--[[------------------------
+
+
+use this cart to precisely
+measure code execution time
+
+--------------------------------
+         ★ overview ★
+--------------------------------
+| tab 0 | usage guide          |
+| tab 1 | (internals)          |
+| tab 2 | your code here       |
+--------------------------------
+
+
+-----------------------
+-- ★ usage guide ★ --
+-----------------------
+
+
+웃: i have two code snippets;
+    which one is faster?
+
+🐱: edit the last tab with your
+    snippets, then run the cart.
+    it will tell you precisely
+    how much cpu it takes to
+    run each snippet.
+
+    the results are also copied
+    to your clipboard.
+
+
+
+웃: what do the numbers mean?
+
+🐱: the cpu cost is reported
+    as lua and system cycle
+    counts. look up stat(1)
+    and stat(2) for more info.
+
+    if you're not sure, just
+    look at the first number.
+    lower is faster (better)
+
+
+
+웃: why "{locals={9}}"
+    in the example?
+
+🐱: accessing local variables
+    is faster than global vars.
+
+    so if your test involves
+    local variables, simulate
+    this by passing them in:
+
+      prof(function(a)
+        sqrt(a)
+      end,{ locals={9} })
+
+    /!\     /!\     /!\     /!\
+    local values from outside
+    the current scope are also
+    slower to access! example:
+
+      global = 4
+      local outer = 4
+      prof(function(x)
+        local _ = x --fast
+      end,function(x)
+        local _ = outer --slow
+      end,function(x)
+        local _ = global --slow
+      end,{ locals={4} })
+    /!\     /!\     /!\     /!\
+
+
+
+웃: can i do "prof(myfunc)"?
+
+🐱: no, this sometimes gives
+    wrong results! always use
+    inline functions:
+
+      prof(function()
+        --code for myfunc here
+      end)
+
+    as an example, "prof(sin)"
+    reports "-2" -- wrong! but
+    "prof(function()sin()end)"
+    correctly reports "4"
+
+    (see the technical notes at
+    the start of the next tab
+    for a brief explanation.
+    technically, "prof(myfunc)"
+    will work if myfunc was made
+    by the user, but you will
+    risk confusing yourself)
+
+
+
+---------------
+ ★ method 2 ★
+---------------
+
+
+
+this cart is based on
+code by samhocevar:
+https://www.lexaloffle.com/bbs/?pid=60198#p
+
+if you do this method, be very
+careful with local/global vars.
+it's very easy to accidentally
+measure the wrong thing.
+
+here's an example of how to
+measure cycles (ignoring this
+cart and using the old method)
+
+  function _init()
+    local a=11.2 -- locals
+
+    local n=1024
+    flip()
+    local tot1,sys1=stat(1),stat(2)
+    for i=1,n do   end --calibrate
+    local tot2,sys2=stat(1),stat(2)
+    for i=1,n do local _=sqrt(a) end --measure
+    local tot3,sys3=stat(1),stat(2)
+
+    function cyc(t0,t1,t2) return ((t2-t1)-(t1-t0))*128/n*256/stat(8)*256 end
+    local lua = cyc(tot1-sys1,tot2-sys2,tot3-sys3)
+    local sys = cyc(sys1,sys2,sys3)
+    print(lua.."+"..sys.."="..(lua+sys).." (lua+sys)")
+  end
+
+run this once, see the results,
+then change the "measure" line
+to some other code you want
+to measure.
+
+note: wrapping the code inside
+"_init()" is required, otherwise
+builtin functions like "sin"
+will be measured wrong.
+(the reason is explained at
+the start of the next tab)
+
+
+
+---------------
+ ★ method 3 ★
+---------------
+
+
+
+another way to measure cpu cost
+is to run something like this:
+
+  function _draw()
+    cls(1)
+    local x=9
+    for i=1,1000 do
+      local a=sqrt(x) --snippet1
+  --    local b=x^0.5 --snippet2
+    end
+  end
+
+while running, press ctrl-p to
+see the performance monitor.
+the middle number shows how much
+of cpu is being used, as a
+fraction. (0.60 = 60% used)
+
+now, change the comments on the
+two code snippets inside _draw()
+and re-run. compare the new
+result with the old to determine
+which snippet is faster.
+
+note: every loop iteration costs
+an additional 2 cycles, so the
+ratio of the two fractions will
+not match the ratio of the 
+execution time of the snippets.
+but this method can quickly tell
+you which snippet is faster.
+
+
+
+]]
+
+-->8
+--[[ profiler.lua
+more info: https://www.lexaloffle.com/bbs/?tid=46117
+
+usage:
+  prof(function()
+    memcpy(0,0x200,64)
+  end,function()
+    poke4(0,peek4(0x200,16))
+  end)
+
+passing locals:
+  prof(
+    function(a,b)
+      local c=(a+1)*(b+1)-1
+    end,
+    function(a,b)
+      local c=a*b+a+b
+    end,
+    {locals={3,5}}
+  )
+
+getting global/local variables exactly right
+is very tricky; you should always use inline
+functions like above; if you try e.g. prof(sin)
+the results will be wrong.
+
+
+# minutiae / notes to self:
+---------------------------
+doing this at top-level is awkward:
+  for _=1,n do       end -- calibrate
+  for _=1,n do sin() end -- measure
+b/c sin is secretly local at top-level,
+so it gives a misleading result (3 cycles).
+do it inside _init instead for a
+more representative result (4 cycles).
+
+## separate issue:
+------------------
+if you call prof(sin), it gives the wrong result (-2 cycles) because
+it's comparing sin() against noop() (not truly nothing).
+but we want the noop() there for normal inline prof() calls,
+to avoid measuring the cost of the indirection
+(calling func() from inside prof() is irrelevant to
+how cpu-expensive func()'s body is)
+]]
+
+-- prof(fn1,fn2,...,fnN,[opts])
+--
+-- opts.locals: values to pass
+-- opts.name: text label
+-- opts.n: number of iterations
+function prof(...)
+  local funcs={...}
+  local opts=type(funcs[#funcs])=="table" and deli(funcs) or {}
+
+  -- build output string
+  local msg=""
+  local function log(s)
+    msg..=s.."\n"
+  end
+
+  if opts.name then
+    log("prof: "..opts.name)
+  end
+  for fn in all(funcs) do
+    local dat=prof_one(fn,opts)
+    log(sub("  "..dat.total,-3)
+      .." ("
+      ..dat.lua
+      .." lua, "
+      ..dat.sys
+      .." sys)")
+  end
+
+  -- copy to clipboard
+  printh(msg,"@clip")
+  -- print + pause
+  cls()
+  stop(msg)
+end
+
+function prof_one(func, opts)
+  opts = opts or {}
+  local n = opts.n or 0x200 --how many times to call func
+  local locals = opts.locals or {} --locals to pass func
+
+  -- we want to type
+  --   local m = 0x80_0000/n
+  -- but 8MHz is too large to fit in a pico-8 number,
+  -- so we do (0x80_0000>>16)/(n>>16) instead
+  -- (n is always an integer, so n>>16 won't lose any bits)
+  local m = 0x80/(n>>16)
+  assert(0x80/m << 16 == n, "n is too small") -- make sure m didn't overflow
+  local fps = stat(8)
+
+  -- given three timestamps (pre-calibration, middle, post-measurement),
+  --   calculate how many more CPU cycles func() took compared to noop()
+  -- derivation:
+  --   T := ((t2-t1)-(t1-t0))/n (frames)
+  --     this is the extra time for each func call, compared to noop
+  --     this is measured in #-of-frames -- it will be a small fraction for most ops
+  --   F := 1/30 (seconds/frame) (or 1/60 if this test is running at 60fps)
+  --     this is just the framerate that the tests run at, not the framerate of your game
+  --   M := 256*256*128 = 0x80_0000 = 8MHz (cycles/second)
+  --     (PICO-8 runs at 8MHz; see https://www.lexaloffle.com/dl/docs/pico-8_manual.html#CPU)
+  --   cycles := T frames * F seconds/frame * M cycles/second
+  -- optimization / working around pico-8's fixed point numbers:
+  --   T2 := T*n = (t2-t1)-(t1-t0)
+  --   M2 := M/n = (M>>16)/(n>>16) := m (e.g. when n is 0x1000, m is 0x800)
+  --   cycles := T2*M2*F
+  local function cycles(t0,t1,t2)
+    local diff = (t2-t1)-(t1-t0)
+    local e1 = "must use inline functions -- see usage guide"
+    assert(0<=diff,e1)
+    local thresh = 0x7fff.ffff/(m/fps)
+    local e2 = "code is too large or slow -- try profiling manually with stat(1)"
+    assert(diff<=thresh,e2)
+    return diff*(m/fps)
+  end
+
+  local noop = function() end -- this must be local, because func is local
+  flip() --avoid flipping mid-measurement
+  local atot,asys=stat(1),stat(2)
+  for _=1,n do noop(unpack(locals)) end -- calibrate
+  local btot,bsys=stat(1),stat(2)
+  for _=1,n do func(unpack(locals)) end -- measure
+  local ctot,csys=stat(1),stat(2)
+
+  -- gather results
+  local tot=cycles(atot,btot,ctot)
+  local sys=cycles(asys,bsys,csys)
+  return {
+    lua=tot-sys,
+    sys=sys,
+    total=tot,
+  }
+end
+
+-->8
+-- your code here
+
+--edit me:
+prof(function(dx,dy)
+  local d = max(abs(dx),abs(dy))
+  local n = min(abs(dx),abs(dy)) / d
+  return sqrt(n*n + 1) * d
+end,function(dx, dy)
+  local d,n=abs(dx),abs(dy)
+  if (d<n) d,n=n,d
+  n/=d
+  return (n*n + 1)^0.5 * d
+end,function(dx,dy)
+  local d,n=abs(dx),abs(dy)
+  if (d<n) d,n=n,d
+  n/=d
+  return sqrt(n*n + 1) * d
+end,function(dx,dy)
+ local s = sin(atan2(dx,dy))
+ if (s==0) return abs(dx)
+ return abs(dy/s)
+end,{ locals={3,4} })
+
+-- "locals" (optional) are
+-- passed in as args. see the
+-- usage guide for details.
+
+__label__
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+__sfx__
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zotprofiling.p8

@@ -0,0 +1,598 @@
+pico-8 cartridge // http://www.pico-8.com
+version 42
+__lua__
+-- prof: cpu cycle counter v1.4
+--  BY PANCELOR
+--[[------------------------
+
+
+use this cart to precisely
+measure code execution time
+
+--------------------------------
+         ★ overview ★
+--------------------------------
+| tab 0 | usage guide          |
+| tab 1 | (internals)          |
+| tab 2 | your code here       |
+--------------------------------
+
+
+-----------------------
+-- ★ usage guide ★ --
+-----------------------
+
+
+웃: i have two code snippets;
+    which one is faster?
+
+🐱: edit the last tab with your
+    snippets, then run the cart.
+    it will tell you precisely
+    how much cpu it takes to
+    run each snippet.
+
+    the results are also copied
+    to your clipboard.
+
+
+
+웃: what do the numbers mean?
+
+🐱: the cpu cost is reported
+    as lua and system cycle
+    counts. look up stat(1)
+    and stat(2) for more info.
+
+    if you're not sure, just
+    look at the first number.
+    lower is faster (better)
+
+
+
+웃: why "{locals={9}}"
+    in the example?
+
+🐱: accessing local variables
+    is faster than global vars.
+
+    so if your test involves
+    local variables, simulate
+    this by passing them in:
+
+      prof(function(a)
+        sqrt(a)
+      end,{ locals={9} })
+
+    /!\     /!\     /!\     /!\
+    local values from outside
+    the current scope are also
+    slower to access! example:
+
+      global = 4
+      local outer = 4
+      prof(function(x)
+        local _ = x --fast
+      end,function(x)
+        local _ = outer --slow
+      end,function(x)
+        local _ = global --slow
+      end,{ locals={4} })
+    /!\     /!\     /!\     /!\
+
+
+
+웃: can i do "prof(myfunc)"?
+
+🐱: no, this sometimes gives
+    wrong results! always use
+    inline functions:
+
+      prof(function()
+        --code for myfunc here
+      end)
+
+    as an example, "prof(sin)"
+    reports "-2" -- wrong! but
+    "prof(function()sin()end)"
+    correctly reports "4"
+
+    (see the technical notes at
+    the start of the next tab
+    for a brief explanation.
+    technically, "prof(myfunc)"
+    will work if myfunc was made
+    by the user, but you will
+    risk confusing yourself)
+
+
+
+---------------
+ ★ method 2 ★
+---------------
+
+
+
+this cart is based on
+code by samhocevar:
+https://www.lexaloffle.com/bbs/?pid=60198#p
+
+if you do this method, be very
+careful with local/global vars.
+it's very easy to accidentally
+measure the wrong thing.
+
+here's an example of how to
+measure cycles (ignoring this
+cart and using the old method)
+
+  function _init()
+    local a=11.2 -- locals
+
+    local n=1024
+    flip()
+    local tot1,sys1=stat(1),stat(2)
+    for i=1,n do   end --calibrate
+    local tot2,sys2=stat(1),stat(2)
+    for i=1,n do local _=sqrt(a) end --measure
+    local tot3,sys3=stat(1),stat(2)
+
+    function cyc(t0,t1,t2) return ((t2-t1)-(t1-t0))*128/n*256/stat(8)*256 end
+    local lua = cyc(tot1-sys1,tot2-sys2,tot3-sys3)
+    local sys = cyc(sys1,sys2,sys3)
+    print(lua.."+"..sys.."="..(lua+sys).." (lua+sys)")
+  end
+
+run this once, see the results,
+then change the "measure" line
+to some other code you want
+to measure.
+
+note: wrapping the code inside
+"_init()" is required, otherwise
+builtin functions like "sin"
+will be measured wrong.
+(the reason is explained at
+the start of the next tab)
+
+
+
+---------------
+ ★ method 3 ★
+---------------
+
+
+
+another way to measure cpu cost
+is to run something like this:
+
+  function _draw()
+    cls(1)
+    local x=9
+    for i=1,1000 do
+      local a=sqrt(x) --snippet1
+  --    local b=x^0.5 --snippet2
+    end
+  end
+
+while running, press ctrl-p to
+see the performance monitor.
+the middle number shows how much
+of cpu is being used, as a
+fraction. (0.60 = 60% used)
+
+now, change the comments on the
+two code snippets inside _draw()
+and re-run. compare the new
+result with the old to determine
+which snippet is faster.
+
+note: every loop iteration costs
+an additional 2 cycles, so the
+ratio of the two fractions will
+not match the ratio of the 
+execution time of the snippets.
+but this method can quickly tell
+you which snippet is faster.
+
+
+
+]]
+
+-->8
+--[[ profiler.lua
+more info: https://www.lexaloffle.com/bbs/?tid=46117
+
+usage:
+  prof(function()
+    memcpy(0,0x200,64)
+  end,function()
+    poke4(0,peek4(0x200,16))
+  end)
+
+passing locals:
+  prof(
+    function(a,b)
+      local c=(a+1)*(b+1)-1
+    end,
+    function(a,b)
+      local c=a*b+a+b
+    end,
+    {locals={3,5}}
+  )
+
+getting global/local variables exactly right
+is very tricky; you should always use inline
+functions like above; if you try e.g. prof(sin)
+the results will be wrong.
+
+
+# minutiae / notes to self:
+---------------------------
+doing this at top-level is awkward:
+  for _=1,n do       end -- calibrate
+  for _=1,n do sin() end -- measure
+b/c sin is secretly local at top-level,
+so it gives a misleading result (3 cycles).
+do it inside _init instead for a
+more representative result (4 cycles).
+
+## separate issue:
+------------------
+if you call prof(sin), it gives the wrong result (-2 cycles) because
+it's comparing sin() against noop() (not truly nothing).
+but we want the noop() there for normal inline prof() calls,
+to avoid measuring the cost of the indirection
+(calling func() from inside prof() is irrelevant to
+how cpu-expensive func()'s body is)
+]]
+
+-- prof(fn1,fn2,...,fnN,[opts])
+--
+-- opts.locals: values to pass
+-- opts.name: text label
+-- opts.n: number of iterations
+function prof(...)
+  cls()
+  local funcs={...}
+  local opts=type(funcs[#funcs])=="table" and deli(funcs) or {}
+
+  -- build output string
+  local msg=""
+  local function log(s)
+    msg..=s.."\n"
+  end
+
+  if opts.name then
+    log("prof: "..opts.name)
+  end
+  for fn in all(funcs) do
+    local dat=prof_one(fn,opts)
+    log(sub("  "..dat.total,-3)
+      .." ("
+      ..dat.lua
+      .." lua, "
+      ..dat.sys
+      .." sys)")
+  end
+
+  -- copy to clipboard
+  printh(msg,"@clip")
+  -- print + pause
+  while btn() == 0 do
+   flip()
+  end
+  color(6)
+  stop(msg)
+end
+
+function prof_one(func, opts)
+  opts = opts or {}
+  local n = opts.n or 0x200 --how many times to call func
+  local locals = opts.locals or {} --locals to pass func
+
+  -- we want to type
+  --   local m = 0x80_0000/n
+  -- but 8MHz is too large to fit in a pico-8 number,
+  -- so we do (0x80_0000>>16)/(n>>16) instead
+  -- (n is always an integer, so n>>16 won't lose any bits)
+  local m = 0x80/(n>>16)
+  assert(0x80/m << 16 == n, "n is too small") -- make sure m didn't overflow
+  local fps = stat(8)
+
+  -- given three timestamps (pre-calibration, middle, post-measurement),
+  --   calculate how many more CPU cycles func() took compared to noop()
+  -- derivation:
+  --   T := ((t2-t1)-(t1-t0))/n (frames)
+  --     this is the extra time for each func call, compared to noop
+  --     this is measured in #-of-frames -- it will be a small fraction for most ops
+  --   F := 1/30 (seconds/frame) (or 1/60 if this test is running at 60fps)
+  --     this is just the framerate that the tests run at, not the framerate of your game
+  --   M := 256*256*128 = 0x80_0000 = 8MHz (cycles/second)
+  --     (PICO-8 runs at 8MHz; see https://www.lexaloffle.com/dl/docs/pico-8_manual.html#CPU)
+  --   cycles := T frames * F seconds/frame * M cycles/second
+  -- optimization / working around pico-8's fixed point numbers:
+  --   T2 := T*n = (t2-t1)-(t1-t0)
+  --   M2 := M/n = (M>>16)/(n>>16) := m (e.g. when n is 0x1000, m is 0x800)
+  --   cycles := T2*M2*F
+  local function cycles(t0,t1,t2)
+    local diff = (t2-t1)-(t1-t0)
+    local e1 = "must use inline functions -- see usage guide"
+    assert(0<=diff,e1)
+    local thresh = 0x7fff.ffff/(m/fps)
+    local e2 = "code is too large or slow -- try profiling manually with stat(1)"
+    assert(diff<=thresh,e2)
+    return diff*(m/fps)
+  end
+
+  local noop = function() end -- this must be local, because func is local
+  flip() --avoid flipping mid-measurement
+  local atot,asys=stat(1),stat(2)
+  for _=1,n do noop(unpack(locals)) end -- calibrate
+  local btot,bsys=stat(1),stat(2)
+  for _=1,n do func(unpack(locals)) end -- measure
+  local ctot,csys=stat(1),stat(2)
+
+  -- gather results
+  local tot=cycles(atot,btot,ctot)
+  local sys=cycles(asys,bsys,csys)
+  return {
+    lua=tot-sys,
+    sys=sys,
+    total=tot,
+  }
+end
+
+-->8
+-- your code here
+
+--edit me:
+
+function linefill(ax,ay,dx,dy,r,c)
+ if(c) color(c)
+ -- avoid overflow
+ -- credits: https://www.lexaloffle.com/bbs/?tid=28999
+ local d,n = abs(dx),abs(dy)
+ if (d<n) d,n=n,d
+ n/=d
+ d*=sqrt(n*n+1)
+ if(d<0.001) return
+ local ca,sa=dx/d,-dy/d
+
+ -- polygon points
+ local s={
+  {0,-r},{d,-r},{d,r},{0,r}
+ }
+ local u,v,spans=s[4][1],s[4][2],{}
+ local x0,y0=ax+u*ca+v*sa,ay-u*sa+v*ca
+ for i=1,4 do
+  local u,v=unpack(s[i])
+  local x1,y1=ax+u*ca+v*sa,ay-u*sa+v*ca
+  local _x1,_y1=x1,y1
+  if(y0>y1) x0,y0,x1,y1=x1,y1,x0,y0
+  local dx=(x1-x0)/(y1-y0)
+  if(y0<0) x0-=y0*dx y0=-1
+  local cy0=y0\1+1
+  -- sub-pix shift
+  x0+=(cy0-y0)*dx
+  for y=y0\1+1,min(y1\1,127) do
+   -- open span?
+   local span=spans[y]
+   if span then
+       rectfill(x0,y,span,y)
+   else
+       spans[y]=x0
+   end
+   x0+=dx
+  end
+  x0,y0=_x1,_y1
+ end
+end
+
+function quickzot(x,y,r,dx,dy,hot,warm,cold)
+ local x0, y0, r2 = x-dx, y-dy, r/2
+ rectfill(x0-0.5-r2, y0-0.5-r2, x0+r2+0.5, y0+r2+0.5, cold)
+ local a = atan2(dx,dy)-0.25
+ local tdx,tdy=cos(a), sin(a)
+ for i=-r*0.65,r*0.65,0.65 do
+  line(x0+i*tdx, y0+i*tdy, x+i*tdx, y+i*tdy, warm)
+ end
+ rectfill(x-r2,y-r2,x+r2,y+r2,hot)
+end
+
+function zot(x,y,r,dx,dy,hot,warm,cold)
+ local x0,y0,sdx,sdy=x-dx,y-dy,sgn(dx),sgn(dy)
+ local rx,ry=r*sdx,r*sdy
+ if cold then
+  rectfill(x0-rx,y0-ry,x0+rx,y0+ry,cold)
+  local sdxh,sdyh=sdx/2,sdy/2
+  line(x0-rx-sdxh,y0+ry+sdyh,x-rx,y+ry,cold)
+  line(x0+rx+sdxh,y0-ry-sdyh,x+rx,y-ry,cold)
+ end
+ for i=-r,r do
+  line(x0+i*sdx,y0-ry,x+rx,y-i*sdy,warm)
+  line(x0-rx,y0+i*sdy,x-i*sdx,y+ry,warm)
+ end
+ for i=-r,r do
+  line(x0,y0,x+rx,y-i*sdy,hot)
+  line(x0,y0,x-i*sdx,y+ry,hot)
+ end
+end
+
+function respr(x,y,dx,dy,r,s)
+ if (r==0) r=0.5
+ local n=ceil(max(abs(dx),abs(dy))/r/2)
+ local d1x,d1y=dx/n,dy/n
+ r/=4
+ for i=1,n do
+  spr(s,x,y,r,r)
+  x+=d1x
+  y+=d1y
+ end
+ pal()
+ spr(s,x,y,r,r)
+end
+
+darkpal = {
+ [7]=4,
+ [9]=2,
+ [10]=4,
+ [8]=2
+}
+
+prof(function(dx, dy, r)
+  linefill(32,32,dx,dy,r,10)
+end,function(dx, dy, r)
+  quickzot(96,32,r,dx,dy,10,9,8)
+end,function(dx,dy,r)
+  zot(32,96,r,dx,dy,10,9,8)
+end,function(dx,dy,r)
+  pal(darkpal)
+  respr(96,96,dx,dy,r,r)
+end,{ locals={4,-9,2} })
+
+-- "locals" (optional) are
+-- passed in as args. see the
+-- usage guide for details.
+
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