-- util: math, screen & text helpers

function lerp(a,b,t) return a+(b-a)*t end

function eio(t) return t*t*(3-2*t) end

function clmp(t) return mid(0,t,1) end

function appr(v,t,a) return v>t and max(v-a,t) or min(v+a,t) end

-- axis-aligned overlap: point (ax,ay) within (r,s) of point (bx,by)
function ov(ax,ay,bx,by,r,s) return abs(ax-bx)<r and abs(ay-by)<s end

function grad(y0,y1,a,b)
 local h=(y1-y0)/5
 for i=1,5 do
  fillp(gpat[i])
  rectfill(0,y0+(i-1)*h,127,y0+i*h,a+b*16)
 end
 fillp()
end

function fadeover(step)
 if step<=0 then return end
 -- fadep is keyed 1..5; step arrives fractional from the splash, so floor+clamp
 -- (a raw fractional index returns nil -> arithmetic-on-nil crash).
 fillp(fadep[mid(1,flr(step),5)]+0x0.8)
 rectfill(0,0,127,127,0)
 fillp()
end

-- ember dissolve: the black cover burns away left->right, shedding embers off the
-- wavy burn front. e=0 full cover -> e=1 clear. reuses the flame palette (fcol).
function wipe(e)
 for i=0,127 do
  local x=191*e-32+sin(i*0.2)*12
  rectfill(x,i,127,i,0)
  pset(x-rnd(12),i,fcol(rnd(1)))
 end
end

function pal2(c) pal(12,c) pal(13,c) end

function skin_pal()
 local s=sk_c[bf_skin+1]
 if s[1]~=12 then pal(12,s[1]) pal(13,s[2]) end
end

function gbox(a,b,c,d) fillp(0x5a5a.8) rectfill(a,b,c,d,5) fillp() end  -- dithered glow box

function fcol(f) return f<0.3 and 7 or f<0.55 and 10 or f<0.8 and 9 or 8 end
function bcol(f) return f<0.3 and 1 or f<0.8 and 12 or 7 end

function fmt_time(s) return (s\60)..":"..(s%60<10 and "0" or "")..(s%60) end

function pr_c(s,x,y,c) print(s,x-#s*2,y,c) end

function pso(s,x,y,c)
 print(s,x+1,y+1,0) print(s,x,y,c)
end

function ptc(s,x,y,c,oc)
 print(s,x-#s*2+1,y+1,oc or 1) print(s,x-#s*2,y,c)
end


function bf_sx(sp) return bfly_seq[flr(t()*sp)%4+1]*8 end

function bf_idx(sp) return bfly_seq[flr(t()*sp)%4+1] end