Comparing the cosine table to math.cos

Let's see how closely Stellar 7's cosine table compares to math.cos().

cpu = manager:machine().devices[":maincpu"];mem = cpu.spaces["program"]

function max(a,b) if a>b then return a else return b end end 
function min(a,b) if a<b then return a else return b end end
function round(x) if x<0 then return math.floor(x-0.5) else return math.floor (x+0.5) end end

function clearpage(page) page = page or 1 for i=page*8192,page*8192+8192-1 do mem:write_u8(i,0) end end

function showpage(pg) pg = pg or 1 mem:write_u8(0xc057,0) mem:write_u8(0xc050,0) mem:write_u8(0xc052,0) mem:write_u8(0xc054+pg-1,0) end

function calcyaddr(line,page) page = page or 1 return line % 8 * 1024 + math.floor(line / 64) * 40 + math.floor((line%64) / 8) * 128 + (8192 * page) end

function plot(x,y,page) page=page or 1 x = max(0,x) x = min(x,279) y = max(0,y) y = min(y,191) mem:write_u8(calcyaddr(y,page)+math.floor(x/7),mem:read_u8(calcyaddr(y,page)+math.floor(x/7))|(1<<(x%7))) end

function draw_text(x,y,text) emu:pause() manager:machine().screens[":screen"]:draw_text(x,y,text) end
function draw_line(x,y,x2,y2,color) emu:pause() color=color or 0xffffffff manager:machine().screens[":screen"]:draw_line(x,y,x2,y2,color) end

clearpage()
sc=40 
for i=0,255 do 
cosvalue=mem:read_u8(0xf00+i) signbit=(cosvalue&0x80) cosvalue=cosvalue&0x7F 
if signbit~=0  then cosvalue=-cosvalue end 
print(i,cosvalue,math.cos(i/256*2*3.14159)*128,cosvalue-math.cos(i/256*2*3.14159)*128) 
plot (i,96+round((cosvalue-math.cos(i/256*2*3.14159)*128)*sc)) 
plot (i,96+sc) 
plot (i,96-sc) 
plot (i,96+math.floor(cosvalue/128*96)) 
plot (i,96+math.floor(math.cos(i/256*2*3.14159)*92)) end 
draw_text(0,0,"costable is higher curve\n cos() is lower curve\n  difference range is within +/- 1/128th")


-- all as one line

clearpage() sc=40 for i=0,255 do cosvalue=mem:read_u8(0xf00+i) signbit=(cosvalue&0x80) cosvalue=cosvalue&0x7F if signbit~=0  then cosvalue=-cosvalue end print(i,cosvalue,math.cos(i/256*2*3.14159)*128,cosvalue-math.cos(i/256*2*3.14)*128) plot(i,96+round((cosvalue-math.cos(i/256*2*3.14159)*128)*sc)) plot(i,96+sc) plot (i,96-sc) plot (i,96+math.floor(cosvalue/128*96)) plot (i,96+math.floor(math.cos(i/256*2*3.14159)*92)) end draw_text(0,0,"costable is higher curve\n cos() is lower curve\n  difference range is within +/- 1/128th")


-- emu:unpause() to get the draw_text and draw_lines off the screen
-- also you may need to step the debugger window to get the mame window to update

There's some interesting patterns in the difference between the cosine table and math.cos. It's never more than 1/128 or about +/- 1% difference. The horizontal lines are the range -(1/128) to +(1/128).

I wonder how this compares to Ulugh Beg's cos table.