[VA] Short & Sweet Math Challenge #24: "2019 Spring Special 5-tier"

[Albert Chan]

Below Lua code scale cin argument to [sin(0.5), 0.5], do cin, then undo asin/sin's

local sin, asin = math.sin, math.asin

function cin(x)
    local y, n = x*x, 0
    while y > 0.25 do x=sin(x); y=x*x; n=n+1 end
    if y < 0.0324 then   -- |x| < 0.18
        local z = y*(0.00013898 + y*0.00003744) + 13583/29393280
        x = x - x*y*(1/18 + y*(7/1080 + y*(643/408240 + y*z)))
        return n==0 and x or asin(x)
    end    
    while y < 0.229848847 do x=asin(x); y=x*x; n=n-1 end

    y = y - 0.2399        -- |x| = [sin(0.5), 0.5]
    y = 0.013724194890539722 + y*(
          0.058965322546572385 + y*(
          0.007795773378183463 + y*(
          0.002109528417736682 + y*(
          0.000663984666232017 + y*(
          0.000199482968029459 )))))

    x = x - x*y             -- x = cin(x)
    for i=1,n do x = asin(x) end
    for i=1,-n do x = sin(x) end
    return x
end

Result *very* accurate. Example:

x = 2.019
cin(x) = 1.02692 331869 35764
cin(cin(x)) = 0.956628 929996 1186
cin(cin(cin(x))) = 0.90122 698939 98129
math.sin(x)      = 0.90122 698939 98126