Calcuator forensics history question

[Albert Chan]

(04-20-2021 08:05 AM)J-F Garnier Wrote:  All these variants are based on the same quirk. they look complicate but the bottleneck is the COS ACOS sequence with an argument less than 1 degree (since it comes from SIN)

Is this why versin was invented ?

(04-19-2021 06:29 AM)Garth Wilson Wrote:  There is no 4-digit number which, when taking its ACOS, will result in 1.0° (two digits), let alone 1.000° (four digits).

Using versin / arcversine, we do well with 4-signficant digits.

lua> versin = function(x) return 2*sin(x/2)^2 end
lua> arcversin = function(x) return 2*asin(sqrt(x/2)) end

lua> versin(rad(1))                         -- 1 - cos(1°)
0.00015230484360876083
lua> deg(arcversin(0.0001523))      -- acos(1 - 0.0001523), then rad→deg
0.999984098436689