sin(x) & cos(x) for x = 10²² in radians

[Albert Chan]

(10-03-2023 07:56 PM)Ajaja Wrote:  In Python operator ^ means XOR. You should use here 10**22 or just 1e22.

10^22 = 0x1.0f0cf064dd592p+73

It is the biggest pow-of-10 that can be exactly store in IEEE double. (10^23 need 54 bits)
Perhaps this is the reason for picking it, to compare both decimal and binary machines.

(10-05-2023 01:33 PM)dm319 Wrote:  Do you think the hp-20s uses a similar look up table?

Very likely.

Of course, there are ways to do this without table.
We don't need pi ... we just keep throwing precisions to it

lua> qd = require'qd' -- quad double, precision = 4*53 bits
lua> t = 1e22 / qd.pow(5,40) -- about 1e-6
lua> tt = t*t
lua> s = t*(1 - tt/6*(1 - tt/20*(1 - tt/42*(1 - tt/72*(1 - tt/110)))))
lua> s -- ≈ sin(10^22 / 5^40)
1.0995116277757784620007025274123330676478201219099885281501104800e-06

Now, map 40 times, sin(x) --> sin(5x)

lua> m5 = fn'x: x*(5-x*x*(4+16*(1-x)*(1+x)))'
lua> for i=1,40 do s = m5(s) end
lua> s -- ≈ sin(10^22)
-8.5220084976718880177270589375302936826176863529279677310847219854e-01