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

[Albert Chan]

(10-06-2023 08:40 AM)J-F Garnier Wrote:  Actually, the Saturn machines are using the PI/4 constant with 31 digits.

Thanks for the info.

I still think code somehow adjusted stored 31-digits pi/4 (error ≈ -1/4 ULP)
Otherwise, it cannot match HP71B SIN(x) signatures.

HP71B Wrote:>for i=21 to 30 @ sin(10^i) @ next i
-.667120177071
-.852200849762
 .701140639796
-.996472229026
-.744789854871
 .853455100159
 .718062857184
-.987830531786
 .999958451937
-9.10311968368E-2

32 digits of pi, it mached them all.

Quote:C:\> seq 21 30 | rpn pi =-32 2x st [ 10 $ pow dup rt / f rt x - sin ?12 k
-0.667120177071
-0.852200849762
 0.701140639796
-0.996472229026
-0.744789854871
 0.853455100159
 0.718062857184
-0.987830531786
 0.999958451937
-0.0910311968368

31 digits of pi/4 (= 32 digits of pi, error = -1 ULP), no match:

Quote:C:\> seq 21 30 | rpn pi 4/ =-31 8x st [ 10 $ pow dup rt / f rt x - sin ?12 k
-0.667120177095
-0.852200849929
 0.701140642065
-0.996472231697
-0.744789642463
 0.853456759079
 0.718085010496
-0.987780973718
 0.999982401941
-0.0592916087884

Note: "[ ..." means setup a pipe, i → round(sin(remainder(10^i, t ≈ 2*pi)), -12)