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

[J-F Garnier]

(10-06-2023 03:19 PM)Albert Chan Wrote:  

(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.

Comment from the trig code:
"The absolute value of the argument is reduced by 2*Pi, then by Pi/2, and Pi/4."

The 2*Pi value is derived from Pi/4 by successive doubling, then truncated (not rounded) to 31 digits:
so 2*Pi is 6.283185307179586476925286766559
which is a very good value for 2*Pi !

I can't imagine HP did it in that way by chance.

J-F