Approximate pi to 24 digits via keyboard

[Dieter]

(02-01-2015 12:21 AM)Rick314 Wrote:  Hi Dieter. I think what you said here is incorrect. The "newer 12-digit calculators" store the value of pi internally to 12 digits.

Sorry if I was not clear about that. Of course these calculators return a 12-digit-value if you press the pi key, but I referred to the internal trig algorithms that contain a value for pi in much higher precision.

(02-01-2015 12:21 AM)Rick314 Wrote:  The point of this post is that calculators vary in their sin(x) algorithm for values of x very close to pi. Just speaking pure math, not calculators or rounding errors or related, if x = 3.14159265358 (exactly) then sin(x) = 9.793238462643383...e-12.

Right. And that's where the internal pi value (as used in the trig algorithms) comes in. While some algorithms use just 13 digits (most HP 10 digit machines) others may use a much higher precision value. Maybe someone knows the number of pi digits for different HP CPUs and algorithms. The assembler listing shown in this thread states 31 digits for pi/4.

Dieter