Accuracy and the power function
02-16-2014, 03:11 PM
Post: #2
 Joe Horn Senior Member Posts: 1,861 Joined: Dec 2013
RE: Accuracy and the power function
(02-16-2014 02:43 PM)Dieter Wrote:  Let's assume $$2\large\pi$$ = 6,28318530718, i.e. the best possible 12-digit value. Now evaluate some powers of this:

$$6,28318530718^{-76} = 2,179 3651 6466 35... · 10^{-61}$$
$$6,28318530718^{ 200} = 4,324 8761 1401 74... · 10^{ 159}$$
$$6,28318530718^{ 372} = 8,373 5772 1132 00... · 10^{ 296}$$

The middle example contains an extraneous digit near the end. It should read:
$$6,28318530718^{ 200} = 4,324\ 8761\ 1407\ 46... · 10^{ 159}$$

Quote:Please try this with your 12-digit HP and see what you get.

On the HP 50g, the errors on these calculations are 1 ULP, -1 ULP, and -4 ULP, respectively.

<0|ɸ|0>
-Joe-
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 Messages In This Thread Accuracy and the power function - Dieter - 02-16-2014, 02:43 PM RE: Accuracy and the power function - Joe Horn - 02-16-2014 03:11 PM RE: Accuracy and the power function - Dieter - 02-16-2014, 05:45 PM RE: Accuracy and the power function - Joe Horn - 02-16-2014, 10:11 PM RE: Accuracy and the power function - Dieter - 02-18-2014, 08:28 PM RE: Accuracy and the power function - Joe Horn - 02-19-2014, 12:33 AM RE: Accuracy and the power function - Werner - 02-19-2014, 09:54 AM RE: Accuracy and the power function - walter b - 02-19-2014, 11:36 AM RE: Accuracy and the power function - Dieter - 02-19-2014, 12:35 PM RE: Accuracy and the power function - Werner - 02-19-2014, 11:47 AM RE: Accuracy and the power function - Werner - 02-19-2014, 01:07 PM RE: Accuracy and the power function - Dieter - 02-20-2014, 05:17 PM RE: Accuracy and the power function - Werner - 02-21-2014, 07:11 AM RE: Accuracy and the power function - Dieter - 02-23-2014, 02:19 PM RE: Accuracy and the power function - Thomas Klemm - 02-23-2014, 08:09 PM RE: Accuracy and the power function - Werner - 02-23-2014, 09:06 PM

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