Accuracy of Woodstocks

[Matt Agajanian]

Hello all.

What are the accuracy, algorithm and computational improvements of the Woodstock series over the 35 and 45?

[David Hayden]

Check the "Technology" section at the bottom of the entry for the calculators on this web site. You'll find information on the technology used for the various models.

[Matt Agajanian]

Thanks for the compass point.

[Eric Smith]

The "early" Woodstocks (21, 22, 25, 25C) have only slightly improved accuracy over the Classics.

The biggest improvements in the math algorithms are the ones found in the 27, 19C/29C, and 67/97. I'm not sure whether the 91 and 92 use these algorithms or the older ones.

Some minor further improvements were made in the 30-series, 41, and 10-series, all of which use essentially the same algorithms.

The math algorithms got a rewrite for the 71B computer using Saturn, to be compliant with the IEEE 854 radix-independent floating point standard. These routines, minus some of the IEEE features, were used in all of the Saturn-based or Saturn-emulating calculators (clamshell, Pioneer, and graphing).

[Paul Berger (Canada)]

While the 71B was designed to be complaint with IEEE floating point the math routines may predate it by a little bit, it would seem that I get the same results on a 75 or 85 as I do on a 71 so it would seem likely that they are using the same algorithims. The other thing that would contribute to this is the internal representation of floating point numbers has the same precision on the capricorn and saturn processors. Both use 64 bit registers internally for holding floating point numbers, the only difference is the placement of the sign in the register. The author of the BASIC section of the HP Journal article about the 85 says:

"High accuracy has been obtained for the HP-85 mathematical functions by using essentially those algorithmsdeveloped first for the HP-67/97 and subsequently improved for the HP-32E, the HP-34C, and the HP-41C as discussed in previous articles.1"5 These algorithms are adjusted for the larger HP-85 word size to retain accuracy. Real number calculations in the HP-85 are performed in ternally to fifteen significant decimal digits and rounded to twelve digits for presentation to the user."

[Eric Smith]

The Capricorn architecture used for the Series-80 and 75 is totally different than the Saturn architecture used in the 71B and later, with Saturn clearly being an evolution from the Nut architecture of the 41C. Study of the 71B code makes it apparent that it was an evolution of the code from the 41C, and the use of the same word length notwithstanding, it has no obvious heritage from the Capricorn code.

[Paul Berger (Canada)]

I am quite aware of the difference in architecture of the two processors, however that does not preclude them using the same algorithms. I will admit I am not a professional programmer however it seems to me that the concept of an algorithm is independent of
of the architecture of the processor, the architecture will only dictate the implementation of the algorithm. It may be that the two platforms where completely independent implementations, they both have the same roots, that being the algorithms used on the last couple generations of the bit serial processors. With the implementation just being updated to take advantage of the extra precision of the new processors, which just happens to be the same on both. It would seem be a very big coincidence that the 71,75, and 85 would so consistently agree on answers for things like logarithms, and trig functions if the algorithms used did not have a common base.

[Eric Smith]

Sure, but the common base is the algorithms that originated in the HP-35, and evolved through the 67, 30-series, and 41C. The 75/Series-80 doesn't appear to have influenced the Saturn routines in any significant way. The fact that they ended up with the same precision is more a matter of that they both happened to have a 64-bit word, and not because one is a derivative of the other.