Relative speed of 15C, 34S and 42S

[Dieter]

(12-26-2017 10:11 AM)Werner Wrote:  The 42S performs dot products with enhanced precision, so if only Free42 would do the same..

The 42s, as all HP calculators since about 1976 I know of, uses extended precision for all internal functions. That's usually 3 additional digits which are used during internal calculations. So your wish may apply not only to the dot product but to any function.

And this is how the 34s works, at least for those functions that do not rely on XROM code which is limited to 34 digits. Instead of the dot product try (√2+i) · (√2+2i) which includes a similar calculation. The real part of the result is √2 · √2 – 1 · 2 which, for the 34-digit value of √2, rounds to 2 – 2 so that Free42 and probably also DM42 will return 0 here. The 34s uses more internal digits, it returns –2,222285911147240187798653227487960 E–34 which is correct in all digits. Imagine what internal precision is required for this result. Is there any other calculator that comes close?

Try the example on a hardware 42s (or a 35s), and you get –8,75 E–12 or –8,76 E–12 for the real part. This shows the three internal guard digits. The latter result is returned by the 35s and rounded up instead of down (actually it's –8,754...E–12). This may happen if you approach the internal precision limits.

But let's not forget: DM42 works with 34 digits. The 42s has 12, or 15 with extended precision. So let's be fair. ;-)

Dieter