HP 42s Value Display

[Albert Chan]

Kahan Wrote:After you've done it seven times, your telephone number changes. Do you feel that that's honest? Is this an honest ad?

I think TI's ad is honest, showing usefulness of exposed excess precision.

exp(ln(x) ± ε) = x * exp(±ε) ≈ x * (1±ε)

x is 10-digits telephone number --> ln(x) = ln(1e9 .. 1e10) ≈ 20.7 .. 23.0

HP with 10 digits precision, max(ε) = 50 ULP, where ULP = 1e-10

Example, in HP12C

9985550000
LN   --> 23.02440488
E^X --> 9985549951

Compare this to TI, e^ln(e^ln(e^ln(e^ln(e^ln(e^ln(e^ln(x))))))) only move at most 1 ULP!
(If it did move more than 1 ULP, Kahan would not have said 7 times)