800 Part 4½ Family Range, Compatibility, and Evolution
Section 3½ Evolution of HP Calculators
 
 

The exponential routine in reverse is used as the routine for natural logs, with only the mantissa operated upon. Then the exponent is multiplied by in 10 and added to the answer. This routine also yields these log₁₀ and are hyperbolic functions:

Accuracy

It can he seen from the discussion of the algorithms that extreme care has been taken to use routines that have accuracy commensurate with the dynamic range of the calculator. For example; the square root has a maximum possible relative error of 1 part in 10¹⁰ over the full range of the machine.

There are many algorithms for determining the sine of an angle; most of these have points of high error. The sine routine in the Model 9100A has consistent low error regardless of quadrant. Marrying a full floating decimal calculator with unique mathematical algorithms results in accuracy of better than 10 displayed digits.