Appendix E: A Detailed Look at f 247
format to i n or ^ n, where n is an integer,
*
implies that the
In this formula, n is the number of digits specified in the display format and
m(x) is the exponent of the function's value at x that would appear if the
value were displayed in i display format.
The uncertainty is proportional to the factor 10
m(x)
, which represents the
magnitude of the function's value at x. Therefore, i and ^ display
formats imply an uncertainty in the function that is relative to the function's
magnitude.
Similarly, if a function value is display in • n, the rounding of the
display implies that the uncertainty in the function's values is
Since this uncertainty is independent of the function's magnitude, •
display format implies an uncertainty that is absolute.
Each time the f algorithm samples the function at a value of x, it also
derives a sample of (x), the uncertainty of the function's value at x. This is
calculated using the number of digits n currently specified in the display
format and (if the display format is set to i or ^) the magnitude
m(x) of the function's value at x certainty of the
approximation to the desired integral, is the integral (x):
*
Although i 8 or 9 generally results in the same display as i 7, it will result in a smaller
uncertainty of a calculated integral. (The same is true for the ^ format.) A negative value for n (which
can be set by using the Index register) will also affect the uncertainty of an f calculation. The minimum
value for n that will affect uncertainty is -6. A number in R
I
less than -6 will be interpreted as -6.
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