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Limitations
370 Generating User Defined Functions
'C' sin(-1.570798)
-1.000000
'C' sin(-1.256639)
-0.951057
'C' sin(-0.942479)
-0.809018
'C' sin(-0.628319)
-0.587786
'C' sin(-0.314160)
-0.309017
'C' sin(0.000000)
0.000000
'C' sin(0.314160)
0.309017
'C' sin(0.628319)
0.587786
'C' sin(0.942479)
0.809018
'C' sin(1.256639)
0.951057
'C' sin(1.570798)
1.000000
Table 6-2. 'C' Sin(x) Vs. HP E1415 Haversine Function
As stated earlier, there are limitations to using this custom function
technique. These limitations are directly proportional to the non-linearity of
the desired waveform. For example, suppose you wanted to represent the
function X*X*X over a range of +/-1000. The resulting binary range would
be +/-1024, and the segments would be partitioned at 1024/64 intervals.
This means that every 16 units would yield an Mx+B calculation over that
segment. As long as you input numbers VERY close to those cardinal
points, you will get good results. Strictly speaking, you will get perfect
results if you only calculate at the cardinal points, which may be reasonable
for your application if you limit your input values to exactly those 128
points.
You may also shift the waveform anywhere along the X-axis, and
Build_table() will provide the necessary offset calculations to generate the
proper table. Be aware too that shifting the table out to greater magnitudes
of X may also impact the precision of your results dependent upon the
linearity of your waveform. Suffice it to say that you will get your best
results and it will be easiest for you to grasp what your doing if you stay near
the X=0 point since most of the results of your measurements will have
1e-6..16 values for volts.
One final note. You may see truncation errors in the fourth digit of your
results. This is because only 15 bits of your input value is sent to the
function. This occurs because the same technique used for Custom EU
conversion is used here, and the method assumes input values are from the
16 bit A/D (15 bits = sign bit). This is evident in Table 1 where the first and
last entries return ±0.9999 rather than ±1. For most applications this
accuracy should be more than adequate.
'HP E1415' sin(-1.570798)
'HP E1415' sin(-1.256639)
'HP E1415' sin(-0.942479)
'HP E1415' sin(-0.628319)
'HP E1415' sin(-0.314160)
'HP E1415' sin(0.000000)
'HP E1415' sin(0.314160)
'HP E1415' sin(0.628319)
'HP E1415' sin(0.942479)
'HP E1415' sin(1.256639)
'HP E1415' sin(1.570798)
-0.999905
-0.950965
-0.808944
-0.587740
-0.308998
0.000000
0.308998
0.587740
0.808944
0.950965
0.999905
Appendix F
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