Page 335 - Programming Microcontrollers in C

320 Chapter 6 Large Microcontrollers

Result =15 + 50 – 15)( (67 – 40 ) = 38.625
80 – 40
Notice that there is a product and a division that is the same for
all input values between 40 and 80 in this case. This calculation is
the slope of the line between the two points being interpolated. Usu­
ally table look-up operations are used where time constraints on the
program are great so that these operations, multiply and divide (es­
pecially divide), are unwelcome in these programs. There is a way to
avoid the divide operation. Note that between each set of points the
slope is a constant. Therefore, if the slope of the line is built into the
table, the calculation would involve one subtraction, one multiply,
and one addition. Let us modify the table above to contain the slopes
of the lines between each point.

20 5 0.5
40 15 0.875
80 50 1.75
120 120 2
180 240
Table 6-4: Look-Up Table With Slopes

Note that the slope of the line runs from the lower point to the
next point. Therefore, there is no slope for the last point. When this
table is built in memory, it consists of a header followed by a four-
byte entry for each entry in the table. The header consists of a single
byte that indicates the length of the table. In this case, since the table
starts with an independent variable value of 20, there are expected to
be no input values less than 20. If there are, however, the value of 5
will be used for these output values. Also, if the value of the indepen­
dent variable is greater than the maximum of 180, a value of 240 will
be returned from the routine. With data from the above table, the
calculation above would reduce to

Result = 15 + 0.875(67 - 40) = 38.625
which requires a multiply, a subtract and one add. Of course, the
routine will truncate the fractional part of the result so that the value
returned will be 38.