Embedded Software and Motor Control Libraries for PXR40xx

Function GFLIB_Tan_F16
Figure 4-42. Course of the function GFLIB_Tan
The GFLIB_Tan_F16 function is implemented with consideration to fixed point
fractional arithmetic, hence all tangent values falling beyond [-1, 1) are truncated to -1
and 1 respectively. This truncation is applied for angles in the ranges [-3 π/4, - π/4) and
[ π/4, 3 π/4). As can be further seen from Figure 4-42, tangent values are identical for
angles in the ranges:
1. [- π/4, 0) and [3 π/4, π)
2. [- π,- 3 π/4) and [0, π/4)
Moreover, it can be observed from Figure 4-42 that the course of the tan(x) function
output for angles in interval 1. is identical, but with the opposite sign, to output for angles
in interval 2. Therefore, the approximation of the tangent function over the entire defined
range of input angles can be simplified to an approximation for angles in the range [0, π/
4), and then, depending on the input angle, the result will be negated. In order to increase
the accuracy of approximation without the need for a higher order polynomial, the
interval [0, π/4) is further divided into eight equally spaced sub intervals, and polynomial
approximation is done for each interval respectively. Such a division results in eight sets
of polynomial coefficients.
The GFLIB_Tan_F16 function uses fixed point fractional arithmetic, so to cast the
fractional value of the input angle f16In [-1, 1) into the correct range [- π, π), the fixed
point input angle f16In must be multiplied by π. Then the fixed point fractional
implementation of the approximation polynomial, used for calculation of each sub sector,
is defined as follows:
Equation GFLIB_Tan_Eq2
Embedded Software and Motor Control Libraries for PXR40xx, Rev. 1.0
426 Freescale Semiconductor, Inc.