Embedded Software and Motor Control Libraries for PXR40xx

Function GFLIB_Sin_F32
4.79.2 Arguments
Table 4-100. GFLIB_Sin_F32 arguments
Type Name Direction Description
tFrac32 f32In input Input argument is a 32-bit number that contains an angle in
radians between [- π, π) normalized between [-1, 1).
const
GFLIB_SIN_T_F32
*const
4.79.3 Return
pParam input Pointer to an array of Taylor coefficients.
The function returns the sin of the input argument as a fixed point 32-bit number,
normalized between [-1, 1).
4.79.4 Description
The GFLIB_Sin_F32 function provides a computational method for calculation of a
standard trigonometric sine function sin(x), using the 9th order Taylor polynomial
approximation. The Taylor polynomial approximation of a sine function is described as
follows:
where x is the input angle.
Equation GFLIB_Sin_Eq1
The 9th order polynomial approximation is chosen as sufficient an order to achieve the
best ratio between calculation accuracy and speed of calculation. Because the
GFLIB_Sin_F32 function is implemented with consideration to fixed point fractional
arithmetic, all variables are normalized to fit into the [-1, 1) range. Therefore, in order to
cast the fractional value of the input angle f32In [-1, 1) into the correct range [- π, π), the
input f32In must be multiplied by π. So the fixed point fractional implementation of the
GFLIB_Sin_F32 function, using 9th order Taylor approximation, is given as follows:
Equation GFLIB_Sin_Eq2
Embedded Software and Motor Control Libraries for PXR40xx, Rev. 1.0
400 Freescale Semiconductor, Inc.