Project Requirements:
To create a fixed point math library with macros to perform the following operations with 8.8 precision fixed point math using the RL78’s Multiply/Divide/Accumulate peripheral:
(a) Conversion
• FL_TO_FX(a)……………………………………….Floating point to Fixed point conversion
• FX_TO_FL(a) ………………………………………Fixed point to Floating point conversion
(b) Basic Operations
• FX_ADD(a,b)……………………………………….Fixed point Addition of 2 numbers
• FX_SUB(a,b)……………………………………….Fixed point Subtraction of 2 numbers
• FX_MUL(a,b)……………………………………….Fixed point Multiplication of 2 numbers
• FX_DIV(a,b) ………………………………………..Fixed point Division of 2 numbers
(c) Exponentiation
• FX_POW(a,b)………………………………………Fixed point Power function
• FX_SQRT(a)………………………………………..Fixed point Square Root function
(d) Trigonometry using polynomial approximations
• FX_SIN(a)…………………………………………..Fixed point Sine function
• FX_COS(a)…………………………………………Fixed point Cosine function
• FX_TAN(a)………………………………………….Fixed point Tangent function
• FX_ARCSIN(a)……………………………………..Fixed point Arc Sine function
• FX_ARCCOS(a)……………………………………Fixed point Arc Cosine function
• FX_ARCTAN(a)……………………………………Fixed point Arc Tangent function
The detailed analysis of these macros w.r.t execution time and percentage error is given in the report. Please take a look at our report for the details. Contact us for any further clarifications or information.
Project Achievements:
The fixed point library was created and successfully tested for the required math functions. For every
algorithm, the designated hardware multiply/divide/accumulate unit has been used to reduce the execution t
ime. Profiling was done to realize the advantages of the fixed point arithmetic implemented with RL78’s
hardware multiply/divide/accumulate unit w.r.t its performance over the floating point counterpart. Also
error analysis was done to calculate the error for each provided function which can be kept in mind when
implementing fixed point math instead of floating point math in future applications.
Demonstration of the Functionality of Fixed Point Library :
For demonstrating the functionality of the macros in the fixed point library, some sample mathematical functions were developed. The results of four of these functions were displayed on the LCD. The functions displayed are (a+b)2, sin2(a)+cos2(a), √a and 2*a*b. Both the decimal equivalent and the corresponding floating point value after fixed to float operation were displayed for clarity. To make sure that the error remains minimized over a wide range of input values, arguments passed to these macros were changed dynamically using a for loop. A video showing this demonstration can be found on the website created for this project. Also later, profiling, showing the time taken to execute each mathematical function for both fixed point and floating point arithmetic were demonstrated.
