Simple Arithmetic Operations - 2022.1 English

This example shows some simple arithmetic operations and type conversions. The following shows the xlSimpleArith.m file, which specifies the xlSimpleArith M-function.

function [z1, z2, z3, z4] = xlSimpleArith(a, b)
  % xlSimpleArith demonstrates some of the arithmetic operations
  % supported by the Xilinx MCode block. The function uses xfix()
  % to create Xilinx fixed-point numbers with appropriate
  % container types.%
  % You must use a xfix() to specify type, number of bits, and
  % binary point position to convert floating point values to
  % Xilinx fixed-point constants or variables.
  % By default, the xfix call uses xlTruncate
  % and xlWrap for quantization and overflow modes. 
  % const1 is Ufix_8_3 
  const1 = xfix({xlUnsigned, 8, 3}, 1.53); 
  % const2 is Fix_10_4 
  const2 = xfix({xlSigned, 10, 4, xlRound, xlWrap}, 5.687); 
  z1 = a + const1; 
  z2 = -b - const2;
  z3 = z1 - z2; 
  % convert z3 to Fix_12_8 with saturation for overflow 
  z3 = xfix({xlSigned, 12, 8, xlTruncate, xlSaturate}, z3); 
  % z4 is true if both inputs are positive 
  z4 = a>const1 & b>-1;

This M-function uses addition and subtraction operators. The MCode block calculates these operations in full precision, which means the output precision is sufficient to carry out the operation without losing information.

One thing worth discussing is the xfix function call. The function requires two arguments: the first for fixed-point data type precision and the second indicating the value. The precision is specified in a cell array. The first element of the precision cell array is the type value. It can be one of three different types: xlUnsigned, xlSigned, or xlBoolean. The second element is the number of bits of the fixed-point number. The third is the binary point position. If the element is xlBoolean, there is no need to specify the number of bits and binary point position. The number of bits and binary point position must be specified in pair. The fourth element is the quantization mode and the fifth element is the overflow mode. The quantization mode can be one of xlTruncate, xlRound, or xlRoundBanker. The overflow mode can be one of xlWrap, xlSaturate, or xlThrowOverflow. Quanitization mode and overflow mode must be specified as a pair. If the quantization-overflow mode pair is not specified, the xfix function uses xlTruncate and xlWrap for signed and unsigned numbers. The second argument of the xfix function can be either a double or a Xilinx fixed-point number. If a constant is an integer number, there is no need to use the xfix function. The Mcode block converts it to the appropriate fixed-point number automatically.

After setting the dialog box parameter MATLAB function to xlSimpleArith, the block shows two input ports a and b, and four output ports z1, z2, z3, and z4.

M-functions using Xilinx data types and functions can be tested in the MATLAB Command Window. For example, if you type: [z1, z2, z3, z4] = xlSimpleArith(2, 3) in the MATLAB Command Window, you'll get the following lines:

UFix(9, 3): 3.500000 
Fix(12, 4): -8.687500 
Fix(12, 8): 7.996094 
Bool: true 

Notice that the two integer arguments (2 and 3) are converted to fixed-point numbers automatically. If you have a floating-point number as an argument, an xfix call is required.