Mastering Verilog Math Functions for Efficient Hardware Design

Verilog math functions can be used in place of constant expressions and supports both integer and real maths.

Integer Math Functions

The function $clog2 returns the ceiling of log₂ of the given argument. This is typically used to calculate the minimum width required to address a memory of given size.

For example, if the design has 7 parallel adders, then the minimum number of bits required to represent all 7 adders is $clog2 of 7 that yields 3.

  
  
module des 
  #(parameter NUM_UNITS = 7) 
  
  // Use of this system function helps to reduce the 
  // number of input wires to this module
  (input [$clog2(NUM_UNITS)-1:0] active_unit);
  
  initial 
    $monitor("active_unit = %d", active_unit);
endmodule

`define NUM_UNITS 5

module tb;
  integer i;
  reg [`NUM_UNITS-1:0] 	active_unit;
  
  des #(.NUM_UNITS(`NUM_UNITS)) u0(active_unit);
  
  initial begin
    active_unit     = 1;     
	#10 active_unit = 7;
    #10 active_unit = 8;    
  end
endmodule

  

Note that the signal active_unit has 3-bits to store total 5 units.

Simulation Log

xcelium> run
active_unit = 001
active_unit = 111
active_unit = 000
xmsim: *W,RNQUIE: Simulation is complete.

Real Math Functions

These system functions accept real arguments and return a real number.

Function	Description
$ln(x)	Natural logarithm log(x)
$log10(x)	Decimal Logarithm log10(x)
exp(x)	Exponential of x (ex) where e=2.718281828...
sqrt(x)	Square root of x
$pow(x, y)	xy
$floor(x)	Floor x
$ceil(x)	Ceiling x
$sin(x)	Sine of x where x is in radians
$cos(x)	Cosine of x where x is in radians
$tan(x)	Tangent of x where x is in radians
$asin(x)	Arc-Sine of x
$acos(x)	Arc-Cosine of x
$atan(x)	Arc-tangent of x
$atan2(x, y)	Arc-tangent of x/y
$hypot(x, y)	Hypotenuse of x and y : sqrt(xx + yy)
$sinh(x)	Hyperbolic Sine of x
$cosh(x)	Hyperbolic-Cosine of x
$tanh(x)	Hyperbolic-Tangent of x
$asinh(x)	Arc-hyperbolic Sine of x
$acosh(x)	Arc-hyperbolic Cosine of x
$atanh(x)	Arc-hyperbolic tangent of x

  
  

module tb;
  real x, y;
  
  initial begin
    x = 10000;
    $display("$log10(%0.3f) = %0.3f", x, $log10(x));
    
    x = 1;
    $display("$ln(%0.3f) = %0.3f", x, $ln(x));
    
    x = 2;
    $display("$exp(%0.3f) = %0.3f", x, $exp(x));
    
    x = 25;
    $display("$sqrt(%0.3f) = %0.3f", x, $sqrt(x));
    
    x = 5;
    y = 3;
    $display("$pow(%0.3f, %0.3f) = %0.3f", x, y, $pow(x, y));
    
    x = 2.7813;
    $display("$floor(%0.3f) = %0.3f", x, $floor(x));
    
    x = 7.1111;
    $display("$ceil(%0.3f) = %0.3f", x, $ceil(x));
    
    x = 30 * (22.0/7.0) / 180;   // convert 30 degrees to radians
    $display("$sin(%0.3f) = %0.3f", x, $sin(x));
    
    x = 90 * (22.0/7.0) / 180;
    $display("$cos(%0.3f) = %0.3f", x, $cos(x));
    
    x = 45 * (22.0/7.0) / 180;
    $display("$tan(%0.3f) = %0.3f", x, $tan(x));
    
    x = 0.5;
    $display("$asin(%0.3f) = %0.3f rad, %0.3f deg", x, $asin(x), $asin(x) * 7.0/22.0 * 180);
    
    x = 0;
    $display("$acos(%0.3f) = %0.3f rad, %0.3f deg", x, $acos(x), $acos(x) * 7.0/22.0 * 180);
    
    x = 1;
    $display("$atan(%0.3f) = %0.3f rad, %f deg", x, $atan(x), $atan(x) * 7.0/22.0 * 180);    
  end
endmodule


  

Simulation Log

xcelium> run
$log10(10000.000) = 4.000
$ln(1.000) = 0.000
$exp(2.000) = 7.389
$sqrt(25.000) = 5.000
$pow(5.000, 3.000) = 125.000
$floor(2.781) = 2.000
$ceil(7.111) = 8.000
$sin(0.524) = 0.500
$cos(1.571) = -0.001
$tan(0.786) = 1.001
$asin(0.500) = 0.524 rad, 29.988 deg
$acos(0.000) = 1.571 rad, 89.964 deg
$atan(1.000) = 0.785 rad, 44.981895 deg
xmsim: *W,RNQUIE: Simulation is complete.