Verilog - Float (16-bit) to real conversion

verilog float

I have a Sine Cosine ROM module which I generated from Matlab using a half-precision function available from the Matlab site. It consists of a 10 bit address space and a 16-bit data bus.



I am getting extremely large (and incorrect) numbers from the simulation.


I have pasted an example simulation output.

# 0.00 radians --> sin = 131072.0000 cos = 1.0000
# 0.01 radians --> sin = 131072.0000 cos = 1.0000
# 0.01 radians --> sin = 16777216.0000 cos = 1.0000
# 0.01 radians --> sin = 16777216.0000 cos = 1.0000

...

# 6.27 radians --> sin = 4261412864.0000 cos = 1.0000
# 6.27 radians --> sin = 4278190080.0000 cos = 1.0000
# 6.28 radians --> sin = 4278190080.0000 cos = 1.0000
# 6.28 radians --> sin = 4294836224.0000 cos = 1.0000

The testbench contains the main problem inside the monitor statement.

$monitor ("%1.2f radians --> sin = %1.4f cos = %1.4f", (address * 2 * pi / 1023),
((-1)**(sine[15])) * (1'b1 + (sine[9:0] >> 10)) * (2 ** (sine[14:10] - 5'd15)),
((-1)**(cosine[15])) * (1'b1 + (cosine[9:0] >> 10)) * (2 ** (cosine[14:10] - 5'd15)) );

My questions are as follows:

Is my monitor statement set up correctly to convert from 16-bit floating point to real (x.xxxx format).

What is the max number of decimal digits that half precision (16 bit floating point) would produce to the right of the decimal point? Since I am dealing with sin and cosine from 0 to 2pi (with a radius of 1) I only need 1 digit to the left.





I have uploaded my module and test-bench to the following address.

**broken link removed**

The individual files are stored at:

**broken link removed**
**broken link removed**

Any help is greatly appreciated.

Thank You,
Vahe

float verilog

Which result do you expect for sine[9:0] >> 10? It's identical to zero for all values of sine, I think.
Also sine[14:10] - 5'd15 don't give negative results due to default Verilog data types.

float in verilog

Thank you for the help.

I was able to solve the problem.

My testbench pasted attached below. The monitor statement and added integer declarations are the important changes I made.


Thank you once again. I hope this will help some one else facing a similar issue.

Vahe


# 0.00 radians --> sin = 0.0000 cos = 1.0000
# 0.01 radians --> sin = 0.0000 cos = 1.0000
# 0.01 radians --> sin = 0.0061 cos = 1.0000
# 0.01 radians --> sin = 0.0061 cos = 1.0000
# 0.01 radians --> sin = 0.0123 cos = 1.0000
# 0.02 radians --> sin = 0.0123 cos = 1.0000
# 0.02 radians --> sin = 0.0184 cos = 1.0000
# 0.02 radians --> sin = 0.0184 cos = 1.0000
# 0.02 radians --> sin = 0.0246 cos = 0.9995
# 0.03 radians --> sin = 0.0246 cos = 0.9995
# 0.03 radians --> sin = 0.0307 cos = 0.9995
# 0.04 radians --> sin = 0.0307 cos = 0.9995
# 0.04 radians --> sin = 0.0368 cos = 0.9995
# 0.04 radians --> sin = 0.0368 cos = 0.9995
# 0.04 radians --> sin = 0.0430 cos = 0.9990
# 0.05 radians --> sin = 0.0430 cos = 0.9990
# 0.05 radians --> sin = 0.0491 cos = 0.9990

...



# 6.24 radians --> sin = -0.0430 cos = 0.9990
# 6.24 radians --> sin = -0.0368 cos = 0.9995
# 6.25 radians --> sin = -0.0368 cos = 0.9995
# 6.25 radians --> sin = -0.0307 cos = 0.9995
# 6.26 radians --> sin = -0.0307 cos = 0.9995
# 6.26 radians --> sin = -0.0246 cos = 0.9995
# 6.26 radians --> sin = -0.0246 cos = 0.9995
# 6.26 radians --> sin = -0.0184 cos = 1.0000
# 6.27 radians --> sin = -0.0184 cos = 1.0000
# 6.27 radians --> sin = -0.0123 cos = 1.0000
# 6.27 radians --> sin = -0.0123 cos = 1.0000
# 6.27 radians --> sin = -0.0061 cos = 1.0000
# 6.28 radians --> sin = -0.0061 cos = 1.0000
# 6.28 radians --> sin = -0.0000 cos = 1.0000




`timescale 1ns / 1ps

module sync_rom_tb_v;

// Inputs
reg clock;
reg [9:0] address;

// Outputs
wire [15:0] sine;
wire [15:0] cosine;

real pi = 3.14;


// Instantiate the Unit Under Test (UUT)
sync_rom uut (
.clock(clock),
.address(address),
.sine(sine),
.cosine(cosine)
);


integer cosine_significand;
integer sine_significand;

integer sine_sign;
integer cosine_sign;

integer sine_exponent;
integer cosine_exponent;

always @ (sine, cosine)
begin

sine_significand = sine[9:0];
cosine_significand = cosine[9:0];

sine_sign = sine[15];
cosine_sign = cosine[15];

sine_exponent = sine[14:10];
cosine_exponent = cosine[14:10];

$monitor ("%1.2f radians --> sin = %1.4f cos = %1.4f", (address * 2 * pi / 1023),
((-1)**(sine_sign)) * (1 + ($itor(sine_significand) / 1024)) * ( (sine_exponent < 15) ? (1.0000 / 2 ** (-1*(sine_exponent - 15))) : ( 2 ** (sine_exponent - 15)) ),
((-1)**(cosine_sign)) * (1 + ($itor(cosine_significand) / 1024)) * ( (cosine_exponent < 15) ? (1.0000 / 2 ** (-1*(cosine_exponent - 15))) : ( 2 ** (cosine_exponent - 15)) ) );

end


initial
begin
// Initialize Inputs
clock = 0;
address = 0;
end

always
begin
#50 clock = ~clock;
end

integer i;

always
begin

for (i = 0; i < 1024; i=i+1)
begin
#100 address = i;
end


// Wait 100 ns for global reset to finish
#100 $finish;

// Add stimulus here

end

endmodule