How to Implement Division Operations in FPGA?

Implementing division operations in FPGAs requires careful consideration of performance, resource usage, and precision. Here are several methods, each with trade-offs:

1. Using Vendor IP Cores (Easiest)

Most FPGA vendors provide optimized division IP cores:

• Xilinx: Divider Generator (LogiCORE)

• Intel: LPM_DIVIDE (Altera)

• Supported types:

  • Integer division (no remainder)

  • Fixed-point division

  • Floating-point division (IEEE 754)

Pros:
✅ Optimized for speed/resource usage
✅ Supports pipelining
Cons:
❌ Limited customization

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2. Shift-Subtract (Restoring) Algorithm

Basic iterative method for integer division:

verilog

module divider #(parameter WIDTH=8) (
    input [WIDTH-1:0] dividend,
    input [WIDTH-1:0] divisor,
    output reg [WIDTH-1:0] quotient,
    output reg [WIDTH-1:0] remainder
);
    reg [2*WIDTH-1:0] AQ;
    integer i;

    always @(*) begin
        AQ = { {WIDTH{1'b0}}, dividend };
        for (i = 0; i < WIDTH; i = i+1) begin
            AQ = AQ << 1;
            if (AQ[2*WIDTH-1:WIDTH] >= divisor) begin
                AQ[2*WIDTH-1:WIDTH] = AQ[2*WIDTH-1:WIDTH] - divisor;
                AQ[0] = 1'b1;
            end
        end
        quotient = AQ[WIDTH-1:0];
        remainder = AQ[2*WIDTH-1:WIDTH];
    end
endmodule

Characteristics:

• Latency: N cycles (N = bit width)

• Resources: Minimal (no DSPs)

• Best for: Low-frequency designs

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3. Newton-Raphson Method (High Precision)

Used for floating-point/fixed-point division:

1. Compute reciprocal of divisor using NR iterations:

   

2. Multiply result with dividend

FPGA Implementation:

• Requires 3-4 iterations for single-precision float

• Uses DSP blocks for multiplications

Pros:
✅ Fast convergence
✅ High precision
Cons:
❌ Complex implementation
❌ Needs multiplier units

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4. Goldschmidt's Algorithm

Alternative iterative method:

1. Scale numerator/denominator to near 1.0

2. Iteratively improve approximation:

   

   ​

FPGA Benefits:

• Better pipelining than Newton-Raphson

• Used in high-performance designs

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5. CORDIC (Coordinate Rotation)

For fixed-point division (when already using CORDIC for other functions):

Limitations:

• Requires many iterations

• Best when sharing CORDIC hardware

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6. Lookup Table (LUT) + Linear Approximation

1. Store reciprocal LUT for divisor range

2. Use linear interpolation for refinement

Example:

verilog

reg [15:0] reciprocal_lut[0:255]; // 8-bit divisor -> 16-bit reciprocal

always @(posedge clk) begin
    reciprocal = reciprocal_lut[divisor[7:0]];
    quotient = (dividend * reciprocal) >> 16;
end

Best for: Small operand ranges

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Performance Comparison

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Key Optimization Techniques

1. Pipelining:

   • Break operations into stages

   • Example: 32-bit divider with 8-stage pipeline

2. Early Termination:

   • Stop iterations when error threshold met

3. DSP Block Utilization:

   • Use built-in multipliers for NR/Goldschmidt

4. Variable Precision:

   • Adjust iterations based on required accuracy

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Recommendations

• For beginners: Use vendor IP cores

• Low-latency needs: LUT + linear approx

• High precision: Newton-Raphson/Goldschmidt

• Resource-constrained: Shift-subtract