Source

Binary Integer Adder/Subtractor, with Saturation

This is a basic signed integer adder/subtractor, with carry-in and carry-out. The operation is selected with add_sub: setting it to 0 for an add (A+B), and to 1 for a subtract (A-B). This assignment matches the convention of sign bits, which may end up being convenient.

If the result of the addition/subtraction falls outside of the inclusive minimum or maximum limits, the result is clipped (saturated) to the nearest exceeded limit. The maximum limit must be greater or equal than the minimum limit. If the limits are reversed, such that max_limit < min_limit, the result will be meaningless.

Internally, we perform the addition/subtraction on WORD_WIDTH + 1 bits so an overflow cannot happen, and thus the saturation logic is a pair of simple signed comparisons in the larger range. This is also likely optimal, as the delay from one extra bit of carry is less than that of any extra logic to handle overflows.

Also, we internally perform the addition/subtraction as unsigned so we can easily handle the carry_in bit. The signed comparisons are done in a separate module which implements signed/unsigned comparisons as raw logic, to avoid having to make sure all compared values are declared signed, else the comparison silently defaults to unsigned!

`default_nettype none

module Adder_Subtractor_Binary_Saturating
#(
    parameter       WORD_WIDTH          = 0
)
(
    input   wire    [WORD_WIDTH-1:0]    max_limit,
    input   wire    [WORD_WIDTH-1:0]    min_limit,
    input   wire                        add_sub,    // 0/1 -> A+B/A-B
    input   wire                        carry_in,
    input   wire    [WORD_WIDTH-1:0]    A_in,
    input   wire    [WORD_WIDTH-1:0]    B_in,
    output  reg     [WORD_WIDTH-1:0]    sum_out,
    output  reg                         carry_out
);

    localparam WORD_ZERO            = {WORD_WIDTH{1'b0}};
    localparam WORD_WIDTH_EXTENDED  = WORD_WIDTH + 1;
    localparam WORD_ZERO_EXTENDED   = {WORD_WIDTH_EXTENDED{1'b0}};

    initial begin
        sum_out     = WORD_ZERO;
        carry_out   = 1'b0;
    end

Extend the inputs to prevent overflow over their original range. We extend them as signed integers, despite declaring them as unsigned.

    wire [WORD_WIDTH_EXTENDED-1:0] A_in_extended;

    Width_Extender
    #(
        .WORD_WIDTH_IN  (WORD_WIDTH),
        .SIGNED         (1),
        .WORD_WIDTH_OUT (WORD_WIDTH_EXTENDED)  // Must be greater or equal to WORD_WIDTH_IN
    )
    extend_A
    (
        .original_input     (A_in),
        .extended_output    (A_in_extended)
    );

    wire [WORD_WIDTH_EXTENDED-1:0] B_in_extended;

    Width_Extender
    #(
        .WORD_WIDTH_IN  (WORD_WIDTH),
        .SIGNED         (1),
        .WORD_WIDTH_OUT (WORD_WIDTH_EXTENDED)  // Must be greater or equal to WORD_WIDTH_IN
    )
    extend_B
    (
        .original_input     (B_in),
        .extended_output    (B_in_extended)
    );

Extend the limits in the same way, as if signed integers.

    wire [WORD_WIDTH_EXTENDED-1:0] max_limit_extended;

    Width_Extender
    #(
        .WORD_WIDTH_IN  (WORD_WIDTH),
        .SIGNED         (1),
        .WORD_WIDTH_OUT (WORD_WIDTH_EXTENDED)  // Must be greater or equal to WORD_WIDTH_IN
    )
    extend_max_limit
    (
        .original_input     (max_limit),
        .extended_output    (max_limit_extended)
    );

    wire [WORD_WIDTH_EXTENDED-1:0] min_limit_extended;

    Width_Extender
    #(
        .WORD_WIDTH_IN  (WORD_WIDTH),
        .SIGNED         (1),
        .WORD_WIDTH_OUT (WORD_WIDTH_EXTENDED)  // Must be greater or equal to WORD_WIDTH_IN
    )
    extend_min_limit
    (
        .original_input     (min_limit),
        .extended_output    (min_limit_extended)
    );

Then select and perform the addition or subtraction in the usual way. NOTE: we don't capture the extended carry_out, as it will never be set since the inputs are too small. We compute the carry_out later.

    wire [WORD_WIDTH_EXTENDED-1:0] sum_out_extended;

    Adder_Subtractor_Binary
    #(
        .WORD_WIDTH (WORD_WIDTH_EXTENDED)
    )
    extended_add_sub
    (
        .add_sub    (add_sub), // 0/1 -> A+B/A-B
        .carry_in   (carry_in),
        .A_in       (A_in_extended),
        .B_in       (B_in_extended),
        .sum_out    (sum_out_extended),
        // verilator lint_off PINCONNECTEMPTY
        .carry_out  ()
        // verilator lint_on  PINCONNECTEMPTY
    );

Check if the sum_out_extended is past the min/max limits. Using these arithmetic predicate modules removes the need to get all the signed declarations correct, else we accidentally and silently fall back to unsigned comparisons!

    wire over_max_limit;

    Arithmetic_Predicates_Binary
    #(
        .WORD_WIDTH (WORD_WIDTH_EXTENDED)
    )
    max_limit_check
    (
        .A                  (sum_out_extended),
        .B                  (max_limit_extended),
        
        // verilator lint_off PINCONNECTEMPTY
        .A_eq_B             (),
        
        .A_lt_B_unsigned    (),
        .A_lte_B_unsigned   (),
        .A_gt_B_unsigned    (),
        .A_gte_B_unsigned   (),
        
        .A_lt_B_signed      (),
        .A_lte_B_signed     (),
        .A_gt_B_signed      (over_max_limit),
        .A_gte_B_signed     ()
        // verilator lint_on  PINCONNECTEMPTY
    );

    wire under_min_limit;

    Arithmetic_Predicates_Binary
    #(
        .WORD_WIDTH (WORD_WIDTH_EXTENDED)
    )
    min_limit_check
    (
        .A                  (sum_out_extended),
        .B                  (min_limit_extended),
        
        // verilator lint_off PINCONNECTEMPTY
        .A_eq_B             (),
        
        .A_lt_B_unsigned    (),
        .A_lte_B_unsigned   (),
        .A_gt_B_unsigned    (),
        .A_gte_B_unsigned   (),
        
        .A_lt_B_signed      (under_min_limit),
        .A_lte_B_signed     (),
        .A_gt_B_signed      (),
        .A_gte_B_signed     ()
        // verilator lint_on  PINCONNECTEMPTY
    );

After, clip the sum to the limits. This must be done as a signed comparison so we can place the limits anywhere in the positive or negative integers, so long as max_limit >= min_limit, as signed integers.

And finally, truncate the output back to the input WORD_WIDTH, and set the carry_out to the MSB of the extended sum, which is the carry_out for the sum/difference of the original inputs.

    reg [WORD_WIDTH_EXTENDED-1:0] sum_out_extended_clipped = WORD_ZERO_EXTENDED;

    always @(*) begin
        sum_out_extended_clipped    = (over_max_limit  == 1'b1) ? max_limit_extended : sum_out_extended;
        sum_out_extended_clipped    = (under_min_limit == 1'b1) ? min_limit_extended : sum_out_extended_clipped;
        sum_out                     = sum_out_extended_clipped [WORD_WIDTH-1:0];
        carry_out                   = sum_out_extended [WORD_WIDTH_EXTENDED-1];
    end

endmodule

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