// rc_alpha_q15.vh
// Plain Verilog-2001 constant function: R(ohm), C(pF), Fs(Hz) -> alpha_q15 (Q1.15)
// Uses fixed-point approximation: 1 - exp(-x) ≈ x - x^2/2 + x^3/6, where x = 1/(Fs*R*C)
// All integer math; suitable for elaboration-time constant folding (e.g., XST).

`ifndef RC_ALPHA_Q15_VH
`define RC_ALPHA_Q15_VH

function integer alpha_q15_from_rc;
    input integer R_OHM; // resistance in ohms
    input integer C_PF;  // capacitance in picofarads
    input integer FS_HZ; // sampling frequency in Hz

    integer N; // fractional bits for x (QN)
    reg  [127:0] num_1e12_sllN;
    reg  [127:0] denom_u;
    reg  [127:0] x_qN;        // x in QN
    reg  [255:0] x2;          // x^2 in Q(2N)
    reg  [383:0] x3;          // x^3 in Q(3N)

    integer term1_q15;        // x -> Q1.15
    integer term2_q15;        // x^2/2 -> Q1.15
    integer term3_q15;        // x^3/6 -> Q1.15
    integer acc;              // accumulator for result
begin
    // Choose QN for x. N=24 is a good balance for accuracy/width.
    N = 24;

    // x = 1 / (Fs * R * C) with C in pF  ==>  x = 1e12 / (Fs * R * C_PF)
    // x_qN = round( x * 2^N ) = round( (1e12 << N) / denom )
    num_1e12_sllN = 128'd1000000000000 << N;

    // denom = Fs * R * C_PF  (fits in 64..96 bits for typical values)
    denom_u = 0;
    denom_u = denom_u + FS_HZ[127:0];
    denom_u = denom_u * R_OHM[127:0];
    denom_u = denom_u * C_PF[127:0];

    // rounded divide for x_qN
    x_qN = (num_1e12_sllN + (denom_u >> 1)) / denom_u;

    // Powers
    x2 = x_qN * x_qN;       // 128x128 -> 256
    x3 = x2 * x_qN;         // 256x128 -> 384

    // term1 = x -> shift from QN to Q15
    term1_q15 = (x_qN >> (N - 15)) & 16'hFFFF;

    // term2 = x^2 / 2  -> shift from Q(2N) to Q15 and divide by 2
    term2_q15 = (x2 >> (2*N - 15 + 1)) & 16'hFFFF;

    // term3 = x^3 / 6  -> shift from Q(3N) to Q15, then divide by 6 (rounded)
    begin : gen_term3
        reg [383:0] tmp_q15_wide;
        reg [383:0] tmp_div6;
        tmp_q15_wide = (x3 >> (3*N - 15));
        tmp_div6     = (tmp_q15_wide + 6'd3) / 6; // +3 for rounding
        term3_q15    = tmp_div6[15:0];
    end

    // Combine: alpha_q15 = x - x^2/2 + x^3/6 ; clamp to [0, 0x7FFF]
    acc = term1_q15 - term2_q15 + term3_q15;
    if (acc < 0)               acc = 0;
    else if (acc > 16'h7FFF)   acc = 16'h7FFF;

    alpha_q15_from_rc = acc;
end
endfunction

`endif