inversion.h

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#ifndef CC_INVERSION_H__
#define CC_INVERSION_H__

namespace l1ct {

  constexpr int ceillog2(int x) { return (x <= 2) ? 1 : 1 + ceillog2((x + 1) / 2); }

  template <class data_T, int N>
  inline float real_val_from_idx(unsigned i) {
    // Treat the index as the top N bits
    static constexpr int NB = ceillog2(N);  // number of address bits for table
    data_T x(0);
    // The MSB of 1 is implicit in the table
    x[x.width - 1] = 1;
    // So we can use the next NB bits for real data
    x(x.width - 2, x.width - NB - 1) = i;
    return (float)x;
  }

  template <class data_T, int N>
  inline unsigned idx_from_real_val(data_T x) {
    // Slice the top N bits to get an index into the table
    static constexpr int NB = ceillog2(N);  // number of address bits for table
    // Slice the top-1 NB bits of the value
    // the MSB of '1' is implicit, so only slice below that
    ap_uint<NB> y = x(x.width - 2, x.width - NB - 1);
    return (unsigned)y(NB - 1, 0);
  }

  template <class data_T, class table_T, int N>
  void init_invert_table(table_T table_out[N]) {
    // The template data_T is the data type used to address the table
    for (unsigned i = 0; i < N; i++) {
      float x = real_val_from_idx<data_T, N>(i);
      table_T inv_x = 1 / x;
      table_out[i] = inv_x;
    }
  }

  template <class in_t, class table_t, int N>
  table_t invert_with_shift(in_t in) {
    table_t inv_table[N];
    init_invert_table<in_t, table_t, N>(inv_table);

    // find the first '1' in the denominator
    int msb = 0;
    for (int b = 0; b < in.width; b++) {
      // #pragma HLS unroll
      if (in[b])
        msb = b;
    }
    // shift up the denominator such that the left-most bit (msb) is '1'
    in_t in_shifted = in << (in.width - msb - 1);
    // lookup the inverse of the shifted input
    int idx = idx_from_real_val<in_t, N>(in_shifted);
    table_t inv_in = inv_table[idx];
    // shift the output back
    table_t out = inv_in << (in.width - msb - 1);
    return out;
  }

}  // namespace l1ct
#endif