xref: /libCEED/include/ceed/jit-source/cuda/cuda-ref-basis-tensor-at-points.h (revision d4cc18453651bd0f94c1a2e078b2646a92dafdcc)

// Copyright (c) 2017-2026, Lawrence Livermore National Security, LLC and other CEED contributors.
// All Rights Reserved. See the top-level LICENSE and NOTICE files for details.
//
// SPDX-License-Identifier: BSD-2-Clause
//
// This file is part of CEED:  http://github.com/ceed

/// @file
/// Internal header for CUDA tensor product basis with AtPoints evaluation
#include <ceed/types.h>

//------------------------------------------------------------------------------
// Chebyshev values
//------------------------------------------------------------------------------
template <int Q_1D>
inline __device__ void ChebyshevPolynomialsAtPoint(const CeedScalar x, CeedScalar *chebyshev_x) {
  chebyshev_x[0] = 1.0;
  chebyshev_x[1] = 2 * x;
  for (CeedInt i = 2; i < Q_1D; i++) chebyshev_x[i] = 2 * x * chebyshev_x[i - 1] - chebyshev_x[i - 2];
}

template <int Q_1D>
inline __device__ void ChebyshevDerivativeAtPoint(const CeedScalar x, CeedScalar *chebyshev_dx) {
  CeedScalar chebyshev_x[3];

  chebyshev_x[1]  = 1.0;
  chebyshev_x[2]  = 2 * x;
  chebyshev_dx[0] = 0.0;
  chebyshev_dx[1] = 2.0;
  for (CeedInt i = 2; i < Q_1D; i++) {
    chebyshev_x[(i + 1) % 3] = 2 * x * chebyshev_x[(i + 0) % 3] - chebyshev_x[(i + 2) % 3];
    chebyshev_dx[i]          = 2 * x * chebyshev_dx[i - 1] + 2 * chebyshev_x[(i + 0) % 3] - chebyshev_dx[i - 2];
  }
}

//------------------------------------------------------------------------------
// Tensor Basis Kernels AtPoints
//------------------------------------------------------------------------------

//------------------------------------------------------------------------------
// Interp
//------------------------------------------------------------------------------
extern "C" __global__ void InterpAtPoints(const CeedInt num_elem, const CeedScalar *__restrict__ chebyshev_interp_1d,
                                          const CeedInt *__restrict__ points_per_elem, const CeedScalar *__restrict__ coords,
                                          const CeedScalar *__restrict__ u, CeedScalar *__restrict__ v) {
  const CeedInt i = threadIdx.x;

  __shared__ CeedScalar s_mem[BASIS_Q_1D * BASIS_P_1D + 2 * BASIS_BUF_LEN + POINTS_BUFF_LEN * BASIS_Q_1D];
  CeedScalar           *s_chebyshev_interp_1d = s_mem;
  CeedScalar           *s_buffer_1            = s_mem + BASIS_Q_1D * BASIS_P_1D;
  CeedScalar           *s_buffer_2            = s_buffer_1 + BASIS_BUF_LEN;
  CeedScalar           *s_chebyshev_coeffs    = s_buffer_2 + BASIS_BUF_LEN;
  CeedScalar            chebyshev_x[BASIS_Q_1D], buffer_1[POINTS_BUFF_LEN], buffer_2[POINTS_BUFF_LEN];
  for (CeedInt k = i; k < BASIS_Q_1D * BASIS_P_1D; k += blockDim.x) {
    s_chebyshev_interp_1d[k] = chebyshev_interp_1d[k];
  }

  const CeedInt P             = BASIS_P_1D;
  const CeedInt Q             = BASIS_Q_1D;
  const CeedInt u_stride      = BASIS_NUM_NODES;
  const CeedInt v_stride      = BASIS_NUM_PTS;
  const CeedInt u_comp_stride = num_elem * BASIS_NUM_NODES;
  const CeedInt v_comp_stride = num_elem * BASIS_NUM_PTS;
  const CeedInt u_size        = BASIS_NUM_NODES;

  // Apply basis element by element
  for (CeedInt elem = blockIdx.x; elem < num_elem; elem += gridDim.x) {
    for (CeedInt comp = 0; comp < BASIS_NUM_COMP; comp++) {
      const CeedScalar *cur_u = &u[elem * u_stride + comp * u_comp_stride];
      CeedScalar       *cur_v = &v[elem * v_stride + comp * v_comp_stride];
      CeedInt           pre   = u_size;
      CeedInt           post  = 1;

      // Map to coefficients
      for (CeedInt d = 0; d < BASIS_DIM; d++) {
        __syncthreads();
        // Update buffers used
        pre /= P;
        const CeedScalar *in       = d == 0 ? cur_u : (d % 2 ? s_buffer_2 : s_buffer_1);
        CeedScalar       *out      = d == BASIS_DIM - 1 ? s_chebyshev_coeffs : (d % 2 ? s_buffer_1 : s_buffer_2);
        const CeedInt     writeLen = pre * post * Q;

        // Contract along middle index
        for (CeedInt k = i; k < writeLen; k += blockDim.x) {
          const CeedInt c   = k % post;
          const CeedInt j   = (k / post) % Q;
          const CeedInt a   = k / (post * Q);
          CeedScalar    v_k = 0;

          for (CeedInt b = 0; b < P; b++) v_k += s_chebyshev_interp_1d[j * BASIS_P_1D + b] * in[(a * P + b) * post + c];
          out[k] = v_k;
        }
        post *= Q;
      }

      // Map to point
      __syncthreads();
      for (CeedInt p = threadIdx.x; p < BASIS_NUM_PTS; p += blockDim.x) {
        pre  = BASIS_NUM_QPTS;
        post = 1;
        for (CeedInt d = 0; d < BASIS_DIM; d++) {
          // Update buffers used
          pre /= Q;
          const CeedScalar *in  = d == 0 ? s_chebyshev_coeffs : (d % 2 ? buffer_2 : buffer_1);
          CeedScalar       *out = d == BASIS_DIM - 1 ? (&cur_v[p]) : (d % 2 ? buffer_1 : buffer_2);

          // Build Chebyshev polynomial values
          ChebyshevPolynomialsAtPoint<BASIS_Q_1D>(coords[elem * v_stride + d * v_comp_stride + p], chebyshev_x);

          // Contract along middle index
          for (CeedInt a = 0; a < pre; a++) {
            for (CeedInt c = 0; c < post; c++) {
              CeedScalar v_k = 0;

              for (CeedInt b = 0; b < Q; b++) v_k += chebyshev_x[b] * in[(a * Q + b) * post + c];
              out[a * post + c] = v_k;
            }
          }
          post *= 1;
        }
      }
    }
  }
}

extern "C" __global__ void InterpTransposeAtPoints(const CeedInt num_elem, const CeedScalar *__restrict__ chebyshev_interp_1d,
                                                   const CeedInt *__restrict__ points_per_elem, const CeedScalar *__restrict__ coords,
                                                   const CeedScalar *__restrict__ u, CeedScalar *__restrict__ v) {
  const CeedInt i = threadIdx.x;

  __shared__ CeedScalar s_mem[BASIS_Q_1D * BASIS_P_1D + 2 * BASIS_BUF_LEN + POINTS_BUFF_LEN * BASIS_Q_1D];
  CeedScalar           *s_chebyshev_interp_1d = s_mem;
  CeedScalar           *s_buffer_1            = s_mem + BASIS_Q_1D * BASIS_P_1D;
  CeedScalar           *s_buffer_2            = s_buffer_1 + BASIS_BUF_LEN;
  CeedScalar           *s_chebyshev_coeffs    = s_buffer_2 + BASIS_BUF_LEN;
  CeedScalar            chebyshev_x[BASIS_Q_1D], buffer_1[POINTS_BUFF_LEN], buffer_2[POINTS_BUFF_LEN];
  for (CeedInt k = i; k < BASIS_Q_1D * BASIS_P_1D; k += blockDim.x) {
    s_chebyshev_interp_1d[k] = chebyshev_interp_1d[k];
  }

  const CeedInt P             = BASIS_P_1D;
  const CeedInt Q             = BASIS_Q_1D;
  const CeedInt u_stride      = BASIS_NUM_PTS;
  const CeedInt v_stride      = BASIS_NUM_NODES;
  const CeedInt u_comp_stride = num_elem * BASIS_NUM_PTS;
  const CeedInt v_comp_stride = num_elem * BASIS_NUM_NODES;
  const CeedInt u_size        = BASIS_NUM_PTS;

  // Apply basis element by element
  for (CeedInt elem = blockIdx.x; elem < num_elem; elem += gridDim.x) {
    for (CeedInt comp = 0; comp < BASIS_NUM_COMP; comp++) {
      const CeedScalar *cur_u = &u[elem * u_stride + comp * u_comp_stride];
      CeedScalar       *cur_v = &v[elem * v_stride + comp * v_comp_stride];
      CeedInt           pre   = 1;
      CeedInt           post  = 1;

      // Clear Chebyshev coeffs
      for (CeedInt k = i; k < BASIS_NUM_QPTS; k += blockDim.x) {
        s_chebyshev_coeffs[k] = 0.0;
      }

      // Map from point
      __syncthreads();
      for (CeedInt p = threadIdx.x; p < BASIS_NUM_PTS; p += blockDim.x) {
        if (p >= points_per_elem[elem]) continue;
        pre  = 1;
        post = 1;
        for (CeedInt d = 0; d < BASIS_DIM; d++) {
          // Update buffers used
          pre /= 1;
          const CeedScalar *in  = d == 0 ? (&cur_u[p]) : (d % 2 ? buffer_2 : buffer_1);
          CeedScalar       *out = d == BASIS_DIM - 1 ? s_chebyshev_coeffs : (d % 2 ? buffer_1 : buffer_2);

          // Build Chebyshev polynomial values
          ChebyshevPolynomialsAtPoint<BASIS_Q_1D>(coords[elem * u_stride + d * u_comp_stride + p], chebyshev_x);

          // Contract along middle index
          for (CeedInt a = 0; a < pre; a++) {
            for (CeedInt c = 0; c < post; c++) {
              if (d == BASIS_DIM - 1) {
                for (CeedInt j = 0; j < Q; j++) atomicAdd(&out[(a * Q + (j + p) % Q) * post + c], chebyshev_x[(j + p) % Q] * in[a * post + c]);
              } else {
                for (CeedInt j = 0; j < Q; j++) out[(a * Q + j) * post + c] = chebyshev_x[j] * in[a * post + c];
              }
            }
          }
          post *= Q;
        }
      }

      // Map from coefficients
      pre  = BASIS_NUM_QPTS;
      post = 1;
      for (CeedInt d = 0; d < BASIS_DIM; d++) {
        __syncthreads();
        // Update buffers used
        pre /= Q;
        const CeedScalar *in       = d == 0 ? s_chebyshev_coeffs : (d % 2 ? s_buffer_2 : s_buffer_1);
        CeedScalar       *out      = d == BASIS_DIM - 1 ? cur_v : (d % 2 ? s_buffer_1 : s_buffer_2);
        const CeedInt     writeLen = pre * post * P;

        // Contract along middle index
        for (CeedInt k = i; k < writeLen; k += blockDim.x) {
          const CeedInt c   = k % post;
          const CeedInt j   = (k / post) % P;
          const CeedInt a   = k / (post * P);
          CeedScalar    v_k = 0;

          for (CeedInt b = 0; b < Q; b++) v_k += s_chebyshev_interp_1d[j + b * BASIS_P_1D] * in[(a * Q + b) * post + c];
          if (d == BASIS_DIM - 1) out[k] += v_k;
          else out[k] = v_k;
        }
        post *= P;
      }
    }
  }
}

//------------------------------------------------------------------------------
// Grad
//------------------------------------------------------------------------------
extern "C" __global__ void GradAtPoints(const CeedInt num_elem, const CeedScalar *__restrict__ chebyshev_interp_1d,
                                        const CeedInt *__restrict__ points_per_elem, const CeedScalar *__restrict__ coords,
                                        const CeedScalar *__restrict__ u, CeedScalar *__restrict__ v) {
  const CeedInt i = threadIdx.x;

  __shared__ CeedScalar s_mem[BASIS_Q_1D * BASIS_P_1D + 2 * BASIS_BUF_LEN + POINTS_BUFF_LEN * BASIS_Q_1D];
  CeedScalar           *s_chebyshev_interp_1d = s_mem;
  CeedScalar           *s_buffer_1            = s_mem + BASIS_Q_1D * BASIS_P_1D;
  CeedScalar           *s_buffer_2            = s_buffer_1 + BASIS_BUF_LEN;
  CeedScalar           *s_chebyshev_coeffs    = s_buffer_2 + BASIS_BUF_LEN;
  CeedScalar            chebyshev_x[BASIS_Q_1D], buffer_1[POINTS_BUFF_LEN], buffer_2[POINTS_BUFF_LEN];
  for (CeedInt k = i; k < BASIS_Q_1D * BASIS_P_1D; k += blockDim.x) {
    s_chebyshev_interp_1d[k] = chebyshev_interp_1d[k];
  }

  const CeedInt P             = BASIS_P_1D;
  const CeedInt Q             = BASIS_Q_1D;
  const CeedInt u_stride      = BASIS_NUM_NODES;
  const CeedInt v_stride      = BASIS_NUM_PTS;
  const CeedInt u_comp_stride = num_elem * BASIS_NUM_NODES;
  const CeedInt v_comp_stride = num_elem * BASIS_NUM_PTS;
  const CeedInt u_size        = BASIS_NUM_NODES;
  const CeedInt u_dim_stride  = 0;
  const CeedInt v_dim_stride  = num_elem * BASIS_NUM_PTS * BASIS_NUM_COMP;

  // Apply basis element by element
  for (CeedInt elem = blockIdx.x; elem < num_elem; elem += gridDim.x) {
    for (CeedInt comp = 0; comp < BASIS_NUM_COMP; comp++) {
      const CeedScalar *cur_u = &u[elem * u_stride + comp * u_comp_stride];
      CeedInt           pre   = u_size;
      CeedInt           post  = 1;

      // Map to coefficients
      for (CeedInt d = 0; d < BASIS_DIM; d++) {
        __syncthreads();
        // Update buffers used
        pre /= P;
        const CeedScalar *in       = d == 0 ? cur_u : (d % 2 ? s_buffer_2 : s_buffer_1);
        CeedScalar       *out      = d == BASIS_DIM - 1 ? s_chebyshev_coeffs : (d % 2 ? s_buffer_1 : s_buffer_2);
        const CeedInt     writeLen = pre * post * Q;

        // Contract along middle index
        for (CeedInt k = i; k < writeLen; k += blockDim.x) {
          const CeedInt c   = k % post;
          const CeedInt j   = (k / post) % Q;
          const CeedInt a   = k / (post * Q);
          CeedScalar    v_k = 0;

          for (CeedInt b = 0; b < P; b++) v_k += s_chebyshev_interp_1d[j * BASIS_P_1D + b] * in[(a * P + b) * post + c];
          out[k] = v_k;
        }
        post *= Q;
      }

      // Map to point
      __syncthreads();
      for (CeedInt p = threadIdx.x; p < BASIS_NUM_PTS; p += blockDim.x) {
        for (CeedInt dim_1 = 0; dim_1 < BASIS_DIM; dim_1++) {
          CeedScalar *cur_v = &v[elem * v_stride + dim_1 * v_dim_stride + comp * v_comp_stride];

          pre  = BASIS_NUM_QPTS;
          post = 1;
          for (CeedInt dim_2 = 0; dim_2 < BASIS_DIM; dim_2++) {
            // Update buffers used
            pre /= Q;
            const CeedScalar *in  = dim_2 == 0 ? s_chebyshev_coeffs : (dim_2 % 2 ? buffer_2 : buffer_1);
            CeedScalar       *out = dim_2 == BASIS_DIM - 1 ? (cur_v + p) : (dim_2 % 2 ? buffer_1 : buffer_2);

            // Build Chebyshev polynomial values
            if (dim_1 == dim_2) ChebyshevDerivativeAtPoint<BASIS_Q_1D>(coords[elem * v_stride + dim_2 * v_comp_stride + p], chebyshev_x);
            else ChebyshevPolynomialsAtPoint<BASIS_Q_1D>(coords[elem * v_stride + dim_2 * v_comp_stride + p], chebyshev_x);

            // Contract along middle index
            for (CeedInt a = 0; a < pre; a++) {
              for (CeedInt c = 0; c < post; c++) {
                CeedScalar v_k = 0;

                for (CeedInt b = 0; b < Q; b++) v_k += chebyshev_x[b] * in[(a * Q + b) * post + c];
                out[a * post + c] = v_k;
              }
            }
            post *= 1;
          }
        }
      }
    }
  }
}

extern "C" __global__ void GradTransposeAtPoints(const CeedInt num_elem, const CeedScalar *__restrict__ chebyshev_interp_1d,
                                                 const CeedInt *__restrict__ points_per_elem, const CeedScalar *__restrict__ coords,
                                                 const CeedScalar *__restrict__ u, CeedScalar *__restrict__ v) {
  const CeedInt i = threadIdx.x;

  __shared__ CeedScalar s_mem[BASIS_Q_1D * BASIS_P_1D + 2 * BASIS_BUF_LEN + POINTS_BUFF_LEN * BASIS_Q_1D];
  CeedScalar           *s_chebyshev_interp_1d = s_mem;
  CeedScalar           *s_buffer_1            = s_mem + BASIS_Q_1D * BASIS_P_1D;
  CeedScalar           *s_buffer_2            = s_buffer_1 + BASIS_BUF_LEN;
  CeedScalar           *s_chebyshev_coeffs    = s_buffer_2 + BASIS_BUF_LEN;
  CeedScalar            chebyshev_x[BASIS_Q_1D], buffer_1[POINTS_BUFF_LEN], buffer_2[POINTS_BUFF_LEN];
  for (CeedInt k = i; k < BASIS_Q_1D * BASIS_P_1D; k += blockDim.x) {
    s_chebyshev_interp_1d[k] = chebyshev_interp_1d[k];
  }

  const CeedInt P             = BASIS_P_1D;
  const CeedInt Q             = BASIS_Q_1D;
  const CeedInt u_stride      = BASIS_NUM_PTS;
  const CeedInt v_stride      = BASIS_NUM_NODES;
  const CeedInt u_comp_stride = num_elem * BASIS_NUM_PTS;
  const CeedInt v_comp_stride = num_elem * BASIS_NUM_NODES;
  const CeedInt u_size        = BASIS_NUM_PTS;
  const CeedInt u_dim_stride  = num_elem * BASIS_NUM_PTS * BASIS_NUM_COMP;
  const CeedInt v_dim_stride  = 0;

  // Apply basis element by element
  for (CeedInt elem = blockIdx.x; elem < num_elem; elem += gridDim.x) {
    for (CeedInt comp = 0; comp < BASIS_NUM_COMP; comp++) {
      CeedScalar *cur_v = &v[elem * v_stride + comp * v_comp_stride];
      CeedInt     pre   = 1;
      CeedInt     post  = 1;

      // Clear Chebyshev coeffs
      for (CeedInt k = i; k < BASIS_NUM_QPTS; k += blockDim.x) {
        s_chebyshev_coeffs[k] = 0.0;
      }

      // Map from point
      __syncthreads();
      for (CeedInt p = threadIdx.x; p < BASIS_NUM_PTS; p += blockDim.x) {
        if (p >= points_per_elem[elem]) continue;
        for (CeedInt dim_1 = 0; dim_1 < BASIS_DIM; dim_1++) {
          const CeedScalar *cur_u = &u[elem * u_stride + dim_1 * u_dim_stride + comp * u_comp_stride];

          pre  = 1;
          post = 1;
          for (CeedInt dim_2 = 0; dim_2 < BASIS_DIM; dim_2++) {
            // Update buffers used
            pre /= 1;
            const CeedScalar *in  = dim_2 == 0 ? (cur_u + p) : (dim_2 % 2 ? buffer_2 : buffer_1);
            CeedScalar       *out = dim_2 == BASIS_DIM - 1 ? s_chebyshev_coeffs : (dim_2 % 2 ? buffer_1 : buffer_2);

            // Build Chebyshev polynomial values
            if (dim_1 == dim_2) ChebyshevDerivativeAtPoint<BASIS_Q_1D>(coords[elem * u_stride + dim_2 * u_comp_stride + p], chebyshev_x);
            else ChebyshevPolynomialsAtPoint<BASIS_Q_1D>(coords[elem * u_stride + dim_2 * u_comp_stride + p], chebyshev_x);

            // Contract along middle index
            for (CeedInt a = 0; a < pre; a++) {
              for (CeedInt c = 0; c < post; c++) {
                if (dim_2 == BASIS_DIM - 1) {
                  for (CeedInt j = 0; j < Q; j++) atomicAdd(&out[(a * Q + (j + p) % Q) * post + c], chebyshev_x[(j + p) % Q] * in[a * post + c]);
                } else {
                  for (CeedInt j = 0; j < Q; j++) out[(a * Q + j) * post + c] = chebyshev_x[j] * in[a * post + c];
                }
              }
            }
            post *= Q;
          }
        }
      }

      // Map from coefficients
      pre  = BASIS_NUM_QPTS;
      post = 1;
      for (CeedInt d = 0; d < BASIS_DIM; d++) {
        __syncthreads();
        // Update buffers used
        pre /= Q;
        const CeedScalar *in       = d == 0 ? s_chebyshev_coeffs : (d % 2 ? s_buffer_2 : s_buffer_1);
        CeedScalar       *out      = d == BASIS_DIM - 1 ? cur_v : (d % 2 ? s_buffer_1 : s_buffer_2);
        const CeedInt     writeLen = pre * post * P;

        // Contract along middle index
        for (CeedInt k = i; k < writeLen; k += blockDim.x) {
          const CeedInt c   = k % post;
          const CeedInt j   = (k / post) % P;
          const CeedInt a   = k / (post * P);
          CeedScalar    v_k = 0;

          for (CeedInt b = 0; b < Q; b++) v_k += s_chebyshev_interp_1d[j + b * BASIS_P_1D] * in[(a * Q + b) * post + c];
          if (d == BASIS_DIM - 1) out[k] += v_k;
          else out[k] = v_k;
        }
        post *= P;
      }
    }
  }
}