etops 26.2.1

Einsum tree operations.

The etops package provides a Python interface for the Tiled Execution IR (TEIR). It enables users to define, configure, optimize, and execute complex tensor contractions and elementwise operations. The package is built on top of the einsum_ir C++ backend and exposes advanced features such as dimension fusion, dimension splitting, and backend-specific optimizations.

Main Features

• Abstractions for tensor operations and configuration

• Support for multiple data types (float32, float64)

• Primitive operations: zero, copy, relu, gemm, brgemm, etc.

• Dimension execution strategies: primitive, sequential, shared, space-filling curve (SFC)

• Dimension and stride configuration for advanced memory layouts

• Interface for built-in contraction optimizer

• Pythonic API with dataclass-based configuration

Installation

Install the package using pip:

pip install etops

Unary Examples

Below are some examples showing how to configure and execute unary tensor operations:

import etops

# ---------------------------------------
# First example:
#   Matrix transpose using copy primitive
#   Compares the result with NumPy
# ---------------------------------------
# Define a transpose configuration
top_config = etops.TensorOperationConfig(
    backend    =   "tpp",
    data_type  =   etops.float32,
    prim_first =   etops.prim.none,
    prim_main  =   etops.prim.copy,
    prim_last  =   etops.prim.none,
    dim_types  =   (etops.dim.c,     etops.dim.c    ),
    exec_types =   (etops.exec.prim, etops.exec.prim),
    dim_sizes  =   (3,               4              ),
    strides    = (((4,               1               ),   # in
                   (1,               3               )),) # out
)

# Create the TensorOperation instance
top = etops.TensorOperation(top_config)

# Create input and output arrays
import numpy as np
A = np.random.randn(3,4).astype(np.float32)
B = np.random.randn(4,3).astype(np.float32)

top.execute(A, None, B)

B_np = np.einsum("ij->ji", A)

# Check correctness
error_abs = np.max( np.abs(B - B_np) )
print("Matrix Transpose using copy primitive:")
print(f"  Max absolute error: {error_abs:.6e}")

# -------------------------------------------------
# Second example:
#   Permutation of a 4D tensor using copy primitive
#   Compares the result with NumPy
# -------------------------------------------------
# Define a permutation configuration
perm_config = etops.TensorOperationConfig(
    backend     =   "tpp",
    data_type   =   etops.float32,
    prim_first  =   etops.prim.none,
    prim_main   =   etops.prim.copy,
    prim_last   =   etops.prim.none,
    dim_types   =   (etops.dim.c,    etops.dim.c,     etops.dim.c,     etops.dim.c    ),
    exec_types  =   (etops.exec.seq, etops.exec.seq,  etops.exec.prim, etops.exec.prim),
    dim_sizes   =   (2,              4,               3,               5              ),
    strides     = (((3*4*5,          5,               4*5,             1              ),   # in
                    (3,              2*3,             1,               4*2*3          )),) # out
)

# Create the TensorOperation instance
perm_op = etops.TensorOperation(perm_config)

# Create input and output arrays
A = np.random.randn(2,3,4,5).astype(np.float32)
B = np.random.randn(5,4,2,3).astype(np.float32)

perm_op.execute(A, None, B)

B_np = np.einsum("abcd->dcab", A)

# Check correctness
error_abs = np.max( np.abs(B - B_np) )
print("4D Tensor Permutation using copy primitive:")
print(f"  Max absolute error: {error_abs:.6e}")

# -------------------------------------------------
# Third example:
#   Permutation of a 4D tensor using copy primitive
#   Uses the built-in optimization routine
#   Compares the result with NumPy
# -------------------------------------------------
perm_config = etops.TensorOperationConfig(
    data_type   =   etops.float32,
    prim_first  =   etops.prim.none,
    prim_main   =   etops.prim.copy,
    prim_last   =   etops.prim.none,
    dim_types   =   (etops.dim.c,    etops.dim.c,     etops.dim.c,    etops.dim.c   ),
    exec_types  =   (etops.exec.seq, etops.exec.seq,  etops.exec.seq, etops.exec.seq),
    dim_sizes   =   (2,              4,               3,              5             ),
    strides     = (((3*4*5,          5,               4*5,            1             ),   # in
                    (3,              2*3,             1,              4*2*3         )),) # out
)

# Use default optimization config
optimized_config = etops.optimize(perm_config)

# Create the TensorOperation instance
perm_op = etops.TensorOperation(optimized_config)

# Create input and output arrays
A = np.random.randn(2,3,4,5).astype(np.float32)
B = np.random.randn(5,4,2,3).astype(np.float32)

# Execute the operation
perm_op.execute(A, None, B)

B_np = np.einsum("abcd->dcab", A)

# Check correctness
error_abs = np.max( np.abs(B - B_np) )
print("4D Tensor Permutation using optimized copy primitive:")
print(f"  Max absolute error: {error_abs:.6e}")

Binary Examples

Below are some examples showing how to configure and execute binary tensor operations:

import etops

# -----------------------------------------
# First example:
#   Column-major GEMM operation
#   Compares the result with NumPy's einsum
# -----------------------------------------
# Define a column-major GEMM configuration
top_config = etops.TensorOperationConfig(
    backend    =   "tpp",
    data_type  =   etops.float32,
    prim_first =   etops.prim.zero,
    prim_main  =   etops.prim.gemm,
    prim_last  =   etops.prim.none,
    dim_types  =   (etops.dim.m,     etops.dim.n,     etops.dim.k    ),
    exec_types =   (etops.exec.prim, etops.exec.prim, etops.exec.prim),
    dim_sizes  =   (64,              32,              128            ),
    strides    = (((1,               0,               64             ),   # in0
                   (0,               128,             1              ),   # in1
                   (1,               64,              0              )),) # out
)

# Create the TensorOperation instance
top = etops.TensorOperation(top_config)

# Create input and output arrays
import numpy as np
A = np.random.randn(128,64).astype(np.float32)
B = np.random.randn(32,128).astype(np.float32)
C = np.random.randn(32, 64).astype(np.float32)

# Execute the operation
top.execute(A, B, C)

C_np = np.einsum("km,nk->nm", A, B)

# Compute absolute and relative errors
error_abs = np.max( np.abs(C - C_np) )
error_rel = np.max( np.abs(C - C_np) / (np.abs(C_np) + 1e-8) )
print("Column-major GEMM operation:")
print(f"  Max absolute error: {error_abs:.6e}")
print(f"  Max relative error: {error_rel:.6e}")

# -----------------------------------------
# Second example:
#   Batched GEMM operation
#   Compares the result with torch's einsum
# -----------------------------------------
# Define a batched GEMM configuration
batched_config =    etops.TensorOperationConfig(
    backend    =    "tpp",
    data_type  =    etops.float32,
    prim_first =    etops.prim.zero,
    prim_main  =    etops.prim.gemm,
    prim_last  =    etops.prim.none,
    dim_types  =   (etops.dim.c,       etops.dim.m,     etops.dim.n,     etops.dim.k    ),
    exec_types =   (etops.exec.shared, etops.exec.prim, etops.exec.prim, etops.exec.prim),
    dim_sizes  =   (48,                64,              32,              128            ),
    strides    = (((128*64,            1,               0,               64             ),   # in0
                   (32*128,            0,               128,             1              ),   # in1
                   (32*64,             1,               64,              0              )),) # out
)
# Create the batched TensorOperation instance
top = etops.TensorOperation(batched_config)

import torch
# Create input and output arrays
A = torch.randn(48, 128, 64, dtype=torch.float32)
B = torch.randn(48, 32, 128, dtype=torch.float32)
C = torch.randn(48, 32, 64,  dtype=torch.float32)

# Execute the operation
top.execute(A, B, C)

C_torch = torch.einsum("bkm,bnk->bnm", A, B)

# Compute absolute and relative errors
error_abs = torch.max(torch.abs(C - C_torch))
error_rel = torch.max(torch.abs(C - C_torch) / (torch.abs(C_torch) + 1e-8))

print("Batched GEMM operation:")
print(f"  Max absolute error: {error_abs:.6e}")
print(f"  Max relative error: {error_rel:.6e}")

#--------------------------------------------
# Third example:
#   GEMM operation with row-major first input
#   packed to column-major
#   Compares the result with NumPy's einsum
# -------------------------------------------

# Define a row-major GEMM configuration with packing
top_config = etops.TensorOperationConfig(
    backend    =   "tpp",
    data_type  =   etops.float32,
    prim_first =   etops.prim.zero,
    prim_main  =   etops.prim.gemm,
    prim_last  =   etops.prim.none,
    dim_types  =   (etops.dim.m,     etops.dim.n,     etops.dim.k    ),
    exec_types =   (etops.exec.prim, etops.exec.prim, etops.exec.prim),
    dim_sizes  =   (64,              32,              128            ),
    strides    = (((1,               0,               64             ),   # in 0
                   (0,               128,             1              ),   # in 1
                   (1,               64,              0              )),  # out
                  ((128,             0,               1              ),   # packing in 0
                   (0,               0,               0              ),   # packing in 1
                   (0,               0,               0              )),) # packing out
)

# Create the TensorOperation instance
top = etops.TensorOperation(top_config)

# Create input and output arrays
import numpy as np
A = np.random.randn(64,128).astype(np.float32)
B = np.random.randn(32,128).astype(np.float32)
C = np.random.randn(32, 64).astype(np.float32)

# Execute the operation
top.execute(A, B, C)

A_T = np.transpose(A)
C_np = np.einsum("km,nk->nm", A_T, B)

# Compute absolute and relative errors
error_abs = np.max( np.abs(C - C_np) )
error_rel = np.max( np.abs(C - C_np) / (np.abs(C_np) + 1e-8) )
print("GEMM operation with packing:")
print(f"  Max absolute error: {error_abs:.6e}")
print(f"  Max relative error: {error_rel:.6e}")

# -----------------------------------------------
# Fourth example:
#   Batch-reduce GEMM operation with optimization
#   Compares the result with torch's einsum
# -----------------------------------------------
# Define a batch-reduce GEMM configuration
batched_config =   etops.TensorOperationConfig(
    data_type  =   etops.float32,
    prim_first =   etops.prim.zero,
    prim_main  =   etops.prim.gemm,
    prim_last  =   etops.prim.none,
    dim_types  =   (etops.dim.k,    etops.dim.m,    etops.dim.n,    etops.dim.k   ),
    exec_types =   (etops.exec.seq, etops.exec.seq, etops.exec.seq, etops.exec.seq),
    dim_sizes  =   (48,             64,             32,             128           ),
    strides    = (((128*64,         1,              0,              64            ),   # in0
                   (32*128,         0,              128,            1             ),   # in1
                   (0,              1,              64,             0             )),) # out
)

# Optimize the configuration
optimized_config = etops.optimize(
    batched_config,
    {
        "target_m":            16,
        "target_n":            12,
        "target_k":            64,
        "num_threads":         4,
        "br_gemm_support":     True,
        "packed_gemm_support": True
    }
)

# Create the optimized TensorOperation instance
top = etops.TensorOperation(optimized_config)

import torch
# Create input and output arrays
A = torch.randn(48, 128, 64, dtype=torch.float32)
B = torch.randn(48, 32, 128, dtype=torch.float32)
C = torch.randn(    32, 64,  dtype=torch.float32)

# Execute the operation
top.execute(A, B, C)

C_torch = torch.einsum("bkm,bnk->nm", A, B)

# Compute absolute and relative errors
error_abs = torch.max(torch.abs(C - C_torch))
error_rel = torch.max(torch.abs(C - C_torch) / (torch.abs(C_torch) + 1e-8))
print("Batch-reduce GEMM operation:")
print(f"  Max absolute error: {error_abs:.6e}")
print(f"  Max relative error: {error_rel:.6e}")

See the source code and inline documentation for more advanced usage.