Porting from C to Cpp using Multidimensional Subscript Operator

In ifos3d a 3D field e.g. vx is represented by the type float ***.

• vx is an array of size nrow with elements of type float **
• vx[.] is mapped to an array of size nrow * ncol with elements of float *
• vx[.][.] is mapped to an array of nrow * ncol * ndep with elements of float
• As the index of the fields may not start at zero, this data structure requires to substract offsets from the pointers, which may lead to pointer underflows.

With C++ multidimensional subscript operators:

• The pointer underflow problem can be avoided
• The memory for the pointer structure can be saved
• Alignment information can be added to the data array to improve performance
• Assertions can be used to check that all tensor accesses are valid.

The simplest form of this subscript operator would look like:

constexpr float &float3DTensorT::operator[](const int &i, const int &j, const int &k) noexcept
{
    assert(_lb_i <= i and i <= _ub_i);
    assert(_lb_j <= j and j <= _ub_j);
    assert(_lb_k <= k and k <= _ub_k);
    const size_t index = i * _stride_i + j * _stride_j + k - offset;
    assert(index < _size);
    return data[index];
}

Tensor element access syntax would change from vel->vx[j][i][k] to vel.vx[j, i, k]

Performance Comparison

Hardware	Compiler	Runtime C-Code	Runtime C++-Code	Performance
AMD Zen4	GCC 13	248.45s	237.04s	5%
AMD Zen4	GCC 13 (fast-math)	242.12s	235.10s	3%
AMD Zen4	AOCC 5.0	223.31s	219.49s	2%
Intel Xeon	GCC 13	198.61s	196.36s	1%
Intel Raptor Lake	icx 2025.1	306.77s	293.90s	4%