Description
The difference between xyyEQU and xyyEQUB is usually that the latter avoids round-off errors by returning scaling matrices who entries are powers of the floating point radix and the xGEEQUB documentation explains the difference very well. The xPOEQU and xPOEQUB obey the same naming rule but the documentation does not highlight the difference so you have to look at the source code to understand the difference. Seeing that xSYEQUB, xHEEQUB do not return radix powers, the routines are misnomers.
I am currently preparing a patch for the xPOEQUB documentation that highlights the difference to xPOEQU.
The Sca/LAPACK Program Style guide forbids breaking backward compatibility (see here) but clearly, it is a misnomer. In face of the broken documentation of xSYEQUB, xHEEQUB, I wonder if anyone is actually using this routine. In addition, these routines are not implemented in Intel MKL so I propose to ignore the backwards compatibility issue and just start rounding the entries of the scaling matrix to radix powers.