Bold italic math with unicode-math

Question

How can I get the output I get without unicode-math using unicode-math, preferably (not necessarily) using the same code (\boldmath)? I would like the solution to work with at least the XITS and Latin Modern fonts, both of which have no build-in bold math font..

edit: I can see attention is fading away. Of course it is not possible to make non-bold fonts 'truly bold', but the output Word produces when you make formulae bold is acceptable, and Cambria Math also doesn't have a bold font. You can even make XITS and Latin Modern bold in math just by pressing CTRL+B. I accept any answer that makes LaTeX behave like Word in this.

Without unicode-math

\documentclass{article}
\begin{document}
  This should be entirely bold: {\boldmath$O(\log n)$} \\
  This should not be bold: $O(\log n)$
\end{document}

I get nice-looking output:

.

With unicode-math, the code

\documentclass{article}
\usepackage{unicode-math}
\setmainfont{XITS}
\setmathfont{XITS Math}
\begin{document}
This should be entirely bold: {\boldmath$O(\log n)$} \\
This should not be bold: $O(\log n)$
\end{document}

gives

.

I already tried a bunch of things, for example the following code.

\documentclass{article}
\usepackage{unicode-math}
\setmainfont{XITS}
\setmathfont{XITS Math}
\setmathfont[range=\mathup/{greek,Greek,latin,Latin,num}]{XITS}
\setmathfont[range=\mathit/{greek,Greek,latin,Latin,num}]{XITS Italic}
\setmathfont[range=\mathbfup/{greek,Greek,latin,Latin,num}]{XITS Bold}
\setmathfont[range=\mathbfit/{greek,Greek,latin,Latin,num}]{XITS Bold Italic}
\begin{document}
This should be entirely bold: {\boldmath$O(\log n)$} \\
This should not be bold: $O(\log n)$
\end{document}

Which unfortunately gives me this:

.

Word output looks like this:

.

Answer 1

A "poor person's \boldmath can be obtained by

\documentclass{article}
\usepackage{unicode-math}
\setmainfont{XITS}
\setmathfont{XITS Math}
\setmathfont[version=bold,FakeBold=3.5]{XITS Math}

\begin{document}
This should be entirely bold: {\boldmath$O(\log n)$} \\
This should not be bold: $O(\log n)$
\end{document}

I presume that this is how word processors fake bold for fonts not having a real one.

Note: choosing XITS "non math" for math symbols may have adverse effects.

Answer 2

When using the package unicode-math, you will find the \bm and \boldsymbol don't work. You can nonetheless specify how you want it to deal with your bold math symbols using an option while loading it. \usepackage[bold-style=ISO]{unicode-math} will give the recommended italic bold math symbols for both greek and latin characters, while \usepackage[bold-style=TEX]{unicode-math} will give upright latin characters. This is explained in the unicode-math documentation.

A mwe:

\documentclass{article}
\usepackage[bold-style=ISO]{unicode-math}
%\usepackage[bold-style=TEX]{unicode-math}
\setmainfont{XITS}
\setmathfont{XITS Math}
\begin{document}
This is bold and italic $\mathbf{O(\log n)}+\mathbf{O(\lambda,\,\epsilon)}$ where it must :)
\end{document}