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Several years later I just realized that this code could be greatly simplified. First, let's formalize the need for overflow handling in __arch_xprod64(). Assuming n = UINT64_MAX, there are 2 cases where an overflow may occur: 1) If a bias must be added, we have m_lo * n_lo + m or m_lo * 0xffffffff + ((m_hi << 32) + m_lo) or ((m_lo << 32) - m_lo) + ((m_hi << 32) + m_lo) or (m_lo + m_hi) << 32 which must be < (1 << 64). So the criteria for no overflow is m_lo + m_hi < (1 << 32). 2) The cross product m_lo * n_hi + m_hi * n_lo or m_lo * 0xffffffff + m_hi * 0xffffffff or ((m_lo << 32) - m_lo) + ((m_hi << 32) - m_hi). Assuming the top result from the previous step (m_lo + m_hi) that must be added to this, we get (m_lo + m_hi) << 32 again. So let's have a straight and simpler version when this is true. Otherwise some reordering allows for taking care of possible overflows without any actual conditionals. And prevent from generating both code variants by making sure this is considered only if m is perceived as constant by the compiler. This, in turn, allows for greatly simplifying __div64_const32(). The "special case" may go as well as the regular case works just fine without needing a bias. Then reduction should be applied all the time as minimizing m is the key. Signed-off-by: Nicolas Pitre <npitre@baylibre.com> Signed-off-by: Arnd Bergmann <arnd@arndb.de> |
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Linux kernel
============
There are several guides for kernel developers and users. These guides can
be rendered in a number of formats, like HTML and PDF. Please read
Documentation/admin-guide/README.rst first.
In order to build the documentation, use ``make htmldocs`` or
``make pdfdocs``. The formatted documentation can also be read online at:
https://www.kernel.org/doc/html/latest/
There are various text files in the Documentation/ subdirectory,
several of them using the reStructuredText markup notation.
Please read the Documentation/process/changes.rst file, as it contains the
requirements for building and running the kernel, and information about
the problems which may result by upgrading your kernel.