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Diffstat (limited to '')
| -rw-r--r-- | doc/arithmetic.tex | 36 |
1 files changed, 35 insertions, 1 deletions
diff --git a/doc/arithmetic.tex b/doc/arithmetic.tex index 4601a7a..2e15a75 100644 --- a/doc/arithmetic.tex +++ b/doc/arithmetic.tex @@ -186,6 +186,7 @@ lend you a hand. \} \end{alltt} +% Floored division \begin{alltt} void \textcolor{c}{/* \textrm{All arguments most be unique.} */} divmod_floor(z_t q, z_t r, z_t n, z_t d) @@ -196,9 +197,10 @@ lend you a hand. \} \end{alltt} +% Ceiled division \begin{alltt} void \textcolor{c}{/* \textrm{All arguments most be unique.} */} - divmod_ceil(z_t q, z_t r, z_t n, z_t d) + divmod_ceiling(z_t q, z_t r, z_t n, z_t d) \{ zdivmod(q, r, n, d); if (!zzero(r) && isneg(n) == isneg(d)) @@ -206,6 +208,10 @@ lend you a hand. \} \end{alltt} +% Division with round half aways from zero +% This rounding method is also called: +% round half toward infinity +% commercial rounding \begin{alltt} /* \textrm{This is how we normally round numbers.} */ void \textcolor{c}{/* \textrm{All arguments most be unique.} */} @@ -227,6 +233,9 @@ not award you a face-slap. % Had positive punishment % been legal or even mildly pedagogical. But I would % not put it past Coca-Cola. +% Division with round half toward zero +% This rounding method is also called: +% round half away from infinity \begin{alltt} void \textcolor{c}{/* \textrm{All arguments most be unique.} */} divmod_half_to_zero(z_t q, z_t r, z_t n, z_t d) @@ -241,6 +250,9 @@ not award you a face-slap. % Had positive punishment \} \end{alltt} +% Division with round half up +% This rounding method is also called: +% round half towards positive infinity \begin{alltt} void \textcolor{c}{/* \textrm{All arguments most be unique.} */} divmod_half_up(z_t q, z_t r, z_t n, z_t d) @@ -256,6 +268,9 @@ not award you a face-slap. % Had positive punishment \} \end{alltt} +% Division with round half down +% This rounding method is also called: +% round half towards negative infinity \begin{alltt} void \textcolor{c}{/* \textrm{All arguments most be unique.} */} divmod_half_down(z_t q, z_t r, z_t n, z_t d) @@ -271,6 +286,16 @@ not award you a face-slap. % Had positive punishment \} \end{alltt} +% Division with round half to even +% This rounding method is also called: +% unbiased rounding (really stupid name) +% convergent rounding (also quite stupid name) +% statistician's rounding +% Dutch rounding +% Gaussian rounding +% odd–even rounding +% bankers' rounding +% It is the default rounding method used in IEEE 754. \begin{alltt} void \textcolor{c}{/* \textrm{All arguments most be unique.} */} divmod_half_to_even(z_t q, z_t r, z_t n, z_t d) @@ -288,6 +313,7 @@ not award you a face-slap. % Had positive punishment \} \end{alltt} +% Division with round half to odd \newpage \begin{alltt} void \textcolor{c}{/* \textrm{All arguments most be unique.} */} @@ -306,6 +332,14 @@ not award you a face-slap. % Had positive punishment \} \end{alltt} +% Other standard methods include stochastic rounding +% and round half alternatingly, and what is is +% New Zealand called “Swedish rounding”, which is +% no longer used in Sweden, and is just normal round +% half aways from zero but with 0.5 rather than +% 1 as the integral unit, and is just a special case +% of a more general rounding method. + Currently, libzahl uses an almost trivial division algorithm. It operates on positive numbers. It begins by left-shifting the divisor as must as possible with |