Merge pull request #815 from dylanhmorris/814-fix-log-diff-exp-description

Clarify `log_diff_exp` behavior at `x == y`

Author: bob-carpenter

src/functions-reference/real-valued_basic_functions.qmd

@@ -1601,8 +1601,12 @@ The logarithm of one minus the natural exponentiation of x
 Return the natural logarithm of the difference of the natural
 exponentiation of x and the natural exponentiation of y. \begin{equation*}
 \mathrm{log\_diff\_exp}(x,y) = \begin{cases} \log(\exp(x)-\exp(y)) &
-\text{if } x > y \\[6pt] \textrm{NaN} & \text{otherwise} \end{cases}
+\text{if } +\infty > x \ge y \\[6pt] 
+\textrm{NaN} & \text{otherwise} \end{cases}
 \end{equation*}
+
+When x is equal to y, `log_diff_exp(x, y)` returns $-\infty$, consistent with `log(0)` returning $-\infty$. This includes the case in which x and y are both equal to $-\infty$, which corresponds to `log(0 - 0)` because `exp(negative_infinity())` returns 0.
+
 {{< since 2.0 >}}
 
 <!-- R; log_diff_exp; (T1 x, T2 y); -->