diff --git a/doc/specs/stdlib_selection.md b/doc/specs/stdlib_selection.md
index b6694047c..8523ef289 100644
--- a/doc/specs/stdlib_selection.md
+++ b/doc/specs/stdlib_selection.md
@@ -23,6 +23,7 @@ which implements selection algorithms.
 ## Overview of the module
 
 The module `stdlib_selection` defines two generic subroutines:
+
 * `select` is used to find the k-th smallest entry of an array. The input
 array is also modified in-place, and on return will be partially sorted
 such that `all(array(1:k) <= array(k)))`  and `all(array(k) <= array((k+1):size(array)))` is true.
@@ -159,7 +160,7 @@ Generic subroutine.
 
 `array` : shall be a rank one array of any of the types:
 `integer(int8)`, `integer(int16)`, `integer(int32)`, `integer(int64)`,
-`real(sp)`, `real(dp)`, `real(xdp), `real(qp)`. It is an `intent(in)` argument. On input it is
+`real(sp)`, `real(dp)`, `real(xdp)`, `real(qp)`. It is an `intent(in)` argument. On input it is
 the array in which we search for the k-th smallest entry.
 
 `indx`: shall be a rank one array with the same size as `array`, containing all integers
@@ -198,7 +199,7 @@ The code does not support `NaN` elements in `array`; it will run, but there is
 no consistent interpretation given to the order of `NaN` entries of `array`
 compared to other entries.
 
-While it is essential that that `indx` contains a permutation of the integers `1:size(array)`, 
+While it is essential that `indx` contains a permutation of the integers `1:size(array)`, 
 the code does not check for this. For example if `size(array) == 4`, then we could have 
 `indx = [4, 2, 1, 3]` or `indx = [1, 2, 3, 4]`, but not `indx = [2, 1, 2, 4]`. It is the user's
 responsibility to avoid such errors.
diff --git a/src/stdlib_selection.fypp b/src/stdlib_selection.fypp
index 4a963c5b8..277fd2eb4 100644
--- a/src/stdlib_selection.fypp
+++ b/src/stdlib_selection.fypp
@@ -4,6 +4,8 @@
 ! The index arrays are of all INT_KINDS_TYPES
 
 module stdlib_selection
+!! Quickly find the k-th smallest value of an array, or the index of the k-th smallest value.
+!! ([Specification](../page/specs/stdlib_selection.html))
 !
 ! This code was modified from the "Coretran" implementation "quickSelect" by
 ! Leon Foks, https://github.com/leonfoks/coretran/tree/master/src/sorting
@@ -85,9 +87,10 @@ contains
           r = size(a, kind=ip)
           if(present(right)) r = right
 
-          if(k < 1_ip .or. k > size(a, kind=ip) .or. l > r .or. l < 1_ip .or. &
-              r > size(a, kind=ip)) then
-              error stop "select must have 1 <= k <= size(a), and 1 <= left <= right <= size(a)";
+          if(l > r .or. l < 1_ip .or. r > size(a, kind=ip) &
+              .or. k < l .or. k > r                        & !i.e. if k is not in the interval [l; r]  
+              ) then
+              error stop "select must have  1 <= left <= k <= right <= size(a)";
           end if
 
           searchk: do
@@ -201,9 +204,10 @@ contains
               error stop "arg_select must have size(a) == size(indx)"
           end if
 
-          if(k < 1_ip .or. k > size(a, kind=ip) .or. l > r .or. l < 1_ip .or. &
-              r > size(a, kind=ip)) then
-              error stop "arg_select must have 1 <= k <= size(a), and 1 <= left <= right <= size(a)";
+          if(l > r .or. l < 1_ip .or. r > size(a, kind=ip) &
+              .or. k < l .or. k > r                        & !i.e. if k is not in the interval [l; r]  
+              ) then
+              error stop "arg_select must have 1 <= left <= k <= right <= size(a)";
           end if
 
           searchk: do