Bsearch doc for Array and Range (#4838)

This PR creates doc/bsearch.rdoc to provide common documentation for bsearch in Array and Range.

array.c

@@ -3422,89 +3422,8 @@ static VALUE rb_ary_bsearch_index(VALUE ary);
  *    array.bsearch -> new_enumerator
  *
  *  Returns an element from +self+ selected by a binary search.
- *  +self+ should be sorted, but this is not checked.
  *
- *  By using binary search, finds a value from this array which meets
+ *  See {Binary Searching}[doc/bsearch_rdoc.html].
- *  the given condition in <tt>O(log n)</tt> where +n+ is the size of the array.
- *
- *  There are two search modes:
- *  - <b>Find-minimum mode</b>: the block should return +true+ or +false+.
- *  - <b>Find-any mode</b>: the block should return a numeric value.
- *
- *  The block should not mix the modes by and sometimes returning +true+ or +false+
- *  and sometimes returning a numeric value, but this is not checked.
- *
- *  <b>Find-Minimum Mode</b>
- *
- *  In find-minimum mode, the block always returns +true+ or +false+.
- *  The further requirement (though not checked) is that
- *  there are no indexes +i+ and +j+ such that:
- *  - <tt>0 <= i < j <= self.size</tt>.
- *  - The block returns +true+ for <tt>self[i]</tt> and +false+ for <tt>self[j]</tt>.
- *
- *  In find-minimum mode, method bsearch returns the first element for which the block returns true.
- *
- *  Examples:
- *    a = [0, 4, 7, 10, 12]
- *    a.bsearch {|x| x >= 4 } # => 4
- *    a.bsearch {|x| x >= 6 } # => 7
- *    a.bsearch {|x| x >= -1 } # => 0
- *    a.bsearch {|x| x >= 100 } # => nil
- *
- *  Less formally: the block is such that all +false+-evaluating elements
- *  precede all +true+-evaluating elements.
- *
- *  These make sense as blocks in find-minimum mode:
- *    a = [0, 4, 7, 10, 12]
- *    a.map {|x| x >= 4 } # => [false, true, true, true, true]
- *    a.map {|x| x >= 6 } # => [false, false, true, true, true]
- *    a.map {|x| x >= -1 } # => [true, true, true, true, true]
- *    a.map {|x| x >= 100 } # => [false, false, false, false, false]
- *
- *  This would not make sense:
- *    a = [0, 4, 7, 10, 12]
- *    a.map {|x| x == 7 } # => [false, false, true, false, false]
- *
- *  <b>Find-Any Mode</b>
- *
- *  In find-any mode, the block always returns a numeric value.
- *  The further requirement (though not checked) is that
- *  there are no indexes +i+ and +j+ such that:
- *  - <tt>0 <= i < j <= self.size</tt>.
- *  - The block returns a negative value for <tt>self[i]</tt>
- *    and a positive value for <tt>self[j]</tt>.
- *  - The block returns a negative value for <tt>self[i]</tt> and zero <tt>self[j]</tt>.
- *  - The block returns zero for <tt>self[i]</tt> and a positive value for <tt>self[j]</tt>.
- *
- *  In find-any mode, method bsearch returns some element
- *  for which the block returns zero, or +nil+ if no such element is found.
- *
- *  Examples:
- *    a = [0, 4, 7, 10, 12]
- *    a.bsearch {|element| 7 <=> element } # => 7
- *    a.bsearch {|element| -1 <=> element } # => nil
- *    a.bsearch {|element| 5 <=> element } # => nil
- *    a.bsearch {|element| 15 <=> element } # => nil
- *
- *  Less formally: the block is such that:
- *  - All positive-evaluating elements precede all zero-evaluating elements.
- *  - All positive-evaluating elements precede all negative-evaluating elements.
- *  - All zero-evaluating elements precede all negative-evaluating elements.
- *
- *  These make sense as blocks in find-any mode:
- *    a = [0, 4, 7, 10, 12]
- *    a.map {|element| 7 <=> element } # => [1, 1, 0, -1, -1]
- *    a.map {|element| -1 <=> element } # => [-1, -1, -1, -1, -1]
- *    a.map {|element| 5 <=> element } # => [1, 1, -1, -1, -1]
- *    a.map {|element| 15 <=> element } # => [1, 1, 1, 1, 1]
- *
- *  This would not make sense:
- *    a = [0, 4, 7, 10, 12]
- *    a.map {|element| element <=> 7 } # => [-1, -1, 0, 1, 1]
- *
- *  Returns an enumerator if no block given:
- *    a = [0, 4, 7, 10, 12]
- *    a.bsearch # => #<Enumerator: [0, 4, 7, 10, 12]:bsearch>
  */
 
 static VALUE

doc/bsearch.rdoc

@@ -0,0 +1,120 @@
+== Binary Searching
+
+A few Ruby methods support binary searching in a collection:
+
+Array#bsearch:: Returns an element selected via a binary search
+                as determined by a given block.
+Array#bsearch_index:: Returns the index of an element selected via a binary search
+                      as determined by a given block.
+Range#bsearch:: Returns an element selected via a binary search
+                as determined by a given block.
+
+Each of these methods returns an enumerator if no block is given.
+
+Given a block, each of these methods returns an element (or element index) from +self+
+as determined by a binary search.
+The search finds an element of +self+ which meets
+the given condition in <tt>O(log n)</tt> operations, where +n+ is the count of elements.
++self+ should be sorted, but this is not checked.
+
+There are two search modes:
+
+Find-minimum mode:: method +bsearch+ returns the first element for which
+                    the block returns +true+;
+                    the block must return +true+ or +false+.
+Find-any mode:: method +bsearch+ some element, if any, for which
+                the block returns zero.
+                the block must return a numeric value.
+
+The block should not mix the modes by sometimes returning +true+ or +false+
+and other times returning a numeric value, but this is not checked.
+
+<b>Find-Minimum Mode</b>
+
+In find-minimum mode, the block must return +true+ or +false+.
+The further requirement (though not checked) is that
+there are no indexes +i+ and +j+ such that:
+
+- <tt>0 <= i < j <= self.size</tt>.
+- The block returns +true+ for <tt>self[i]</tt> and +false+ for <tt>self[j]</tt>.
+
+Less formally: the block is such that all +false+-evaluating elements
+precede all +true+-evaluating elements.
+
+In find-minimum mode, method +bsearch+ returns the first element
+for which the block returns +true+.
+
+Examples:
+
+  a = [0, 4, 7, 10, 12]
+  a.bsearch {|x| x >= 4 } # => 4
+  a.bsearch {|x| x >= 6 } # => 7
+  a.bsearch {|x| x >= -1 } # => 0
+  a.bsearch {|x| x >= 100 } # => nil
+
+  r = (0...a.size)
+  r.bsearch {|i| a[i] >= 4 } #=> 1
+  r.bsearch {|i| a[i] >= 6 } #=> 2
+  r.bsearch {|i| a[i] >= 8 } #=> 3
+  r.bsearch {|i| a[i] >= 100 } #=> nil
+  r = (0.0...Float::INFINITY)
+  r.bsearch {|x| Math.log(x) >= 0 } #=> 1.0
+
+These blocks make sense in find-minimum mode:
+
+  a = [0, 4, 7, 10, 12]
+  a.map {|x| x >= 4 } # => [false, true, true, true, true]
+  a.map {|x| x >= 6 } # => [false, false, true, true, true]
+  a.map {|x| x >= -1 } # => [true, true, true, true, true]
+  a.map {|x| x >= 100 } # => [false, false, false, false, false]
+
+This would not make sense:
+
+  a.map {|x| x == 7 } # => [false, false, true, false, false]
+
+<b>Find-Any Mode</b>
+
+In find-any mode, the block must return a numeric value.
+The further requirement (though not checked) is that
+there are no indexes +i+ and +j+ such that:
+
+- <tt>0 <= i < j <= self.size</tt>.
+- The block returns a negative value for <tt>self[i]</tt>
+  and a positive value for <tt>self[j]</tt>.
+- The block returns a negative value for <tt>self[i]</tt> and zero <tt>self[j]</tt>.
+- The block returns zero for <tt>self[i]</tt> and a positive value for <tt>self[j]</tt>.
+
+Less formally: the block is such that:
+
+- All positive-evaluating elements precede all zero-evaluating elements.
+- All positive-evaluating elements precede all negative-evaluating elements.
+- All zero-evaluating elements precede all negative-evaluating elements.
+
+In find-any mode, method +bsearch+ returns some element
+for which the block returns zero, or +nil+ if no such element is found.
+
+Examples:
+
+  a = [0, 4, 7, 10, 12]
+  a.bsearch {|element| 7 <=> element } # => 7
+  a.bsearch {|element| -1 <=> element } # => nil
+  a.bsearch {|element| 5 <=> element } # => nil
+  a.bsearch {|element| 15 <=> element } # => nil
+
+  a = [0, 100, 100, 100, 200]
+  r = (0..4)
+  r.bsearch {|i| 100 - a[i] } #=> 1, 2 or 3
+  r.bsearch {|i| 300 - a[i] } #=> nil
+  r.bsearch {|i|  50 - a[i] } #=> nil
+
+These blocks make sense in find-any mode:
+
+  a = [0, 4, 7, 10, 12]
+  a.map {|element| 7 <=> element } # => [1, 1, 0, -1, -1]
+  a.map {|element| -1 <=> element } # => [-1, -1, -1, -1, -1]
+  a.map {|element| 5 <=> element } # => [1, 1, -1, -1, -1]
+  a.map {|element| 15 <=> element } # => [1, 1, 1, 1, 1]
+
+This would not make sense:
+
+  a.map {|element| element <=> 7 } # => [-1, -1, 0, 1, 1]

range.c

@@ -662,52 +662,10 @@ bsearch_integer_range(VALUE beg, VALUE end, int excl)
  *  call-seq:
  *     rng.bsearch {|obj| block }  -> value
  *
- *  By using binary search, finds a value in range which meets the given
+ *  Returns an element from +self+ selected by a binary search.
- *  condition in O(log n) where n is the size of the range.
  *
- *  You can use this method in two use cases: a find-minimum mode and
+ *  See {Binary Searching}[doc/bsearch_rdoc.html].
- *  a find-any mode.  In either case, the elements of the range must be
- *  monotone (or sorted) with respect to the block.
  *
- *  In find-minimum mode (this is a good choice for typical use case),
- *  the block must return true or false, and there must be a value x
- *  so that:
- *
- *  - the block returns false for any value which is less than x, and
- *  - the block returns true for any value which is greater than or
- *    equal to x.
- *
- *  If x is within the range, this method returns the value x.
- *  Otherwise, it returns nil.
- *
- *     ary = [0, 4, 7, 10, 12]
- *     (0...ary.size).bsearch {|i| ary[i] >= 4 } #=> 1
- *     (0...ary.size).bsearch {|i| ary[i] >= 6 } #=> 2
- *     (0...ary.size).bsearch {|i| ary[i] >= 8 } #=> 3
- *     (0...ary.size).bsearch {|i| ary[i] >= 100 } #=> nil
- *
- *     (0.0...Float::INFINITY).bsearch {|x| Math.log(x) >= 0 } #=> 1.0
- *
- *  In find-any mode (this behaves like libc's bsearch(3)), the block
- *  must return a number, and there must be two values x and y (x <= y)
- *  so that:
- *
- *  - the block returns a positive number for v if v < x,
- *  - the block returns zero for v if x <= v < y, and
- *  - the block returns a negative number for v if y <= v.
- *
- *  This method returns any value which is within the intersection of
- *  the given range and x...y (if any).  If there is no value that
- *  satisfies the condition, it returns nil.
- *
- *     ary = [0, 100, 100, 100, 200]
- *     (0..4).bsearch {|i| 100 - ary[i] } #=> 1, 2 or 3
- *     (0..4).bsearch {|i| 300 - ary[i] } #=> nil
- *     (0..4).bsearch {|i|  50 - ary[i] } #=> nil
- *
- *  You must not mix the two modes at a time; the block must always
- *  return either true/false, or always return a number.  It is
- *  undefined which value is actually picked up at each iteration.
  */
 
 static VALUE