Updated reducer docs according to recent changes

Author: JohanMabille

docs/source/operator.rst

@@ -218,6 +218,39 @@ the evaluation and get the result:
     xt::xarray<double> arr = some_init_function({3, 2, 4, 6, 5});
     double res = xt::reduce([](double a, double b) { return a*a + b*b; }, arr)();
 
+The ``value_type`` of a reducer is the traditional result type of the reducing operation. For instance,
+the ``value_type`` of the reducer for the sum is:
+
+- ``int`` if the underlying expression holds ``int`` values
+- ``int`` if the underlying expression holds ``short`` values, because ``short + short`` = ``int``
+
+You can pass a template argument to the reducer functions to specify the type of the initial value of
+the reduction. This allows you to "promote" the value type of the reducer and limit overflows in
+computation:
+
+.. code::
+
+    #include "xtensor/xarray.hpp"
+    #include "xtensor/xreducer.hpp"
+
+    xt::xarray<int> arr = some_init_function({3, 2, 4, 6, 5});
+    auto s1 = xt::sum<short>(arr); // No effect, short + int = int
+    auto s2 = xt::sum<long int>(arr); // The value_type of s2 is long int
+
+When you write generic code and you want to limit overflows, you can use ``xt::big_promote_value_type_t``
+as shown below:
+
+.. code::
+
+    #include "xtensor/xarray.hpp"
+    #include "xtensor/xreducer.hpp"
+    
+    template <class E>
+    void my_computation(E&& e)
+    {
+        auto s = xt::sum<xt::big_promote_value_type_t<E>>(e);
+    }
+
 Accumulators
 ------------
 

docs/source/quickref/reducer.rst

@@ -30,6 +30,15 @@ Sum
     // Outputs {6, 15}, but r3 is an unevaluated expression
     // the values are computed upon each access
 
+    auto r4 = xt::sum<long int>(a, {1});
+    // r4 holds long int values
+
+    auto r5 = xt::sum<short>(a, {1});
+    // r5 hols int values
+
+    auto r6 = xt::sum<xt::big_promote_value_type<decltype(a)>>(a, {1});
+    // r6 holds long long int values
+
 Prod
 ----
 
@@ -40,6 +49,8 @@ Prod
     xt::xarray<int> r1 = xt::prod(a);
     int r2 = xt::prod(a)();
     auto r3 = xt::prod(a, {0});
+    auro r4 = xt::prod<long int>(a, {0});
+    auto r5 = xt::prod<xt::big_promote_value_type<decltype(a)>>(a, {1});
 
 Mean
 ----