Implement the non-execution policy versions of `inclusive_scan` and `transform_ inclusive_scan` for C++17

[mclow.lists]

Summary

This is the last of three patches - D33997 and D34038 were the first two.
When this lands, we'll have all of the new (non-parallel) algorithms that were added in C++17.

include/numeric

     exclusive_scan(InputIterator first, InputIterator last, 
                    OutputIterator result, T init, BinaryOperation binary_op); // C++17
 
+template<class InputIterator, class OutputIterator>
+    OutputIterator
+    inclusive_scan(InputIterator first, InputIterator last, OutputIterator result);  // C++17
+
+template<class InputIterator, class OutputIterator, class BinaryOperation>
+    OutputIterator
+    inclusive_scan(InputIterator first, InputIterator last,
+                   OutputIterator result, BinaryOperation binary_op);  // C++17
+
+template<class InputIterator, class OutputIterator, class BinaryOperation, class T>
+    OutputIterator
+    inclusive_scan(InputIterator first, InputIterator last,
+                   OutputIterator result, BinaryOperation binary_op, T init);  // C++17
+
 template<class InputIterator, class OutputIterator, class T,
          class BinaryOperation, class UnaryOperation>
     OutputIterator

                              OutputIterator result, T init,
                              BinaryOperation binary_op, UnaryOperation unary_op);  // C++17
 
+template<class InputIterator, class OutputIterator,
+         class BinaryOperation, class UnaryOperation>
+  OutputIterator
+  transform_inclusive_scan(InputIterator first, InputIterator last,
+                             OutputIterator result,
+                             BinaryOperation binary_op, UnaryOperation unary_op);  // C++17
+                                          
+template<class InputIterator, class OutputIterator,
+         class BinaryOperation, class UnaryOperation, class T>
+  OutputIterator
+  transform_inclusive_scan(InputIterator first, InputIterator last,
+                             OutputIterator result,
+                             BinaryOperation binary_op, UnaryOperation unary_op,
+                             T init);  // C++17
+
 template <class InputIterator, class OutputIterator>
     OutputIterator
     adjacent_difference(InputIterator first, InputIterator last, OutputIterator result);

     return _VSTD::exclusive_scan(__first, __last, __result, __init, _VSTD::plus<>());
 }
 
+template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp>
+_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last, 
+                               _OutputIterator __result, _BinaryOp __b,  _Tp __init)
+{
+    for (; __first != __last; ++__first, (void) ++__result) {
+        __init = __b(__init, *__first);
+        *__result = __init;
+        }
+    return __result;
+}
+
+template <class _InputIterator, class _OutputIterator, class _BinaryOp>
+_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last, 
+                               _OutputIterator __result, _BinaryOp __b)
+{
+    if (__first != __last) {
+        typename std::iterator_traits<_InputIterator>::value_type __init = *__first;
+        *__result++ = __init;
+        if (++__first != __last)
+            return _VSTD::inclusive_scan(__first, __last, __result, __b, __init);
+        }
+
+    return __result;
+}
+
+template <class _InputIterator, class _OutputIterator>
+_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last, 
+                               _OutputIterator __result)
+{
+    return _VSTD::inclusive_scan(__first, __last, __result, std::plus<>());
+}
+
 template <class _InputIterator, class _OutputIterator, class _Tp, 
           class _BinaryOp, class _UnaryOp>
 inline _LIBCPP_INLINE_VISIBILITY

     }
     return __result;
 }
+
+template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp, class _UnaryOp>
+_OutputIterator transform_inclusive_scan(_InputIterator __first, _InputIterator __last, 
+                           _OutputIterator __result, _BinaryOp __b, _UnaryOp __u, _Tp __init)
+{
+    for (; __first != __last; ++__first, (void) ++__result) {
+        __init = __b(__init, __u(*__first));
+        *__result = __init;
+        }
+
+    return __result;
+}
+
+template <class _InputIterator, class _OutputIterator, class _BinaryOp, class _UnaryOp>
+_OutputIterator transform_inclusive_scan(_InputIterator __first, _InputIterator __last, 
+                               _OutputIterator __result, _BinaryOp __b, _UnaryOp __u)
+{
+    if (__first != __last) {
+        typename std::iterator_traits<_InputIterator>::value_type __init = __u(*__first);
+        *__result++ = __init;
+        if (++__first != __last)
+            return _VSTD::transform_inclusive_scan(__first, __last, __result, __b, __u, __init);
+        }
+    
+    return __result;
+}
 #endif
 
 template <class _InputIterator, class _OutputIterator>

test/std/numerics/numeric.ops/inclusive.scan/inclusive_scan.pass.cpp

+//===----------------------------------------------------------------------===//
+//
+//                     The LLVM Compiler Infrastructure
+//
+// This file is dual licensed under the MIT and the University of Illinois Open
+// Source Licenses. See LICENSE.TXT for details.
+//
+//===----------------------------------------------------------------------===//
+
+// <numeric>
+// UNSUPPORTED: c++98, c++03, c++11, c++14
+
+// template<class InputIterator, class OutputIterator, class T>
+//     OutputIterator inclusive_scan(InputIterator first, InputIterator last,
+//                                   OutputIterator result, T init);
+// 
+
+#include <numeric>
+#include <vector>
+#include <cassert>
+
+#include "test_iterators.h"
+
+template <class Iter1, class Iter2>
+void
+test(Iter1 first, Iter1 last, Iter2 rFirst, Iter2 rLast)
+{
+    std::vector<typename std::iterator_traits<Iter1>::value_type> v;
+    
+//  Not in place
+    std::inclusive_scan(first, last, std::back_inserter(v));
+    assert(std::equal(v.begin(), v.end(), rFirst, rLast));
+
+//  In place
+    v.clear();
+    v.assign(first, last);
+    std::inclusive_scan(v.begin(), v.end(), v.begin());
+    assert(std::equal(v.begin(), v.end(), rFirst, rLast));  
+}
+
+
+template <class Iter>
+void
+test()
+{
+          int ia[]   = {1, 3, 5, 7,  9};
+    const int pRes[] = {1, 4, 9, 16, 25};
+    const unsigned sa = sizeof(ia) / sizeof(ia[0]);
+    static_assert(sa == sizeof(pRes) / sizeof(pRes[0]));       // just to be sure
+
+    for (unsigned int i = 0; i < sa; ++i )
+        test(Iter(ia), Iter(ia + i), pRes, pRes + i);
+}
+
+int triangle(int n) { return n*(n+1)/2; }
+
+//  Basic sanity
+void basic_tests()
+{
+    {
+    std::vector<int> v(10);
+    std::fill(v.begin(), v.end(), 3);
+    std::inclusive_scan(v.begin(), v.end(), v.begin());
+    for (size_t i = 0; i < v.size(); ++i)
+        assert(v[i] == (int)(i+1) * 3);
+    }
+
+    {
+    std::vector<int> v(10);
+    std::iota(v.begin(), v.end(), 0);
+    std::inclusive_scan(v.begin(), v.end(), v.begin());
+    for (size_t i = 0; i < v.size(); ++i)
+        assert(v[i] == triangle(i));
+    }
+
+    {
+    std::vector<int> v(10);
+    std::iota(v.begin(), v.end(), 1);
+    std::inclusive_scan(v.begin(), v.end(), v.begin());
+    for (size_t i = 0; i < v.size(); ++i)
+        assert(v[i] == triangle(i + 1));
+    }
+
+    {
+    std::vector<int> v, res;
+    std::inclusive_scan(v.begin(), v.end(), std::back_inserter(res));
+    assert(res.empty());
+    }
+}
+
+int main()
+{
+    basic_tests();
+
+//  All the iterator categories
+    test<input_iterator        <const int*> >();
+    test<forward_iterator      <const int*> >();
+    test<bidirectional_iterator<const int*> >();
+    test<random_access_iterator<const int*> >();
+    test<const int*>();
+    test<      int*>();
+}

test/std/numerics/numeric.ops/inclusive.scan/inclusive_scan_op.pass.cpp

+//===----------------------------------------------------------------------===//
+//
+//                     The LLVM Compiler Infrastructure
+//
+// This file is dual licensed under the MIT and the University of Illinois Open
+// Source Licenses. See LICENSE.TXT for details.
+//
+//===----------------------------------------------------------------------===//
+
+// <numeric>
+// UNSUPPORTED: c++98, c++03, c++11, c++14
+
+// template<class InputIterator, class OutputIterator, class T, class BinaryOperation>
+//     OutputIterator
+//     inclusive_scan(InputIterator first, InputIterator last,
+//                    OutputIterator result, 
+//                    BinaryOperation binary_op); // C++17
+
+#include <numeric>
+#include <vector>
+#include <cassert>
+#include <iostream>
+
+#include "test_iterators.h"
+
+template <class Iter1, class T, class Op, class Iter2>
+void
+test(Iter1 first, Iter1 last, Op op, Iter2 rFirst, Iter2 rLast)
+{
+    std::vector<typename std::iterator_traits<Iter1>::value_type> v;
+
+//  Not in place
+    std::inclusive_scan(first, last, std::back_inserter(v), op);
+    assert(std::equal(v.begin(), v.end(), rFirst, rLast));
+
+//  In place
+    v.clear();
+    v.assign(first, last);
+    std::inclusive_scan(v.begin(), v.end(), v.begin(), op);
+    assert(std::equal(v.begin(), v.end(), rFirst, rLast));  
+}
+
+
+template <class Iter>
+void
+test()
+{
+          int ia[]   = {1, 3,  5,   7,   9};
+    const int pRes[] = {1, 4,  9,  16,  25};
+    const int mRes[] = {1, 3, 15, 105, 945};
+    const unsigned sa = sizeof(ia) / sizeof(ia[0]);
+    static_assert(sa == sizeof(pRes) / sizeof(pRes[0]));       // just to be sure
+    static_assert(sa == sizeof(mRes) / sizeof(mRes[0]));       // just to be sure
+
+    for (unsigned int i = 0; i < sa; ++i ) {
+        test(Iter(ia), Iter(ia + i), std::plus<>(),       pRes, pRes + i);
+        test(Iter(ia), Iter(ia + i), std::multiplies<>(), mRes, mRes + i);
+        }
+}
+
+int triangle(int n) { return n*(n+1)/2; }
+
+//  Basic sanity
+void basic_tests()
+{
+    {
+    std::vector<int> v(10);
+    std::fill(v.begin(), v.end(), 3);
+    std::inclusive_scan(v.begin(), v.end(), v.begin(), std::plus<>());
+    for (size_t i = 0; i < v.size(); ++i)
+        assert(v[i] == (int)(i+1) * 3);
+    }
+
+    {
+    std::vector<int> v(10);
+    std::iota(v.begin(), v.end(), 0);
+    std::inclusive_scan(v.begin(), v.end(), v.begin(), std::plus<>());
+    for (size_t i = 0; i < v.size(); ++i)
+        assert(v[i] == triangle(i));
+    }
+
+    {
+    std::vector<int> v(10);
+    std::iota(v.begin(), v.end(), 1);
+    std::inclusive_scan(v.begin(), v.end(), v.begin(), std::plus<>());
+    for (size_t i = 0; i < v.size(); ++i)
+        assert(v[i] == triangle(i + 1));
+    }
+
+    {
+    std::vector<int> v, res;
+    std::inclusive_scan(v.begin(), v.end(), std::back_inserter(res), std::plus<>());
+    assert(res.empty());
+    }
+}
+
+
+int main()
+{
+
+    basic_tests();
+    
+//  All the iterator categories
+//     test<input_iterator        <const int*> >();
+//     test<forward_iterator      <const int*> >();
+//     test<bidirectional_iterator<const int*> >();
+//     test<random_access_iterator<const int*> >();
+//     test<const int*>();
+//     test<      int*>();
+
+}
+ 
 No newline at end of file

test/std/numerics/numeric.ops/inclusive.scan/inclusive_scan_op_init.pass.cpp

+//===----------------------------------------------------------------------===//
+//
+//                     The LLVM Compiler Infrastructure
+//
+// This file is dual licensed under the MIT and the University of Illinois Open
+// Source Licenses. See LICENSE.TXT for details.
+//
+//===----------------------------------------------------------------------===//
+
+// <numeric>
+// UNSUPPORTED: c++98, c++03, c++11, c++14
+
+// template<class InputIterator, class OutputIterator, class T, class BinaryOperation>
+//     OutputIterator
+//     inclusive_scan(InputIterator first, InputIterator last,
+//                    OutputIterator result, 
+//                    BinaryOperation binary_op, T init); // C++17
+
+#include <numeric>
+#include <vector>
+#include <cassert>
+
+#include "test_iterators.h"
+
+template <class Iter1, class T, class Op, class Iter2>
+void
+test(Iter1 first, Iter1 last, Op op, T init, Iter2 rFirst, Iter2 rLast)
+{
+    std::vector<typename std::iterator_traits<Iter1>::value_type> v;
+
+//  Not in place
+    std::inclusive_scan(first, last, std::back_inserter(v), op, init);
+    assert(std::equal(v.begin(), v.end(), rFirst, rLast));
+
+//  In place
+    v.clear();
+    v.assign(first, last);
+    std::inclusive_scan(v.begin(), v.end(), v.begin(), op, init);
+    assert(std::equal(v.begin(), v.end(), rFirst, rLast));  
+}
+
+
+template <class Iter>
+void
+test()
+{
+          int ia[]   = {1, 3,  5,   7,   9};
+    const int pRes[] = {1, 4,  9,  16,  25};
+    const int mRes[] = {1, 3, 15, 105, 945};
+    const unsigned sa = sizeof(ia) / sizeof(ia[0]);
+    static_assert(sa == sizeof(pRes) / sizeof(pRes[0]));       // just to be sure
+    static_assert(sa == sizeof(mRes) / sizeof(mRes[0]));       // just to be sure
+
+    for (unsigned int i = 0; i < sa; ++i ) {
+        test(Iter(ia), Iter(ia + i), std::plus<>(),       0, pRes, pRes + i);
+        test(Iter(ia), Iter(ia + i), std::multiplies<>(), 1, mRes, mRes + i);
+        }
+}
+
+int triangle(int n) { return n*(n+1)/2; }
+
+//  Basic sanity
+void basic_tests()
+{
+    {
+    std::vector<int> v(10);
+    std::fill(v.begin(), v.end(), 3);
+    std::inclusive_scan(v.begin(), v.end(), v.begin(), std::plus<>(), 50);
+    for (size_t i = 0; i < v.size(); ++i)
+        assert(v[i] == 50 + (int)(i+1) * 3);
+    }
+
+    {
+    std::vector<int> v(10);
+    std::iota(v.begin(), v.end(), 0);
+    std::inclusive_scan(v.begin(), v.end(), v.begin(), std::plus<>(), 40);
+    for (size_t i = 0; i < v.size(); ++i)
+        assert(v[i] == 40 + triangle(i));
+    }
+
+    {
+    std::vector<int> v(10);
+    std::iota(v.begin(), v.end(), 1);
+    std::inclusive_scan(v.begin(), v.end(), v.begin(), std::plus<>(), 30);
+    for (size_t i = 0; i < v.size(); ++i)
+        assert(v[i] == 30 + triangle(i + 1));
+    }
+
+    {
+    std::vector<int> v, res;
+    std::inclusive_scan(v.begin(), v.end(), std::back_inserter(res), std::plus<>(), 40);
+    assert(res.empty());
+    }
+
+//  Make sure that the calculations are done using the init typedef
+    {
+    std::vector<unsigned char> v(10);
+    std::iota(v.begin(), v.end(), 1);
+    std::vector<int> res;
+    std::inclusive_scan(v.begin(), v.end(), std::back_inserter(res), std::multiplies<>(), 1);
+
+    assert(res.size() == 10);
+    int j = 1;
+    assert(res[0] == 1);
+    for (size_t i = 1; i < v.size(); ++i)
+    {
+        j *= i + 1;
+        assert(res[i] == j);
+    }
+    }
+}
+
+
+int main()
+{
+
+    basic_tests();
+    
+//  All the iterator categories
+    test<input_iterator        <const int*> >();
+    test<forward_iterator      <const int*> >();
+    test<bidirectional_iterator<const int*> >();
+    test<random_access_iterator<const int*> >();
+    test<const int*>();
+    test<      int*>();
+
+}
+ 
 No newline at end of file

test/std/numerics/numeric.ops/transform.inclusive.scan/transform_inclusive_scan_bop_uop.pass.cpp

+//===----------------------------------------------------------------------===//
+//
+//                     The LLVM Compiler Infrastructure
+//
+// This file is dual licensed under the MIT and the University of Illinois Open
+// Source Licenses. See LICENSE.TXT for details.
+//
+//===----------------------------------------------------------------------===//
+
+// <numeric>
+// UNSUPPORTED: c++98, c++03, c++11, c++14
+
+// template<class InputIterator, class OutputIterator, class T, 
+//          class BinaryOperation, class UnaryOperation>
+//   OutputIterator transform_inclusive_scan(InputIterator first, InputIterator last,
+//                                           OutputIterator result,
+//                                           BinaryOperation binary_op,
+//                                           UnaryOperation unary_op);
+
+
+#include <numeric>
+#include <vector>
+#include <cassert>
+#include <iostream>
+
+#include "test_iterators.h"
+
+template <class _Tp = void>
+struct identity : std::unary_function<_Tp, _Tp>
+{
+    constexpr const _Tp& operator()(const _Tp& __x) const { return __x;}
+};
+
+template <>
+struct identity<void>
+{
+    template <class _Tp>
+    constexpr auto operator()(_Tp&& __x) const
+    _NOEXCEPT_(noexcept(_VSTD::forward<_Tp>(__x)))
+    -> decltype        (_VSTD::forward<_Tp>(__x))
+        { return        _VSTD::forward<_Tp>(__x); }
+};
+
+template <class Iter1, class BOp, class UOp, class Iter2>
+void
+test(Iter1 first, Iter1 last, BOp bop, UOp uop, Iter2 rFirst, Iter2 rLast)
+{
+    std::vector<typename std::iterator_traits<Iter1>::value_type> v;
+//  Test not in-place
+    std::transform_inclusive_scan(first, last, std::back_inserter(v), bop, uop);
+    assert(std::equal(v.begin(), v.end(), rFirst, rLast));
+
+//  Test in-place
+    v.clear();
+    v.assign(first, last);
+    std::transform_inclusive_scan(v.begin(), v.end(), v.begin(), bop, uop);
+    assert(std::equal(v.begin(), v.end(), rFirst, rLast));
+}
+
+
+template <class Iter>
+void
+test()
+{
+          int ia[]     = {  1,  3,   5,   7,    9};
+    const int pResI0[] = {  1,  4,   9,  16,   25};        // with identity
+    const int mResI0[] = {  1,  3,  15, 105,  945};        
+    const int pResN0[] = { -1, -4,  -9, -16,  -25};        // with negate
+    const int mResN0[] = { -1,  3, -15, 105, -945};
+    const unsigned sa = sizeof(ia) / sizeof(ia[0]);
+    static_assert(sa == sizeof(pResI0) / sizeof(pResI0[0]));       // just to be sure
+    static_assert(sa == sizeof(mResI0) / sizeof(mResI0[0]));       // just to be sure
+    static_assert(sa == sizeof(pResN0) / sizeof(pResN0[0]));       // just to be sure
+    static_assert(sa == sizeof(mResN0) / sizeof(mResN0[0]));       // just to be sure
+
+    for (unsigned int i = 0; i < sa; ++i ) {
+        test(Iter(ia), Iter(ia + i), std::plus<>(),       identity<>(),    pResI0, pResI0 + i);
+        test(Iter(ia), Iter(ia + i), std::multiplies<>(), identity<>(),    mResI0, mResI0 + i);
+        test(Iter(ia), Iter(ia + i), std::plus<>(),       std::negate<>(), pResN0, pResN0 + i);
+        test(Iter(ia), Iter(ia + i), std::multiplies<>(), std::negate<>(), mResN0, mResN0 + i);
+        }
+}
+
+int triangle(int n) { return n*(n+1)/2; }
+
+//  Basic sanity
+void basic_tests()
+{
+    {
+    std::vector<int> v(10);
+    std::fill(v.begin(), v.end(), 3);
+    std::transform_inclusive_scan(v.begin(), v.end(), v.begin(), std::plus<>(), identity<>());
+   std::copy(v.begin(), v.end(), std::ostream_iterator<int>(std::cout, " "));
+  std::cout << std::endl; 
+    for (size_t i = 0; i < v.size(); ++i)
+        assert(v[i] == (int)(i+1) * 3);
+    }
+
+    {
+    std::vector<int> v(10);
+    std::iota(v.begin(), v.end(), 0);
+    std::transform_inclusive_scan(v.begin(), v.end(), v.begin(), std::plus<>(), identity<>());
+    for (size_t i = 0; i < v.size(); ++i)
+        assert(v[i] == triangle(i));
+    }
+
+    {
+    std::vector<int> v(10);
+    std::iota(v.begin(), v.end(), 1);
+    std::transform_inclusive_scan(v.begin(), v.end(), v.begin(), std::plus<>(), identity<>());
+    for (size_t i = 0; i < v.size(); ++i)
+        assert(v[i] == triangle(i + 1));
+    }
+
+    {
+    std::vector<int> v, res;
+    std::transform_inclusive_scan(v.begin(), v.end(), std::back_inserter(res), std::plus<>(), identity<>());
+    assert(res.empty());
+    }
+}
+
+int main()
+{
+    basic_tests();
+    
+//  All the iterator categories
+    test<input_iterator        <const int*> >();
+    test<forward_iterator      <const int*> >();
+    test<bidirectional_iterator<const int*> >();
+    test<random_access_iterator<const int*> >();
+    test<const int*>();
+    test<      int*>();
+}

test/std/numerics/numeric.ops/transform.inclusive.scan/transform_inclusive_scan_bop_uop_init.pass.cpp

+//===----------------------------------------------------------------------===//
+//
+//                     The LLVM Compiler Infrastructure
+//
+// This file is dual licensed under the MIT and the University of Illinois Open
+// Source Licenses. See LICENSE.TXT for details.
+//
+//===----------------------------------------------------------------------===//
+
+// <numeric>
+// UNSUPPORTED: c++98, c++03, c++11, c++14
+
+// template<class InputIterator, class OutputIterator, class T, 
+//          class BinaryOperation, class UnaryOperation>
+//   OutputIterator transform_inclusive_scan(InputIterator first, InputIterator last,
+//                                           OutputIterator result,
+//                                           BinaryOperation binary_op,
+//                                           UnaryOperation unary_op,
+//                                           T init);
+
+
+#include <numeric>
+#include <vector>
+#include <cassert>
+
+#include "test_iterators.h"
+
+template <class _Tp = void>
+struct identity : std::unary_function<_Tp, _Tp>
+{
+    constexpr const _Tp& operator()(const _Tp& __x) const { return __x;}
+};
+
+template <>
+struct identity<void>
+{
+    template <class _Tp>
+    constexpr auto operator()(_Tp&& __x) const
+    _NOEXCEPT_(noexcept(_VSTD::forward<_Tp>(__x)))
+    -> decltype        (_VSTD::forward<_Tp>(__x))
+        { return        _VSTD::forward<_Tp>(__x); }
+};
+
+template <class Iter1, class BOp, class UOp, class T, class Iter2>
+void
+test(Iter1 first, Iter1 last, BOp bop, UOp uop, T init, Iter2 rFirst, Iter2 rLast)
+{
+    std::vector<typename std::iterator_traits<Iter1>::value_type> v;
+//  Test not in-place
+    std::transform_inclusive_scan(first, last, std::back_inserter(v), bop, uop, init);
+    assert(std::equal(v.begin(), v.end(), rFirst, rLast));
+
+//  Test in-place
+    v.clear();
+    v.assign(first, last);
+    std::transform_inclusive_scan(v.begin(), v.end(), v.begin(), bop, uop, init);
+    assert(std::equal(v.begin(), v.end(), rFirst, rLast));
+}
+
+
+template <class Iter>
+void
+test()
+{
+          int ia[]     = {  1,  3,   5,    7,     9};
+    const int pResI0[] = {  1,  4,   9,   16,    25};        // with identity
+    const int mResI0[] = {  0,  0,   0,    0,     0};        
+    const int pResN0[] = { -1, -4,  -9,  -16,   -25};        // with negate
+    const int mResN0[] = {  0,  0,   0,    0,     0};
+    const int pResI2[] = {  3,  6,  11,   18,    27};        // with identity
+    const int mResI2[] = {  2,  6,  30,  210,  1890};        
+    const int pResN2[] = {  1, -2,  -7,  -14,   -23};        // with negate
+    const int mResN2[] = { -2,  6, -30,  210, -1890};
+    const unsigned sa = sizeof(ia) / sizeof(ia[0]);
+    static_assert(sa == sizeof(pResI0) / sizeof(pResI0[0]));       // just to be sure
+    static_assert(sa == sizeof(mResI0) / sizeof(mResI0[0]));       // just to be sure
+    static_assert(sa == sizeof(pResN0) / sizeof(pResN0[0]));       // just to be sure
+    static_assert(sa == sizeof(mResN0) / sizeof(mResN0[0]));       // just to be sure
+    static_assert(sa == sizeof(pResI2) / sizeof(pResI2[0]));       // just to be sure
+    static_assert(sa == sizeof(mResI2) / sizeof(mResI2[0]));       // just to be sure
+    static_assert(sa == sizeof(pResN2) / sizeof(pResN2[0]));       // just to be sure
+    static_assert(sa == sizeof(mResN2) / sizeof(mResN2[0]));       // just to be sure
+
+    for (unsigned int i = 0; i < sa; ++i ) {
+        test(Iter(ia), Iter(ia + i), std::plus<>(),       identity<>(),    0, pResI0, pResI0 + i);
+        test(Iter(ia), Iter(ia + i), std::multiplies<>(), identity<>(),    0, mResI0, mResI0 + i);
+        test(Iter(ia), Iter(ia + i), std::plus<>(),       std::negate<>(), 0, pResN0, pResN0 + i);
+        test(Iter(ia), Iter(ia + i), std::multiplies<>(), std::negate<>(), 0, mResN0, mResN0 + i);
+        test(Iter(ia), Iter(ia + i), std::plus<>(),       identity<>(),    2, pResI2, pResI2 + i);
+        test(Iter(ia), Iter(ia + i), std::multiplies<>(), identity<>(),    2, mResI2, mResI2 + i);
+        test(Iter(ia), Iter(ia + i), std::plus<>(),       std::negate<>(), 2, pResN2, pResN2 + i);
+        test(Iter(ia), Iter(ia + i), std::multiplies<>(), std::negate<>(), 2, mResN2, mResN2 + i);
+        }
+}
+
+int triangle(int n) { return n*(n+1)/2; }
+
+//  Basic sanity
+void basic_tests()
+{
+    {
+    std::vector<int> v(10);
+    std::fill(v.begin(), v.end(), 3);
+    std::transform_inclusive_scan(v.begin(), v.end(), v.begin(), std::plus<>(), identity<>(), 50);
+    for (size_t i = 0; i < v.size(); ++i)
+        assert(v[i] == 50 + (int) (i + 1) * 3);
+    }
+
+    {
+    std::vector<int> v(10);
+    std::iota(v.begin(), v.end(), 0);
+    std::transform_inclusive_scan(v.begin(), v.end(), v.begin(), std::plus<>(), identity<>(), 30);
+    for (size_t i = 0; i < v.size(); ++i)
+        assert(v[i] == 30 + triangle(i));
+    }
+
+    {
+    std::vector<int> v(10);
+    std::iota(v.begin(), v.end(), 1);
+    std::transform_inclusive_scan(v.begin(), v.end(), v.begin(), std::plus<>(), identity<>(), 40);
+    for (size_t i = 0; i < v.size(); ++i)
+        assert(v[i] == 40 + triangle(i + 1));
+    }
+
+    {
+    std::vector<int> v, res;
+    std::transform_inclusive_scan(v.begin(), v.end(), std::back_inserter(res), std::plus<>(), identity<>(), 1);
+    assert(res.empty());
+    }
+
+//  Make sure that the calculations are done using the init typedef
+    {
+    std::vector<unsigned char> v(10);
+    std::iota(v.begin(), v.end(), 1);
+    std::vector<int> res;
+    std::transform_inclusive_scan(v.begin(), v.end(), std::back_inserter(res), std::multiplies<>(), identity<>(), 1);
+
+    assert(res.size() == 10);
+    int j = 1;
+    assert(res[0] == 1);
+    for (size_t i = 1; i < res.size(); ++i)
+    {
+        j *= i + 1;
+        assert(res[i] == j);
+    }
+    }
+}
+
+int main()
+{
+    basic_tests();
+    
+//  All the iterator categories
+    test<input_iterator        <const int*> >();
+    test<forward_iterator      <const int*> >();
+    test<bidirectional_iterator<const int*> >();
+    test<random_access_iterator<const int*> >();
+    test<const int*>();
+    test<      int*>();
+}