arraysumfunctor: fast sum a double array, use for SUM() in Calc

This adds an array sum functor which sums a double array in a
as fast as possible way. There are 2 implementations: SSE2 and
a simple unrolled implementation. SSE2 implementation is used if
SSE2 is detected at runtime.

Additional info:
SSE implementation at first processes the array until the array is
aligned by 16-bit boundary (should only process 1 element).
Then the array is processed by summing 8 values in one pass (using
4 variables that are 128-bit wide) where SSE operation can process
2 double values in one call.

Change-Id: I24494b08cae049aa3eabcb086867f1bdd4128374

sc/source/core/inc/arraysumfunctor.hxx

+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ */
+
+#ifndef INCLUDED_SC_SOURCE_CORE_INC_ARRAYSUMFUNCTOR_HXX
+#define INCLUDED_SC_SOURCE_CORE_INC_ARRAYSUMFUNCTOR_HXX
+
+#include <emmintrin.h>
+#include <tools/cpuid.hxx>
+
+namespace sc
+{
+
+template<typename T, unsigned int N>
+inline bool isAligned(const T* pointer)
+{
+    return 0 == (uintptr_t(pointer) % N);
+}
+
+struct ArraySumFunctor
+{
+private:
+    const double* mpArray;
+    size_t mnSize;
+
+public:
+    ArraySumFunctor(const double* pArray, size_t nSize)
+        : mpArray(pArray)
+        , mnSize(nSize)
+    {
+    }
+
+    double operator() ()
+    {
+        static bool hasSSE2 = tools::cpuid::hasSSE2();
+
+        double fSum = 0.0;
+        size_t i = 0;
+        const double* pCurrent = mpArray;
+
+        if (hasSSE2)
+        {
+            while (!isAligned<double, 16>(pCurrent))
+            {
+                fSum += *pCurrent++;
+                i++;
+            }
+            fSum += executeSSE2(i, pCurrent);
+        }
+        else
+            fSum += executeUnrolled(i, pCurrent);
+
+        // sum rest of the array
+
+        for (; i < mnSize; ++i)
+            fSum += mpArray[i];
+
+        return fSum;
+    }
+
+private:
+    inline double executeSSE2(size_t& i, const double* pCurrent) const
+    {
+        double fSum = 0.0;
+        size_t nRealSize = mnSize - i;
+        size_t nUnrolledSize = nRealSize - (nRealSize % 8);
+
+        if (nUnrolledSize > 0)
+        {
+            __m128d sum1 = _mm_setzero_pd();
+            __m128d sum2 = _mm_setzero_pd();
+            __m128d sum3 = _mm_setzero_pd();
+            __m128d sum4 = _mm_setzero_pd();
+
+            for (; i < nUnrolledSize; i += 8)
+            {
+                __m128d load1 = _mm_load_pd(pCurrent);
+                sum1 = _mm_add_pd(sum1, load1);
+                pCurrent += 2;
+
+                __m128d load2 = _mm_load_pd(pCurrent);
+                sum2 = _mm_add_pd(sum2, load2);
+                pCurrent += 2;
+
+                __m128d load3 = _mm_load_pd(pCurrent);
+                sum3 = _mm_add_pd(sum3, load3);
+                pCurrent += 2;
+
+                __m128d load4 = _mm_load_pd(pCurrent);
+                sum4 = _mm_add_pd(sum4, load4);
+                pCurrent += 2;
+            }
+            sum1 = _mm_add_pd(_mm_add_pd(sum1, sum2), _mm_add_pd(sum3, sum4));
+
+            double temp;
+
+            _mm_storel_pd(&temp, sum1);
+            fSum += temp;
+
+            _mm_storeh_pd(&temp, sum1);
+            fSum += temp;
+        }
+        return fSum;
+    }
+
+    inline double executeUnrolled(size_t& i, const double* pCurrent) const
+    {
+        size_t nRealSize = mnSize - i;
+        size_t nUnrolledSize = nRealSize - (nRealSize % 4);
+
+        if (nUnrolledSize > 0)
+        {
+            double sum0 = 0.0;
+            double sum1 = 0.0;
+            double sum2 = 0.0;
+            double sum3 = 0.0;
+
+            for (; i < nUnrolledSize; i += 4)
+            {
+                sum0 += *pCurrent++;
+                sum1 += *pCurrent++;
+                sum2 += *pCurrent++;
+                sum3 += *pCurrent++;
+            }
+            return sum0 + sum1 + sum2 + sum3;
+        }
+        return 0.0;
+    }
+};
+
+} // end namespace sc
+
+#endif
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */

sc/source/core/tool/interpr6.cxx

@@ -26,6 +26,8 @@
 #include "mtvcellfunc.hxx"
 #include "scmatrix.hxx"
 
+#include "arraysumfunctor.hxx"
+
 #include <formula/token.hxx>
 
 using namespace formula;
@@ -235,18 +237,9 @@ public:
                 if (nDataSize == 0)
                     return;
 
-                size_t nUnrolled = (nDataSize & 0x3) >> 2;
+                sc::ArraySumFunctor functor(p, nDataSize);
 
-                // Try to encourage the compiler/CPU to do something sensible for the next.
-                for (i = 0; i < nUnrolled; i+=4)
-                {
-                    mfRest += p[i];
-                    mfRest += p[i+1];
-                    mfRest += p[i+2];
-                    mfRest += p[i+3];
-                }
-                for (; i < nDataSize; ++i)
-                    mfRest += p[i];
+                mfRest += functor();
                 break;
             }