/* -*- 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/.
*
*/
#include <arraysumfunctor.hxx>
#include <tools/simdsupport.hxx>
#include <stdlib.h>
#if SC_USE_SSE2
namespace sc::op
{
/** Kahan sum with SSE2.
*/
static inline void sumSSE2(__m128d& sum, __m128d& err,
const __m128d& value)
{
const __m128d ANNULATE_SIGN_BIT = _mm_castsi128_pd(_mm_set1_epi64x(0x7FFF
'FFFF'FFFF
'FFFF));
// Temporal parameter
__m128d t = _mm_add_pd(sum, value);
// Absolute value of the total sum
__m128d asum = _mm_and_pd(sum, ANNULATE_SIGN_BIT);
// Absolute value of the value to add
__m128d avalue = _mm_and_pd(value, ANNULATE_SIGN_BIT);
// Compare the absolute values sum >= value
__m128d mask = _mm_cmpge_pd(asum, avalue);
// The following code has this form ( a - t + b)
// Case 1: a = sum b = value
// Case 2: a = value b = sum
__m128d a = _mm_add_pd(_mm_and_pd(mask, sum), _mm_andnot_pd(mask, value));
__m128d b = _mm_add_pd(_mm_and_pd(mask, value), _mm_andnot_pd(mask, sum));
err = _mm_add_pd(err, _mm_add_pd(_mm_sub_pd(a, t), b));
// Store result
sum = t;
}
/** Execute Kahan sum with SSE2.
*/
KahanSum executeSSE2(size_t& i, size_t nSize,
const double* pCurrent)
{
// Make sure we don't fall out of bounds.
// This works by sums of 8 terms.
// So the 8'th term is i+7
// If we iterate until nSize won't fall out of bounds
if (nSize > i + 7)
{
// Setup sums and errors as 0
__m128d sum1 = _mm_setzero_pd();
__m128d err1 = _mm_setzero_pd();
__m128d sum2 = _mm_setzero_pd();
__m128d err2 = _mm_setzero_pd();
__m128d sum3 = _mm_setzero_pd();
__m128d err3 = _mm_setzero_pd();
__m128d sum4 = _mm_setzero_pd();
__m128d err4 = _mm_setzero_pd();
for (; i + 7 < nSize; i += 8)
{
// Kahan sum 1
__m128d load1 = _mm_loadu_pd(pCurrent);
sumSSE2(sum1, err1, load1);
pCurrent += 2;
// Kahan sum 2
__m128d load2 = _mm_loadu_pd(pCurrent);
sumSSE2(sum2, err2, load2);
pCurrent += 2;
// Kahan sum 3
__m128d load3 = _mm_loadu_pd(pCurrent);
sumSSE2(sum3, err3, load3);
pCurrent += 2;
// Kahan sum 4
__m128d load4 = _mm_loadu_pd(pCurrent);
sumSSE2(sum4, err4, load4);
pCurrent += 2;
}
// Now we combine pairwise summation with Kahan summation
// 1+2 3+4 -> 1, 3
sumSSE2(sum1, err1, sum2);
sumSSE2(sum1, err1, err2);
sumSSE2(sum3, err3, sum4);
sumSSE2(sum3, err3, err4);
// 1+3 -> 1
sumSSE2(sum1, err1, sum3);
sumSSE2(sum1, err1, err3);
// Store results
double sums[2];
double errs[2];
_mm_storeu_pd(&sums[0], sum1);
_mm_storeu_pd(&errs[0], err1);
// First Kahan & pairwise summation
// 0+1 -> 0
KahanSum::sumNeumaierNormal(sums[0], errs[0], sums[1]);
KahanSum::sumNeumaierNormal(sums[0], errs[0], errs[1]);
// Store result
return { sums[0], errs[0] };
}
return { 0.0, 0.0 };
}
}
// namespace
#endif
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