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/*
* Copyright (C) 2024 Apple Inc. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY APPLE INC. ``AS IS'' AND ANY
* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL APPLE INC. OR
* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
* OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/*
* This is the Math.sumPrecise() polyfill by Kevin Gibbons, ported to C++. Original LICENSE is as follows:
*
* BSD 3-Clause License
*
* Copyright (c) 2024 Kevin Gibbons
*
* Redistribution and use in source and binary forms, with or without modification,
* are permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions
* and the following disclaimer in the documentation and/or other materials provided with the distribution.
*
* 3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse
* or promote products derived from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS “AS IS” AND ANY EXPRESS OR IMPLIED
* WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN
* IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#include "config.h"
#include <wtf/PreciseSum.h>
#include <cmath>
namespace WTF {
static constexpr double MAX_DOUBLE = 1.79769313486231570815e+308;
static constexpr double PENULTIMATE_DOUBLE = 1.79769313486231550856e+308;
static constexpr double MAX_ULP = MAX_DOUBLE - PENULTIMATE_DOUBLE;
static constexpr double TWO_POW_1023 = 8.98846567431158e+307;
ALWAYS_INLINE std::pair<double, double> twosum(double x, double y)
{
double hi = x + y;
double lo = y - (hi - x);
return std::make_pair(hi, lo);
}
void PreciseSum::add(double x)
{
if (!(!x && std::signbit(x)))
m_everyValueIsNegativeZero = false;
unsigned actuallyUsedPartials = 0;
for (double y : m_partials) {
if (std::fabs(x) < std::fabs(y))
std::swap(x, y);
auto pair = twosum(x, y);
if (std::isinf(std::fabs(pair.first))) {
double sign = pair.first < 0 ? -1 : 1;
m_overflow += sign;
x = (x - sign * TWO_POW_1023) - sign * TWO_POW_1023;
if (std::fabs(x) < std::fabs(y))
std::swap(x, y);
pair = twosum(x, y);
}
if (auto lo = pair.second) {
m_partials[actuallyUsedPartials] = lo;
++actuallyUsedPartials;
}
x = pair.first;
}
m_partials.shrink(actuallyUsedPartials);
if (x)
m_partials.append(x);
}
double PreciseSum::compute()
{
if (m_everyValueIsNegativeZero)
return -0.0;
int32_t n = m_partials.size() - 1;
double hi = 0;
double lo = 0;
if (m_overflow) {
double next = n >= 0 ? m_partials[n] : 0;
--n;
if (std::fabs(m_overflow) > 1 || (m_overflow > 0 && next > 0) || (m_overflow < 0 && next < 0))
return m_overflow > 0 ? std::numeric_limits<double>::infinity() : -std::numeric_limits<double>::infinity();
auto pair = twosum(m_overflow * TWO_POW_1023, next / 2);
hi = pair.first;
lo = pair.second * 2;
if (std::isinf(std::fabs(hi * 2))) {
// silly edge case: rounding to the maximum value
// MAX_DOUBLE has a 1 in the last place of its significand, so if we subtract exactly half a ULP from 2**1024, the result rounds away from it (i.e. to infinity) under ties-to-even
// but if the next partial has the opposite sign of the current value, we need to round towards MAX_DOUBLE instead
// this is the same as the "handle rounding" case below, but there's only one potentially-finite case we need to worry about, so we just hardcode that one
if (hi > 0) {
if (hi == TWO_POW_1023 && lo == -(MAX_ULP / 2) && n >= 0 && m_partials[n] < 0)
return MAX_DOUBLE;
return std::numeric_limits<double>::infinity();
}
if (hi == -TWO_POW_1023 && lo == (MAX_ULP / 2) && n >= 0 && m_partials[n] > 0)
return -MAX_DOUBLE;
return -std::numeric_limits<double>::infinity();
}
if (lo) {
m_partials[n + 1] = lo;
++n;
lo = 0;
}
hi *= 2;
}
while (n >= 0) {
double x = hi;
double y = m_partials[n];
--n;
auto pair = twosum(x, y);
hi = pair.first;
lo = pair.second;
if (lo)
break;
}
// handle rounding
// when the roundoff error is exactly half of the ULP for the result, we need to check one more partial to know which way to round
if (n >= 0 && ((lo < 0 && m_partials[n] < 0) || (lo > 0 && m_partials[n] > 0))) {
double y = lo * 2;
double x = hi + y;
double yr = x - hi;
if (y == yr)
hi = x;
}
return hi;
}
} // namespace WTF
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