492 lines
13 KiB
C++
492 lines
13 KiB
C++
/* -*- Mode:C++; c-file-style:"gnu"; indent-tabs-mode:nil; -*- */
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/*
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* Copyright (c) 2006 INRIA
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License version 2 as
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* published by the Free Software Foundation;
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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*
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* Author: Mathieu Lacage <mathieu.lacage@sophia.inria.fr>
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*/
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#include "high-precision-128.h"
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#include "ns3/test.h"
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#include "ns3/fatal-error.h"
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#include <math.h>
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#include <iostream>
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namespace ns3 {
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#ifdef GATHER_STATISTICS
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int HighPrecision::m_nfastadds = 0;
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int HighPrecision::m_nfastsubs = 0;
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int HighPrecision::m_nfastmuls = 0;
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int HighPrecision::m_nfastcmps = 0;
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int HighPrecision::m_nfastgets = 0;
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int HighPrecision::m_nslowadds = 0;
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int HighPrecision::m_nslowsubs = 0;
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int HighPrecision::m_nslowmuls = 0;
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int HighPrecision::m_nslowcmps = 0;
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int HighPrecision::m_nslowgets = 0;
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int HighPrecision::m_ndivs = 0;
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int HighPrecision::m_nconversions = 0;
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void
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HighPrecision::PrintStats (void)
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{
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double nadds = m_nfastadds + m_nslowadds;
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double nsubs = m_nfastsubs + m_nslowsubs;
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double ncmps = m_nfastcmps + m_nslowcmps;
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double nmuls = m_nfastmuls + m_nslowmuls;
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double ngets = m_nfastgets + m_nslowgets;
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double fast_add_ratio = m_nfastadds / nadds;
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double fast_sub_ratio = m_nfastsubs / nsubs;
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double fast_cmp_ratio = m_nfastcmps / ncmps;
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double fast_mul_ratio = m_nfastmuls / nmuls;
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double fast_get_ratio = m_nfastgets / ngets;
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std::cout << "add=" << fast_add_ratio << std::endl
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<< "sub=" << fast_sub_ratio << std::endl
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<< "cmp=" << fast_cmp_ratio << std::endl
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<< "mul=" << fast_mul_ratio << std::endl
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<< "get=" << fast_get_ratio << std::endl
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<< "nadds=" << nadds << std::endl
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<< "nsubs=" << nsubs << std::endl
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<< "ncmps=" << ncmps << std::endl
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<< "nmuls=" << nmuls << std::endl
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<< "ngets=" << ngets << std::endl
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<< "ndivs=" << m_ndivs << std::endl
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<< "nconversions=" << m_nconversions << std::endl
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;
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}
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#else
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void
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HighPrecision::PrintStats (void)
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{
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}
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#endif /* GATHER_STATISTICS */
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const double HighPrecision::MAX_64 = 18446744073709551615.0;
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HighPrecision::HighPrecision (double value)
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{
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int64_t hi = (int64_t) floor (value);
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uint64_t lo = (uint64_t) ((value - floor (value)) * MAX_64);
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if (lo == 0)
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{
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m_isFast = true;
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m_fastValue = hi;
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return;
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}
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else
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{
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m_isFast = false;
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m_slowValue = _cairo_int64_to_int128 (hi);
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m_slowValue = _cairo_int128_lsl (m_slowValue, 64);
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cairo_int128_t clo = _cairo_uint128_to_int128 (_cairo_uint64_to_uint128 (lo));
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m_slowValue = _cairo_int128_add (m_slowValue, clo);
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}
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}
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void
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HighPrecision::EnsureSlow (void)
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{
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if (m_isFast)
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{
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HP128INC (m_nconversions++);
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m_slowValue = _cairo_int64_to_int128 (m_fastValue);
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m_slowValue = _cairo_int128_lsl (m_slowValue, 64);
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m_isFast = false;
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}
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}
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int64_t
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HighPrecision::SlowGetInteger (void) const
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{
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cairo_int128_t value = _cairo_int128_rsa (m_slowValue, 64);
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return _cairo_int128_to_int64 (value);
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}
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double
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HighPrecision::SlowGetDouble (void) const
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{
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bool is_negative = _cairo_int128_negative (m_slowValue);
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cairo_int128_t value = is_negative ? _cairo_int128_negate (m_slowValue) : m_slowValue;
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cairo_int128_t hi = _cairo_int128_rsa (value, 64);
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cairo_uint128_t lo = _cairo_int128_sub (value, _cairo_uint128_lsl (hi, 64));
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double flo = _cairo_uint128_to_uint64 (lo);
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flo /= MAX_64;
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double retval = _cairo_uint128_to_uint64 (hi);
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retval += flo;
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retval *= is_negative ? -1.0 : 1.0;
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return retval;
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}
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bool
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HighPrecision::SlowAdd (HighPrecision const &o)
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{
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EnsureSlow ();
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const_cast<HighPrecision &> (o).EnsureSlow ();
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m_slowValue = _cairo_int128_add (m_slowValue, o.m_slowValue);
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return false;
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}
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bool
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HighPrecision::SlowSub (HighPrecision const &o)
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{
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EnsureSlow ();
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const_cast<HighPrecision &> (o).EnsureSlow ();
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m_slowValue = _cairo_int128_sub (m_slowValue, o.m_slowValue);
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return false;
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}
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bool
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HighPrecision::SlowMul (HighPrecision const &o)
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{
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EnsureSlow ();
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const_cast<HighPrecision &> (o).EnsureSlow ();
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// use the 128 bits multiplication
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m_slowValue = Mul128 (m_slowValue,o.m_slowValue);
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return false;
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}
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/**
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* this function multiplies two 128 bits fractions considering
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* the high 64 bits as the integer part and the low 64 bits
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* as the fractional part. It takes into account the sign
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* of the operands to produce a signed 128 bits result.
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*/
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cairo_int128_t
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HighPrecision::Mul128 (cairo_int128_t sa, cairo_int128_t sb )
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{
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bool negResult, negA, negB;
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negA = _cairo_int128_negative (sa);
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negB = _cairo_int128_negative (sb);
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// the result is negative only if one of the operand is negative
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negResult = (negA && !negB) || (!negA && negB);
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// now take the absolute part to make sure that the resulting operands are positive
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cairo_uint128_t a, b;
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a = _cairo_int128_to_uint128 (sa);
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b = _cairo_int128_to_uint128 (sb);
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a = negA ? _cairo_uint128_negate (a) : a;
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b = negB ? _cairo_uint128_negate (b) : b;
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cairo_uint128_t result;
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cairo_uint128_t hiPart,loPart,midPart;
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// Multiplying (a.h 2^64 + a.l) x (b.h 2^64 + b.l) =
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// 2^128 a.h b.h + 2^64*(a.h b.l+b.h a.l) + a.l b.l
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// get the low part a.l b.l
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// multiply the fractional part
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loPart = _cairo_uint64x64_128_mul (a.lo, b.lo);
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// compute the middle part 2^64*(a.h b.l+b.h a.l)
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midPart = _cairo_uint128_add (_cairo_uint64x64_128_mul (a.lo, b.hi),
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_cairo_uint64x64_128_mul (a.hi, b.lo));
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// truncate the low part
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result.lo = _cairo_uint64_add (loPart.hi,midPart.lo);
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// compute the high part 2^128 a.h b.h
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hiPart = _cairo_uint64x64_128_mul (a.hi, b.hi);
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// truncate the high part and only use the low part
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result.hi = _cairo_uint64_add (hiPart.lo,midPart.hi);
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// if the high part is not zero, put a warning
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if (hiPart.hi != 0)
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{
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NS_FATAL_ERROR ("High precision 128 bits multiplication error: multiplication overflow.");
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}
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// add the sign to the result
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result = negResult ? _cairo_uint128_negate (result) : result;
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return _cairo_uint128_to_int128 (result);
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}
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bool
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HighPrecision::Div (HighPrecision const &o)
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{
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HP128INC (m_ndivs++);
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EnsureSlow ();
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const_cast<HighPrecision &> (o).EnsureSlow ();
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cairo_int128_t result = Div128 (m_slowValue, o.m_slowValue);
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m_slowValue = result;
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return false;
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}
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cairo_int128_t
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HighPrecision::Div128 (cairo_int128_t sa, cairo_int128_t sb)
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{
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bool negResult, negA, negB;
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// take the sign of the operands
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negA = _cairo_int128_negative (sa);
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negB = _cairo_int128_negative (sb);
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// the result is negative only if one of the operand is negative
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negResult = (negA && !negB) || (!negA && negB);
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// now take the absolute part to make sure that the resulting operands are positive
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cairo_uint128_t a, b;
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a = _cairo_int128_to_uint128 (sa);
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b = _cairo_int128_to_uint128 (sb);
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a = negA ? _cairo_uint128_negate (a) : a;
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b = negB ? _cairo_uint128_negate (b) : b;
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cairo_uquorem128_t qr = _cairo_uint128_divrem (a, b);
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cairo_uint128_t result = _cairo_uint128_lsl (qr.quo, 64);
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// Now, manage the remainder
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cairo_uint128_t tmp = _cairo_uint128_rsl (qr.rem, 64);
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cairo_uint128_t zero = _cairo_uint64_to_uint128 (0);
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cairo_uint128_t rem, div;
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if (_cairo_uint128_eq (tmp, zero))
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{
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rem = _cairo_uint128_lsl (qr.rem, 64);
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div = b;
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}
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else
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{
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rem = qr.rem;
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div = _cairo_uint128_rsl (b, 64);
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}
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qr = _cairo_uint128_divrem (rem, div);
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result = _cairo_uint128_add (result, qr.quo);
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result = negResult ? _cairo_uint128_negate (result) : result;
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return _cairo_uint128_to_int128 (result);
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}
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int
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HighPrecision::SlowCompare (HighPrecision const &o) const
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{
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const_cast<HighPrecision *> (this)->EnsureSlow ();
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const_cast<HighPrecision &> (o).EnsureSlow ();
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if (_cairo_int128_lt (m_slowValue, o.m_slowValue))
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{
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return -1;
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}
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else if (_cairo_int128_eq (m_slowValue, o.m_slowValue))
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{
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return 0;
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}
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else
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{
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return 1;
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}
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}
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} // namespace ns3
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#include "ns3/test.h"
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#define CHECK_EXPECTED(a,b) \
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NS_TEST_ASSERT_MSG_EQ (a.GetInteger (),b,"Arithmetic failure: " << (a.GetInteger ()) << "!=" << (b))
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#define V(v) \
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HighPrecision (v, false)
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namespace ns3 {
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class Hp128ArithmeticTestCase : public TestCase
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{
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public:
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Hp128ArithmeticTestCase ();
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virtual bool DoRun (void);
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};
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Hp128ArithmeticTestCase::Hp128ArithmeticTestCase ()
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: TestCase ("Check basic arithmetic operations")
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{
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}
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bool
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Hp128ArithmeticTestCase::DoRun (void)
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{
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HighPrecision a, b;
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a = HighPrecision (1, false);
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b = HighPrecision (1, false);
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a.Sub (b);
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CHECK_EXPECTED (a, 0);
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a = V (1);
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a.Sub (V (2));
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CHECK_EXPECTED (a, -1);
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a = V (1);
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a.Sub (V (3));
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CHECK_EXPECTED (a, -2);
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a = V (1);
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a.Sub (V (-1));
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CHECK_EXPECTED (a, 2);
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a = V (1);
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a.Sub (V (-2));
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CHECK_EXPECTED (a, 3);
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a = V (-3);
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a.Sub (V (-4));
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CHECK_EXPECTED (a, 1);
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a = V (-2);
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a.Sub (V (3));
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CHECK_EXPECTED (a, -5);
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a = V (1);
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a.Add (V (2));
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CHECK_EXPECTED (a, 3);
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a = V (1);
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a.Add (V (-3));
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CHECK_EXPECTED (a, -2);
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a = V (0);
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a.Add (V (0));
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CHECK_EXPECTED (a, 0);
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a = V (0);
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a.Mul (V (0));
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CHECK_EXPECTED (a, 0);
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a = V (0);
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a.Mul (V (1));
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CHECK_EXPECTED (a, 0);
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a = V (0);
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a.Mul (V (-1));
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CHECK_EXPECTED (a, 0);
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a = V (1);
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a.Mul (V (0));
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CHECK_EXPECTED (a, 0);
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a = V (1);
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a.Mul (V (1));
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CHECK_EXPECTED (a, 1);
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a = V (1);
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a.Mul (V (-1));
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CHECK_EXPECTED (a, -1);
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a = V (-1);
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a.Mul (V (-1));
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CHECK_EXPECTED (a, 1);
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a = V (0);
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a.Mul (V (1));
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CHECK_EXPECTED (a, 0);
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a = V (0);
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a.Mul (V (-1));
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CHECK_EXPECTED (a, 0);
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a = V (1);
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a.Mul (V (1));
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CHECK_EXPECTED (a, 1);
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a = V (1);
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a.Mul (V (-1));
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CHECK_EXPECTED (a, -1);
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a = V (-1);
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a.Mul (V (1));
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CHECK_EXPECTED (a, -1);
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a = V (-1);
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a.Mul (V (-1));
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CHECK_EXPECTED (a, 1);
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a = V (2);
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a.Mul (V (3));
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a.Div (V (3));
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CHECK_EXPECTED (a, 2);
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// Below, the division loses precision because 2/3 is not
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// representable exactly in 64.64 integers. So, we got
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// something super close but the final rounding kills us.
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a = V (2);
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a.Div (V (3));
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a.Mul (V (3));
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CHECK_EXPECTED (a, 1);
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// The example below shows that we really do not lose
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// much precision internally: it is almost always the
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// final conversion which loses precision.
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a = V (2000000000);
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a.Div (V (3));
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a.Mul (V (3));
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CHECK_EXPECTED (a, 1999999999);
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return false;
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}
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class Hp128Bug455TestCase : public TestCase
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{
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public:
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Hp128Bug455TestCase ();
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virtual bool DoRun (void);
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};
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Hp128Bug455TestCase::Hp128Bug455TestCase ()
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: TestCase ("Test case for bug 455")
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{
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}
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bool
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Hp128Bug455TestCase::DoRun (void)
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{
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HighPrecision a = HighPrecision (0.1);
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a.Div (HighPrecision (1.25));
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NS_TEST_ASSERT_MSG_EQ (a.GetDouble (), 0.08, "The original testcase");
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a = HighPrecision (0.5);
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a.Mul (HighPrecision (5));
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NS_TEST_ASSERT_MSG_EQ (a.GetDouble (), 2.5, "Simple test for multiplication");
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a = HighPrecision (-0.5);
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a.Mul (HighPrecision (5));
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NS_TEST_ASSERT_MSG_EQ (a.GetDouble (), -2.5, "Test sign, first operation negative");
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a = HighPrecision (-0.5);
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a.Mul (HighPrecision (-5));
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NS_TEST_ASSERT_MSG_EQ (a.GetDouble (), 2.5, "both operands negative");
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a = HighPrecision (0.5);
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a.Mul (HighPrecision (-5));
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NS_TEST_ASSERT_MSG_EQ (a.GetDouble (), -2.5, "only second operand negative");
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return false;
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}
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class Hp128Bug863TestCase : public TestCase
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{
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public:
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Hp128Bug863TestCase ();
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virtual bool DoRun (void);
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};
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Hp128Bug863TestCase::Hp128Bug863TestCase ()
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: TestCase ("Test case for bug 863")
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{
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}
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bool
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Hp128Bug863TestCase::DoRun (void)
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{
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HighPrecision a = HighPrecision (0.9);
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a.Div (HighPrecision (1));
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NS_TEST_ASSERT_MSG_EQ (a.GetDouble (), 0.9, "The original testcase");
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a = HighPrecision (0.5);
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a.Div (HighPrecision (0.5));
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NS_TEST_ASSERT_MSG_EQ (a.GetDouble (), 1.0, "Simple test for division");
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a = HighPrecision (-0.5);
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a.Div (HighPrecision (0.5));
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NS_TEST_ASSERT_MSG_EQ (a.GetDouble (), -1.0, "first argument negative");
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a = HighPrecision (0.5);
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a.Div (HighPrecision (-0.5));
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NS_TEST_ASSERT_MSG_EQ (a.GetDouble (), -1.0, "second argument negative");
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a = HighPrecision (-0.5);
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a.Div (HighPrecision (-0.5));
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NS_TEST_ASSERT_MSG_EQ (a.GetDouble (), 1.0, "both arguments negative");
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return false;
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}
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static class HighPrecision128TestSuite : public TestSuite
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{
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public:
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HighPrecision128TestSuite ()
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: TestSuite ("high-precision-128", UNIT)
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{
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AddTestCase (new Hp128ArithmeticTestCase ());
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AddTestCase (new Hp128Bug455TestCase ());
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AddTestCase (new Hp128Bug863TestCase ());
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}
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} g_highPrecision128TestSuite;
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} // namespace ns3
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