A Discrete-Event Network Simulator
API
int64x64-cairo.cc
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1 /* -*- Mode:C++; c-file-style:"gnu"; indent-tabs-mode:nil; -*- */
2 /*
3  * Copyright (c) 2006 INRIA
4  *
5  * This program is free software; you can redistribute it and/or modify
6  * it under the terms of the GNU General Public License version 2 as
7  * published by the Free Software Foundation;
8  *
9  * This program is distributed in the hope that it will be useful,
10  * but WITHOUT ANY WARRANTY; without even the implied warranty of
11  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12  * GNU General Public License for more details.
13  *
14  * You should have received a copy of the GNU General Public License
15  * along with this program; if not, write to the Free Software
16  * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
17  *
18  * Author: Mathieu Lacage <mathieu.lacage@sophia.inria.fr>
19  */
20 #include "test.h"
21 #include "abort.h"
22 #include "assert.h"
23 #include "log.h"
24 #include <cmath>
25 #include <iostream>
26 #include "int64x64-cairo.h"
27 
28 // Include directly to allow optimizations within this compilation unit.
29 extern "C" {
30 #include "cairo-wideint.c"
31 }
32 
39 namespace ns3 {
40 
41 // Note: Logging in this file is largely avoided due to the
42 // number of calls that are made to these functions and the possibility
43 // of causing recursions leading to stack overflow
44 NS_LOG_COMPONENT_DEFINE ("int64x64-cairo");
45 
57 static inline
58 bool
60  const cairo_int128_t sb,
61  cairo_uint128_t & ua,
62  cairo_uint128_t & ub)
63 {
64  bool negA = _cairo_int128_negative (sa);
65  bool negB = _cairo_int128_negative (sb);
66  ua = _cairo_int128_to_uint128 (sa);
67  ub = _cairo_int128_to_uint128 (sb);
68  ua = negA ? _cairo_uint128_negate (ua) : ua;
69  ub = negB ? _cairo_uint128_negate (ub) : ub;
70  return (negA && !negB) || (!negA && negB);
71 }
72 
73 void
74 int64x64_t::Mul (const int64x64_t & o)
75 {
76  cairo_uint128_t a, b;
77  bool sign = output_sign (_v, o._v, a, b);
78  cairo_uint128_t result = Umul (a, b);
79  _v = sign ? _cairo_uint128_negate (result) : result;
80 }
81 
82 cairo_uint128_t
83 int64x64_t::Umul (const cairo_uint128_t a, const cairo_uint128_t b)
84 {
85  cairo_uint128_t result;
86  cairo_uint128_t hiPart, loPart, midPart;
87  cairo_uint128_t res1, res2;
88 
89  // Multiplying (a.h 2^64 + a.l) x (b.h 2^64 + b.l) =
90  // 2^128 a.h b.h + 2^64*(a.h b.l+b.h a.l) + a.l b.l
91  // get the low part a.l b.l
92  // multiply the fractional part
93  loPart = _cairo_uint64x64_128_mul (a.lo, b.lo);
94  // compute the middle part 2^64*(a.h b.l+b.h a.l)
95  midPart = _cairo_uint128_add (_cairo_uint64x64_128_mul (a.lo, b.hi),
96  _cairo_uint64x64_128_mul (a.hi, b.lo));
97  // compute the high part 2^128 a.h b.h
98  hiPart = _cairo_uint64x64_128_mul (a.hi, b.hi);
99  // if the high part is not zero, put a warning
100  NS_ABORT_MSG_IF (hiPart.hi != 0,
101  "High precision 128 bits multiplication error: multiplication overflow.");
102 
103  // Adding 64-bit terms to get 128-bit results, with carries
104  res1 = _cairo_uint64_to_uint128 (loPart.hi);
105  res2 = _cairo_uint64_to_uint128 (midPart.lo);
106  result = _cairo_uint128_add (res1, res2);
107 
108  res1 = _cairo_uint64_to_uint128 (midPart.hi);
109  res2 = _cairo_uint64_to_uint128 (hiPart.lo);
110  res1 = _cairo_uint128_add (res1, res2);
111  res1 = _cairo_uint128_lsl (res1, 64);
112 
113  result = _cairo_uint128_add (result, res1);
114 
115  return result;
116 }
117 
118 void
119 int64x64_t::Div (const int64x64_t & o)
120 {
121  cairo_uint128_t a, b;
122  bool sign = output_sign (_v, o._v, a, b);
123  cairo_uint128_t result = Udiv (a, b);
124  _v = sign ? _cairo_uint128_negate (result) : result;
125 }
126 
127 cairo_uint128_t
128 int64x64_t::Udiv (const cairo_uint128_t a, const cairo_uint128_t b)
129 {
130  cairo_uint128_t den = b;
132  cairo_uint128_t result = qr.quo;
133  cairo_uint128_t rem = qr.rem;
134 
135  // Now, manage the remainder
136  const uint64_t DIGITS = 64; // Number of fraction digits (bits) we need
137  const cairo_uint128_t ZERO = _cairo_uint32_to_uint128 ((uint32_t)0);
138 
139  NS_ASSERT_MSG (_cairo_uint128_lt (rem, den),
140  "Remainder not less than divisor");
141 
142  uint64_t digis = 0; // Number of digits we have already
143  uint64_t shift = 0; // Number we are going to get this round
144 
145  // Skip trailing zeros in divisor
146  while ( (shift < DIGITS) && !(den.lo & 0x1))
147  {
148  ++shift;
149  den = _cairo_uint128_rsl (den, 1);
150  }
151 
152  while ( (digis < DIGITS) && !(_cairo_uint128_eq (rem, ZERO)) )
153  {
154  // Skip leading zeros in remainder
155  while ( (digis + shift < DIGITS)
156  && !(rem.hi & HPCAIRO_MASK_HI_BIT) )
157  {
158  ++shift;
159  rem = _cairo_int128_lsl (rem, 1);
160  }
161 
162  // Cast off denominator bits if:
163  // Need more digits and
164  // LSB is zero or
165  // rem < den
166  while ( (digis + shift < DIGITS)
167  && ( !(den.lo & 0x1) || _cairo_uint128_lt (rem, den) ) )
168  {
169  ++shift;
170  den = _cairo_uint128_rsl (den, 1);
171  }
172 
173  // Do the division
174  qr = _cairo_uint128_divrem (rem, den);
175 
176  // Add in the quotient as shift bits of the fraction
177  result = _cairo_uint128_lsl (result, static_cast<int> (shift));
178  result = _cairo_uint128_add (result, qr.quo);
179  rem = qr.rem;
180  digis += shift;
181  shift = 0;
182  }
183  // Did we run out of remainder?
184  if (digis < DIGITS)
185  {
186  shift = DIGITS - digis;
187  result = _cairo_uint128_lsl (result, static_cast<int> (shift));
188  }
189 
190  return result;
191 }
192 
193 void
195 {
196  bool sign = _cairo_int128_negative (_v);
197  cairo_uint128_t a = sign ? _cairo_int128_negate (_v) : _v;
198  cairo_uint128_t result = UmulByInvert (a, o._v);
199 
200  _v = sign ? _cairo_int128_negate (result) : result;
201 }
202 
203 cairo_uint128_t
204 int64x64_t::UmulByInvert (const cairo_uint128_t a, const cairo_uint128_t b)
205 {
206  cairo_uint128_t result;
207  cairo_uint128_t hi, mid;
208  hi = _cairo_uint64x64_128_mul (a.hi, b.hi);
209  mid = _cairo_uint128_add (_cairo_uint64x64_128_mul (a.hi, b.lo),
210  _cairo_uint64x64_128_mul (a.lo, b.hi));
211  mid.lo = mid.hi;
212  mid.hi = 0;
213  result = _cairo_uint128_add (hi,mid);
214  return result;
215 }
216 
218 int64x64_t::Invert (const uint64_t v)
219 {
220  NS_ASSERT (v > 1);
221  cairo_uint128_t a, factor;
222  a.hi = 1;
223  a.lo = 0;
224  factor.hi = 0;
225  factor.lo = v;
226  int64x64_t result;
227  result._v = Udiv (a, factor);
228  int64x64_t tmp = int64x64_t (v, 0);
229  tmp.MulByInvert (result);
230  if (tmp.GetHigh () != 1)
231  {
232  cairo_uint128_t one = { 1, 0};
233  result._v = _cairo_uint128_add (result._v, one);
234  }
235  return result;
236 }
237 
238 
239 } // namespace ns3
Declaration of the ns3::int64x64_t type using the Cairo implementation.
cairo_uint128_t cairo_I _cairo_uint32_to_uint128(uint32_t i)
NS_ASSERT_MSG(false, "Ipv4AddressGenerator::MaskToIndex(): Impossible")
High precision numerical type, implementing Q64.64 fixed precision.
Definition: int64x64-128.h:45
cairo_uint128_t cairo_I _cairo_uint128_lsl(cairo_uint128_t a, int shift)
static int64x64_t Invert(const uint64_t v)
Compute the inverse of an integer value.
#define NS_ASSERT(condition)
At runtime, in debugging builds, if this condition is not true, the program prints the source file...
Definition: assert.h:67
static uint128_t Udiv(const uint128_t a, const uint128_t b)
Unsigned division of Q64.64 values.
#define NS_LOG_COMPONENT_DEFINE(name)
Define a Log component with a specific name.
Definition: log.h:205
void MulByInvert(const int64x64_t &o)
Multiply this value by a Q0.128 value, presumably representing an inverse, completing a division oper...
ns3::TestCase, ns3::TestSuite, ns3::TestRunner declarations, and NS_TEST_ASSERT macro definitions...
Implementation of the cairo_x functions which implement high precision arithmetic.
cairo_uint128_t cairo_I _cairo_uint128_add(cairo_uint128_t a, cairo_uint128_t b)
NS_ASSERT() and NS_ASSERT_MSG() macro definitions.
int128_t _v
The Q64.64 value.
Definition: int64x64-128.h:366
void Mul(const int64x64_t &o)
Implement *=.
Definition: int64x64-128.cc:64
int64x64_t()
Default constructor.
Definition: int64x64-128.h:87
static uint128_t UmulByInvert(const uint128_t a, const uint128_t b)
Unsigned multiplication of Q64.64 and Q0.128 values.
Every class exported by the ns3 library is enclosed in the ns3 namespace.
#define _cairo_int128_negative(a)
cairo_uint128_t cairo_I _cairo_uint64_to_uint128(cairo_uint64_t i)
int cairo_I _cairo_uint128_lt(cairo_uint128_t a, cairo_uint128_t b)
int cairo_I _cairo_uint128_eq(cairo_uint128_t a, cairo_uint128_t b)
cairo_uint128_t cairo_I _cairo_uint128_negate(cairo_uint128_t a)
#define _cairo_int128_lsl(a, b)
static uint128_t Umul(const uint128_t a, const uint128_t b)
Unsigned multiplication of Q64.64 values.
Definition: int64x64-128.cc:73
#define NS_ABORT_MSG_IF(cond, msg)
Abnormal program termination if a condition is true, with a message.
Definition: abort.h:108
void Div(const int64x64_t &o)
Implement /=.
#define _cairo_int128_negate(a)
static const uint64_t HPCAIRO_MASK_HI_BIT
High bit of fractional part.
cairo_uquorem128_t cairo_I _cairo_uint128_divrem(cairo_uint128_t num, cairo_uint128_t den)
#define _cairo_int128_to_uint128(i)
cairo_uint128_t cairo_I _cairo_uint64x64_128_mul(cairo_uint64_t a, cairo_uint64_t b)
Debug message logging.
cairo_uint128_t cairo_I _cairo_uint128_rsl(cairo_uint128_t a, int shift)
int64_t GetHigh(void) const
Get the integer portion.
Definition: int64x64-128.h:222
NS_ABORT_x macro definitions.
static bool output_sign(const int128_t sa, const int128_t sb, uint128_t &ua, uint128_t &ub)
Compute the sign of the result of multiplying or dividing Q64.64 fixed precision operands.
Definition: int64x64-128.cc:51