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
33 /**
34 * \file
35 * \ingroup highprec
36 * Implementation of the ns3::int64x64_t type using the Cairo implementation.
37 */
38
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
46 /**
47 * \ingroup highprec
48 * Compute the sign of the result of multiplying or dividing
49 * Q64.64 fixed precision operands.
50 *
51 * \param [in] sa The signed value of the first operand.
52 * \param [in] sb The signed value of the second operand.
53 * \param [out] ua The unsigned magnitude of the first operand.
54 * \param [out] ub The unsigned magnitude of the second operand.
55 * \returns True if the result will be negative.
56 */
57 static inline
58 bool
output_sign(const cairo_int128_t sa,const cairo_int128_t sb,cairo_uint128_t & ua,cairo_uint128_t & ub)59 output_sign (const cairo_int128_t sa,
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
Mul(const int64x64_t & o)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
Umul(const cairo_uint128_t a,const cairo_uint128_t b)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
Div(const int64x64_t & o)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
Udiv(const cairo_uint128_t a,const cairo_uint128_t b)128 int64x64_t::Udiv (const cairo_uint128_t a, const cairo_uint128_t b)
129 {
130 cairo_uint128_t den = b;
131 cairo_uquorem128_t qr = _cairo_uint128_divrem (a, 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
MulByInvert(const int64x64_t & o)194 int64x64_t::MulByInvert (const int64x64_t & o)
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
UmulByInvert(const cairo_uint128_t a,const cairo_uint128_t b)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
217 int64x64_t
Invert(const uint64_t v)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
240