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11210 libm should be cstyle(1ONBLD) clean
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--- old/usr/src/lib/libm/common/C/exp.c
+++ new/usr/src/lib/libm/common/C/exp.c
1 1 /*
2 2 * CDDL HEADER START
3 3 *
4 4 * The contents of this file are subject to the terms of the
5 5 * Common Development and Distribution License (the "License").
6 6 * You may not use this file except in compliance with the License.
7 7 *
8 8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9 9 * or http://www.opensolaris.org/os/licensing.
10 10 * See the License for the specific language governing permissions
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11 11 * and limitations under the License.
12 12 *
13 13 * When distributing Covered Code, include this CDDL HEADER in each
14 14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15 15 * If applicable, add the following below this CDDL HEADER, with the
16 16 * fields enclosed by brackets "[]" replaced with your own identifying
17 17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 18 *
19 19 * CDDL HEADER END
20 20 */
21 +
21 22 /*
22 23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
23 24 */
25 +
24 26 /*
25 27 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
26 28 * Use is subject to license terms.
27 29 */
28 30
29 31 #pragma weak __exp = exp
30 32
31 33 /*
32 34 * exp(x)
33 35 * Hybrid algorithm of Peter Tang's Table driven method (for large
34 36 * arguments) and an accurate table (for small arguments).
35 37 * Written by K.C. Ng, November 1988.
36 38 * Method (large arguments):
37 39 * 1. Argument Reduction: given the input x, find r and integer k
38 40 * and j such that
39 41 * x = (k+j/32)*(ln2) + r, |r| <= (1/64)*ln2
40 42 *
41 43 * 2. exp(x) = 2^k * (2^(j/32) + 2^(j/32)*expm1(r))
42 44 * a. expm1(r) is approximated by a polynomial:
43 45 * expm1(r) ~ r + t1*r^2 + t2*r^3 + ... + t5*r^6
44 46 * Here t1 = 1/2 exactly.
45 47 * b. 2^(j/32) is represented to twice double precision
46 48 * as TBL[2j]+TBL[2j+1].
47 49 *
48 50 * Note: If divide were fast enough, we could use another approximation
49 51 * in 2.a:
50 52 * expm1(r) ~ (2r)/(2-R), R = r - r^2*(t1 + t2*r^2)
51 53 * (for the same t1 and t2 as above)
52 54 *
53 55 * Special cases:
54 56 * exp(INF) is INF, exp(NaN) is NaN;
55 57 * exp(-INF)= 0;
56 58 * for finite argument, only exp(0)=1 is exact.
57 59 *
58 60 * Accuracy:
59 61 * According to an error analysis, the error is always less than
60 62 * an ulp (unit in the last place). The largest errors observed
61 63 * are less than 0.55 ulp for normal results and less than 0.75 ulp
62 64 * for subnormal results.
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63 65 *
64 66 * Misc. info.
65 67 * For IEEE double
66 68 * if x > 7.09782712893383973096e+02 then exp(x) overflow
67 69 * if x < -7.45133219101941108420e+02 then exp(x) underflow
68 70 */
69 71
70 72 #include "libm.h"
71 73
72 74 static const double TBL[] = {
73 - 1.00000000000000000000e+00, 0.00000000000000000000e+00,
74 - 1.02189714865411662714e+00, 5.10922502897344389359e-17,
75 - 1.04427378242741375480e+00, 8.55188970553796365958e-17,
75 + 1.00000000000000000000e+00, 0.00000000000000000000e+00,
76 + 1.02189714865411662714e+00, 5.10922502897344389359e-17,
77 + 1.04427378242741375480e+00, 8.55188970553796365958e-17,
76 78 1.06714040067682369717e+00, -7.89985396684158212226e-17,
77 79 1.09050773266525768967e+00, -3.04678207981247114697e-17,
78 - 1.11438674259589243221e+00, 1.04102784568455709549e-16,
79 - 1.13878863475669156458e+00, 8.91281267602540777782e-17,
80 - 1.16372485877757747552e+00, 3.82920483692409349872e-17,
81 - 1.18920711500272102690e+00, 3.98201523146564611098e-17,
80 + 1.11438674259589243221e+00, 1.04102784568455709549e-16,
81 + 1.13878863475669156458e+00, 8.91281267602540777782e-17,
82 + 1.16372485877757747552e+00, 3.82920483692409349872e-17,
83 + 1.18920711500272102690e+00, 3.98201523146564611098e-17,
82 84 1.21524735998046895524e+00, -7.71263069268148813091e-17,
83 - 1.24185781207348400201e+00, 4.65802759183693679123e-17,
84 - 1.26905095719173321989e+00, 2.66793213134218609523e-18,
85 - 1.29683955465100964055e+00, 2.53825027948883149593e-17,
85 + 1.24185781207348400201e+00, 4.65802759183693679123e-17,
86 + 1.26905095719173321989e+00, 2.66793213134218609523e-18,
87 + 1.29683955465100964055e+00, 2.53825027948883149593e-17,
86 88 1.32523664315974132322e+00, -2.85873121003886075697e-17,
87 - 1.35425554693689265129e+00, 7.70094837980298946162e-17,
89 + 1.35425554693689265129e+00, 7.70094837980298946162e-17,
88 90 1.38390988196383202258e+00, -6.77051165879478628716e-17,
89 91 1.41421356237309514547e+00, -9.66729331345291345105e-17,
90 92 1.44518080697704665027e+00, -3.02375813499398731940e-17,
91 93 1.47682614593949934623e+00, -3.48399455689279579579e-17,
92 94 1.50916442759342284141e+00, -1.01645532775429503911e-16,
93 - 1.54221082540794074411e+00, 7.94983480969762085616e-17,
95 + 1.54221082540794074411e+00, 7.94983480969762085616e-17,
94 96 1.57598084510788649659e+00, -1.01369164712783039808e-17,
95 - 1.61049033194925428347e+00, 2.47071925697978878522e-17,
97 + 1.61049033194925428347e+00, 2.47071925697978878522e-17,
96 98 1.64575547815396494578e+00, -1.01256799136747726038e-16,
97 - 1.68179283050742900407e+00, 8.19901002058149652013e-17,
99 + 1.68179283050742900407e+00, 8.19901002058149652013e-17,
98 100 1.71861929812247793414e+00, -1.85138041826311098821e-17,
99 - 1.75625216037329945351e+00, 2.96014069544887330703e-17,
100 - 1.79470907500310716820e+00, 1.82274584279120867698e-17,
101 - 1.83400808640934243066e+00, 3.28310722424562658722e-17,
101 + 1.75625216037329945351e+00, 2.96014069544887330703e-17,
102 + 1.79470907500310716820e+00, 1.82274584279120867698e-17,
103 + 1.83400808640934243066e+00, 3.28310722424562658722e-17,
102 104 1.87416763411029996256e+00, -6.12276341300414256164e-17,
103 105 1.91520656139714740007e+00, -1.06199460561959626376e-16,
104 - 1.95714412417540017941e+00, 8.96076779103666776760e-17,
106 + 1.95714412417540017941e+00, 8.96076779103666776760e-17,
105 107 };
106 108
107 109 /*
108 110 * For i = 0, ..., 66,
109 111 * TBL2[2*i] is a double precision number near (i+1)*2^-6, and
110 112 * TBL2[2*i+1] = exp(TBL2[2*i]) to within a relative error less
111 113 * than 2^-60.
112 114 *
113 115 * For i = 67, ..., 133,
114 116 * TBL2[2*i] is a double precision number near -(i+1)*2^-6, and
115 117 * TBL2[2*i+1] = exp(TBL2[2*i]) to within a relative error less
116 118 * than 2^-60.
117 119 */
118 120 static const double TBL2[] = {
119 121 1.56249999999984491572e-02, 1.01574770858668417262e+00,
120 122 3.12499999999998716305e-02, 1.03174340749910253834e+00,
121 123 4.68750000000011102230e-02, 1.04799100201663386578e+00,
122 124 6.24999999999990632493e-02, 1.06449445891785843266e+00,
123 125 7.81249999999999444888e-02, 1.08125780744903954300e+00,
124 126 9.37500000000013322676e-02, 1.09828514030782731226e+00,
125 127 1.09375000000001346145e-01, 1.11558061464248226002e+00,
126 128 1.24999999999999417133e-01, 1.13314845306682565607e+00,
127 129 1.40624999999995337063e-01, 1.15099294469117108264e+00,
128 130 1.56249999999996141975e-01, 1.16911844616949989195e+00,
129 131 1.71874999999992894573e-01, 1.18752938276309216725e+00,
130 132 1.87500000000000888178e-01, 1.20623024942098178158e+00,
131 133 2.03124999999361649516e-01, 1.22522561187652545556e+00,
132 134 2.18750000000000416334e-01, 1.24452010776609567344e+00,
133 135 2.34375000000003524958e-01, 1.26411844775347081971e+00,
134 136 2.50000000000006328271e-01, 1.28402541668774961003e+00,
135 137 2.65624999999982791543e-01, 1.30424587476761533189e+00,
136 138 2.81249999999993727240e-01, 1.32478475872885725906e+00,
137 139 2.96875000000003275158e-01, 1.34564708304941493822e+00,
138 140 3.12500000000002886580e-01, 1.36683794117380030819e+00,
139 141 3.28124999999993394173e-01, 1.38836250675661765364e+00,
140 142 3.43749999999998612221e-01, 1.41022603492570874906e+00,
141 143 3.59374999999992450483e-01, 1.43243386356506730017e+00,
142 144 3.74999999999991395772e-01, 1.45499141461818881638e+00,
143 145 3.90624999999997613020e-01, 1.47790419541173490003e+00,
144 146 4.06249999999991895372e-01, 1.50117780000011058483e+00,
145 147 4.21874999999996613820e-01, 1.52481791053132154090e+00,
146 148 4.37500000000004607426e-01, 1.54883029863414023453e+00,
147 149 4.53125000000004274359e-01, 1.57322082682725961078e+00,
148 150 4.68750000000008326673e-01, 1.59799544995064657371e+00,
149 151 4.84374999999985456078e-01, 1.62316021661928200359e+00,
150 152 4.99999999999997335465e-01, 1.64872127070012375327e+00,
151 153 5.15625000000000222045e-01, 1.67468485281178436352e+00,
152 154 5.31250000000003441691e-01, 1.70105730184840653330e+00,
153 155 5.46874999999999111822e-01, 1.72784505652716169344e+00,
154 156 5.62499999999999333866e-01, 1.75505465696029738787e+00,
155 157 5.78124999999993338662e-01, 1.78269274625180318417e+00,
156 158 5.93749999999999666933e-01, 1.81076607211938656050e+00,
157 159 6.09375000000003441691e-01, 1.83928148854178719063e+00,
158 160 6.24999999999995559108e-01, 1.86824595743221411048e+00,
159 161 6.40625000000009103829e-01, 1.89766655033813602671e+00,
160 162 6.56249999999993782751e-01, 1.92755045016753268072e+00,
161 163 6.71875000000002109424e-01, 1.95790495294292221651e+00,
162 164 6.87499999999992450483e-01, 1.98873746958227681780e+00,
163 165 7.03125000000004996004e-01, 2.02005552770870666635e+00,
164 166 7.18750000000007105427e-01, 2.05186677348799140219e+00,
165 167 7.34375000000008770762e-01, 2.08417897349558689513e+00,
166 168 7.49999999999983901766e-01, 2.11700001661264058939e+00,
167 169 7.65624999999997002398e-01, 2.15033791595229351046e+00,
168 170 7.81250000000005884182e-01, 2.18420081081563077774e+00,
169 171 7.96874999999991451283e-01, 2.21859696867912603579e+00,
170 172 8.12500000000000000000e-01, 2.25353478721320854561e+00,
171 173 8.28125000000008215650e-01, 2.28902279633221983346e+00,
172 174 8.43749999999997890576e-01, 2.32506966027711614586e+00,
173 175 8.59374999999999444888e-01, 2.36168417973090827289e+00,
174 176 8.75000000000003219647e-01, 2.39887529396710563745e+00,
175 177 8.90625000000013433699e-01, 2.43665208303232461162e+00,
176 178 9.06249999999980571097e-01, 2.47502376996297712708e+00,
177 179 9.21874999999984456878e-01, 2.51399972303748420188e+00,
178 180 9.37500000000001887379e-01, 2.55358945806293169412e+00,
179 181 9.53125000000003330669e-01, 2.59380264069854327147e+00,
180 182 9.68749999999989119814e-01, 2.63464908881560244680e+00,
181 183 9.84374999999997890576e-01, 2.67613877489447116176e+00,
182 184 1.00000000000001154632e+00, 2.71828182845907662113e+00,
183 185 1.01562499999999333866e+00, 2.76108853855008318234e+00,
184 186 1.03124999999995980993e+00, 2.80456935623711389738e+00,
185 187 1.04687499999999933387e+00, 2.84873489717039740654e+00,
186 188 -1.56249999999999514277e-02, 9.84496437005408453480e-01,
187 189 -3.12499999999955972718e-02, 9.69233234476348348707e-01,
188 190 -4.68749999999993824384e-02, 9.54206665969188905230e-01,
189 191 -6.24999999999976130205e-02, 9.39413062813478028090e-01,
190 192 -7.81249999999989314103e-02, 9.24848813216205822840e-01,
191 193 -9.37499999999995975442e-02, 9.10510361380034494161e-01,
192 194 -1.09374999999998584466e-01, 8.96394206635151680196e-01,
193 195 -1.24999999999998556710e-01, 8.82496902584596676355e-01,
194 196 -1.40624999999999361622e-01, 8.68815056262843721235e-01,
195 197 -1.56249999999999111822e-01, 8.55345327307423297647e-01,
196 198 -1.71874999999924144012e-01, 8.42084427143446223596e-01,
197 199 -1.87499999999996752598e-01, 8.29029118180403035154e-01,
198 200 -2.03124999999988037347e-01, 8.16176213022349550386e-01,
199 201 -2.18749999999995947686e-01, 8.03522573689063990265e-01,
200 202 -2.34374999999996419531e-01, 7.91065110850298847112e-01,
201 203 -2.49999999999996280753e-01, 7.78800783071407765057e-01,
202 204 -2.65624999999999888978e-01, 7.66726596070820165529e-01,
203 205 -2.81249999999989397370e-01, 7.54839601989015340777e-01,
204 206 -2.96874999999996114219e-01, 7.43136898668761203268e-01,
205 207 -3.12499999999999555911e-01, 7.31615628946642115871e-01,
206 208 -3.28124999999993782751e-01, 7.20272979955444259126e-01,
207 209 -3.43749999999997946087e-01, 7.09106182437399867879e-01,
208 210 -3.59374999999994337863e-01, 6.98112510068129799023e-01,
209 211 -3.74999999999994615418e-01, 6.87289278790975899369e-01,
210 212 -3.90624999999999000799e-01, 6.76633846161729612945e-01,
211 213 -4.06249999999947264406e-01, 6.66143610703522903727e-01,
212 214 -4.21874999999988453681e-01, 6.55816011271509125002e-01,
213 215 -4.37499999999999111822e-01, 6.45648526427892610613e-01,
214 216 -4.53124999999999278355e-01, 6.35638673826052436056e-01,
215 217 -4.68749999999999278355e-01, 6.25784009604591573428e-01,
216 218 -4.84374999999992894573e-01, 6.16082127790682609891e-01,
217 219 -4.99999999999998168132e-01, 6.06530659712634534486e-01,
218 220 -5.15625000000000000000e-01, 5.97127273421627413619e-01,
219 221 -5.31249999999989785948e-01, 5.87869673122352498496e-01,
220 222 -5.46874999999972688514e-01, 5.78755598612500032907e-01,
221 223 -5.62500000000000000000e-01, 5.69782824730923009859e-01,
222 224 -5.78124999999992339461e-01, 5.60949160814475100700e-01,
223 225 -5.93749999999948707696e-01, 5.52252450163048691500e-01,
224 226 -6.09374999999552580121e-01, 5.43690569513243682209e-01,
225 227 -6.24999999999984789945e-01, 5.35261428518998383375e-01,
226 228 -6.40624999999983457677e-01, 5.26962969243379708573e-01,
227 229 -6.56249999999998334665e-01, 5.18793165653890220312e-01,
228 230 -6.71874999999943378626e-01, 5.10750023129039609771e-01,
229 231 -6.87499999999997002398e-01, 5.02831577970942467104e-01,
230 232 -7.03124999999991118216e-01, 4.95035896926202978463e-01,
231 233 -7.18749999999991340260e-01, 4.87361076713623331269e-01,
232 234 -7.34374999999985678123e-01, 4.79805243559684402310e-01,
233 235 -7.49999999999997335465e-01, 4.72366552741015965911e-01,
234 236 -7.65624999999993782751e-01, 4.65043188134059204408e-01,
235 237 -7.81249999999863220523e-01, 4.57833361771676883301e-01,
236 238 -7.96874999999998112621e-01, 4.50735313406363247157e-01,
237 239 -8.12499999999990119015e-01, 4.43747310081084256339e-01,
238 240 -8.28124999999996003197e-01, 4.36867645705559026759e-01,
239 241 -8.43749999999988120614e-01, 4.30094640640067360504e-01,
240 242 -8.59374999999994115818e-01, 4.23426641285265303871e-01,
241 243 -8.74999999999977129406e-01, 4.16862019678517936594e-01,
242 244 -8.90624999999983346655e-01, 4.10399173096376801428e-01,
243 245 -9.06249999999991784350e-01, 4.04036523663345414903e-01,
244 246 -9.21874999999994004796e-01, 3.97772517966614058693e-01,
245 247 -9.37499999999994337863e-01, 3.91605626676801210628e-01,
246 248 -9.53124999999999444888e-01, 3.85534344174578935682e-01,
247 249 -9.68749999999986677324e-01, 3.79557188183094640355e-01,
248 250 -9.84374999999992339461e-01, 3.73672699406045860648e-01,
249 251 -9.99999999999995892175e-01, 3.67879441171443832825e-01,
250 252 -1.01562499999994315658e+00, 3.62175999080846300338e-01,
251 253 -1.03124999999991096011e+00, 3.56560980663978732697e-01,
252 254 -1.04687499999999067413e+00, 3.51033015038813400732e-01,
253 255 };
254 256
255 257 static const double C[] = {
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256 258 0.5,
257 259 4.61662413084468283841e+01, /* 0x40471547, 0x652b82fe */
258 260 2.16608493865351192653e-02, /* 0x3f962e42, 0xfee00000 */
259 261 5.96317165397058656257e-12, /* 0x3d9a39ef, 0x35793c76 */
260 262 1.6666666666526086527e-1, /* 3fc5555555548f7c */
261 263 4.1666666666226079285e-2, /* 3fa5555555545d4e */
262 264 8.3333679843421958056e-3, /* 3f811115b7aa905e */
263 265 1.3888949086377719040e-3, /* 3f56c1728d739765 */
264 266 1.0,
265 267 0.0,
266 - 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
267 - 7.45133219101941108420e+02, /* 0x40874910, 0xD52D3051 */
268 - 5.55111512312578270212e-17, /* 0x3c900000, 0x00000000 */
268 + 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
269 + 7.45133219101941108420e+02, /* 0x40874910, 0xD52D3051 */
270 + 5.55111512312578270212e-17, /* 0x3c900000, 0x00000000 */
269 271 };
270 272
271 -#define half C[0]
272 -#define invln2_32 C[1]
273 -#define ln2_32hi C[2]
274 -#define ln2_32lo C[3]
275 -#define t2 C[4]
276 -#define t3 C[5]
277 -#define t4 C[6]
278 -#define t5 C[7]
279 -#define one C[8]
280 -#define zero C[9]
281 -#define threshold1 C[10]
282 -#define threshold2 C[11]
283 -#define twom54 C[12]
273 +#define half C[0]
274 +#define invln2_32 C[1]
275 +#define ln2_32hi C[2]
276 +#define ln2_32lo C[3]
277 +#define t2 C[4]
278 +#define t3 C[5]
279 +#define t4 C[6]
280 +#define t5 C[7]
281 +#define one C[8]
282 +#define zero C[9]
283 +#define threshold1 C[10]
284 +#define threshold2 C[11]
285 +#define twom54 C[12]
284 286
285 287 double
286 -exp(double x) {
287 - double y, z, t;
288 - int hx, ix, k, j, m;
288 +exp(double x)
289 +{
290 + double y, z, t;
291 + int hx, ix, k, j, m;
289 292
290 293 ix = ((int *)&x)[HIWORD];
291 294 hx = ix & ~0x80000000;
292 295
293 - if (hx < 0x3ff0a2b2) { /* |x| < 3/2 ln 2 */
294 - if (hx < 0x3f862e42) { /* |x| < 1/64 ln 2 */
296 + if (hx < 0x3ff0a2b2) { /* |x| < 3/2 ln 2 */
297 + if (hx < 0x3f862e42) { /* |x| < 1/64 ln 2 */
295 298 if (hx < 0x3ed00000) { /* |x| < 2^-18 */
296 299 volatile int dummy __unused;
297 300
298 301 dummy = (int)x; /* raise inexact if x != 0 */
299 302 #ifdef lint
300 303 dummy = dummy;
301 304 #endif
305 +
302 306 if (hx < 0x3e300000)
303 307 return (one + x);
308 +
304 309 return (one + x * (one + half * x));
305 310 }
311 +
306 312 t = x * x;
307 - y = x + (t * (half + x * t2) +
308 - (t * t) * (t3 + x * t4 + t * t5));
313 + y = x + (t * (half + x * t2) + (t * t) * (t3 + x * t4 +
314 + t * t5));
309 315 return (one + y);
310 316 }
311 317
312 318 /* find the multiple of 2^-6 nearest x */
313 319 k = hx >> 20;
314 320 j = (0x00100000 | (hx & 0x000fffff)) >> (0x40c - k);
315 321 j = (j - 1) & ~1;
322 +
316 323 if (ix < 0)
317 324 j += 134;
325 +
318 326 z = x - TBL2[j];
319 327 t = z * z;
320 - y = z + (t * (half + z * t2) +
321 - (t * t) * (t3 + z * t4 + t * t5));
322 - return (TBL2[j+1] + TBL2[j+1] * y);
328 + y = z + (t * (half + z * t2) + (t * t) * (t3 + z * t4 + t *
329 + t5));
330 + return (TBL2[j + 1] + TBL2[j + 1] * y);
323 331 }
324 332
325 - if (hx >= 0x40862e42) { /* x is large, infinite, or nan */
333 + if (hx >= 0x40862e42) { /* x is large, infinite, or nan */
326 334 if (hx >= 0x7ff00000) {
327 335 if (ix == 0xfff00000 && ((int *)&x)[LOWORD] == 0)
328 336 return (zero);
337 +
329 338 return (x * x);
330 339 }
340 +
331 341 if (x > threshold1)
332 342 return (_SVID_libm_err(x, x, 6));
343 +
333 344 if (-x > threshold2)
334 345 return (_SVID_libm_err(x, x, 7));
335 346 }
336 347
337 348 t = invln2_32 * x;
349 +
338 350 if (ix < 0)
339 351 t -= half;
340 352 else
341 353 t += half;
354 +
342 355 k = (int)t;
343 356 j = (k & 0x1f) << 1;
344 357 m = k >> 5;
345 358 z = (x - k * ln2_32hi) - k * ln2_32lo;
346 359
347 360 /* z is now in primary range */
348 361 t = z * z;
349 362 y = z + (t * (half + z * t2) + (t * t) * (t3 + z * t4 + t * t5));
350 - y = TBL[j] + (TBL[j+1] + TBL[j] * y);
363 + y = TBL[j] + (TBL[j + 1] + TBL[j] * y);
364 +
351 365 if (m < -1021) {
352 366 ((int *)&y)[HIWORD] += (m + 54) << 20;
353 367 return (twom54 * y);
354 368 }
369 +
355 370 ((int *)&y)[HIWORD] += m << 20;
356 371 return (y);
357 372 }
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