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49 <div class="headertitle">
50 <h1>arm_sin_q31.c</h1> </div>
52 <div class="contents">
53 <a href="arm__sin__q31_8c.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">/* ---------------------------------------------------------------------- </span>
54 <a name="l00002"></a>00002 <span class="comment">* Copyright (C) 2010 ARM Limited. All rights reserved. </span>
55 <a name="l00003"></a>00003 <span class="comment">* </span>
56 <a name="l00004"></a>00004 <span class="comment">* $Date: 15. July 2011 </span>
57 <a name="l00005"></a>00005 <span class="comment">* $Revision: V1.0.10 </span>
58 <a name="l00006"></a>00006 <span class="comment">* </span>
59 <a name="l00007"></a>00007 <span class="comment">* Project: CMSIS DSP Library </span>
60 <a name="l00008"></a>00008 <span class="comment">* Title: arm_sin_q31.c </span>
61 <a name="l00009"></a>00009 <span class="comment">* </span>
62 <a name="l00010"></a>00010 <span class="comment">* Description: Fast sine calculation for Q31 values. </span>
63 <a name="l00011"></a>00011 <span class="comment">* </span>
64 <a name="l00012"></a>00012 <span class="comment">* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0</span>
65 <a name="l00013"></a>00013 <span class="comment">* </span>
66 <a name="l00014"></a>00014 <span class="comment">* Version 1.0.10 2011/7/15 </span>
67 <a name="l00015"></a>00015 <span class="comment">* Big Endian support added and Merged M0 and M3/M4 Source code. </span>
68 <a name="l00016"></a>00016 <span class="comment">* </span>
69 <a name="l00017"></a>00017 <span class="comment">* Version 1.0.3 2010/11/29 </span>
70 <a name="l00018"></a>00018 <span class="comment">* Re-organized the CMSIS folders and updated documentation. </span>
71 <a name="l00019"></a>00019 <span class="comment">* </span>
72 <a name="l00020"></a>00020 <span class="comment">* Version 1.0.2 2010/11/11 </span>
73 <a name="l00021"></a>00021 <span class="comment">* Documentation updated. </span>
74 <a name="l00022"></a>00022 <span class="comment">* </span>
75 <a name="l00023"></a>00023 <span class="comment">* Version 1.0.1 2010/10/05 </span>
76 <a name="l00024"></a>00024 <span class="comment">* Production release and review comments incorporated. </span>
77 <a name="l00025"></a>00025 <span class="comment">* </span>
78 <a name="l00026"></a>00026 <span class="comment">* Version 1.0.0 2010/09/20 </span>
79 <a name="l00027"></a>00027 <span class="comment">* Production release and review comments incorporated. </span>
80 <a name="l00028"></a>00028 <span class="comment">* -------------------------------------------------------------------- */</span>
81 <a name="l00029"></a>00029
82 <a name="l00030"></a>00030 <span class="preprocessor">#include "<a class="code" href="arm__math_8h.html">arm_math.h</a>"</span>
83 <a name="l00031"></a>00031
84 <a name="l00059"></a><a class="code" href="group__sin.html#gab1ffde7f3deee5adc75ba8b3d0a53106">00059</a> <span class="keyword">static</span> <span class="keyword">const</span> <a class="code" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0" title="32-bit fractional data type in 1.31 format.">q31_t</a> <a class="code" href="group__sin.html#gab1ffde7f3deee5adc75ba8b3d0a53106">sinTableQ31</a>[259] = {
85 <a name="l00060"></a>00060 0xfcdbd541, 0x0, 0x3242abf, 0x647d97c, 0x96a9049, 0xc8bd35e, 0xfab272b,
86 <a name="l00061"></a>00061 0x12c8106f,
87 <a name="l00062"></a>00062 0x15e21445, 0x18f8b83c, 0x1c0b826a, 0x1f19f97b, 0x2223a4c5, 0x25280c5e,
88 <a name="l00063"></a>00063 0x2826b928, 0x2b1f34eb,
89 <a name="l00064"></a>00064 0x2e110a62, 0x30fbc54d, 0x33def287, 0x36ba2014, 0x398cdd32, 0x3c56ba70,
90 <a name="l00065"></a>00065 0x3f1749b8, 0x41ce1e65,
91 <a name="l00066"></a>00066 0x447acd50, 0x471cece7, 0x49b41533, 0x4c3fdff4, 0x4ebfe8a5, 0x5133cc94,
92 <a name="l00067"></a>00067 0x539b2af0, 0x55f5a4d2,
93 <a name="l00068"></a>00068 0x5842dd54, 0x5a82799a, 0x5cb420e0, 0x5ed77c8a, 0x60ec3830, 0x62f201ac,
94 <a name="l00069"></a>00069 0x64e88926, 0x66cf8120,
95 <a name="l00070"></a>00070 0x68a69e81, 0x6a6d98a4, 0x6c242960, 0x6dca0d14, 0x6f5f02b2, 0x70e2cbc6,
96 <a name="l00071"></a>00071 0x72552c85, 0x73b5ebd1,
97 <a name="l00072"></a>00072 0x7504d345, 0x7641af3d, 0x776c4edb, 0x78848414, 0x798a23b1, 0x7a7d055b,
98 <a name="l00073"></a>00073 0x7b5d039e, 0x7c29fbee,
99 <a name="l00074"></a>00074 0x7ce3ceb2, 0x7d8a5f40, 0x7e1d93ea, 0x7e9d55fc, 0x7f0991c4, 0x7f62368f,
100 <a name="l00075"></a>00075 0x7fa736b4, 0x7fd8878e,
101 <a name="l00076"></a>00076 0x7ff62182, 0x7fffffff, 0x7ff62182, 0x7fd8878e, 0x7fa736b4, 0x7f62368f,
102 <a name="l00077"></a>00077 0x7f0991c4, 0x7e9d55fc,
103 <a name="l00078"></a>00078 0x7e1d93ea, 0x7d8a5f40, 0x7ce3ceb2, 0x7c29fbee, 0x7b5d039e, 0x7a7d055b,
104 <a name="l00079"></a>00079 0x798a23b1, 0x78848414,
105 <a name="l00080"></a>00080 0x776c4edb, 0x7641af3d, 0x7504d345, 0x73b5ebd1, 0x72552c85, 0x70e2cbc6,
106 <a name="l00081"></a>00081 0x6f5f02b2, 0x6dca0d14,
107 <a name="l00082"></a>00082 0x6c242960, 0x6a6d98a4, 0x68a69e81, 0x66cf8120, 0x64e88926, 0x62f201ac,
108 <a name="l00083"></a>00083 0x60ec3830, 0x5ed77c8a,
109 <a name="l00084"></a>00084 0x5cb420e0, 0x5a82799a, 0x5842dd54, 0x55f5a4d2, 0x539b2af0, 0x5133cc94,
110 <a name="l00085"></a>00085 0x4ebfe8a5, 0x4c3fdff4,
111 <a name="l00086"></a>00086 0x49b41533, 0x471cece7, 0x447acd50, 0x41ce1e65, 0x3f1749b8, 0x3c56ba70,
112 <a name="l00087"></a>00087 0x398cdd32, 0x36ba2014,
113 <a name="l00088"></a>00088 0x33def287, 0x30fbc54d, 0x2e110a62, 0x2b1f34eb, 0x2826b928, 0x25280c5e,
114 <a name="l00089"></a>00089 0x2223a4c5, 0x1f19f97b,
115 <a name="l00090"></a>00090 0x1c0b826a, 0x18f8b83c, 0x15e21445, 0x12c8106f, 0xfab272b, 0xc8bd35e,
116 <a name="l00091"></a>00091 0x96a9049, 0x647d97c,
117 <a name="l00092"></a>00092 0x3242abf, 0x0, 0xfcdbd541, 0xf9b82684, 0xf6956fb7, 0xf3742ca2, 0xf054d8d5,
118 <a name="l00093"></a>00093 0xed37ef91,
119 <a name="l00094"></a>00094 0xea1debbb, 0xe70747c4, 0xe3f47d96, 0xe0e60685, 0xdddc5b3b, 0xdad7f3a2,
120 <a name="l00095"></a>00095 0xd7d946d8, 0xd4e0cb15,
121 <a name="l00096"></a>00096 0xd1eef59e, 0xcf043ab3, 0xcc210d79, 0xc945dfec, 0xc67322ce, 0xc3a94590,
122 <a name="l00097"></a>00097 0xc0e8b648, 0xbe31e19b,
123 <a name="l00098"></a>00098 0xbb8532b0, 0xb8e31319, 0xb64beacd, 0xb3c0200c, 0xb140175b, 0xaecc336c,
124 <a name="l00099"></a>00099 0xac64d510, 0xaa0a5b2e,
125 <a name="l00100"></a>00100 0xa7bd22ac, 0xa57d8666, 0xa34bdf20, 0xa1288376, 0x9f13c7d0, 0x9d0dfe54,
126 <a name="l00101"></a>00101 0x9b1776da, 0x99307ee0,
127 <a name="l00102"></a>00102 0x9759617f, 0x9592675c, 0x93dbd6a0, 0x9235f2ec, 0x90a0fd4e, 0x8f1d343a,
128 <a name="l00103"></a>00103 0x8daad37b, 0x8c4a142f,
129 <a name="l00104"></a>00104 0x8afb2cbb, 0x89be50c3, 0x8893b125, 0x877b7bec, 0x8675dc4f, 0x8582faa5,
130 <a name="l00105"></a>00105 0x84a2fc62, 0x83d60412,
131 <a name="l00106"></a>00106 0x831c314e, 0x8275a0c0, 0x81e26c16, 0x8162aa04, 0x80f66e3c, 0x809dc971,
132 <a name="l00107"></a>00107 0x8058c94c, 0x80277872,
133 <a name="l00108"></a>00108 0x8009de7e, 0x80000000, 0x8009de7e, 0x80277872, 0x8058c94c, 0x809dc971,
134 <a name="l00109"></a>00109 0x80f66e3c, 0x8162aa04,
135 <a name="l00110"></a>00110 0x81e26c16, 0x8275a0c0, 0x831c314e, 0x83d60412, 0x84a2fc62, 0x8582faa5,
136 <a name="l00111"></a>00111 0x8675dc4f, 0x877b7bec,
137 <a name="l00112"></a>00112 0x8893b125, 0x89be50c3, 0x8afb2cbb, 0x8c4a142f, 0x8daad37b, 0x8f1d343a,
138 <a name="l00113"></a>00113 0x90a0fd4e, 0x9235f2ec,
139 <a name="l00114"></a>00114 0x93dbd6a0, 0x9592675c, 0x9759617f, 0x99307ee0, 0x9b1776da, 0x9d0dfe54,
140 <a name="l00115"></a>00115 0x9f13c7d0, 0xa1288376,
141 <a name="l00116"></a>00116 0xa34bdf20, 0xa57d8666, 0xa7bd22ac, 0xaa0a5b2e, 0xac64d510, 0xaecc336c,
142 <a name="l00117"></a>00117 0xb140175b, 0xb3c0200c,
143 <a name="l00118"></a>00118 0xb64beacd, 0xb8e31319, 0xbb8532b0, 0xbe31e19b, 0xc0e8b648, 0xc3a94590,
144 <a name="l00119"></a>00119 0xc67322ce, 0xc945dfec,
145 <a name="l00120"></a>00120 0xcc210d79, 0xcf043ab3, 0xd1eef59e, 0xd4e0cb15, 0xd7d946d8, 0xdad7f3a2,
146 <a name="l00121"></a>00121 0xdddc5b3b, 0xe0e60685,
147 <a name="l00122"></a>00122 0xe3f47d96, 0xe70747c4, 0xea1debbb, 0xed37ef91, 0xf054d8d5, 0xf3742ca2,
148 <a name="l00123"></a>00123 0xf6956fb7, 0xf9b82684,
149 <a name="l00124"></a>00124 0xfcdbd541, 0x0, 0x3242abf
150 <a name="l00125"></a>00125 };
151 <a name="l00126"></a>00126
152 <a name="l00127"></a>00127
153 <a name="l00136"></a><a class="code" href="group__sin.html#ga57aade7d8892585992cdc6375bd82f9c">00136</a> <a class="code" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0" title="32-bit fractional data type in 1.31 format.">q31_t</a> <a class="code" href="group__sin.html#ga57aade7d8892585992cdc6375bd82f9c" title="Fast approximation to the trigonometric sine function for Q31 data.">arm_sin_q31</a>(
154 <a name="l00137"></a>00137 <a class="code" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0" title="32-bit fractional data type in 1.31 format.">q31_t</a> x)
155 <a name="l00138"></a>00138 {
156 <a name="l00139"></a>00139 <a class="code" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0" title="32-bit fractional data type in 1.31 format.">q31_t</a> sinVal, in, in2; <span class="comment">/* Temporary variables for input, output */</span>
157 <a name="l00140"></a>00140 uint32_t index; <span class="comment">/* Index variables */</span>
158 <a name="l00141"></a>00141 <a class="code" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0" title="32-bit fractional data type in 1.31 format.">q31_t</a> wa, wb, wc, wd; <span class="comment">/* Cubic interpolation coefficients */</span>
159 <a name="l00142"></a>00142 <a class="code" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0" title="32-bit fractional data type in 1.31 format.">q31_t</a> a, b, c, d; <span class="comment">/* Four nearest output values */</span>
160 <a name="l00143"></a>00143 <a class="code" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0" title="32-bit fractional data type in 1.31 format.">q31_t</a> *tablePtr; <span class="comment">/* Pointer to table */</span>
161 <a name="l00144"></a>00144 <a class="code" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0" title="32-bit fractional data type in 1.31 format.">q31_t</a> fract, fractCube, fractSquare; <span class="comment">/* Temporary values for fractional values */</span>
162 <a name="l00145"></a>00145 <a class="code" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0" title="32-bit fractional data type in 1.31 format.">q31_t</a> oneBy6 = 0x15555555; <span class="comment">/* Fixed point value of 1/6 */</span>
163 <a name="l00146"></a>00146 <a class="code" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0" title="32-bit fractional data type in 1.31 format.">q31_t</a> tableSpacing = <a class="code" href="arm__math_8h.html#a8407c9e1347d10e3bcf0a7014f1fb2ff">TABLE_SPACING_Q31</a>; <span class="comment">/* Table spacing */</span>
164 <a name="l00147"></a>00147 <a class="code" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0" title="32-bit fractional data type in 1.31 format.">q31_t</a> temp; <span class="comment">/* Temporary variable for intermediate process */</span>
165 <a name="l00148"></a>00148
166 <a name="l00149"></a>00149 in = x;
167 <a name="l00150"></a>00150
168 <a name="l00151"></a>00151 <span class="comment">/* Calculate the nearest index */</span>
169 <a name="l00152"></a>00152 index = (uint32_t) in / (uint32_t) tableSpacing;
170 <a name="l00153"></a>00153
171 <a name="l00154"></a>00154 <span class="comment">/* Calculate the nearest value of input */</span>
172 <a name="l00155"></a>00155 in2 = (<a class="code" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0" title="32-bit fractional data type in 1.31 format.">q31_t</a>) index *tableSpacing;
173 <a name="l00156"></a>00156
174 <a name="l00157"></a>00157 <span class="comment">/* Calculation of fractional value */</span>
175 <a name="l00158"></a>00158 fract = (in - in2) << 8;
176 <a name="l00159"></a>00159
177 <a name="l00160"></a>00160 <span class="comment">/* fractSquare = fract * fract */</span>
178 <a name="l00161"></a>00161 fractSquare = ((<a class="code" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0" title="32-bit fractional data type in 1.31 format.">q31_t</a>) (((<a class="code" href="arm__math_8h.html#a5aea1cb12fc02d9d44c8abf217eaa5c6" title="64-bit fractional data type in 1.63 format.">q63_t</a>) fract * fract) >> 32));
179 <a name="l00162"></a>00162 fractSquare = fractSquare << 1;
180 <a name="l00163"></a>00163
181 <a name="l00164"></a>00164 <span class="comment">/* fractCube = fract * fract * fract */</span>
182 <a name="l00165"></a>00165 fractCube = ((<a class="code" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0" title="32-bit fractional data type in 1.31 format.">q31_t</a>) (((<a class="code" href="arm__math_8h.html#a5aea1cb12fc02d9d44c8abf217eaa5c6" title="64-bit fractional data type in 1.63 format.">q63_t</a>) fractSquare * fract) >> 32));
183 <a name="l00166"></a>00166 fractCube = fractCube << 1;
184 <a name="l00167"></a>00167
185 <a name="l00168"></a>00168 <span class="comment">/* Initialise table pointer */</span>
186 <a name="l00169"></a>00169 tablePtr = (<a class="code" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0" title="32-bit fractional data type in 1.31 format.">q31_t</a> *) & <a class="code" href="group__sin.html#gab1ffde7f3deee5adc75ba8b3d0a53106">sinTableQ31</a>[index];
187 <a name="l00170"></a>00170
188 <a name="l00171"></a>00171 <span class="comment">/* Cubic interpolation process */</span>
189 <a name="l00172"></a>00172 <span class="comment">/* Calculation of wa */</span>
190 <a name="l00173"></a>00173 <span class="comment">/* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAAAAAA)*fract; */</span>
191 <a name="l00174"></a>00174 wa = ((<a class="code" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0" title="32-bit fractional data type in 1.31 format.">q31_t</a>) (((<a class="code" href="arm__math_8h.html#a5aea1cb12fc02d9d44c8abf217eaa5c6" title="64-bit fractional data type in 1.63 format.">q63_t</a>) oneBy6 * fractCube) >> 32));
192 <a name="l00175"></a>00175 temp = 0x2AAAAAAA;
193 <a name="l00176"></a>00176 wa = (<a class="code" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0" title="32-bit fractional data type in 1.31 format.">q31_t</a>) ((((<a class="code" href="arm__math_8h.html#a5aea1cb12fc02d9d44c8abf217eaa5c6" title="64-bit fractional data type in 1.63 format.">q63_t</a>) wa << 32) + ((q63_t) temp * fract)) >> 32);
194 <a name="l00177"></a>00177 wa = -(wa << 1u);
195 <a name="l00178"></a>00178 wa += (fractSquare >> 1u);
196 <a name="l00179"></a>00179
197 <a name="l00180"></a>00180 <span class="comment">/* Read first nearest value of output from the sin table */</span>
198 <a name="l00181"></a>00181 a = *tablePtr++;
199 <a name="l00182"></a>00182
200 <a name="l00183"></a>00183 <span class="comment">/* sinVal = a*wa */</span>
201 <a name="l00184"></a>00184 sinVal = ((<a class="code" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0" title="32-bit fractional data type in 1.31 format.">q31_t</a>) (((<a class="code" href="arm__math_8h.html#a5aea1cb12fc02d9d44c8abf217eaa5c6" title="64-bit fractional data type in 1.63 format.">q63_t</a>) a * wa) >> 32));
202 <a name="l00185"></a>00185
203 <a name="l00186"></a>00186 <span class="comment">/* q31(1.31) Fixed point value of 1 */</span>
204 <a name="l00187"></a>00187 temp = 0x7FFFFFFF;
205 <a name="l00188"></a>00188
206 <a name="l00189"></a>00189 <span class="comment">/* Calculation of wb */</span>
207 <a name="l00190"></a>00190 wb = ((fractCube >> 1u) - (fractSquare + (fract >> 1u))) + temp;
208 <a name="l00191"></a>00191
209 <a name="l00192"></a>00192 <span class="comment">/* Read second nearest value of output from the sin table */</span>
210 <a name="l00193"></a>00193 b = *tablePtr++;
211 <a name="l00194"></a>00194
212 <a name="l00195"></a>00195 <span class="comment">/* sinVal += b*wb */</span>
213 <a name="l00196"></a>00196 sinVal = (<a class="code" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0" title="32-bit fractional data type in 1.31 format.">q31_t</a>) ((((<a class="code" href="arm__math_8h.html#a5aea1cb12fc02d9d44c8abf217eaa5c6" title="64-bit fractional data type in 1.63 format.">q63_t</a>) sinVal << 32) + (q63_t) b * (wb)) >> 32);
214 <a name="l00197"></a>00197
215 <a name="l00198"></a>00198 <span class="comment">/* Calculation of wc */</span>
216 <a name="l00199"></a>00199 wc = -fractCube + fractSquare;
217 <a name="l00200"></a>00200 wc = (wc >> 1u) + fract;
218 <a name="l00201"></a>00201
219 <a name="l00202"></a>00202 <span class="comment">/* Read third nearest value of output from the sin table */</span>
220 <a name="l00203"></a>00203 c = *tablePtr++;
221 <a name="l00204"></a>00204
222 <a name="l00205"></a>00205 <span class="comment">/* sinVal += c*wc */</span>
223 <a name="l00206"></a>00206 sinVal = (<a class="code" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0" title="32-bit fractional data type in 1.31 format.">q31_t</a>) ((((<a class="code" href="arm__math_8h.html#a5aea1cb12fc02d9d44c8abf217eaa5c6" title="64-bit fractional data type in 1.63 format.">q63_t</a>) sinVal << 32) + ((q63_t) c * wc)) >> 32);
224 <a name="l00207"></a>00207
225 <a name="l00208"></a>00208 <span class="comment">/* Calculation of wd */</span>
226 <a name="l00209"></a>00209 <span class="comment">/* wd = (oneBy6) * fractCube - (oneBy6) * fract; */</span>
227 <a name="l00210"></a>00210 fractCube = fractCube - fract;
228 <a name="l00211"></a>00211 wd = ((<a class="code" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0" title="32-bit fractional data type in 1.31 format.">q31_t</a>) (((<a class="code" href="arm__math_8h.html#a5aea1cb12fc02d9d44c8abf217eaa5c6" title="64-bit fractional data type in 1.63 format.">q63_t</a>) oneBy6 * fractCube) >> 32));
229 <a name="l00212"></a>00212 wd = (wd << 1u);
230 <a name="l00213"></a>00213
231 <a name="l00214"></a>00214 <span class="comment">/* Read fourth nearest value of output from the sin table */</span>
232 <a name="l00215"></a>00215 d = *tablePtr++;
233 <a name="l00216"></a>00216
234 <a name="l00217"></a>00217 <span class="comment">/* sinVal += d*wd; */</span>
235 <a name="l00218"></a>00218 sinVal = (<a class="code" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0" title="32-bit fractional data type in 1.31 format.">q31_t</a>) ((((<a class="code" href="arm__math_8h.html#a5aea1cb12fc02d9d44c8abf217eaa5c6" title="64-bit fractional data type in 1.63 format.">q63_t</a>) sinVal << 32) + ((q63_t) d * wd)) >> 32);
236 <a name="l00219"></a>00219
237 <a name="l00220"></a>00220 <span class="comment">/* convert sinVal in 2.30 format to 1.31 format */</span>
238 <a name="l00221"></a>00221 <span class="keywordflow">return</span> (sinVal << 1u);
239 <a name="l00222"></a>00222
240 <a name="l00223"></a>00223 }
241 <a name="l00224"></a>00224
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