CMSIS DSP library
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arm_cos_q31.c
00001 /* ---------------------------------------------------------------------- 00002 * Copyright (C) 2010-2013 ARM Limited. All rights reserved. 00003 * 00004 * $Date: 17. January 2013 00005 * $Revision: V1.4.1 00006 * 00007 * Project: CMSIS DSP Library 00008 * Title: arm_cos_q31.c 00009 * 00010 * Description: Fast cosine calculation for Q31 values. 00011 * 00012 * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 00013 * 00014 * Redistribution and use in source and binary forms, with or without 00015 * modification, are permitted provided that the following conditions 00016 * are met: 00017 * - Redistributions of source code must retain the above copyright 00018 * notice, this list of conditions and the following disclaimer. 00019 * - Redistributions in binary form must reproduce the above copyright 00020 * notice, this list of conditions and the following disclaimer in 00021 * the documentation and/or other materials provided with the 00022 * distribution. 00023 * - Neither the name of ARM LIMITED nor the names of its contributors 00024 * may be used to endorse or promote products derived from this 00025 * software without specific prior written permission. 00026 * 00027 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 00028 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 00029 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS 00030 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 00031 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, 00032 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, 00033 * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 00034 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER 00035 * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 00036 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN 00037 * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 00038 * POSSIBILITY OF SUCH DAMAGE. 00039 * -------------------------------------------------------------------- */ 00040 00041 #include "arm_math.h" 00042 00043 /** 00044 * @ingroup groupFastMath 00045 */ 00046 00047 /** 00048 * @addtogroup cos 00049 * @{ 00050 */ 00051 00052 /** 00053 * \par 00054 * Table values are in Q31 (1.31 fixed-point format) and generation is done in 00055 * three steps. First, generate cos values in floating point: 00056 * <pre> 00057 * tableSize = 256; 00058 * for(n = -1; n < (tableSize + 1); n++) 00059 * { 00060 * cosTable[n+1]= cos(2*pi*n/tableSize); 00061 * } </pre> 00062 * where pi value is 3.14159265358979 00063 * \par 00064 * Second, convert floating-point to Q31 (Fixed point): 00065 * (cosTable[i] * pow(2, 31)) 00066 * \par 00067 * Finally, round to the nearest integer value: 00068 * cosTable[i] += (cosTable[i] > 0 ? 0.5 :-0.5); 00069 */ 00070 00071 00072 static const q31_t cosTableQ31 [259] = { 00073 0x7ff62182, 0x7fffffff, 0x7ff62182, 0x7fd8878e, 0x7fa736b4, 0x7f62368f, 00074 0x7f0991c4, 0x7e9d55fc, 00075 0x7e1d93ea, 0x7d8a5f40, 0x7ce3ceb2, 0x7c29fbee, 0x7b5d039e, 0x7a7d055b, 00076 0x798a23b1, 0x78848414, 00077 0x776c4edb, 0x7641af3d, 0x7504d345, 0x73b5ebd1, 0x72552c85, 0x70e2cbc6, 00078 0x6f5f02b2, 0x6dca0d14, 00079 0x6c242960, 0x6a6d98a4, 0x68a69e81, 0x66cf8120, 0x64e88926, 0x62f201ac, 00080 0x60ec3830, 0x5ed77c8a, 00081 0x5cb420e0, 0x5a82799a, 0x5842dd54, 0x55f5a4d2, 0x539b2af0, 0x5133cc94, 00082 0x4ebfe8a5, 0x4c3fdff4, 00083 0x49b41533, 0x471cece7, 0x447acd50, 0x41ce1e65, 0x3f1749b8, 0x3c56ba70, 00084 0x398cdd32, 0x36ba2014, 00085 0x33def287, 0x30fbc54d, 0x2e110a62, 0x2b1f34eb, 0x2826b928, 0x25280c5e, 00086 0x2223a4c5, 0x1f19f97b, 00087 0x1c0b826a, 0x18f8b83c, 0x15e21445, 0x12c8106f, 0xfab272b, 0xc8bd35e, 00088 0x96a9049, 0x647d97c, 00089 0x3242abf, 0x0, 0xfcdbd541, 0xf9b82684, 0xf6956fb7, 0xf3742ca2, 0xf054d8d5, 00090 0xed37ef91, 00091 0xea1debbb, 0xe70747c4, 0xe3f47d96, 0xe0e60685, 0xdddc5b3b, 0xdad7f3a2, 00092 0xd7d946d8, 0xd4e0cb15, 00093 0xd1eef59e, 0xcf043ab3, 0xcc210d79, 0xc945dfec, 0xc67322ce, 0xc3a94590, 00094 0xc0e8b648, 0xbe31e19b, 00095 0xbb8532b0, 0xb8e31319, 0xb64beacd, 0xb3c0200c, 0xb140175b, 0xaecc336c, 00096 0xac64d510, 0xaa0a5b2e, 00097 0xa7bd22ac, 0xa57d8666, 0xa34bdf20, 0xa1288376, 0x9f13c7d0, 0x9d0dfe54, 00098 0x9b1776da, 0x99307ee0, 00099 0x9759617f, 0x9592675c, 0x93dbd6a0, 0x9235f2ec, 0x90a0fd4e, 0x8f1d343a, 00100 0x8daad37b, 0x8c4a142f, 00101 0x8afb2cbb, 0x89be50c3, 0x8893b125, 0x877b7bec, 0x8675dc4f, 0x8582faa5, 00102 0x84a2fc62, 0x83d60412, 00103 0x831c314e, 0x8275a0c0, 0x81e26c16, 0x8162aa04, 0x80f66e3c, 0x809dc971, 00104 0x8058c94c, 0x80277872, 00105 0x8009de7e, 0x80000000, 0x8009de7e, 0x80277872, 0x8058c94c, 0x809dc971, 00106 0x80f66e3c, 0x8162aa04, 00107 0x81e26c16, 0x8275a0c0, 0x831c314e, 0x83d60412, 0x84a2fc62, 0x8582faa5, 00108 0x8675dc4f, 0x877b7bec, 00109 0x8893b125, 0x89be50c3, 0x8afb2cbb, 0x8c4a142f, 0x8daad37b, 0x8f1d343a, 00110 0x90a0fd4e, 0x9235f2ec, 00111 0x93dbd6a0, 0x9592675c, 0x9759617f, 0x99307ee0, 0x9b1776da, 0x9d0dfe54, 00112 0x9f13c7d0, 0xa1288376, 00113 0xa34bdf20, 0xa57d8666, 0xa7bd22ac, 0xaa0a5b2e, 0xac64d510, 0xaecc336c, 00114 0xb140175b, 0xb3c0200c, 00115 0xb64beacd, 0xb8e31319, 0xbb8532b0, 0xbe31e19b, 0xc0e8b648, 0xc3a94590, 00116 0xc67322ce, 0xc945dfec, 00117 0xcc210d79, 0xcf043ab3, 0xd1eef59e, 0xd4e0cb15, 0xd7d946d8, 0xdad7f3a2, 00118 0xdddc5b3b, 0xe0e60685, 00119 0xe3f47d96, 0xe70747c4, 0xea1debbb, 0xed37ef91, 0xf054d8d5, 0xf3742ca2, 00120 0xf6956fb7, 0xf9b82684, 00121 0xfcdbd541, 0x0, 0x3242abf, 0x647d97c, 0x96a9049, 0xc8bd35e, 0xfab272b, 00122 0x12c8106f, 00123 0x15e21445, 0x18f8b83c, 0x1c0b826a, 0x1f19f97b, 0x2223a4c5, 0x25280c5e, 00124 0x2826b928, 0x2b1f34eb, 00125 0x2e110a62, 0x30fbc54d, 0x33def287, 0x36ba2014, 0x398cdd32, 0x3c56ba70, 00126 0x3f1749b8, 0x41ce1e65, 00127 0x447acd50, 0x471cece7, 0x49b41533, 0x4c3fdff4, 0x4ebfe8a5, 0x5133cc94, 00128 0x539b2af0, 0x55f5a4d2, 00129 0x5842dd54, 0x5a82799a, 0x5cb420e0, 0x5ed77c8a, 0x60ec3830, 0x62f201ac, 00130 0x64e88926, 0x66cf8120, 00131 0x68a69e81, 0x6a6d98a4, 0x6c242960, 0x6dca0d14, 0x6f5f02b2, 0x70e2cbc6, 00132 0x72552c85, 0x73b5ebd1, 00133 0x7504d345, 0x7641af3d, 0x776c4edb, 0x78848414, 0x798a23b1, 0x7a7d055b, 00134 0x7b5d039e, 0x7c29fbee, 00135 0x7ce3ceb2, 0x7d8a5f40, 0x7e1d93ea, 0x7e9d55fc, 0x7f0991c4, 0x7f62368f, 00136 0x7fa736b4, 0x7fd8878e, 00137 0x7ff62182, 0x7fffffff, 0x7ff62182 00138 }; 00139 00140 /** 00141 * @brief Fast approximation to the trigonometric cosine function for Q31 data. 00142 * @param[in] x Scaled input value in radians. 00143 * @return cos(x). 00144 * 00145 * The Q31 input value is in the range [0 +0.9999] and is mapped to a radian 00146 * value in the range [0 2*pi). 00147 */ 00148 00149 q31_t arm_cos_q31( 00150 q31_t x) 00151 { 00152 q31_t cosVal, in, in2; /* Temporary variables for input, output */ 00153 q31_t wa, wb, wc, wd; /* Cubic interpolation coefficients */ 00154 q31_t a, b, c, d; /* Four nearest output values */ 00155 q31_t *tablePtr; /* Pointer to table */ 00156 q31_t fract, fractCube, fractSquare; /* Temporary values for fractional values */ 00157 q31_t oneBy6 = 0x15555555; /* Fixed point value of 1/6 */ 00158 q31_t tableSpacing = TABLE_SPACING_Q31; /* Table spacing */ 00159 q31_t temp; /* Temporary variable for intermediate process */ 00160 int32_t index; /* Index variable */ 00161 00162 in = x; 00163 00164 /* Calculate the nearest index */ 00165 index = in / tableSpacing; 00166 00167 /* Calculate the nearest value of input */ 00168 in2 = ((q31_t) index) * tableSpacing; 00169 00170 /* Calculation of fractional value */ 00171 fract = (in - in2) << 8; 00172 00173 /* fractSquare = fract * fract */ 00174 fractSquare = ((q31_t) (((q63_t) fract * fract) >> 32)); 00175 fractSquare = fractSquare << 1; 00176 00177 /* fractCube = fract * fract * fract */ 00178 fractCube = ((q31_t) (((q63_t) fractSquare * fract) >> 32)); 00179 fractCube = fractCube << 1; 00180 00181 /* Checking min and max index of table */ 00182 if(index < 0) 00183 { 00184 index = 0; 00185 } 00186 else if(index > 256) 00187 { 00188 index = 256; 00189 } 00190 00191 /* Initialise table pointer */ 00192 tablePtr = (q31_t *) & cosTableQ31 [index]; 00193 00194 /* Cubic interpolation process */ 00195 /* Calculation of wa */ 00196 /* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAAAAAA)*fract; */ 00197 wa = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32)); 00198 temp = 0x2AAAAAAA; 00199 wa = (q31_t) ((((q63_t) wa << 32) + ((q63_t) temp * fract)) >> 32); 00200 wa = -(wa << 1u); 00201 wa += (fractSquare >> 1u); 00202 00203 /* Read first nearest value of output from the cos table */ 00204 a = *tablePtr++; 00205 00206 /* cosVal = a*wa */ 00207 cosVal = ((q31_t) (((q63_t) a * wa) >> 32)); 00208 00209 /* q31(1.31) Fixed point value of 1 */ 00210 temp = 0x7FFFFFFF; 00211 00212 /* Calculation of wb */ 00213 wb = ((fractCube >> 1u) - (fractSquare + (fract >> 1u))) + temp; 00214 /* Read second nearest value of output from the cos table */ 00215 b = *tablePtr++; 00216 00217 /* cosVal += b*wb */ 00218 cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) b * (wb))) >> 32); 00219 00220 /* Calculation of wc */ 00221 wc = -fractCube + fractSquare; 00222 wc = (wc >> 1u) + fract; 00223 /* Read third nearest values of output value from the cos table */ 00224 c = *tablePtr++; 00225 00226 /* cosVal += c*wc */ 00227 cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) c * (wc))) >> 32); 00228 00229 /* Calculation of wd */ 00230 /* wd = (oneBy6)*fractCube - (oneBy6)*fract; */ 00231 fractCube = fractCube - fract; 00232 wd = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32)); 00233 wd = (wd << 1u); 00234 00235 /* Read fourth nearest value of output from the cos table */ 00236 d = *tablePtr++; 00237 00238 /* cosVal += d*wd; */ 00239 cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) d * (wd))) >> 32); 00240 00241 00242 /* convert cosVal in 2.30 format to 1.31 format */ 00243 return (__QADD(cosVal, cosVal)); 00244 00245 } 00246 00247 /** 00248 * @} end of cos group 00249 */
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