arm_cos_q31.c
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00001 /* ---------------------------------------------------------------------- 00002 * Copyright (C) 2011 ARM Limited. All rights reserved. 00003 * 00004 * $Date: 15. December 2011 00005 * $Revision: V2.0.0 00006 * 00007 * Project: Cortex-R DSP Library 00008 * Title: arm_cos_q31.c 00009 * 00010 * Description: Fast cosine calculation for Q31 values. 00011 * 00012 * Target Processor: Cortex-R4/R5 00013 * 00014 * Version 1.0.0 2011/03/08 00015 * Alpha release. 00016 * 00017 * Version 1.0.1 2011/09/30 00018 * Beta release. 00019 * 00020 * Version 2.0.0 2011/12/15 00021 * Final release. 00022 * 00023 * -------------------------------------------------------------------- */ 00024 #include "arm_math.h" 00025 00054 static const q31_t cosTableQ31[259] = { 00055 0x7ff62182, 0x7fffffff, 0x7ff62182, 0x7fd8878e, 0x7fa736b4, 0x7f62368f, 00056 0x7f0991c4, 0x7e9d55fc, 00057 0x7e1d93ea, 0x7d8a5f40, 0x7ce3ceb2, 0x7c29fbee, 0x7b5d039e, 0x7a7d055b, 00058 0x798a23b1, 0x78848414, 00059 0x776c4edb, 0x7641af3d, 0x7504d345, 0x73b5ebd1, 0x72552c85, 0x70e2cbc6, 00060 0x6f5f02b2, 0x6dca0d14, 00061 0x6c242960, 0x6a6d98a4, 0x68a69e81, 0x66cf8120, 0x64e88926, 0x62f201ac, 00062 0x60ec3830, 0x5ed77c8a, 00063 0x5cb420e0, 0x5a82799a, 0x5842dd54, 0x55f5a4d2, 0x539b2af0, 0x5133cc94, 00064 0x4ebfe8a5, 0x4c3fdff4, 00065 0x49b41533, 0x471cece7, 0x447acd50, 0x41ce1e65, 0x3f1749b8, 0x3c56ba70, 00066 0x398cdd32, 0x36ba2014, 00067 0x33def287, 0x30fbc54d, 0x2e110a62, 0x2b1f34eb, 0x2826b928, 0x25280c5e, 00068 0x2223a4c5, 0x1f19f97b, 00069 0x1c0b826a, 0x18f8b83c, 0x15e21445, 0x12c8106f, 0xfab272b, 0xc8bd35e, 00070 0x96a9049, 0x647d97c, 00071 0x3242abf, 0x0, 0xfcdbd541, 0xf9b82684, 0xf6956fb7, 0xf3742ca2, 0xf054d8d5, 00072 0xed37ef91, 00073 0xea1debbb, 0xe70747c4, 0xe3f47d96, 0xe0e60685, 0xdddc5b3b, 0xdad7f3a2, 00074 0xd7d946d8, 0xd4e0cb15, 00075 0xd1eef59e, 0xcf043ab3, 0xcc210d79, 0xc945dfec, 0xc67322ce, 0xc3a94590, 00076 0xc0e8b648, 0xbe31e19b, 00077 0xbb8532b0, 0xb8e31319, 0xb64beacd, 0xb3c0200c, 0xb140175b, 0xaecc336c, 00078 0xac64d510, 0xaa0a5b2e, 00079 0xa7bd22ac, 0xa57d8666, 0xa34bdf20, 0xa1288376, 0x9f13c7d0, 0x9d0dfe54, 00080 0x9b1776da, 0x99307ee0, 00081 0x9759617f, 0x9592675c, 0x93dbd6a0, 0x9235f2ec, 0x90a0fd4e, 0x8f1d343a, 00082 0x8daad37b, 0x8c4a142f, 00083 0x8afb2cbb, 0x89be50c3, 0x8893b125, 0x877b7bec, 0x8675dc4f, 0x8582faa5, 00084 0x84a2fc62, 0x83d60412, 00085 0x831c314e, 0x8275a0c0, 0x81e26c16, 0x8162aa04, 0x80f66e3c, 0x809dc971, 00086 0x8058c94c, 0x80277872, 00087 0x8009de7e, 0x80000000, 0x8009de7e, 0x80277872, 0x8058c94c, 0x809dc971, 00088 0x80f66e3c, 0x8162aa04, 00089 0x81e26c16, 0x8275a0c0, 0x831c314e, 0x83d60412, 0x84a2fc62, 0x8582faa5, 00090 0x8675dc4f, 0x877b7bec, 00091 0x8893b125, 0x89be50c3, 0x8afb2cbb, 0x8c4a142f, 0x8daad37b, 0x8f1d343a, 00092 0x90a0fd4e, 0x9235f2ec, 00093 0x93dbd6a0, 0x9592675c, 0x9759617f, 0x99307ee0, 0x9b1776da, 0x9d0dfe54, 00094 0x9f13c7d0, 0xa1288376, 00095 0xa34bdf20, 0xa57d8666, 0xa7bd22ac, 0xaa0a5b2e, 0xac64d510, 0xaecc336c, 00096 0xb140175b, 0xb3c0200c, 00097 0xb64beacd, 0xb8e31319, 0xbb8532b0, 0xbe31e19b, 0xc0e8b648, 0xc3a94590, 00098 0xc67322ce, 0xc945dfec, 00099 0xcc210d79, 0xcf043ab3, 0xd1eef59e, 0xd4e0cb15, 0xd7d946d8, 0xdad7f3a2, 00100 0xdddc5b3b, 0xe0e60685, 00101 0xe3f47d96, 0xe70747c4, 0xea1debbb, 0xed37ef91, 0xf054d8d5, 0xf3742ca2, 00102 0xf6956fb7, 0xf9b82684, 00103 0xfcdbd541, 0x0, 0x3242abf, 0x647d97c, 0x96a9049, 0xc8bd35e, 0xfab272b, 00104 0x12c8106f, 00105 0x15e21445, 0x18f8b83c, 0x1c0b826a, 0x1f19f97b, 0x2223a4c5, 0x25280c5e, 00106 0x2826b928, 0x2b1f34eb, 00107 0x2e110a62, 0x30fbc54d, 0x33def287, 0x36ba2014, 0x398cdd32, 0x3c56ba70, 00108 0x3f1749b8, 0x41ce1e65, 00109 0x447acd50, 0x471cece7, 0x49b41533, 0x4c3fdff4, 0x4ebfe8a5, 0x5133cc94, 00110 0x539b2af0, 0x55f5a4d2, 00111 0x5842dd54, 0x5a82799a, 0x5cb420e0, 0x5ed77c8a, 0x60ec3830, 0x62f201ac, 00112 0x64e88926, 0x66cf8120, 00113 0x68a69e81, 0x6a6d98a4, 0x6c242960, 0x6dca0d14, 0x6f5f02b2, 0x70e2cbc6, 00114 0x72552c85, 0x73b5ebd1, 00115 0x7504d345, 0x7641af3d, 0x776c4edb, 0x78848414, 0x798a23b1, 0x7a7d055b, 00116 0x7b5d039e, 0x7c29fbee, 00117 0x7ce3ceb2, 0x7d8a5f40, 0x7e1d93ea, 0x7e9d55fc, 0x7f0991c4, 0x7f62368f, 00118 0x7fa736b4, 0x7fd8878e, 00119 0x7ff62182, 0x7fffffff, 0x7ff62182 00120 }; 00121 00130 q31_t arm_cos_q31( 00131 q31_t x) 00132 { 00133 q31_t cosVal, in, in2; /* Temporary variables for input, output */ 00134 uint32_t index; /* Index variables */ 00135 q31_t wa, wb, wc, wd; /* Cubic interpolation coefficients */ 00136 q31_t a, b, c, d; /* Four nearest output values */ 00137 q31_t *tablePtr; /* Pointer to table */ 00138 q31_t fract, fractCube, fractSquare; /* Temporary values for fractional values */ 00139 q31_t oneBy6 = 0x15555555; /* Fixed point value of 1/6 */ 00140 q31_t tableSpacing = TABLE_SPACING_Q31; /* Table spacing */ 00141 q31_t temp; /* Temporary variable for intermediate process */ 00142 00143 in = x; 00144 00145 /* Calculate the nearest index */ 00146 index = (uint32_t) in / (uint32_t) tableSpacing; 00147 00148 /* Calculate the nearest value of input */ 00149 in2 = ((q31_t) index) * tableSpacing; 00150 00151 /* Calculation of fractional value */ 00152 fract = (in - in2) << 8; 00153 00154 /* fractSquare = fract * fract */ 00155 fractSquare = ((q31_t) (((q63_t) fract * fract) >> 32)); 00156 fractSquare = fractSquare << 1; 00157 00158 /* fractCube = fract * fract * fract */ 00159 fractCube = ((q31_t) (((q63_t) fractSquare * fract) >> 32)); 00160 fractCube = fractCube << 1; 00161 00162 /* Initialise table pointer */ 00163 tablePtr = (q31_t *) & cosTableQ31[index]; 00164 00165 /* Cubic interpolation process */ 00166 /* Calculation of wa */ 00167 /* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAAAAAA)*fract; */ 00168 wa = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32)); 00169 temp = 0x2AAAAAAA; 00170 wa = (q31_t) ((((q63_t) wa << 32) + ((q63_t) temp * fract)) >> 32); 00171 00172 /* q31(1.31) Fixed point value of 1 */ 00173 temp = 0x7FFFFFFF; 00174 00175 /* Calculation of wb */ 00176 wb = ((fractCube >> 1u) - (fractSquare + (fract >> 1u))) + temp; 00177 00178 wa = -(wa << 1u); 00179 wa += (fractSquare >> 1u); 00180 00181 /* Read first nearest value of output from the cos table */ 00182 a = *tablePtr++; 00183 00184 /* cosVal = a*wa */ 00185 cosVal = ((q31_t) (((q63_t) a * wa) >> 32)); 00186 00187 /* Read second nearest value of output from the cos table */ 00188 b = *tablePtr++; 00189 00190 /* cosVal += b*wb */ 00191 cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) b * (wb))) >> 32); 00192 00193 /* Calculation of wc */ 00194 wc = -fractCube + fractSquare; 00195 wc = (wc >> 1u) + fract; 00196 00197 /* Read third nearest values of output value from the cos table */ 00198 c = *tablePtr++; 00199 00200 /* cosVal += c*wc */ 00201 cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) c * (wc))) >> 32); 00202 00203 /* Calculation of wd */ 00204 /* wd = (oneBy6)*fractCube - (oneBy6)*fract; */ 00205 fractCube = fractCube - fract; 00206 wd = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32)); 00207 wd = (wd << 1u); 00208 00209 /* Read fourth nearest value of output from the cos table */ 00210 d = *tablePtr++; 00211 00212 /* cosVal += d*wd; */ 00213 cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) d * (wd))) >> 32); 00214 00215 /* convert cosVal in 2.30 format to 1.31 format */ 00216 return (cosVal << 1u); 00217 00218 } 00219
