CMSIS DSP Software Library: arm_sin_q31.c Source File
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arm_sin_q31.c
Go to the documentation of this file.00001 /* ----------------------------------------------------------------------
00002 * Copyright (C) 2010 ARM Limited. All rights reserved.
00003 *
00004 * $Date: 29. November 2010
00005 * $Revision: V1.0.3
00006 *
00007 * Project: CMSIS DSP Library
00008 * Title: arm_sin_q31.c
00009 *
00010 * Description: Fast sine calculation for Q31 values.
00011 *
00012 * Target Processor: Cortex-M4/Cortex-M3
00013 *
00014 * Version 1.0.3 2010/11/29
00015 * Re-organized the CMSIS folders and updated documentation.
00016 *
00017 * Version 1.0.2 2010/11/11
00018 * Documentation updated.
00019 *
00020 * Version 1.0.1 2010/10/05
00021 * Production release and review comments incorporated.
00022 *
00023 * Version 1.0.0 2010/09/20
00024 * Production release and review comments incorporated.
00025 * -------------------------------------------------------------------- */
00026
00027 #include "arm_math.h"
00028
00056 static const q31_t sinTableQ31[259] = {
00057 0xfcdbd541, 0x0, 0x3242abf, 0x647d97c, 0x96a9049, 0xc8bd35e, 0xfab272b,
00058 0x12c8106f,
00059 0x15e21445, 0x18f8b83c, 0x1c0b826a, 0x1f19f97b, 0x2223a4c5, 0x25280c5e,
00060 0x2826b928, 0x2b1f34eb,
00061 0x2e110a62, 0x30fbc54d, 0x33def287, 0x36ba2014, 0x398cdd32, 0x3c56ba70,
00062 0x3f1749b8, 0x41ce1e65,
00063 0x447acd50, 0x471cece7, 0x49b41533, 0x4c3fdff4, 0x4ebfe8a5, 0x5133cc94,
00064 0x539b2af0, 0x55f5a4d2,
00065 0x5842dd54, 0x5a82799a, 0x5cb420e0, 0x5ed77c8a, 0x60ec3830, 0x62f201ac,
00066 0x64e88926, 0x66cf8120,
00067 0x68a69e81, 0x6a6d98a4, 0x6c242960, 0x6dca0d14, 0x6f5f02b2, 0x70e2cbc6,
00068 0x72552c85, 0x73b5ebd1,
00069 0x7504d345, 0x7641af3d, 0x776c4edb, 0x78848414, 0x798a23b1, 0x7a7d055b,
00070 0x7b5d039e, 0x7c29fbee,
00071 0x7ce3ceb2, 0x7d8a5f40, 0x7e1d93ea, 0x7e9d55fc, 0x7f0991c4, 0x7f62368f,
00072 0x7fa736b4, 0x7fd8878e,
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
00122 };
00123
00124
00133 q31_t arm_sin_q31(
00134 q31_t x)
00135 {
00136 q31_t sinVal, fract, in, in2; /* Temporary variables for input, output */
00137 uint32_t index; /* Index variables */
00138 q31_t wa, wb, wc, wd; /* Cubic interpolation coefficients */
00139 q31_t a, b, c, d; /* Four nearest output values */
00140 q31_t *tablePtr; /* Pointer to table */
00141 q31_t fractCube, fractSquare; /* Temporary values for fractional value */
00142 q31_t oneBy6 = 0x15555555; /* Fixed point value of 1/6 */
00143 q31_t tableSpacing = TABLE_SPACING_Q31; /* Table spacing */
00144 q31_t temp; /* Temporary variable for intermediate process */
00145
00146 in = x;
00147
00148 /* Calculate the nearest index */
00149 index = (uint32_t) in / (uint32_t) tableSpacing;
00150
00151 /* Calculate the nearest value of input */
00152 in2 = (q31_t) index *tableSpacing;
00153
00154 /* Calculation of fractional value */
00155 fract = (in - in2) << 8;
00156
00157 /* fractSquare = fract * fract */
00158 fractSquare = ((q31_t) (((q63_t) fract * fract) >> 32));
00159 fractSquare = fractSquare << 1;
00160
00161 /* fractCube = fract * fract * fract */
00162 fractCube = ((q31_t) (((q63_t) fractSquare * fract) >> 32));
00163 fractCube = fractCube << 1;
00164
00165 /* Initialise table pointer */
00166 tablePtr = (q31_t *) & sinTableQ31[index];
00167
00168 /* Cubic interpolation process */
00169 /* Calculation of wa */
00170 /* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAAAAAA)*fract; */
00171 wa = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32));
00172 temp = 0x2AAAAAAA;
00173 wa = (q31_t) ((((q63_t) wa << 32) + ((q63_t) temp * fract)) >> 32);
00174 wa = -(wa << 1u);
00175 wa += (fractSquare >> 1u);
00176
00177 /* Read first nearest value of output from the sin table */
00178 a = *tablePtr++;
00179
00180 /* sinVal = a*wa */
00181 sinVal = ((q31_t) (((q63_t) a * wa) >> 32));
00182
00183 /* q31(1.31) Fixed point value of 1 */
00184 temp = 0x7FFFFFFF;
00185
00186 /* Calculation of wb */
00187 wb = ((fractCube >> 1u) - (fractSquare + (fract >> 1u))) + temp;
00188
00189 /* Read second nearest value of output from the sin table */
00190 b = *tablePtr++;
00191
00192 /* sinVal += b*wb */
00193 sinVal = (q31_t) ((((q63_t) sinVal << 32) + (q63_t) b * (wb)) >> 32);
00194
00195 /* Calculation of wc */
00196 wc = -fractCube + fractSquare;
00197 wc = (wc >> 1u) + fract;
00198
00199 /* Read third nearest value of output from the sin table */
00200 c = *tablePtr++;
00201
00202 /* sinVal += c*wc */
00203 sinVal = (q31_t) ((((q63_t) sinVal << 32) + ((q63_t) c * wc)) >> 32);
00204
00205 /* Calculation of wd */
00206 /* wd = (oneBy6) * fractCube - (oneBy6) * fract; */
00207 fractCube = fractCube - fract;
00208 wd = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32));
00209 wd = (wd << 1u);
00210
00211 /* Read fourth nearest value of output from the sin table */
00212 d = *tablePtr++;
00213
00214 /* sinVal += d*wd; */
00215 sinVal = (q31_t) ((((q63_t) sinVal << 32) + ((q63_t) d * wd)) >> 32);
00216
00217 /* convert sinVal in 2.30 format to 1.31 format */
00218 return (sinVal << 1u);
00219
00220 }
00221
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