不韋 呂 / Mbed 2 deprecated CQ_FixedPointSin_CMSIS

CQ出版社インターフェース誌の2017年8月号で解説している，固定小数点演算で sin 関数の値を求める二つの関数を比較するためのプログラムの全体．

Dependencies:   mbed

arm_sin_q15.c@0:9b1d4712f862, 2017-08-02 (annotated)

Committer:
MikamiUitOpen
Date:
Wed Aug 02 12:01:51 2017 +0000
Revision:
0:9b1d4712f862
1

Who changed what in which revision?

UserRevisionLine numberNew contents of line
MikamiUitOpen 0:9b1d4712f862 1 /* ----------------------------------------------------------------------
MikamiUitOpen 0:9b1d4712f862 2 * Copyright (C) 2010 ARM Limited. All rights reserved.
MikamiUitOpen 0:9b1d4712f862 3 *
MikamiUitOpen 0:9b1d4712f862 4 * $Date: 29. November 2010
MikamiUitOpen 0:9b1d4712f862 5 * $Revision: V1.0.3
MikamiUitOpen 0:9b1d4712f862 6 *
MikamiUitOpen 0:9b1d4712f862 7 * Project: CMSIS DSP Library
MikamiUitOpen 0:9b1d4712f862 8 * Title: arm_sin_q15.c
MikamiUitOpen 0:9b1d4712f862 9 *
MikamiUitOpen 0:9b1d4712f862 10 * Description: Fast sine calculation for Q15 values.
MikamiUitOpen 0:9b1d4712f862 11 *
MikamiUitOpen 0:9b1d4712f862 12 * Target Processor: Cortex-M4/Cortex-M3
MikamiUitOpen 0:9b1d4712f862 13 *
MikamiUitOpen 0:9b1d4712f862 14 * Version 1.0.3 2010/11/29
MikamiUitOpen 0:9b1d4712f862 15 * Re-organized the CMSIS folders and updated documentation.
MikamiUitOpen 0:9b1d4712f862 16 *
MikamiUitOpen 0:9b1d4712f862 17 * Version 1.0.2 2010/11/11
MikamiUitOpen 0:9b1d4712f862 18 * Documentation updated.
MikamiUitOpen 0:9b1d4712f862 19 *
MikamiUitOpen 0:9b1d4712f862 20 * Version 1.0.1 2010/10/05
MikamiUitOpen 0:9b1d4712f862 21 * Production release and review comments incorporated.
MikamiUitOpen 0:9b1d4712f862 22 *
MikamiUitOpen 0:9b1d4712f862 23 * Version 1.0.0 2010/09/20
MikamiUitOpen 0:9b1d4712f862 24 * Production release and review comments incorporated.
MikamiUitOpen 0:9b1d4712f862 25 * -------------------------------------------------------------------- */
MikamiUitOpen 0:9b1d4712f862 26
MikamiUitOpen 0:9b1d4712f862 27 #include "arm_math.h"
MikamiUitOpen 0:9b1d4712f862 28
MikamiUitOpen 0:9b1d4712f862 29 /**
MikamiUitOpen 0:9b1d4712f862 30 * @ingroup groupFastMath
MikamiUitOpen 0:9b1d4712f862 31 */
MikamiUitOpen 0:9b1d4712f862 32
MikamiUitOpen 0:9b1d4712f862 33 /**
MikamiUitOpen 0:9b1d4712f862 34 * @addtogroup sin
MikamiUitOpen 0:9b1d4712f862 35 * @{
MikamiUitOpen 0:9b1d4712f862 36 */
MikamiUitOpen 0:9b1d4712f862 37
MikamiUitOpen 0:9b1d4712f862 38
MikamiUitOpen 0:9b1d4712f862 39 /**
MikamiUitOpen 0:9b1d4712f862 40 * \par
MikamiUitOpen 0:9b1d4712f862 41 * Example code for Generation of Q15 Sin Table:
MikamiUitOpen 0:9b1d4712f862 42 * \par
MikamiUitOpen 0:9b1d4712f862 43 * <pre>tableSize = 256;
MikamiUitOpen 0:9b1d4712f862 44 * for(n = -1; n < (tableSize + 1); n++)
MikamiUitOpen 0:9b1d4712f862 45 * {
MikamiUitOpen 0:9b1d4712f862 46 * sinTable[n+1]=sin(2*pi*n/tableSize);
MikamiUitOpen 0:9b1d4712f862 47 * } </pre>
MikamiUitOpen 0:9b1d4712f862 48 * where pi value is 3.14159265358979
MikamiUitOpen 0:9b1d4712f862 49 * \par
MikamiUitOpen 0:9b1d4712f862 50 * Convert Floating point to Q15(Fixed point):
MikamiUitOpen 0:9b1d4712f862 51 * (sinTable[i] * pow(2, 15))
MikamiUitOpen 0:9b1d4712f862 52 * \par
MikamiUitOpen 0:9b1d4712f862 53 * rounding to nearest integer is done
MikamiUitOpen 0:9b1d4712f862 54 * sinTable[i] += (sinTable[i] > 0 ? 0.5 :-0.5);
MikamiUitOpen 0:9b1d4712f862 55 */
MikamiUitOpen 0:9b1d4712f862 56
MikamiUitOpen 0:9b1d4712f862 57
MikamiUitOpen 0:9b1d4712f862 58 static const q15_t sinTableQ15[259] = {
MikamiUitOpen 0:9b1d4712f862 59 0xfcdc, 0x0, 0x324, 0x648, 0x96b, 0xc8c, 0xfab, 0x12c8,
MikamiUitOpen 0:9b1d4712f862 60 0x15e2, 0x18f9, 0x1c0c, 0x1f1a, 0x2224, 0x2528, 0x2827, 0x2b1f,
MikamiUitOpen 0:9b1d4712f862 61 0x2e11, 0x30fc, 0x33df, 0x36ba, 0x398d, 0x3c57, 0x3f17, 0x41ce,
MikamiUitOpen 0:9b1d4712f862 62 0x447b, 0x471d, 0x49b4, 0x4c40, 0x4ec0, 0x5134, 0x539b, 0x55f6,
MikamiUitOpen 0:9b1d4712f862 63 0x5843, 0x5a82, 0x5cb4, 0x5ed7, 0x60ec, 0x62f2, 0x64e9, 0x66d0,
MikamiUitOpen 0:9b1d4712f862 64 0x68a7, 0x6a6e, 0x6c24, 0x6dca, 0x6f5f, 0x70e3, 0x7255, 0x73b6,
MikamiUitOpen 0:9b1d4712f862 65 0x7505, 0x7642, 0x776c, 0x7885, 0x798a, 0x7a7d, 0x7b5d, 0x7c2a,
MikamiUitOpen 0:9b1d4712f862 66 0x7ce4, 0x7d8a, 0x7e1e, 0x7e9d, 0x7f0a, 0x7f62, 0x7fa7, 0x7fd9,
MikamiUitOpen 0:9b1d4712f862 67 0x7ff6, 0x7fff, 0x7ff6, 0x7fd9, 0x7fa7, 0x7f62, 0x7f0a, 0x7e9d,
MikamiUitOpen 0:9b1d4712f862 68 0x7e1e, 0x7d8a, 0x7ce4, 0x7c2a, 0x7b5d, 0x7a7d, 0x798a, 0x7885,
MikamiUitOpen 0:9b1d4712f862 69 0x776c, 0x7642, 0x7505, 0x73b6, 0x7255, 0x70e3, 0x6f5f, 0x6dca,
MikamiUitOpen 0:9b1d4712f862 70 0x6c24, 0x6a6e, 0x68a7, 0x66d0, 0x64e9, 0x62f2, 0x60ec, 0x5ed7,
MikamiUitOpen 0:9b1d4712f862 71 0x5cb4, 0x5a82, 0x5843, 0x55f6, 0x539b, 0x5134, 0x4ec0, 0x4c40,
MikamiUitOpen 0:9b1d4712f862 72 0x49b4, 0x471d, 0x447b, 0x41ce, 0x3f17, 0x3c57, 0x398d, 0x36ba,
MikamiUitOpen 0:9b1d4712f862 73 0x33df, 0x30fc, 0x2e11, 0x2b1f, 0x2827, 0x2528, 0x2224, 0x1f1a,
MikamiUitOpen 0:9b1d4712f862 74 0x1c0c, 0x18f9, 0x15e2, 0x12c8, 0xfab, 0xc8c, 0x96b, 0x648,
MikamiUitOpen 0:9b1d4712f862 75 0x324, 0x0, 0xfcdc, 0xf9b8, 0xf695, 0xf374, 0xf055, 0xed38,
MikamiUitOpen 0:9b1d4712f862 76 0xea1e, 0xe707, 0xe3f4, 0xe0e6, 0xdddc, 0xdad8, 0xd7d9, 0xd4e1,
MikamiUitOpen 0:9b1d4712f862 77 0xd1ef, 0xcf04, 0xcc21, 0xc946, 0xc673, 0xc3a9, 0xc0e9, 0xbe32,
MikamiUitOpen 0:9b1d4712f862 78 0xbb85, 0xb8e3, 0xb64c, 0xb3c0, 0xb140, 0xaecc, 0xac65, 0xaa0a,
MikamiUitOpen 0:9b1d4712f862 79 0xa7bd, 0xa57e, 0xa34c, 0xa129, 0x9f14, 0x9d0e, 0x9b17, 0x9930,
MikamiUitOpen 0:9b1d4712f862 80 0x9759, 0x9592, 0x93dc, 0x9236, 0x90a1, 0x8f1d, 0x8dab, 0x8c4a,
MikamiUitOpen 0:9b1d4712f862 81 0x8afb, 0x89be, 0x8894, 0x877b, 0x8676, 0x8583, 0x84a3, 0x83d6,
MikamiUitOpen 0:9b1d4712f862 82 0x831c, 0x8276, 0x81e2, 0x8163, 0x80f6, 0x809e, 0x8059, 0x8027,
MikamiUitOpen 0:9b1d4712f862 83 0x800a, 0x8000, 0x800a, 0x8027, 0x8059, 0x809e, 0x80f6, 0x8163,
MikamiUitOpen 0:9b1d4712f862 84 0x81e2, 0x8276, 0x831c, 0x83d6, 0x84a3, 0x8583, 0x8676, 0x877b,
MikamiUitOpen 0:9b1d4712f862 85 0x8894, 0x89be, 0x8afb, 0x8c4a, 0x8dab, 0x8f1d, 0x90a1, 0x9236,
MikamiUitOpen 0:9b1d4712f862 86 0x93dc, 0x9592, 0x9759, 0x9930, 0x9b17, 0x9d0e, 0x9f14, 0xa129,
MikamiUitOpen 0:9b1d4712f862 87 0xa34c, 0xa57e, 0xa7bd, 0xaa0a, 0xac65, 0xaecc, 0xb140, 0xb3c0,
MikamiUitOpen 0:9b1d4712f862 88 0xb64c, 0xb8e3, 0xbb85, 0xbe32, 0xc0e9, 0xc3a9, 0xc673, 0xc946,
MikamiUitOpen 0:9b1d4712f862 89 0xcc21, 0xcf04, 0xd1ef, 0xd4e1, 0xd7d9, 0xdad8, 0xdddc, 0xe0e6,
MikamiUitOpen 0:9b1d4712f862 90 0xe3f4, 0xe707, 0xea1e, 0xed38, 0xf055, 0xf374, 0xf695, 0xf9b8,
MikamiUitOpen 0:9b1d4712f862 91 0xfcdc, 0x0, 0x324
MikamiUitOpen 0:9b1d4712f862 92 };
MikamiUitOpen 0:9b1d4712f862 93
MikamiUitOpen 0:9b1d4712f862 94
MikamiUitOpen 0:9b1d4712f862 95 /**
MikamiUitOpen 0:9b1d4712f862 96 * @brief Fast approximation to the trigonometric sine function for Q15 data.
MikamiUitOpen 0:9b1d4712f862 97 * @param[in] x Scaled input value in radians.
MikamiUitOpen 0:9b1d4712f862 98 * @return sin(x).
MikamiUitOpen 0:9b1d4712f862 99 *
MikamiUitOpen 0:9b1d4712f862 100 * The Q15 input value is in the range [0 +1) and is mapped to a radian value in the range [0 2*pi).
MikamiUitOpen 0:9b1d4712f862 101 */
MikamiUitOpen 0:9b1d4712f862 102
MikamiUitOpen 0:9b1d4712f862 103 q15_t arm_sin_q15(
MikamiUitOpen 0:9b1d4712f862 104 q15_t x)
MikamiUitOpen 0:9b1d4712f862 105 {
MikamiUitOpen 0:9b1d4712f862 106 q31_t sinVal; /* Temporary variables output */
MikamiUitOpen 0:9b1d4712f862 107 q15_t *tablePtr; /* Pointer to table */
MikamiUitOpen 0:9b1d4712f862 108 q15_t fract, in, in2; /* Temporary variables for input, output */
MikamiUitOpen 0:9b1d4712f862 109 q31_t wa, wb, wc, wd; /* Cubic interpolation coefficients */
MikamiUitOpen 0:9b1d4712f862 110 q15_t a, b, c, d; /* Four nearest output values */
MikamiUitOpen 0:9b1d4712f862 111 q15_t fractCube, fractSquare; /* Temporary values for fractional value */
MikamiUitOpen 0:9b1d4712f862 112 q15_t oneBy6 = 0x1555; /* Fixed point value of 1/6 */
MikamiUitOpen 0:9b1d4712f862 113 q15_t tableSpacing = TABLE_SPACING_Q15; /* Table spacing */
MikamiUitOpen 0:9b1d4712f862 114 int32_t index; /* Index variable */
MikamiUitOpen 0:9b1d4712f862 115
MikamiUitOpen 0:9b1d4712f862 116 in = x;
MikamiUitOpen 0:9b1d4712f862 117
MikamiUitOpen 0:9b1d4712f862 118 /* Calculate the nearest index */
MikamiUitOpen 0:9b1d4712f862 119 index = (int32_t) in / tableSpacing;
MikamiUitOpen 0:9b1d4712f862 120
MikamiUitOpen 0:9b1d4712f862 121 /* Calculate the nearest value of input */
MikamiUitOpen 0:9b1d4712f862 122 in2 = (q15_t) ((index) * tableSpacing);
MikamiUitOpen 0:9b1d4712f862 123
MikamiUitOpen 0:9b1d4712f862 124 /* Calculation of fractional value */
MikamiUitOpen 0:9b1d4712f862 125 fract = (in - in2) << 8;
MikamiUitOpen 0:9b1d4712f862 126
MikamiUitOpen 0:9b1d4712f862 127 /* fractSquare = fract * fract */
MikamiUitOpen 0:9b1d4712f862 128 fractSquare = (q15_t) ((fract * fract) >> 15);
MikamiUitOpen 0:9b1d4712f862 129
MikamiUitOpen 0:9b1d4712f862 130 /* fractCube = fract * fract * fract */
MikamiUitOpen 0:9b1d4712f862 131 fractCube = (q15_t) ((fractSquare * fract) >> 15);
MikamiUitOpen 0:9b1d4712f862 132
MikamiUitOpen 0:9b1d4712f862 133 /* Initialise table pointer */
MikamiUitOpen 0:9b1d4712f862 134 tablePtr = (q15_t *) & sinTableQ15[index];
MikamiUitOpen 0:9b1d4712f862 135
MikamiUitOpen 0:9b1d4712f862 136 /* Cubic interpolation process */
MikamiUitOpen 0:9b1d4712f862 137 /* Calculation of wa */
MikamiUitOpen 0:9b1d4712f862 138 /* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAA)*fract; */
MikamiUitOpen 0:9b1d4712f862 139 wa = (q31_t) oneBy6 *fractCube;
MikamiUitOpen 0:9b1d4712f862 140 wa += (q31_t) 0x2AAA * fract;
MikamiUitOpen 0:9b1d4712f862 141 wa = -(wa >> 15);
MikamiUitOpen 0:9b1d4712f862 142 wa += ((q31_t) fractSquare >> 1u);
MikamiUitOpen 0:9b1d4712f862 143
MikamiUitOpen 0:9b1d4712f862 144 /* Read first nearest value of output from the sin table */
MikamiUitOpen 0:9b1d4712f862 145 a = *tablePtr++;
MikamiUitOpen 0:9b1d4712f862 146
MikamiUitOpen 0:9b1d4712f862 147 /* sinVal = a * wa */
MikamiUitOpen 0:9b1d4712f862 148 sinVal = a * wa;
MikamiUitOpen 0:9b1d4712f862 149
MikamiUitOpen 0:9b1d4712f862 150 /* Calculation of wb */
MikamiUitOpen 0:9b1d4712f862 151 wb = (((q31_t) fractCube >> 1u) - (q31_t) fractSquare) -
MikamiUitOpen 0:9b1d4712f862 152 (((q31_t) fract >> 1u) - 0x7FFF);
MikamiUitOpen 0:9b1d4712f862 153
MikamiUitOpen 0:9b1d4712f862 154 /* Read second nearest value of output from the sin table */
MikamiUitOpen 0:9b1d4712f862 155 b = *tablePtr++;
MikamiUitOpen 0:9b1d4712f862 156
MikamiUitOpen 0:9b1d4712f862 157 /* sinVal += b*wb */
MikamiUitOpen 0:9b1d4712f862 158 sinVal += b * wb;
MikamiUitOpen 0:9b1d4712f862 159
MikamiUitOpen 0:9b1d4712f862 160
MikamiUitOpen 0:9b1d4712f862 161 /* Calculation of wc */
MikamiUitOpen 0:9b1d4712f862 162 wc = -(q31_t) fractCube + fractSquare;
MikamiUitOpen 0:9b1d4712f862 163 wc = (wc >> 1u) + fract;
MikamiUitOpen 0:9b1d4712f862 164
MikamiUitOpen 0:9b1d4712f862 165 /* Read third nearest value of output from the sin table */
MikamiUitOpen 0:9b1d4712f862 166 c = *tablePtr++;
MikamiUitOpen 0:9b1d4712f862 167
MikamiUitOpen 0:9b1d4712f862 168 /* sinVal += c*wc */
MikamiUitOpen 0:9b1d4712f862 169 sinVal += c * wc;
MikamiUitOpen 0:9b1d4712f862 170
MikamiUitOpen 0:9b1d4712f862 171 /* Calculation of wd */
MikamiUitOpen 0:9b1d4712f862 172 /* wd = (oneBy6)*fractCube - (oneBy6)*fract; */
MikamiUitOpen 0:9b1d4712f862 173 fractCube = fractCube - fract;
MikamiUitOpen 0:9b1d4712f862 174 wd = ((q15_t) (((q31_t) oneBy6 * fractCube) >> 15));
MikamiUitOpen 0:9b1d4712f862 175
MikamiUitOpen 0:9b1d4712f862 176 /* Read fourth nearest value of output from the sin table */
MikamiUitOpen 0:9b1d4712f862 177 d = *tablePtr++;
MikamiUitOpen 0:9b1d4712f862 178
MikamiUitOpen 0:9b1d4712f862 179 /* sinVal += d*wd; */
MikamiUitOpen 0:9b1d4712f862 180 sinVal += d * wd;
MikamiUitOpen 0:9b1d4712f862 181
MikamiUitOpen 0:9b1d4712f862 182 /* Return the output value in 1.15(q15) format */
MikamiUitOpen 0:9b1d4712f862 183 return ((q15_t) (sinVal >> 15u));
MikamiUitOpen 0:9b1d4712f862 184
MikamiUitOpen 0:9b1d4712f862 185 }
MikamiUitOpen 0:9b1d4712f862 186
MikamiUitOpen 0:9b1d4712f862 187 /**
MikamiUitOpen 0:9b1d4712f862 188 * @} end of sin group
MikamiUitOpen 0:9b1d4712f862 189 */