不韋 呂
/
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.
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?
User | Revision | Line number | New contents of line |
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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 | */ |