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CMSIS DSP library

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cmsis_dsp/FastMathFunctions/arm_sin_q15.c@3:7a284390b0ce, 2013-11-08 (annotated)

Committer:
mbed_official
Date:
Fri Nov 08 13:45:10 2013 +0000
Revision:
3:7a284390b0ce
Parent:
2:da51fb522205
Child:
5:3762170b6d4d
Synchronized with git revision e69956aba2f68a2a26ac26b051f8d349deaa1ce8

Who changed what in which revision?

UserRevisionLine numberNew contents of line
emilmont 1:fdd22bb7aa52 1 /* ----------------------------------------------------------------------
mbed_official 3:7a284390b0ce 2 * Copyright (C) 2010-2013 ARM Limited. All rights reserved.
emilmont 1:fdd22bb7aa52 3 *
mbed_official 3:7a284390b0ce 4 * $Date: 17. January 2013
mbed_official 3:7a284390b0ce 5 * $Revision: V1.4.1
emilmont 1:fdd22bb7aa52 6 *
emilmont 2:da51fb522205 7 * Project: CMSIS DSP Library
emilmont 2:da51fb522205 8 * Title: arm_sin_q15.c
emilmont 1:fdd22bb7aa52 9 *
emilmont 2:da51fb522205 10 * Description: Fast sine calculation for Q15 values.
emilmont 1:fdd22bb7aa52 11 *
emilmont 1:fdd22bb7aa52 12 * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
emilmont 1:fdd22bb7aa52 13 *
mbed_official 3:7a284390b0ce 14 * Redistribution and use in source and binary forms, with or without
mbed_official 3:7a284390b0ce 15 * modification, are permitted provided that the following conditions
mbed_official 3:7a284390b0ce 16 * are met:
mbed_official 3:7a284390b0ce 17 * - Redistributions of source code must retain the above copyright
mbed_official 3:7a284390b0ce 18 * notice, this list of conditions and the following disclaimer.
mbed_official 3:7a284390b0ce 19 * - Redistributions in binary form must reproduce the above copyright
mbed_official 3:7a284390b0ce 20 * notice, this list of conditions and the following disclaimer in
mbed_official 3:7a284390b0ce 21 * the documentation and/or other materials provided with the
mbed_official 3:7a284390b0ce 22 * distribution.
mbed_official 3:7a284390b0ce 23 * - Neither the name of ARM LIMITED nor the names of its contributors
mbed_official 3:7a284390b0ce 24 * may be used to endorse or promote products derived from this
mbed_official 3:7a284390b0ce 25 * software without specific prior written permission.
mbed_official 3:7a284390b0ce 26 *
mbed_official 3:7a284390b0ce 27 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
mbed_official 3:7a284390b0ce 28 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
mbed_official 3:7a284390b0ce 29 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
mbed_official 3:7a284390b0ce 30 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
mbed_official 3:7a284390b0ce 31 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
mbed_official 3:7a284390b0ce 32 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
mbed_official 3:7a284390b0ce 33 * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
mbed_official 3:7a284390b0ce 34 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
mbed_official 3:7a284390b0ce 35 * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
mbed_official 3:7a284390b0ce 36 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
mbed_official 3:7a284390b0ce 37 * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
mbed_official 3:7a284390b0ce 38 * POSSIBILITY OF SUCH DAMAGE.
emilmont 1:fdd22bb7aa52 39 * -------------------------------------------------------------------- */
emilmont 1:fdd22bb7aa52 40
emilmont 1:fdd22bb7aa52 41 #include "arm_math.h"
emilmont 1:fdd22bb7aa52 42
emilmont 1:fdd22bb7aa52 43 /**
emilmont 1:fdd22bb7aa52 44 * @ingroup groupFastMath
emilmont 1:fdd22bb7aa52 45 */
emilmont 1:fdd22bb7aa52 46
emilmont 1:fdd22bb7aa52 47 /**
emilmont 1:fdd22bb7aa52 48 * @addtogroup sin
emilmont 1:fdd22bb7aa52 49 * @{
emilmont 1:fdd22bb7aa52 50 */
emilmont 1:fdd22bb7aa52 51
emilmont 1:fdd22bb7aa52 52
mbed_official 3:7a284390b0ce 53 /**
mbed_official 3:7a284390b0ce 54 * \par
mbed_official 3:7a284390b0ce 55 * Table values are in Q15 (1.15 fixed-point format) and generation is done in
mbed_official 3:7a284390b0ce 56 * three steps. First, generate sin values in floating point:
mbed_official 3:7a284390b0ce 57 * <pre>
mbed_official 3:7a284390b0ce 58 * tableSize = 256;
emilmont 1:fdd22bb7aa52 59 * for(n = -1; n < (tableSize + 1); n++)
emilmont 1:fdd22bb7aa52 60 * {
mbed_official 3:7a284390b0ce 61 * sinTable[n+1]= sin(2*pi*n/tableSize);
mbed_official 3:7a284390b0ce 62 * } </pre>
emilmont 1:fdd22bb7aa52 63 * where pi value is 3.14159265358979
emilmont 1:fdd22bb7aa52 64 * \par
mbed_official 3:7a284390b0ce 65 * Second, convert floating-point to Q15 (fixed-point):
emilmont 2:da51fb522205 66 * (sinTable[i] * pow(2, 15))
emilmont 1:fdd22bb7aa52 67 * \par
mbed_official 3:7a284390b0ce 68 * Finally, round to the nearest integer value:
emilmont 2:da51fb522205 69 * sinTable[i] += (sinTable[i] > 0 ? 0.5 :-0.5);
mbed_official 3:7a284390b0ce 70 */
emilmont 1:fdd22bb7aa52 71
emilmont 1:fdd22bb7aa52 72 static const q15_t sinTableQ15[259] = {
emilmont 1:fdd22bb7aa52 73 0xfcdc, 0x0, 0x324, 0x648, 0x96b, 0xc8c, 0xfab, 0x12c8,
emilmont 1:fdd22bb7aa52 74 0x15e2, 0x18f9, 0x1c0c, 0x1f1a, 0x2224, 0x2528, 0x2827, 0x2b1f,
emilmont 1:fdd22bb7aa52 75 0x2e11, 0x30fc, 0x33df, 0x36ba, 0x398d, 0x3c57, 0x3f17, 0x41ce,
emilmont 1:fdd22bb7aa52 76 0x447b, 0x471d, 0x49b4, 0x4c40, 0x4ec0, 0x5134, 0x539b, 0x55f6,
emilmont 1:fdd22bb7aa52 77 0x5843, 0x5a82, 0x5cb4, 0x5ed7, 0x60ec, 0x62f2, 0x64e9, 0x66d0,
emilmont 1:fdd22bb7aa52 78 0x68a7, 0x6a6e, 0x6c24, 0x6dca, 0x6f5f, 0x70e3, 0x7255, 0x73b6,
emilmont 1:fdd22bb7aa52 79 0x7505, 0x7642, 0x776c, 0x7885, 0x798a, 0x7a7d, 0x7b5d, 0x7c2a,
emilmont 1:fdd22bb7aa52 80 0x7ce4, 0x7d8a, 0x7e1e, 0x7e9d, 0x7f0a, 0x7f62, 0x7fa7, 0x7fd9,
emilmont 1:fdd22bb7aa52 81 0x7ff6, 0x7fff, 0x7ff6, 0x7fd9, 0x7fa7, 0x7f62, 0x7f0a, 0x7e9d,
emilmont 1:fdd22bb7aa52 82 0x7e1e, 0x7d8a, 0x7ce4, 0x7c2a, 0x7b5d, 0x7a7d, 0x798a, 0x7885,
emilmont 1:fdd22bb7aa52 83 0x776c, 0x7642, 0x7505, 0x73b6, 0x7255, 0x70e3, 0x6f5f, 0x6dca,
emilmont 1:fdd22bb7aa52 84 0x6c24, 0x6a6e, 0x68a7, 0x66d0, 0x64e9, 0x62f2, 0x60ec, 0x5ed7,
emilmont 1:fdd22bb7aa52 85 0x5cb4, 0x5a82, 0x5843, 0x55f6, 0x539b, 0x5134, 0x4ec0, 0x4c40,
emilmont 1:fdd22bb7aa52 86 0x49b4, 0x471d, 0x447b, 0x41ce, 0x3f17, 0x3c57, 0x398d, 0x36ba,
emilmont 1:fdd22bb7aa52 87 0x33df, 0x30fc, 0x2e11, 0x2b1f, 0x2827, 0x2528, 0x2224, 0x1f1a,
emilmont 1:fdd22bb7aa52 88 0x1c0c, 0x18f9, 0x15e2, 0x12c8, 0xfab, 0xc8c, 0x96b, 0x648,
emilmont 1:fdd22bb7aa52 89 0x324, 0x0, 0xfcdc, 0xf9b8, 0xf695, 0xf374, 0xf055, 0xed38,
emilmont 1:fdd22bb7aa52 90 0xea1e, 0xe707, 0xe3f4, 0xe0e6, 0xdddc, 0xdad8, 0xd7d9, 0xd4e1,
emilmont 1:fdd22bb7aa52 91 0xd1ef, 0xcf04, 0xcc21, 0xc946, 0xc673, 0xc3a9, 0xc0e9, 0xbe32,
emilmont 1:fdd22bb7aa52 92 0xbb85, 0xb8e3, 0xb64c, 0xb3c0, 0xb140, 0xaecc, 0xac65, 0xaa0a,
emilmont 1:fdd22bb7aa52 93 0xa7bd, 0xa57e, 0xa34c, 0xa129, 0x9f14, 0x9d0e, 0x9b17, 0x9930,
emilmont 1:fdd22bb7aa52 94 0x9759, 0x9592, 0x93dc, 0x9236, 0x90a1, 0x8f1d, 0x8dab, 0x8c4a,
emilmont 1:fdd22bb7aa52 95 0x8afb, 0x89be, 0x8894, 0x877b, 0x8676, 0x8583, 0x84a3, 0x83d6,
emilmont 1:fdd22bb7aa52 96 0x831c, 0x8276, 0x81e2, 0x8163, 0x80f6, 0x809e, 0x8059, 0x8027,
emilmont 1:fdd22bb7aa52 97 0x800a, 0x8000, 0x800a, 0x8027, 0x8059, 0x809e, 0x80f6, 0x8163,
emilmont 1:fdd22bb7aa52 98 0x81e2, 0x8276, 0x831c, 0x83d6, 0x84a3, 0x8583, 0x8676, 0x877b,
emilmont 1:fdd22bb7aa52 99 0x8894, 0x89be, 0x8afb, 0x8c4a, 0x8dab, 0x8f1d, 0x90a1, 0x9236,
emilmont 1:fdd22bb7aa52 100 0x93dc, 0x9592, 0x9759, 0x9930, 0x9b17, 0x9d0e, 0x9f14, 0xa129,
emilmont 1:fdd22bb7aa52 101 0xa34c, 0xa57e, 0xa7bd, 0xaa0a, 0xac65, 0xaecc, 0xb140, 0xb3c0,
emilmont 1:fdd22bb7aa52 102 0xb64c, 0xb8e3, 0xbb85, 0xbe32, 0xc0e9, 0xc3a9, 0xc673, 0xc946,
emilmont 1:fdd22bb7aa52 103 0xcc21, 0xcf04, 0xd1ef, 0xd4e1, 0xd7d9, 0xdad8, 0xdddc, 0xe0e6,
emilmont 1:fdd22bb7aa52 104 0xe3f4, 0xe707, 0xea1e, 0xed38, 0xf055, 0xf374, 0xf695, 0xf9b8,
emilmont 1:fdd22bb7aa52 105 0xfcdc, 0x0, 0x324
emilmont 1:fdd22bb7aa52 106 };
emilmont 1:fdd22bb7aa52 107
emilmont 1:fdd22bb7aa52 108
emilmont 1:fdd22bb7aa52 109 /**
emilmont 1:fdd22bb7aa52 110 * @brief Fast approximation to the trigonometric sine function for Q15 data.
emilmont 1:fdd22bb7aa52 111 * @param[in] x Scaled input value in radians.
emilmont 1:fdd22bb7aa52 112 * @return sin(x).
emilmont 1:fdd22bb7aa52 113 *
mbed_official 3:7a284390b0ce 114 * The Q15 input value is in the range [0 +0.9999] and is mapped to a radian value in the range [0 2*pi).
emilmont 1:fdd22bb7aa52 115 */
emilmont 1:fdd22bb7aa52 116
emilmont 1:fdd22bb7aa52 117 q15_t arm_sin_q15(
emilmont 1:fdd22bb7aa52 118 q15_t x)
emilmont 1:fdd22bb7aa52 119 {
emilmont 1:fdd22bb7aa52 120 q31_t sinVal; /* Temporary variables output */
emilmont 1:fdd22bb7aa52 121 q15_t *tablePtr; /* Pointer to table */
emilmont 1:fdd22bb7aa52 122 q15_t fract, in, in2; /* Temporary variables for input, output */
emilmont 1:fdd22bb7aa52 123 q31_t wa, wb, wc, wd; /* Cubic interpolation coefficients */
emilmont 1:fdd22bb7aa52 124 q15_t a, b, c, d; /* Four nearest output values */
emilmont 1:fdd22bb7aa52 125 q15_t fractCube, fractSquare; /* Temporary values for fractional value */
emilmont 1:fdd22bb7aa52 126 q15_t oneBy6 = 0x1555; /* Fixed point value of 1/6 */
emilmont 1:fdd22bb7aa52 127 q15_t tableSpacing = TABLE_SPACING_Q15; /* Table spacing */
emilmont 1:fdd22bb7aa52 128 int32_t index; /* Index variable */
emilmont 1:fdd22bb7aa52 129
emilmont 1:fdd22bb7aa52 130 in = x;
emilmont 1:fdd22bb7aa52 131
emilmont 1:fdd22bb7aa52 132 /* Calculate the nearest index */
emilmont 1:fdd22bb7aa52 133 index = (int32_t) in / tableSpacing;
emilmont 1:fdd22bb7aa52 134
emilmont 1:fdd22bb7aa52 135 /* Calculate the nearest value of input */
emilmont 1:fdd22bb7aa52 136 in2 = (q15_t) ((index) * tableSpacing);
emilmont 1:fdd22bb7aa52 137
emilmont 1:fdd22bb7aa52 138 /* Calculation of fractional value */
emilmont 1:fdd22bb7aa52 139 fract = (in - in2) << 8;
emilmont 1:fdd22bb7aa52 140
emilmont 1:fdd22bb7aa52 141 /* fractSquare = fract * fract */
emilmont 1:fdd22bb7aa52 142 fractSquare = (q15_t) ((fract * fract) >> 15);
emilmont 1:fdd22bb7aa52 143
emilmont 1:fdd22bb7aa52 144 /* fractCube = fract * fract * fract */
emilmont 1:fdd22bb7aa52 145 fractCube = (q15_t) ((fractSquare * fract) >> 15);
emilmont 1:fdd22bb7aa52 146
emilmont 1:fdd22bb7aa52 147 /* Checking min and max index of table */
emilmont 1:fdd22bb7aa52 148 if(index < 0)
emilmont 1:fdd22bb7aa52 149 {
emilmont 1:fdd22bb7aa52 150 index = 0;
emilmont 1:fdd22bb7aa52 151 }
emilmont 1:fdd22bb7aa52 152 else if(index > 256)
emilmont 1:fdd22bb7aa52 153 {
emilmont 1:fdd22bb7aa52 154 index = 256;
emilmont 1:fdd22bb7aa52 155 }
emilmont 1:fdd22bb7aa52 156
emilmont 1:fdd22bb7aa52 157 /* Initialise table pointer */
emilmont 1:fdd22bb7aa52 158 tablePtr = (q15_t *) & sinTableQ15[index];
emilmont 1:fdd22bb7aa52 159
emilmont 1:fdd22bb7aa52 160 /* Cubic interpolation process */
emilmont 1:fdd22bb7aa52 161 /* Calculation of wa */
emilmont 1:fdd22bb7aa52 162 /* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAA)*fract; */
emilmont 1:fdd22bb7aa52 163 wa = (q31_t) oneBy6 *fractCube;
emilmont 1:fdd22bb7aa52 164 wa += (q31_t) 0x2AAA *fract;
emilmont 1:fdd22bb7aa52 165 wa = -(wa >> 15);
emilmont 1:fdd22bb7aa52 166 wa += ((q31_t) fractSquare >> 1u);
emilmont 1:fdd22bb7aa52 167
emilmont 1:fdd22bb7aa52 168 /* Read first nearest value of output from the sin table */
emilmont 1:fdd22bb7aa52 169 a = *tablePtr++;
emilmont 1:fdd22bb7aa52 170
emilmont 1:fdd22bb7aa52 171 /* sinVal = a * wa */
emilmont 1:fdd22bb7aa52 172 sinVal = a * wa;
emilmont 1:fdd22bb7aa52 173
emilmont 1:fdd22bb7aa52 174 /* Calculation of wb */
emilmont 1:fdd22bb7aa52 175 wb = (((q31_t) fractCube >> 1u) - (q31_t) fractSquare) -
emilmont 1:fdd22bb7aa52 176 (((q31_t) fract >> 1u) - 0x7FFF);
emilmont 1:fdd22bb7aa52 177
emilmont 1:fdd22bb7aa52 178 /* Read second nearest value of output from the sin table */
emilmont 1:fdd22bb7aa52 179 b = *tablePtr++;
emilmont 1:fdd22bb7aa52 180
emilmont 1:fdd22bb7aa52 181 /* sinVal += b*wb */
emilmont 1:fdd22bb7aa52 182 sinVal += b * wb;
emilmont 1:fdd22bb7aa52 183
emilmont 1:fdd22bb7aa52 184
emilmont 1:fdd22bb7aa52 185 /* Calculation of wc */
emilmont 1:fdd22bb7aa52 186 wc = -(q31_t) fractCube + fractSquare;
emilmont 1:fdd22bb7aa52 187 wc = (wc >> 1u) + fract;
emilmont 1:fdd22bb7aa52 188
emilmont 1:fdd22bb7aa52 189 /* Read third nearest value of output from the sin table */
emilmont 1:fdd22bb7aa52 190 c = *tablePtr++;
emilmont 1:fdd22bb7aa52 191
emilmont 1:fdd22bb7aa52 192 /* sinVal += c*wc */
emilmont 1:fdd22bb7aa52 193 sinVal += c * wc;
emilmont 1:fdd22bb7aa52 194
emilmont 1:fdd22bb7aa52 195 /* Calculation of wd */
emilmont 1:fdd22bb7aa52 196 /* wd = (oneBy6)*fractCube - (oneBy6)*fract; */
emilmont 1:fdd22bb7aa52 197 fractCube = fractCube - fract;
emilmont 1:fdd22bb7aa52 198 wd = ((q15_t) (((q31_t) oneBy6 * fractCube) >> 15));
emilmont 1:fdd22bb7aa52 199
emilmont 1:fdd22bb7aa52 200 /* Read fourth nearest value of output from the sin table */
emilmont 1:fdd22bb7aa52 201 d = *tablePtr++;
emilmont 1:fdd22bb7aa52 202
emilmont 1:fdd22bb7aa52 203 /* sinVal += d*wd; */
emilmont 1:fdd22bb7aa52 204 sinVal += d * wd;
emilmont 1:fdd22bb7aa52 205
emilmont 1:fdd22bb7aa52 206 /* Convert output value in 1.15(q15) format and saturate */
emilmont 1:fdd22bb7aa52 207 sinVal = __SSAT((sinVal >> 15), 16);
emilmont 1:fdd22bb7aa52 208
emilmont 1:fdd22bb7aa52 209 /* Return the output value in 1.15(q15) format */
emilmont 1:fdd22bb7aa52 210 return ((q15_t) sinVal);
emilmont 1:fdd22bb7aa52 211
emilmont 1:fdd22bb7aa52 212 }
emilmont 1:fdd22bb7aa52 213
emilmont 1:fdd22bb7aa52 214 /**
emilmont 1:fdd22bb7aa52 215 * @} end of sin group
emilmont 1:fdd22bb7aa52 216 */